Z3---4.15.1.THM-Prf.s

%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : NUM628+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% Computer : n013.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 : Sat Jun 21 05:21:39 AM UTC 2025

% Result   : Theorem 2.74s 2.93s
% Output   : Proof 2.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :  129
% Syntax   : Number of formulae    :  344 (  82 unt;   0 typ;   0 def)
%            Number of atoms       : 11990 (1578 equ)
%            Maximal formula atoms :  180 (  34 avg)
%            Number of connectives : 19880 (8577   ~;7186   |;2743   &)
%                                         ( 976 <=>; 398  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   31 (  10 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of FOOLs       :  343 ( 343 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   16 (  14 usr;   1 prp; 0-3 aty)
%            Number of functors    :   29 (  29 usr;  15 con; 0-2 aty)
%            Number of variables   : 2701 (2650   !;   0   ?;2701   :)

% Comments : 
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
    aElementOf0: ( $i * $i ) > $o ).

tff(slbdtsldtrb0_type,type,
    slbdtsldtrb0: ( $i * $i ) > $i ).

tff(xk_type,type,
    xk: $i ).

tff(sdtmndt0_type,type,
    sdtmndt0: ( $i * $i ) > $i ).

tff(szmzizndt0_type,type,
    szmzizndt0: $i > $i ).

tff(sdtlpdtrp0_type,type,
    sdtlpdtrp0: ( $i * $i ) > $i ).

tff(xn_type,type,
    xn: $i ).

tff(xN_type,type,
    xN: $i ).

tff(xQ_type,type,
    xQ: $i ).

tff(aSubsetOf0_type,type,
    aSubsetOf0: ( $i * $i ) > $o ).

tff(aSet0_type,type,
    aSet0: $i > $o ).

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

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

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

tff(tptp_fun_W3_33_type,type,
    tptp_fun_W3_33: ( $i * $i ) > $i ).

tff(sbrdtbr0_type,type,
    sbrdtbr0: $i > $i ).

tff(xP_type,type,
    xP: $i ).

tff(tptp_fun_W2_31_type,type,
    tptp_fun_W2_31: ( $i * $i ) > $i ).

tff(isCountable0_type,type,
    isCountable0: $i > $o ).

tff(szNzAzT0_type,type,
    szNzAzT0: $i ).

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

tff(szDzizrdt0_type,type,
    szDzizrdt0: $i > $i ).

tff(xd_type,type,
    xd: $i ).

tff(szDzozmdt0_type,type,
    szDzozmdt0: $i > $i ).

tff(xp_type,type,
    xp: $i ).

tff(xe_type,type,
    xe: $i ).

tff(tptp_fun_W1_29_type,type,
    tptp_fun_W1_29: $i > $i ).

tff(xS_type,type,
    xS: $i ).

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

tff(aFunction0_type,type,
    aFunction0: $i > $o ).

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

tff(xc_type,type,
    xc: $i ).

tff(xC_type,type,
    xC: $i ).

tff(xO_type,type,
    xO: $i ).

tff(xK_type,type,
    xK: $i ).

tff(tptp_fun_W2_39_type,type,
    tptp_fun_W2_39: ( $i * $i ) > $i ).

tff(1,plain,
    ( ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) )
  <=> ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(2,axiom,
    ( aSet0(xP)
    & ! [W0: $i] :
        ( aElementOf0(W0,xQ)
       => sdtlseqdt0(szmzizndt0(xQ),W0) )
    & ! [W0: $i] :
        ( aElementOf0(W0,xP)
      <=> ( aElement0(W0)
          & aElementOf0(W0,xQ)
          & ( W0 != szmzizndt0(xQ) ) ) )
    & ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5164) ).

tff(3,plain,
    xP = sdtmndt0(xQ,szmzizndt0(xQ)),
    inference(and_elim,[status(thm)],[2]) ).

tff(4,plain,
    xP = sdtmndt0(xQ,szmzizndt0(xQ)),
    inference(modus_ponens,[status(thm)],[3,1]) ).

tff(5,plain,
    sdtmndt0(xQ,szmzizndt0(xQ)) = xP,
    inference(symmetry,[status(thm)],[4]) ).

tff(6,plain,
    ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
  <=> aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
    inference(monotonicity,[status(thm)],[5]) ).

tff(7,plain,
    ( aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
  <=> aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
    inference(symmetry,[status(thm)],[6]) ).

tff(8,plain,
    ( aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
  <=> aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
    inference(rewrite,[status(thm)],[]) ).

tff(9,axiom,
    ( ! [W0: $i] :
        ( aElementOf0(W0,xP)
       => aElementOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) )
    & aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5334) ).

tff(10,plain,
    aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
    inference(and_elim,[status(thm)],[9]) ).

tff(11,plain,
    aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
    inference(modus_ponens,[status(thm)],[10,8]) ).

tff(12,plain,
    aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),
    inference(modus_ponens,[status(thm)],[11,7]) ).

tff(13,plain,
    ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
    | ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
    | aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
    | ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
    inference(tautology,[status(thm)],[]) ).

tff(14,plain,
    ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
    | ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
    | aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
    inference(unit_resolution,[status(thm)],[13,12]) ).

tff(15,plain,
    ( ( sbrdtbr0(xP) = xk )
  <=> ( sbrdtbr0(xP) = xk ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(16,axiom,
    sbrdtbr0(xP) = xk,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5217) ).

tff(17,plain,
    sbrdtbr0(xP) = xk,
    inference(modus_ponens,[status(thm)],[16,15]) ).

tff(18,plain,
    sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) = sbrdtbr0(xP),
    inference(monotonicity,[status(thm)],[5]) ).

tff(19,plain,
    sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) = xk,
    inference(transitivity,[status(thm)],[18,17]) ).

tff(20,plain,
    ( ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
        | ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
            | ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
            | aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) )
    | ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
    | ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
        | ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
        | aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
    inference(tautology,[status(thm)],[]) ).

tff(21,plain,
    ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
      | ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
          | aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
    inference(unit_resolution,[status(thm)],[20,19,14]) ).

tff(22,plain,
    ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
    | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
        | ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
            | ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
            | aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) )
    | ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
    | ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
        | ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
        | aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
    inference(tautology,[status(thm)],[]) ).

tff(23,plain,
    ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
    | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
        | ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
            | ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
            | aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ),
    inference(unit_resolution,[status(thm)],[22,21]) ).

tff(24,plain,
    ( aElementOf0(xn,szNzAzT0)
  <=> aElementOf0(xn,szNzAzT0) ),
    inference(rewrite,[status(thm)],[]) ).

tff(25,axiom,
    ( aElementOf0(xn,szDzozmdt0(xd))
    & ( sdtlpdtrp0(xd,xn) = szDzizrdt0(xd) )
    & aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
    & aElementOf0(xn,szNzAzT0)
    & ( sdtlpdtrp0(xe,xn) = xp ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5309) ).

tff(26,plain,
    ( aElementOf0(xn,szDzozmdt0(xd))
    & ( sdtlpdtrp0(xd,xn) = szDzizrdt0(xd) )
    & aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
    & aElementOf0(xn,szNzAzT0) ),
    inference(and_elim,[status(thm)],[25]) ).

tff(27,plain,
    aElementOf0(xn,szNzAzT0),
    inference(and_elim,[status(thm)],[26]) ).

tff(28,plain,
    aElementOf0(xn,szNzAzT0),
    inference(modus_ponens,[status(thm)],[27,24]) ).

tff(29,plain,
    ^ [W0: $i] :
      rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | aElementOf0(W1,szNzAzT0) )
              | ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              | ~ aSet0(sdtlpdtrp0(xN,W0))
              | ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              | ~ aSet0(sdtlpdtrp0(xN,W0))
              | ~ isCountable0(sdtlpdtrp0(xN,W0))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | aElementOf0(W1,szNzAzT0) ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(30,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ ( ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | aElementOf0(W1,szNzAzT0) )
            | ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
            | ~ aSet0(sdtlpdtrp0(xN,W0))
            | ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
            | ~ aSet0(sdtlpdtrp0(xN,W0))
            | ~ isCountable0(sdtlpdtrp0(xN,W0))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | aElementOf0(W1,szNzAzT0) ) ) ) ),
    inference(quant_intro,[status(thm)],[29]) ).

tff(31,plain,
    ^ [W0: $i] :
      refl(( ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | aElementOf0(W1,szNzAzT0) )
              | ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              | ~ aSet0(sdtlpdtrp0(xN,W0))
              | ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | aElementOf0(W1,szNzAzT0) )
              | ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              | ~ aSet0(sdtlpdtrp0(xN,W0))
              | ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(32,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ ( ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | aElementOf0(W1,szNzAzT0) )
            | ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
            | ~ aSet0(sdtlpdtrp0(xN,W0))
            | ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ ( ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | aElementOf0(W1,szNzAzT0) )
            | ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
            | ~ aSet0(sdtlpdtrp0(xN,W0))
            | ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
    inference(quant_intro,[status(thm)],[31]) ).

tff(33,plain,
    ^ [W0: $i] :
      rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | aElementOf0(W1,szNzAzT0) )
              | ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              | ~ aSet0(sdtlpdtrp0(xN,W0))
              | ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | aElementOf0(W1,szNzAzT0) )
              | ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              | ~ aSet0(sdtlpdtrp0(xN,W0))
              | ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(34,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ ( ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | aElementOf0(W1,szNzAzT0) )
            | ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
            | ~ aSet0(sdtlpdtrp0(xN,W0))
            | ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ ( ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | aElementOf0(W1,szNzAzT0) )
            | ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
            | ~ aSet0(sdtlpdtrp0(xN,W0))
            | ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
    inference(quant_intro,[status(thm)],[33]) ).

tff(35,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ ( ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | aElementOf0(W1,szNzAzT0) )
            | ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
            | ~ aSet0(sdtlpdtrp0(xN,W0))
            | ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ ( ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | aElementOf0(W1,szNzAzT0) )
            | ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
            | ~ aSet0(sdtlpdtrp0(xN,W0))
            | ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
    inference(transitivity,[status(thm)],[34,32]) ).

tff(36,plain,
    ^ [W0: $i] :
      rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
          | ( aSet0(sdtlpdtrp0(xN,W0))
            & ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                | aElementOf0(W1,szNzAzT0) )
            & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
            & isCountable0(sdtlpdtrp0(xN,W0)) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | aElementOf0(W1,szNzAzT0) )
              | ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              | ~ aSet0(sdtlpdtrp0(xN,W0))
              | ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(37,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ( aSet0(sdtlpdtrp0(xN,W0))
          & ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
              | aElementOf0(W1,szNzAzT0) )
          & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
          & isCountable0(sdtlpdtrp0(xN,W0)) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ ( ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | aElementOf0(W1,szNzAzT0) )
            | ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
            | ~ aSet0(sdtlpdtrp0(xN,W0))
            | ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
    inference(quant_intro,[status(thm)],[36]) ).

tff(38,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ( aSet0(sdtlpdtrp0(xN,W0))
          & ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
              | aElementOf0(W1,szNzAzT0) )
          & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
          & isCountable0(sdtlpdtrp0(xN,W0)) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ( aSet0(sdtlpdtrp0(xN,W0))
          & ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
              | aElementOf0(W1,szNzAzT0) )
          & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
          & isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(39,plain,
    ^ [W0: $i] :
      trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( aSet0(sdtlpdtrp0(xN,W0))
                      & ! [W1: $i] :
                          ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                         => aElementOf0(W1,szNzAzT0) ) )
                  <=> ( aSet0(sdtlpdtrp0(xN,W0))
                      & ! [W1: $i] :
                          ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | aElementOf0(W1,szNzAzT0) ) ) )),
                  ( ( aSet0(sdtlpdtrp0(xN,W0))
                    & ! [W1: $i] :
                        ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                       => aElementOf0(W1,szNzAzT0) )
                    & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
                <=> ( aSet0(sdtlpdtrp0(xN,W0))
                    & ! [W1: $i] :
                        ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | aElementOf0(W1,szNzAzT0) )
                    & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) ) )),
                rewrite(( ( aSet0(sdtlpdtrp0(xN,W0))
                    & ! [W1: $i] :
                        ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | aElementOf0(W1,szNzAzT0) )
                    & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
                <=> ( aSet0(sdtlpdtrp0(xN,W0))
                    & ! [W1: $i] :
                        ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | aElementOf0(W1,szNzAzT0) )
                    & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) ) )),
                ( ( aSet0(sdtlpdtrp0(xN,W0))
                  & ! [W1: $i] :
                      ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                     => aElementOf0(W1,szNzAzT0) )
                  & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
              <=> ( aSet0(sdtlpdtrp0(xN,W0))
                  & ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | aElementOf0(W1,szNzAzT0) )
                  & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) ) )),
              ( ( aSet0(sdtlpdtrp0(xN,W0))
                & ! [W1: $i] :
                    ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                   => aElementOf0(W1,szNzAzT0) )
                & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                & isCountable0(sdtlpdtrp0(xN,W0)) )
            <=> ( aSet0(sdtlpdtrp0(xN,W0))
                & ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | aElementOf0(W1,szNzAzT0) )
                & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                & isCountable0(sdtlpdtrp0(xN,W0)) ) )),
            rewrite(( ( aSet0(sdtlpdtrp0(xN,W0))
                & ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | aElementOf0(W1,szNzAzT0) )
                & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                & isCountable0(sdtlpdtrp0(xN,W0)) )
            <=> ( aSet0(sdtlpdtrp0(xN,W0))
                & ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | aElementOf0(W1,szNzAzT0) )
                & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                & isCountable0(sdtlpdtrp0(xN,W0)) ) )),
            ( ( aSet0(sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                 => aElementOf0(W1,szNzAzT0) )
              & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              & isCountable0(sdtlpdtrp0(xN,W0)) )
          <=> ( aSet0(sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | aElementOf0(W1,szNzAzT0) )
              & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              & isCountable0(sdtlpdtrp0(xN,W0)) ) )),
          ( ( aElementOf0(W0,szNzAzT0)
           => ( aSet0(sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                 => aElementOf0(W1,szNzAzT0) )
              & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              & isCountable0(sdtlpdtrp0(xN,W0)) ) )
        <=> ( aElementOf0(W0,szNzAzT0)
           => ( aSet0(sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | aElementOf0(W1,szNzAzT0) )
              & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              & isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
        rewrite(( ( aElementOf0(W0,szNzAzT0)
           => ( aSet0(sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | aElementOf0(W1,szNzAzT0) )
              & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              & isCountable0(sdtlpdtrp0(xN,W0)) ) )
        <=> ( ~ aElementOf0(W0,szNzAzT0)
            | ( aSet0(sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | aElementOf0(W1,szNzAzT0) )
              & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              & isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
        ( ( aElementOf0(W0,szNzAzT0)
         => ( aSet0(sdtlpdtrp0(xN,W0))
            & ! [W1: $i] :
                ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
               => aElementOf0(W1,szNzAzT0) )
            & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
            & isCountable0(sdtlpdtrp0(xN,W0)) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ( aSet0(sdtlpdtrp0(xN,W0))
            & ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                | aElementOf0(W1,szNzAzT0) )
            & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
            & isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(40,plain,
    ( ! [W0: $i] :
        ( aElementOf0(W0,szNzAzT0)
       => ( aSet0(sdtlpdtrp0(xN,W0))
          & ! [W1: $i] :
              ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
             => aElementOf0(W1,szNzAzT0) )
          & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
          & isCountable0(sdtlpdtrp0(xN,W0)) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ( aSet0(sdtlpdtrp0(xN,W0))
          & ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
              | aElementOf0(W1,szNzAzT0) )
          & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
          & isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
    inference(quant_intro,[status(thm)],[39]) ).

tff(41,axiom,
    ! [W0: $i] :
      ( aElementOf0(W0,szNzAzT0)
     => ( aSet0(sdtlpdtrp0(xN,W0))
        & ! [W1: $i] :
            ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
           => aElementOf0(W1,szNzAzT0) )
        & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
        & isCountable0(sdtlpdtrp0(xN,W0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3671) ).

tff(42,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ( aSet0(sdtlpdtrp0(xN,W0))
        & ! [W1: $i] :
            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
            | aElementOf0(W1,szNzAzT0) )
        & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
        & isCountable0(sdtlpdtrp0(xN,W0)) ) ),
    inference(modus_ponens,[status(thm)],[41,40]) ).

tff(43,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ( aSet0(sdtlpdtrp0(xN,W0))
        & ! [W1: $i] :
            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
            | aElementOf0(W1,szNzAzT0) )
        & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
        & isCountable0(sdtlpdtrp0(xN,W0)) ) ),
    inference(modus_ponens,[status(thm)],[42,38]) ).

tff(44,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ( aSet0(sdtlpdtrp0(xN,W0))
        & ! [W1: $i] :
            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
            | aElementOf0(W1,szNzAzT0) )
        & aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
        & isCountable0(sdtlpdtrp0(xN,W0)) ) ),
    inference(skolemize,[status(sab)],[43]) ).

tff(45,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ~ ( ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                | aElementOf0(W1,szNzAzT0) )
          | ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
          | ~ aSet0(sdtlpdtrp0(xN,W0))
          | ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ),
    inference(modus_ponens,[status(thm)],[44,37]) ).

tff(46,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ~ ( ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                | aElementOf0(W1,szNzAzT0) )
          | ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
          | ~ aSet0(sdtlpdtrp0(xN,W0))
          | ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ),
    inference(modus_ponens,[status(thm)],[45,35]) ).

tff(47,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
          | ~ aSet0(sdtlpdtrp0(xN,W0))
          | ~ isCountable0(sdtlpdtrp0(xN,W0))
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                | aElementOf0(W1,szNzAzT0) ) ) ),
    inference(modus_ponens,[status(thm)],[46,30]) ).

tff(48,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                | ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ isCountable0(sdtlpdtrp0(xN,W0))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | aElementOf0(W1,szNzAzT0) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
          | ~ isCountable0(sdtlpdtrp0(xN,xn))
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | aElementOf0(W1,szNzAzT0) )
          | ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0) ) )
  <=> ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                | ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ isCountable0(sdtlpdtrp0(xN,W0))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | aElementOf0(W1,szNzAzT0) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
          | ~ isCountable0(sdtlpdtrp0(xN,xn))
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | aElementOf0(W1,szNzAzT0) )
          | ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(49,plain,
    ( ( ~ aElementOf0(xn,szNzAzT0)
      | ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0)
          | ~ aSet0(sdtlpdtrp0(xN,xn))
          | ~ isCountable0(sdtlpdtrp0(xN,xn))
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | aElementOf0(W1,szNzAzT0) ) ) )
  <=> ( ~ aElementOf0(xn,szNzAzT0)
      | ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
          | ~ isCountable0(sdtlpdtrp0(xN,xn))
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | aElementOf0(W1,szNzAzT0) )
          | ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(50,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                | ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ isCountable0(sdtlpdtrp0(xN,W0))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | aElementOf0(W1,szNzAzT0) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0)
          | ~ aSet0(sdtlpdtrp0(xN,xn))
          | ~ isCountable0(sdtlpdtrp0(xN,xn))
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | aElementOf0(W1,szNzAzT0) ) ) )
  <=> ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                | ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ isCountable0(sdtlpdtrp0(xN,W0))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | aElementOf0(W1,szNzAzT0) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
          | ~ isCountable0(sdtlpdtrp0(xN,xn))
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | aElementOf0(W1,szNzAzT0) )
          | ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0) ) ) ),
    inference(monotonicity,[status(thm)],[49]) ).

tff(51,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                | ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ isCountable0(sdtlpdtrp0(xN,W0))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | aElementOf0(W1,szNzAzT0) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0)
          | ~ aSet0(sdtlpdtrp0(xN,xn))
          | ~ isCountable0(sdtlpdtrp0(xN,xn))
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | aElementOf0(W1,szNzAzT0) ) ) )
  <=> ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                | ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ isCountable0(sdtlpdtrp0(xN,W0))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | aElementOf0(W1,szNzAzT0) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
          | ~ isCountable0(sdtlpdtrp0(xN,xn))
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | aElementOf0(W1,szNzAzT0) )
          | ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0) ) ) ),
    inference(transitivity,[status(thm)],[50,48]) ).

tff(52,plain,
    ( ~ ! [W0: $i] :
          ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              | ~ aSet0(sdtlpdtrp0(xN,W0))
              | ~ isCountable0(sdtlpdtrp0(xN,W0))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | aElementOf0(W1,szNzAzT0) ) ) )
    | ~ aElementOf0(xn,szNzAzT0)
    | ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0)
        | ~ aSet0(sdtlpdtrp0(xN,xn))
        | ~ isCountable0(sdtlpdtrp0(xN,xn))
        | ~ ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
              | aElementOf0(W1,szNzAzT0) ) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(53,plain,
    ( ~ ! [W0: $i] :
          ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              | ~ aSet0(sdtlpdtrp0(xN,W0))
              | ~ isCountable0(sdtlpdtrp0(xN,W0))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | aElementOf0(W1,szNzAzT0) ) ) )
    | ~ aElementOf0(xn,szNzAzT0)
    | ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
        | ~ isCountable0(sdtlpdtrp0(xN,xn))
        | ~ ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
              | aElementOf0(W1,szNzAzT0) )
        | ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0) ) ),
    inference(modus_ponens,[status(thm)],[52,51]) ).

tff(54,plain,
    ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
      | ~ isCountable0(sdtlpdtrp0(xN,xn))
      | ~ ! [W1: $i] :
            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
            | aElementOf0(W1,szNzAzT0) )
      | ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0) ),
    inference(unit_resolution,[status(thm)],[53,47,28]) ).

tff(55,plain,
    ( ~ aSet0(sdtlpdtrp0(xN,xn))
    | ~ isCountable0(sdtlpdtrp0(xN,xn))
    | ~ ! [W1: $i] :
          ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
          | aElementOf0(W1,szNzAzT0) )
    | ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0)
    | isCountable0(sdtlpdtrp0(xN,xn)) ),
    inference(tautology,[status(thm)],[]) ).

tff(56,plain,
    isCountable0(sdtlpdtrp0(xN,xn)),
    inference(unit_resolution,[status(thm)],[55,54]) ).

tff(57,plain,
    ( ~ aSet0(sdtlpdtrp0(xN,xn))
    | ~ isCountable0(sdtlpdtrp0(xN,xn))
    | ~ ! [W1: $i] :
          ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
          | aElementOf0(W1,szNzAzT0) )
    | ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0)
    | aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0) ),
    inference(tautology,[status(thm)],[]) ).

tff(58,plain,
    aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0),
    inference(unit_resolution,[status(thm)],[57,54]) ).

tff(59,plain,
    ( aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0)
    | ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
        | ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
            | aElementOf0(tptp_fun_W1_29(xn),szNzAzT0) ) )
    | ~ aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0) ),
    inference(tautology,[status(thm)],[]) ).

tff(60,plain,
    ( aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0)
    | ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
        | ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
            | aElementOf0(tptp_fun_W1_29(xn),szNzAzT0) ) ) ),
    inference(unit_resolution,[status(thm)],[59,58]) ).

tff(61,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ isCountable0(sdtlpdtrp0(xN,W0))
        | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
            | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                    | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
        | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
            | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            | ~ ! [W1: $i] :
                  ~ ( ( ~ aElement0(W1)
                      | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                  <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ isCountable0(sdtlpdtrp0(xN,W0))
        | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
            | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                    | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
        | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
            | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            | ~ ! [W1: $i] :
                  ~ ( ( ~ aElement0(W1)
                      | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                  <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(62,plain,
    ^ [W0: $i] :
      trans(monotonicity(rewrite(( ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ ! [W1: $i] :
                      ~ ( ( ~ aElement0(W1)
                          | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                      | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
          <=> ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                | ~ ! [W1: $i] :
                      ~ ( ( ~ aElement0(W1)
                          | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                      | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )),
          rewrite(( ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                    | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                        | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
          <=> ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                    | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                        | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) ) )),
          ( ( ~ aElementOf0(W0,szNzAzT0)
            | ~ isCountable0(sdtlpdtrp0(xN,W0))
            | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ ! [W1: $i] :
                      ~ ( ( ~ aElement0(W1)
                          | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                      | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
            | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                    | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                        | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) ) )
        <=> ( ~ aElementOf0(W0,szNzAzT0)
            | ~ isCountable0(sdtlpdtrp0(xN,W0))
            | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                | ~ ! [W1: $i] :
                      ~ ( ( ~ aElement0(W1)
                          | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                      | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
            | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                    | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                        | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) ) ) )),
        rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
            | ~ isCountable0(sdtlpdtrp0(xN,W0))
            | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                | ~ ! [W1: $i] :
                      ~ ( ( ~ aElement0(W1)
                          | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                      | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
            | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                    | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                        | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) ) )
        <=> ( ~ aElementOf0(W0,szNzAzT0)
            | ~ isCountable0(sdtlpdtrp0(xN,W0))
            | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                    | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                        | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
            | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                | ~ ! [W1: $i] :
                      ~ ( ( ~ aElement0(W1)
                          | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                      | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) )),
        ( ( ~ aElementOf0(W0,szNzAzT0)
          | ~ isCountable0(sdtlpdtrp0(xN,W0))
          | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ ! [W1: $i] :
                    ~ ( ( ~ aElement0(W1)
                        | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                    <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                    | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
          | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                  | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                      | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ~ isCountable0(sdtlpdtrp0(xN,W0))
          | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                  | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                      | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
          | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
              | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              | ~ ! [W1: $i] :
                    ~ ( ( ~ aElement0(W1)
                        | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                    <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                    | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(63,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ isCountable0(sdtlpdtrp0(xN,W0))
        | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ ! [W1: $i] :
                  ~ ( ( ~ aElement0(W1)
                      | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                  <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
        | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
            | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                    | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ isCountable0(sdtlpdtrp0(xN,W0))
        | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
            | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                    | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
        | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
            | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            | ~ ! [W1: $i] :
                  ~ ( ( ~ aElement0(W1)
                      | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                  <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ),
    inference(quant_intro,[status(thm)],[62]) ).

tff(64,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ isCountable0(sdtlpdtrp0(xN,W0))
        | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ ! [W1: $i] :
                  ~ ( ( ~ aElement0(W1)
                      | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                  <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
        | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
            | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                    | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ isCountable0(sdtlpdtrp0(xN,W0))
        | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
            | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                    | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
        | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
            | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            | ~ ! [W1: $i] :
                  ~ ( ( ~ aElement0(W1)
                      | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                  <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ),
    inference(transitivity,[status(thm)],[63,61]) ).

tff(65,plain,
    ^ [W0: $i] :
      refl(( ( ~ aElementOf0(W0,szNzAzT0)
          | ~ isCountable0(sdtlpdtrp0(xN,W0))
          | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ ! [W1: $i] :
                    ~ ( ( ~ aElement0(W1)
                        | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                    <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                    | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
          | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                  | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                      | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ~ isCountable0(sdtlpdtrp0(xN,W0))
          | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ ! [W1: $i] :
                    ~ ( ( ~ aElement0(W1)
                        | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                    <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                    | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
          | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                  | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                      | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(66,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ isCountable0(sdtlpdtrp0(xN,W0))
        | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ ! [W1: $i] :
                  ~ ( ( ~ aElement0(W1)
                      | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                  <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
        | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
            | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                    | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ isCountable0(sdtlpdtrp0(xN,W0))
        | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ ! [W1: $i] :
                  ~ ( ( ~ aElement0(W1)
                      | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                  <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
        | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
            | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                    | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) ) ) ),
    inference(quant_intro,[status(thm)],[65]) ).

tff(67,plain,
    ^ [W0: $i] :
      rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
          | ~ isCountable0(sdtlpdtrp0(xN,W0))
          | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ ! [W1: $i] :
                    ~ ( ( ~ aElement0(W1)
                        | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                    <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                    | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
          | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                  | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                      | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ~ isCountable0(sdtlpdtrp0(xN,W0))
          | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ ! [W1: $i] :
                    ~ ( ( ~ aElement0(W1)
                        | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                    <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                    | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
          | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                  | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                      | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(68,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ isCountable0(sdtlpdtrp0(xN,W0))
        | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ ! [W1: $i] :
                  ~ ( ( ~ aElement0(W1)
                      | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                  <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
        | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
            | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                    | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ isCountable0(sdtlpdtrp0(xN,W0))
        | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ ! [W1: $i] :
                  ~ ( ( ~ aElement0(W1)
                      | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                  <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
        | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
            | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                    | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) ) ) ),
    inference(quant_intro,[status(thm)],[67]) ).

tff(69,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ isCountable0(sdtlpdtrp0(xN,W0))
        | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ ! [W1: $i] :
                  ~ ( ( ~ aElement0(W1)
                      | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                  <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
        | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
            | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                    | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ isCountable0(sdtlpdtrp0(xN,W0))
        | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ ! [W1: $i] :
                  ~ ( ( ~ aElement0(W1)
                      | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                  <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
        | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
            | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                    | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) ) ) ),
    inference(transitivity,[status(thm)],[68,66]) ).

tff(70,plain,
    ^ [W0: $i] :
      trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
                    trans(trans(monotonicity(rewrite(( ( aElement0(W1)
                              & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                              & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                          <=> ~ ( ~ aElement0(W1)
                                | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )),
                          ( ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          <=> ( aElement0(W1)
                              & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                              & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                        <=> ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          <=> ~ ( ~ aElement0(W1)
                                | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )),
                        rewrite(( ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          <=> ~ ( ~ aElement0(W1)
                                | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                        <=> ~ ( ( ~ aElement0(W1)
                                | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                            <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
                        ( ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        <=> ( aElement0(W1)
                            & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                            & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                      <=> ~ ( ( ~ aElement0(W1)
                              | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                              | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                          <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
                      rewrite(( ~ ( ( ~ aElement0(W1)
                              | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                              | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                          <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      <=> ~ ( ( ~ aElement0(W1)
                              | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                              | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                          <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
                      ( ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      <=> ( aElement0(W1)
                          & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                    <=> ~ ( ( ~ aElement0(W1)
                            | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                            | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                        <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ))),
                ( ! [W1: $i] :
                    ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W1)
                      & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
              <=> ! [W1: $i] :
                    ~ ( ( ~ aElement0(W1)
                        | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                    <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
              ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & ! [W1: $i] :
                    ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W1)
                      & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                & ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                    | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
            <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & ! [W1: $i] :
                    ~ ( ( ~ aElement0(W1)
                        | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                    <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                & ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                    | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )),
            rewrite(( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & ! [W1: $i] :
                    ~ ( ( ~ aElement0(W1)
                        | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                    <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                & ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                    | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
            <=> ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  | ~ ! [W1: $i] :
                        ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                  | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  | ~ ! [W1: $i] :
                        ~ ( ( ~ aElement0(W1)
                            | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                            | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                        <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  | ~ ! [W1: $i] :
                        ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                        | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )),
            ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & ! [W1: $i] :
                  ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                <=> ( aElement0(W1)
                    & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
              & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
          <=> ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ ! [W1: $i] :
                      ~ ( ( ~ aElement0(W1)
                          | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                      | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )),
          rewrite(( ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              & ( ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                    | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
          <=> ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                    | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                        | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) ) )),
          ( ( ~ aElementOf0(W0,szNzAzT0)
            | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & ! [W1: $i] :
                  ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                <=> ( aElement0(W1)
                    & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
              & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
            | ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              & ( ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                    | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
            | ~ isCountable0(sdtlpdtrp0(xN,W0)) )
        <=> ( ~ aElementOf0(W0,szNzAzT0)
            | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ ! [W1: $i] :
                      ~ ( ( ~ aElement0(W1)
                          | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                      | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
            | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                    | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                        | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
            | ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )),
        rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
            | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ ! [W1: $i] :
                      ~ ( ( ~ aElement0(W1)
                          | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                      | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
            | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                    | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                        | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
            | ~ isCountable0(sdtlpdtrp0(xN,W0)) )
        <=> ( ~ aElementOf0(W0,szNzAzT0)
            | ~ isCountable0(sdtlpdtrp0(xN,W0))
            | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ ! [W1: $i] :
                      ~ ( ( ~ aElement0(W1)
                          | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                      | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
            | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                    | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                        | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) ) ) )),
        ( ( ~ aElementOf0(W0,szNzAzT0)
          | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            & ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            & ! [W1: $i] :
                ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              <=> ( aElement0(W1)
                  & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
            & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
            & ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
          | ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
            & ( ~ aSet0(sdtlpdtrp0(xN,W0))
              | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                  | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
          | ~ isCountable0(sdtlpdtrp0(xN,W0)) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ~ isCountable0(sdtlpdtrp0(xN,W0))
          | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ ! [W1: $i] :
                    ~ ( ( ~ aElement0(W1)
                        | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                    <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                    | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
          | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                  | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                      | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(71,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
          & ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
          & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          & ! [W1: $i] :
              ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            <=> ( aElement0(W1)
                & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
          & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
          & ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
              | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
          & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
        | ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
          & ( ~ aSet0(sdtlpdtrp0(xN,W0))
            | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
        | ~ isCountable0(sdtlpdtrp0(xN,W0)) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ isCountable0(sdtlpdtrp0(xN,W0))
        | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ ! [W1: $i] :
                  ~ ( ( ~ aElement0(W1)
                      | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                  <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
        | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
            | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                    | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) ) ) ),
    inference(quant_intro,[status(thm)],[70]) ).

tff(72,plain,
    ^ [W0: $i] :
      trans(monotonicity(rewrite(( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & ! [W1: $i] :
                  ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                <=> ( aElement0(W1)
                    & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
              & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
          <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & ! [W1: $i] :
                  ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                <=> ( aElement0(W1)
                    & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
              & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )),
          rewrite(( ( ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                & ( ~ aSet0(sdtlpdtrp0(xN,W0))
                  | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                      | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
              | ~ isCountable0(sdtlpdtrp0(xN,W0)) )
          <=> ( ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                & ( ~ aSet0(sdtlpdtrp0(xN,W0))
                  | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                      | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
              | ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )),
          ( ( ~ aElementOf0(W0,szNzAzT0)
            | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & ! [W1: $i] :
                  ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                <=> ( aElement0(W1)
                    & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
              & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
            | ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              & ( ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                    | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
            | ~ isCountable0(sdtlpdtrp0(xN,W0)) )
        <=> ( ~ aElementOf0(W0,szNzAzT0)
            | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & ! [W1: $i] :
                  ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                <=> ( aElement0(W1)
                    & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
              & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
            | ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              & ( ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                    | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
            | ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )),
        rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
            | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & ! [W1: $i] :
                  ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                <=> ( aElement0(W1)
                    & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
              & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
            | ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              & ( ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                    | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
            | ~ isCountable0(sdtlpdtrp0(xN,W0)) )
        <=> ( ~ aElementOf0(W0,szNzAzT0)
            | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & ! [W1: $i] :
                  ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                <=> ( aElement0(W1)
                    & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
              & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
            | ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              & ( ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                    | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
            | ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )),
        ( ( ~ aElementOf0(W0,szNzAzT0)
          | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            & ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            & ! [W1: $i] :
                ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              <=> ( aElement0(W1)
                  & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
            & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
            & ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
          | ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
            & ( ~ aSet0(sdtlpdtrp0(xN,W0))
              | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                  | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
          | ~ isCountable0(sdtlpdtrp0(xN,W0)) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            & ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            & ! [W1: $i] :
                ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              <=> ( aElement0(W1)
                  & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
            & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
            & ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
          | ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
            & ( ~ aSet0(sdtlpdtrp0(xN,W0))
              | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                  | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
          | ~ isCountable0(sdtlpdtrp0(xN,W0)) ) )),
    inference(bind,[status(th)],[]) ).

tff(73,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
          & ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
          & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          & ! [W1: $i] :
              ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            <=> ( aElement0(W1)
                & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
          & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
          & ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
              | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
          & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
        | ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
          & ( ~ aSet0(sdtlpdtrp0(xN,W0))
            | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
        | ~ isCountable0(sdtlpdtrp0(xN,W0)) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
          & ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
          & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          & ! [W1: $i] :
              ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            <=> ( aElement0(W1)
                & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
          & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
          & ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
              | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
          & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
        | ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
          & ( ~ aSet0(sdtlpdtrp0(xN,W0))
            | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
        | ~ isCountable0(sdtlpdtrp0(xN,W0)) ) ),
    inference(quant_intro,[status(thm)],[72]) ).

