TSTP Solution File: NUM576+3 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : NUM576+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n003.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 : Sun Sep 18 13:10:37 EDT 2022

% Result   : Theorem 0.19s 0.56s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   39
% Syntax   : Number of formulae    :   84 (  23 unt;   8 typ;   0 def)
%            Number of atoms       :  689 (  65 equ)
%            Maximal formula atoms :   20 (   9 avg)
%            Number of connectives :  924 ( 369   ~; 386   |;  90   &)
%                                         (  63 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :   58 (  58 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   4   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-1 aty)
%            Number of variables   :  132 ( 116   !;   0   ?; 132   :)

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

tff(xi_type,type,
    xi: $i ).

tff(xj_type,type,
    xj: $i ).

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

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

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

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

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

tff(1,plain,
    ( ~ sdtlseqdt0(szszuzczcdt0(xi),xj)
  <=> ~ sdtlseqdt0(szszuzczcdt0(xi),xj) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,plain,
    ( ~ ( ( xi != xj )
       => ( sdtlseqdt0(szszuzczcdt0(xj),xi)
          | sdtlseqdt0(szszuzczcdt0(xi),xj) ) )
  <=> ~ ( ( xi = xj )
        | sdtlseqdt0(szszuzczcdt0(xj),xi)
        | sdtlseqdt0(szszuzczcdt0(xi),xj) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(3,axiom,
    ~ ( ( xi != xj )
     => ( sdtlseqdt0(szszuzczcdt0(xj),xi)
        | sdtlseqdt0(szszuzczcdt0(xi),xj) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

tff(4,plain,
    ~ ( ( xi = xj )
      | sdtlseqdt0(szszuzczcdt0(xj),xi)
      | sdtlseqdt0(szszuzczcdt0(xi),xj) ),
    inference(modus_ponens,[status(thm)],[3,2]) ).

tff(5,plain,
    ~ sdtlseqdt0(szszuzczcdt0(xi),xj),
    inference(or_elim,[status(thm)],[4]) ).

tff(6,plain,
    ~ sdtlseqdt0(szszuzczcdt0(xi),xj),
    inference(modus_ponens,[status(thm)],[5,1]) ).

tff(7,plain,
    ( aElementOf0(xj,szNzAzT0)
  <=> aElementOf0(xj,szDzozmdt0(xN)) ),
    inference(rewrite,[status(thm)],]) ).

tff(8,plain,
    ( aElementOf0(xj,szNzAzT0)
  <=> aElementOf0(xj,szNzAzT0) ),
    inference(rewrite,[status(thm)],]) ).

tff(9,axiom,
    ( aElementOf0(xi,szNzAzT0)
    & aElementOf0(xj,szNzAzT0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3856) ).

tff(10,plain,
    aElementOf0(xj,szNzAzT0),
    inference(and_elim,[status(thm)],[9]) ).

tff(11,plain,
    aElementOf0(xj,szNzAzT0),
    inference(modus_ponens,[status(thm)],[10,8]) ).

tff(12,plain,
    aElementOf0(xj,szDzozmdt0(xN)),
    inference(modus_ponens,[status(thm)],[11,7]) ).

tff(13,plain,
    ( aElementOf0(xi,szNzAzT0)
  <=> aElementOf0(xi,szDzozmdt0(xN)) ),
    inference(rewrite,[status(thm)],]) ).

tff(14,plain,
    ( aElementOf0(xi,szNzAzT0)
  <=> aElementOf0(xi,szNzAzT0) ),
    inference(rewrite,[status(thm)],]) ).

tff(15,plain,
    aElementOf0(xi,szNzAzT0),
    inference(and_elim,[status(thm)],[9]) ).

tff(16,plain,
    aElementOf0(xi,szNzAzT0),
    inference(modus_ponens,[status(thm)],[15,14]) ).

tff(17,plain,
    aElementOf0(xi,szDzozmdt0(xN)),
    inference(modus_ponens,[status(thm)],[16,13]) ).

tff(18,plain,
    ^ [W0: $i,W1: $i] :
      refl(
        ( ( sdtlseqdt0(W0,W1)
          | sdtlseqdt0(szszuzczcdt0(W1),W0)
          | ~ aElementOf0(W1,szDzozmdt0(xN))
          | ~ aElementOf0(W0,szDzozmdt0(xN)) )
      <=> ( sdtlseqdt0(W0,W1)
          | sdtlseqdt0(szszuzczcdt0(W1),W0)
          | ~ aElementOf0(W1,szDzozmdt0(xN))
          | ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
    inference(bind,[status(th)],]) ).

tff(19,plain,
    ( ! [W0: $i,W1: $i] :
        ( sdtlseqdt0(W0,W1)
        | sdtlseqdt0(szszuzczcdt0(W1),W0)
        | ~ aElementOf0(W1,szDzozmdt0(xN))
        | ~ aElementOf0(W0,szDzozmdt0(xN)) )
  <=> ! [W0: $i,W1: $i] :
        ( sdtlseqdt0(W0,W1)
        | sdtlseqdt0(szszuzczcdt0(W1),W0)
        | ~ aElementOf0(W1,szDzozmdt0(xN))
        | ~ aElementOf0(W0,szDzozmdt0(xN)) ) ),
    inference(quant_intro,[status(thm)],[18]) ).

