TSTP Solution File: NUM423+3 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : NUM423+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n022.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 13:09:36 EDT 2022

% Result   : Theorem 0.20s 0.40s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   37
% Syntax   : Number of formulae    :   84 (  21 unt;   9 typ;   0 def)
%            Number of atoms       :  295 ( 167 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  436 ( 233   ~; 123   |;  46   &)
%                                         (  28 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of FOOLs       :   17 (  17 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   6   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   68 (  47   !;  12   ?;  68   :)

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

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

tff(xa_type,type,
    xa: $i ).

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

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

tff(xq_type,type,
    xq: $i ).

tff(aInteger0_type,type,
    aInteger0: $i > $o ).

tff(aDivisorOf0_type,type,
    aDivisorOf0: ( $i * $i ) > $o ).

tff(sdteqdtlpzmzozddtrp0_type,type,
    sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).

tff(1,plain,
    ( aInteger0(xa)
  <=> aInteger0(xa) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    ( aInteger0(xa)
    & aInteger0(xq)
    & ( xq != sz00 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__671) ).

tff(3,plain,
    ( aInteger0(xa)
    & aInteger0(xq) ),
    inference(and_elim,[status(thm)],[2]) ).

tff(4,plain,
    aInteger0(xa),
    inference(and_elim,[status(thm)],[3]) ).

tff(5,plain,
    aInteger0(xa),
    inference(modus_ponens,[status(thm)],[4,1]) ).

tff(6,plain,
    ^ [W0: $i] :
      refl(
        ( ( ~ aInteger0(W0)
          | ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
              | ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) )
      <=> ( ~ aInteger0(W0)
          | ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
              | ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(7,plain,
    ( ! [W0: $i] :
        ( ~ aInteger0(W0)
        | ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
            | ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) )
  <=> ! [W0: $i] :
        ( ~ aInteger0(W0)
        | ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
            | ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) ) ),
    inference(quant_intro,[status(thm)],[6]) ).

tff(8,plain,
    ^ [W0: $i] :
      rewrite(
        ( ( ~ aInteger0(W0)
          | ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
            & ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) )
      <=> ( ~ aInteger0(W0)
          | ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
              | ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(9,plain,
    ( ! [W0: $i] :
        ( ~ aInteger0(W0)
        | ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
          & ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) )
  <=> ! [W0: $i] :
        ( ~ aInteger0(W0)
        | ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
            | ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) ) ),
    inference(quant_intro,[status(thm)],[8]) ).

tff(10,plain,
    ( ! [W0: $i] :
        ( ~ aInteger0(W0)
        | ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
          & ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) )
  <=> ! [W0: $i] :
        ( ~ aInteger0(W0)
        | ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
          & ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(11,plain,
    ^ [W0: $i] :
      rewrite(
        ( ( aInteger0(W0)
         => ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
            & ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) )
      <=> ( ~ aInteger0(W0)
          | ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
            & ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(12,plain,
    ( ! [W0: $i] :
        ( aInteger0(W0)
       => ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
          & ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) )
  <=> ! [W0: $i] :
        ( ~ aInteger0(W0)
        | ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
          & ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ) ),
    inference(quant_intro,[status(thm)],[11]) ).

tff(13,axiom,
    ! [W0: $i] :
      ( aInteger0(W0)
     => ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
        & ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).

tff(14,plain,
    ! [W0: $i] :
      ( ~ aInteger0(W0)
      | ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
        & ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ),
    inference(modus_ponens,[status(thm)],[13,12]) ).

tff(15,plain,
    ! [W0: $i] :
      ( ~ aInteger0(W0)
      | ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
        & ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ),
    inference(modus_ponens,[status(thm)],[14,10]) ).

tff(16,plain,
    ! [W0: $i] :
      ( ~ aInteger0(W0)
      | ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
        & ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ),
    inference(skolemize,[status(sab)],[15]) ).