tff(74,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
          & ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
          & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          & ! [W1: $i] :
              ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            <=> ( aElement0(W1)
                & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
          & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
          & ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
              | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
          & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
        | ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              | ( aSet0(sdtlpdtrp0(xN,W0))
                & ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | aElementOf0(W1,szNzAzT0) ) ) )
            & isCountable0(sdtlpdtrp0(xN,W0)) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
          & ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
          & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          & ! [W1: $i] :
              ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            <=> ( aElement0(W1)
                & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
          & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
          & ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
              | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
          & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
        | ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              | ( aSet0(sdtlpdtrp0(xN,W0))
                & ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | aElementOf0(W1,szNzAzT0) ) ) )
            & isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(75,plain,
    ^ [W0: $i] :
      trans(monotonicity(trans(monotonicity(rewrite(( ( ( ( aSet0(sdtlpdtrp0(xN,W0))
                      & ! [W1: $i] :
                          ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                         => aElementOf0(W1,szNzAzT0) ) )
                    | aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
                  & isCountable0(sdtlpdtrp0(xN,W0)) )
              <=> ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                    | ( aSet0(sdtlpdtrp0(xN,W0))
                      & ! [W1: $i] :
                          ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | aElementOf0(W1,szNzAzT0) ) ) )
                  & isCountable0(sdtlpdtrp0(xN,W0)) ) )),
              trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                          & ! [W1: $i] :
                                              ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                             => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) ) )
                                      <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                          & ! [W1: $i] :
                                              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) ) ) )),
                                      ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                        & ! [W1: $i] :
                                            ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                           => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                                        & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                    <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                        & ! [W1: $i] :
                                            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                                        & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
                                    rewrite(( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                        & ! [W1: $i] :
                                            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                                        & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                    <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                        & ! [W1: $i] :
                                            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                                        & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
                                    ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                      & ! [W1: $i] :
                                          ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                         => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                                      & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                  <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                      & ! [W1: $i] :
                                          ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                                      & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
                                  quant_intro(proof_bind(^ [W1: $i] :
                                        rewrite(( ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                          <=> ( aElement0(W1)
                                              & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                              & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                        <=> ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                          <=> ( aElement0(W1)
                                              & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                              & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ))),
                                    ( ! [W1: $i] :
                                        ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                      <=> ( aElement0(W1)
                                          & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                          & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                  <=> ! [W1: $i] :
                                        ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                      <=> ( aElement0(W1)
                                          & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                          & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )),
                                  ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                    & ! [W1: $i] :
                                        ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                                    & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    & ! [W1: $i] :
                                        ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                      <=> ( aElement0(W1)
                                          & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                          & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                                <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                    & ! [W1: $i] :
                                        ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                                    & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    & ! [W1: $i] :
                                        ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                      <=> ( aElement0(W1)
                                          & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                          & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) )),
                                rewrite(( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                    & ! [W1: $i] :
                                        ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                                    & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    & ! [W1: $i] :
                                        ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                      <=> ( aElement0(W1)
                                          & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                          & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                                <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                    & ! [W1: $i] :
                                        ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                                    & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    & ! [W1: $i] :
                                        ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                      <=> ( aElement0(W1)
                                          & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                          & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) )),
                                ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                  & ! [W1: $i] :
                                      ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                     => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                                  & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  & ! [W1: $i] :
                                      ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    <=> ( aElement0(W1)
                                        & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                        & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                              <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                  & ! [W1: $i] :
                                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                                  & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  & ! [W1: $i] :
                                      ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    <=> ( aElement0(W1)
                                        & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                        & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) )),
                              ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                & ! [W1: $i] :
                                    ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                   => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                & ! [W1: $i] :
                                    ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  <=> ( aElement0(W1)
                                      & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                      & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
                            <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                & ! [W1: $i] :
                                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                & ! [W1: $i] :
                                    ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  <=> ( aElement0(W1)
                                      & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                      & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )),
                            rewrite(( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                & ! [W1: $i] :
                                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                & ! [W1: $i] :
                                    ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  <=> ( aElement0(W1)
                                      & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                      & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
                            <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                & ! [W1: $i] :
                                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                & ! [W1: $i] :
                                    ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  <=> ( aElement0(W1)
                                      & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                      & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )),
                            ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                              & ! [W1: $i] :
                                  ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                 => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                              & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              & ! [W1: $i] :
                                  ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                <=> ( aElement0(W1)
                                    & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                    & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                              & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
                          <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                              & ! [W1: $i] :
                                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                              & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              & ! [W1: $i] :
                                  ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                <=> ( aElement0(W1)
                                    & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                    & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                              & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )),
                          quant_intro(proof_bind(^ [W1: $i] :
                                rewrite(( ( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                                   => aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                <=> ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                                    | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ))),
                            ( ! [W1: $i] :
                                ( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                               => aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                          <=> ! [W1: $i] :
                                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                                | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
                          ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                            & ! [W1: $i] :
                                ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                               => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & ! [W1: $i] :
                                ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              <=> ( aElement0(W1)
                                  & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                  & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                            & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                            & ! [W1: $i] :
                                ( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                               => aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                        <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                            & ! [W1: $i] :
                                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & ! [W1: $i] :
                                ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              <=> ( aElement0(W1)
                                  & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                  & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                            & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                            & ! [W1: $i] :
                                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                                | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )),
                        rewrite(( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                            & ! [W1: $i] :
                                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & ! [W1: $i] :
                                ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              <=> ( aElement0(W1)
                                  & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                  & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                            & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                            & ! [W1: $i] :
                                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                                | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                        <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                            & ! [W1: $i] :
                                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & ! [W1: $i] :
                                ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              <=> ( aElement0(W1)
                                  & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                  & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                            & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                            & ! [W1: $i] :
                                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                                | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )),
                        ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                          & ! [W1: $i] :
                              ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                             => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                          & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          & ! [W1: $i] :
                              ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            <=> ( aElement0(W1)
                                & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                          & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                          & ! [W1: $i] :
                              ( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                             => aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                      <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                          & ! [W1: $i] :
                              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                          & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          & ! [W1: $i] :
                              ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            <=> ( aElement0(W1)
                                & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                          & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                          & ! [W1: $i] :
                              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                              | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )),
                      ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        & ! [W1: $i] :
                            ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                           => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                        & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        & ! [W1: $i] :
                            ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          <=> ( aElement0(W1)
                              & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                              & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                        & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                        & ! [W1: $i] :
                            ( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                           => aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                        & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        & ! [W1: $i] :
                            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                        & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        & ! [W1: $i] :
                            ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          <=> ( aElement0(W1)
                              & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                              & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                        & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                        & ! [W1: $i] :
                            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                            | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                        & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
                    rewrite(( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        & ! [W1: $i] :
                            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                        & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        & ! [W1: $i] :
                            ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          <=> ( aElement0(W1)
                              & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                              & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                        & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                        & ! [W1: $i] :
                            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                            | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                        & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        & ! [W1: $i] :
                            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                        & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        & ! [W1: $i] :
                            ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          <=> ( aElement0(W1)
                              & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                              & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                        & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                        & ! [W1: $i] :
                            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                            | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                        & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
                    ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      & ! [W1: $i] :
                          ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                         => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                      & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & ! [W1: $i] :
                          ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        <=> ( aElement0(W1)
                            & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                            & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                      & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                      & ! [W1: $i] :
                          ( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                         => aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      & ! [W1: $i] :
                          ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                      & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & ! [W1: $i] :
                          ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        <=> ( aElement0(W1)
                            & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                            & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                      & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                      & ! [W1: $i] :
                          ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                          | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
                  ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    & ! [W1: $i] :
                        ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                    & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & ! [W1: $i] :
                        ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      <=> ( aElement0(W1)
                          & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                    & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                    & ! [W1: $i] :
                        ( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                       => aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
                <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    & ! [W1: $i] :
                        ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                    & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & ! [W1: $i] :
                        ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      <=> ( aElement0(W1)
                          & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                    & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                    & ! [W1: $i] :
                        ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                        | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )),
                rewrite(( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    & ! [W1: $i] :
                        ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                    & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & ! [W1: $i] :
                        ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      <=> ( aElement0(W1)
                          & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                    & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                    & ! [W1: $i] :
                        ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                        | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
                <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    & ! [W1: $i] :
                        ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                    & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & ! [W1: $i] :
                        ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      <=> ( aElement0(W1)
                          & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                    & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                    & ! [W1: $i] :
                        ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                        | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )),
                ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  & ! [W1: $i] :
                      ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                     => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                  & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ! [W1: $i] :
                      ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    <=> ( aElement0(W1)
                        & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                  & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  & ! [W1: $i] :
                      ( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                     => aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
              <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  & ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                  & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ! [W1: $i] :
                      ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    <=> ( aElement0(W1)
                        & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                  & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  & ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                      | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )),
              ( ( ( ( ( aSet0(sdtlpdtrp0(xN,W0))
                      & ! [W1: $i] :
                          ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                         => aElementOf0(W1,szNzAzT0) ) )
                    | aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
                  & isCountable0(sdtlpdtrp0(xN,W0)) )
               => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  & ! [W1: $i] :
                      ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                     => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                  & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ! [W1: $i] :
                      ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    <=> ( aElement0(W1)
                        & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                  & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  & ! [W1: $i] :
                      ( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                     => aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
            <=> ( ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                    | ( aSet0(sdtlpdtrp0(xN,W0))
                      & ! [W1: $i] :
                          ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | aElementOf0(W1,szNzAzT0) ) ) )
                  & isCountable0(sdtlpdtrp0(xN,W0)) )
               => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  & ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                  & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ! [W1: $i] :
                      ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    <=> ( aElement0(W1)
                        & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                  & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  & ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                      | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) )),
            rewrite(( ( ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                    | ( aSet0(sdtlpdtrp0(xN,W0))
                      & ! [W1: $i] :
                          ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | aElementOf0(W1,szNzAzT0) ) ) )
                  & isCountable0(sdtlpdtrp0(xN,W0)) )
               => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  & ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                  & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ! [W1: $i] :
                      ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    <=> ( aElement0(W1)
                        & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                  & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  & ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                      | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
            <=> ( ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                      | ( aSet0(sdtlpdtrp0(xN,W0))
                        & ! [W1: $i] :
                            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                            | aElementOf0(W1,szNzAzT0) ) ) )
                    & isCountable0(sdtlpdtrp0(xN,W0)) )
                | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  & ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                  & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ! [W1: $i] :
                      ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    <=> ( aElement0(W1)
                        & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                  & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  & ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                      | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) )),
            ( ( ( ( ( aSet0(sdtlpdtrp0(xN,W0))
                    & ! [W1: $i] :
                        ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                       => aElementOf0(W1,szNzAzT0) ) )
                  | aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
                & isCountable0(sdtlpdtrp0(xN,W0)) )
             => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W1: $i] :
                    ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                   => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & ! [W1: $i] :
                    ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W1)
                      & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                & ! [W1: $i] :
                    ( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                   => aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
          <=> ( ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                    | ( aSet0(sdtlpdtrp0(xN,W0))
                      & ! [W1: $i] :
                          ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | aElementOf0(W1,szNzAzT0) ) ) )
                  & isCountable0(sdtlpdtrp0(xN,W0)) )
              | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & ! [W1: $i] :
                    ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W1)
                      & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                & ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                    | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) )),
          ( ( aElementOf0(W0,szNzAzT0)
           => ( ( ( ( aSet0(sdtlpdtrp0(xN,W0))
                    & ! [W1: $i] :
                        ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                       => aElementOf0(W1,szNzAzT0) ) )
                  | aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
                & isCountable0(sdtlpdtrp0(xN,W0)) )
             => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W1: $i] :
                    ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                   => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & ! [W1: $i] :
                    ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W1)
                      & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                & ! [W1: $i] :
                    ( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                   => aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) )
        <=> ( aElementOf0(W0,szNzAzT0)
           => ( ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                    | ( aSet0(sdtlpdtrp0(xN,W0))
                      & ! [W1: $i] :
                          ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | aElementOf0(W1,szNzAzT0) ) ) )
                  & isCountable0(sdtlpdtrp0(xN,W0)) )
              | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & ! [W1: $i] :
                    ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W1)
                      & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                & ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                    | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) )),
        rewrite(( ( aElementOf0(W0,szNzAzT0)
           => ( ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                    | ( aSet0(sdtlpdtrp0(xN,W0))
                      & ! [W1: $i] :
                          ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | aElementOf0(W1,szNzAzT0) ) ) )
                  & isCountable0(sdtlpdtrp0(xN,W0)) )
              | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & ! [W1: $i] :
                    ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W1)
                      & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                & ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                    | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) )
        <=> ( ~ aElementOf0(W0,szNzAzT0)
            | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & ! [W1: $i] :
                  ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                <=> ( aElement0(W1)
                    & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
              & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
            | ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                  | ( aSet0(sdtlpdtrp0(xN,W0))
                    & ! [W1: $i] :
                        ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | aElementOf0(W1,szNzAzT0) ) ) )
                & isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
        ( ( aElementOf0(W0,szNzAzT0)
         => ( ( ( ( aSet0(sdtlpdtrp0(xN,W0))
                  & ! [W1: $i] :
                      ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                     => aElementOf0(W1,szNzAzT0) ) )
                | aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
              & isCountable0(sdtlpdtrp0(xN,W0)) )
           => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                 => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & ! [W1: $i] :
                  ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                <=> ( aElement0(W1)
                    & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
              & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
              & ! [W1: $i] :
                  ( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                 => aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            & ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            & ! [W1: $i] :
                ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              <=> ( aElement0(W1)
                  & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
            & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
            & ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
          | ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                | ( aSet0(sdtlpdtrp0(xN,W0))
                  & ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | aElementOf0(W1,szNzAzT0) ) ) )
              & isCountable0(sdtlpdtrp0(xN,W0)) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(76,plain,
    ( ! [W0: $i] :
        ( aElementOf0(W0,szNzAzT0)
       => ( ( ( ( aSet0(sdtlpdtrp0(xN,W0))
                & ! [W1: $i] :
                    ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                   => aElementOf0(W1,szNzAzT0) ) )
              | aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
            & isCountable0(sdtlpdtrp0(xN,W0)) )
         => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            & ! [W1: $i] :
                ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
               => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            & ! [W1: $i] :
                ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              <=> ( aElement0(W1)
                  & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
            & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
            & ! [W1: $i] :
                ( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
               => aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
          & ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
          & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          & ! [W1: $i] :
              ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            <=> ( aElement0(W1)
                & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
          & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
          & ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
              | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
          & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
        | ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              | ( aSet0(sdtlpdtrp0(xN,W0))
                & ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | aElementOf0(W1,szNzAzT0) ) ) )
            & isCountable0(sdtlpdtrp0(xN,W0)) ) ) ),
    inference(quant_intro,[status(thm)],[75]) ).

tff(77,axiom,
    ( aFunction0(xN)
    & ( szDzozmdt0(xN) = szNzAzT0 )
    & ( sdtlpdtrp0(xN,sz00) = xS )
    & ! [W0: $i] :
        ( aElementOf0(W0,szNzAzT0)
       => ( ( ( ( aSet0(sdtlpdtrp0(xN,W0))
                & ! [W1: $i] :
                    ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                   => aElementOf0(W1,szNzAzT0) ) )
              | aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
            & isCountable0(sdtlpdtrp0(xN,W0)) )
         => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            & ! [W1: $i] :
                ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
               => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            & ! [W1: $i] :
                ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              <=> ( aElement0(W1)
                  & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
            & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
            & ! [W1: $i] :
                ( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
               => aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3623) ).

tff(78,plain,
    ! [W0: $i] :
      ( aElementOf0(W0,szNzAzT0)
     => ( ( ( ( aSet0(sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                 => aElementOf0(W1,szNzAzT0) ) )
            | aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
          & isCountable0(sdtlpdtrp0(xN,W0)) )
       => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
          & ! [W1: $i] :
              ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
             => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
          & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          & ! [W1: $i] :
              ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            <=> ( aElement0(W1)
                & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
          & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
          & ! [W1: $i] :
              ( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
             => aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
          & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ),
    inference(and_elim,[status(thm)],[77]) ).

tff(79,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
        & ! [W1: $i] :
            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
        & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
        & ! [W1: $i] :
            ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          <=> ( aElement0(W1)
              & aElementOf0(W1,sdtlpdtrp0(xN,W0))
              & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
        & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
        & ! [W1: $i] :
            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
            | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
        & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
        & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
      | ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
            | ( aSet0(sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | aElementOf0(W1,szNzAzT0) ) ) )
          & isCountable0(sdtlpdtrp0(xN,W0)) ) ),
    inference(modus_ponens,[status(thm)],[78,76]) ).

tff(80,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
        & ! [W1: $i] :
            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
        & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
        & ! [W1: $i] :
            ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          <=> ( aElement0(W1)
              & aElementOf0(W1,sdtlpdtrp0(xN,W0))
              & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
        & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
        & ! [W1: $i] :
            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
            | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
        & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
        & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
      | ~ ( ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
            | ( aSet0(sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | aElementOf0(W1,szNzAzT0) ) ) )
          & isCountable0(sdtlpdtrp0(xN,W0)) ) ),
    inference(modus_ponens,[status(thm)],[79,74]) ).

tff(81,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
        & ! [W1: $i] :
            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
        & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
        & ! [W1: $i] :
            ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          <=> ( aElement0(W1)
              & aElementOf0(W1,sdtlpdtrp0(xN,W0))
              & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
        & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
        & ! [W1: $i] :
            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
            | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
        & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
        & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
      | ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
        & ( ~ aSet0(sdtlpdtrp0(xN,W0))
          | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
              | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
      | ~ isCountable0(sdtlpdtrp0(xN,W0)) ),
    inference(skolemize,[status(sab)],[80]) ).

tff(82,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
        & ! [W1: $i] :
            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
        & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
        & ! [W1: $i] :
            ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          <=> ( aElement0(W1)
              & aElementOf0(W1,sdtlpdtrp0(xN,W0))
              & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
        & aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
        & ! [W1: $i] :
            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
            | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
        & aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
        & isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
      | ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
        & ( ~ aSet0(sdtlpdtrp0(xN,W0))
          | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
              | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
      | ~ isCountable0(sdtlpdtrp0(xN,W0)) ),
    inference(modus_ponens,[status(thm)],[81,73]) ).

tff(83,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ~ isCountable0(sdtlpdtrp0(xN,W0))
      | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          | ~ ! [W1: $i] :
                ~ ( ( ~ aElement0(W1)
                    | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
          | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
          | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
      | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
          | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
              | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                  | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) ) ),
    inference(modus_ponens,[status(thm)],[82,71]) ).

tff(84,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ~ isCountable0(sdtlpdtrp0(xN,W0))
      | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          | ~ ! [W1: $i] :
                ~ ( ( ~ aElement0(W1)
                    | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
          | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
          | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
      | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
          | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
              | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                  | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) ) ),
    inference(modus_ponens,[status(thm)],[83,69]) ).

tff(85,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ~ isCountable0(sdtlpdtrp0(xN,W0))
      | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
          | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
              | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                  | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
      | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
          | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
          | ~ ! [W1: $i] :
                ~ ( ( ~ aElement0(W1)
                    | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ),
    inference(modus_ponens,[status(thm)],[84,64]) ).

tff(86,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ isCountable0(sdtlpdtrp0(xN,W0))
            | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                    | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                        | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
            | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                | ~ ! [W1: $i] :
                      ~ ( ( ~ aElement0(W1)
                          | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                      | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ~ isCountable0(sdtlpdtrp0(xN,xn))
      | ~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0)
          | ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
              | ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
                  | aElementOf0(tptp_fun_W1_29(xn),szNzAzT0) ) ) )
      | ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ ! [W1: $i] :
                ~ ( ( ~ aElement0(W1)
                    | ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                    | ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
  <=> ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ isCountable0(sdtlpdtrp0(xN,W0))
            | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                    | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                        | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
            | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                | ~ ! [W1: $i] :
                      ~ ( ( ~ aElement0(W1)
                          | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                      | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ~ isCountable0(sdtlpdtrp0(xN,xn))
      | ~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0)
          | ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
              | ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
                  | aElementOf0(tptp_fun_W1_29(xn),szNzAzT0) ) ) )
      | ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ ! [W1: $i] :
                ~ ( ( ~ aElement0(W1)
                    | ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                    | ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(87,plain,
    ( ( ~ aElementOf0(xn,szNzAzT0)
      | ~ isCountable0(sdtlpdtrp0(xN,xn))
      | ~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0)
          | ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
              | ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
                  | aElementOf0(tptp_fun_W1_29(xn),szNzAzT0) ) ) )
      | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
          | ~ ! [W1: $i] :
                ~ ( ( ~ aElement0(W1)
                    | ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                    | ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
  <=> ( ~ aElementOf0(xn,szNzAzT0)
      | ~ isCountable0(sdtlpdtrp0(xN,xn))
      | ~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0)
          | ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
              | ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
                  | aElementOf0(tptp_fun_W1_29(xn),szNzAzT0) ) ) )
      | ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ ! [W1: $i] :
                ~ ( ( ~ aElement0(W1)
                    | ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                    | ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(88,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ isCountable0(sdtlpdtrp0(xN,W0))
            | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                    | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                        | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
            | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                | ~ ! [W1: $i] :
                      ~ ( ( ~ aElement0(W1)
                          | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                      | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ~ isCountable0(sdtlpdtrp0(xN,xn))
      | ~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0)
          | ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
              | ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
                  | aElementOf0(tptp_fun_W1_29(xn),szNzAzT0) ) ) )
      | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
          | ~ ! [W1: $i] :
                ~ ( ( ~ aElement0(W1)
                    | ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                    | ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
  <=> ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ isCountable0(sdtlpdtrp0(xN,W0))
            | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                    | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                        | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
            | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                | ~ ! [W1: $i] :
                      ~ ( ( ~ aElement0(W1)
                          | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                      | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ~ isCountable0(sdtlpdtrp0(xN,xn))
      | ~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0)
          | ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
              | ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
                  | aElementOf0(tptp_fun_W1_29(xn),szNzAzT0) ) ) )
      | ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ ! [W1: $i] :
                ~ ( ( ~ aElement0(W1)
                    | ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                    | ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ),
    inference(monotonicity,[status(thm)],[87]) ).

tff(89,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ isCountable0(sdtlpdtrp0(xN,W0))
            | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                    | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                        | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
            | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                | ~ ! [W1: $i] :
                      ~ ( ( ~ aElement0(W1)
                          | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                      | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ~ isCountable0(sdtlpdtrp0(xN,xn))
      | ~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0)
          | ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
              | ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
                  | aElementOf0(tptp_fun_W1_29(xn),szNzAzT0) ) ) )
      | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
          | ~ ! [W1: $i] :
                ~ ( ( ~ aElement0(W1)
                    | ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                    | ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
  <=> ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ isCountable0(sdtlpdtrp0(xN,W0))
            | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                    | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                        | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
            | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                | ~ ! [W1: $i] :
                      ~ ( ( ~ aElement0(W1)
                          | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                      | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ~ isCountable0(sdtlpdtrp0(xN,xn))
      | ~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0)
          | ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
              | ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
                  | aElementOf0(tptp_fun_W1_29(xn),szNzAzT0) ) ) )
      | ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ ! [W1: $i] :
                ~ ( ( ~ aElement0(W1)
                    | ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                    | ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ),
    inference(transitivity,[status(thm)],[88,86]) ).

tff(90,plain,
    ( ~ ! [W0: $i] :
          ( ~ aElementOf0(W0,szNzAzT0)
          | ~ isCountable0(sdtlpdtrp0(xN,W0))
          | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                  | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                      | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
          | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
              | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              | ~ ! [W1: $i] :
                    ~ ( ( ~ aElement0(W1)
                        | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                    <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                    | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
    | ~ aElementOf0(xn,szNzAzT0)
    | ~ isCountable0(sdtlpdtrp0(xN,xn))
    | ~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0)
        | ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
            | ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
                | aElementOf0(tptp_fun_W1_29(xn),szNzAzT0) ) ) )
    | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
        | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
        | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
        | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
        | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
        | ~ ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
        | ~ ! [W1: $i] :
              ~ ( ( ~ aElement0(W1)
                  | ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                  | ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
              <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
        | ~ ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
              | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(91,plain,
    ( ~ ! [W0: $i] :
          ( ~ aElementOf0(W0,szNzAzT0)
          | ~ isCountable0(sdtlpdtrp0(xN,W0))
          | ~ ( aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              | ~ ( ~ aSet0(sdtlpdtrp0(xN,W0))
                  | ~ ( ~ aElementOf0(tptp_fun_W1_29(W0),sdtlpdtrp0(xN,W0))
                      | aElementOf0(tptp_fun_W1_29(W0),szNzAzT0) ) ) )
          | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
              | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              | ~ ! [W1: $i] :
                    ~ ( ( ~ aElement0(W1)
                        | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                    <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                    | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
    | ~ aElementOf0(xn,szNzAzT0)
    | ~ isCountable0(sdtlpdtrp0(xN,xn))
    | ~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0)
        | ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
            | ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
                | aElementOf0(tptp_fun_W1_29(xn),szNzAzT0) ) ) )
    | ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
        | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
        | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
        | ~ ! [W1: $i] :
              ~ ( ( ~ aElement0(W1)
                  | ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                  | ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
              <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
        | ~ ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
        | ~ ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
              | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
        | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
        | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ),
    inference(modus_ponens,[status(thm)],[90,89]) ).

tff(92,plain,
    ( ~ isCountable0(sdtlpdtrp0(xN,xn))
    | ~ ( aSubsetOf0(sdtlpdtrp0(xN,xn),szNzAzT0)
        | ~ ( ~ aSet0(sdtlpdtrp0(xN,xn))
            | ~ ( ~ aElementOf0(tptp_fun_W1_29(xn),sdtlpdtrp0(xN,xn))
                | aElementOf0(tptp_fun_W1_29(xn),szNzAzT0) ) ) )
    | ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
        | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
        | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
        | ~ ! [W1: $i] :
              ~ ( ( ~ aElement0(W1)
                  | ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                  | ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
              <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
        | ~ ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
        | ~ ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
              | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
        | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
        | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ),
    inference(unit_resolution,[status(thm)],[91,85,28]) ).

tff(93,plain,
    ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
      | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
      | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
      | ~ ! [W1: $i] :
            ~ ( ( ~ aElement0(W1)
                | ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
            <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
      | ~ ! [W1: $i] :
            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
      | ~ ! [W1: $i] :
            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
            | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
      | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
      | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ),
    inference(unit_resolution,[status(thm)],[92,60,56]) ).

tff(94,plain,
    ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
    | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
    | ~ ! [W1: $i] :
          ~ ( ( ~ aElement0(W1)
              | ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
              | ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
          <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
    | ~ ! [W1: $i] :
          ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
    | ~ ! [W1: $i] :
          ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
    | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
    | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
    | aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ),
    inference(tautology,[status(thm)],[]) ).

tff(95,plain,
    aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))),
    inference(unit_resolution,[status(thm)],[94,93]) ).

tff(96,plain,
    ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
    | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
    | ~ ! [W2: $i] :
          ~ ( ( ~ aElement0(W2)
              | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
          <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
    | ~ ! [W2: $i] :
          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
    | aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
    | ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
        | ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
            | aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
    | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ),
    inference(tautology,[status(thm)],[]) ).

tff(97,plain,
    ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
    | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
    | ~ ! [W2: $i] :
          ~ ( ( ~ aElement0(W2)
              | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
          <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
    | ~ ! [W2: $i] :
          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
    | aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
    | ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
        | ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
            | aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ),
    inference(unit_resolution,[status(thm)],[96,95]) ).

tff(98,plain,
    ^ [W0: $i] :
      refl(( ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ~ aElementOf0(szszuzczcdt0(W0),szNzAzT0)
              | ( szszuzczcdt0(W0) = sz00 ) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ~ aElementOf0(szszuzczcdt0(W0),szNzAzT0)
              | ( szszuzczcdt0(W0) = sz00 ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(99,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ ( ~ aElementOf0(szszuzczcdt0(W0),szNzAzT0)
            | ( szszuzczcdt0(W0) = sz00 ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ ( ~ aElementOf0(szszuzczcdt0(W0),szNzAzT0)
            | ( szszuzczcdt0(W0) = sz00 ) ) ) ),
    inference(quant_intro,[status(thm)],[98]) ).

tff(100,plain,
    ^ [W0: $i] :
      rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
          | ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
            & ( szszuzczcdt0(W0) != sz00 ) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ~ aElementOf0(szszuzczcdt0(W0),szNzAzT0)
              | ( szszuzczcdt0(W0) = sz00 ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(101,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
          & ( szszuzczcdt0(W0) != sz00 ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ ( ~ aElementOf0(szszuzczcdt0(W0),szNzAzT0)
            | ( szszuzczcdt0(W0) = sz00 ) ) ) ),
    inference(quant_intro,[status(thm)],[100]) ).

tff(102,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
          & ( szszuzczcdt0(W0) != sz00 ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
          & ( szszuzczcdt0(W0) != sz00 ) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(103,plain,
    ^ [W0: $i] :
      rewrite(( ( aElementOf0(W0,szNzAzT0)
         => ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
            & ( szszuzczcdt0(W0) != sz00 ) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
            & ( szszuzczcdt0(W0) != sz00 ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(104,plain,
    ( ! [W0: $i] :
        ( aElementOf0(W0,szNzAzT0)
       => ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
          & ( szszuzczcdt0(W0) != sz00 ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
          & ( szszuzczcdt0(W0) != sz00 ) ) ) ),
    inference(quant_intro,[status(thm)],[103]) ).

tff(105,axiom,
    ! [W0: $i] :
      ( aElementOf0(W0,szNzAzT0)
     => ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
        & ( szszuzczcdt0(W0) != sz00 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNum) ).

tff(106,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
        & ( szszuzczcdt0(W0) != sz00 ) ) ),
    inference(modus_ponens,[status(thm)],[105,104]) ).

tff(107,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
        & ( szszuzczcdt0(W0) != sz00 ) ) ),
    inference(modus_ponens,[status(thm)],[106,102]) ).

tff(108,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
        & ( szszuzczcdt0(W0) != sz00 ) ) ),
    inference(skolemize,[status(sab)],[107]) ).

tff(109,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ~ ( ~ aElementOf0(szszuzczcdt0(W0),szNzAzT0)
          | ( szszuzczcdt0(W0) = sz00 ) ) ),
    inference(modus_ponens,[status(thm)],[108,101]) ).

tff(110,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ~ ( ~ aElementOf0(szszuzczcdt0(W0),szNzAzT0)
          | ( szszuzczcdt0(W0) = sz00 ) ) ),
    inference(modus_ponens,[status(thm)],[109,99]) ).

tff(111,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ ( ~ aElementOf0(szszuzczcdt0(W0),szNzAzT0)
                | ( szszuzczcdt0(W0) = sz00 ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ~ ( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
          | ( szszuzczcdt0(xn) = sz00 ) ) )
  <=> ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ ( ~ aElementOf0(szszuzczcdt0(W0),szNzAzT0)
                | ( szszuzczcdt0(W0) = sz00 ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ~ ( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
          | ( szszuzczcdt0(xn) = sz00 ) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(112,plain,
    ( ~ ! [W0: $i] :
          ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ~ aElementOf0(szszuzczcdt0(W0),szNzAzT0)
              | ( szszuzczcdt0(W0) = sz00 ) ) )
    | ~ aElementOf0(xn,szNzAzT0)
    | ~ ( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
        | ( szszuzczcdt0(xn) = sz00 ) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(113,plain,
    ( ~ ! [W0: $i] :
          ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ~ aElementOf0(szszuzczcdt0(W0),szNzAzT0)
              | ( szszuzczcdt0(W0) = sz00 ) ) )
    | ~ aElementOf0(xn,szNzAzT0)
    | ~ ( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
        | ( szszuzczcdt0(xn) = sz00 ) ) ),
    inference(modus_ponens,[status(thm)],[112,111]) ).

tff(114,plain,
    ~ ( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
      | ( szszuzczcdt0(xn) = sz00 ) ),
    inference(unit_resolution,[status(thm)],[113,110,28]) ).

tff(115,plain,
    ( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
    | ( szszuzczcdt0(xn) = sz00 )
    | aElementOf0(szszuzczcdt0(xn),szNzAzT0) ),
    inference(tautology,[status(thm)],[]) ).

tff(116,plain,
    aElementOf0(szszuzczcdt0(xn),szNzAzT0),
    inference(unit_resolution,[status(thm)],[115,114]) ).

tff(117,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                | ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ isCountable0(sdtlpdtrp0(xN,W0))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | aElementOf0(W1,szNzAzT0) ) ) )
      | ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
      | ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),szNzAzT0)
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                | aElementOf0(W1,szNzAzT0) ) ) )
  <=> ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                | ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ isCountable0(sdtlpdtrp0(xN,W0))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | aElementOf0(W1,szNzAzT0) ) ) )
      | ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
      | ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),szNzAzT0)
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                | aElementOf0(W1,szNzAzT0) ) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(118,plain,
    ( ( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
      | ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),szNzAzT0)
          | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                | aElementOf0(W1,szNzAzT0) ) ) )
  <=> ( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
      | ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),szNzAzT0)
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                | aElementOf0(W1,szNzAzT0) ) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(119,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                | ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ isCountable0(sdtlpdtrp0(xN,W0))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | aElementOf0(W1,szNzAzT0) ) ) )
      | ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
      | ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),szNzAzT0)
          | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                | aElementOf0(W1,szNzAzT0) ) ) )
  <=> ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                | ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ isCountable0(sdtlpdtrp0(xN,W0))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | aElementOf0(W1,szNzAzT0) ) ) )
      | ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
      | ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),szNzAzT0)
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                | aElementOf0(W1,szNzAzT0) ) ) ) ),
    inference(monotonicity,[status(thm)],[118]) ).

tff(120,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                | ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ isCountable0(sdtlpdtrp0(xN,W0))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | aElementOf0(W1,szNzAzT0) ) ) )
      | ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
      | ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),szNzAzT0)
          | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                | aElementOf0(W1,szNzAzT0) ) ) )
  <=> ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
                | ~ aSet0(sdtlpdtrp0(xN,W0))
                | ~ isCountable0(sdtlpdtrp0(xN,W0))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | aElementOf0(W1,szNzAzT0) ) ) )
      | ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
      | ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),szNzAzT0)
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                | aElementOf0(W1,szNzAzT0) ) ) ) ),
    inference(transitivity,[status(thm)],[119,117]) ).

tff(121,plain,
    ( ~ ! [W0: $i] :
          ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              | ~ aSet0(sdtlpdtrp0(xN,W0))
              | ~ isCountable0(sdtlpdtrp0(xN,W0))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | aElementOf0(W1,szNzAzT0) ) ) )
    | ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
    | ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),szNzAzT0)
        | ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
        | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
        | ~ ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
              | aElementOf0(W1,szNzAzT0) ) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(122,plain,
    ( ~ ! [W0: $i] :
          ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0)
              | ~ aSet0(sdtlpdtrp0(xN,W0))
              | ~ isCountable0(sdtlpdtrp0(xN,W0))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | aElementOf0(W1,szNzAzT0) ) ) )
    | ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
    | ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
        | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
        | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),szNzAzT0)
        | ~ ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
              | aElementOf0(W1,szNzAzT0) ) ) ),
    inference(modus_ponens,[status(thm)],[121,120]) ).

tff(123,plain,
    ( ~ aElementOf0(szszuzczcdt0(xn),szNzAzT0)
    | ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
        | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
        | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),szNzAzT0)
        | ~ ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
              | aElementOf0(W1,szNzAzT0) ) ) ),
    inference(unit_resolution,[status(thm)],[122,47]) ).

tff(124,plain,
    ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
      | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
      | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),szNzAzT0)
      | ~ ! [W1: $i] :
            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
            | aElementOf0(W1,szNzAzT0) ) ),
    inference(unit_resolution,[status(thm)],[123,116]) ).

tff(125,plain,
    ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
    | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
    | ~ aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),szNzAzT0)
    | ~ ! [W1: $i] :
          ( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | aElementOf0(W1,szNzAzT0) )
    | isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
    inference(tautology,[status(thm)],[]) ).

tff(126,plain,
    isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn))),
    inference(unit_resolution,[status(thm)],[125,124]) ).

tff(127,plain,
    ^ [W0: $i] :
      rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
          | ! [W1: $i] :
              ( ~ isCountable0(W1)
              | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  | ~ ! [W2: $i] :
                        ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                  | ~ ( ~ aSet0(W1)
                      | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                          | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                  | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  | ~ ! [W2: $i] :
                        ~ ( ( ~ aElement0(W2)
                            | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                        <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
              | ! [W2: $i] :
                  ( ~ aSet0(W2)
                  | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      | ~ ! [W3: $i] :
                            ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                      | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ ! [W3: $i] :
                            ~ ( ( ~ aElement0(W3)
                                | ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                | ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                            <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      | ~ ! [W3: $i] :
                            ( ~ aElementOf0(W3,W2)
                            | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
                  | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                      | ~ ( ( sbrdtbr0(W2) != xk )
                          | ~ ( aSubsetOf0(W2,W1)
                              | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                              | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ! [W1: $i] :
              ( ~ isCountable0(W1)
              | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  | ~ ( ~ aSet0(W1)
                      | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                          | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                  | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  | ~ ! [W2: $i] :
                        ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                  | ~ ! [W2: $i] :
                        ~ ( ( ~ aElement0(W2)
                            | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                        <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
              | ! [W2: $i] :
                  ( ~ aSet0(W2)
                  | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                      | ~ ( ( sbrdtbr0(W2) != xk )
                          | ~ ( aSubsetOf0(W2,W1)
                              | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                              | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
                  | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                      | ~ ! [W3: $i] :
                            ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                      | ~ ! [W3: $i] :
                            ~ ( ( ~ aElement0(W3)
                                | ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                | ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                            <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      | ~ ! [W3: $i] :
                            ( ~ aElementOf0(W3,W2)
                            | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(128,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ! [W1: $i] :
            ( ~ isCountable0(W1)
            | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                | ~ ( ~ aSet0(W1)
                    | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                        | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ ! [W2: $i] :
                      ~ ( ( ~ aElement0(W2)
                          | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
            | ! [W2: $i] :
                ( ~ aSet0(W2)
                | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    | ~ ! [W3: $i] :
                          ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ ! [W3: $i] :
                          ~ ( ( ~ aElement0(W3)
                              | ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                              | ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                          <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    | ~ ! [W3: $i] :
                          ( ~ aElementOf0(W3,W2)
                          | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
                | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                    | ~ ( ( sbrdtbr0(W2) != xk )
                        | ~ ( aSubsetOf0(W2,W1)
                            | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                            | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ! [W1: $i] :
            ( ~ isCountable0(W1)
            | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ ( ~ aSet0(W1)
                    | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                        | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                | ~ ! [W2: $i] :
                      ~ ( ( ~ aElement0(W2)
                          | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
            | ! [W2: $i] :
                ( ~ aSet0(W2)
                | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                    | ~ ( ( sbrdtbr0(W2) != xk )
                        | ~ ( aSubsetOf0(W2,W1)
                            | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                            | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
                | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                    | ~ ! [W3: $i] :
                          ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                    | ~ ! [W3: $i] :
                          ~ ( ( ~ aElement0(W3)
                              | ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                              | ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                          <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    | ~ ! [W3: $i] :
                          ( ~ aElementOf0(W3,W2)
                          | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ) ),
    inference(quant_intro,[status(thm)],[127]) ).

tff(129,plain,
    ^ [W0: $i] :
      refl(( ( ~ aElementOf0(W0,szNzAzT0)
          | ! [W1: $i] :
              ( ~ isCountable0(W1)
              | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  | ~ ! [W2: $i] :
                        ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                  | ~ ( ~ aSet0(W1)
                      | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                          | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                  | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  | ~ ! [W2: $i] :
                        ~ ( ( ~ aElement0(W2)
                            | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                        <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
              | ! [W2: $i] :
                  ( ~ aSet0(W2)
                  | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      | ~ ! [W3: $i] :
                            ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                      | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ ! [W3: $i] :
                            ~ ( ( ~ aElement0(W3)
                                | ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                | ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                            <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      | ~ ! [W3: $i] :
                            ( ~ aElementOf0(W3,W2)
                            | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
                  | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                      | ~ ( ( sbrdtbr0(W2) != xk )
                          | ~ ( aSubsetOf0(W2,W1)
                              | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                              | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ! [W1: $i] :
              ( ~ isCountable0(W1)
              | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  | ~ ! [W2: $i] :
                        ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                  | ~ ( ~ aSet0(W1)
                      | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                          | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                  | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  | ~ ! [W2: $i] :
                        ~ ( ( ~ aElement0(W2)
                            | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                        <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
              | ! [W2: $i] :
                  ( ~ aSet0(W2)
                  | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      | ~ ! [W3: $i] :
                            ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                      | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ ! [W3: $i] :
                            ~ ( ( ~ aElement0(W3)
                                | ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                | ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                            <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      | ~ ! [W3: $i] :
                            ( ~ aElementOf0(W3,W2)
                            | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
                  | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                      | ~ ( ( sbrdtbr0(W2) != xk )
                          | ~ ( aSubsetOf0(W2,W1)
                              | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                              | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(130,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ! [W1: $i] :
            ( ~ isCountable0(W1)
            | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                | ~ ( ~ aSet0(W1)
                    | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                        | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ ! [W2: $i] :
                      ~ ( ( ~ aElement0(W2)
                          | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
            | ! [W2: $i] :
                ( ~ aSet0(W2)
                | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    | ~ ! [W3: $i] :
                          ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ ! [W3: $i] :
                          ~ ( ( ~ aElement0(W3)
                              | ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                              | ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                          <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    | ~ ! [W3: $i] :
                          ( ~ aElementOf0(W3,W2)
                          | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
                | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                    | ~ ( ( sbrdtbr0(W2) != xk )
                        | ~ ( aSubsetOf0(W2,W1)
                            | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                            | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ! [W1: $i] :
            ( ~ isCountable0(W1)
            | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                | ~ ( ~ aSet0(W1)
                    | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                        | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ ! [W2: $i] :
                      ~ ( ( ~ aElement0(W2)
                          | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
            | ! [W2: $i] :
                ( ~ aSet0(W2)
                | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    | ~ ! [W3: $i] :
                          ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ ! [W3: $i] :
                          ~ ( ( ~ aElement0(W3)
                              | ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                              | ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                          <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    | ~ ! [W3: $i] :
                          ( ~ aElementOf0(W3,W2)
                          | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
                | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                    | ~ ( ( sbrdtbr0(W2) != xk )
                        | ~ ( aSubsetOf0(W2,W1)
                            | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                            | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) ) ),
    inference(quant_intro,[status(thm)],[129]) ).

tff(131,plain,
    ^ [W0: $i] :
      rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
          | ! [W1: $i] :
              ( ~ isCountable0(W1)
              | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  | ~ ! [W2: $i] :
                        ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                  | ~ ( ~ aSet0(W1)
                      | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                          | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                  | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  | ~ ! [W2: $i] :
                        ~ ( ( ~ aElement0(W2)
                            | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                        <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
              | ! [W2: $i] :
                  ( ~ aSet0(W2)
                  | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      | ~ ! [W3: $i] :
                            ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                      | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ ! [W3: $i] :
                            ~ ( ( ~ aElement0(W3)
                                | ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                | ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                            <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      | ~ ! [W3: $i] :
                            ( ~ aElementOf0(W3,W2)
                            | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
                  | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                      | ~ ( ( sbrdtbr0(W2) != xk )
                          | ~ ( aSubsetOf0(W2,W1)
                              | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                              | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ! [W1: $i] :
              ( ~ isCountable0(W1)
              | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  | ~ ! [W2: $i] :
                        ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                  | ~ ( ~ aSet0(W1)
                      | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                          | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                  | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  | ~ ! [W2: $i] :
                        ~ ( ( ~ aElement0(W2)
                            | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                        <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
              | ! [W2: $i] :
                  ( ~ aSet0(W2)
                  | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      | ~ ! [W3: $i] :
                            ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                      | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ ! [W3: $i] :
                            ~ ( ( ~ aElement0(W3)
                                | ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                | ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                            <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      | ~ ! [W3: $i] :
                            ( ~ aElementOf0(W3,W2)
                            | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
                  | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                      | ~ ( ( sbrdtbr0(W2) != xk )
                          | ~ ( aSubsetOf0(W2,W1)
                              | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                              | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(132,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ! [W1: $i] :
            ( ~ isCountable0(W1)
            | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                | ~ ( ~ aSet0(W1)
                    | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                        | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ ! [W2: $i] :
                      ~ ( ( ~ aElement0(W2)
                          | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
            | ! [W2: $i] :
                ( ~ aSet0(W2)
                | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    | ~ ! [W3: $i] :
                          ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ ! [W3: $i] :
                          ~ ( ( ~ aElement0(W3)
                              | ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                              | ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                          <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    | ~ ! [W3: $i] :
                          ( ~ aElementOf0(W3,W2)
                          | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
                | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                    | ~ ( ( sbrdtbr0(W2) != xk )
                        | ~ ( aSubsetOf0(W2,W1)
                            | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                            | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ! [W1: $i] :
            ( ~ isCountable0(W1)
            | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                | ~ ( ~ aSet0(W1)
                    | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                        | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ ! [W2: $i] :
                      ~ ( ( ~ aElement0(W2)
                          | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
            | ! [W2: $i] :
                ( ~ aSet0(W2)
                | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    | ~ ! [W3: $i] :
                          ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ ! [W3: $i] :
                          ~ ( ( ~ aElement0(W3)
                              | ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                              | ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                          <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    | ~ ! [W3: $i] :
                          ( ~ aElementOf0(W3,W2)
                          | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
                | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                    | ~ ( ( sbrdtbr0(W2) != xk )
                        | ~ ( aSubsetOf0(W2,W1)
                            | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                            | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) ) ),
    inference(quant_intro,[status(thm)],[131]) ).