tff(20,plain,
    ^ [W0: $i,W1: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( aElementOf0(W0,szDzozmdt0(xN))
                  & aElementOf0(W1,szDzozmdt0(xN)) )
              <=> ~ ( ~ aElementOf0(W1,szDzozmdt0(xN))
                    | ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
              ( ~ ( aElementOf0(W0,szDzozmdt0(xN))
                  & aElementOf0(W1,szDzozmdt0(xN)) )
            <=> ~ ~ ( ~ aElementOf0(W1,szDzozmdt0(xN))
                    | ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
            rewrite(
              ( ~ ~ ( ~ aElementOf0(W1,szDzozmdt0(xN))
                    | ~ aElementOf0(W0,szDzozmdt0(xN)) )
            <=> ( ~ aElementOf0(W1,szDzozmdt0(xN))
                | ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
            ( ~ ( aElementOf0(W0,szDzozmdt0(xN))
                & aElementOf0(W1,szDzozmdt0(xN)) )
          <=> ( ~ aElementOf0(W1,szDzozmdt0(xN))
              | ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
          ( ( sdtlseqdt0(W0,W1)
            | sdtlseqdt0(szszuzczcdt0(W1),W0)
            | ~ ( aElementOf0(W0,szDzozmdt0(xN))
                & aElementOf0(W1,szDzozmdt0(xN)) ) )
        <=> ( sdtlseqdt0(W0,W1)
            | sdtlseqdt0(szszuzczcdt0(W1),W0)
            | ~ aElementOf0(W1,szDzozmdt0(xN))
            | ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
        rewrite(
          ( ( sdtlseqdt0(W0,W1)
            | sdtlseqdt0(szszuzczcdt0(W1),W0)
            | ~ aElementOf0(W1,szDzozmdt0(xN))
            | ~ aElementOf0(W0,szDzozmdt0(xN)) )
        <=> ( sdtlseqdt0(W0,W1)
            | sdtlseqdt0(szszuzczcdt0(W1),W0)
            | ~ aElementOf0(W1,szDzozmdt0(xN))
            | ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
        ( ( sdtlseqdt0(W0,W1)
          | sdtlseqdt0(szszuzczcdt0(W1),W0)
          | ~ ( aElementOf0(W0,szDzozmdt0(xN))
              & aElementOf0(W1,szDzozmdt0(xN)) ) )
      <=> ( sdtlseqdt0(W0,W1)
          | sdtlseqdt0(szszuzczcdt0(W1),W0)
          | ~ aElementOf0(W1,szDzozmdt0(xN))
          | ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
    inference(bind,[status(th)],]) ).

tff(21,plain,
    ( ! [W0: $i,W1: $i] :
        ( sdtlseqdt0(W0,W1)
        | sdtlseqdt0(szszuzczcdt0(W1),W0)
        | ~ ( aElementOf0(W0,szDzozmdt0(xN))
            & aElementOf0(W1,szDzozmdt0(xN)) ) )
  <=> ! [W0: $i,W1: $i] :
        ( sdtlseqdt0(W0,W1)
        | sdtlseqdt0(szszuzczcdt0(W1),W0)
        | ~ aElementOf0(W1,szDzozmdt0(xN))
        | ~ aElementOf0(W0,szDzozmdt0(xN)) ) ),
    inference(quant_intro,[status(thm)],[20]) ).

tff(22,plain,
    ^ [W0: $i,W1: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ~ ( aElementOf0(W0,szNzAzT0)
                & aElementOf0(W1,szNzAzT0) )
          <=> ~ ( aElementOf0(W0,szDzozmdt0(xN))
                & aElementOf0(W1,szDzozmdt0(xN)) ) )),
          ( ( sdtlseqdt0(W0,W1)
            | sdtlseqdt0(szszuzczcdt0(W1),W0)
            | ~ ( aElementOf0(W0,szNzAzT0)
                & aElementOf0(W1,szNzAzT0) ) )
        <=> ( sdtlseqdt0(W0,W1)
            | sdtlseqdt0(szszuzczcdt0(W1),W0)
            | ~ ( aElementOf0(W0,szDzozmdt0(xN))
                & aElementOf0(W1,szDzozmdt0(xN)) ) ) )),
        rewrite(
          ( ( sdtlseqdt0(W0,W1)
            | sdtlseqdt0(szszuzczcdt0(W1),W0)
            | ~ ( aElementOf0(W0,szDzozmdt0(xN))
                & aElementOf0(W1,szDzozmdt0(xN)) ) )
        <=> ( sdtlseqdt0(W0,W1)
            | sdtlseqdt0(szszuzczcdt0(W1),W0)
            | ~ ( aElementOf0(W0,szDzozmdt0(xN))
                & aElementOf0(W1,szDzozmdt0(xN)) ) ) )),
        ( ( sdtlseqdt0(W0,W1)
          | sdtlseqdt0(szszuzczcdt0(W1),W0)
          | ~ ( aElementOf0(W0,szNzAzT0)
              & aElementOf0(W1,szNzAzT0) ) )
      <=> ( sdtlseqdt0(W0,W1)
          | sdtlseqdt0(szszuzczcdt0(W1),W0)
          | ~ ( aElementOf0(W0,szDzozmdt0(xN))
              & aElementOf0(W1,szDzozmdt0(xN)) ) ) )),
    inference(bind,[status(th)],]) ).

tff(23,plain,
    ( ! [W0: $i,W1: $i] :
        ( sdtlseqdt0(W0,W1)
        | sdtlseqdt0(szszuzczcdt0(W1),W0)
        | ~ ( aElementOf0(W0,szNzAzT0)
            & aElementOf0(W1,szNzAzT0) ) )
  <=> ! [W0: $i,W1: $i] :
        ( sdtlseqdt0(W0,W1)
        | sdtlseqdt0(szszuzczcdt0(W1),W0)
        | ~ ( aElementOf0(W0,szDzozmdt0(xN))
            & aElementOf0(W1,szDzozmdt0(xN)) ) ) ),
    inference(quant_intro,[status(thm)],[22]) ).

tff(24,plain,
    ( ! [W0: $i,W1: $i] :
        ( sdtlseqdt0(W0,W1)
        | sdtlseqdt0(szszuzczcdt0(W1),W0)
        | ~ ( aElementOf0(W0,szNzAzT0)
            & aElementOf0(W1,szNzAzT0) ) )
  <=> ! [W0: $i,W1: $i] :
        ( sdtlseqdt0(W0,W1)
        | sdtlseqdt0(szszuzczcdt0(W1),W0)
        | ~ ( aElementOf0(W0,szNzAzT0)
            & aElementOf0(W1,szNzAzT0) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(25,plain,
    ^ [W0: $i,W1: $i] :
      rewrite(
        ( ( ( aElementOf0(W0,szNzAzT0)
            & aElementOf0(W1,szNzAzT0) )
         => ( sdtlseqdt0(W0,W1)
            | sdtlseqdt0(szszuzczcdt0(W1),W0) ) )
      <=> ( sdtlseqdt0(W0,W1)
          | sdtlseqdt0(szszuzczcdt0(W1),W0)
          | ~ ( aElementOf0(W0,szNzAzT0)
              & aElementOf0(W1,szNzAzT0) ) ) )),
    inference(bind,[status(th)],]) ).