tff(17,plain,
    ! [W0: $i] :
      ( ~ aInteger0(W0)
      | ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
          | ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) ),
    inference(modus_ponens,[status(thm)],[16,9]) ).

tff(18,plain,
    ! [W0: $i] :
      ( ~ aInteger0(W0)
      | ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
          | ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) ),
    inference(modus_ponens,[status(thm)],[17,7]) ).

tff(19,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ aInteger0(W0)
            | ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
                | ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) )
      | ~ aInteger0(xa)
      | ~ ( ( sdtpldt0(xa,smndt0(xa)) != sz00 )
          | ( sz00 != sdtpldt0(smndt0(xa),xa) ) ) )
  <=> ( ~ ! [W0: $i] :
            ( ~ aInteger0(W0)
            | ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
                | ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) )
      | ~ aInteger0(xa)
      | ~ ( ( sdtpldt0(xa,smndt0(xa)) != sz00 )
          | ( sz00 != sdtpldt0(smndt0(xa),xa) ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(20,plain,
    ( ~ ! [W0: $i] :
          ( ~ aInteger0(W0)
          | ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
              | ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) )
    | ~ aInteger0(xa)
    | ~ ( ( sdtpldt0(xa,smndt0(xa)) != sz00 )
        | ( sz00 != sdtpldt0(smndt0(xa),xa) ) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(21,plain,
    ( ~ ! [W0: $i] :
          ( ~ aInteger0(W0)
          | ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
              | ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) )
    | ~ aInteger0(xa)
    | ~ ( ( sdtpldt0(xa,smndt0(xa)) != sz00 )
        | ( sz00 != sdtpldt0(smndt0(xa),xa) ) ) ),
    inference(modus_ponens,[status(thm)],[20,19]) ).

tff(22,plain,
    ~ ( ( sdtpldt0(xa,smndt0(xa)) != sz00 )
      | ( sz00 != sdtpldt0(smndt0(xa),xa) ) ),
    inference(unit_resolution,[status(thm)],[21,18,5]) ).

tff(23,plain,
    ( ( sdtpldt0(xa,smndt0(xa)) != sz00 )
    | ( sz00 != sdtpldt0(smndt0(xa),xa) )
    | ( sdtpldt0(xa,smndt0(xa)) = sz00 ) ),
    inference(tautology,[status(thm)],]) ).

tff(24,plain,
    sdtpldt0(xa,smndt0(xa)) = sz00,
    inference(unit_resolution,[status(thm)],[23,22]) ).

tff(25,plain,
    sz00 = sdtpldt0(xa,smndt0(xa)),
    inference(symmetry,[status(thm)],[24]) ).

tff(26,plain,
    ( aInteger0(xq)
  <=> aInteger0(xq) ),
    inference(rewrite,[status(thm)],]) ).

tff(27,plain,
    aInteger0(xq),
    inference(and_elim,[status(thm)],[3]) ).

tff(28,plain,
    aInteger0(xq),
    inference(modus_ponens,[status(thm)],[27,26]) ).

tff(29,plain,
    ^ [W0: $i] :
      refl(
        ( ( ~ aInteger0(W0)
          | ~ ( ( sdtasdt0(W0,sz00) != sz00 )
              | ( sz00 != sdtasdt0(sz00,W0) ) ) )
      <=> ( ~ aInteger0(W0)
          | ~ ( ( sdtasdt0(W0,sz00) != sz00 )
              | ( sz00 != sdtasdt0(sz00,W0) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(30,plain,
    ( ! [W0: $i] :
        ( ~ aInteger0(W0)
        | ~ ( ( sdtasdt0(W0,sz00) != sz00 )
            | ( sz00 != sdtasdt0(sz00,W0) ) ) )
  <=> ! [W0: $i] :
        ( ~ aInteger0(W0)
        | ~ ( ( sdtasdt0(W0,sz00) != sz00 )
            | ( sz00 != sdtasdt0(sz00,W0) ) ) ) ),
    inference(quant_intro,[status(thm)],[29]) ).