tff(133,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ! [W1: $i] :
            ( ~ isCountable0(W1)
            | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                | ~ ( ~ aSet0(W1)
                    | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                        | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ ! [W2: $i] :
                      ~ ( ( ~ aElement0(W2)
                          | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
            | ! [W2: $i] :
                ( ~ aSet0(W2)
                | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    | ~ ! [W3: $i] :
                          ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ ! [W3: $i] :
                          ~ ( ( ~ aElement0(W3)
                              | ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                              | ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                          <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    | ~ ! [W3: $i] :
                          ( ~ aElementOf0(W3,W2)
                          | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
                | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                    | ~ ( ( sbrdtbr0(W2) != xk )
                        | ~ ( aSubsetOf0(W2,W1)
                            | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                            | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ! [W1: $i] :
            ( ~ isCountable0(W1)
            | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                | ~ ( ~ aSet0(W1)
                    | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                        | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ ! [W2: $i] :
                      ~ ( ( ~ aElement0(W2)
                          | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
            | ! [W2: $i] :
                ( ~ aSet0(W2)
                | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    | ~ ! [W3: $i] :
                          ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ ! [W3: $i] :
                          ~ ( ( ~ aElement0(W3)
                              | ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                              | ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                          <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    | ~ ! [W3: $i] :
                          ( ~ aElementOf0(W3,W2)
                          | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
                | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                    | ~ ( ( sbrdtbr0(W2) != xk )
                        | ~ ( aSubsetOf0(W2,W1)
                            | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                            | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) ) ),
    inference(transitivity,[status(thm)],[132,130]) ).

tff(134,plain,
    ^ [W0: $i] :
      rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
          | ! [W1: $i] :
              ( ~ isCountable0(W1)
              | ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & ! [W2: $i] :
                    ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W2)
                      & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                      & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                & ( ~ aSet0(W1)
                  | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                      | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
              | ! [W2: $i] :
                  ( ~ aSet0(W2)
                  | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    & ! [W3: $i] :
                        ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                    & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & ! [W3: $i] :
                        ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      <=> ( aElement0(W3)
                          & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                          & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                    & ! [W3: $i] :
                        ( ~ aElementOf0(W3,W2)
                        | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
                  | ( ~ aElementOf0(W2,slbdtsldtrb0(W1,xk))
                    & ( ( sbrdtbr0(W2) != xk )
                      | ( ~ aSubsetOf0(W2,W1)
                        & ~ ( ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                            | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ! [W1: $i] :
              ( ~ isCountable0(W1)
              | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  | ~ ! [W2: $i] :
                        ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                  | ~ ( ~ aSet0(W1)
                      | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                          | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                  | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  | ~ ! [W2: $i] :
                        ~ ( ( ~ aElement0(W2)
                            | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                        <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
              | ! [W2: $i] :
                  ( ~ aSet0(W2)
                  | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      | ~ ! [W3: $i] :
                            ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                      | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ ! [W3: $i] :
                            ~ ( ( ~ aElement0(W3)
                                | ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                | ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                            <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      | ~ ! [W3: $i] :
                            ( ~ aElementOf0(W3,W2)
                            | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
                  | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                      | ~ ( ( sbrdtbr0(W2) != xk )
                          | ~ ( aSubsetOf0(W2,W1)
                              | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                              | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(135,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ! [W1: $i] :
            ( ~ isCountable0(W1)
            | ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              & ! [W2: $i] :
                  ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & ! [W2: $i] :
                  ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                <=> ( aElement0(W2)
                    & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                    & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
              & ( ~ aSet0(W1)
                | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                    | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
            | ! [W2: $i] :
                ( ~ aSet0(W2)
                | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  & ! [W3: $i] :
                      ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                  & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ! [W3: $i] :
                      ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    <=> ( aElement0(W3)
                        & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                        & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                  & ! [W3: $i] :
                      ( ~ aElementOf0(W3,W2)
                      | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
                | ( ~ aElementOf0(W2,slbdtsldtrb0(W1,xk))
                  & ( ( sbrdtbr0(W2) != xk )
                    | ( ~ aSubsetOf0(W2,W1)
                      & ~ ( ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                          | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ! [W1: $i] :
            ( ~ isCountable0(W1)
            | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                | ~ ( ~ aSet0(W1)
                    | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                        | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ ! [W2: $i] :
                      ~ ( ( ~ aElement0(W2)
                          | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
            | ! [W2: $i] :
                ( ~ aSet0(W2)
                | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    | ~ ! [W3: $i] :
                          ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ ! [W3: $i] :
                          ~ ( ( ~ aElement0(W3)
                              | ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                              | ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                          <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    | ~ ! [W3: $i] :
                          ( ~ aElementOf0(W3,W2)
                          | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
                | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                    | ~ ( ( sbrdtbr0(W2) != xk )
                        | ~ ( aSubsetOf0(W2,W1)
                            | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                            | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) ) ),
    inference(quant_intro,[status(thm)],[134]) ).

tff(136,plain,
    ^ [W0: $i] :
      rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
          | ! [W1: $i] :
              ( ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & ! [W2: $i] :
                    ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W2)
                      & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                      & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                & ( ~ aSet0(W1)
                  | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                      | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
              | ~ isCountable0(W1)
              | ! [W2: $i] :
                  ( ~ aSet0(W2)
                  | ( ~ aElementOf0(W2,slbdtsldtrb0(W1,xk))
                    & ( ( ~ aSubsetOf0(W2,W1)
                        & ~ ( ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                            | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) )
                      | ( sbrdtbr0(W2) != xk ) ) )
                  | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    & ! [W3: $i] :
                        ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                    & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & ! [W3: $i] :
                        ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      <=> ( aElement0(W3)
                          & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                          & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                    & ! [W3: $i] :
                        ( ~ aElementOf0(W3,W2)
                        | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ! [W1: $i] :
              ( ~ isCountable0(W1)
              | ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & ! [W2: $i] :
                    ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W2)
                      & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                      & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                & ( ~ aSet0(W1)
                  | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                      | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
              | ! [W2: $i] :
                  ( ~ aSet0(W2)
                  | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    & ! [W3: $i] :
                        ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                    & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & ! [W3: $i] :
                        ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      <=> ( aElement0(W3)
                          & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                          & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                    & ! [W3: $i] :
                        ( ~ aElementOf0(W3,W2)
                        | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
                  | ( ~ aElementOf0(W2,slbdtsldtrb0(W1,xk))
                    & ( ( sbrdtbr0(W2) != xk )
                      | ( ~ aSubsetOf0(W2,W1)
                        & ~ ( ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                            | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(137,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ! [W1: $i] :
            ( ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              & ! [W2: $i] :
                  ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & ! [W2: $i] :
                  ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                <=> ( aElement0(W2)
                    & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                    & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
              & ( ~ aSet0(W1)
                | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                    | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
            | ~ isCountable0(W1)
            | ! [W2: $i] :
                ( ~ aSet0(W2)
                | ( ~ aElementOf0(W2,slbdtsldtrb0(W1,xk))
                  & ( ( ~ aSubsetOf0(W2,W1)
                      & ~ ( ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                          | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) )
                    | ( sbrdtbr0(W2) != xk ) ) )
                | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  & ! [W3: $i] :
                      ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                  & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ! [W3: $i] :
                      ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    <=> ( aElement0(W3)
                        & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                        & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                  & ! [W3: $i] :
                      ( ~ aElementOf0(W3,W2)
                      | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ! [W1: $i] :
            ( ~ isCountable0(W1)
            | ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              & ! [W2: $i] :
                  ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & ! [W2: $i] :
                  ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                <=> ( aElement0(W2)
                    & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                    & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
              & ( ~ aSet0(W1)
                | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                    | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
            | ! [W2: $i] :
                ( ~ aSet0(W2)
                | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  & ! [W3: $i] :
                      ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                  & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ! [W3: $i] :
                      ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    <=> ( aElement0(W3)
                        & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                        & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                  & ! [W3: $i] :
                      ( ~ aElementOf0(W3,W2)
                      | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
                | ( ~ aElementOf0(W2,slbdtsldtrb0(W1,xk))
                  & ( ( sbrdtbr0(W2) != xk )
                    | ( ~ aSubsetOf0(W2,W1)
                      & ~ ( ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                          | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) ) ) ),
    inference(quant_intro,[status(thm)],[136]) ).

tff(138,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ! [W1: $i] :
            ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      & ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                  | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & ! [W2: $i] :
                          ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        <=> ( aElement0(W2)
                            & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                  | ( aSet0(W1)
                    & ! [W2: $i] :
                        ( ~ aElementOf0(W2,W1)
                        | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                & isCountable0(W1) )
            | ! [W2: $i] :
                ( ~ ( aSet0(W2)
                    & ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                      | ( ( aSubsetOf0(W2,W1)
                          | ! [W3: $i] :
                              ( ~ aElementOf0(W3,W2)
                              | aElementOf0(W3,W1) ) )
                        & ( sbrdtbr0(W2) = xk ) ) ) )
                | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  & ! [W3: $i] :
                      ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                  & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ! [W3: $i] :
                      ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    <=> ( aElement0(W3)
                        & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                        & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                  & ! [W3: $i] :
                      ( ~ aElementOf0(W3,W2)
                      | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ! [W1: $i] :
            ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      & ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                  | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & ! [W2: $i] :
                          ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        <=> ( aElement0(W2)
                            & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                  | ( aSet0(W1)
                    & ! [W2: $i] :
                        ( ~ aElementOf0(W2,W1)
                        | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                & isCountable0(W1) )
            | ! [W2: $i] :
                ( ~ ( aSet0(W2)
                    & ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                      | ( ( aSubsetOf0(W2,W1)
                          | ! [W3: $i] :
                              ( ~ aElementOf0(W3,W2)
                              | aElementOf0(W3,W1) ) )
                        & ( sbrdtbr0(W2) = xk ) ) ) )
                | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  & ! [W3: $i] :
                      ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                  & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ! [W3: $i] :
                      ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    <=> ( aElement0(W3)
                        & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                        & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                  & ! [W3: $i] :
                      ( ~ aElementOf0(W3,W2)
                      | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(139,plain,
    ^ [W0: $i] :
      trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
                trans(monotonicity(rewrite(( ( ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                            & ! [W2: $i] :
                                ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                               => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                         => ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              & ! [W2: $i] :
                                  ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                <=> ( aElement0(W2)
                                    & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                    & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                           => ( ( aSet0(W1)
                                & ! [W2: $i] :
                                    ( aElementOf0(W2,W1)
                                   => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                              | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                        & isCountable0(W1) )
                    <=> ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                              & ! [W2: $i] :
                                  ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                          | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              & ! [W2: $i] :
                                  ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                <=> ( aElement0(W2)
                                    & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                    & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                          | ( aSet0(W1)
                            & ! [W2: $i] :
                                ( ~ aElementOf0(W2,W1)
                                | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                        & isCountable0(W1) ) )),
                    quant_intro(proof_bind(^ [W2: $i] :
                          trans(monotonicity(rewrite(( ( aSet0(W2)
                                  & ( ( ( ! [W3: $i] :
                                            ( aElementOf0(W3,W2)
                                           => aElementOf0(W3,W1) )
                                        | aSubsetOf0(W2,W1) )
                                      & ( sbrdtbr0(W2) = xk ) )
                                    | aElementOf0(W2,slbdtsldtrb0(W1,xk)) ) )
                              <=> ( aSet0(W2)
                                  & ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                                    | ( ( aSubsetOf0(W2,W1)
                                        | ! [W3: $i] :
                                            ( ~ aElementOf0(W3,W2)
                                            | aElementOf0(W3,W1) ) )
                                      & ( sbrdtbr0(W2) = xk ) ) ) ) )),
                              trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                                      & ! [W3: $i] :
                                                          ( aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                         => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) ) )
                                                  <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                                      & ! [W3: $i] :
                                                          ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) ) ) )),
                                                  ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                                    & ! [W3: $i] :
                                                        ( aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                                    & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                                <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                                    & ! [W3: $i] :
                                                        ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                                    & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
                                                rewrite(( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                                    & ! [W3: $i] :
                                                        ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                                    & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                                <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                                    & ! [W3: $i] :
                                                        ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                                    & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
                                                ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                                  & ! [W3: $i] :
                                                      ( aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                     => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                                  & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                              <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                                  & ! [W3: $i] :
                                                      ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                                  & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
                                              quant_intro(proof_bind(^ [W3: $i] :
                                                    rewrite(( ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                                      <=> ( aElement0(W3)
                                                          & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                          & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                                    <=> ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                                      <=> ( aElement0(W3)
                                                          & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                          & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ))),
                                                ( ! [W3: $i] :
                                                    ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                                  <=> ( aElement0(W3)
                                                      & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                      & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                              <=> ! [W3: $i] :
                                                    ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                                  <=> ( aElement0(W3)
                                                      & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                      & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )),
                                              ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                                & ! [W3: $i] :
                                                    ( aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                   => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                                & ! [W3: $i] :
                                                    ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                                  <=> ( aElement0(W3)
                                                      & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                      & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                                            <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                                & ! [W3: $i] :
                                                    ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                                & ! [W3: $i] :
                                                    ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                                  <=> ( aElement0(W3)
                                                      & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                      & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) )),
                                            rewrite(( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                                & ! [W3: $i] :
                                                    ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                                & ! [W3: $i] :
                                                    ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                                  <=> ( aElement0(W3)
                                                      & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                      & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                                            <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                                & ! [W3: $i] :
                                                    ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                                & ! [W3: $i] :
                                                    ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                                  <=> ( aElement0(W3)
                                                      & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                      & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) )),
                                            ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                              & ! [W3: $i] :
                                                  ( aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                 => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                              & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                              & ! [W3: $i] :
                                                  ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                                <=> ( aElement0(W3)
                                                    & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                    & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                                          <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                              & ! [W3: $i] :
                                                  ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                              & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                              & ! [W3: $i] :
                                                  ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                                <=> ( aElement0(W3)
                                                    & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                    & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) )),
                                          quant_intro(proof_bind(^ [W3: $i] :
                                                rewrite(( ( aElementOf0(W3,W2)
                                                   => aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                                <=> ( ~ aElementOf0(W3,W2)
                                                    | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ))),
                                            ( ! [W3: $i] :
                                                ( aElementOf0(W3,W2)
                                               => aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                          <=> ! [W3: $i] :
                                                ( ~ aElementOf0(W3,W2)
                                                | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
                                          ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                            & ! [W3: $i] :
                                                ( aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                               => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                            & ! [W3: $i] :
                                                ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                              <=> ( aElement0(W3)
                                                  & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                  & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                            & ! [W3: $i] :
                                                ( aElementOf0(W3,W2)
                                               => aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                                        <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                            & ! [W3: $i] :
                                                ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                            & ! [W3: $i] :
                                                ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                              <=> ( aElement0(W3)
                                                  & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                  & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                            & ! [W3: $i] :
                                                ( ~ aElementOf0(W3,W2)
                                                | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )),
                                        rewrite(( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                            & ! [W3: $i] :
                                                ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                            & ! [W3: $i] :
                                                ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                              <=> ( aElement0(W3)
                                                  & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                  & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                            & ! [W3: $i] :
                                                ( ~ aElementOf0(W3,W2)
                                                | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                                        <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                            & ! [W3: $i] :
                                                ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                            & ! [W3: $i] :
                                                ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                              <=> ( aElement0(W3)
                                                  & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                  & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                            & ! [W3: $i] :
                                                ( ~ aElementOf0(W3,W2)
                                                | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )),
                                        ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                          & ! [W3: $i] :
                                              ( aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                             => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                          & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                          & ! [W3: $i] :
                                              ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                            <=> ( aElement0(W3)
                                                & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                          & ! [W3: $i] :
                                              ( aElementOf0(W3,W2)
                                             => aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                                      <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                          & ! [W3: $i] :
                                              ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                          & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                          & ! [W3: $i] :
                                              ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                            <=> ( aElement0(W3)
                                                & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                                & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                          & ! [W3: $i] :
                                              ( ~ aElementOf0(W3,W2)
                                              | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )),
                                      ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                        & ! [W3: $i] :
                                            ( aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                           => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                        & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                        & ! [W3: $i] :
                                            ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                          <=> ( aElement0(W3)
                                              & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                              & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                        & ! [W3: $i] :
                                            ( aElementOf0(W3,W2)
                                           => aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                        & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                    <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                        & ! [W3: $i] :
                                            ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                        & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                        & ! [W3: $i] :
                                            ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                          <=> ( aElement0(W3)
                                              & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                              & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                        & ! [W3: $i] :
                                            ( ~ aElementOf0(W3,W2)
                                            | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                        & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
                                    rewrite(( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                        & ! [W3: $i] :
                                            ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                        & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                        & ! [W3: $i] :
                                            ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                          <=> ( aElement0(W3)
                                              & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                              & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                        & ! [W3: $i] :
                                            ( ~ aElementOf0(W3,W2)
                                            | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                        & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                    <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                        & ! [W3: $i] :
                                            ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                        & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                        & ! [W3: $i] :
                                            ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                          <=> ( aElement0(W3)
                                              & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                              & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                        & ! [W3: $i] :
                                            ( ~ aElementOf0(W3,W2)
                                            | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                        & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
                                    ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                      & ! [W3: $i] :
                                          ( aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                         => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                      & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                      & ! [W3: $i] :
                                          ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                        <=> ( aElement0(W3)
                                            & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                            & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                      & ! [W3: $i] :
                                          ( aElementOf0(W3,W2)
                                         => aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                      & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                  <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                      & ! [W3: $i] :
                                          ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                      & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                      & ! [W3: $i] :
                                          ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                        <=> ( aElement0(W3)
                                            & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                            & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                      & ! [W3: $i] :
                                          ( ~ aElementOf0(W3,W2)
                                          | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                      & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
                                  ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                    & ! [W3: $i] :
                                        ( aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                    & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    & ! [W3: $i] :
                                        ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                      <=> ( aElement0(W3)
                                          & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                          & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                    & ! [W3: $i] :
                                        ( aElementOf0(W3,W2)
                                       => aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                    & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
                                <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                    & ! [W3: $i] :
                                        ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                    & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    & ! [W3: $i] :
                                        ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                      <=> ( aElement0(W3)
                                          & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                          & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                    & ! [W3: $i] :
                                        ( ~ aElementOf0(W3,W2)
                                        | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                    & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) )),
                                rewrite(( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                    & ! [W3: $i] :
                                        ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                    & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    & ! [W3: $i] :
                                        ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                      <=> ( aElement0(W3)
                                          & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                          & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                    & ! [W3: $i] :
                                        ( ~ aElementOf0(W3,W2)
                                        | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                    & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
                                <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                    & ! [W3: $i] :
                                        ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                    & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    & ! [W3: $i] :
                                        ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                      <=> ( aElement0(W3)
                                          & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                          & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                    & ! [W3: $i] :
                                        ( ~ aElementOf0(W3,W2)
                                        | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                    & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) )),
                                ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                  & ! [W3: $i] :
                                      ( aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                     => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                  & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  & ! [W3: $i] :
                                      ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    <=> ( aElement0(W3)
                                        & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                        & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                  & ! [W3: $i] :
                                      ( aElementOf0(W3,W2)
                                     => aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                  & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
                              <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                  & ! [W3: $i] :
                                      ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                  & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  & ! [W3: $i] :
                                      ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    <=> ( aElement0(W3)
                                        & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                        & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                  & ! [W3: $i] :
                                      ( ~ aElementOf0(W3,W2)
                                      | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                  & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) )),
                              ( ( ( aSet0(W2)
                                  & ( ( ( ! [W3: $i] :
                                            ( aElementOf0(W3,W2)
                                           => aElementOf0(W3,W1) )
                                        | aSubsetOf0(W2,W1) )
                                      & ( sbrdtbr0(W2) = xk ) )
                                    | aElementOf0(W2,slbdtsldtrb0(W1,xk)) ) )
                               => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                  & ! [W3: $i] :
                                      ( aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                     => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                  & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  & ! [W3: $i] :
                                      ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    <=> ( aElement0(W3)
                                        & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                        & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                  & ! [W3: $i] :
                                      ( aElementOf0(W3,W2)
                                     => aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                  & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) )
                            <=> ( ( aSet0(W2)
                                  & ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                                    | ( ( aSubsetOf0(W2,W1)
                                        | ! [W3: $i] :
                                            ( ~ aElementOf0(W3,W2)
                                            | aElementOf0(W3,W1) ) )
                                      & ( sbrdtbr0(W2) = xk ) ) ) )
                               => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                  & ! [W3: $i] :
                                      ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                  & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  & ! [W3: $i] :
                                      ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    <=> ( aElement0(W3)
                                        & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                        & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                  & ! [W3: $i] :
                                      ( ~ aElementOf0(W3,W2)
                                      | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                  & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) )),
                            rewrite(( ( ( aSet0(W2)
                                  & ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                                    | ( ( aSubsetOf0(W2,W1)
                                        | ! [W3: $i] :
                                            ( ~ aElementOf0(W3,W2)
                                            | aElementOf0(W3,W1) ) )
                                      & ( sbrdtbr0(W2) = xk ) ) ) )
                               => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                  & ! [W3: $i] :
                                      ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                  & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  & ! [W3: $i] :
                                      ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    <=> ( aElement0(W3)
                                        & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                        & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                  & ! [W3: $i] :
                                      ( ~ aElementOf0(W3,W2)
                                      | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                  & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) )
                            <=> ( ~ ( aSet0(W2)
                                    & ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                                      | ( ( aSubsetOf0(W2,W1)
                                          | ! [W3: $i] :
                                              ( ~ aElementOf0(W3,W2)
                                              | aElementOf0(W3,W1) ) )
                                        & ( sbrdtbr0(W2) = xk ) ) ) )
                                | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                  & ! [W3: $i] :
                                      ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                  & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  & ! [W3: $i] :
                                      ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    <=> ( aElement0(W3)
                                        & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                        & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                  & ! [W3: $i] :
                                      ( ~ aElementOf0(W3,W2)
                                      | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                  & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) )),
                            ( ( ( aSet0(W2)
                                & ( ( ( ! [W3: $i] :
                                          ( aElementOf0(W3,W2)
                                         => aElementOf0(W3,W1) )
                                      | aSubsetOf0(W2,W1) )
                                    & ( sbrdtbr0(W2) = xk ) )
                                  | aElementOf0(W2,slbdtsldtrb0(W1,xk)) ) )
                             => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                & ! [W3: $i] :
                                    ( aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                   => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                & ! [W3: $i] :
                                    ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  <=> ( aElement0(W3)
                                      & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                      & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                & ! [W3: $i] :
                                    ( aElementOf0(W3,W2)
                                   => aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) )
                          <=> ( ~ ( aSet0(W2)
                                  & ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                                    | ( ( aSubsetOf0(W2,W1)
                                        | ! [W3: $i] :
                                            ( ~ aElementOf0(W3,W2)
                                            | aElementOf0(W3,W1) ) )
                                      & ( sbrdtbr0(W2) = xk ) ) ) )
                              | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                & ! [W3: $i] :
                                    ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                & ! [W3: $i] :
                                    ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  <=> ( aElement0(W3)
                                      & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                      & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                & ! [W3: $i] :
                                    ( ~ aElementOf0(W3,W2)
                                    | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ))),
                      ( ! [W2: $i] :
                          ( ( aSet0(W2)
                            & ( ( ( ! [W3: $i] :
                                      ( aElementOf0(W3,W2)
                                     => aElementOf0(W3,W1) )
                                  | aSubsetOf0(W2,W1) )
                                & ( sbrdtbr0(W2) = xk ) )
                              | aElementOf0(W2,slbdtsldtrb0(W1,xk)) ) )
                         => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                            & ! [W3: $i] :
                                ( aElementOf0(W3,sdtlpdtrp0(xN,W0))
                               => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & ! [W3: $i] :
                                ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              <=> ( aElement0(W3)
                                  & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                  & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                            & ! [W3: $i] :
                                ( aElementOf0(W3,W2)
                               => aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                            & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) )
                    <=> ! [W2: $i] :
                          ( ~ ( aSet0(W2)
                              & ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                                | ( ( aSubsetOf0(W2,W1)
                                    | ! [W3: $i] :
                                        ( ~ aElementOf0(W3,W2)
                                        | aElementOf0(W3,W1) ) )
                                  & ( sbrdtbr0(W2) = xk ) ) ) )
                          | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                            & ! [W3: $i] :
                                ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & ! [W3: $i] :
                                ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              <=> ( aElement0(W3)
                                  & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                  & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                            & ! [W3: $i] :
                                ( ~ aElementOf0(W3,W2)
                                | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                            & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) )),
                    ( ( ( ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                            & ! [W2: $i] :
                                ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                               => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                         => ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              & ! [W2: $i] :
                                  ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                <=> ( aElement0(W2)
                                    & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                    & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                           => ( ( aSet0(W1)
                                & ! [W2: $i] :
                                    ( aElementOf0(W2,W1)
                                   => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                              | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                        & isCountable0(W1) )
                     => ! [W2: $i] :
                          ( ( aSet0(W2)
                            & ( ( ( ! [W3: $i] :
                                      ( aElementOf0(W3,W2)
                                     => aElementOf0(W3,W1) )
                                  | aSubsetOf0(W2,W1) )
                                & ( sbrdtbr0(W2) = xk ) )
                              | aElementOf0(W2,slbdtsldtrb0(W1,xk)) ) )
                         => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                            & ! [W3: $i] :
                                ( aElementOf0(W3,sdtlpdtrp0(xN,W0))
                               => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & ! [W3: $i] :
                                ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              <=> ( aElement0(W3)
                                  & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                  & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                            & ! [W3: $i] :
                                ( aElementOf0(W3,W2)
                               => aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                            & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) )
                  <=> ( ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                              & ! [W2: $i] :
                                  ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                          | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              & ! [W2: $i] :
                                  ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                <=> ( aElement0(W2)
                                    & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                    & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                          | ( aSet0(W1)
                            & ! [W2: $i] :
                                ( ~ aElementOf0(W2,W1)
                                | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                        & isCountable0(W1) )
                     => ! [W2: $i] :
                          ( ~ ( aSet0(W2)
                              & ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                                | ( ( aSubsetOf0(W2,W1)
                                    | ! [W3: $i] :
                                        ( ~ aElementOf0(W3,W2)
                                        | aElementOf0(W3,W1) ) )
                                  & ( sbrdtbr0(W2) = xk ) ) ) )
                          | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                            & ! [W3: $i] :
                                ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & ! [W3: $i] :
                                ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              <=> ( aElement0(W3)
                                  & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                  & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                            & ! [W3: $i] :
                                ( ~ aElementOf0(W3,W2)
                                | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                            & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )),
                  rewrite(( ( ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                              & ! [W2: $i] :
                                  ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                          | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              & ! [W2: $i] :
                                  ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                <=> ( aElement0(W2)
                                    & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                    & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                          | ( aSet0(W1)
                            & ! [W2: $i] :
                                ( ~ aElementOf0(W2,W1)
                                | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                        & isCountable0(W1) )
                     => ! [W2: $i] :
                          ( ~ ( aSet0(W2)
                              & ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                                | ( ( aSubsetOf0(W2,W1)
                                    | ! [W3: $i] :
                                        ( ~ aElementOf0(W3,W2)
                                        | aElementOf0(W3,W1) ) )
                                  & ( sbrdtbr0(W2) = xk ) ) ) )
                          | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                            & ! [W3: $i] :
                                ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & ! [W3: $i] :
                                ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              <=> ( aElement0(W3)
                                  & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                  & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                            & ! [W3: $i] :
                                ( ~ aElementOf0(W3,W2)
                                | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                            & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) )
                  <=> ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                & ! [W2: $i] :
                                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                            | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                & ! [W2: $i] :
                                    ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  <=> ( aElement0(W2)
                                      & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                      & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                            | ( aSet0(W1)
                              & ! [W2: $i] :
                                  ( ~ aElementOf0(W2,W1)
                                  | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                          & isCountable0(W1) )
                      | ! [W2: $i] :
                          ( ~ ( aSet0(W2)
                              & ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                                | ( ( aSubsetOf0(W2,W1)
                                    | ! [W3: $i] :
                                        ( ~ aElementOf0(W3,W2)
                                        | aElementOf0(W3,W1) ) )
                                  & ( sbrdtbr0(W2) = xk ) ) ) )
                          | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                            & ! [W3: $i] :
                                ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & ! [W3: $i] :
                                ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              <=> ( aElement0(W3)
                                  & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                  & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                            & ! [W3: $i] :
                                ( ~ aElementOf0(W3,W2)
                                | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                            & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )),
                  ( ( ( ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                          & ! [W2: $i] :
                              ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                             => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                       => ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & ! [W2: $i] :
                                ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              <=> ( aElement0(W2)
                                  & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                  & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                         => ( ( aSet0(W1)
                              & ! [W2: $i] :
                                  ( aElementOf0(W2,W1)
                                 => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                            | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                      & isCountable0(W1) )
                   => ! [W2: $i] :
                        ( ( aSet0(W2)
                          & ( ( ( ! [W3: $i] :
                                    ( aElementOf0(W3,W2)
                                   => aElementOf0(W3,W1) )
                                | aSubsetOf0(W2,W1) )
                              & ( sbrdtbr0(W2) = xk ) )
                            | aElementOf0(W2,slbdtsldtrb0(W1,xk)) ) )
                       => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                          & ! [W3: $i] :
                              ( aElementOf0(W3,sdtlpdtrp0(xN,W0))
                             => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                          & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          & ! [W3: $i] :
                              ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            <=> ( aElement0(W3)
                                & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                          & ! [W3: $i] :
                              ( aElementOf0(W3,W2)
                             => aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                          & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) )
                <=> ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                              & ! [W2: $i] :
                                  ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                          | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              & ! [W2: $i] :
                                  ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                <=> ( aElement0(W2)
                                    & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                    & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                          | ( aSet0(W1)
                            & ! [W2: $i] :
                                ( ~ aElementOf0(W2,W1)
                                | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                        & isCountable0(W1) )
                    | ! [W2: $i] :
                        ( ~ ( aSet0(W2)
                            & ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                              | ( ( aSubsetOf0(W2,W1)
                                  | ! [W3: $i] :
                                      ( ~ aElementOf0(W3,W2)
                                      | aElementOf0(W3,W1) ) )
                                & ( sbrdtbr0(W2) = xk ) ) ) )
                        | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                          & ! [W3: $i] :
                              ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                          & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          & ! [W3: $i] :
                              ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            <=> ( aElement0(W3)
                                & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                          & ! [W3: $i] :
                              ( ~ aElementOf0(W3,W2)
                              | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                          & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) ))),
            ( ! [W1: $i] :
                ( ( ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      & ! [W2: $i] :
                          ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                         => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                   => ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        & ! [W2: $i] :
                            ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          <=> ( aElement0(W2)
                              & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                     => ( ( aSet0(W1)
                          & ! [W2: $i] :
                              ( aElementOf0(W2,W1)
                             => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                        | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                  & isCountable0(W1) )
               => ! [W2: $i] :
                    ( ( aSet0(W2)
                      & ( ( ( ! [W3: $i] :
                                ( aElementOf0(W3,W2)
                               => aElementOf0(W3,W1) )
                            | aSubsetOf0(W2,W1) )
                          & ( sbrdtbr0(W2) = xk ) )
                        | aElementOf0(W2,slbdtsldtrb0(W1,xk)) ) )
                   => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      & ! [W3: $i] :
                          ( aElementOf0(W3,sdtlpdtrp0(xN,W0))
                         => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                      & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & ! [W3: $i] :
                          ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        <=> ( aElement0(W3)
                            & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                            & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                      & ! [W3: $i] :
                          ( aElementOf0(W3,W2)
                         => aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) )
          <=> ! [W1: $i] :
                ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                          & ! [W2: $i] :
                              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                      | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          & ! [W2: $i] :
                              ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            <=> ( aElement0(W2)
                                & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                      | ( aSet0(W1)
                        & ! [W2: $i] :
                            ( ~ aElementOf0(W2,W1)
                            | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                    & isCountable0(W1) )
                | ! [W2: $i] :
                    ( ~ ( aSet0(W2)
                        & ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                          | ( ( aSubsetOf0(W2,W1)
                              | ! [W3: $i] :
                                  ( ~ aElementOf0(W3,W2)
                                  | aElementOf0(W3,W1) ) )
                            & ( sbrdtbr0(W2) = xk ) ) ) )
                    | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      & ! [W3: $i] :
                          ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                      & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & ! [W3: $i] :
                          ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        <=> ( aElement0(W3)
                            & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                            & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                      & ! [W3: $i] :
                          ( ~ aElementOf0(W3,W2)
                          | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )),
          ( ( aElementOf0(W0,szNzAzT0)
           => ! [W1: $i] :
                ( ( ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      & ! [W2: $i] :
                          ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                         => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                   => ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        & ! [W2: $i] :
                            ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          <=> ( aElement0(W2)
                              & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                     => ( ( aSet0(W1)
                          & ! [W2: $i] :
                              ( aElementOf0(W2,W1)
                             => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                        | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                  & isCountable0(W1) )
               => ! [W2: $i] :
                    ( ( aSet0(W2)
                      & ( ( ( ! [W3: $i] :
                                ( aElementOf0(W3,W2)
                               => aElementOf0(W3,W1) )
                            | aSubsetOf0(W2,W1) )
                          & ( sbrdtbr0(W2) = xk ) )
                        | aElementOf0(W2,slbdtsldtrb0(W1,xk)) ) )
                   => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      & ! [W3: $i] :
                          ( aElementOf0(W3,sdtlpdtrp0(xN,W0))
                         => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                      & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & ! [W3: $i] :
                          ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        <=> ( aElement0(W3)
                            & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                            & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                      & ! [W3: $i] :
                          ( aElementOf0(W3,W2)
                         => aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )
        <=> ( aElementOf0(W0,szNzAzT0)
           => ! [W1: $i] :
                ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                          & ! [W2: $i] :
                              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                      | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          & ! [W2: $i] :
                              ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            <=> ( aElement0(W2)
                                & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                      | ( aSet0(W1)
                        & ! [W2: $i] :
                            ( ~ aElementOf0(W2,W1)
                            | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                    & isCountable0(W1) )
                | ! [W2: $i] :
                    ( ~ ( aSet0(W2)
                        & ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                          | ( ( aSubsetOf0(W2,W1)
                              | ! [W3: $i] :
                                  ( ~ aElementOf0(W3,W2)
                                  | aElementOf0(W3,W1) ) )
                            & ( sbrdtbr0(W2) = xk ) ) ) )
                    | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      & ! [W3: $i] :
                          ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                      & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & ! [W3: $i] :
                          ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        <=> ( aElement0(W3)
                            & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                            & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                      & ! [W3: $i] :
                          ( ~ aElementOf0(W3,W2)
                          | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) ) )),
        rewrite(( ( aElementOf0(W0,szNzAzT0)
           => ! [W1: $i] :
                ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                          & ! [W2: $i] :
                              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                      | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          & ! [W2: $i] :
                              ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            <=> ( aElement0(W2)
                                & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                      | ( aSet0(W1)
                        & ! [W2: $i] :
                            ( ~ aElementOf0(W2,W1)
                            | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                    & isCountable0(W1) )
                | ! [W2: $i] :
                    ( ~ ( aSet0(W2)
                        & ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                          | ( ( aSubsetOf0(W2,W1)
                              | ! [W3: $i] :
                                  ( ~ aElementOf0(W3,W2)
                                  | aElementOf0(W3,W1) ) )
                            & ( sbrdtbr0(W2) = xk ) ) ) )
                    | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      & ! [W3: $i] :
                          ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                      & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & ! [W3: $i] :
                          ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        <=> ( aElement0(W3)
                            & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                            & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                      & ! [W3: $i] :
                          ( ~ aElementOf0(W3,W2)
                          | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )
        <=> ( ~ aElementOf0(W0,szNzAzT0)
            | ! [W1: $i] :
                ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                          & ! [W2: $i] :
                              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                      | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          & ! [W2: $i] :
                              ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            <=> ( aElement0(W2)
                                & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                      | ( aSet0(W1)
                        & ! [W2: $i] :
                            ( ~ aElementOf0(W2,W1)
                            | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                    & isCountable0(W1) )
                | ! [W2: $i] :
                    ( ~ ( aSet0(W2)
                        & ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                          | ( ( aSubsetOf0(W2,W1)
                              | ! [W3: $i] :
                                  ( ~ aElementOf0(W3,W2)
                                  | aElementOf0(W3,W1) ) )
                            & ( sbrdtbr0(W2) = xk ) ) ) )
                    | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      & ! [W3: $i] :
                          ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                      & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & ! [W3: $i] :
                          ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        <=> ( aElement0(W3)
                            & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                            & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                      & ! [W3: $i] :
                          ( ~ aElementOf0(W3,W2)
                          | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) ) )),
        ( ( aElementOf0(W0,szNzAzT0)
         => ! [W1: $i] :
              ( ( ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    & ! [W2: $i] :
                        ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                 => ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & ! [W2: $i] :
                          ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        <=> ( aElement0(W2)
                            & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                   => ( ( aSet0(W1)
                        & ! [W2: $i] :
                            ( aElementOf0(W2,W1)
                           => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                      | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                & isCountable0(W1) )
             => ! [W2: $i] :
                  ( ( aSet0(W2)
                    & ( ( ( ! [W3: $i] :
                              ( aElementOf0(W3,W2)
                             => aElementOf0(W3,W1) )
                          | aSubsetOf0(W2,W1) )
                        & ( sbrdtbr0(W2) = xk ) )
                      | aElementOf0(W2,slbdtsldtrb0(W1,xk)) ) )
                 => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    & ! [W3: $i] :
                        ( aElementOf0(W3,sdtlpdtrp0(xN,W0))
                       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                    & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & ! [W3: $i] :
                        ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      <=> ( aElement0(W3)
                          & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                          & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                    & ! [W3: $i] :
                        ( aElementOf0(W3,W2)
                       => aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ! [W1: $i] :
              ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        & ! [W2: $i] :
                            ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                    | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        & ! [W2: $i] :
                            ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          <=> ( aElement0(W2)
                              & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                    | ( aSet0(W1)
                      & ! [W2: $i] :
                          ( ~ aElementOf0(W2,W1)
                          | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                  & isCountable0(W1) )
              | ! [W2: $i] :
                  ( ~ ( aSet0(W2)
                      & ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                        | ( ( aSubsetOf0(W2,W1)
                            | ! [W3: $i] :
                                ( ~ aElementOf0(W3,W2)
                                | aElementOf0(W3,W1) ) )
                          & ( sbrdtbr0(W2) = xk ) ) ) )
                  | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    & ! [W3: $i] :
                        ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                    & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & ! [W3: $i] :
                        ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      <=> ( aElement0(W3)
                          & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                          & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                    & ! [W3: $i] :
                        ( ~ aElementOf0(W3,W2)
                        | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(140,plain,
    ( ! [W0: $i] :
        ( aElementOf0(W0,szNzAzT0)
       => ! [W1: $i] :
            ( ( ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  & ! [W2: $i] :
                      ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                     => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
               => ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & ! [W2: $i] :
                        ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      <=> ( aElement0(W2)
                          & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                 => ( ( aSet0(W1)
                      & ! [W2: $i] :
                          ( aElementOf0(W2,W1)
                         => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                    | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
              & isCountable0(W1) )
           => ! [W2: $i] :
                ( ( aSet0(W2)
                  & ( ( ( ! [W3: $i] :
                            ( aElementOf0(W3,W2)
                           => aElementOf0(W3,W1) )
                        | aSubsetOf0(W2,W1) )
                      & ( sbrdtbr0(W2) = xk ) )
                    | aElementOf0(W2,slbdtsldtrb0(W1,xk)) ) )
               => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  & ! [W3: $i] :
                      ( aElementOf0(W3,sdtlpdtrp0(xN,W0))
                     => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                  & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ! [W3: $i] :
                      ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    <=> ( aElement0(W3)
                        & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                        & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                  & ! [W3: $i] :
                      ( aElementOf0(W3,W2)
                     => aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ! [W1: $i] :
            ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      & ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                  | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & ! [W2: $i] :
                          ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        <=> ( aElement0(W2)
                            & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                  | ( aSet0(W1)
                    & ! [W2: $i] :
                        ( ~ aElementOf0(W2,W1)
                        | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                & isCountable0(W1) )
            | ! [W2: $i] :
                ( ~ ( aSet0(W2)
                    & ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                      | ( ( aSubsetOf0(W2,W1)
                          | ! [W3: $i] :
                              ( ~ aElementOf0(W3,W2)
                              | aElementOf0(W3,W1) ) )
                        & ( sbrdtbr0(W2) = xk ) ) ) )
                | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  & ! [W3: $i] :
                      ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                  & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ! [W3: $i] :
                      ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    <=> ( aElement0(W3)
                        & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                        & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                  & ! [W3: $i] :
                      ( ~ aElementOf0(W3,W2)
                      | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) ) ),
    inference(quant_intro,[status(thm)],[139]) ).

tff(141,axiom,
    ! [W0: $i] :
      ( aElementOf0(W0,szNzAzT0)
     => ! [W1: $i] :
          ( ( ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W2: $i] :
                    ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                   => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
             => ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ! [W2: $i] :
                      ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    <=> ( aElement0(W2)
                        & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                        & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
               => ( ( aSet0(W1)
                    & ! [W2: $i] :
                        ( aElementOf0(W2,W1)
                       => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                  | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
            & isCountable0(W1) )
         => ! [W2: $i] :
              ( ( aSet0(W2)
                & ( ( ( ! [W3: $i] :
                          ( aElementOf0(W3,W2)
                         => aElementOf0(W3,W1) )
                      | aSubsetOf0(W2,W1) )
                    & ( sbrdtbr0(W2) = xk ) )
                  | aElementOf0(W2,slbdtsldtrb0(W1,xk)) ) )
             => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W3: $i] :
                    ( aElementOf0(W3,sdtlpdtrp0(xN,W0))
                   => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & ! [W3: $i] :
                    ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W3)
                      & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                      & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                & ! [W3: $i] :
                    ( aElementOf0(W3,W2)
                   => aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4331) ).