tff(26,plain,
    ( ! [W0: $i,W1: $i] :
        ( ( aElementOf0(W0,szNzAzT0)
          & aElementOf0(W1,szNzAzT0) )
       => ( sdtlseqdt0(W0,W1)
          | sdtlseqdt0(szszuzczcdt0(W1),W0) ) )
  <=> ! [W0: $i,W1: $i] :
        ( sdtlseqdt0(W0,W1)
        | sdtlseqdt0(szszuzczcdt0(W1),W0)
        | ~ ( aElementOf0(W0,szNzAzT0)
            & aElementOf0(W1,szNzAzT0) ) ) ),
    inference(quant_intro,[status(thm)],[25]) ).

tff(27,axiom,
    ! [W0: $i,W1: $i] :
      ( ( aElementOf0(W0,szNzAzT0)
        & aElementOf0(W1,szNzAzT0) )
     => ( sdtlseqdt0(W0,W1)
        | sdtlseqdt0(szszuzczcdt0(W1),W0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessTotal) ).

tff(28,plain,
    ! [W0: $i,W1: $i] :
      ( sdtlseqdt0(W0,W1)
      | sdtlseqdt0(szszuzczcdt0(W1),W0)
      | ~ ( aElementOf0(W0,szNzAzT0)
          & aElementOf0(W1,szNzAzT0) ) ),
    inference(modus_ponens,[status(thm)],[27,26]) ).

tff(29,plain,
    ! [W0: $i,W1: $i] :
      ( sdtlseqdt0(W0,W1)
      | sdtlseqdt0(szszuzczcdt0(W1),W0)
      | ~ ( aElementOf0(W0,szNzAzT0)
          & aElementOf0(W1,szNzAzT0) ) ),
    inference(modus_ponens,[status(thm)],[28,24]) ).

tff(30,plain,
    ! [W0: $i,W1: $i] :
      ( sdtlseqdt0(W0,W1)
      | sdtlseqdt0(szszuzczcdt0(W1),W0)
      | ~ ( aElementOf0(W0,szDzozmdt0(xN))
          & aElementOf0(W1,szDzozmdt0(xN)) ) ),
    inference(modus_ponens,[status(thm)],[29,23]) ).

tff(31,plain,
    ! [W0: $i,W1: $i] :
      ( sdtlseqdt0(W0,W1)
      | sdtlseqdt0(szszuzczcdt0(W1),W0)
      | ~ ( aElementOf0(W0,szDzozmdt0(xN))
          & aElementOf0(W1,szDzozmdt0(xN)) ) ),
    inference(skolemize,[status(sab)],[30]) ).

tff(32,plain,
    ! [W0: $i,W1: $i] :
      ( sdtlseqdt0(W0,W1)
      | sdtlseqdt0(szszuzczcdt0(W1),W0)
      | ~ aElementOf0(W1,szDzozmdt0(xN))
      | ~ aElementOf0(W0,szDzozmdt0(xN)) ),
    inference(modus_ponens,[status(thm)],[31,21]) ).

tff(33,plain,
    ! [W0: $i,W1: $i] :
      ( sdtlseqdt0(W0,W1)
      | sdtlseqdt0(szszuzczcdt0(W1),W0)
      | ~ aElementOf0(W1,szDzozmdt0(xN))
      | ~ aElementOf0(W0,szDzozmdt0(xN)) ),
    inference(modus_ponens,[status(thm)],[32,19]) ).

tff(34,plain,
    ( ( ~ ! [W0: $i,W1: $i] :
            ( sdtlseqdt0(W0,W1)
            | sdtlseqdt0(szszuzczcdt0(W1),W0)
            | ~ aElementOf0(W1,szDzozmdt0(xN))
            | ~ aElementOf0(W0,szDzozmdt0(xN)) )
      | sdtlseqdt0(szszuzczcdt0(xi),xj)
      | ~ aElementOf0(xi,szDzozmdt0(xN))
      | ~ aElementOf0(xj,szDzozmdt0(xN))
      | sdtlseqdt0(xj,xi) )
  <=> ( ~ ! [W0: $i,W1: $i] :
            ( sdtlseqdt0(W0,W1)
            | sdtlseqdt0(szszuzczcdt0(W1),W0)
            | ~ aElementOf0(W1,szDzozmdt0(xN))
            | ~ aElementOf0(W0,szDzozmdt0(xN)) )
      | sdtlseqdt0(szszuzczcdt0(xi),xj)
      | ~ aElementOf0(xi,szDzozmdt0(xN))
      | ~ aElementOf0(xj,szDzozmdt0(xN))
      | sdtlseqdt0(xj,xi) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(35,plain,
    ( ( sdtlseqdt0(xj,xi)
      | sdtlseqdt0(szszuzczcdt0(xi),xj)
      | ~ aElementOf0(xi,szDzozmdt0(xN))
      | ~ aElementOf0(xj,szDzozmdt0(xN)) )
  <=> ( sdtlseqdt0(szszuzczcdt0(xi),xj)
      | ~ aElementOf0(xi,szDzozmdt0(xN))
      | ~ aElementOf0(xj,szDzozmdt0(xN))
      | sdtlseqdt0(xj,xi) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(36,plain,
    ( ( ~ ! [W0: $i,W1: $i] :
            ( sdtlseqdt0(W0,W1)
            | sdtlseqdt0(szszuzczcdt0(W1),W0)
            | ~ aElementOf0(W1,szDzozmdt0(xN))
            | ~ aElementOf0(W0,szDzozmdt0(xN)) )
      | sdtlseqdt0(xj,xi)
      | sdtlseqdt0(szszuzczcdt0(xi),xj)
      | ~ aElementOf0(xi,szDzozmdt0(xN))
      | ~ aElementOf0(xj,szDzozmdt0(xN)) )
  <=> ( ~ ! [W0: $i,W1: $i] :
            ( sdtlseqdt0(W0,W1)
            | sdtlseqdt0(szszuzczcdt0(W1),W0)
            | ~ aElementOf0(W1,szDzozmdt0(xN))
            | ~ aElementOf0(W0,szDzozmdt0(xN)) )
      | sdtlseqdt0(szszuzczcdt0(xi),xj)
      | ~ aElementOf0(xi,szDzozmdt0(xN))
      | ~ aElementOf0(xj,szDzozmdt0(xN))
      | sdtlseqdt0(xj,xi) ) ),
    inference(monotonicity,[status(thm)],[35]) ).