tff(142,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ! [W1: $i] :
          ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    & ! [W2: $i] :
                        ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & ! [W2: $i] :
                        ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      <=> ( aElement0(W2)
                          & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                | ( aSet0(W1)
                  & ! [W2: $i] :
                      ( ~ aElementOf0(W2,W1)
                      | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
              & isCountable0(W1) )
          | ! [W2: $i] :
              ( ~ ( aSet0(W2)
                  & ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                    | ( ( aSubsetOf0(W2,W1)
                        | ! [W3: $i] :
                            ( ~ aElementOf0(W3,W2)
                            | aElementOf0(W3,W1) ) )
                      & ( sbrdtbr0(W2) = xk ) ) ) )
              | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W3: $i] :
                    ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & ! [W3: $i] :
                    ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W3)
                      & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                      & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                & ! [W3: $i] :
                    ( ~ aElementOf0(W3,W2)
                    | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) ),
    inference(modus_ponens,[status(thm)],[141,140]) ).

tff(143,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ! [W1: $i] :
          ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    & ! [W2: $i] :
                        ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & ! [W2: $i] :
                        ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      <=> ( aElement0(W2)
                          & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                | ( aSet0(W1)
                  & ! [W2: $i] :
                      ( ~ aElementOf0(W2,W1)
                      | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
              & isCountable0(W1) )
          | ! [W2: $i] :
              ( ~ ( aSet0(W2)
                  & ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                    | ( ( aSubsetOf0(W2,W1)
                        | ! [W3: $i] :
                            ( ~ aElementOf0(W3,W2)
                            | aElementOf0(W3,W1) ) )
                      & ( sbrdtbr0(W2) = xk ) ) ) )
              | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W3: $i] :
                    ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & ! [W3: $i] :
                    ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W3)
                      & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                      & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                & ! [W3: $i] :
                    ( ~ aElementOf0(W3,W2)
                    | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) ),
    inference(modus_ponens,[status(thm)],[142,138]) ).

tff(144,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ! [W1: $i] :
          ( ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            & ! [W2: $i] :
                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            & ! [W2: $i] :
                ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              <=> ( aElement0(W2)
                  & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                  & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
            & ( ~ aSet0(W1)
              | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                  | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
          | ~ isCountable0(W1)
          | ! [W2: $i] :
              ( ~ aSet0(W2)
              | ( ~ aElementOf0(W2,slbdtsldtrb0(W1,xk))
                & ( ( ~ aSubsetOf0(W2,W1)
                    & ~ ( ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                        | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) )
                  | ( sbrdtbr0(W2) != xk ) ) )
              | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W3: $i] :
                    ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & ! [W3: $i] :
                    ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W3)
                      & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                      & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                & ! [W3: $i] :
                    ( ~ aElementOf0(W3,W2)
                    | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) ),
    inference(skolemize,[status(sab)],[143]) ).

tff(145,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ! [W1: $i] :
          ( ~ isCountable0(W1)
          | ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            & ! [W2: $i] :
                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            & ! [W2: $i] :
                ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              <=> ( aElement0(W2)
                  & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                  & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
            & ( ~ aSet0(W1)
              | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                  | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
          | ! [W2: $i] :
              ( ~ aSet0(W2)
              | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W3: $i] :
                    ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & ! [W3: $i] :
                    ( aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W3)
                      & aElementOf0(W3,sdtlpdtrp0(xN,W0))
                      & ( W3 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                & ! [W3: $i] :
                    ( ~ aElementOf0(W3,W2)
                    | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                & aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
              | ( ~ aElementOf0(W2,slbdtsldtrb0(W1,xk))
                & ( ( sbrdtbr0(W2) != xk )
                  | ( ~ aSubsetOf0(W2,W1)
                    & ~ ( ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                        | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) ) ),
    inference(modus_ponens,[status(thm)],[144,137]) ).

tff(146,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ! [W1: $i] :
          ( ~ isCountable0(W1)
          | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              | ~ ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
              | ~ ( ~ aSet0(W1)
                  | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                      | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ ! [W2: $i] :
                    ~ ( ( ~ aElement0(W2)
                        | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                    <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
          | ! [W2: $i] :
              ( ~ aSet0(W2)
              | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  | ~ ! [W3: $i] :
                        ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                  | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  | ~ ! [W3: $i] :
                        ~ ( ( ~ aElement0(W3)
                            | ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                            | ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                        <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  | ~ ! [W3: $i] :
                        ( ~ aElementOf0(W3,W2)
                        | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
              | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                  | ~ ( ( sbrdtbr0(W2) != xk )
                      | ~ ( aSubsetOf0(W2,W1)
                          | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                          | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) ),
    inference(modus_ponens,[status(thm)],[145,135]) ).

tff(147,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ! [W1: $i] :
          ( ~ isCountable0(W1)
          | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              | ~ ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
              | ~ ( ~ aSet0(W1)
                  | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                      | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ ! [W2: $i] :
                    ~ ( ( ~ aElement0(W2)
                        | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                    <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
          | ! [W2: $i] :
              ( ~ aSet0(W2)
              | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  | ~ ! [W3: $i] :
                        ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                  | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  | ~ ! [W3: $i] :
                        ~ ( ( ~ aElement0(W3)
                            | ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                            | ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                        <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  | ~ ! [W3: $i] :
                        ( ~ aElementOf0(W3,W2)
                        | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) )
              | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                  | ~ ( ( sbrdtbr0(W2) != xk )
                      | ~ ( aSubsetOf0(W2,W1)
                          | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                          | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) ) ) ) ),
    inference(modus_ponens,[status(thm)],[146,133]) ).

tff(148,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ! [W1: $i] :
          ( ~ isCountable0(W1)
          | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              | ~ ( ~ aSet0(W1)
                  | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                      | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
              | ~ ! [W2: $i] :
                    ~ ( ( ~ aElement0(W2)
                        | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                    <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
          | ! [W2: $i] :
              ( ~ aSet0(W2)
              | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                  | ~ ( ( sbrdtbr0(W2) != xk )
                      | ~ ( aSubsetOf0(W2,W1)
                          | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                          | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
              | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                  | ~ ! [W3: $i] :
                        ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                  | ~ ! [W3: $i] :
                        ~ ( ( ~ aElement0(W3)
                            | ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                            | ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                        <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  | ~ ! [W3: $i] :
                        ( ~ aElementOf0(W3,W2)
                        | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ),
    inference(modus_ponens,[status(thm)],[147,128]) ).

tff(149,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ! [W1: $i] :
                ( ~ isCountable0(W1)
                | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    | ~ ( ~ aSet0(W1)
                        | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                            | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                    | ~ ! [W2: $i] :
                          ~ ( ( ~ aElement0(W2)
                              | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                          <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                | ! [W2: $i] :
                    ( ~ aSet0(W2)
                    | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                        | ~ ( ( sbrdtbr0(W2) != xk )
                            | ~ ( aSubsetOf0(W2,W1)
                                | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                                | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
                    | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                        | ~ ! [W3: $i] :
                              ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                        | ~ ! [W3: $i] :
                              ~ ( ( ~ aElement0(W3)
                                  | ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                  | ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                              <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                        | ~ ! [W3: $i] :
                              ( ~ aElementOf0(W3,W2)
                              | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ! [W1: $i] :
          ( ~ isCountable0(W1)
          | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
              | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ ! [W2: $i] :
                    ~ ( ( ~ aElement0(W2)
                        | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                    <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
              | ~ ( ~ aSet0(W1)
                  | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                      | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
          | ! [W2: $i] :
              ( ~ aSet0(W2)
              | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                  | ~ ( ( sbrdtbr0(W2) != xk )
                      | ~ ( aSubsetOf0(W2,W1)
                          | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                          | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
              | ~ ( ~ ! [W3: $i] :
                        ~ ( ( ~ aElement0(W3)
                            | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                            | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                        <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                  | ~ ! [W3: $i] :
                        ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
                  | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                  | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                  | ~ ! [W3: $i] :
                        ( ~ aElementOf0(W3,W2)
                        | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                  | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                  | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) )
  <=> ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ! [W1: $i] :
                ( ~ isCountable0(W1)
                | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    | ~ ( ~ aSet0(W1)
                        | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                            | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                    | ~ ! [W2: $i] :
                          ~ ( ( ~ aElement0(W2)
                              | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                          <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                | ! [W2: $i] :
                    ( ~ aSet0(W2)
                    | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                        | ~ ( ( sbrdtbr0(W2) != xk )
                            | ~ ( aSubsetOf0(W2,W1)
                                | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                                | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
                    | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                        | ~ ! [W3: $i] :
                              ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                        | ~ ! [W3: $i] :
                              ~ ( ( ~ aElement0(W3)
                                  | ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                  | ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                              <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                        | ~ ! [W3: $i] :
                              ( ~ aElementOf0(W3,W2)
                              | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ! [W1: $i] :
          ( ~ isCountable0(W1)
          | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
              | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ ! [W2: $i] :
                    ~ ( ( ~ aElement0(W2)
                        | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                    <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
              | ~ ( ~ aSet0(W1)
                  | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                      | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
          | ! [W2: $i] :
              ( ~ aSet0(W2)
              | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                  | ~ ( ( sbrdtbr0(W2) != xk )
                      | ~ ( aSubsetOf0(W2,W1)
                          | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                          | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
              | ~ ( ~ ! [W3: $i] :
                        ~ ( ( ~ aElement0(W3)
                            | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                            | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                        <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                  | ~ ! [W3: $i] :
                        ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
                  | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                  | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                  | ~ ! [W3: $i] :
                        ( ~ aElementOf0(W3,W2)
                        | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                  | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                  | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(150,plain,
    ( ( ~ aElementOf0(xn,szNzAzT0)
      | ! [W1: $i] :
          ( ~ isCountable0(W1)
          | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
              | ~ ( ~ aSet0(W1)
                  | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                      | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
              | ~ ! [W2: $i] :
                    ~ ( ( ~ aElement0(W2)
                        | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                    <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
          | ! [W2: $i] :
              ( ~ aSet0(W2)
              | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                  | ~ ( ( sbrdtbr0(W2) != xk )
                      | ~ ( aSubsetOf0(W2,W1)
                          | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                          | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
              | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                  | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                  | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                  | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                  | ~ ! [W3: $i] :
                        ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
                  | ~ ! [W3: $i] :
                        ~ ( ( ~ aElement0(W3)
                            | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                            | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                        <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                  | ~ ! [W3: $i] :
                        ( ~ aElementOf0(W3,W2)
                        | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
  <=> ( ~ aElementOf0(xn,szNzAzT0)
      | ! [W1: $i] :
          ( ~ isCountable0(W1)
          | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
              | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ ! [W2: $i] :
                    ~ ( ( ~ aElement0(W2)
                        | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                    <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
              | ~ ( ~ aSet0(W1)
                  | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                      | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
          | ! [W2: $i] :
              ( ~ aSet0(W2)
              | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                  | ~ ( ( sbrdtbr0(W2) != xk )
                      | ~ ( aSubsetOf0(W2,W1)
                          | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                          | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
              | ~ ( ~ ! [W3: $i] :
                        ~ ( ( ~ aElement0(W3)
                            | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                            | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                        <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                  | ~ ! [W3: $i] :
                        ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
                  | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                  | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                  | ~ ! [W3: $i] :
                        ( ~ aElementOf0(W3,W2)
                        | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                  | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                  | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(151,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ! [W1: $i] :
                ( ~ isCountable0(W1)
                | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    | ~ ( ~ aSet0(W1)
                        | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                            | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                    | ~ ! [W2: $i] :
                          ~ ( ( ~ aElement0(W2)
                              | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                          <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                | ! [W2: $i] :
                    ( ~ aSet0(W2)
                    | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                        | ~ ( ( sbrdtbr0(W2) != xk )
                            | ~ ( aSubsetOf0(W2,W1)
                                | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                                | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
                    | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                        | ~ ! [W3: $i] :
                              ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                        | ~ ! [W3: $i] :
                              ~ ( ( ~ aElement0(W3)
                                  | ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                  | ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                              <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                        | ~ ! [W3: $i] :
                              ( ~ aElementOf0(W3,W2)
                              | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ! [W1: $i] :
          ( ~ isCountable0(W1)
          | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
              | ~ ( ~ aSet0(W1)
                  | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                      | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
              | ~ ! [W2: $i] :
                    ~ ( ( ~ aElement0(W2)
                        | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                    <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
          | ! [W2: $i] :
              ( ~ aSet0(W2)
              | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                  | ~ ( ( sbrdtbr0(W2) != xk )
                      | ~ ( aSubsetOf0(W2,W1)
                          | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                          | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
              | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                  | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                  | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                  | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                  | ~ ! [W3: $i] :
                        ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
                  | ~ ! [W3: $i] :
                        ~ ( ( ~ aElement0(W3)
                            | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                            | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                        <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                  | ~ ! [W3: $i] :
                        ( ~ aElementOf0(W3,W2)
                        | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
  <=> ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ! [W1: $i] :
                ( ~ isCountable0(W1)
                | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    | ~ ( ~ aSet0(W1)
                        | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                            | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                    | ~ ! [W2: $i] :
                          ~ ( ( ~ aElement0(W2)
                              | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                          <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                | ! [W2: $i] :
                    ( ~ aSet0(W2)
                    | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                        | ~ ( ( sbrdtbr0(W2) != xk )
                            | ~ ( aSubsetOf0(W2,W1)
                                | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                                | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
                    | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                        | ~ ! [W3: $i] :
                              ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                        | ~ ! [W3: $i] :
                              ~ ( ( ~ aElement0(W3)
                                  | ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                  | ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                              <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                        | ~ ! [W3: $i] :
                              ( ~ aElementOf0(W3,W2)
                              | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ! [W1: $i] :
          ( ~ isCountable0(W1)
          | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
              | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ ! [W2: $i] :
                    ~ ( ( ~ aElement0(W2)
                        | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                    <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
              | ~ ( ~ aSet0(W1)
                  | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                      | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
          | ! [W2: $i] :
              ( ~ aSet0(W2)
              | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                  | ~ ( ( sbrdtbr0(W2) != xk )
                      | ~ ( aSubsetOf0(W2,W1)
                          | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                          | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
              | ~ ( ~ ! [W3: $i] :
                        ~ ( ( ~ aElement0(W3)
                            | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                            | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                        <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                  | ~ ! [W3: $i] :
                        ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
                  | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                  | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                  | ~ ! [W3: $i] :
                        ( ~ aElementOf0(W3,W2)
                        | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                  | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                  | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) ),
    inference(monotonicity,[status(thm)],[150]) ).

tff(152,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ! [W1: $i] :
                ( ~ isCountable0(W1)
                | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    | ~ ( ~ aSet0(W1)
                        | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                            | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                    | ~ ! [W2: $i] :
                          ~ ( ( ~ aElement0(W2)
                              | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                          <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                | ! [W2: $i] :
                    ( ~ aSet0(W2)
                    | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                        | ~ ( ( sbrdtbr0(W2) != xk )
                            | ~ ( aSubsetOf0(W2,W1)
                                | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                                | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
                    | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                        | ~ ! [W3: $i] :
                              ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                        | ~ ! [W3: $i] :
                              ~ ( ( ~ aElement0(W3)
                                  | ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                  | ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                              <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                        | ~ ! [W3: $i] :
                              ( ~ aElementOf0(W3,W2)
                              | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ! [W1: $i] :
          ( ~ isCountable0(W1)
          | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
              | ~ ( ~ aSet0(W1)
                  | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                      | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
              | ~ ! [W2: $i] :
                    ~ ( ( ~ aElement0(W2)
                        | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                    <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
          | ! [W2: $i] :
              ( ~ aSet0(W2)
              | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                  | ~ ( ( sbrdtbr0(W2) != xk )
                      | ~ ( aSubsetOf0(W2,W1)
                          | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                          | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
              | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                  | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                  | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                  | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                  | ~ ! [W3: $i] :
                        ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
                  | ~ ! [W3: $i] :
                        ~ ( ( ~ aElement0(W3)
                            | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                            | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                        <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                  | ~ ! [W3: $i] :
                        ( ~ aElementOf0(W3,W2)
                        | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
  <=> ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ! [W1: $i] :
                ( ~ isCountable0(W1)
                | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    | ~ ( ~ aSet0(W1)
                        | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                            | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                    | ~ ! [W2: $i] :
                          ~ ( ( ~ aElement0(W2)
                              | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                          <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                | ! [W2: $i] :
                    ( ~ aSet0(W2)
                    | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                        | ~ ( ( sbrdtbr0(W2) != xk )
                            | ~ ( aSubsetOf0(W2,W1)
                                | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                                | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
                    | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                        | ~ ! [W3: $i] :
                              ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                        | ~ ! [W3: $i] :
                              ~ ( ( ~ aElement0(W3)
                                  | ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                  | ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                              <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                        | ~ ! [W3: $i] :
                              ( ~ aElementOf0(W3,W2)
                              | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ! [W1: $i] :
          ( ~ isCountable0(W1)
          | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
              | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ ! [W2: $i] :
                    ~ ( ( ~ aElement0(W2)
                        | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                    <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
              | ~ ( ~ aSet0(W1)
                  | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                      | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
          | ! [W2: $i] :
              ( ~ aSet0(W2)
              | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                  | ~ ( ( sbrdtbr0(W2) != xk )
                      | ~ ( aSubsetOf0(W2,W1)
                          | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                          | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
              | ~ ( ~ ! [W3: $i] :
                        ~ ( ( ~ aElement0(W3)
                            | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                            | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                        <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                  | ~ ! [W3: $i] :
                        ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
                  | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                  | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                  | ~ ! [W3: $i] :
                        ( ~ aElementOf0(W3,W2)
                        | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                  | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                  | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) ),
    inference(transitivity,[status(thm)],[151,149]) ).

tff(153,plain,
    ( ~ ! [W0: $i] :
          ( ~ aElementOf0(W0,szNzAzT0)
          | ! [W1: $i] :
              ( ~ isCountable0(W1)
              | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  | ~ ( ~ aSet0(W1)
                      | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                          | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                  | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  | ~ ! [W2: $i] :
                        ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                  | ~ ! [W2: $i] :
                        ~ ( ( ~ aElement0(W2)
                            | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                        <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
              | ! [W2: $i] :
                  ( ~ aSet0(W2)
                  | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                      | ~ ( ( sbrdtbr0(W2) != xk )
                          | ~ ( aSubsetOf0(W2,W1)
                              | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                              | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
                  | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                      | ~ ! [W3: $i] :
                            ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                      | ~ ! [W3: $i] :
                            ~ ( ( ~ aElement0(W3)
                                | ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                | ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                            <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      | ~ ! [W3: $i] :
                            ( ~ aElementOf0(W3,W2)
                            | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
    | ~ aElementOf0(xn,szNzAzT0)
    | ! [W1: $i] :
        ( ~ isCountable0(W1)
        | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
            | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
            | ~ ( ~ aSet0(W1)
                | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                    | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
            | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
            | ~ ! [W2: $i] :
                  ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
            | ~ ! [W2: $i] :
                  ~ ( ( ~ aElement0(W2)
                      | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                      | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                  <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
        | ! [W2: $i] :
            ( ~ aSet0(W2)
            | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                | ~ ( ( sbrdtbr0(W2) != xk )
                    | ~ ( aSubsetOf0(W2,W1)
                        | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                        | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
            | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                | ~ ! [W3: $i] :
                      ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
                | ~ ! [W3: $i] :
                      ~ ( ( ~ aElement0(W3)
                          | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                          | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                      <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ ! [W3: $i] :
                      ( ~ aElementOf0(W3,W2)
                      | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(154,plain,
    ( ~ ! [W0: $i] :
          ( ~ aElementOf0(W0,szNzAzT0)
          | ! [W1: $i] :
              ( ~ isCountable0(W1)
              | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  | ~ ( ~ aSet0(W1)
                      | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                          | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                  | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  | ~ ! [W2: $i] :
                        ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                  | ~ ! [W2: $i] :
                        ~ ( ( ~ aElement0(W2)
                            | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                        <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
              | ! [W2: $i] :
                  ( ~ aSet0(W2)
                  | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                      | ~ ( ( sbrdtbr0(W2) != xk )
                          | ~ ( aSubsetOf0(W2,W1)
                              | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                              | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
                  | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                      | ~ ! [W3: $i] :
                            ( ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W3) )
                      | ~ ! [W3: $i] :
                            ~ ( ( ~ aElement0(W3)
                                | ~ aElementOf0(W3,sdtlpdtrp0(xN,W0))
                                | ( W3 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                            <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      | ~ ! [W3: $i] :
                            ( ~ aElementOf0(W3,W2)
                            | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
    | ~ aElementOf0(xn,szNzAzT0)
    | ! [W1: $i] :
        ( ~ isCountable0(W1)
        | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
            | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
            | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
            | ~ ! [W2: $i] :
                  ~ ( ( ~ aElement0(W2)
                      | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                      | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                  <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
            | ~ ! [W2: $i] :
                  ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
            | ~ ( ~ aSet0(W1)
                | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                    | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
        | ! [W2: $i] :
            ( ~ aSet0(W2)
            | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                | ~ ( ( sbrdtbr0(W2) != xk )
                    | ~ ( aSubsetOf0(W2,W1)
                        | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                        | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
            | ~ ( ~ ! [W3: $i] :
                      ~ ( ( ~ aElement0(W3)
                          | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                          | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                      <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ ! [W3: $i] :
                      ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                | ~ ! [W3: $i] :
                      ( ~ aElementOf0(W3,W2)
                      | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ),
    inference(modus_ponens,[status(thm)],[153,152]) ).

tff(155,plain,
    ! [W1: $i] :
      ( ~ isCountable0(W1)
      | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ ! [W2: $i] :
                ~ ( ( ~ aElement0(W2)
                    | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W2: $i] :
                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
          | ~ ( ~ aSet0(W1)
              | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                  | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
      | ! [W2: $i] :
          ( ~ aSet0(W2)
          | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
              | ~ ( ( sbrdtbr0(W2) != xk )
                  | ~ ( aSubsetOf0(W2,W1)
                      | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                      | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
          | ~ ( ~ ! [W3: $i] :
                    ~ ( ( ~ aElement0(W3)
                        | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                        | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                    <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ ! [W3: $i] :
                    ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
              | ~ ! [W3: $i] :
                    ( ~ aElementOf0(W3,W2)
                    | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
              | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ),
    inference(unit_resolution,[status(thm)],[154,148,28]) ).

tff(156,plain,
    ( ( ~ ! [W1: $i] :
            ( ~ isCountable0(W1)
            | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | ~ ! [W2: $i] :
                      ~ ( ( ~ aElement0(W2)
                          | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                      <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                | ~ ( ~ aSet0(W1)
                    | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                        | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
            | ! [W2: $i] :
                ( ~ aSet0(W2)
                | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                    | ~ ( ( sbrdtbr0(W2) != xk )
                        | ~ ( aSubsetOf0(W2,W1)
                            | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                            | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
                | ~ ( ~ ! [W3: $i] :
                          ~ ( ( ~ aElement0(W3)
                              | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                              | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                          <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                    | ~ ! [W3: $i] :
                          ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
                    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                    | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                    | ~ ! [W3: $i] :
                          ( ~ aElementOf0(W3,W2)
                          | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                    | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                    | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
      | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
      | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ ! [W2: $i] :
                ~ ( ( ~ aElement0(W2)
                    | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W2: $i] :
                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
          | aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
              | ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                  | aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
      | ! [W2: $i] :
          ( ~ aSet0(W2)
          | ~ ( ~ ! [W3: $i] :
                    ~ ( ( ~ aElement0(W3)
                        | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                        | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                    <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ ! [W3: $i] :
                    ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
              | ~ ! [W3: $i] :
                    ( ~ aElementOf0(W3,W2)
                    | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
              | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
              | ~ ( ( sbrdtbr0(W2) != xk )
                  | ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                      | aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                      | ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2) ) ) ) ) )
  <=> ( ~ ! [W1: $i] :
            ( ~ isCountable0(W1)
            | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | ~ ! [W2: $i] :
                      ~ ( ( ~ aElement0(W2)
                          | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                      <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                | ~ ( ~ aSet0(W1)
                    | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                        | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
            | ! [W2: $i] :
                ( ~ aSet0(W2)
                | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                    | ~ ( ( sbrdtbr0(W2) != xk )
                        | ~ ( aSubsetOf0(W2,W1)
                            | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                            | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
                | ~ ( ~ ! [W3: $i] :
                          ~ ( ( ~ aElement0(W3)
                              | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                              | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                          <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                    | ~ ! [W3: $i] :
                          ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
                    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                    | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                    | ~ ! [W3: $i] :
                          ( ~ aElementOf0(W3,W2)
                          | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                    | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                    | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
      | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
      | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ ! [W2: $i] :
                ~ ( ( ~ aElement0(W2)
                    | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W2: $i] :
                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
          | aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
              | ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                  | aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
      | ! [W2: $i] :
          ( ~ aSet0(W2)
          | ~ ( ~ ! [W3: $i] :
                    ~ ( ( ~ aElement0(W3)
                        | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                        | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                    <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ ! [W3: $i] :
                    ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
              | ~ ! [W3: $i] :
                    ( ~ aElementOf0(W3,W2)
                    | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
              | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
              | ~ ( ( sbrdtbr0(W2) != xk )
                  | ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                      | aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                      | ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2) ) ) ) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(157,plain,
    ( ( ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
      | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ ! [W2: $i] :
                ~ ( ( ~ aElement0(W2)
                    | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W2: $i] :
                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
          | ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
              | ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                  | aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
      | ! [W2: $i] :
          ( ~ aSet0(W2)
          | ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
              | ~ ( ( sbrdtbr0(W2) != xk )
                  | ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                      | ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2)
                      | aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) )
          | ~ ( ~ ! [W3: $i] :
                    ~ ( ( ~ aElement0(W3)
                        | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                        | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                    <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ ! [W3: $i] :
                    ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
              | ~ ! [W3: $i] :
                    ( ~ aElementOf0(W3,W2)
                    | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
              | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
  <=> ( ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
      | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ ! [W2: $i] :
                ~ ( ( ~ aElement0(W2)
                    | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W2: $i] :
                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
          | aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
              | ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                  | aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
      | ! [W2: $i] :
          ( ~ aSet0(W2)
          | ~ ( ~ ! [W3: $i] :
                    ~ ( ( ~ aElement0(W3)
                        | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                        | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                    <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ ! [W3: $i] :
                    ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
              | ~ ! [W3: $i] :
                    ( ~ aElementOf0(W3,W2)
                    | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
              | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
              | ~ ( ( sbrdtbr0(W2) != xk )
                  | ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                      | aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                      | ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2) ) ) ) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(158,plain,
    ( ( ~ ! [W1: $i] :
            ( ~ isCountable0(W1)
            | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | ~ ! [W2: $i] :
                      ~ ( ( ~ aElement0(W2)
                          | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                      <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                | ~ ( ~ aSet0(W1)
                    | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                        | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
            | ! [W2: $i] :
                ( ~ aSet0(W2)
                | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                    | ~ ( ( sbrdtbr0(W2) != xk )
                        | ~ ( aSubsetOf0(W2,W1)
                            | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                            | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
                | ~ ( ~ ! [W3: $i] :
                          ~ ( ( ~ aElement0(W3)
                              | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                              | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                          <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                    | ~ ! [W3: $i] :
                          ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
                    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                    | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                    | ~ ! [W3: $i] :
                          ( ~ aElementOf0(W3,W2)
                          | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                    | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                    | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
      | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
      | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ ! [W2: $i] :
                ~ ( ( ~ aElement0(W2)
                    | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W2: $i] :
                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
          | ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
              | ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                  | aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
      | ! [W2: $i] :
          ( ~ aSet0(W2)
          | ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
              | ~ ( ( sbrdtbr0(W2) != xk )
                  | ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                      | ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2)
                      | aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) )
          | ~ ( ~ ! [W3: $i] :
                    ~ ( ( ~ aElement0(W3)
                        | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                        | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                    <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ ! [W3: $i] :
                    ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
              | ~ ! [W3: $i] :
                    ( ~ aElementOf0(W3,W2)
                    | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
              | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
  <=> ( ~ ! [W1: $i] :
            ( ~ isCountable0(W1)
            | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | ~ ! [W2: $i] :
                      ~ ( ( ~ aElement0(W2)
                          | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                      <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                | ~ ( ~ aSet0(W1)
                    | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                        | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
            | ! [W2: $i] :
                ( ~ aSet0(W2)
                | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                    | ~ ( ( sbrdtbr0(W2) != xk )
                        | ~ ( aSubsetOf0(W2,W1)
                            | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                            | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
                | ~ ( ~ ! [W3: $i] :
                          ~ ( ( ~ aElement0(W3)
                              | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                              | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                          <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                    | ~ ! [W3: $i] :
                          ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
                    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                    | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                    | ~ ! [W3: $i] :
                          ( ~ aElementOf0(W3,W2)
                          | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                    | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                    | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
      | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
      | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ ! [W2: $i] :
                ~ ( ( ~ aElement0(W2)
                    | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W2: $i] :
                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
          | aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
              | ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                  | aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
      | ! [W2: $i] :
          ( ~ aSet0(W2)
          | ~ ( ~ ! [W3: $i] :
                    ~ ( ( ~ aElement0(W3)
                        | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                        | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                    <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ ! [W3: $i] :
                    ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
              | ~ ! [W3: $i] :
                    ( ~ aElementOf0(W3,W2)
                    | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
              | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
              | ~ ( ( sbrdtbr0(W2) != xk )
                  | ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                      | aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                      | ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2) ) ) ) ) ) ),
    inference(monotonicity,[status(thm)],[157]) ).

tff(159,plain,
    ( ( ~ ! [W1: $i] :
            ( ~ isCountable0(W1)
            | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | ~ ! [W2: $i] :
                      ~ ( ( ~ aElement0(W2)
                          | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                      <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                | ~ ( ~ aSet0(W1)
                    | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                        | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
            | ! [W2: $i] :
                ( ~ aSet0(W2)
                | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                    | ~ ( ( sbrdtbr0(W2) != xk )
                        | ~ ( aSubsetOf0(W2,W1)
                            | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                            | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
                | ~ ( ~ ! [W3: $i] :
                          ~ ( ( ~ aElement0(W3)
                              | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                              | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                          <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                    | ~ ! [W3: $i] :
                          ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
                    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                    | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                    | ~ ! [W3: $i] :
                          ( ~ aElementOf0(W3,W2)
                          | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                    | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                    | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
      | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
      | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ ! [W2: $i] :
                ~ ( ( ~ aElement0(W2)
                    | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W2: $i] :
                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
          | ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
              | ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                  | aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
      | ! [W2: $i] :
          ( ~ aSet0(W2)
          | ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
              | ~ ( ( sbrdtbr0(W2) != xk )
                  | ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                      | ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2)
                      | aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) )
          | ~ ( ~ ! [W3: $i] :
                    ~ ( ( ~ aElement0(W3)
                        | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                        | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                    <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ ! [W3: $i] :
                    ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
              | ~ ! [W3: $i] :
                    ( ~ aElementOf0(W3,W2)
                    | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
              | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
  <=> ( ~ ! [W1: $i] :
            ( ~ isCountable0(W1)
            | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | ~ ! [W2: $i] :
                      ~ ( ( ~ aElement0(W2)
                          | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                      <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                | ~ ( ~ aSet0(W1)
                    | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                        | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
            | ! [W2: $i] :
                ( ~ aSet0(W2)
                | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                    | ~ ( ( sbrdtbr0(W2) != xk )
                        | ~ ( aSubsetOf0(W2,W1)
                            | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                            | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
                | ~ ( ~ ! [W3: $i] :
                          ~ ( ( ~ aElement0(W3)
                              | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                              | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                          <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                    | ~ ! [W3: $i] :
                          ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
                    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                    | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                    | ~ ! [W3: $i] :
                          ( ~ aElementOf0(W3,W2)
                          | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                    | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                    | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
      | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
      | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ ! [W2: $i] :
                ~ ( ( ~ aElement0(W2)
                    | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W2: $i] :
                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
          | aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
              | ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                  | aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
      | ! [W2: $i] :
          ( ~ aSet0(W2)
          | ~ ( ~ ! [W3: $i] :
                    ~ ( ( ~ aElement0(W3)
                        | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                        | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                    <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ ! [W3: $i] :
                    ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
              | ~ ! [W3: $i] :
                    ( ~ aElementOf0(W3,W2)
                    | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
              | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
              | ~ ( ( sbrdtbr0(W2) != xk )
                  | ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                      | aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                      | ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2) ) ) ) ) ) ),
    inference(transitivity,[status(thm)],[158,156]) ).

tff(160,plain,
    ( ~ ! [W1: $i] :
          ( ~ isCountable0(W1)
          | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
              | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ ! [W2: $i] :
                    ~ ( ( ~ aElement0(W2)
                        | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                    <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
              | ~ ( ~ aSet0(W1)
                  | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                      | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
          | ! [W2: $i] :
              ( ~ aSet0(W2)
              | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                  | ~ ( ( sbrdtbr0(W2) != xk )
                      | ~ ( aSubsetOf0(W2,W1)
                          | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                          | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
              | ~ ( ~ ! [W3: $i] :
                        ~ ( ( ~ aElement0(W3)
                            | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                            | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                        <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                  | ~ ! [W3: $i] :
                        ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
                  | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                  | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                  | ~ ! [W3: $i] :
                        ( ~ aElementOf0(W3,W2)
                        | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                  | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                  | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
    | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
    | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
        | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
        | aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
        | ~ ! [W2: $i] :
              ~ ( ( ~ aElement0(W2)
                  | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                  | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
              <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
        | ~ ! [W2: $i] :
              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
        | ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
            | ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                | aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
    | ! [W2: $i] :
        ( ~ aSet0(W2)
        | ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
            | ~ ( ( sbrdtbr0(W2) != xk )
                | ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                    | ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2)
                    | aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) )
        | ~ ( ~ ! [W3: $i] :
                  ~ ( ( ~ aElement0(W3)
                      | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                      | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                  <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
            | ~ ! [W3: $i] :
                  ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
            | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
            | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
            | ~ ! [W3: $i] :
                  ( ~ aElementOf0(W3,W2)
                  | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
            | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
            | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(161,plain,
    ( ~ ! [W1: $i] :
          ( ~ isCountable0(W1)
          | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
              | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ ! [W2: $i] :
                    ~ ( ( ~ aElement0(W2)
                        | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                    <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
              | ~ ( ~ aSet0(W1)
                  | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                      | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
          | ! [W2: $i] :
              ( ~ aSet0(W2)
              | ~ ( aElementOf0(W2,slbdtsldtrb0(W1,xk))
                  | ~ ( ( sbrdtbr0(W2) != xk )
                      | ~ ( aSubsetOf0(W2,W1)
                          | ~ aElementOf0(tptp_fun_W3_33(W2,W1),W2)
                          | aElementOf0(tptp_fun_W3_33(W2,W1),W1) ) ) )
              | ~ ( ~ ! [W3: $i] :
                        ~ ( ( ~ aElement0(W3)
                            | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                            | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                        <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                  | ~ ! [W3: $i] :
                        ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
                  | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                  | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                  | ~ ! [W3: $i] :
                        ( ~ aElementOf0(W3,W2)
                        | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                  | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                  | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
    | ~ isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
    | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
        | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
        | ~ ! [W2: $i] :
              ~ ( ( ~ aElement0(W2)
                  | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                  | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
              <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
        | ~ ! [W2: $i] :
              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
        | aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
        | ~ ( ~ aSet0(sdtlpdtrp0(xN,szszuzczcdt0(xn)))
            | ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                | aElementOf0(tptp_fun_W2_31(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
    | ! [W2: $i] :
        ( ~ aSet0(W2)
        | ~ ( ~ ! [W3: $i] :
                  ~ ( ( ~ aElement0(W3)
                      | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                      | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                  <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
            | ~ ! [W3: $i] :
                  ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
            | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
            | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
            | ~ ! [W3: $i] :
                  ( ~ aElementOf0(W3,W2)
                  | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
            | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
            | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
        | ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
            | ~ ( ( sbrdtbr0(W2) != xk )
                | ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                    | aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                    | ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2) ) ) ) ) ),
    inference(modus_ponens,[status(thm)],[160,159]) ).

tff(162,plain,
    ! [W2: $i] :
      ( ~ aSet0(W2)
      | ~ ( ~ ! [W3: $i] :
                ~ ( ( ~ aElement0(W3)
                    | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                    | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W3: $i] :
                ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ ! [W3: $i] :
                ( ~ aElementOf0(W3,W2)
                | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
          | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
      | ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
          | ~ ( ( sbrdtbr0(W2) != xk )
              | ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                  | aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                  | ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2) ) ) ) ),
    inference(unit_resolution,[status(thm)],[161,155,126,97]) ).

tff(163,plain,
    ( aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
  <=> aSet0(xP) ),
    inference(monotonicity,[status(thm)],[5]) ).

tff(164,plain,
    ( aSet0(xP)
  <=> aSet0(sdtmndt0(xQ,szmzizndt0(xQ))) ),
    inference(symmetry,[status(thm)],[163]) ).

tff(165,plain,
    ( aSet0(xP)
  <=> aSet0(xP) ),
    inference(rewrite,[status(thm)],[]) ).

tff(166,plain,
    ( aSet0(xP)
    & ! [W0: $i] :
        ( aElementOf0(W0,xQ)
       => sdtlseqdt0(szmzizndt0(xQ),W0) )
    & ! [W0: $i] :
        ( aElementOf0(W0,xP)
      <=> ( aElement0(W0)
          & aElementOf0(W0,xQ)
          & ( W0 != szmzizndt0(xQ) ) ) ) ),
    inference(and_elim,[status(thm)],[2]) ).

tff(167,plain,
    ( aSet0(xP)
    & ! [W0: $i] :
        ( aElementOf0(W0,xQ)
       => sdtlseqdt0(szmzizndt0(xQ),W0) ) ),
    inference(and_elim,[status(thm)],[166]) ).

tff(168,plain,
    aSet0(xP),
    inference(and_elim,[status(thm)],[167]) ).

tff(169,plain,
    aSet0(xP),
    inference(modus_ponens,[status(thm)],[168,165]) ).

tff(170,plain,
    aSet0(sdtmndt0(xQ,szmzizndt0(xQ))),
    inference(modus_ponens,[status(thm)],[169,164]) ).

tff(171,plain,
    ( ( ~ ! [W2: $i] :
            ( ~ aSet0(W2)
            | ~ ( ~ ! [W3: $i] :
                      ~ ( ( ~ aElement0(W3)
                          | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                          | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                      <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ ! [W3: $i] :
                      ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                | ~ ! [W3: $i] :
                      ( ~ aElementOf0(W3,W2)
                      | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
            | ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
                | ~ ( ( sbrdtbr0(W2) != xk )
                    | ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                        | aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                        | ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2) ) ) ) )
      | ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
      | ~ ( ~ ! [W3: $i] :
                ~ ( ( ~ aElement0(W3)
                    | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                    | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W3: $i] :
                ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
          | ~ ! [W3: $i] :
                ( ~ aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
                | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
      | ~ ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
          | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
              | ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                  | ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
                  | aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
  <=> ( ~ ! [W2: $i] :
            ( ~ aSet0(W2)
            | ~ ( ~ ! [W3: $i] :
                      ~ ( ( ~ aElement0(W3)
                          | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                          | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                      <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ ! [W3: $i] :
                      ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                | ~ ! [W3: $i] :
                      ( ~ aElementOf0(W3,W2)
                      | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
            | ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
                | ~ ( ( sbrdtbr0(W2) != xk )
                    | ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                        | aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                        | ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2) ) ) ) )
      | ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
      | ~ ( ~ ! [W3: $i] :
                ~ ( ( ~ aElement0(W3)
                    | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                    | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W3: $i] :
                ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
          | ~ ! [W3: $i] :
                ( ~ aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
                | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
      | ~ ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
          | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
              | ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                  | ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
                  | aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(172,plain,
    ( ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
      | ~ ( ~ ! [W3: $i] :
                ~ ( ( ~ aElement0(W3)
                    | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                    | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W3: $i] :
                ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ ! [W3: $i] :
                ( ~ aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
                | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
          | ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
      | ~ ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
          | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
              | ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                  | aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                  | ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ))) ) ) ) )
  <=> ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
      | ~ ( ~ ! [W3: $i] :
                ~ ( ( ~ aElement0(W3)
                    | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                    | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W3: $i] :
                ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
          | ~ ! [W3: $i] :
                ( ~ aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
                | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
      | ~ ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
          | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
              | ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                  | ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
                  | aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(173,plain,
    ( ( ~ ! [W2: $i] :
            ( ~ aSet0(W2)
            | ~ ( ~ ! [W3: $i] :
                      ~ ( ( ~ aElement0(W3)
                          | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                          | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                      <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ ! [W3: $i] :
                      ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                | ~ ! [W3: $i] :
                      ( ~ aElementOf0(W3,W2)
                      | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
            | ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
                | ~ ( ( sbrdtbr0(W2) != xk )
                    | ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                        | aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                        | ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2) ) ) ) )
      | ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
      | ~ ( ~ ! [W3: $i] :
                ~ ( ( ~ aElement0(W3)
                    | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                    | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W3: $i] :
                ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ ! [W3: $i] :
                ( ~ aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
                | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
          | ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
      | ~ ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
          | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
              | ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                  | aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                  | ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ))) ) ) ) )
  <=> ( ~ ! [W2: $i] :
            ( ~ aSet0(W2)
            | ~ ( ~ ! [W3: $i] :
                      ~ ( ( ~ aElement0(W3)
                          | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                          | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                      <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ ! [W3: $i] :
                      ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                | ~ ! [W3: $i] :
                      ( ~ aElementOf0(W3,W2)
                      | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
            | ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
                | ~ ( ( sbrdtbr0(W2) != xk )
                    | ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                        | aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                        | ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2) ) ) ) )
      | ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
      | ~ ( ~ ! [W3: $i] :
                ~ ( ( ~ aElement0(W3)
                    | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                    | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W3: $i] :
                ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
          | ~ ! [W3: $i] :
                ( ~ aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
                | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
      | ~ ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
          | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
              | ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                  | ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
                  | aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) ),
    inference(monotonicity,[status(thm)],[172]) ).

tff(174,plain,
    ( ( ~ ! [W2: $i] :
            ( ~ aSet0(W2)
            | ~ ( ~ ! [W3: $i] :
                      ~ ( ( ~ aElement0(W3)
                          | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                          | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                      <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ ! [W3: $i] :
                      ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                | ~ ! [W3: $i] :
                      ( ~ aElementOf0(W3,W2)
                      | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
            | ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
                | ~ ( ( sbrdtbr0(W2) != xk )
                    | ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                        | aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                        | ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2) ) ) ) )
      | ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
      | ~ ( ~ ! [W3: $i] :
                ~ ( ( ~ aElement0(W3)
                    | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                    | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W3: $i] :
                ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ ! [W3: $i] :
                ( ~ aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
                | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
          | ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
      | ~ ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
          | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
              | ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                  | aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                  | ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ))) ) ) ) )
  <=> ( ~ ! [W2: $i] :
            ( ~ aSet0(W2)
            | ~ ( ~ ! [W3: $i] :
                      ~ ( ( ~ aElement0(W3)
                          | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                          | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                      <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ ! [W3: $i] :
                      ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                | ~ ! [W3: $i] :
                      ( ~ aElementOf0(W3,W2)
                      | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
            | ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
                | ~ ( ( sbrdtbr0(W2) != xk )
                    | ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                        | aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                        | ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2) ) ) ) )
      | ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
      | ~ ( ~ ! [W3: $i] :
                ~ ( ( ~ aElement0(W3)
                    | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                    | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W3: $i] :
                ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
          | ~ ! [W3: $i] :
                ( ~ aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
                | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
      | ~ ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
          | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
              | ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                  | ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
                  | aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) ),
    inference(transitivity,[status(thm)],[173,171]) ).

tff(175,plain,
    ( ~ ! [W2: $i] :
          ( ~ aSet0(W2)
          | ~ ( ~ ! [W3: $i] :
                    ~ ( ( ~ aElement0(W3)
                        | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                        | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                    <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ ! [W3: $i] :
                    ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
              | ~ ! [W3: $i] :
                    ( ~ aElementOf0(W3,W2)
                    | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
              | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
              | ~ ( ( sbrdtbr0(W2) != xk )
                  | ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                      | aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                      | ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2) ) ) ) )
    | ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
    | ~ ( ~ ! [W3: $i] :
              ~ ( ( ~ aElement0(W3)
                  | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                  | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
              <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
        | ~ ! [W3: $i] :
              ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
        | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
        | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
        | ~ ! [W3: $i] :
              ( ~ aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
              | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
        | ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
        | ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
    | ~ ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
        | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
            | ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                | aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                | ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ))) ) ) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(176,plain,
    ( ~ ! [W2: $i] :
          ( ~ aSet0(W2)
          | ~ ( ~ ! [W3: $i] :
                    ~ ( ( ~ aElement0(W3)
                        | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                        | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                    <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ ! [W3: $i] :
                    ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
              | ~ ! [W3: $i] :
                    ( ~ aElementOf0(W3,W2)
                    | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ aElementOf0(W2,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
              | ~ aSubsetOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
              | ~ ( ( sbrdtbr0(W2) != xk )
                  | ~ ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                      | aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                      | ~ aElementOf0(tptp_fun_W3_33(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))),W2) ) ) ) )
    | ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
    | ~ ( ~ ! [W3: $i] :
              ~ ( ( ~ aElement0(W3)
                  | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                  | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
              <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
        | ~ ! [W3: $i] :
              ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
        | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
        | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
        | ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
        | ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
        | ~ ! [W3: $i] :
              ( ~ aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
              | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
    | ~ ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
        | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
            | ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                | ~ aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtmndt0(xQ,szmzizndt0(xQ)))
                | aElementOf0(tptp_fun_W3_33(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ),
    inference(modus_ponens,[status(thm)],[175,174]) ).

tff(177,plain,
    ~ ( ~ ! [W3: $i] :
            ~ ( ( ~ aElement0(W3)
                | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
                | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
            <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
      | ~ ! [W3: $i] :
            ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
      | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
      | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
      | ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
      | ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
      | ~ ! [W3: $i] :
            ( ~ aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
            | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ),
    inference(unit_resolution,[status(thm)],[176,170,162,23]) ).

tff(178,plain,
    ( ~ ! [W3: $i] :
          ~ ( ( ~ aElement0(W3)
              | ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
              | ( W3 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
          <=> aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
    | ~ ! [W3: $i] :
          ( ~ aElementOf0(W3,sdtlpdtrp0(xN,xn))
          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W3) )
    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
    | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
    | ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
    | ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
    | ~ ! [W3: $i] :
          ( ~ aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ)))
          | aElementOf0(W3,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
    | aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) ),
    inference(tautology,[status(thm)],[]) ).

tff(179,plain,
    aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)),
    inference(unit_resolution,[status(thm)],[178,177]) ).

tff(180,plain,
    ( ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(xc,xQ) )
  <=> ( sdtlpdtrp0(xc,xQ) = sdtlpdtrp0(xd,xn) ) ),
    inference(commutativity,[status(thm)],[]) ).

tff(181,plain,
    ( ( xp = szmzizndt0(xQ) )
  <=> ( xp = szmzizndt0(xQ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(182,axiom,
    ( aElementOf0(xp,xQ)
    & ! [W0: $i] :
        ( aElementOf0(W0,xQ)
       => sdtlseqdt0(xp,W0) )
    & ( xp = szmzizndt0(xQ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5147) ).

tff(183,plain,
    xp = szmzizndt0(xQ),
    inference(and_elim,[status(thm)],[182]) ).

tff(184,plain,
    xp = szmzizndt0(xQ),
    inference(modus_ponens,[status(thm)],[183,181]) ).

tff(185,plain,
    szmzizndt0(xQ) = xp,
    inference(symmetry,[status(thm)],[184]) ).

tff(186,plain,
    ( aElementOf0(szmzizndt0(xQ),xQ)
  <=> aElementOf0(xp,xQ) ),
    inference(monotonicity,[status(thm)],[185]) ).

tff(187,plain,
    ( aElementOf0(xp,xQ)
  <=> aElementOf0(szmzizndt0(xQ),xQ) ),
    inference(symmetry,[status(thm)],[186]) ).

tff(188,plain,
    ( aElementOf0(xp,xQ)
  <=> aElementOf0(xp,xQ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(189,plain,
    ( aElementOf0(xp,xQ)
    & ! [W0: $i] :
        ( aElementOf0(W0,xQ)
       => sdtlseqdt0(xp,W0) ) ),
    inference(and_elim,[status(thm)],[182]) ).

tff(190,plain,
    aElementOf0(xp,xQ),
    inference(and_elim,[status(thm)],[189]) ).

tff(191,plain,
    aElementOf0(xp,xQ),
    inference(modus_ponens,[status(thm)],[190,188]) ).

tff(192,plain,
    aElementOf0(szmzizndt0(xQ),xQ),
    inference(modus_ponens,[status(thm)],[191,187]) ).

tff(193,plain,
    ( aSet0(xQ)
  <=> aSet0(xQ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(194,axiom,
    ( aSet0(xQ)
    & ! [W0: $i] :
        ( aElementOf0(W0,xQ)
       => aElementOf0(W0,xO) )
    & aSubsetOf0(xQ,xO)
    & ( sbrdtbr0(xQ) = xK )
    & aElementOf0(xQ,slbdtsldtrb0(xO,xK)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5078) ).

tff(195,plain,
    ( aSet0(xQ)
    & ! [W0: $i] :
        ( aElementOf0(W0,xQ)
       => aElementOf0(W0,xO) )
    & aSubsetOf0(xQ,xO)
    & ( sbrdtbr0(xQ) = xK ) ),
    inference(and_elim,[status(thm)],[194]) ).

tff(196,plain,
    ( aSet0(xQ)
    & ! [W0: $i] :
        ( aElementOf0(W0,xQ)
       => aElementOf0(W0,xO) )
    & aSubsetOf0(xQ,xO) ),
    inference(and_elim,[status(thm)],[195]) ).

tff(197,plain,
    ( aSet0(xQ)
    & ! [W0: $i] :
        ( aElementOf0(W0,xQ)
       => aElementOf0(W0,xO) ) ),
    inference(and_elim,[status(thm)],[196]) ).

tff(198,plain,
    aSet0(xQ),
    inference(and_elim,[status(thm)],[197]) ).

tff(199,plain,
    aSet0(xQ),
    inference(modus_ponens,[status(thm)],[198,193]) ).

tff(200,plain,
    ^ [W0: $i] :
      refl(( ( ~ aSet0(W0)
          | ! [W1: $i] :
              ( ~ aElementOf0(W1,W0)
              | ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
      <=> ( ~ aSet0(W0)
          | ! [W1: $i] :
              ( ~ aElementOf0(W1,W0)
              | ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(201,plain,
    ( ! [W0: $i] :
        ( ~ aSet0(W0)
        | ! [W1: $i] :
            ( ~ aElementOf0(W1,W0)
            | ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
  <=> ! [W0: $i] :
        ( ~ aSet0(W0)
        | ! [W1: $i] :
            ( ~ aElementOf0(W1,W0)
            | ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) ),
    inference(quant_intro,[status(thm)],[200]) ).

tff(202,plain,
    ^ [W0: $i] :
      rewrite(( ( ~ aSet0(W0)
          | ! [W1: $i] :
              ( ~ aElementOf0(W1,W0)
              | ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
      <=> ( ~ aSet0(W0)
          | ! [W1: $i] :
              ( ~ aElementOf0(W1,W0)
              | ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(203,plain,
    ( ! [W0: $i] :
        ( ~ aSet0(W0)
        | ! [W1: $i] :
            ( ~ aElementOf0(W1,W0)
            | ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
  <=> ! [W0: $i] :
        ( ~ aSet0(W0)
        | ! [W1: $i] :
            ( ~ aElementOf0(W1,W0)
            | ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) ),
    inference(quant_intro,[status(thm)],[202]) ).

tff(204,plain,
    ( ! [W0: $i] :
        ( ~ aSet0(W0)
        | ! [W1: $i] :
            ( ~ aElementOf0(W1,W0)
            | ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
  <=> ! [W0: $i] :
        ( ~ aSet0(W0)
        | ! [W1: $i] :
            ( ~ aElementOf0(W1,W0)
            | ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) ),
    inference(transitivity,[status(thm)],[203,201]) ).

tff(205,plain,
    ( ! [W0: $i] :
        ( ~ aSet0(W0)
        | ! [W1: $i] :
            ( ~ aElementOf0(W1,W0)
            | ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
  <=> ! [W0: $i] :
        ( ~ aSet0(W0)
        | ! [W1: $i] :
            ( ~ aElementOf0(W1,W0)
            | ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(206,plain,
    ^ [W0: $i] :
      trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
                rewrite(( ( aElementOf0(W1,W0)
                   => ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) )
                <=> ( ~ aElementOf0(W1,W0)
                    | ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ))),
            ( ! [W1: $i] :
                ( aElementOf0(W1,W0)
               => ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) )
          <=> ! [W1: $i] :
                ( ~ aElementOf0(W1,W0)
                | ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )),
          ( ( aSet0(W0)
           => ! [W1: $i] :
                ( aElementOf0(W1,W0)
               => ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
        <=> ( aSet0(W0)
           => ! [W1: $i] :
                ( ~ aElementOf0(W1,W0)
                | ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) )),
        rewrite(( ( aSet0(W0)
           => ! [W1: $i] :
                ( ~ aElementOf0(W1,W0)
                | ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
        <=> ( ~ aSet0(W0)
            | ! [W1: $i] :
                ( ~ aElementOf0(W1,W0)
                | ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) )),
        ( ( aSet0(W0)
         => ! [W1: $i] :
              ( aElementOf0(W1,W0)
             => ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
      <=> ( ~ aSet0(W0)
          | ! [W1: $i] :
              ( ~ aElementOf0(W1,W0)
              | ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(207,plain,
    ( ! [W0: $i] :
        ( aSet0(W0)
       => ! [W1: $i] :
            ( aElementOf0(W1,W0)
           => ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
  <=> ! [W0: $i] :
        ( ~ aSet0(W0)
        | ! [W1: $i] :
            ( ~ aElementOf0(W1,W0)
            | ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) ),
    inference(quant_intro,[status(thm)],[206]) ).

tff(208,axiom,
    ! [W0: $i] :
      ( aSet0(W0)
     => ! [W1: $i] :
          ( aElementOf0(W1,W0)
         => ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mConsDiff) ).

tff(209,plain,
    ! [W0: $i] :
      ( ~ aSet0(W0)
      | ! [W1: $i] :
          ( ~ aElementOf0(W1,W0)
          | ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ),
    inference(modus_ponens,[status(thm)],[208,207]) ).

tff(210,plain,
    ! [W0: $i] :
      ( ~ aSet0(W0)
      | ! [W1: $i] :
          ( ~ aElementOf0(W1,W0)
          | ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ),
    inference(modus_ponens,[status(thm)],[209,205]) ).

tff(211,plain,
    ! [W0: $i] :
      ( ~ aSet0(W0)
      | ! [W1: $i] :
          ( ~ aElementOf0(W1,W0)
          | ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ),
    inference(skolemize,[status(sab)],[210]) ).

tff(212,plain,
    ! [W0: $i] :
      ( ~ aSet0(W0)
      | ! [W1: $i] :
          ( ~ aElementOf0(W1,W0)
          | ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ),
    inference(modus_ponens,[status(thm)],[211,204]) ).

tff(213,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ aSet0(W0)
            | ! [W1: $i] :
                ( ~ aElementOf0(W1,W0)
                | ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
      | ~ aSet0(xQ)
      | ! [W1: $i] :
          ( ~ aElementOf0(W1,xQ)
          | ( sdtpldt0(sdtmndt0(xQ,W1),W1) = xQ ) ) )
  <=> ( ~ ! [W0: $i] :
            ( ~ aSet0(W0)
            | ! [W1: $i] :
                ( ~ aElementOf0(W1,W0)
                | ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
      | ~ aSet0(xQ)
      | ! [W1: $i] :
          ( ~ aElementOf0(W1,xQ)
          | ( sdtpldt0(sdtmndt0(xQ,W1),W1) = xQ ) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(214,plain,
    ( ~ ! [W0: $i] :
          ( ~ aSet0(W0)
          | ! [W1: $i] :
              ( ~ aElementOf0(W1,W0)
              | ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
    | ~ aSet0(xQ)
    | ! [W1: $i] :
        ( ~ aElementOf0(W1,xQ)
        | ( sdtpldt0(sdtmndt0(xQ,W1),W1) = xQ ) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(215,plain,
    ( ~ ! [W0: $i] :
          ( ~ aSet0(W0)
          | ! [W1: $i] :
              ( ~ aElementOf0(W1,W0)
              | ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
    | ~ aSet0(xQ)
    | ! [W1: $i] :
        ( ~ aElementOf0(W1,xQ)
        | ( sdtpldt0(sdtmndt0(xQ,W1),W1) = xQ ) ) ),
    inference(modus_ponens,[status(thm)],[214,213]) ).

tff(216,plain,
    ! [W1: $i] :
      ( ~ aElementOf0(W1,xQ)
      | ( sdtpldt0(sdtmndt0(xQ,W1),W1) = xQ ) ),
    inference(unit_resolution,[status(thm)],[215,212,199]) ).

tff(217,plain,
    ( ( ~ ! [W1: $i] :
            ( ~ aElementOf0(W1,xQ)
            | ( sdtpldt0(sdtmndt0(xQ,W1),W1) = xQ ) )
      | ~ aElementOf0(szmzizndt0(xQ),xQ)
      | ( sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ)) = xQ ) )
  <=> ( ~ ! [W1: $i] :
            ( ~ aElementOf0(W1,xQ)
            | ( sdtpldt0(sdtmndt0(xQ,W1),W1) = xQ ) )
      | ~ aElementOf0(szmzizndt0(xQ),xQ)
      | ( sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ)) = xQ ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(218,plain,
    ( ~ ! [W1: $i] :
          ( ~ aElementOf0(W1,xQ)
          | ( sdtpldt0(sdtmndt0(xQ,W1),W1) = xQ ) )
    | ~ aElementOf0(szmzizndt0(xQ),xQ)
    | ( sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ)) = xQ ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(219,plain,
    ( ~ ! [W1: $i] :
          ( ~ aElementOf0(W1,xQ)
          | ( sdtpldt0(sdtmndt0(xQ,W1),W1) = xQ ) )
    | ~ aElementOf0(szmzizndt0(xQ),xQ)
    | ( sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ)) = xQ ) ),
    inference(modus_ponens,[status(thm)],[218,217]) ).

tff(220,plain,
    sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ)) = xQ,
    inference(unit_resolution,[status(thm)],[219,216,192]) ).

tff(221,plain,
    ( ( sdtlpdtrp0(xe,xn) = xp )
  <=> ( sdtlpdtrp0(xe,xn) = xp ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(222,plain,
    sdtlpdtrp0(xe,xn) = xp,
    inference(and_elim,[status(thm)],[25]) ).

tff(223,plain,
    sdtlpdtrp0(xe,xn) = xp,
    inference(modus_ponens,[status(thm)],[222,221]) ).

tff(224,plain,
    ^ [W0: $i] :
      refl(( ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
              | ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
              | ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(225,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
            | ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
            | ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ) ),
    inference(quant_intro,[status(thm)],[224]) ).

tff(226,plain,
    ^ [W0: $i] :
      rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
              | ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
              | ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(227,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
            | ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
            | ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ) ),
    inference(quant_intro,[status(thm)],[226]) ).

tff(228,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
            | ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
            | ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ) ),
    inference(transitivity,[status(thm)],[227,225]) ).

tff(229,plain,
    ^ [W0: $i] :
      rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
          | ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
            & ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
            & ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
              | ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(230,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
          & ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
              | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
          & ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
            | ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ) ),
    inference(quant_intro,[status(thm)],[229]) ).

tff(231,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
          & ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
              | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
          & ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
          & ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
              | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
          & ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(232,plain,
    ^ [W0: $i] :
      trans(monotonicity(trans(monotonicity(rewrite(( ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
                  & ! [W1: $i] :
                      ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                     => sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) )
              <=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
                  & ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )),
              ( ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
                & ! [W1: $i] :
                    ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                   => sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
                & ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
            <=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
                & ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
                & ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )),
            rewrite(( ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
                & ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
                & ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
            <=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
                & ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
                & ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )),
            ( ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                 => sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
              & ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
          <=> ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
              & ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )),
          ( ( aElementOf0(W0,szNzAzT0)
           => ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                 => sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
              & ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
        <=> ( aElementOf0(W0,szNzAzT0)
           => ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
              & ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )),
        rewrite(( ( aElementOf0(W0,szNzAzT0)
           => ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
              & ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
        <=> ( ~ aElementOf0(W0,szNzAzT0)
            | ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
              & ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )),
        ( ( aElementOf0(W0,szNzAzT0)
         => ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
            & ! [W1: $i] :
                ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
               => sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
            & ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
            & ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
            & ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(233,plain,
    ( ! [W0: $i] :
        ( aElementOf0(W0,szNzAzT0)
       => ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
          & ! [W1: $i] :
              ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
             => sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
          & ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
          & ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
              | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
          & ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ),
    inference(quant_intro,[status(thm)],[232]) ).

tff(234,axiom,
    ( aFunction0(xe)
    & ( szDzozmdt0(xe) = szNzAzT0 )
    & ! [W0: $i] :
        ( aElementOf0(W0,szNzAzT0)
       => ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
          & ! [W1: $i] :
              ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
             => sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
          & ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4660) ).

tff(235,plain,
    ! [W0: $i] :
      ( aElementOf0(W0,szNzAzT0)
     => ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
        & ! [W1: $i] :
            ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
           => sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
        & ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
    inference(and_elim,[status(thm)],[234]) ).

tff(236,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
        & ! [W1: $i] :
            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
            | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
        & ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
    inference(modus_ponens,[status(thm)],[235,233]) ).

tff(237,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
        & ! [W1: $i] :
            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
            | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
        & ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
    inference(modus_ponens,[status(thm)],[236,231]) ).

tff(238,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ( aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
        & ! [W1: $i] :
            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
            | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) )
        & ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
    inference(skolemize,[status(sab)],[237]) ).

tff(239,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
          | ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ),
    inference(modus_ponens,[status(thm)],[238,230]) ).

tff(240,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
          | ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) ),
    inference(modus_ponens,[status(thm)],[239,228]) ).

tff(241,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
                | ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ~ ( ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) )
          | ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
          | ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
  <=> ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
                | ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ~ ( ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) )
          | ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
          | ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(242,plain,
    ( ( ~ aElementOf0(xn,szNzAzT0)
      | ~ ( ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) )
          | ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) ) ) )
  <=> ( ~ aElementOf0(xn,szNzAzT0)
      | ~ ( ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) )
          | ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
          | ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(243,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
                | ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ~ ( ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) )
          | ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) ) ) )
  <=> ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
                | ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ~ ( ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) )
          | ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
          | ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ),
    inference(monotonicity,[status(thm)],[242]) ).

tff(244,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
                | ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ~ ( ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) )
          | ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) ) ) )
  <=> ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
                | ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ~ ( ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) )
          | ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
          | ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ) ),
    inference(transitivity,[status(thm)],[243,241]) ).

tff(245,plain,
    ( ~ ! [W0: $i] :
          ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
              | ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
    | ~ aElementOf0(xn,szNzAzT0)
    | ~ ( ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) )
        | ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
        | ~ ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
              | sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) ) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(246,plain,
    ( ~ ! [W0: $i] :
          ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ( sdtlpdtrp0(xe,W0) != szmzizndt0(sdtlpdtrp0(xN,W0)) )
              | ~ aElementOf0(sdtlpdtrp0(xe,W0),sdtlpdtrp0(xN,W0))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(sdtlpdtrp0(xe,W0),W1) ) ) )
    | ~ aElementOf0(xn,szNzAzT0)
    | ~ ( ~ ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
              | sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) )
        | ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
        | ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) ),
    inference(modus_ponens,[status(thm)],[245,244]) ).

tff(247,plain,
    ~ ( ~ ! [W1: $i] :
            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
            | sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) )
      | ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
      | ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) ) ),
    inference(unit_resolution,[status(thm)],[246,240,28]) ).

tff(248,plain,
    ( ~ ! [W1: $i] :
          ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
          | sdtlseqdt0(sdtlpdtrp0(xe,xn),W1) )
    | ~ aElementOf0(sdtlpdtrp0(xe,xn),sdtlpdtrp0(xN,xn))
    | ( sdtlpdtrp0(xe,xn) != szmzizndt0(sdtlpdtrp0(xN,xn)) )
    | ( sdtlpdtrp0(xe,xn) = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ),
    inference(tautology,[status(thm)],[]) ).

tff(249,plain,
    sdtlpdtrp0(xe,xn) = szmzizndt0(sdtlpdtrp0(xN,xn)),
    inference(unit_resolution,[status(thm)],[248,247]) ).

tff(250,plain,
    szmzizndt0(sdtlpdtrp0(xN,xn)) = sdtlpdtrp0(xe,xn),
    inference(symmetry,[status(thm)],[249]) ).

tff(251,plain,
    szmzizndt0(sdtlpdtrp0(xN,xn)) = szmzizndt0(xQ),
    inference(transitivity,[status(thm)],[250,223,184]) ).

tff(252,plain,
    sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))) = sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(xQ)),
    inference(monotonicity,[status(thm)],[251]) ).

tff(253,plain,
    sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn))) = xQ,
    inference(transitivity,[status(thm)],[252,220]) ).

tff(254,plain,
    sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(xc,xQ),
    inference(monotonicity,[status(thm)],[253]) ).

tff(255,plain,
    ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
    | ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
    | aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
    | ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
    inference(tautology,[status(thm)],[]) ).

tff(256,plain,
    ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
    | ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
    | aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
    inference(unit_resolution,[status(thm)],[255,12]) ).

tff(257,plain,
    ( ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
        | ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
            | ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
            | aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) )
    | ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
    | ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
        | ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
        | aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
    inference(tautology,[status(thm)],[]) ).

tff(258,plain,
    ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
      | ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
          | ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
          | aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
    inference(unit_resolution,[status(thm)],[257,19,256]) ).

tff(259,plain,
    ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
    | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
        | ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
            | ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
            | aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) )
    | ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
    | ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
        | ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
        | aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
    inference(tautology,[status(thm)],[]) ).

tff(260,plain,
    ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
    | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
        | ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
            | ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
            | aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ),
    inference(unit_resolution,[status(thm)],[259,258]) ).

tff(261,plain,
    ^ [W0: $i] :
      refl(( ( ~ aElementOf0(W0,szNzAzT0)
          | ! [W1: $i] :
              ( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
              | ~ aSet0(W1)
              | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                  | ~ ( ( sbrdtbr0(W1) != xk )
                      | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                          | ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
                          | aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ! [W1: $i] :
              ( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
              | ~ aSet0(W1)
              | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                  | ~ ( ( sbrdtbr0(W1) != xk )
                      | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                          | ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
                          | aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(262,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ! [W1: $i] :
            ( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
            | ~ aSet0(W1)
            | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                | ~ ( ( sbrdtbr0(W1) != xk )
                    | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                        | ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
                        | aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ! [W1: $i] :
            ( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
            | ~ aSet0(W1)
            | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                | ~ ( ( sbrdtbr0(W1) != xk )
                    | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                        | ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
                        | aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) ),
    inference(quant_intro,[status(thm)],[261]) ).

tff(263,plain,
    ^ [W0: $i] :
      rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
          | ! [W1: $i] :
              ( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
              | ~ aSet0(W1)
              | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                  | ~ ( ( sbrdtbr0(W1) != xk )
                      | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                          | ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
                          | aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ! [W1: $i] :
              ( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
              | ~ aSet0(W1)
              | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                  | ~ ( ( sbrdtbr0(W1) != xk )
                      | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                          | ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
                          | aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(264,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ! [W1: $i] :
            ( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
            | ~ aSet0(W1)
            | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                | ~ ( ( sbrdtbr0(W1) != xk )
                    | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                        | ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
                        | aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ! [W1: $i] :
            ( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
            | ~ aSet0(W1)
            | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                | ~ ( ( sbrdtbr0(W1) != xk )
                    | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                        | ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
                        | aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) ),
    inference(quant_intro,[status(thm)],[263]) ).

tff(265,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ! [W1: $i] :
            ( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
            | ~ aSet0(W1)
            | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                | ~ ( ( sbrdtbr0(W1) != xk )
                    | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                        | ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
                        | aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ! [W1: $i] :
            ( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
            | ~ aSet0(W1)
            | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                | ~ ( ( sbrdtbr0(W1) != xk )
                    | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                        | ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
                        | aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) ),
    inference(transitivity,[status(thm)],[264,262]) ).

tff(266,plain,
    ^ [W0: $i] :
      rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
          | ! [W1: $i] :
              ( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
              | ~ aSet0(W1)
              | ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                & ( ( sbrdtbr0(W1) != xk )
                  | ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                    & ~ ( ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
                        | aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ! [W1: $i] :
              ( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
              | ~ aSet0(W1)
              | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                  | ~ ( ( sbrdtbr0(W1) != xk )
                      | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                          | ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
                          | aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(267,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ! [W1: $i] :
            ( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
            | ~ aSet0(W1)
            | ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
              & ( ( sbrdtbr0(W1) != xk )
                | ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  & ~ ( ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
                      | aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ! [W1: $i] :
            ( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
            | ~ aSet0(W1)
            | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                | ~ ( ( sbrdtbr0(W1) != xk )
                    | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                        | ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
                        | aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) ),
    inference(quant_intro,[status(thm)],[266]) ).

tff(268,plain,
    ^ [W0: $i] :
      rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
          | ! [W1: $i] :
              ( ~ aSet0(W1)
              | ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                & ( ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                    & ~ ( ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
                        | aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
                  | ( sbrdtbr0(W1) != xk ) ) )
              | ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ! [W1: $i] :
              ( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
              | ~ aSet0(W1)
              | ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                & ( ( sbrdtbr0(W1) != xk )
                  | ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                    & ~ ( ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
                        | aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(269,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ! [W1: $i] :
            ( ~ aSet0(W1)
            | ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
              & ( ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  & ~ ( ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
                      | aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
                | ( sbrdtbr0(W1) != xk ) ) )
            | ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ! [W1: $i] :
            ( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
            | ~ aSet0(W1)
            | ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
              & ( ( sbrdtbr0(W1) != xk )
                | ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                  & ~ ( ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
                      | aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) ) ),
    inference(quant_intro,[status(thm)],[268]) ).

tff(270,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ! [W1: $i] :
            ( ~ ( aSet0(W1)
                & ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                  | ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                      | ! [W2: $i] :
                          ( ~ aElementOf0(W2,W1)
                          | aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
                    & ( sbrdtbr0(W1) = xk ) ) ) )
            | ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ! [W1: $i] :
            ( ~ ( aSet0(W1)
                & ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                  | ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                      | ! [W2: $i] :
                          ( ~ aElementOf0(W2,W1)
                          | aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
                    & ( sbrdtbr0(W1) = xk ) ) ) )
            | ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(271,plain,
    ^ [W0: $i] :
      trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
                trans(monotonicity(rewrite(( ( aSet0(W1)
                        & ( ( ( ! [W2: $i] :
                                  ( aElementOf0(W2,W1)
                                 => aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
                              | aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
                            & ( sbrdtbr0(W1) = xk ) )
                          | aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) )
                    <=> ( aSet0(W1)
                        & ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                          | ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                              | ! [W2: $i] :
                                  ( ~ aElementOf0(W2,W1)
                                  | aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
                            & ( sbrdtbr0(W1) = xk ) ) ) ) )),
                    ( ( ( aSet0(W1)
                        & ( ( ( ! [W2: $i] :
                                  ( aElementOf0(W2,W1)
                                 => aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
                              | aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
                            & ( sbrdtbr0(W1) = xk ) )
                          | aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) )
                     => ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) )
                  <=> ( ( aSet0(W1)
                        & ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                          | ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                              | ! [W2: $i] :
                                  ( ~ aElementOf0(W2,W1)
                                  | aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
                            & ( sbrdtbr0(W1) = xk ) ) ) )
                     => ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )),
                  rewrite(( ( ( aSet0(W1)
                        & ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                          | ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                              | ! [W2: $i] :
                                  ( ~ aElementOf0(W2,W1)
                                  | aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
                            & ( sbrdtbr0(W1) = xk ) ) ) )
                     => ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) )
                  <=> ( ~ ( aSet0(W1)
                          & ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                            | ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                                | ! [W2: $i] :
                                    ( ~ aElementOf0(W2,W1)
                                    | aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
                              & ( sbrdtbr0(W1) = xk ) ) ) )
                      | ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )),
                  ( ( ( aSet0(W1)
                      & ( ( ( ! [W2: $i] :
                                ( aElementOf0(W2,W1)
                               => aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
                            | aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
                          & ( sbrdtbr0(W1) = xk ) )
                        | aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) )
                   => ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) )
                <=> ( ~ ( aSet0(W1)
                        & ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                          | ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                              | ! [W2: $i] :
                                  ( ~ aElementOf0(W2,W1)
                                  | aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
                            & ( sbrdtbr0(W1) = xk ) ) ) )
                    | ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ))),
            ( ! [W1: $i] :
                ( ( aSet0(W1)
                  & ( ( ( ! [W2: $i] :
                            ( aElementOf0(W2,W1)
                           => aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
                        | aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
                      & ( sbrdtbr0(W1) = xk ) )
                    | aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) )
               => ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) )
          <=> ! [W1: $i] :
                ( ~ ( aSet0(W1)
                    & ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                      | ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                          | ! [W2: $i] :
                              ( ~ aElementOf0(W2,W1)
                              | aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
                        & ( sbrdtbr0(W1) = xk ) ) ) )
                | ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )),
          ( ( aElementOf0(W0,szNzAzT0)
           => ! [W1: $i] :
                ( ( aSet0(W1)
                  & ( ( ( ! [W2: $i] :
                            ( aElementOf0(W2,W1)
                           => aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
                        | aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
                      & ( sbrdtbr0(W1) = xk ) )
                    | aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) )
               => ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )
        <=> ( aElementOf0(W0,szNzAzT0)
           => ! [W1: $i] :
                ( ~ ( aSet0(W1)
                    & ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                      | ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                          | ! [W2: $i] :
                              ( ~ aElementOf0(W2,W1)
                              | aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
                        & ( sbrdtbr0(W1) = xk ) ) ) )
                | ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ) )),
        rewrite(( ( aElementOf0(W0,szNzAzT0)
           => ! [W1: $i] :
                ( ~ ( aSet0(W1)
                    & ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                      | ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                          | ! [W2: $i] :
                              ( ~ aElementOf0(W2,W1)
                              | aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
                        & ( sbrdtbr0(W1) = xk ) ) ) )
                | ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )
        <=> ( ~ aElementOf0(W0,szNzAzT0)
            | ! [W1: $i] :
                ( ~ ( aSet0(W1)
                    & ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                      | ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                          | ! [W2: $i] :
                              ( ~ aElementOf0(W2,W1)
                              | aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
                        & ( sbrdtbr0(W1) = xk ) ) ) )
                | ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ) )),
        ( ( aElementOf0(W0,szNzAzT0)
         => ! [W1: $i] :
              ( ( aSet0(W1)
                & ( ( ( ! [W2: $i] :
                          ( aElementOf0(W2,W1)
                         => aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
                      | aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
                    & ( sbrdtbr0(W1) = xk ) )
                  | aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) )
             => ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ! [W1: $i] :
              ( ~ ( aSet0(W1)
                  & ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                    | ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                        | ! [W2: $i] :
                            ( ~ aElementOf0(W2,W1)
                            | aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
                      & ( sbrdtbr0(W1) = xk ) ) ) )
              | ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(272,plain,
    ( ! [W0: $i] :
        ( aElementOf0(W0,szNzAzT0)
       => ! [W1: $i] :
            ( ( aSet0(W1)
              & ( ( ( ! [W2: $i] :
                        ( aElementOf0(W2,W1)
                       => aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
                    | aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
                  & ( sbrdtbr0(W1) = xk ) )
                | aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) )
           => ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ! [W1: $i] :
            ( ~ ( aSet0(W1)
                & ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                  | ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                      | ! [W2: $i] :
                          ( ~ aElementOf0(W2,W1)
                          | aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
                    & ( sbrdtbr0(W1) = xk ) ) ) )
            | ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ) ),
    inference(quant_intro,[status(thm)],[271]) ).

tff(273,axiom,
    ( aFunction0(xd)
    & ( szDzozmdt0(xd) = szNzAzT0 )
    & ! [W0: $i] :
        ( aElementOf0(W0,szNzAzT0)
       => ! [W1: $i] :
            ( ( aSet0(W1)
              & ( ( ( ! [W2: $i] :
                        ( aElementOf0(W2,W1)
                       => aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
                    | aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
                  & ( sbrdtbr0(W1) = xk ) )
                | aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) )
           => ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4730) ).

tff(274,plain,
    ! [W0: $i] :
      ( aElementOf0(W0,szNzAzT0)
     => ! [W1: $i] :
          ( ( aSet0(W1)
            & ( ( ( ! [W2: $i] :
                      ( aElementOf0(W2,W1)
                     => aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
                  | aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0))) )
                & ( sbrdtbr0(W1) = xk ) )
              | aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) ) )
         => ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ),
    inference(and_elim,[status(thm)],[273]) ).

tff(275,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ! [W1: $i] :
          ( ~ ( aSet0(W1)
              & ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                | ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                    | ! [W2: $i] :
                        ( ~ aElementOf0(W2,W1)
                        | aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
                  & ( sbrdtbr0(W1) = xk ) ) ) )
          | ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ),
    inference(modus_ponens,[status(thm)],[274,272]) ).

tff(276,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ! [W1: $i] :
          ( ~ ( aSet0(W1)
              & ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                | ( ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                    | ! [W2: $i] :
                        ( ~ aElementOf0(W2,W1)
                        | aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
                  & ( sbrdtbr0(W1) = xk ) ) ) )
          | ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ),
    inference(modus_ponens,[status(thm)],[275,270]) ).

tff(277,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ! [W1: $i] :
          ( ~ aSet0(W1)
          | ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
            & ( ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                & ~ ( ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
                    | aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) )
              | ( sbrdtbr0(W1) != xk ) ) )
          | ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ),
    inference(skolemize,[status(sab)],[276]) ).

tff(278,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ! [W1: $i] :
          ( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
          | ~ aSet0(W1)
          | ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
            & ( ( sbrdtbr0(W1) != xk )
              | ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                & ~ ( ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
                    | aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ) ),
    inference(modus_ponens,[status(thm)],[277,269]) ).

tff(279,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ! [W1: $i] :
          ( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
          | ~ aSet0(W1)
          | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
              | ~ ( ( sbrdtbr0(W1) != xk )
                  | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                      | ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
                      | aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ),
    inference(modus_ponens,[status(thm)],[278,267]) ).

tff(280,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ! [W1: $i] :
          ( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
          | ~ aSet0(W1)
          | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
              | ~ ( ( sbrdtbr0(W1) != xk )
                  | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                      | ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
                      | aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) ),
    inference(modus_ponens,[status(thm)],[279,265]) ).

tff(281,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ! [W1: $i] :
                ( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
                | ~ aSet0(W1)
                | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                    | ~ ( ( sbrdtbr0(W1) != xk )
                        | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                            | ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
                            | aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ! [W1: $i] :
          ( ~ aSet0(W1)
          | ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
          | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
              | ~ ( ( sbrdtbr0(W1) != xk )
                  | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                      | ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
                      | aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) )
  <=> ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ! [W1: $i] :
                ( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
                | ~ aSet0(W1)
                | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                    | ~ ( ( sbrdtbr0(W1) != xk )
                        | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                            | ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
                            | aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ! [W1: $i] :
          ( ~ aSet0(W1)
          | ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
          | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
              | ~ ( ( sbrdtbr0(W1) != xk )
                  | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                      | ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
                      | aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(282,plain,
    ( ( ~ aElementOf0(xn,szNzAzT0)
      | ! [W1: $i] :
          ( ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
          | ~ aSet0(W1)
          | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
              | ~ ( ( sbrdtbr0(W1) != xk )
                  | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                      | ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
                      | aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) )
  <=> ( ~ aElementOf0(xn,szNzAzT0)
      | ! [W1: $i] :
          ( ~ aSet0(W1)
          | ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
          | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
              | ~ ( ( sbrdtbr0(W1) != xk )
                  | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                      | ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
                      | aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(283,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ! [W1: $i] :
                ( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
                | ~ aSet0(W1)
                | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                    | ~ ( ( sbrdtbr0(W1) != xk )
                        | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                            | ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
                            | aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ! [W1: $i] :
          ( ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
          | ~ aSet0(W1)
          | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
              | ~ ( ( sbrdtbr0(W1) != xk )
                  | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                      | ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
                      | aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) )
  <=> ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ! [W1: $i] :
                ( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
                | ~ aSet0(W1)
                | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                    | ~ ( ( sbrdtbr0(W1) != xk )
                        | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                            | ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
                            | aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ! [W1: $i] :
          ( ~ aSet0(W1)
          | ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
          | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
              | ~ ( ( sbrdtbr0(W1) != xk )
                  | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                      | ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
                      | aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) ) ),
    inference(monotonicity,[status(thm)],[282]) ).