tff(37,plain,
    ( ( ~ ! [W0: $i,W1: $i] :
            ( sdtlseqdt0(W0,W1)
            | sdtlseqdt0(szszuzczcdt0(W1),W0)
            | ~ aElementOf0(W1,szDzozmdt0(xN))
            | ~ aElementOf0(W0,szDzozmdt0(xN)) )
      | sdtlseqdt0(xj,xi)
      | sdtlseqdt0(szszuzczcdt0(xi),xj)
      | ~ aElementOf0(xi,szDzozmdt0(xN))
      | ~ aElementOf0(xj,szDzozmdt0(xN)) )
  <=> ( ~ ! [W0: $i,W1: $i] :
            ( sdtlseqdt0(W0,W1)
            | sdtlseqdt0(szszuzczcdt0(W1),W0)
            | ~ aElementOf0(W1,szDzozmdt0(xN))
            | ~ aElementOf0(W0,szDzozmdt0(xN)) )
      | sdtlseqdt0(szszuzczcdt0(xi),xj)
      | ~ aElementOf0(xi,szDzozmdt0(xN))
      | ~ aElementOf0(xj,szDzozmdt0(xN))
      | sdtlseqdt0(xj,xi) ) ),
    inference(transitivity,[status(thm)],[36,34]) ).

tff(38,plain,
    ( ~ ! [W0: $i,W1: $i] :
          ( sdtlseqdt0(W0,W1)
          | sdtlseqdt0(szszuzczcdt0(W1),W0)
          | ~ aElementOf0(W1,szDzozmdt0(xN))
          | ~ aElementOf0(W0,szDzozmdt0(xN)) )
    | sdtlseqdt0(xj,xi)
    | sdtlseqdt0(szszuzczcdt0(xi),xj)
    | ~ aElementOf0(xi,szDzozmdt0(xN))
    | ~ aElementOf0(xj,szDzozmdt0(xN)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(39,plain,
    ( ~ ! [W0: $i,W1: $i] :
          ( sdtlseqdt0(W0,W1)
          | sdtlseqdt0(szszuzczcdt0(W1),W0)
          | ~ aElementOf0(W1,szDzozmdt0(xN))
          | ~ aElementOf0(W0,szDzozmdt0(xN)) )
    | sdtlseqdt0(szszuzczcdt0(xi),xj)
    | ~ aElementOf0(xi,szDzozmdt0(xN))
    | ~ aElementOf0(xj,szDzozmdt0(xN))
    | sdtlseqdt0(xj,xi) ),
    inference(modus_ponens,[status(thm)],[38,37]) ).

tff(40,plain,
    sdtlseqdt0(xj,xi),
    inference(unit_resolution,[status(thm)],[39,33,17,12,6]) ).

tff(41,plain,
    ( ~ sdtlseqdt0(szszuzczcdt0(xj),xi)
  <=> ~ sdtlseqdt0(szszuzczcdt0(xj),xi) ),
    inference(rewrite,[status(thm)],]) ).

tff(42,plain,
    ~ sdtlseqdt0(szszuzczcdt0(xj),xi),
    inference(or_elim,[status(thm)],[4]) ).

tff(43,plain,
    ~ sdtlseqdt0(szszuzczcdt0(xj),xi),
    inference(modus_ponens,[status(thm)],[42,41]) ).

tff(44,plain,
    ( ( ~ ! [W0: $i,W1: $i] :
            ( sdtlseqdt0(W0,W1)
            | sdtlseqdt0(szszuzczcdt0(W1),W0)
            | ~ aElementOf0(W1,szDzozmdt0(xN))
            | ~ aElementOf0(W0,szDzozmdt0(xN)) )
      | sdtlseqdt0(szszuzczcdt0(xj),xi)
      | ~ aElementOf0(xi,szDzozmdt0(xN))
      | ~ aElementOf0(xj,szDzozmdt0(xN))
      | sdtlseqdt0(xi,xj) )
  <=> ( ~ ! [W0: $i,W1: $i] :
            ( sdtlseqdt0(W0,W1)
            | sdtlseqdt0(szszuzczcdt0(W1),W0)
            | ~ aElementOf0(W1,szDzozmdt0(xN))
            | ~ aElementOf0(W0,szDzozmdt0(xN)) )
      | sdtlseqdt0(szszuzczcdt0(xj),xi)
      | ~ aElementOf0(xi,szDzozmdt0(xN))
      | ~ aElementOf0(xj,szDzozmdt0(xN))
      | sdtlseqdt0(xi,xj) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(45,plain,
    ( ( sdtlseqdt0(xi,xj)
      | sdtlseqdt0(szszuzczcdt0(xj),xi)
      | ~ aElementOf0(xj,szDzozmdt0(xN))
      | ~ aElementOf0(xi,szDzozmdt0(xN)) )
  <=> ( sdtlseqdt0(szszuzczcdt0(xj),xi)
      | ~ aElementOf0(xi,szDzozmdt0(xN))
      | ~ aElementOf0(xj,szDzozmdt0(xN))
      | sdtlseqdt0(xi,xj) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(46,plain,
    ( ( ~ ! [W0: $i,W1: $i] :
            ( sdtlseqdt0(W0,W1)
            | sdtlseqdt0(szszuzczcdt0(W1),W0)
            | ~ aElementOf0(W1,szDzozmdt0(xN))
            | ~ aElementOf0(W0,szDzozmdt0(xN)) )
      | sdtlseqdt0(xi,xj)
      | sdtlseqdt0(szszuzczcdt0(xj),xi)
      | ~ aElementOf0(xj,szDzozmdt0(xN))
      | ~ aElementOf0(xi,szDzozmdt0(xN)) )
  <=> ( ~ ! [W0: $i,W1: $i] :
            ( sdtlseqdt0(W0,W1)
            | sdtlseqdt0(szszuzczcdt0(W1),W0)
            | ~ aElementOf0(W1,szDzozmdt0(xN))
            | ~ aElementOf0(W0,szDzozmdt0(xN)) )
      | sdtlseqdt0(szszuzczcdt0(xj),xi)
      | ~ aElementOf0(xi,szDzozmdt0(xN))
      | ~ aElementOf0(xj,szDzozmdt0(xN))
      | sdtlseqdt0(xi,xj) ) ),
    inference(monotonicity,[status(thm)],[45]) ).