tff(284,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ! [W1: $i] :
                ( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
                | ~ aSet0(W1)
                | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                    | ~ ( ( sbrdtbr0(W1) != xk )
                        | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                            | ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
                            | aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ! [W1: $i] :
          ( ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
          | ~ aSet0(W1)
          | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
              | ~ ( ( sbrdtbr0(W1) != xk )
                  | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                      | ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
                      | aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) )
  <=> ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ! [W1: $i] :
                ( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
                | ~ aSet0(W1)
                | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                    | ~ ( ( sbrdtbr0(W1) != xk )
                        | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                            | ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
                            | aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ! [W1: $i] :
          ( ~ aSet0(W1)
          | ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
          | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
              | ~ ( ( sbrdtbr0(W1) != xk )
                  | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                      | ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
                      | aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) ) ),
    inference(transitivity,[status(thm)],[283,281]) ).

tff(285,plain,
    ( ~ ! [W0: $i] :
          ( ~ aElementOf0(W0,szNzAzT0)
          | ! [W1: $i] :
              ( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
              | ~ aSet0(W1)
              | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                  | ~ ( ( sbrdtbr0(W1) != xk )
                      | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                          | ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
                          | aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
    | ~ aElementOf0(xn,szNzAzT0)
    | ! [W1: $i] :
        ( ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
        | ~ aSet0(W1)
        | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
            | ~ ( ( sbrdtbr0(W1) != xk )
                | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                    | ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
                    | aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(286,plain,
    ( ~ ! [W0: $i] :
          ( ~ aElementOf0(W0,szNzAzT0)
          | ! [W1: $i] :
              ( ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) )
              | ~ aSet0(W1)
              | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
                  | ~ ( ( sbrdtbr0(W1) != xk )
                      | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
                          | ~ aElementOf0(tptp_fun_W2_39(W1,W0),W1)
                          | aElementOf0(tptp_fun_W2_39(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ) )
    | ~ aElementOf0(xn,szNzAzT0)
    | ! [W1: $i] :
        ( ~ aSet0(W1)
        | ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
        | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
            | ~ ( ( sbrdtbr0(W1) != xk )
                | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                    | ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
                    | aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) ),
    inference(modus_ponens,[status(thm)],[285,284]) ).

tff(287,plain,
    ! [W1: $i] :
      ( ~ aSet0(W1)
      | ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
      | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
          | ~ ( ( sbrdtbr0(W1) != xk )
              | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                  | ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
                  | aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ),
    inference(unit_resolution,[status(thm)],[286,280,28]) ).

tff(288,plain,
    ( ( ~ ! [W1: $i] :
            ( ~ aSet0(W1)
            | ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
            | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
                | ~ ( ( sbrdtbr0(W1) != xk )
                    | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                        | ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
                        | aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
      | ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
      | ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) )
      | ~ ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
          | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
              | ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                  | ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
                  | aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
  <=> ( ~ ! [W1: $i] :
            ( ~ aSet0(W1)
            | ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
            | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
                | ~ ( ( sbrdtbr0(W1) != xk )
                    | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                        | ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
                        | aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
      | ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
      | ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) )
      | ~ ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
          | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
              | ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                  | ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
                  | aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(289,plain,
    ( ~ ! [W1: $i] :
          ( ~ aSet0(W1)
          | ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
          | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
              | ~ ( ( sbrdtbr0(W1) != xk )
                  | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                      | ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
                      | aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
    | ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
    | ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) )
    | ~ ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
        | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
            | ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                | ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
                | aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(290,plain,
    ( ~ ! [W1: $i] :
          ( ~ aSet0(W1)
          | ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) )
          | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
              | ~ ( ( sbrdtbr0(W1) != xk )
                  | ~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                      | ~ aElementOf0(tptp_fun_W2_39(W1,xn),W1)
                      | aElementOf0(tptp_fun_W2_39(W1,xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) )
    | ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
    | ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) )
    | ~ ( aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xn)),xk))
        | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
            | ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
                | ~ aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
                | aElementOf0(tptp_fun_W2_39(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ),
    inference(modus_ponens,[status(thm)],[289,288]) ).

tff(291,plain,
    sdtlpdtrp0(xd,xn) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))),
    inference(unit_resolution,[status(thm)],[290,170,287,260]) ).

tff(292,plain,
    sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) = sdtlpdtrp0(xd,xn),
    inference(symmetry,[status(thm)],[291]) ).

tff(293,plain,
    ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) = sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
  <=> ( sdtlpdtrp0(xd,xn) = sdtlpdtrp0(xc,xQ) ) ),
    inference(monotonicity,[status(thm)],[292,254]) ).

tff(294,plain,
    ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) = sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
  <=> ( sdtlpdtrp0(xc,xQ) = sdtlpdtrp0(xd,xn) ) ),
    inference(transitivity,[status(thm)],[293,180]) ).

tff(295,plain,
    ( ( sdtlpdtrp0(xc,xQ) = sdtlpdtrp0(xd,xn) )
  <=> ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) = sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ),
    inference(symmetry,[status(thm)],[294]) ).

tff(296,plain,
    ( ( sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn) )
  <=> ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ),
    inference(monotonicity,[status(thm)],[295]) ).

tff(297,plain,
    ( ( sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn) )
  <=> ( sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(298,axiom,
    sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

tff(299,plain,
    sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn),
    inference(modus_ponens,[status(thm)],[298,297]) ).

tff(300,plain,
    sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))),
    inference(modus_ponens,[status(thm)],[299,296]) ).

tff(301,plain,
    ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
    | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
    | ~ ! [W2: $i] :
          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
    | ~ ! [W2: $i] :
          ~ ( ( ~ aElement0(W2)
              | ~ ( aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
                  | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
          <=> aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
    | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) = sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ),
    inference(tautology,[status(thm)],[]) ).

tff(302,plain,
    ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
    | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
    | ~ ! [W2: $i] :
          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
    | ~ ! [W2: $i] :
          ~ ( ( ~ aElement0(W2)
              | ~ ( aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
                  | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
          <=> aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ),
    inference(unit_resolution,[status(thm)],[301,300]) ).

tff(303,plain,
    ^ [W0: $i] :
      rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ ! [W1: $i] :
                    ~ ( ( ~ aElement0(W1)
                        | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                    <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              | ~ aFunction0(sdtlpdtrp0(xC,W0))
              | ~ ! [W1: $i] :
                    ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                          | ~ ( ~ aSet0(W1)
                              | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ~ ! [W2: $i] :
                                    ( ~ aElementOf0(W2,W1)
                                    | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                              | ( sbrdtbr0(W1) != xk ) ) )
                      | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                          | ( sbrdtbr0(W1) != xk )
                          | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ~ ( ~ aSet0(W1)
                                  | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                      | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
              | ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
              | ~ ! [W1: $i] :
                    ( ~ aSet0(W1)
                    | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                        | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        | ~ ! [W2: $i] :
                              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                        | ~ ( ( sbrdtbr0(W1) != xk )
                            | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                | ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                        | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        | ~ ! [W2: $i] :
                              ~ ( ( ~ aElement0(W2)
                                  | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                  | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                              <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                    | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        | ~ ! [W2: $i] :
                              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                        | ~ ! [W2: $i] :
                              ~ ( ( ~ aElement0(W2)
                                  | ~ ( aElementOf0(W2,W1)
                                      | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                              <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                        | ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ aFunction0(sdtlpdtrp0(xC,W0))
              | ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              | ~ ! [W1: $i] :
                    ~ ( ( ~ aElement0(W1)
                        | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                    <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              | ~ ! [W1: $i] :
                    ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                          | ~ ( ~ aSet0(W1)
                              | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ( sbrdtbr0(W1) != xk )
                              | ~ ! [W2: $i] :
                                    ( ~ aElementOf0(W2,W1)
                                    | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                      | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                          | ( sbrdtbr0(W1) != xk )
                          | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ~ ( ~ aSet0(W1)
                                  | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                      | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
              | ~ ! [W1: $i] :
                    ( ~ aSet0(W1)
                    | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                        | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        | ~ ( ( sbrdtbr0(W1) != xk )
                            | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                | ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                        | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        | ~ ! [W2: $i] :
                              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                        | ~ ! [W2: $i] :
                              ~ ( ( ~ aElement0(W2)
                                  | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                  | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                              <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                    | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        | ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                        | ~ ! [W2: $i] :
                              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                        | ~ ! [W2: $i] :
                              ~ ( ( ~ aElement0(W2)
                                  | ~ ( aElementOf0(W2,W1)
                                      | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                              <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(304,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ ! [W1: $i] :
                  ~ ( ( ~ aElement0(W1)
                      | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                  <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ aFunction0(sdtlpdtrp0(xC,W0))
            | ~ ! [W1: $i] :
                  ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                        | ~ ( ~ aSet0(W1)
                            | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            | ~ ! [W2: $i] :
                                  ( ~ aElementOf0(W2,W1)
                                  | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                            | ( sbrdtbr0(W1) != xk ) ) )
                    | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                        | ( sbrdtbr0(W1) != xk )
                        | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            | ~ ( ~ aSet0(W1)
                                | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                    | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
            | ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
            | ~ ! [W1: $i] :
                  ( ~ aSet0(W1)
                  | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                      | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      | ~ ! [W2: $i] :
                            ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                      | ~ ( ( sbrdtbr0(W1) != xk )
                          | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                              | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                      | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ ! [W2: $i] :
                            ~ ( ( ~ aElement0(W2)
                                | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                            <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                  | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      | ~ ! [W2: $i] :
                            ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                      | ~ ! [W2: $i] :
                            ~ ( ( ~ aElement0(W2)
                                | ~ ( aElementOf0(W2,W1)
                                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                            <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      | ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ aFunction0(sdtlpdtrp0(xC,W0))
            | ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            | ~ ! [W1: $i] :
                  ~ ( ( ~ aElement0(W1)
                      | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                  <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ ! [W1: $i] :
                  ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                        | ~ ( ~ aSet0(W1)
                            | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            | ( sbrdtbr0(W1) != xk )
                            | ~ ! [W2: $i] :
                                  ( ~ aElementOf0(W2,W1)
                                  | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                    | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                        | ( sbrdtbr0(W1) != xk )
                        | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            | ~ ( ~ aSet0(W1)
                                | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                    | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
            | ~ ! [W1: $i] :
                  ( ~ aSet0(W1)
                  | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                      | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      | ~ ( ( sbrdtbr0(W1) != xk )
                          | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                              | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                      | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ ! [W2: $i] :
                            ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                      | ~ ! [W2: $i] :
                            ~ ( ( ~ aElement0(W2)
                                | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                            <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                  | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      | ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      | ~ ! [W2: $i] :
                            ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                      | ~ ! [W2: $i] :
                            ~ ( ( ~ aElement0(W2)
                                | ~ ( aElementOf0(W2,W1)
                                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                            <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ) ),
    inference(quant_intro,[status(thm)],[303]) ).

tff(305,plain,
    ^ [W0: $i] :
      refl(( ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ ! [W1: $i] :
                    ~ ( ( ~ aElement0(W1)
                        | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                    <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              | ~ aFunction0(sdtlpdtrp0(xC,W0))
              | ~ ! [W1: $i] :
                    ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                          | ~ ( ~ aSet0(W1)
                              | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ~ ! [W2: $i] :
                                    ( ~ aElementOf0(W2,W1)
                                    | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                              | ( sbrdtbr0(W1) != xk ) ) )
                      | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                          | ( sbrdtbr0(W1) != xk )
                          | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ~ ( ~ aSet0(W1)
                                  | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                      | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
              | ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
              | ~ ! [W1: $i] :
                    ( ~ aSet0(W1)
                    | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                        | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        | ~ ! [W2: $i] :
                              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                        | ~ ( ( sbrdtbr0(W1) != xk )
                            | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                | ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                        | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        | ~ ! [W2: $i] :
                              ~ ( ( ~ aElement0(W2)
                                  | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                  | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                              <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                    | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        | ~ ! [W2: $i] :
                              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                        | ~ ! [W2: $i] :
                              ~ ( ( ~ aElement0(W2)
                                  | ~ ( aElementOf0(W2,W1)
                                      | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                              <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                        | ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ ! [W1: $i] :
                    ~ ( ( ~ aElement0(W1)
                        | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                    <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              | ~ aFunction0(sdtlpdtrp0(xC,W0))
              | ~ ! [W1: $i] :
                    ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                          | ~ ( ~ aSet0(W1)
                              | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ~ ! [W2: $i] :
                                    ( ~ aElementOf0(W2,W1)
                                    | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                              | ( sbrdtbr0(W1) != xk ) ) )
                      | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                          | ( sbrdtbr0(W1) != xk )
                          | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ~ ( ~ aSet0(W1)
                                  | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                      | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
              | ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
              | ~ ! [W1: $i] :
                    ( ~ aSet0(W1)
                    | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                        | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        | ~ ! [W2: $i] :
                              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                        | ~ ( ( sbrdtbr0(W1) != xk )
                            | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                | ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                        | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        | ~ ! [W2: $i] :
                              ~ ( ( ~ aElement0(W2)
                                  | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                  | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                              <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                    | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        | ~ ! [W2: $i] :
                              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                        | ~ ! [W2: $i] :
                              ~ ( ( ~ aElement0(W2)
                                  | ~ ( aElementOf0(W2,W1)
                                      | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                              <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                        | ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(306,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ ! [W1: $i] :
                  ~ ( ( ~ aElement0(W1)
                      | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                  <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ aFunction0(sdtlpdtrp0(xC,W0))
            | ~ ! [W1: $i] :
                  ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                        | ~ ( ~ aSet0(W1)
                            | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            | ~ ! [W2: $i] :
                                  ( ~ aElementOf0(W2,W1)
                                  | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                            | ( sbrdtbr0(W1) != xk ) ) )
                    | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                        | ( sbrdtbr0(W1) != xk )
                        | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            | ~ ( ~ aSet0(W1)
                                | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                    | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
            | ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
            | ~ ! [W1: $i] :
                  ( ~ aSet0(W1)
                  | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                      | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      | ~ ! [W2: $i] :
                            ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                      | ~ ( ( sbrdtbr0(W1) != xk )
                          | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                              | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                      | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ ! [W2: $i] :
                            ~ ( ( ~ aElement0(W2)
                                | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                            <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                  | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      | ~ ! [W2: $i] :
                            ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                      | ~ ! [W2: $i] :
                            ~ ( ( ~ aElement0(W2)
                                | ~ ( aElementOf0(W2,W1)
                                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                            <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      | ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ ! [W1: $i] :
                  ~ ( ( ~ aElement0(W1)
                      | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                  <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ aFunction0(sdtlpdtrp0(xC,W0))
            | ~ ! [W1: $i] :
                  ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                        | ~ ( ~ aSet0(W1)
                            | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            | ~ ! [W2: $i] :
                                  ( ~ aElementOf0(W2,W1)
                                  | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                            | ( sbrdtbr0(W1) != xk ) ) )
                    | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                        | ( sbrdtbr0(W1) != xk )
                        | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            | ~ ( ~ aSet0(W1)
                                | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                    | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
            | ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
            | ~ ! [W1: $i] :
                  ( ~ aSet0(W1)
                  | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                      | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      | ~ ! [W2: $i] :
                            ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                      | ~ ( ( sbrdtbr0(W1) != xk )
                          | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                              | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                      | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ ! [W2: $i] :
                            ~ ( ( ~ aElement0(W2)
                                | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                            <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                  | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      | ~ ! [W2: $i] :
                            ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                      | ~ ! [W2: $i] :
                            ~ ( ( ~ aElement0(W2)
                                | ~ ( aElementOf0(W2,W1)
                                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                            <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      | ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ) ),
    inference(quant_intro,[status(thm)],[305]) ).

tff(307,plain,
    ^ [W0: $i] :
      rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ ! [W1: $i] :
                    ~ ( ( ~ aElement0(W1)
                        | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                    <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              | ~ aFunction0(sdtlpdtrp0(xC,W0))
              | ~ ! [W1: $i] :
                    ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                          | ~ ( ~ aSet0(W1)
                              | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ~ ! [W2: $i] :
                                    ( ~ aElementOf0(W2,W1)
                                    | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                              | ( sbrdtbr0(W1) != xk ) ) )
                      | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                          | ( sbrdtbr0(W1) != xk )
                          | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ~ ( ~ aSet0(W1)
                                  | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                      | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
              | ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
              | ~ ! [W1: $i] :
                    ( ~ aSet0(W1)
                    | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                        | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        | ~ ! [W2: $i] :
                              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                        | ~ ( ( sbrdtbr0(W1) != xk )
                            | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                | ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                        | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        | ~ ! [W2: $i] :
                              ~ ( ( ~ aElement0(W2)
                                  | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                  | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                              <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                    | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        | ~ ! [W2: $i] :
                              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                        | ~ ! [W2: $i] :
                              ~ ( ( ~ aElement0(W2)
                                  | ~ ( aElementOf0(W2,W1)
                                      | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                              <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                        | ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ ! [W1: $i] :
                    ~ ( ( ~ aElement0(W1)
                        | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                    <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              | ~ aFunction0(sdtlpdtrp0(xC,W0))
              | ~ ! [W1: $i] :
                    ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                          | ~ ( ~ aSet0(W1)
                              | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ~ ! [W2: $i] :
                                    ( ~ aElementOf0(W2,W1)
                                    | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                              | ( sbrdtbr0(W1) != xk ) ) )
                      | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                          | ( sbrdtbr0(W1) != xk )
                          | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ~ ( ~ aSet0(W1)
                                  | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                      | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
              | ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
              | ~ ! [W1: $i] :
                    ( ~ aSet0(W1)
                    | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                        | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        | ~ ! [W2: $i] :
                              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                        | ~ ( ( sbrdtbr0(W1) != xk )
                            | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                | ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                        | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        | ~ ! [W2: $i] :
                              ~ ( ( ~ aElement0(W2)
                                  | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                  | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                              <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                    | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        | ~ ! [W2: $i] :
                              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                        | ~ ! [W2: $i] :
                              ~ ( ( ~ aElement0(W2)
                                  | ~ ( aElementOf0(W2,W1)
                                      | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                              <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                        | ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(308,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ ! [W1: $i] :
                  ~ ( ( ~ aElement0(W1)
                      | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                  <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ aFunction0(sdtlpdtrp0(xC,W0))
            | ~ ! [W1: $i] :
                  ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                        | ~ ( ~ aSet0(W1)
                            | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            | ~ ! [W2: $i] :
                                  ( ~ aElementOf0(W2,W1)
                                  | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                            | ( sbrdtbr0(W1) != xk ) ) )
                    | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                        | ( sbrdtbr0(W1) != xk )
                        | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            | ~ ( ~ aSet0(W1)
                                | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                    | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
            | ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
            | ~ ! [W1: $i] :
                  ( ~ aSet0(W1)
                  | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                      | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      | ~ ! [W2: $i] :
                            ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                      | ~ ( ( sbrdtbr0(W1) != xk )
                          | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                              | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                      | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ ! [W2: $i] :
                            ~ ( ( ~ aElement0(W2)
                                | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                            <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                  | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      | ~ ! [W2: $i] :
                            ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                      | ~ ! [W2: $i] :
                            ~ ( ( ~ aElement0(W2)
                                | ~ ( aElementOf0(W2,W1)
                                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                            <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      | ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ ! [W1: $i] :
                  ~ ( ( ~ aElement0(W1)
                      | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                  <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ aFunction0(sdtlpdtrp0(xC,W0))
            | ~ ! [W1: $i] :
                  ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                        | ~ ( ~ aSet0(W1)
                            | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            | ~ ! [W2: $i] :
                                  ( ~ aElementOf0(W2,W1)
                                  | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                            | ( sbrdtbr0(W1) != xk ) ) )
                    | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                        | ( sbrdtbr0(W1) != xk )
                        | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            | ~ ( ~ aSet0(W1)
                                | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                    | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
            | ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
            | ~ ! [W1: $i] :
                  ( ~ aSet0(W1)
                  | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                      | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      | ~ ! [W2: $i] :
                            ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                      | ~ ( ( sbrdtbr0(W1) != xk )
                          | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                              | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                      | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ ! [W2: $i] :
                            ~ ( ( ~ aElement0(W2)
                                | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                            <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                  | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      | ~ ! [W2: $i] :
                            ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                      | ~ ! [W2: $i] :
                            ~ ( ( ~ aElement0(W2)
                                | ~ ( aElementOf0(W2,W1)
                                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                            <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      | ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ) ),
    inference(quant_intro,[status(thm)],[307]) ).

tff(309,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ ! [W1: $i] :
                  ~ ( ( ~ aElement0(W1)
                      | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                  <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ aFunction0(sdtlpdtrp0(xC,W0))
            | ~ ! [W1: $i] :
                  ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                        | ~ ( ~ aSet0(W1)
                            | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            | ~ ! [W2: $i] :
                                  ( ~ aElementOf0(W2,W1)
                                  | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                            | ( sbrdtbr0(W1) != xk ) ) )
                    | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                        | ( sbrdtbr0(W1) != xk )
                        | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            | ~ ( ~ aSet0(W1)
                                | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                    | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
            | ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
            | ~ ! [W1: $i] :
                  ( ~ aSet0(W1)
                  | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                      | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      | ~ ! [W2: $i] :
                            ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                      | ~ ( ( sbrdtbr0(W1) != xk )
                          | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                              | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                      | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ ! [W2: $i] :
                            ~ ( ( ~ aElement0(W2)
                                | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                            <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                  | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      | ~ ! [W2: $i] :
                            ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                      | ~ ! [W2: $i] :
                            ~ ( ( ~ aElement0(W2)
                                | ~ ( aElementOf0(W2,W1)
                                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                            <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      | ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ ! [W1: $i] :
                  ~ ( ( ~ aElement0(W1)
                      | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                  <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ aFunction0(sdtlpdtrp0(xC,W0))
            | ~ ! [W1: $i] :
                  ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                        | ~ ( ~ aSet0(W1)
                            | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            | ~ ! [W2: $i] :
                                  ( ~ aElementOf0(W2,W1)
                                  | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                            | ( sbrdtbr0(W1) != xk ) ) )
                    | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                        | ( sbrdtbr0(W1) != xk )
                        | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            | ~ ( ~ aSet0(W1)
                                | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                    | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
            | ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
            | ~ ! [W1: $i] :
                  ( ~ aSet0(W1)
                  | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                      | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      | ~ ! [W2: $i] :
                            ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                      | ~ ( ( sbrdtbr0(W1) != xk )
                          | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                              | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                      | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ ! [W2: $i] :
                            ~ ( ( ~ aElement0(W2)
                                | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                            <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                  | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      | ~ ! [W2: $i] :
                            ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                      | ~ ! [W2: $i] :
                            ~ ( ( ~ aElement0(W2)
                                | ~ ( aElementOf0(W2,W1)
                                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                            <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      | ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ) ),
    inference(transitivity,[status(thm)],[308,306]) ).

tff(310,plain,
    ^ [W0: $i] :
      rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
          | ( aFunction0(sdtlpdtrp0(xC,W0))
            & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            & ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            & ! [W1: $i] :
                ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              <=> ( aElement0(W1)
                  & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
            & ! [W1: $i] :
                ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                  | ( aSet0(W1)
                    & ! [W2: $i] :
                        ( ~ aElementOf0(W2,W1)
                        | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & ( sbrdtbr0(W1) = xk ) ) )
                & ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                  | ( sbrdtbr0(W1) != xk )
                  | ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & ( ~ aSet0(W1)
                      | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                          | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
            & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
            & ! [W1: $i] :
                ( ~ aSet0(W1)
                | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  & ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                  & ! [W2: $i] :
                      ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                    <=> ( aElement0(W2)
                        & ( aElementOf0(W2,W1)
                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                  & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                | ( ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                  & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  & ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                  & ( ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                          | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                    | ( sbrdtbr0(W1) != xk ) )
                  & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ! [W2: $i] :
                      ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    <=> ( aElement0(W2)
                        & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                        & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ ! [W1: $i] :
                    ~ ( ( ~ aElement0(W1)
                        | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                    <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              | ~ aFunction0(sdtlpdtrp0(xC,W0))
              | ~ ! [W1: $i] :
                    ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                          | ~ ( ~ aSet0(W1)
                              | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ~ ! [W2: $i] :
                                    ( ~ aElementOf0(W2,W1)
                                    | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                              | ( sbrdtbr0(W1) != xk ) ) )
                      | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                          | ( sbrdtbr0(W1) != xk )
                          | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ~ ( ~ aSet0(W1)
                                  | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                      | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
              | ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
              | ~ ! [W1: $i] :
                    ( ~ aSet0(W1)
                    | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                        | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        | ~ ! [W2: $i] :
                              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                        | ~ ( ( sbrdtbr0(W1) != xk )
                            | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                | ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                        | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        | ~ ! [W2: $i] :
                              ~ ( ( ~ aElement0(W2)
                                  | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                  | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                              <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                    | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        | ~ ! [W2: $i] :
                              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                        | ~ ! [W2: $i] :
                              ~ ( ( ~ aElement0(W2)
                                  | ~ ( aElementOf0(W2,W1)
                                      | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                              <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                        | ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(311,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ( aFunction0(sdtlpdtrp0(xC,W0))
          & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
          & ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
          & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          & ! [W1: $i] :
              ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            <=> ( aElement0(W1)
                & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
          & ! [W1: $i] :
              ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                | ( aSet0(W1)
                  & ! [W2: $i] :
                      ( ~ aElementOf0(W2,W1)
                      | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ( sbrdtbr0(W1) = xk ) ) )
              & ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                | ( sbrdtbr0(W1) != xk )
                | ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ( ~ aSet0(W1)
                    | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                        | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
          & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
          & ! [W1: $i] :
              ( ~ aSet0(W1)
              | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                & ! [W2: $i] :
                    ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W2)
                      & ( aElementOf0(W2,W1)
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
              | ( ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                & ( ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                        | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                  | ( sbrdtbr0(W1) != xk ) )
                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & ! [W2: $i] :
                    ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W2)
                      & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                      & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            | ~ ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            | ~ ! [W1: $i] :
                  ~ ( ( ~ aElement0(W1)
                      | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                  <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
            | ~ aFunction0(sdtlpdtrp0(xC,W0))
            | ~ ! [W1: $i] :
                  ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                        | ~ ( ~ aSet0(W1)
                            | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            | ~ ! [W2: $i] :
                                  ( ~ aElementOf0(W2,W1)
                                  | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                            | ( sbrdtbr0(W1) != xk ) ) )
                    | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                        | ( sbrdtbr0(W1) != xk )
                        | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            | ~ ( ~ aSet0(W1)
                                | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                    | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
            | ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
            | ~ ! [W1: $i] :
                  ( ~ aSet0(W1)
                  | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                      | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      | ~ ! [W2: $i] :
                            ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                      | ~ ( ( sbrdtbr0(W1) != xk )
                          | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                              | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                      | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ~ ! [W2: $i] :
                            ~ ( ( ~ aElement0(W2)
                                | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                            <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                  | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      | ~ ! [W2: $i] :
                            ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                      | ~ ! [W2: $i] :
                            ~ ( ( ~ aElement0(W2)
                                | ~ ( aElementOf0(W2,W1)
                                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                            <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      | ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ) ),
    inference(quant_intro,[status(thm)],[310]) ).

tff(312,plain,
    ^ [W0: $i] :
      rewrite(( ( ~ aElementOf0(W0,szNzAzT0)
          | ( aFunction0(sdtlpdtrp0(xC,W0))
            & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            & ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            & ! [W1: $i] :
                ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              <=> ( aElement0(W1)
                  & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
            & ! [W1: $i] :
                ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                  | ( aSet0(W1)
                    & ! [W2: $i] :
                        ( ~ aElementOf0(W2,W1)
                        | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & ( sbrdtbr0(W1) = xk ) ) )
                & ( ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & ( ~ aSet0(W1)
                      | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                          | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                  | ( sbrdtbr0(W1) != xk )
                  | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
            & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
            & ! [W1: $i] :
                ( ~ aSet0(W1)
                | ( ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                  & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  & ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                  & ( ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                          | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                    | ( sbrdtbr0(W1) != xk ) )
                  & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ! [W2: $i] :
                      ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    <=> ( aElement0(W2)
                        & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                        & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  & ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                  & ! [W2: $i] :
                      ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                    <=> ( aElement0(W2)
                        & ( aElementOf0(W2,W1)
                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                  & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ( aFunction0(sdtlpdtrp0(xC,W0))
            & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            & ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            & ! [W1: $i] :
                ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              <=> ( aElement0(W1)
                  & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
            & ! [W1: $i] :
                ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                  | ( aSet0(W1)
                    & ! [W2: $i] :
                        ( ~ aElementOf0(W2,W1)
                        | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & ( sbrdtbr0(W1) = xk ) ) )
                & ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                  | ( sbrdtbr0(W1) != xk )
                  | ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & ( ~ aSet0(W1)
                      | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                          | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
            & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
            & ! [W1: $i] :
                ( ~ aSet0(W1)
                | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  & ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                  & ! [W2: $i] :
                      ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                    <=> ( aElement0(W2)
                        & ( aElementOf0(W2,W1)
                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                  & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                | ( ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                  & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  & ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                  & ( ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                          | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                    | ( sbrdtbr0(W1) != xk ) )
                  & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ! [W2: $i] :
                      ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    <=> ( aElement0(W2)
                        & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                        & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(313,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ( aFunction0(sdtlpdtrp0(xC,W0))
          & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
          & ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
          & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          & ! [W1: $i] :
              ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            <=> ( aElement0(W1)
                & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
          & ! [W1: $i] :
              ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                | ( aSet0(W1)
                  & ! [W2: $i] :
                      ( ~ aElementOf0(W2,W1)
                      | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ( sbrdtbr0(W1) = xk ) ) )
              & ( ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ( ~ aSet0(W1)
                    | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                        | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                | ( sbrdtbr0(W1) != xk )
                | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
          & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
          & ! [W1: $i] :
              ( ~ aSet0(W1)
              | ( ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                & ( ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                        | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                  | ( sbrdtbr0(W1) != xk ) )
                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & ! [W2: $i] :
                    ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W2)
                      & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                      & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
              | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                & ! [W2: $i] :
                    ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W2)
                      & ( aElementOf0(W2,W1)
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ( aFunction0(sdtlpdtrp0(xC,W0))
          & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
          & ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
          & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          & ! [W1: $i] :
              ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            <=> ( aElement0(W1)
                & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
          & ! [W1: $i] :
              ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                | ( aSet0(W1)
                  & ! [W2: $i] :
                      ( ~ aElementOf0(W2,W1)
                      | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ( sbrdtbr0(W1) = xk ) ) )
              & ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                | ( sbrdtbr0(W1) != xk )
                | ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ( ~ aSet0(W1)
                    | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                        | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
          & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
          & ! [W1: $i] :
              ( ~ aSet0(W1)
              | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                & ! [W2: $i] :
                    ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W2)
                      & ( aElementOf0(W2,W1)
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
              | ( ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                & ( ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                        | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                  | ( sbrdtbr0(W1) != xk ) )
                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & ! [W2: $i] :
                    ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W2)
                      & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                      & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ) ) ) ),
    inference(quant_intro,[status(thm)],[312]) ).