tff(47,plain,
    ( ( ~ ! [W0: $i,W1: $i] :
            ( sdtlseqdt0(W0,W1)
            | sdtlseqdt0(szszuzczcdt0(W1),W0)
            | ~ aElementOf0(W1,szDzozmdt0(xN))
            | ~ aElementOf0(W0,szDzozmdt0(xN)) )
      | sdtlseqdt0(xi,xj)
      | sdtlseqdt0(szszuzczcdt0(xj),xi)
      | ~ aElementOf0(xj,szDzozmdt0(xN))
      | ~ aElementOf0(xi,szDzozmdt0(xN)) )
  <=> ( ~ ! [W0: $i,W1: $i] :
            ( sdtlseqdt0(W0,W1)
            | sdtlseqdt0(szszuzczcdt0(W1),W0)
            | ~ aElementOf0(W1,szDzozmdt0(xN))
            | ~ aElementOf0(W0,szDzozmdt0(xN)) )
      | sdtlseqdt0(szszuzczcdt0(xj),xi)
      | ~ aElementOf0(xi,szDzozmdt0(xN))
      | ~ aElementOf0(xj,szDzozmdt0(xN))
      | sdtlseqdt0(xi,xj) ) ),
    inference(transitivity,[status(thm)],[46,44]) ).

tff(48,plain,
    ( ~ ! [W0: $i,W1: $i] :
          ( sdtlseqdt0(W0,W1)
          | sdtlseqdt0(szszuzczcdt0(W1),W0)
          | ~ aElementOf0(W1,szDzozmdt0(xN))
          | ~ aElementOf0(W0,szDzozmdt0(xN)) )
    | sdtlseqdt0(xi,xj)
    | sdtlseqdt0(szszuzczcdt0(xj),xi)
    | ~ aElementOf0(xj,szDzozmdt0(xN))
    | ~ aElementOf0(xi,szDzozmdt0(xN)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(49,plain,
    ( ~ ! [W0: $i,W1: $i] :
          ( sdtlseqdt0(W0,W1)
          | sdtlseqdt0(szszuzczcdt0(W1),W0)
          | ~ aElementOf0(W1,szDzozmdt0(xN))
          | ~ aElementOf0(W0,szDzozmdt0(xN)) )
    | sdtlseqdt0(szszuzczcdt0(xj),xi)
    | ~ aElementOf0(xi,szDzozmdt0(xN))
    | ~ aElementOf0(xj,szDzozmdt0(xN))
    | sdtlseqdt0(xi,xj) ),
    inference(modus_ponens,[status(thm)],[48,47]) ).

tff(50,plain,
    sdtlseqdt0(xi,xj),
    inference(unit_resolution,[status(thm)],[49,33,17,12,43]) ).

tff(51,plain,
    ( ( xi != xj )
  <=> ( xi != xj ) ),
    inference(rewrite,[status(thm)],]) ).

tff(52,plain,
    xi != xj,
    inference(or_elim,[status(thm)],[4]) ).

tff(53,plain,
    xi != xj,
    inference(modus_ponens,[status(thm)],[52,51]) ).

tff(54,plain,
    ^ [W0: $i,W1: $i] :
      refl(
        ( ( ( W0 = W1 )
          | ~ sdtlseqdt0(W1,W0)
          | ~ aElementOf0(W1,szDzozmdt0(xN))
          | ~ aElementOf0(W0,szDzozmdt0(xN))
          | ~ sdtlseqdt0(W0,W1) )
      <=> ( ( W0 = W1 )
          | ~ sdtlseqdt0(W1,W0)
          | ~ aElementOf0(W1,szDzozmdt0(xN))
          | ~ aElementOf0(W0,szDzozmdt0(xN))
          | ~ sdtlseqdt0(W0,W1) ) )),
    inference(bind,[status(th)],]) ).

tff(55,plain,
    ( ! [W0: $i,W1: $i] :
        ( ( W0 = W1 )
        | ~ sdtlseqdt0(W1,W0)
        | ~ aElementOf0(W1,szDzozmdt0(xN))
        | ~ aElementOf0(W0,szDzozmdt0(xN))
        | ~ sdtlseqdt0(W0,W1) )
  <=> ! [W0: $i,W1: $i] :
        ( ( W0 = W1 )
        | ~ sdtlseqdt0(W1,W0)
        | ~ aElementOf0(W1,szDzozmdt0(xN))
        | ~ aElementOf0(W0,szDzozmdt0(xN))
        | ~ sdtlseqdt0(W0,W1) ) ),
    inference(quant_intro,[status(thm)],[54]) ).