tff(314,plain,
    ( ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ( aFunction0(sdtlpdtrp0(xC,W0))
          & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
          & ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
          & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          & ! [W1: $i] :
              ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            <=> ( aElement0(W1)
                & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
          & ! [W1: $i] :
              ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                | ( aSet0(W1)
                  & ! [W2: $i] :
                      ( ~ aElementOf0(W2,W1)
                      | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ( sbrdtbr0(W1) = xk ) ) )
              & ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ( aSet0(W1)
                        & ! [W2: $i] :
                            ( ~ aElementOf0(W2,W1)
                            | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                    & ( sbrdtbr0(W1) = xk ) )
                | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
          & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
          & ! [W1: $i] :
              ( ~ ( aSet0(W1)
                  & ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                    | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        & ! [W2: $i] :
                            ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                    | ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        | ! [W2: $i] :
                            ( ~ aElementOf0(W2,W1)
                            | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                      & ( sbrdtbr0(W1) = xk ) )
                    | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        & ! [W2: $i] :
                            ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          <=> ( aElement0(W2)
                              & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ) )
              | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                & ! [W2: $i] :
                    ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W2)
                      & ( aElementOf0(W2,W1)
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ( aFunction0(sdtlpdtrp0(xC,W0))
          & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
          & ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
          & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          & ! [W1: $i] :
              ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            <=> ( aElement0(W1)
                & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
          & ! [W1: $i] :
              ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                | ( aSet0(W1)
                  & ! [W2: $i] :
                      ( ~ aElementOf0(W2,W1)
                      | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ( sbrdtbr0(W1) = xk ) ) )
              & ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ( aSet0(W1)
                        & ! [W2: $i] :
                            ( ~ aElementOf0(W2,W1)
                            | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                    & ( sbrdtbr0(W1) = xk ) )
                | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
          & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
          & ! [W1: $i] :
              ( ~ ( aSet0(W1)
                  & ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                    | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        & ! [W2: $i] :
                            ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                    | ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        | ! [W2: $i] :
                            ( ~ aElementOf0(W2,W1)
                            | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                      & ( sbrdtbr0(W1) = xk ) )
                    | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        & ! [W2: $i] :
                            ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          <=> ( aElement0(W2)
                              & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ) )
              | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                & ! [W2: $i] :
                    ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W2)
                      & ( aElementOf0(W2,W1)
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(315,plain,
    ^ [W0: $i] :
      trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
                                        rewrite(( ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                           => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                                        <=> ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) ) ))),
                                    ( ! [W1: $i] :
                                        ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                                  <=> ! [W1: $i] :
                                        ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) ) )),
                                  ( ( aFunction0(sdtlpdtrp0(xC,W0))
                                    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                    & ! [W1: $i] :
                                        ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) ) )
                                <=> ( aFunction0(sdtlpdtrp0(xC,W0))
                                    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                    & ! [W1: $i] :
                                        ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) ) ) )),
                                rewrite(( ( aFunction0(sdtlpdtrp0(xC,W0))
                                    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                    & ! [W1: $i] :
                                        ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) ) )
                                <=> ( aFunction0(sdtlpdtrp0(xC,W0))
                                    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                    & ! [W1: $i] :
                                        ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) ) ) )),
                                ( ( aFunction0(sdtlpdtrp0(xC,W0))
                                  & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                  & ! [W1: $i] :
                                      ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                     => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) ) )
                              <=> ( aFunction0(sdtlpdtrp0(xC,W0))
                                  & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                  & ! [W1: $i] :
                                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) ) ) )),
                              ( ( aFunction0(sdtlpdtrp0(xC,W0))
                                & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                & ! [W1: $i] :
                                    ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                   => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                            <=> ( aFunction0(sdtlpdtrp0(xC,W0))
                                & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                & ! [W1: $i] :
                                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
                            rewrite(( ( aFunction0(sdtlpdtrp0(xC,W0))
                                & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                & ! [W1: $i] :
                                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                            <=> ( aFunction0(sdtlpdtrp0(xC,W0))
                                & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                & ! [W1: $i] :
                                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
                            ( ( aFunction0(sdtlpdtrp0(xC,W0))
                              & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                              & ! [W1: $i] :
                                  ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                 => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                              & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                          <=> ( aFunction0(sdtlpdtrp0(xC,W0))
                              & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                              & ! [W1: $i] :
                                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                              & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )),
                          quant_intro(proof_bind(^ [W1: $i] :
                                rewrite(( ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  <=> ( aElement0(W1)
                                      & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                      & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                <=> ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  <=> ( aElement0(W1)
                                      & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                      & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ))),
                            ( ! [W1: $i] :
                                ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              <=> ( aElement0(W1)
                                  & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                  & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                          <=> ! [W1: $i] :
                                ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              <=> ( aElement0(W1)
                                  & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                  & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )),
                          ( ( aFunction0(sdtlpdtrp0(xC,W0))
                            & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                            & ! [W1: $i] :
                                ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                               => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & ! [W1: $i] :
                                ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              <=> ( aElement0(W1)
                                  & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                  & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                        <=> ( aFunction0(sdtlpdtrp0(xC,W0))
                            & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                            & ! [W1: $i] :
                                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & ! [W1: $i] :
                                ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              <=> ( aElement0(W1)
                                  & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                  & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) )),
                        rewrite(( ( aFunction0(sdtlpdtrp0(xC,W0))
                            & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                            & ! [W1: $i] :
                                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & ! [W1: $i] :
                                ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              <=> ( aElement0(W1)
                                  & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                  & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                        <=> ( aFunction0(sdtlpdtrp0(xC,W0))
                            & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                            & ! [W1: $i] :
                                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & ! [W1: $i] :
                                ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              <=> ( aElement0(W1)
                                  & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                  & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) )),
                        ( ( aFunction0(sdtlpdtrp0(xC,W0))
                          & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                          & ! [W1: $i] :
                              ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                             => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                          & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          & ! [W1: $i] :
                              ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            <=> ( aElement0(W1)
                                & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                      <=> ( aFunction0(sdtlpdtrp0(xC,W0))
                          & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                          & ! [W1: $i] :
                              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                          & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          & ! [W1: $i] :
                              ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            <=> ( aElement0(W1)
                                & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                                & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) )),
                      quant_intro(proof_bind(^ [W1: $i] :
                            rewrite(( ( ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                                 => ( aSet0(W1)
                                    & ! [W2: $i] :
                                        ( aElementOf0(W2,W1)
                                       => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                    & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    & ( sbrdtbr0(W1) = xk ) ) )
                                & ( ( ( ( aSet0(W1)
                                        & ! [W2: $i] :
                                            ( aElementOf0(W2,W1)
                                           => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                                      | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                    & ( sbrdtbr0(W1) = xk ) )
                                 => aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
                            <=> ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                                  | ( aSet0(W1)
                                    & ! [W2: $i] :
                                        ( ~ aElementOf0(W2,W1)
                                        | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                    & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    & ( sbrdtbr0(W1) = xk ) ) )
                                & ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                        | ( aSet0(W1)
                                          & ! [W2: $i] :
                                              ( ~ aElementOf0(W2,W1)
                                              | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                                      & ( sbrdtbr0(W1) = xk ) )
                                  | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) ) ))),
                        ( ! [W1: $i] :
                            ( ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                             => ( aSet0(W1)
                                & ! [W2: $i] :
                                    ( aElementOf0(W2,W1)
                                   => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                & ( sbrdtbr0(W1) = xk ) ) )
                            & ( ( ( ( aSet0(W1)
                                    & ! [W2: $i] :
                                        ( aElementOf0(W2,W1)
                                       => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                                  | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                & ( sbrdtbr0(W1) = xk ) )
                             => aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
                      <=> ! [W1: $i] :
                            ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                              | ( aSet0(W1)
                                & ! [W2: $i] :
                                    ( ~ aElementOf0(W2,W1)
                                    | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                & ( sbrdtbr0(W1) = xk ) ) )
                            & ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    | ( aSet0(W1)
                                      & ! [W2: $i] :
                                          ( ~ aElementOf0(W2,W1)
                                          | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                                  & ( sbrdtbr0(W1) = xk ) )
                              | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) ) )),
                      ( ( aFunction0(sdtlpdtrp0(xC,W0))
                        & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        & ! [W1: $i] :
                            ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                           => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                        & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        & ! [W1: $i] :
                            ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          <=> ( aElement0(W1)
                              & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                              & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                        & ! [W1: $i] :
                            ( ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                             => ( aSet0(W1)
                                & ! [W2: $i] :
                                    ( aElementOf0(W2,W1)
                                   => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                & ( sbrdtbr0(W1) = xk ) ) )
                            & ( ( ( ( aSet0(W1)
                                    & ! [W2: $i] :
                                        ( aElementOf0(W2,W1)
                                       => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                                  | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                & ( sbrdtbr0(W1) = xk ) )
                             => aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) ) )
                    <=> ( aFunction0(sdtlpdtrp0(xC,W0))
                        & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        & ! [W1: $i] :
                            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                        & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        & ! [W1: $i] :
                            ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          <=> ( aElement0(W1)
                              & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                              & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                        & ! [W1: $i] :
                            ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                              | ( aSet0(W1)
                                & ! [W2: $i] :
                                    ( ~ aElementOf0(W2,W1)
                                    | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                & ( sbrdtbr0(W1) = xk ) ) )
                            & ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    | ( aSet0(W1)
                                      & ! [W2: $i] :
                                          ( ~ aElementOf0(W2,W1)
                                          | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                                  & ( sbrdtbr0(W1) = xk ) )
                              | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) ) ) )),
                    rewrite(( ( aFunction0(sdtlpdtrp0(xC,W0))
                        & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        & ! [W1: $i] :
                            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                        & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        & ! [W1: $i] :
                            ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          <=> ( aElement0(W1)
                              & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                              & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                        & ! [W1: $i] :
                            ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                              | ( aSet0(W1)
                                & ! [W2: $i] :
                                    ( ~ aElementOf0(W2,W1)
                                    | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                & ( sbrdtbr0(W1) = xk ) ) )
                            & ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    | ( aSet0(W1)
                                      & ! [W2: $i] :
                                          ( ~ aElementOf0(W2,W1)
                                          | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                                  & ( sbrdtbr0(W1) = xk ) )
                              | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) ) )
                    <=> ( aFunction0(sdtlpdtrp0(xC,W0))
                        & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        & ! [W1: $i] :
                            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                        & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        & ! [W1: $i] :
                            ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          <=> ( aElement0(W1)
                              & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                              & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                        & ! [W1: $i] :
                            ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                              | ( aSet0(W1)
                                & ! [W2: $i] :
                                    ( ~ aElementOf0(W2,W1)
                                    | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                & ( sbrdtbr0(W1) = xk ) ) )
                            & ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    | ( aSet0(W1)
                                      & ! [W2: $i] :
                                          ( ~ aElementOf0(W2,W1)
                                          | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                                  & ( sbrdtbr0(W1) = xk ) )
                              | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) ) ) )),
                    ( ( aFunction0(sdtlpdtrp0(xC,W0))
                      & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      & ! [W1: $i] :
                          ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                         => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                      & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & ! [W1: $i] :
                          ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        <=> ( aElement0(W1)
                            & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                            & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                      & ! [W1: $i] :
                          ( ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                           => ( aSet0(W1)
                              & ! [W2: $i] :
                                  ( aElementOf0(W2,W1)
                                 => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                              & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              & ( sbrdtbr0(W1) = xk ) ) )
                          & ( ( ( ( aSet0(W1)
                                  & ! [W2: $i] :
                                      ( aElementOf0(W2,W1)
                                     => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                                | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                              & ( sbrdtbr0(W1) = xk ) )
                           => aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) ) )
                  <=> ( aFunction0(sdtlpdtrp0(xC,W0))
                      & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      & ! [W1: $i] :
                          ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                      & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & ! [W1: $i] :
                          ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        <=> ( aElement0(W1)
                            & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                            & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                      & ! [W1: $i] :
                          ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                            | ( aSet0(W1)
                              & ! [W2: $i] :
                                  ( ~ aElementOf0(W2,W1)
                                  | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                              & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              & ( sbrdtbr0(W1) = xk ) ) )
                          & ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  | ( aSet0(W1)
                                    & ! [W2: $i] :
                                        ( ~ aElementOf0(W2,W1)
                                        | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                                & ( sbrdtbr0(W1) = xk ) )
                            | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) ) ) )),
                  ( ( aFunction0(sdtlpdtrp0(xC,W0))
                    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    & ! [W1: $i] :
                        ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                    & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & ! [W1: $i] :
                        ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      <=> ( aElement0(W1)
                          & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                    & ! [W1: $i] :
                        ( ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                         => ( aSet0(W1)
                            & ! [W2: $i] :
                                ( aElementOf0(W2,W1)
                               => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                            & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & ( sbrdtbr0(W1) = xk ) ) )
                        & ( ( ( ( aSet0(W1)
                                & ! [W2: $i] :
                                    ( aElementOf0(W2,W1)
                                   => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                              | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                            & ( sbrdtbr0(W1) = xk ) )
                         => aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
                    & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) ) )
                <=> ( aFunction0(sdtlpdtrp0(xC,W0))
                    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    & ! [W1: $i] :
                        ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                    & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & ! [W1: $i] :
                        ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      <=> ( aElement0(W1)
                          & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                    & ! [W1: $i] :
                        ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                          | ( aSet0(W1)
                            & ! [W2: $i] :
                                ( ~ aElementOf0(W2,W1)
                                | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                            & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & ( sbrdtbr0(W1) = xk ) ) )
                        & ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                | ( aSet0(W1)
                                  & ! [W2: $i] :
                                      ( ~ aElementOf0(W2,W1)
                                      | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                              & ( sbrdtbr0(W1) = xk ) )
                          | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
                    & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) ) ) )),
                rewrite(( ( aFunction0(sdtlpdtrp0(xC,W0))
                    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    & ! [W1: $i] :
                        ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                    & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & ! [W1: $i] :
                        ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      <=> ( aElement0(W1)
                          & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                    & ! [W1: $i] :
                        ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                          | ( aSet0(W1)
                            & ! [W2: $i] :
                                ( ~ aElementOf0(W2,W1)
                                | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                            & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & ( sbrdtbr0(W1) = xk ) ) )
                        & ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                | ( aSet0(W1)
                                  & ! [W2: $i] :
                                      ( ~ aElementOf0(W2,W1)
                                      | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                              & ( sbrdtbr0(W1) = xk ) )
                          | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
                    & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) ) )
                <=> ( aFunction0(sdtlpdtrp0(xC,W0))
                    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    & ! [W1: $i] :
                        ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                    & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & ! [W1: $i] :
                        ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      <=> ( aElement0(W1)
                          & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                    & ! [W1: $i] :
                        ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                          | ( aSet0(W1)
                            & ! [W2: $i] :
                                ( ~ aElementOf0(W2,W1)
                                | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                            & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & ( sbrdtbr0(W1) = xk ) ) )
                        & ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                | ( aSet0(W1)
                                  & ! [W2: $i] :
                                      ( ~ aElementOf0(W2,W1)
                                      | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                              & ( sbrdtbr0(W1) = xk ) )
                          | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
                    & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) ) ) )),
                ( ( aFunction0(sdtlpdtrp0(xC,W0))
                  & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  & ! [W1: $i] :
                      ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                     => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                  & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ! [W1: $i] :
                      ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    <=> ( aElement0(W1)
                        & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                  & ! [W1: $i] :
                      ( ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                       => ( aSet0(W1)
                          & ! [W2: $i] :
                              ( aElementOf0(W2,W1)
                             => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                          & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          & ( sbrdtbr0(W1) = xk ) ) )
                      & ( ( ( ( aSet0(W1)
                              & ! [W2: $i] :
                                  ( aElementOf0(W2,W1)
                                 => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                            | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                          & ( sbrdtbr0(W1) = xk ) )
                       => aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
                  & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) ) )
              <=> ( aFunction0(sdtlpdtrp0(xC,W0))
                  & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  & ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                  & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ! [W1: $i] :
                      ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    <=> ( aElement0(W1)
                        & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                  & ! [W1: $i] :
                      ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                        | ( aSet0(W1)
                          & ! [W2: $i] :
                              ( ~ aElementOf0(W2,W1)
                              | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                          & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          & ( sbrdtbr0(W1) = xk ) ) )
                      & ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ( aSet0(W1)
                                & ! [W2: $i] :
                                    ( ~ aElementOf0(W2,W1)
                                    | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                            & ( sbrdtbr0(W1) = xk ) )
                        | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
                  & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) ) ) )),
              quant_intro(proof_bind(^ [W1: $i] :
                    trans(monotonicity(rewrite(( ( aSet0(W1)
                            & ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                & ! [W2: $i] :
                                    ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                   => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                             => ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  & ! [W2: $i] :
                                      ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    <=> ( aElement0(W2)
                                        & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                        & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                               => ( ( ( ! [W2: $i] :
                                          ( aElementOf0(W2,W1)
                                         => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                      | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                    & ( sbrdtbr0(W1) = xk ) )
                                  | aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )
                        <=> ( aSet0(W1)
                            & ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                              | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                  & ! [W2: $i] :
                                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                              | ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  | ! [W2: $i] :
                                      ( ~ aElementOf0(W2,W1)
                                      | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                                & ( sbrdtbr0(W1) = xk ) )
                              | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  & ! [W2: $i] :
                                      ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    <=> ( aElement0(W2)
                                        & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                        & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ) ) )),
                        trans(monotonicity(trans(monotonicity(rewrite(( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                    & ! [W2: $i] :
                                        ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                                <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                    & ! [W2: $i] :
                                        ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) ) )),
                                ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                  & ! [W2: $i] :
                                      ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                     => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                                  & ! [W2: $i] :
                                      ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    <=> ( aElement0(W2)
                                        & ( aElementOf0(W2,W1)
                                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) )
                              <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                  & ! [W2: $i] :
                                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                                  & ! [W2: $i] :
                                      ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    <=> ( aElement0(W2)
                                        & ( aElementOf0(W2,W1)
                                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ) )),
                              rewrite(( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                  & ! [W2: $i] :
                                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                                  & ! [W2: $i] :
                                      ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    <=> ( aElement0(W2)
                                        & ( aElementOf0(W2,W1)
                                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) )
                              <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                  & ! [W2: $i] :
                                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                                  & ! [W2: $i] :
                                      ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    <=> ( aElement0(W2)
                                        & ( aElementOf0(W2,W1)
                                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ) )),
                              ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                & ! [W2: $i] :
                                    ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                   => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                                & ! [W2: $i] :
                                    ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  <=> ( aElement0(W2)
                                      & ( aElementOf0(W2,W1)
                                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) )
                            <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                & ! [W2: $i] :
                                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                                & ! [W2: $i] :
                                    ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  <=> ( aElement0(W2)
                                      & ( aElementOf0(W2,W1)
                                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ) )),
                            ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                              & ! [W2: $i] :
                                  ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                 => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                              & ! [W2: $i] :
                                  ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                                <=> ( aElement0(W2)
                                    & ( aElementOf0(W2,W1)
                                      | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                              & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                          <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                              & ! [W2: $i] :
                                  ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                              & ! [W2: $i] :
                                  ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                                <=> ( aElement0(W2)
                                    & ( aElementOf0(W2,W1)
                                      | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                              & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )),
                          rewrite(( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                              & ! [W2: $i] :
                                  ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                              & ! [W2: $i] :
                                  ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                                <=> ( aElement0(W2)
                                    & ( aElementOf0(W2,W1)
                                      | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                              & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                          <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                              & ! [W2: $i] :
                                  ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                              & ! [W2: $i] :
                                  ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                                <=> ( aElement0(W2)
                                    & ( aElementOf0(W2,W1)
                                      | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                              & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )),
                          ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                            & ! [W2: $i] :
                                ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                               => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                            & ! [W2: $i] :
                                ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                              <=> ( aElement0(W2)
                                  & ( aElementOf0(W2,W1)
                                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                            & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                        <=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                            & ! [W2: $i] :
                                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                            & ! [W2: $i] :
                                ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                              <=> ( aElement0(W2)
                                  & ( aElementOf0(W2,W1)
                                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                            & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )),
                        ( ( ( aSet0(W1)
                            & ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                & ! [W2: $i] :
                                    ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                   => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                             => ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  & ! [W2: $i] :
                                      ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    <=> ( aElement0(W2)
                                        & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                        & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                               => ( ( ( ! [W2: $i] :
                                          ( aElementOf0(W2,W1)
                                         => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                      | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                    & ( sbrdtbr0(W1) = xk ) )
                                  | aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )
                         => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                            & ! [W2: $i] :
                                ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                               => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                            & ! [W2: $i] :
                                ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                              <=> ( aElement0(W2)
                                  & ( aElementOf0(W2,W1)
                                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                            & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                      <=> ( ( aSet0(W1)
                            & ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                              | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                  & ! [W2: $i] :
                                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                              | ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  | ! [W2: $i] :
                                      ( ~ aElementOf0(W2,W1)
                                      | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                                & ( sbrdtbr0(W1) = xk ) )
                              | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  & ! [W2: $i] :
                                      ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    <=> ( aElement0(W2)
                                        & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                        & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ) )
                         => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                            & ! [W2: $i] :
                                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                            & ! [W2: $i] :
                                ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                              <=> ( aElement0(W2)
                                  & ( aElementOf0(W2,W1)
                                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                            & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) )),
                      rewrite(( ( ( aSet0(W1)
                            & ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                              | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                  & ! [W2: $i] :
                                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                              | ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  | ! [W2: $i] :
                                      ( ~ aElementOf0(W2,W1)
                                      | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                                & ( sbrdtbr0(W1) = xk ) )
                              | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  & ! [W2: $i] :
                                      ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    <=> ( aElement0(W2)
                                        & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                        & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ) )
                         => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                            & ! [W2: $i] :
                                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                            & ! [W2: $i] :
                                ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                              <=> ( aElement0(W2)
                                  & ( aElementOf0(W2,W1)
                                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                            & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                      <=> ( ~ ( aSet0(W1)
                              & ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                                | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                    & ! [W2: $i] :
                                        ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                                | ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    | ! [W2: $i] :
                                        ( ~ aElementOf0(W2,W1)
                                        | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                                  & ( sbrdtbr0(W1) = xk ) )
                                | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    & ! [W2: $i] :
                                        ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                      <=> ( aElement0(W2)
                                          & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                          & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ) )
                          | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                            & ! [W2: $i] :
                                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                            & ! [W2: $i] :
                                ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                              <=> ( aElement0(W2)
                                  & ( aElementOf0(W2,W1)
                                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                            & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) )),
                      ( ( ( aSet0(W1)
                          & ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                              & ! [W2: $i] :
                                  ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                 => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                           => ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                & ! [W2: $i] :
                                    ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  <=> ( aElement0(W2)
                                      & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                      & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                             => ( ( ( ! [W2: $i] :
                                        ( aElementOf0(W2,W1)
                                       => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                    | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                  & ( sbrdtbr0(W1) = xk ) )
                                | aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )
                       => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                          & ! [W2: $i] :
                              ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                             => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                          & ! [W2: $i] :
                              ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                            <=> ( aElement0(W2)
                                & ( aElementOf0(W2,W1)
                                  | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                          & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                    <=> ( ~ ( aSet0(W1)
                            & ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                              | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                                  & ! [W2: $i] :
                                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                              | ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  | ! [W2: $i] :
                                      ( ~ aElementOf0(W2,W1)
                                      | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                                & ( sbrdtbr0(W1) = xk ) )
                              | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  & ! [W2: $i] :
                                      ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                    <=> ( aElement0(W2)
                                        & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                        & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ) )
                        | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                          & ! [W2: $i] :
                              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                          & ! [W2: $i] :
                              ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                            <=> ( aElement0(W2)
                                & ( aElementOf0(W2,W1)
                                  | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                          & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ))),
                ( ! [W1: $i] :
                    ( ( aSet0(W1)
                      & ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                          & ! [W2: $i] :
                              ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                             => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                       => ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & ! [W2: $i] :
                                ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              <=> ( aElement0(W2)
                                  & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                  & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                         => ( ( ( ! [W2: $i] :
                                    ( aElementOf0(W2,W1)
                                   => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                              & ( sbrdtbr0(W1) = xk ) )
                            | aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )
                   => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      & ! [W2: $i] :
                          ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                         => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                      & ! [W2: $i] :
                          ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                        <=> ( aElement0(W2)
                            & ( aElementOf0(W2,W1)
                              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                      & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
              <=> ! [W1: $i] :
                    ( ~ ( aSet0(W1)
                        & ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                          | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                              & ! [W2: $i] :
                                  ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                          | ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ! [W2: $i] :
                                  ( ~ aElementOf0(W2,W1)
                                  | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                            & ( sbrdtbr0(W1) = xk ) )
                          | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              & ! [W2: $i] :
                                  ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                <=> ( aElement0(W2)
                                    & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                    & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ) )
                    | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      & ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                      & ! [W2: $i] :
                          ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                        <=> ( aElement0(W2)
                            & ( aElementOf0(W2,W1)
                              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                      & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) )),
              ( ( aFunction0(sdtlpdtrp0(xC,W0))
                & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W1: $i] :
                    ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                   => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & ! [W1: $i] :
                    ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W1)
                      & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                & ! [W1: $i] :
                    ( ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                     => ( aSet0(W1)
                        & ! [W2: $i] :
                            ( aElementOf0(W2,W1)
                           => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                        & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        & ( sbrdtbr0(W1) = xk ) ) )
                    & ( ( ( ( aSet0(W1)
                            & ! [W2: $i] :
                                ( aElementOf0(W2,W1)
                               => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                          | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                        & ( sbrdtbr0(W1) = xk ) )
                     => aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
                & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
                & ! [W1: $i] :
                    ( ( aSet0(W1)
                      & ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                          & ! [W2: $i] :
                              ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                             => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                       => ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & ! [W2: $i] :
                                ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              <=> ( aElement0(W2)
                                  & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                  & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                         => ( ( ( ! [W2: $i] :
                                    ( aElementOf0(W2,W1)
                                   => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                                | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                              & ( sbrdtbr0(W1) = xk ) )
                            | aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )
                   => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      & ! [W2: $i] :
                          ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                         => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                      & ! [W2: $i] :
                          ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                        <=> ( aElement0(W2)
                            & ( aElementOf0(W2,W1)
                              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                      & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) )
            <=> ( aFunction0(sdtlpdtrp0(xC,W0))
                & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & ! [W1: $i] :
                    ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W1)
                      & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                & ! [W1: $i] :
                    ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                      | ( aSet0(W1)
                        & ! [W2: $i] :
                            ( ~ aElementOf0(W2,W1)
                            | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                        & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        & ( sbrdtbr0(W1) = xk ) ) )
                    & ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            | ( aSet0(W1)
                              & ! [W2: $i] :
                                  ( ~ aElementOf0(W2,W1)
                                  | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                          & ( sbrdtbr0(W1) = xk ) )
                      | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
                & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
                & ! [W1: $i] :
                    ( ~ ( aSet0(W1)
                        & ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                          | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                              & ! [W2: $i] :
                                  ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                          | ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ! [W2: $i] :
                                  ( ~ aElementOf0(W2,W1)
                                  | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                            & ( sbrdtbr0(W1) = xk ) )
                          | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              & ! [W2: $i] :
                                  ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                <=> ( aElement0(W2)
                                    & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                    & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ) )
                    | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      & ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                      & ! [W2: $i] :
                          ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                        <=> ( aElement0(W2)
                            & ( aElementOf0(W2,W1)
                              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                      & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )),
            rewrite(( ( aFunction0(sdtlpdtrp0(xC,W0))
                & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & ! [W1: $i] :
                    ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W1)
                      & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                & ! [W1: $i] :
                    ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                      | ( aSet0(W1)
                        & ! [W2: $i] :
                            ( ~ aElementOf0(W2,W1)
                            | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                        & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        & ( sbrdtbr0(W1) = xk ) ) )
                    & ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            | ( aSet0(W1)
                              & ! [W2: $i] :
                                  ( ~ aElementOf0(W2,W1)
                                  | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                          & ( sbrdtbr0(W1) = xk ) )
                      | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
                & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
                & ! [W1: $i] :
                    ( ~ ( aSet0(W1)
                        & ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                          | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                              & ! [W2: $i] :
                                  ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                          | ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ! [W2: $i] :
                                  ( ~ aElementOf0(W2,W1)
                                  | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                            & ( sbrdtbr0(W1) = xk ) )
                          | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              & ! [W2: $i] :
                                  ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                <=> ( aElement0(W2)
                                    & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                    & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ) )
                    | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      & ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                      & ! [W2: $i] :
                          ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                        <=> ( aElement0(W2)
                            & ( aElementOf0(W2,W1)
                              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                      & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) )
            <=> ( aFunction0(sdtlpdtrp0(xC,W0))
                & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & ! [W1: $i] :
                    ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W1)
                      & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                & ! [W1: $i] :
                    ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                      | ( aSet0(W1)
                        & ! [W2: $i] :
                            ( ~ aElementOf0(W2,W1)
                            | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                        & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        & ( sbrdtbr0(W1) = xk ) ) )
                    & ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            | ( aSet0(W1)
                              & ! [W2: $i] :
                                  ( ~ aElementOf0(W2,W1)
                                  | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                          & ( sbrdtbr0(W1) = xk ) )
                      | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
                & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
                & ! [W1: $i] :
                    ( ~ ( aSet0(W1)
                        & ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                          | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                              & ! [W2: $i] :
                                  ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                          | ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ! [W2: $i] :
                                  ( ~ aElementOf0(W2,W1)
                                  | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                            & ( sbrdtbr0(W1) = xk ) )
                          | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              & ! [W2: $i] :
                                  ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                <=> ( aElement0(W2)
                                    & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                    & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ) )
                    | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      & ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                      & ! [W2: $i] :
                          ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                        <=> ( aElement0(W2)
                            & ( aElementOf0(W2,W1)
                              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                      & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )),
            ( ( aFunction0(sdtlpdtrp0(xC,W0))
              & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                 => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & ! [W1: $i] :
                  ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                <=> ( aElement0(W1)
                    & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
              & ! [W1: $i] :
                  ( ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                   => ( aSet0(W1)
                      & ! [W2: $i] :
                          ( aElementOf0(W2,W1)
                         => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & ( sbrdtbr0(W1) = xk ) ) )
                  & ( ( ( ( aSet0(W1)
                          & ! [W2: $i] :
                              ( aElementOf0(W2,W1)
                             => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                        | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      & ( sbrdtbr0(W1) = xk ) )
                   => aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
              & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
              & ! [W1: $i] :
                  ( ( aSet0(W1)
                    & ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        & ! [W2: $i] :
                            ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                           => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                     => ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          & ! [W2: $i] :
                              ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            <=> ( aElement0(W2)
                                & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                       => ( ( ( ! [W2: $i] :
                                  ( aElementOf0(W2,W1)
                                 => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                              | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                            & ( sbrdtbr0(W1) = xk ) )
                          | aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )
                 => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    & ! [W2: $i] :
                        ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                    & ! [W2: $i] :
                        ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                      <=> ( aElement0(W2)
                          & ( aElementOf0(W2,W1)
                            | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                    & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) )
          <=> ( aFunction0(sdtlpdtrp0(xC,W0))
              & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & ! [W1: $i] :
                  ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                <=> ( aElement0(W1)
                    & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
              & ! [W1: $i] :
                  ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                    | ( aSet0(W1)
                      & ! [W2: $i] :
                          ( ~ aElementOf0(W2,W1)
                          | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & ( sbrdtbr0(W1) = xk ) ) )
                  & ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          | ( aSet0(W1)
                            & ! [W2: $i] :
                                ( ~ aElementOf0(W2,W1)
                                | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                        & ( sbrdtbr0(W1) = xk ) )
                    | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
              & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
              & ! [W1: $i] :
                  ( ~ ( aSet0(W1)
                      & ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                        | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                            & ! [W2: $i] :
                                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                        | ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            | ! [W2: $i] :
                                ( ~ aElementOf0(W2,W1)
                                | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                          & ( sbrdtbr0(W1) = xk ) )
                        | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & ! [W2: $i] :
                                ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              <=> ( aElement0(W2)
                                  & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                  & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ) )
                  | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    & ! [W2: $i] :
                        ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                    & ! [W2: $i] :
                        ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                      <=> ( aElement0(W2)
                          & ( aElementOf0(W2,W1)
                            | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                    & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )),
          ( ( aElementOf0(W0,szNzAzT0)
           => ( aFunction0(sdtlpdtrp0(xC,W0))
              & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
                 => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & ! [W1: $i] :
                  ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                <=> ( aElement0(W1)
                    & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
              & ! [W1: $i] :
                  ( ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                   => ( aSet0(W1)
                      & ! [W2: $i] :
                          ( aElementOf0(W2,W1)
                         => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & ( sbrdtbr0(W1) = xk ) ) )
                  & ( ( ( ( aSet0(W1)
                          & ! [W2: $i] :
                              ( aElementOf0(W2,W1)
                             => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                        | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      & ( sbrdtbr0(W1) = xk ) )
                   => aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
              & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
              & ! [W1: $i] :
                  ( ( aSet0(W1)
                    & ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        & ! [W2: $i] :
                            ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                           => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                     => ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          & ! [W2: $i] :
                              ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            <=> ( aElement0(W2)
                                & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                       => ( ( ( ! [W2: $i] :
                                  ( aElementOf0(W2,W1)
                                 => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                              | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                            & ( sbrdtbr0(W1) = xk ) )
                          | aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )
                 => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    & ! [W2: $i] :
                        ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                    & ! [W2: $i] :
                        ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                      <=> ( aElement0(W2)
                          & ( aElementOf0(W2,W1)
                            | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                    & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
        <=> ( aElementOf0(W0,szNzAzT0)
           => ( aFunction0(sdtlpdtrp0(xC,W0))
              & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & ! [W1: $i] :
                  ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                <=> ( aElement0(W1)
                    & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
              & ! [W1: $i] :
                  ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                    | ( aSet0(W1)
                      & ! [W2: $i] :
                          ( ~ aElementOf0(W2,W1)
                          | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & ( sbrdtbr0(W1) = xk ) ) )
                  & ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          | ( aSet0(W1)
                            & ! [W2: $i] :
                                ( ~ aElementOf0(W2,W1)
                                | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                        & ( sbrdtbr0(W1) = xk ) )
                    | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
              & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
              & ! [W1: $i] :
                  ( ~ ( aSet0(W1)
                      & ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                        | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                            & ! [W2: $i] :
                                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                        | ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            | ! [W2: $i] :
                                ( ~ aElementOf0(W2,W1)
                                | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                          & ( sbrdtbr0(W1) = xk ) )
                        | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & ! [W2: $i] :
                                ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              <=> ( aElement0(W2)
                                  & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                  & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ) )
                  | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    & ! [W2: $i] :
                        ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                    & ! [W2: $i] :
                        ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                      <=> ( aElement0(W2)
                          & ( aElementOf0(W2,W1)
                            | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                    & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ) )),
        rewrite(( ( aElementOf0(W0,szNzAzT0)
           => ( aFunction0(sdtlpdtrp0(xC,W0))
              & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & ! [W1: $i] :
                  ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                <=> ( aElement0(W1)
                    & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
              & ! [W1: $i] :
                  ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                    | ( aSet0(W1)
                      & ! [W2: $i] :
                          ( ~ aElementOf0(W2,W1)
                          | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & ( sbrdtbr0(W1) = xk ) ) )
                  & ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          | ( aSet0(W1)
                            & ! [W2: $i] :
                                ( ~ aElementOf0(W2,W1)
                                | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                        & ( sbrdtbr0(W1) = xk ) )
                    | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
              & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
              & ! [W1: $i] :
                  ( ~ ( aSet0(W1)
                      & ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                        | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                            & ! [W2: $i] :
                                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                        | ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            | ! [W2: $i] :
                                ( ~ aElementOf0(W2,W1)
                                | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                          & ( sbrdtbr0(W1) = xk ) )
                        | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & ! [W2: $i] :
                                ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              <=> ( aElement0(W2)
                                  & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                  & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ) )
                  | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    & ! [W2: $i] :
                        ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                    & ! [W2: $i] :
                        ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                      <=> ( aElement0(W2)
                          & ( aElementOf0(W2,W1)
                            | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                    & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
        <=> ( ~ aElementOf0(W0,szNzAzT0)
            | ( aFunction0(sdtlpdtrp0(xC,W0))
              & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              & ! [W1: $i] :
                  ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & ! [W1: $i] :
                  ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                <=> ( aElement0(W1)
                    & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
              & ! [W1: $i] :
                  ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                    | ( aSet0(W1)
                      & ! [W2: $i] :
                          ( ~ aElementOf0(W2,W1)
                          | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & ( sbrdtbr0(W1) = xk ) ) )
                  & ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          | ( aSet0(W1)
                            & ! [W2: $i] :
                                ( ~ aElementOf0(W2,W1)
                                | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                        & ( sbrdtbr0(W1) = xk ) )
                    | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
              & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
              & ! [W1: $i] :
                  ( ~ ( aSet0(W1)
                      & ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                        | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                            & ! [W2: $i] :
                                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                        | ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            | ! [W2: $i] :
                                ( ~ aElementOf0(W2,W1)
                                | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                          & ( sbrdtbr0(W1) = xk ) )
                        | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            & ! [W2: $i] :
                                ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              <=> ( aElement0(W2)
                                  & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                  & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ) )
                  | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    & ! [W2: $i] :
                        ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                    & ! [W2: $i] :
                        ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                      <=> ( aElement0(W2)
                          & ( aElementOf0(W2,W1)
                            | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                    & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ) )),
        ( ( aElementOf0(W0,szNzAzT0)
         => ( aFunction0(sdtlpdtrp0(xC,W0))
            & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            & ! [W1: $i] :
                ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
               => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            & ! [W1: $i] :
                ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              <=> ( aElement0(W1)
                  & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
            & ! [W1: $i] :
                ( ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                 => ( aSet0(W1)
                    & ! [W2: $i] :
                        ( aElementOf0(W2,W1)
                       => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & ( sbrdtbr0(W1) = xk ) ) )
                & ( ( ( ( aSet0(W1)
                        & ! [W2: $i] :
                            ( aElementOf0(W2,W1)
                           => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                      | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    & ( sbrdtbr0(W1) = xk ) )
                 => aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
            & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
            & ! [W1: $i] :
                ( ( aSet0(W1)
                  & ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      & ! [W2: $i] :
                          ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                         => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                   => ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        & ! [W2: $i] :
                            ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          <=> ( aElement0(W2)
                              & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                     => ( ( ( ! [W2: $i] :
                                ( aElementOf0(W2,W1)
                               => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                            | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                          & ( sbrdtbr0(W1) = xk ) )
                        | aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )
               => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  & ! [W2: $i] :
                      ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                     => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                  & ! [W2: $i] :
                      ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                    <=> ( aElement0(W2)
                        & ( aElementOf0(W2,W1)
                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                  & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
      <=> ( ~ aElementOf0(W0,szNzAzT0)
          | ( aFunction0(sdtlpdtrp0(xC,W0))
            & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
            & ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
            & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            & ! [W1: $i] :
                ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              <=> ( aElement0(W1)
                  & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                  & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
            & ! [W1: $i] :
                ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                  | ( aSet0(W1)
                    & ! [W2: $i] :
                        ( ~ aElementOf0(W2,W1)
                        | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & ( sbrdtbr0(W1) = xk ) ) )
                & ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        | ( aSet0(W1)
                          & ! [W2: $i] :
                              ( ~ aElementOf0(W2,W1)
                              | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                      & ( sbrdtbr0(W1) = xk ) )
                  | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
            & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
            & ! [W1: $i] :
                ( ~ ( aSet0(W1)
                    & ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                      | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                          & ! [W2: $i] :
                              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                      | ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          | ! [W2: $i] :
                              ( ~ aElementOf0(W2,W1)
                              | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                        & ( sbrdtbr0(W1) = xk ) )
                      | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          & ! [W2: $i] :
                              ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            <=> ( aElement0(W2)
                                & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ) )
                | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  & ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                  & ! [W2: $i] :
                      ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                    <=> ( aElement0(W2)
                        & ( aElementOf0(W2,W1)
                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                  & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ) )),
    inference(bind,[status(th)],[]) ).

tff(316,plain,
    ( ! [W0: $i] :
        ( aElementOf0(W0,szNzAzT0)
       => ( aFunction0(sdtlpdtrp0(xC,W0))
          & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
          & ! [W1: $i] :
              ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
             => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
          & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          & ! [W1: $i] :
              ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            <=> ( aElement0(W1)
                & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
          & ! [W1: $i] :
              ( ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
               => ( aSet0(W1)
                  & ! [W2: $i] :
                      ( aElementOf0(W2,W1)
                     => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ( sbrdtbr0(W1) = xk ) ) )
              & ( ( ( ( aSet0(W1)
                      & ! [W2: $i] :
                          ( aElementOf0(W2,W1)
                         => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                    | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  & ( sbrdtbr0(W1) = xk ) )
               => aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
          & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
          & ! [W1: $i] :
              ( ( aSet0(W1)
                & ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    & ! [W2: $i] :
                        ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                 => ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & ! [W2: $i] :
                          ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        <=> ( aElement0(W2)
                            & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                   => ( ( ( ! [W2: $i] :
                              ( aElementOf0(W2,W1)
                             => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                          | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                        & ( sbrdtbr0(W1) = xk ) )
                      | aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )
             => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W2: $i] :
                    ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                   => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                & ! [W2: $i] :
                    ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W2)
                      & ( aElementOf0(W2,W1)
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
  <=> ! [W0: $i] :
        ( ~ aElementOf0(W0,szNzAzT0)
        | ( aFunction0(sdtlpdtrp0(xC,W0))
          & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
          & ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
          & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          & ! [W1: $i] :
              ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            <=> ( aElement0(W1)
                & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
          & ! [W1: $i] :
              ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                | ( aSet0(W1)
                  & ! [W2: $i] :
                      ( ~ aElementOf0(W2,W1)
                      | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ( sbrdtbr0(W1) = xk ) ) )
              & ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ( aSet0(W1)
                        & ! [W2: $i] :
                            ( ~ aElementOf0(W2,W1)
                            | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                    & ( sbrdtbr0(W1) = xk ) )
                | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
          & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
          & ! [W1: $i] :
              ( ~ ( aSet0(W1)
                  & ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                    | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        & ! [W2: $i] :
                            ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                    | ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        | ! [W2: $i] :
                            ( ~ aElementOf0(W2,W1)
                            | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                      & ( sbrdtbr0(W1) = xk ) )
                    | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        & ! [W2: $i] :
                            ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          <=> ( aElement0(W2)
                              & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ) )
              | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                & ! [W2: $i] :
                    ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W2)
                      & ( aElementOf0(W2,W1)
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ) ),
    inference(quant_intro,[status(thm)],[315]) ).

tff(317,axiom,
    ( aFunction0(xC)
    & ( szDzozmdt0(xC) = szNzAzT0 )
    & ! [W0: $i] :
        ( aElementOf0(W0,szNzAzT0)
       => ( aFunction0(sdtlpdtrp0(xC,W0))
          & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
          & ! [W1: $i] :
              ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
             => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
          & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          & ! [W1: $i] :
              ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
            <=> ( aElement0(W1)
                & aElementOf0(W1,sdtlpdtrp0(xN,W0))
                & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
          & ! [W1: $i] :
              ( ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
               => ( aSet0(W1)
                  & ! [W2: $i] :
                      ( aElementOf0(W2,W1)
                     => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ( sbrdtbr0(W1) = xk ) ) )
              & ( ( ( ( aSet0(W1)
                      & ! [W2: $i] :
                          ( aElementOf0(W2,W1)
                         => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                    | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                  & ( sbrdtbr0(W1) = xk ) )
               => aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
          & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
          & ! [W1: $i] :
              ( ( aSet0(W1)
                & ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    & ! [W2: $i] :
                        ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                 => ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & ! [W2: $i] :
                          ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        <=> ( aElement0(W2)
                            & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                   => ( ( ( ! [W2: $i] :
                              ( aElementOf0(W2,W1)
                             => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                          | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                        & ( sbrdtbr0(W1) = xk ) )
                      | aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )
             => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                & ! [W2: $i] :
                    ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                   => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                & ! [W2: $i] :
                    ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                  <=> ( aElement0(W2)
                      & ( aElementOf0(W2,W1)
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4151) ).

tff(318,plain,
    ! [W0: $i] :
      ( aElementOf0(W0,szNzAzT0)
     => ( aFunction0(sdtlpdtrp0(xC,W0))
        & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
        & ! [W1: $i] :
            ( aElementOf0(W1,sdtlpdtrp0(xN,W0))
           => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
        & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
        & ! [W1: $i] :
            ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          <=> ( aElement0(W1)
              & aElementOf0(W1,sdtlpdtrp0(xN,W0))
              & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
        & ! [W1: $i] :
            ( ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
             => ( aSet0(W1)
                & ! [W2: $i] :
                    ( aElementOf0(W2,W1)
                   => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & ( sbrdtbr0(W1) = xk ) ) )
            & ( ( ( ( aSet0(W1)
                    & ! [W2: $i] :
                        ( aElementOf0(W2,W1)
                       => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                  | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                & ( sbrdtbr0(W1) = xk ) )
             => aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
        & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
        & ! [W1: $i] :
            ( ( aSet0(W1)
              & ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                  & ! [W2: $i] :
                      ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                     => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
               => ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    & ! [W2: $i] :
                        ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      <=> ( aElement0(W2)
                          & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
                 => ( ( ( ! [W2: $i] :
                            ( aElementOf0(W2,W1)
                           => aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                        | aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                      & ( sbrdtbr0(W1) = xk ) )
                    | aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk)) ) ) ) )
           => ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              & ! [W2: $i] :
                  ( aElementOf0(W2,sdtlpdtrp0(xN,W0))
                 => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
              & ! [W2: $i] :
                  ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                <=> ( aElement0(W2)
                    & ( aElementOf0(W2,W1)
                      | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
              & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ),
    inference(and_elim,[status(thm)],[317]) ).

tff(319,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ( aFunction0(sdtlpdtrp0(xC,W0))
        & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
        & ! [W1: $i] :
            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
        & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
        & ! [W1: $i] :
            ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          <=> ( aElement0(W1)
              & aElementOf0(W1,sdtlpdtrp0(xN,W0))
              & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
        & ! [W1: $i] :
            ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
              | ( aSet0(W1)
                & ! [W2: $i] :
                    ( ~ aElementOf0(W2,W1)
                    | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & ( sbrdtbr0(W1) = xk ) ) )
            & ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ( aSet0(W1)
                      & ! [W2: $i] :
                          ( ~ aElementOf0(W2,W1)
                          | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                  & ( sbrdtbr0(W1) = xk ) )
              | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
        & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
        & ! [W1: $i] :
            ( ~ ( aSet0(W1)
                & ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                  | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      & ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                  | ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ! [W2: $i] :
                          ( ~ aElementOf0(W2,W1)
                          | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                    & ( sbrdtbr0(W1) = xk ) )
                  | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & ! [W2: $i] :
                          ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        <=> ( aElement0(W2)
                            & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ) )
            | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              & ! [W2: $i] :
                  ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
              & ! [W2: $i] :
                  ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                <=> ( aElement0(W2)
                    & ( aElementOf0(W2,W1)
                      | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
              & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ),
    inference(modus_ponens,[status(thm)],[318,316]) ).

tff(320,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ( aFunction0(sdtlpdtrp0(xC,W0))
        & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
        & ! [W1: $i] :
            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
        & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
        & ! [W1: $i] :
            ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          <=> ( aElement0(W1)
              & aElementOf0(W1,sdtlpdtrp0(xN,W0))
              & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
        & ! [W1: $i] :
            ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
              | ( aSet0(W1)
                & ! [W2: $i] :
                    ( ~ aElementOf0(W2,W1)
                    | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & ( sbrdtbr0(W1) = xk ) ) )
            & ( ~ ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ( aSet0(W1)
                      & ! [W2: $i] :
                          ( ~ aElementOf0(W2,W1)
                          | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                  & ( sbrdtbr0(W1) = xk ) )
              | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
        & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
        & ! [W1: $i] :
            ( ~ ( aSet0(W1)
                & ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                  | ~ ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                      & ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) ) )
                  | ( ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      | ! [W2: $i] :
                          ( ~ aElementOf0(W2,W1)
                          | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                    & ( sbrdtbr0(W1) = xk ) )
                  | ~ ( aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                      & ! [W2: $i] :
                          ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        <=> ( aElement0(W2)
                            & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                            & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ) )
            | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              & ! [W2: $i] :
                  ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
              & ! [W2: $i] :
                  ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                <=> ( aElement0(W2)
                    & ( aElementOf0(W2,W1)
                      | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
              & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ),
    inference(modus_ponens,[status(thm)],[319,314]) ).

tff(321,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ( aFunction0(sdtlpdtrp0(xC,W0))
        & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
        & ! [W1: $i] :
            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
        & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
        & ! [W1: $i] :
            ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          <=> ( aElement0(W1)
              & aElementOf0(W1,sdtlpdtrp0(xN,W0))
              & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
        & ! [W1: $i] :
            ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
              | ( aSet0(W1)
                & ! [W2: $i] :
                    ( ~ aElementOf0(W2,W1)
                    | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & ( sbrdtbr0(W1) = xk ) ) )
            & ( ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & ( ~ aSet0(W1)
                  | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                      | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
              | ( sbrdtbr0(W1) != xk )
              | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0))) ) )
        & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
        & ! [W1: $i] :
            ( ~ aSet0(W1)
            | ( ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
              & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              & ! [W2: $i] :
                  ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
              & ( ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                      | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                | ( sbrdtbr0(W1) != xk ) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & ! [W2: $i] :
                  ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                <=> ( aElement0(W2)
                    & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                    & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
            | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              & ! [W2: $i] :
                  ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
              & ! [W2: $i] :
                  ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                <=> ( aElement0(W2)
                    & ( aElementOf0(W2,W1)
                      | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
              & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ),
    inference(skolemize,[status(sab)],[320]) ).

tff(322,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ( aFunction0(sdtlpdtrp0(xC,W0))
        & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
        & ! [W1: $i] :
            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
        & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
        & ! [W1: $i] :
            ( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          <=> ( aElement0(W1)
              & aElementOf0(W1,sdtlpdtrp0(xN,W0))
              & ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
        & ! [W1: $i] :
            ( ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
              | ( aSet0(W1)
                & ! [W2: $i] :
                    ( ~ aElementOf0(W2,W1)
                    | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                & aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & ( sbrdtbr0(W1) = xk ) ) )
            & ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
              | ( sbrdtbr0(W1) != xk )
              | ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                & ( ~ aSet0(W1)
                  | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                      | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
        & ( szDzozmdt0(sdtlpdtrp0(xC,W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
        & ! [W1: $i] :
            ( ~ aSet0(W1)
            | ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              & ! [W2: $i] :
                  ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
              & ! [W2: $i] :
                  ( aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0))))
                <=> ( aElement0(W2)
                    & ( aElementOf0(W2,W1)
                      | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) )
              & ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) = sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
            | ( ~ aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
              & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              & ! [W2: $i] :
                  ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
              & ( ( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                  & ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                      | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                | ( sbrdtbr0(W1) != xk ) )
              & aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              & ! [W2: $i] :
                  ( aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                <=> ( aElement0(W2)
                    & aElementOf0(W2,sdtlpdtrp0(xN,W0))
                    & ( W2 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ) ) ) ) ),
    inference(modus_ponens,[status(thm)],[321,313]) ).