tff(56,plain,
    ^ [W0: $i,W1: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( sdtlseqdt0(W0,W1)
                  & sdtlseqdt0(W1,W0) )
              <=> ~ ( ~ sdtlseqdt0(W1,W0)
                    | ~ sdtlseqdt0(W0,W1) ) )),
              ( ~ ( sdtlseqdt0(W0,W1)
                  & sdtlseqdt0(W1,W0) )
            <=> ~ ~ ( ~ sdtlseqdt0(W1,W0)
                    | ~ sdtlseqdt0(W0,W1) ) )),
            rewrite(
              ( ~ ~ ( ~ sdtlseqdt0(W1,W0)
                    | ~ sdtlseqdt0(W0,W1) )
            <=> ( ~ sdtlseqdt0(W1,W0)
                | ~ sdtlseqdt0(W0,W1) ) )),
            ( ~ ( sdtlseqdt0(W0,W1)
                & sdtlseqdt0(W1,W0) )
          <=> ( ~ sdtlseqdt0(W1,W0)
              | ~ sdtlseqdt0(W0,W1) ) )),
          trans(
            monotonicity(
              rewrite(
                ( ( aElementOf0(W0,szDzozmdt0(xN))
                  & aElementOf0(W1,szDzozmdt0(xN)) )
              <=> ~ ( ~ aElementOf0(W1,szDzozmdt0(xN))
                    | ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
              ( ~ ( aElementOf0(W0,szDzozmdt0(xN))
                  & aElementOf0(W1,szDzozmdt0(xN)) )
            <=> ~ ~ ( ~ aElementOf0(W1,szDzozmdt0(xN))
                    | ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
            rewrite(
              ( ~ ~ ( ~ aElementOf0(W1,szDzozmdt0(xN))
                    | ~ aElementOf0(W0,szDzozmdt0(xN)) )
            <=> ( ~ aElementOf0(W1,szDzozmdt0(xN))
                | ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
            ( ~ ( aElementOf0(W0,szDzozmdt0(xN))
                & aElementOf0(W1,szDzozmdt0(xN)) )
          <=> ( ~ aElementOf0(W1,szDzozmdt0(xN))
              | ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
          ( ( ( W0 = W1 )
            | ~ ( sdtlseqdt0(W0,W1)
                & sdtlseqdt0(W1,W0) )
            | ~ ( aElementOf0(W0,szDzozmdt0(xN))
                & aElementOf0(W1,szDzozmdt0(xN)) ) )
        <=> ( ( W0 = W1 )
            | ~ sdtlseqdt0(W1,W0)
            | ~ sdtlseqdt0(W0,W1)
            | ~ aElementOf0(W1,szDzozmdt0(xN))
            | ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
        rewrite(
          ( ( ( W0 = W1 )
            | ~ sdtlseqdt0(W1,W0)
            | ~ sdtlseqdt0(W0,W1)
            | ~ aElementOf0(W1,szDzozmdt0(xN))
            | ~ aElementOf0(W0,szDzozmdt0(xN)) )
        <=> ( ( W0 = W1 )
            | ~ sdtlseqdt0(W1,W0)
            | ~ aElementOf0(W1,szDzozmdt0(xN))
            | ~ aElementOf0(W0,szDzozmdt0(xN))
            | ~ sdtlseqdt0(W0,W1) ) )),
        ( ( ( W0 = W1 )
          | ~ ( sdtlseqdt0(W0,W1)
              & sdtlseqdt0(W1,W0) )
          | ~ ( aElementOf0(W0,szDzozmdt0(xN))
              & aElementOf0(W1,szDzozmdt0(xN)) ) )
      <=> ( ( W0 = W1 )
          | ~ sdtlseqdt0(W1,W0)
          | ~ aElementOf0(W1,szDzozmdt0(xN))
          | ~ aElementOf0(W0,szDzozmdt0(xN))
          | ~ sdtlseqdt0(W0,W1) ) )),
    inference(bind,[status(th)],]) ).

tff(57,plain,
    ( ! [W0: $i,W1: $i] :
        ( ( W0 = W1 )
        | ~ ( sdtlseqdt0(W0,W1)
            & sdtlseqdt0(W1,W0) )
        | ~ ( aElementOf0(W0,szDzozmdt0(xN))
            & aElementOf0(W1,szDzozmdt0(xN)) ) )
  <=> ! [W0: $i,W1: $i] :
        ( ( W0 = W1 )
        | ~ sdtlseqdt0(W1,W0)
        | ~ aElementOf0(W1,szDzozmdt0(xN))
        | ~ aElementOf0(W0,szDzozmdt0(xN))
        | ~ sdtlseqdt0(W0,W1) ) ),
    inference(quant_intro,[status(thm)],[56]) ).

tff(58,plain,
    ^ [W0: $i,W1: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ~ ( aElementOf0(W0,szNzAzT0)
                & aElementOf0(W1,szNzAzT0) )
          <=> ~ ( aElementOf0(W0,szDzozmdt0(xN))
                & aElementOf0(W1,szDzozmdt0(xN)) ) )),
          ( ( ( W0 = W1 )
            | ~ ( aElementOf0(W0,szNzAzT0)
                & aElementOf0(W1,szNzAzT0) )
            | ~ ( sdtlseqdt0(W0,W1)
                & sdtlseqdt0(W1,W0) ) )
        <=> ( ( W0 = W1 )
            | ~ ( aElementOf0(W0,szDzozmdt0(xN))
                & aElementOf0(W1,szDzozmdt0(xN)) )
            | ~ ( sdtlseqdt0(W0,W1)
                & sdtlseqdt0(W1,W0) ) ) )),
        rewrite(
          ( ( ( W0 = W1 )
            | ~ ( aElementOf0(W0,szDzozmdt0(xN))
                & aElementOf0(W1,szDzozmdt0(xN)) )
            | ~ ( sdtlseqdt0(W0,W1)
                & sdtlseqdt0(W1,W0) ) )
        <=> ( ( W0 = W1 )
            | ~ ( sdtlseqdt0(W0,W1)
                & sdtlseqdt0(W1,W0) )
            | ~ ( aElementOf0(W0,szDzozmdt0(xN))
                & aElementOf0(W1,szDzozmdt0(xN)) ) ) )),
        ( ( ( W0 = W1 )
          | ~ ( aElementOf0(W0,szNzAzT0)
              & aElementOf0(W1,szNzAzT0) )
          | ~ ( sdtlseqdt0(W0,W1)
              & sdtlseqdt0(W1,W0) ) )
      <=> ( ( W0 = W1 )
          | ~ ( sdtlseqdt0(W0,W1)
              & sdtlseqdt0(W1,W0) )
          | ~ ( aElementOf0(W0,szDzozmdt0(xN))
              & aElementOf0(W1,szDzozmdt0(xN)) ) ) )),
    inference(bind,[status(th)],]) ).

tff(59,plain,
    ( ! [W0: $i,W1: $i] :
        ( ( W0 = W1 )
        | ~ ( aElementOf0(W0,szNzAzT0)
            & aElementOf0(W1,szNzAzT0) )
        | ~ ( sdtlseqdt0(W0,W1)
            & sdtlseqdt0(W1,W0) ) )
  <=> ! [W0: $i,W1: $i] :
        ( ( W0 = W1 )
        | ~ ( sdtlseqdt0(W0,W1)
            & sdtlseqdt0(W1,W0) )
        | ~ ( aElementOf0(W0,szDzozmdt0(xN))
            & aElementOf0(W1,szDzozmdt0(xN)) ) ) ),
    inference(quant_intro,[status(thm)],[58]) ).