tff(323,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          | ~ ! [W1: $i] :
                ~ ( ( ~ aElement0(W1)
                    | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
          | ~ aFunction0(sdtlpdtrp0(xC,W0))
          | ~ ! [W1: $i] :
                ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                      | ~ ( ~ aSet0(W1)
                          | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          | ~ ! [W2: $i] :
                                ( ~ aElementOf0(W2,W1)
                                | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                          | ( sbrdtbr0(W1) != xk ) ) )
                  | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                      | ( sbrdtbr0(W1) != xk )
                      | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          | ~ ( ~ aSet0(W1)
                              | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                  | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
          | ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
          | ~ ! [W1: $i] :
                ( ~ aSet0(W1)
                | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                    | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    | ~ ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                    | ~ ( ( sbrdtbr0(W1) != xk )
                        | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            | ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                            | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ ! [W2: $i] :
                          ~ ( ( ~ aElement0(W2)
                              | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                          <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    | ~ ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                    | ~ ! [W2: $i] :
                          ~ ( ( ~ aElement0(W2)
                              | ~ ( aElementOf0(W2,W1)
                                  | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                          <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    | ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ),
    inference(modus_ponens,[status(thm)],[322,311]) ).

tff(324,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          | ~ ! [W1: $i] :
                ~ ( ( ~ aElement0(W1)
                    | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
          | ~ aFunction0(sdtlpdtrp0(xC,W0))
          | ~ ! [W1: $i] :
                ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                      | ~ ( ~ aSet0(W1)
                          | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          | ~ ! [W2: $i] :
                                ( ~ aElementOf0(W2,W1)
                                | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                          | ( sbrdtbr0(W1) != xk ) ) )
                  | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                      | ( sbrdtbr0(W1) != xk )
                      | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          | ~ ( ~ aSet0(W1)
                              | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                  | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
          | ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
          | ~ ! [W1: $i] :
                ( ~ aSet0(W1)
                | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                    | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    | ~ ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                    | ~ ( ( sbrdtbr0(W1) != xk )
                        | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            | ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                            | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ ! [W2: $i] :
                          ~ ( ( ~ aElement0(W2)
                              | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                          <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    | ~ ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                    | ~ ! [W2: $i] :
                          ~ ( ( ~ aElement0(W2)
                              | ~ ( aElementOf0(W2,W1)
                                  | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                          <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    | ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ),
    inference(modus_ponens,[status(thm)],[323,309]) ).

tff(325,plain,
    ! [W0: $i] :
      ( ~ aElementOf0(W0,szNzAzT0)
      | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
          | ~ aFunction0(sdtlpdtrp0(xC,W0))
          | ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
          | ~ ! [W1: $i] :
                ~ ( ( ~ aElement0(W1)
                    | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
          | ~ ! [W1: $i] :
                ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                      | ~ ( ~ aSet0(W1)
                          | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          | ( sbrdtbr0(W1) != xk )
                          | ~ ! [W2: $i] :
                                ( ~ aElementOf0(W2,W1)
                                | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                  | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                      | ( sbrdtbr0(W1) != xk )
                      | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          | ~ ( ~ aSet0(W1)
                              | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                  | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
          | ~ ! [W1: $i] :
                ( ~ aSet0(W1)
                | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                    | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    | ~ ( ( sbrdtbr0(W1) != xk )
                        | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                            | ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                            | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                    | ~ ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                    | ~ ! [W2: $i] :
                          ~ ( ( ~ aElement0(W2)
                              | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                          <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                    | ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                    | ~ ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                    | ~ ! [W2: $i] :
                          ~ ( ( ~ aElement0(W2)
                              | ~ ( aElementOf0(W2,W1)
                                  | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                          <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) ),
    inference(modus_ponens,[status(thm)],[324,304]) ).

tff(326,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ aFunction0(sdtlpdtrp0(xC,W0))
                | ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                | ~ ! [W1: $i] :
                      ~ ( ( ~ aElement0(W1)
                          | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                | ~ ! [W1: $i] :
                      ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                            | ~ ( ~ aSet0(W1)
                                | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                | ( sbrdtbr0(W1) != xk )
                                | ~ ! [W2: $i] :
                                      ( ~ aElementOf0(W2,W1)
                                      | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                        | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                            | ( sbrdtbr0(W1) != xk )
                            | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                | ~ ( ~ aSet0(W1)
                                    | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                        | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
                | ~ ! [W1: $i] :
                      ( ~ aSet0(W1)
                      | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                          | ~ ( ( sbrdtbr0(W1) != xk )
                              | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  | ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                  | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          | ~ ! [W2: $i] :
                                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                          | ~ ! [W2: $i] :
                                ~ ( ( ~ aElement0(W2)
                                    | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                                <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                      | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                          | ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                          | ~ ! [W2: $i] :
                                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                          | ~ ! [W2: $i] :
                                ~ ( ( ~ aElement0(W2)
                                    | ~ ( aElementOf0(W2,W1)
                                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ ! [W1: $i] :
                ~ ( ( ~ aElement0(W1)
                    | ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                    | ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
          | ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
          | ~ aFunction0(sdtlpdtrp0(xC,xn))
          | ~ ! [W1: $i] :
                ( ~ aSet0(W1)
                | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                    | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                    | aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                    | ~ ! [W2: $i] :
                          ~ ( ( ~ aElement0(W2)
                              | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                          <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                    | ~ ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                    | ~ ( ( sbrdtbr0(W1) != xk )
                        | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                            | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                            | ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
                | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                    | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                    | ~ ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                    | ~ ! [W2: $i] :
                          ~ ( ( ~ aElement0(W2)
                              | ~ ( aElementOf0(W2,W1)
                                  | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
                          <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
          | ~ ! [W1: $i] :
                ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
                      | ~ ( ~ aSet0(W1)
                          | ( sbrdtbr0(W1) != xk )
                          | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                          | ~ ! [W2: $i] :
                                ( ~ aElementOf0(W2,W1)
                                | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
                  | ~ ( ( sbrdtbr0(W1) != xk )
                      | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
                      | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                          | ~ ( ~ aSet0(W1)
                              | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                                  | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) ) ) )
  <=> ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ aFunction0(sdtlpdtrp0(xC,W0))
                | ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                | ~ ! [W1: $i] :
                      ~ ( ( ~ aElement0(W1)
                          | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                | ~ ! [W1: $i] :
                      ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                            | ~ ( ~ aSet0(W1)
                                | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                | ( sbrdtbr0(W1) != xk )
                                | ~ ! [W2: $i] :
                                      ( ~ aElementOf0(W2,W1)
                                      | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                        | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                            | ( sbrdtbr0(W1) != xk )
                            | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                | ~ ( ~ aSet0(W1)
                                    | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                        | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
                | ~ ! [W1: $i] :
                      ( ~ aSet0(W1)
                      | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                          | ~ ( ( sbrdtbr0(W1) != xk )
                              | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  | ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                  | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          | ~ ! [W2: $i] :
                                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                          | ~ ! [W2: $i] :
                                ~ ( ( ~ aElement0(W2)
                                    | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                                <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                      | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                          | ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                          | ~ ! [W2: $i] :
                                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                          | ~ ! [W2: $i] :
                                ~ ( ( ~ aElement0(W2)
                                    | ~ ( aElementOf0(W2,W1)
                                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ ! [W1: $i] :
                ~ ( ( ~ aElement0(W1)
                    | ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                    | ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
          | ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
          | ~ aFunction0(sdtlpdtrp0(xC,xn))
          | ~ ! [W1: $i] :
                ( ~ aSet0(W1)
                | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                    | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                    | aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                    | ~ ! [W2: $i] :
                          ~ ( ( ~ aElement0(W2)
                              | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                          <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                    | ~ ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                    | ~ ( ( sbrdtbr0(W1) != xk )
                        | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                            | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                            | ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
                | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                    | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                    | ~ ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                    | ~ ! [W2: $i] :
                          ~ ( ( ~ aElement0(W2)
                              | ~ ( aElementOf0(W2,W1)
                                  | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
                          <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
          | ~ ! [W1: $i] :
                ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
                      | ~ ( ~ aSet0(W1)
                          | ( sbrdtbr0(W1) != xk )
                          | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                          | ~ ! [W2: $i] :
                                ( ~ aElementOf0(W2,W1)
                                | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
                  | ~ ( ( sbrdtbr0(W1) != xk )
                      | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
                      | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                          | ~ ( ~ aSet0(W1)
                              | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                                  | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) ) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(327,plain,
    ( ( ~ aElementOf0(xn,szNzAzT0)
      | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aFunction0(sdtlpdtrp0(xC,xn))
          | ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
          | ~ ! [W1: $i] :
                ~ ( ( ~ aElement0(W1)
                    | ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                    | ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W1: $i] :
                ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
                      | ~ ( ~ aSet0(W1)
                          | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                          | ( sbrdtbr0(W1) != xk )
                          | ~ ! [W2: $i] :
                                ( ~ aElementOf0(W2,W1)
                                | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
                  | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
                      | ( sbrdtbr0(W1) != xk )
                      | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                          | ~ ( ~ aSet0(W1)
                              | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                                  | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
          | ~ ! [W1: $i] :
                ( ~ aSet0(W1)
                | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                    | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                    | ~ ( ( sbrdtbr0(W1) != xk )
                        | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                            | ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                            | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
                    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                    | ~ ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                    | ~ ! [W2: $i] :
                          ~ ( ( ~ aElement0(W2)
                              | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                          <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
                | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                    | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                    | ~ ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                    | ~ ! [W2: $i] :
                          ~ ( ( ~ aElement0(W2)
                              | ~ ( aElementOf0(W2,W1)
                                  | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
                          <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
  <=> ( ~ aElementOf0(xn,szNzAzT0)
      | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ ! [W1: $i] :
                ~ ( ( ~ aElement0(W1)
                    | ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                    | ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
          | ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
          | ~ aFunction0(sdtlpdtrp0(xC,xn))
          | ~ ! [W1: $i] :
                ( ~ aSet0(W1)
                | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                    | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                    | aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                    | ~ ! [W2: $i] :
                          ~ ( ( ~ aElement0(W2)
                              | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                          <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                    | ~ ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                    | ~ ( ( sbrdtbr0(W1) != xk )
                        | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                            | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                            | ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
                | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                    | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                    | ~ ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                    | ~ ! [W2: $i] :
                          ~ ( ( ~ aElement0(W2)
                              | ~ ( aElementOf0(W2,W1)
                                  | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
                          <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
          | ~ ! [W1: $i] :
                ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
                      | ~ ( ~ aSet0(W1)
                          | ( sbrdtbr0(W1) != xk )
                          | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                          | ~ ! [W2: $i] :
                                ( ~ aElementOf0(W2,W1)
                                | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
                  | ~ ( ( sbrdtbr0(W1) != xk )
                      | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
                      | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                          | ~ ( ~ aSet0(W1)
                              | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                                  | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) ) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(328,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ aFunction0(sdtlpdtrp0(xC,W0))
                | ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                | ~ ! [W1: $i] :
                      ~ ( ( ~ aElement0(W1)
                          | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                | ~ ! [W1: $i] :
                      ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                            | ~ ( ~ aSet0(W1)
                                | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                | ( sbrdtbr0(W1) != xk )
                                | ~ ! [W2: $i] :
                                      ( ~ aElementOf0(W2,W1)
                                      | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                        | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                            | ( sbrdtbr0(W1) != xk )
                            | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                | ~ ( ~ aSet0(W1)
                                    | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                        | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
                | ~ ! [W1: $i] :
                      ( ~ aSet0(W1)
                      | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                          | ~ ( ( sbrdtbr0(W1) != xk )
                              | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  | ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                  | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          | ~ ! [W2: $i] :
                                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                          | ~ ! [W2: $i] :
                                ~ ( ( ~ aElement0(W2)
                                    | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                                <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                      | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                          | ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                          | ~ ! [W2: $i] :
                                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                          | ~ ! [W2: $i] :
                                ~ ( ( ~ aElement0(W2)
                                    | ~ ( aElementOf0(W2,W1)
                                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aFunction0(sdtlpdtrp0(xC,xn))
          | ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
          | ~ ! [W1: $i] :
                ~ ( ( ~ aElement0(W1)
                    | ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                    | ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W1: $i] :
                ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
                      | ~ ( ~ aSet0(W1)
                          | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                          | ( sbrdtbr0(W1) != xk )
                          | ~ ! [W2: $i] :
                                ( ~ aElementOf0(W2,W1)
                                | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
                  | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
                      | ( sbrdtbr0(W1) != xk )
                      | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                          | ~ ( ~ aSet0(W1)
                              | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                                  | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
          | ~ ! [W1: $i] :
                ( ~ aSet0(W1)
                | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                    | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                    | ~ ( ( sbrdtbr0(W1) != xk )
                        | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                            | ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                            | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
                    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                    | ~ ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                    | ~ ! [W2: $i] :
                          ~ ( ( ~ aElement0(W2)
                              | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                          <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
                | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                    | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                    | ~ ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                    | ~ ! [W2: $i] :
                          ~ ( ( ~ aElement0(W2)
                              | ~ ( aElementOf0(W2,W1)
                                  | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
                          <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
  <=> ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ aFunction0(sdtlpdtrp0(xC,W0))
                | ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                | ~ ! [W1: $i] :
                      ~ ( ( ~ aElement0(W1)
                          | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                | ~ ! [W1: $i] :
                      ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                            | ~ ( ~ aSet0(W1)
                                | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                | ( sbrdtbr0(W1) != xk )
                                | ~ ! [W2: $i] :
                                      ( ~ aElementOf0(W2,W1)
                                      | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                        | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                            | ( sbrdtbr0(W1) != xk )
                            | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                | ~ ( ~ aSet0(W1)
                                    | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                        | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
                | ~ ! [W1: $i] :
                      ( ~ aSet0(W1)
                      | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                          | ~ ( ( sbrdtbr0(W1) != xk )
                              | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  | ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                  | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          | ~ ! [W2: $i] :
                                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                          | ~ ! [W2: $i] :
                                ~ ( ( ~ aElement0(W2)
                                    | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                                <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                      | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                          | ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                          | ~ ! [W2: $i] :
                                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                          | ~ ! [W2: $i] :
                                ~ ( ( ~ aElement0(W2)
                                    | ~ ( aElementOf0(W2,W1)
                                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ ! [W1: $i] :
                ~ ( ( ~ aElement0(W1)
                    | ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                    | ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
          | ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
          | ~ aFunction0(sdtlpdtrp0(xC,xn))
          | ~ ! [W1: $i] :
                ( ~ aSet0(W1)
                | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                    | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                    | aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                    | ~ ! [W2: $i] :
                          ~ ( ( ~ aElement0(W2)
                              | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                          <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                    | ~ ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                    | ~ ( ( sbrdtbr0(W1) != xk )
                        | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                            | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                            | ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
                | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                    | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                    | ~ ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                    | ~ ! [W2: $i] :
                          ~ ( ( ~ aElement0(W2)
                              | ~ ( aElementOf0(W2,W1)
                                  | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
                          <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
          | ~ ! [W1: $i] :
                ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
                      | ~ ( ~ aSet0(W1)
                          | ( sbrdtbr0(W1) != xk )
                          | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                          | ~ ! [W2: $i] :
                                ( ~ aElementOf0(W2,W1)
                                | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
                  | ~ ( ( sbrdtbr0(W1) != xk )
                      | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
                      | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                          | ~ ( ~ aSet0(W1)
                              | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                                  | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) ) ) ) ),
    inference(monotonicity,[status(thm)],[327]) ).

tff(329,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ aFunction0(sdtlpdtrp0(xC,W0))
                | ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                | ~ ! [W1: $i] :
                      ~ ( ( ~ aElement0(W1)
                          | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                | ~ ! [W1: $i] :
                      ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                            | ~ ( ~ aSet0(W1)
                                | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                | ( sbrdtbr0(W1) != xk )
                                | ~ ! [W2: $i] :
                                      ( ~ aElementOf0(W2,W1)
                                      | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                        | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                            | ( sbrdtbr0(W1) != xk )
                            | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                | ~ ( ~ aSet0(W1)
                                    | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                        | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
                | ~ ! [W1: $i] :
                      ( ~ aSet0(W1)
                      | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                          | ~ ( ( sbrdtbr0(W1) != xk )
                              | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  | ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                  | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          | ~ ! [W2: $i] :
                                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                          | ~ ! [W2: $i] :
                                ~ ( ( ~ aElement0(W2)
                                    | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                                <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                      | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                          | ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                          | ~ ! [W2: $i] :
                                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                          | ~ ! [W2: $i] :
                                ~ ( ( ~ aElement0(W2)
                                    | ~ ( aElementOf0(W2,W1)
                                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aFunction0(sdtlpdtrp0(xC,xn))
          | ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
          | ~ ! [W1: $i] :
                ~ ( ( ~ aElement0(W1)
                    | ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                    | ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W1: $i] :
                ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
                      | ~ ( ~ aSet0(W1)
                          | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                          | ( sbrdtbr0(W1) != xk )
                          | ~ ! [W2: $i] :
                                ( ~ aElementOf0(W2,W1)
                                | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
                  | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
                      | ( sbrdtbr0(W1) != xk )
                      | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                          | ~ ( ~ aSet0(W1)
                              | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                                  | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
          | ~ ! [W1: $i] :
                ( ~ aSet0(W1)
                | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                    | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                    | ~ ( ( sbrdtbr0(W1) != xk )
                        | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                            | ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                            | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
                    | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                    | ~ ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                    | ~ ! [W2: $i] :
                          ~ ( ( ~ aElement0(W2)
                              | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                          <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
                | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                    | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                    | ~ ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                    | ~ ! [W2: $i] :
                          ~ ( ( ~ aElement0(W2)
                              | ~ ( aElementOf0(W2,W1)
                                  | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
                          <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
  <=> ( ~ ! [W0: $i] :
            ( ~ aElementOf0(W0,szNzAzT0)
            | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                | ~ aFunction0(sdtlpdtrp0(xC,W0))
                | ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
                | ~ ! [W1: $i] :
                      ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
                | ~ ! [W1: $i] :
                      ~ ( ( ~ aElement0(W1)
                          | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                          | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                      <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                | ~ ! [W1: $i] :
                      ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                            | ~ ( ~ aSet0(W1)
                                | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                | ( sbrdtbr0(W1) != xk )
                                | ~ ! [W2: $i] :
                                      ( ~ aElementOf0(W2,W1)
                                      | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                        | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                            | ( sbrdtbr0(W1) != xk )
                            | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                | ~ ( ~ aSet0(W1)
                                    | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                        | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
                | ~ ! [W1: $i] :
                      ( ~ aSet0(W1)
                      | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                          | ~ ( ( sbrdtbr0(W1) != xk )
                              | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                  | ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                  | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                          | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                          | ~ ! [W2: $i] :
                                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                          | ~ ! [W2: $i] :
                                ~ ( ( ~ aElement0(W2)
                                    | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                                <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                      | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                          | ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                          | ~ ! [W2: $i] :
                                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                          | ~ ! [W2: $i] :
                                ~ ( ( ~ aElement0(W2)
                                    | ~ ( aElementOf0(W2,W1)
                                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                                <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
      | ~ aElementOf0(xn,szNzAzT0)
      | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ ! [W1: $i] :
                ~ ( ( ~ aElement0(W1)
                    | ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                    | ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W1: $i] :
                ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
          | ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
          | ~ aFunction0(sdtlpdtrp0(xC,xn))
          | ~ ! [W1: $i] :
                ( ~ aSet0(W1)
                | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                    | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                    | aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                    | ~ ! [W2: $i] :
                          ~ ( ( ~ aElement0(W2)
                              | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                          <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                    | ~ ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                    | ~ ( ( sbrdtbr0(W1) != xk )
                        | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                            | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                            | ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
                | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                    | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                    | ~ ! [W2: $i] :
                          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                    | ~ ! [W2: $i] :
                          ~ ( ( ~ aElement0(W2)
                              | ~ ( aElementOf0(W2,W1)
                                  | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
                          <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
          | ~ ! [W1: $i] :
                ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
                      | ~ ( ~ aSet0(W1)
                          | ( sbrdtbr0(W1) != xk )
                          | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                          | ~ ! [W2: $i] :
                                ( ~ aElementOf0(W2,W1)
                                | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
                  | ~ ( ( sbrdtbr0(W1) != xk )
                      | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
                      | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                          | ~ ( ~ aSet0(W1)
                              | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                                  | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) ) ) ) ),
    inference(transitivity,[status(thm)],[328,326]) ).

tff(330,plain,
    ( ~ ! [W0: $i] :
          ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ aFunction0(sdtlpdtrp0(xC,W0))
              | ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              | ~ ! [W1: $i] :
                    ~ ( ( ~ aElement0(W1)
                        | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                    <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              | ~ ! [W1: $i] :
                    ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                          | ~ ( ~ aSet0(W1)
                              | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ( sbrdtbr0(W1) != xk )
                              | ~ ! [W2: $i] :
                                    ( ~ aElementOf0(W2,W1)
                                    | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                      | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                          | ( sbrdtbr0(W1) != xk )
                          | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ~ ( ~ aSet0(W1)
                                  | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                      | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
              | ~ ! [W1: $i] :
                    ( ~ aSet0(W1)
                    | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                        | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        | ~ ( ( sbrdtbr0(W1) != xk )
                            | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                | ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                        | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        | ~ ! [W2: $i] :
                              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                        | ~ ! [W2: $i] :
                              ~ ( ( ~ aElement0(W2)
                                  | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                  | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                              <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                    | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        | ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                        | ~ ! [W2: $i] :
                              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                        | ~ ! [W2: $i] :
                              ~ ( ( ~ aElement0(W2)
                                  | ~ ( aElementOf0(W2,W1)
                                      | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                              <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
    | ~ aElementOf0(xn,szNzAzT0)
    | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
        | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
        | ~ aFunction0(sdtlpdtrp0(xC,xn))
        | ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
        | ~ ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
        | ~ ! [W1: $i] :
              ~ ( ( ~ aElement0(W1)
                  | ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                  | ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
              <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
        | ~ ! [W1: $i] :
              ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
                    | ~ ( ~ aSet0(W1)
                        | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                        | ( sbrdtbr0(W1) != xk )
                        | ~ ! [W2: $i] :
                              ( ~ aElementOf0(W2,W1)
                              | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
                | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
                    | ( sbrdtbr0(W1) != xk )
                    | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                        | ~ ( ~ aSet0(W1)
                            | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                                | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
        | ~ ! [W1: $i] :
              ( ~ aSet0(W1)
              | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                  | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                  | ~ ( ( sbrdtbr0(W1) != xk )
                      | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                          | ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                          | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
                  | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                  | ~ ! [W2: $i] :
                        ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                  | ~ ! [W2: $i] :
                        ~ ( ( ~ aElement0(W2)
                            | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                            | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                        <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
              | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                  | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                  | ~ ! [W2: $i] :
                        ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                  | ~ ! [W2: $i] :
                        ~ ( ( ~ aElement0(W2)
                            | ~ ( aElementOf0(W2,W1)
                                | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
                        <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(331,plain,
    ( ~ ! [W0: $i] :
          ( ~ aElementOf0(W0,szNzAzT0)
          | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
              | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
              | ~ aFunction0(sdtlpdtrp0(xC,W0))
              | ( szDzozmdt0(sdtlpdtrp0(xC,W0)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk) )
              | ~ ! [W1: $i] :
                    ( ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
              | ~ ! [W1: $i] :
                    ~ ( ( ~ aElement0(W1)
                        | ~ aElementOf0(W1,sdtlpdtrp0(xN,W0))
                        | ( W1 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                    <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
              | ~ ! [W1: $i] :
                    ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                          | ~ ( ~ aSet0(W1)
                              | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ( sbrdtbr0(W1) != xk )
                              | ~ ! [W2: $i] :
                                    ( ~ aElementOf0(W2,W1)
                                    | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) )
                      | ~ ( aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,W0)))
                          | ( sbrdtbr0(W1) != xk )
                          | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                              | ~ ( ~ aSet0(W1)
                                  | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                      | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
              | ~ ! [W1: $i] :
                    ( ~ aSet0(W1)
                    | ~ ( aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))),xk))
                        | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        | ~ ( ( sbrdtbr0(W1) != xk )
                            | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                                | ~ aElementOf0(tptp_fun_W2_31(W1,W0),W1)
                                | aElementOf0(tptp_fun_W2_31(W1,W0),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                        | ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
                        | ~ ! [W2: $i] :
                              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                        | ~ ! [W2: $i] :
                              ~ ( ( ~ aElement0(W2)
                                  | ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                                  | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
                              <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) ) )
                    | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
                        | ( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) )
                        | ~ ! [W2: $i] :
                              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
                              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W2) )
                        | ~ ! [W2: $i] :
                              ~ ( ( ~ aElement0(W2)
                                  | ~ ( aElementOf0(W2,W1)
                                      | ( W2 = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
                              <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,W0)))) ) ) ) ) )
    | ~ aElementOf0(xn,szNzAzT0)
    | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
        | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
        | ~ ! [W1: $i] :
              ~ ( ( ~ aElement0(W1)
                  | ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                  | ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
              <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
        | ~ ! [W1: $i] :
              ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
        | ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
        | ~ aFunction0(sdtlpdtrp0(xC,xn))
        | ~ ! [W1: $i] :
              ( ~ aSet0(W1)
              | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                  | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                  | aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                  | ~ ! [W2: $i] :
                        ~ ( ( ~ aElement0(W2)
                            | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                            | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                        <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                  | ~ ! [W2: $i] :
                        ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                  | ~ ( ( sbrdtbr0(W1) != xk )
                      | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                          | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                          | ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
              | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                  | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                  | ~ ! [W2: $i] :
                        ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                        | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                  | ~ ! [W2: $i] :
                        ~ ( ( ~ aElement0(W2)
                            | ~ ( aElementOf0(W2,W1)
                                | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
                        <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
        | ~ ! [W1: $i] :
              ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
                    | ~ ( ~ aSet0(W1)
                        | ( sbrdtbr0(W1) != xk )
                        | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                        | ~ ! [W2: $i] :
                              ( ~ aElementOf0(W2,W1)
                              | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
                | ~ ( ( sbrdtbr0(W1) != xk )
                    | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
                    | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                        | ~ ( ~ aSet0(W1)
                            | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                                | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) ) ) ),
    inference(modus_ponens,[status(thm)],[330,329]) ).

tff(332,plain,
    ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
      | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
      | ~ ! [W1: $i] :
            ~ ( ( ~ aElement0(W1)
                | ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
                | ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
            <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
      | ~ ! [W1: $i] :
            ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
      | ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
      | ~ aFunction0(sdtlpdtrp0(xC,xn))
      | ~ ! [W1: $i] :
            ( ~ aSet0(W1)
            | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                | aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                | ~ ! [W2: $i] :
                      ~ ( ( ~ aElement0(W2)
                          | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                      <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                | ~ ( ( sbrdtbr0(W1) != xk )
                    | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                        | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                        | ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
            | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                | ~ ! [W2: $i] :
                      ~ ( ( ~ aElement0(W2)
                          | ~ ( aElementOf0(W2,W1)
                              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
                      <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
      | ~ ! [W1: $i] :
            ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
                  | ~ ( ~ aSet0(W1)
                      | ( sbrdtbr0(W1) != xk )
                      | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                      | ~ ! [W2: $i] :
                            ( ~ aElementOf0(W2,W1)
                            | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
              | ~ ( ( sbrdtbr0(W1) != xk )
                  | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
                  | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                      | ~ ( ~ aSet0(W1)
                          | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                              | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) ) ),
    inference(unit_resolution,[status(thm)],[331,325,28]) ).

tff(333,plain,
    ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
    | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
    | ~ ! [W1: $i] :
          ~ ( ( ~ aElement0(W1)
              | ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
              | ( W1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
          <=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
    | ~ ! [W1: $i] :
          ( ~ aElementOf0(W1,sdtlpdtrp0(xN,xn))
          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W1) )
    | ( szDzozmdt0(sdtlpdtrp0(xC,xn)) != slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk) )
    | ~ aFunction0(sdtlpdtrp0(xC,xn))
    | ~ ! [W1: $i] :
          ( ~ aSet0(W1)
          | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
              | aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
              | ~ ! [W2: $i] :
                    ~ ( ( ~ aElement0(W2)
                        | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                    <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
              | ~ ( ( sbrdtbr0(W1) != xk )
                  | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                      | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                      | ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
          | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
              | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
              | ~ ! [W2: $i] :
                    ~ ( ( ~ aElement0(W2)
                        | ~ ( aElementOf0(W2,W1)
                            | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
                    <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
    | ~ ! [W1: $i] :
          ~ ( ~ ( ~ aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
                | ~ ( ~ aSet0(W1)
                    | ( sbrdtbr0(W1) != xk )
                    | ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                    | ~ ! [W2: $i] :
                          ( ~ aElementOf0(W2,W1)
                          | aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
            | ~ ( ( sbrdtbr0(W1) != xk )
                | aElementOf0(W1,szDzozmdt0(sdtlpdtrp0(xC,xn)))
                | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                    | ~ ( ~ aSet0(W1)
                        | ~ ( ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1)
                            | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ) )
    | ! [W1: $i] :
        ( ~ aSet0(W1)
        | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
            | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
            | aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
            | ~ ! [W2: $i] :
                  ~ ( ( ~ aElement0(W2)
                      | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                      | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                  <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
            | ~ ! [W2: $i] :
                  ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
            | ~ ( ( sbrdtbr0(W1) != xk )
                | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                    | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                    | ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
        | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
            | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
            | ~ ! [W2: $i] :
                  ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                  | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
            | ~ ! [W2: $i] :
                  ~ ( ( ~ aElement0(W2)
                      | ~ ( aElementOf0(W2,W1)
                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
                  <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ),
    inference(tautology,[status(thm)],[]) ).

tff(334,plain,
    ! [W1: $i] :
      ( ~ aSet0(W1)
      | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
          | ~ ! [W2: $i] :
                ~ ( ( ~ aElement0(W2)
                    | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W2: $i] :
                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
          | ~ ( ( sbrdtbr0(W1) != xk )
              | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                  | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                  | ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
      | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W2: $i] :
                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
          | ~ ! [W2: $i] :
                ~ ( ( ~ aElement0(W2)
                    | ~ ( aElementOf0(W2,W1)
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
                <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ),
    inference(unit_resolution,[status(thm)],[333,332]) ).

tff(335,plain,
    ( ( ~ ! [W1: $i] :
            ( ~ aSet0(W1)
            | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                | aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                | ~ ! [W2: $i] :
                      ~ ( ( ~ aElement0(W2)
                          | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                      <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                | ~ ( ( sbrdtbr0(W1) != xk )
                    | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                        | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                        | ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
            | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                | ~ ! [W2: $i] :
                      ~ ( ( ~ aElement0(W2)
                          | ~ ( aElementOf0(W2,W1)
                              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
                      <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
      | ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
      | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ ! [W2: $i] :
                ~ ( ( ~ aElement0(W2)
                    | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W2: $i] :
                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
          | aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
          | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
              | ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
                  | aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                  | aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
      | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W2: $i] :
                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
          | ~ ! [W2: $i] :
                ~ ( ( ~ aElement0(W2)
                    | ~ ( aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
                <=> aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
  <=> ( ~ ! [W1: $i] :
            ( ~ aSet0(W1)
            | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                | aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                | ~ ! [W2: $i] :
                      ~ ( ( ~ aElement0(W2)
                          | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                      <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                | ~ ( ( sbrdtbr0(W1) != xk )
                    | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                        | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                        | ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
            | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                | ~ ! [W2: $i] :
                      ~ ( ( ~ aElement0(W2)
                          | ~ ( aElementOf0(W2,W1)
                              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
                      <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
      | ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
      | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ ! [W2: $i] :
                ~ ( ( ~ aElement0(W2)
                    | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W2: $i] :
                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
          | aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
          | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
              | ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
                  | aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                  | aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
      | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W2: $i] :
                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
          | ~ ! [W2: $i] :
                ~ ( ( ~ aElement0(W2)
                    | ~ ( aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
                <=> aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(336,plain,
    ( ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
      | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
          | ~ ! [W2: $i] :
                ~ ( ( ~ aElement0(W2)
                    | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W2: $i] :
                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
          | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
              | ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                  | aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                  | ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
      | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W2: $i] :
                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
          | ~ ! [W2: $i] :
                ~ ( ( ~ aElement0(W2)
                    | ~ ( aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
                <=> aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
  <=> ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
      | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ ! [W2: $i] :
                ~ ( ( ~ aElement0(W2)
                    | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W2: $i] :
                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
          | aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
          | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
              | ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
                  | aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                  | aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
      | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W2: $i] :
                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
          | ~ ! [W2: $i] :
                ~ ( ( ~ aElement0(W2)
                    | ~ ( aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
                <=> aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ),
    inference(rewrite,[status(thm)],[]) ).

tff(337,plain,
    ( ( ~ ! [W1: $i] :
            ( ~ aSet0(W1)
            | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                | aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                | ~ ! [W2: $i] :
                      ~ ( ( ~ aElement0(W2)
                          | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                      <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                | ~ ( ( sbrdtbr0(W1) != xk )
                    | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                        | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                        | ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
            | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                | ~ ! [W2: $i] :
                      ~ ( ( ~ aElement0(W2)
                          | ~ ( aElementOf0(W2,W1)
                              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
                      <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
      | ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
      | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
          | ~ ! [W2: $i] :
                ~ ( ( ~ aElement0(W2)
                    | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W2: $i] :
                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
          | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
              | ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                  | aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                  | ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
      | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W2: $i] :
                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
          | ~ ! [W2: $i] :
                ~ ( ( ~ aElement0(W2)
                    | ~ ( aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
                <=> aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
  <=> ( ~ ! [W1: $i] :
            ( ~ aSet0(W1)
            | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                | aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                | ~ ! [W2: $i] :
                      ~ ( ( ~ aElement0(W2)
                          | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                      <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                | ~ ( ( sbrdtbr0(W1) != xk )
                    | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                        | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                        | ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
            | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                | ~ ! [W2: $i] :
                      ~ ( ( ~ aElement0(W2)
                          | ~ ( aElementOf0(W2,W1)
                              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
                      <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
      | ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
      | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ ! [W2: $i] :
                ~ ( ( ~ aElement0(W2)
                    | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W2: $i] :
                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
          | aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
          | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
              | ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
                  | aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                  | aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
      | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W2: $i] :
                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
          | ~ ! [W2: $i] :
                ~ ( ( ~ aElement0(W2)
                    | ~ ( aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
                <=> aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ),
    inference(monotonicity,[status(thm)],[336]) ).

tff(338,plain,
    ( ( ~ ! [W1: $i] :
            ( ~ aSet0(W1)
            | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                | aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                | ~ ! [W2: $i] :
                      ~ ( ( ~ aElement0(W2)
                          | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                      <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                | ~ ( ( sbrdtbr0(W1) != xk )
                    | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                        | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                        | ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
            | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                | ~ ! [W2: $i] :
                      ~ ( ( ~ aElement0(W2)
                          | ~ ( aElementOf0(W2,W1)
                              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
                      <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
      | ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
      | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
          | ~ ! [W2: $i] :
                ~ ( ( ~ aElement0(W2)
                    | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W2: $i] :
                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
          | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
              | ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                  | aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                  | ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
      | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W2: $i] :
                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
          | ~ ! [W2: $i] :
                ~ ( ( ~ aElement0(W2)
                    | ~ ( aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
                <=> aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
  <=> ( ~ ! [W1: $i] :
            ( ~ aSet0(W1)
            | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                | aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
                | ~ ! [W2: $i] :
                      ~ ( ( ~ aElement0(W2)
                          | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                          | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                      <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                | ~ ( ( sbrdtbr0(W1) != xk )
                    | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                        | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                        | ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
            | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
                | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
                | ~ ! [W2: $i] :
                      ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                      | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
                | ~ ! [W2: $i] :
                      ~ ( ( ~ aElement0(W2)
                          | ~ ( aElementOf0(W2,W1)
                              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
                      <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
      | ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
      | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
          | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ~ ! [W2: $i] :
                ~ ( ( ~ aElement0(W2)
                    | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W2: $i] :
                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
          | aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
          | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
              | ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
                  | aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                  | aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
      | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
          | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
          | ~ ! [W2: $i] :
                ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
          | ~ ! [W2: $i] :
                ~ ( ( ~ aElement0(W2)
                    | ~ ( aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
                <=> aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ) ),
    inference(transitivity,[status(thm)],[337,335]) ).

tff(339,plain,
    ( ~ ! [W1: $i] :
          ( ~ aSet0(W1)
          | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
              | aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
              | ~ ! [W2: $i] :
                    ~ ( ( ~ aElement0(W2)
                        | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                    <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
              | ~ ( ( sbrdtbr0(W1) != xk )
                  | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                      | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                      | ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
          | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
              | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
              | ~ ! [W2: $i] :
                    ~ ( ( ~ aElement0(W2)
                        | ~ ( aElementOf0(W2,W1)
                            | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
                    <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
    | ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
    | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
        | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
        | aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
        | ~ ! [W2: $i] :
              ~ ( ( ~ aElement0(W2)
                  | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                  | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
              <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
        | ~ ! [W2: $i] :
              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
        | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
            | ~ ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
    | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
        | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
        | ~ ! [W2: $i] :
              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
        | ~ ! [W2: $i] :
              ~ ( ( ~ aElement0(W2)
                  | ~ ( aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
                      | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
              <=> aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ),
    inference(quant_inst,[status(thm)],[]) ).

tff(340,plain,
    ( ~ ! [W1: $i] :
          ( ~ aSet0(W1)
          | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
              | aElementOf0(W1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
              | ~ ! [W2: $i] :
                    ~ ( ( ~ aElement0(W2)
                        | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                        | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
                    <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
              | ~ ( ( sbrdtbr0(W1) != xk )
                  | ~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                      | aElementOf0(tptp_fun_W2_31(W1,xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                      | ~ aElementOf0(tptp_fun_W2_31(W1,xn),W1) ) ) )
          | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
              | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),W1) != sdtlpdtrp0(xc,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
              | ~ ! [W2: $i] :
                    ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                    | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
              | ~ ! [W2: $i] :
                    ~ ( ( ~ aElement0(W2)
                        | ~ ( aElementOf0(W2,W1)
                            | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
                    <=> aElementOf0(W2,sdtpldt0(W1,szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
    | ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
    | ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
        | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
        | ~ ! [W2: $i] :
              ~ ( ( ~ aElement0(W2)
                  | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                  | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
              <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
        | ~ ! [W2: $i] :
              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
        | aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
        | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
            | ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
                | aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
    | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
        | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
        | ~ ! [W2: $i] :
              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
        | ~ ! [W2: $i] :
              ~ ( ( ~ aElement0(W2)
                  | ~ ( aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
                      | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
              <=> aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ),
    inference(modus_ponens,[status(thm)],[339,338]) ).

tff(341,plain,
    ( ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
        | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
        | ~ ! [W2: $i] :
              ~ ( ( ~ aElement0(W2)
                  | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                  | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
              <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
        | ~ ! [W2: $i] :
              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
        | aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
        | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
            | ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
                | aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
                | aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) )
    | ~ ( ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
        | ( sdtlpdtrp0(sdtlpdtrp0(xC,xn),sdtmndt0(xQ,szmzizndt0(xQ))) != sdtlpdtrp0(xc,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
        | ~ ! [W2: $i] :
              ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
              | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
        | ~ ! [W2: $i] :
              ~ ( ( ~ aElement0(W2)
                  | ~ ( aElementOf0(W2,sdtmndt0(xQ,szmzizndt0(xQ)))
                      | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
              <=> aElementOf0(W2,sdtpldt0(sdtmndt0(xQ,szmzizndt0(xQ)),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ),
    inference(unit_resolution,[status(thm)],[340,170,334]) ).

tff(342,plain,
    ~ ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
      | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
      | ~ ! [W2: $i] :
            ~ ( ( ~ aElement0(W2)
                | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
                | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
            <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
      | ~ ! [W2: $i] :
            ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
            | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
      | aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
      | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
          | ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
              | aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
              | aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) ) ),
    inference(unit_resolution,[status(thm)],[341,302]) ).

tff(343,plain,
    ( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
    | ~ aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xn)),sdtlpdtrp0(xN,xn))
    | ~ ! [W2: $i] :
          ~ ( ( ~ aElement0(W2)
              | ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
              | ( W2 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) )
          <=> aElementOf0(W2,sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) )
    | ~ ! [W2: $i] :
          ( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
          | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),W2) )
    | aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
    | ~ ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk )
        | ~ ( ~ aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(xQ,szmzizndt0(xQ)))
            | aElementOf0(tptp_fun_W2_31(sdtmndt0(xQ,szmzizndt0(xQ)),xn),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))))
            | aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn)))) ) )
    | ~ aElementOf0(sdtmndt0(xQ,szmzizndt0(xQ)),slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) ),
    inference(tautology,[status(thm)],[]) ).

tff(344,plain,
    $false,
    inference(unit_resolution,[status(thm)],[343,342,179]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : NUM628+3 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12  % Command    : run_E %s %d THM
% 0.12/0.33  % Computer : n013.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Fri Jun 20 01:37:23 EDT 2025
% 0.12/0.34  % CPUTime    : 
% 2.74/2.93  % SZS status Theorem
% 2.74/2.93  % SZS output start Proof
% See solution above
% 2.99/3.16  % E exiting
%------------------------------------------------------------------------------