tff(60,plain,
    ( ! [W0: $i,W1: $i] :
        ( ( W0 = W1 )
        | ~ ( aElementOf0(W0,szNzAzT0)
            & aElementOf0(W1,szNzAzT0) )
        | ~ ( sdtlseqdt0(W0,W1)
            & sdtlseqdt0(W1,W0) ) )
  <=> ! [W0: $i,W1: $i] :
        ( ( W0 = W1 )
        | ~ ( aElementOf0(W0,szNzAzT0)
            & aElementOf0(W1,szNzAzT0) )
        | ~ ( sdtlseqdt0(W0,W1)
            & sdtlseqdt0(W1,W0) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(61,plain,
    ^ [W0: $i,W1: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( ( sdtlseqdt0(W0,W1)
                & sdtlseqdt0(W1,W0) )
             => ( W0 = W1 ) )
          <=> ( ~ ( sdtlseqdt0(W0,W1)
                  & sdtlseqdt0(W1,W0) )
              | ( W0 = W1 ) ) )),
          ( ( ( aElementOf0(W0,szNzAzT0)
              & aElementOf0(W1,szNzAzT0) )
           => ( ( sdtlseqdt0(W0,W1)
                & sdtlseqdt0(W1,W0) )
             => ( W0 = W1 ) ) )
        <=> ( ( aElementOf0(W0,szNzAzT0)
              & aElementOf0(W1,szNzAzT0) )
           => ( ~ ( sdtlseqdt0(W0,W1)
                  & sdtlseqdt0(W1,W0) )
              | ( W0 = W1 ) ) ) )),
        rewrite(
          ( ( ( aElementOf0(W0,szNzAzT0)
              & aElementOf0(W1,szNzAzT0) )
           => ( ~ ( sdtlseqdt0(W0,W1)
                  & sdtlseqdt0(W1,W0) )
              | ( W0 = W1 ) ) )
        <=> ( ( W0 = W1 )
            | ~ ( aElementOf0(W0,szNzAzT0)
                & aElementOf0(W1,szNzAzT0) )
            | ~ ( sdtlseqdt0(W0,W1)
                & sdtlseqdt0(W1,W0) ) ) )),
        ( ( ( aElementOf0(W0,szNzAzT0)
            & aElementOf0(W1,szNzAzT0) )
         => ( ( sdtlseqdt0(W0,W1)
              & sdtlseqdt0(W1,W0) )
           => ( W0 = W1 ) ) )
      <=> ( ( W0 = W1 )
          | ~ ( aElementOf0(W0,szNzAzT0)
              & aElementOf0(W1,szNzAzT0) )
          | ~ ( sdtlseqdt0(W0,W1)
              & sdtlseqdt0(W1,W0) ) ) )),
    inference(bind,[status(th)],]) ).

tff(62,plain,
    ( ! [W0: $i,W1: $i] :
        ( ( aElementOf0(W0,szNzAzT0)
          & aElementOf0(W1,szNzAzT0) )
       => ( ( sdtlseqdt0(W0,W1)
            & sdtlseqdt0(W1,W0) )
         => ( W0 = W1 ) ) )
  <=> ! [W0: $i,W1: $i] :
        ( ( W0 = W1 )
        | ~ ( aElementOf0(W0,szNzAzT0)
            & aElementOf0(W1,szNzAzT0) )
        | ~ ( sdtlseqdt0(W0,W1)
            & sdtlseqdt0(W1,W0) ) ) ),
    inference(quant_intro,[status(thm)],[61]) ).

tff(63,axiom,
    ! [W0: $i,W1: $i] :
      ( ( aElementOf0(W0,szNzAzT0)
        & aElementOf0(W1,szNzAzT0) )
     => ( ( sdtlseqdt0(W0,W1)
          & sdtlseqdt0(W1,W0) )
       => ( W0 = W1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessASymm) ).

tff(64,plain,
    ! [W0: $i,W1: $i] :
      ( ( W0 = W1 )
      | ~ ( aElementOf0(W0,szNzAzT0)
          & aElementOf0(W1,szNzAzT0) )
      | ~ ( sdtlseqdt0(W0,W1)
          & sdtlseqdt0(W1,W0) ) ),
    inference(modus_ponens,[status(thm)],[63,62]) ).

tff(65,plain,
    ! [W0: $i,W1: $i] :
      ( ( W0 = W1 )
      | ~ ( aElementOf0(W0,szNzAzT0)
          & aElementOf0(W1,szNzAzT0) )
      | ~ ( sdtlseqdt0(W0,W1)
          & sdtlseqdt0(W1,W0) ) ),
    inference(modus_ponens,[status(thm)],[64,60]) ).

tff(66,plain,
    ! [W0: $i,W1: $i] :
      ( ( W0 = W1 )
      | ~ ( sdtlseqdt0(W0,W1)
          & sdtlseqdt0(W1,W0) )
      | ~ ( aElementOf0(W0,szDzozmdt0(xN))
          & aElementOf0(W1,szDzozmdt0(xN)) ) ),
    inference(modus_ponens,[status(thm)],[65,59]) ).

tff(67,plain,
    ! [W0: $i,W1: $i] :
      ( ( W0 = W1 )
      | ~ ( sdtlseqdt0(W0,W1)
          & sdtlseqdt0(W1,W0) )
      | ~ ( aElementOf0(W0,szDzozmdt0(xN))
          & aElementOf0(W1,szDzozmdt0(xN)) ) ),
    inference(skolemize,[status(sab)],[66]) ).

tff(68,plain,
    ! [W0: $i,W1: $i] :
      ( ( W0 = W1 )
      | ~ sdtlseqdt0(W1,W0)
      | ~ aElementOf0(W1,szDzozmdt0(xN))
      | ~ aElementOf0(W0,szDzozmdt0(xN))
      | ~ sdtlseqdt0(W0,W1) ),
    inference(modus_ponens,[status(thm)],[67,57]) ).

tff(69,plain,
    ! [W0: $i,W1: $i] :
      ( ( W0 = W1 )
      | ~ sdtlseqdt0(W1,W0)
      | ~ aElementOf0(W1,szDzozmdt0(xN))
      | ~ aElementOf0(W0,szDzozmdt0(xN))
      | ~ sdtlseqdt0(W0,W1) ),
    inference(modus_ponens,[status(thm)],[68,55]) ).

tff(70,plain,
    ( ( ~ ! [W0: $i,W1: $i] :
            ( ( W0 = W1 )
            | ~ sdtlseqdt0(W1,W0)
            | ~ aElementOf0(W1,szDzozmdt0(xN))
            | ~ aElementOf0(W0,szDzozmdt0(xN))
            | ~ sdtlseqdt0(W0,W1) )
      | ( xi = xj )
      | ~ aElementOf0(xi,szDzozmdt0(xN))
      | ~ aElementOf0(xj,szDzozmdt0(xN))
      | ~ sdtlseqdt0(xi,xj)
      | ~ sdtlseqdt0(xj,xi) )
  <=> ( ~ ! [W0: $i,W1: $i] :
            ( ( W0 = W1 )
            | ~ sdtlseqdt0(W1,W0)
            | ~ aElementOf0(W1,szDzozmdt0(xN))
            | ~ aElementOf0(W0,szDzozmdt0(xN))
            | ~ sdtlseqdt0(W0,W1) )
      | ( xi = xj )
      | ~ aElementOf0(xi,szDzozmdt0(xN))
      | ~ aElementOf0(xj,szDzozmdt0(xN))
      | ~ sdtlseqdt0(xi,xj)
      | ~ sdtlseqdt0(xj,xi) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(71,plain,
    ( ( ( xi = xj )
      | ~ sdtlseqdt0(xj,xi)
      | ~ aElementOf0(xj,szDzozmdt0(xN))
      | ~ aElementOf0(xi,szDzozmdt0(xN))
      | ~ sdtlseqdt0(xi,xj) )
  <=> ( ( xi = xj )
      | ~ aElementOf0(xi,szDzozmdt0(xN))
      | ~ aElementOf0(xj,szDzozmdt0(xN))
      | ~ sdtlseqdt0(xi,xj)
      | ~ sdtlseqdt0(xj,xi) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(72,plain,
    ( ( ~ ! [W0: $i,W1: $i] :
            ( ( W0 = W1 )
            | ~ sdtlseqdt0(W1,W0)
            | ~ aElementOf0(W1,szDzozmdt0(xN))
            | ~ aElementOf0(W0,szDzozmdt0(xN))
            | ~ sdtlseqdt0(W0,W1) )
      | ( xi = xj )
      | ~ sdtlseqdt0(xj,xi)
      | ~ aElementOf0(xj,szDzozmdt0(xN))
      | ~ aElementOf0(xi,szDzozmdt0(xN))
      | ~ sdtlseqdt0(xi,xj) )
  <=> ( ~ ! [W0: $i,W1: $i] :
            ( ( W0 = W1 )
            | ~ sdtlseqdt0(W1,W0)
            | ~ aElementOf0(W1,szDzozmdt0(xN))
            | ~ aElementOf0(W0,szDzozmdt0(xN))
            | ~ sdtlseqdt0(W0,W1) )
      | ( xi = xj )
      | ~ aElementOf0(xi,szDzozmdt0(xN))
      | ~ aElementOf0(xj,szDzozmdt0(xN))
      | ~ sdtlseqdt0(xi,xj)
      | ~ sdtlseqdt0(xj,xi) ) ),
    inference(monotonicity,[status(thm)],[71]) ).

tff(73,plain,
    ( ( ~ ! [W0: $i,W1: $i] :
            ( ( W0 = W1 )
            | ~ sdtlseqdt0(W1,W0)
            | ~ aElementOf0(W1,szDzozmdt0(xN))
            | ~ aElementOf0(W0,szDzozmdt0(xN))
            | ~ sdtlseqdt0(W0,W1) )
      | ( xi = xj )
      | ~ sdtlseqdt0(xj,xi)
      | ~ aElementOf0(xj,szDzozmdt0(xN))
      | ~ aElementOf0(xi,szDzozmdt0(xN))
      | ~ sdtlseqdt0(xi,xj) )
  <=> ( ~ ! [W0: $i,W1: $i] :
            ( ( W0 = W1 )
            | ~ sdtlseqdt0(W1,W0)
            | ~ aElementOf0(W1,szDzozmdt0(xN))
            | ~ aElementOf0(W0,szDzozmdt0(xN))
            | ~ sdtlseqdt0(W0,W1) )
      | ( xi = xj )
      | ~ aElementOf0(xi,szDzozmdt0(xN))
      | ~ aElementOf0(xj,szDzozmdt0(xN))
      | ~ sdtlseqdt0(xi,xj)
      | ~ sdtlseqdt0(xj,xi) ) ),
    inference(transitivity,[status(thm)],[72,70]) ).

tff(74,plain,
    ( ~ ! [W0: $i,W1: $i] :
          ( ( W0 = W1 )
          | ~ sdtlseqdt0(W1,W0)
          | ~ aElementOf0(W1,szDzozmdt0(xN))
          | ~ aElementOf0(W0,szDzozmdt0(xN))
          | ~ sdtlseqdt0(W0,W1) )
    | ( xi = xj )
    | ~ sdtlseqdt0(xj,xi)
    | ~ aElementOf0(xj,szDzozmdt0(xN))
    | ~ aElementOf0(xi,szDzozmdt0(xN))
    | ~ sdtlseqdt0(xi,xj) ),
    inference(quant_inst,[status(thm)],]) ).

tff(75,plain,
    ( ~ ! [W0: $i,W1: $i] :
          ( ( W0 = W1 )
          | ~ sdtlseqdt0(W1,W0)
          | ~ aElementOf0(W1,szDzozmdt0(xN))
          | ~ aElementOf0(W0,szDzozmdt0(xN))
          | ~ sdtlseqdt0(W0,W1) )
    | ( xi = xj )
    | ~ aElementOf0(xi,szDzozmdt0(xN))
    | ~ aElementOf0(xj,szDzozmdt0(xN))
    | ~ sdtlseqdt0(xi,xj)
    | ~ sdtlseqdt0(xj,xi) ),
    inference(modus_ponens,[status(thm)],[74,73]) ).

tff(76,plain,
    $false,
    inference(unit_resolution,[status(thm)],[75,69,17,12,53,50,40]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : NUM576+3 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34  % Computer : n003.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Fri Sep  2 11:58:24 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35  Usage: tptp [options] [-file:]file
% 0.12/0.35    -h, -?       prints this message.
% 0.12/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.35    -m, -model   generate model.
% 0.12/0.35    -p, -proof   generate proof.
% 0.12/0.35    -c, -core    generate unsat core of named formulas.
% 0.12/0.35    -st, -statistics display statistics.
% 0.12/0.35    -t:timeout   set timeout (in second).
% 0.12/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35    -<param>:<value> configuration parameter and value.
% 0.12/0.35    -o:<output-file> file to place output in.
% 0.19/0.56  % SZS status Theorem
% 0.19/0.56  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------