tff(31,plain,
    ^ [W0: $i] :
      rewrite(
        ( ( ~ aInteger0(W0)
          | ( ( sdtasdt0(W0,sz00) = sz00 )
            & ( sz00 = sdtasdt0(sz00,W0) ) ) )
      <=> ( ~ aInteger0(W0)
          | ~ ( ( sdtasdt0(W0,sz00) != sz00 )
              | ( sz00 != sdtasdt0(sz00,W0) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(32,plain,
    ( ! [W0: $i] :
        ( ~ aInteger0(W0)
        | ( ( sdtasdt0(W0,sz00) = sz00 )
          & ( sz00 = sdtasdt0(sz00,W0) ) ) )
  <=> ! [W0: $i] :
        ( ~ aInteger0(W0)
        | ~ ( ( sdtasdt0(W0,sz00) != sz00 )
            | ( sz00 != sdtasdt0(sz00,W0) ) ) ) ),
    inference(quant_intro,[status(thm)],[31]) ).

tff(33,plain,
    ( ! [W0: $i] :
        ( ~ aInteger0(W0)
        | ( ( sdtasdt0(W0,sz00) = sz00 )
          & ( sz00 = sdtasdt0(sz00,W0) ) ) )
  <=> ! [W0: $i] :
        ( ~ aInteger0(W0)
        | ( ( sdtasdt0(W0,sz00) = sz00 )
          & ( sz00 = sdtasdt0(sz00,W0) ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(34,plain,
    ^ [W0: $i] :
      rewrite(
        ( ( aInteger0(W0)
         => ( ( sdtasdt0(W0,sz00) = sz00 )
            & ( sz00 = sdtasdt0(sz00,W0) ) ) )
      <=> ( ~ aInteger0(W0)
          | ( ( sdtasdt0(W0,sz00) = sz00 )
            & ( sz00 = sdtasdt0(sz00,W0) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(35,plain,
    ( ! [W0: $i] :
        ( aInteger0(W0)
       => ( ( sdtasdt0(W0,sz00) = sz00 )
          & ( sz00 = sdtasdt0(sz00,W0) ) ) )
  <=> ! [W0: $i] :
        ( ~ aInteger0(W0)
        | ( ( sdtasdt0(W0,sz00) = sz00 )
          & ( sz00 = sdtasdt0(sz00,W0) ) ) ) ),
    inference(quant_intro,[status(thm)],[34]) ).

tff(36,axiom,
    ! [W0: $i] :
      ( aInteger0(W0)
     => ( ( sdtasdt0(W0,sz00) = sz00 )
        & ( sz00 = sdtasdt0(sz00,W0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).

tff(37,plain,
    ! [W0: $i] :
      ( ~ aInteger0(W0)
      | ( ( sdtasdt0(W0,sz00) = sz00 )
        & ( sz00 = sdtasdt0(sz00,W0) ) ) ),
    inference(modus_ponens,[status(thm)],[36,35]) ).

tff(38,plain,
    ! [W0: $i] :
      ( ~ aInteger0(W0)
      | ( ( sdtasdt0(W0,sz00) = sz00 )
        & ( sz00 = sdtasdt0(sz00,W0) ) ) ),
    inference(modus_ponens,[status(thm)],[37,33]) ).

tff(39,plain,
    ! [W0: $i] :
      ( ~ aInteger0(W0)
      | ( ( sdtasdt0(W0,sz00) = sz00 )
        & ( sz00 = sdtasdt0(sz00,W0) ) ) ),
    inference(skolemize,[status(sab)],[38]) ).

tff(40,plain,
    ! [W0: $i] :
      ( ~ aInteger0(W0)
      | ~ ( ( sdtasdt0(W0,sz00) != sz00 )
          | ( sz00 != sdtasdt0(sz00,W0) ) ) ),
    inference(modus_ponens,[status(thm)],[39,32]) ).

tff(41,plain,
    ! [W0: $i] :
      ( ~ aInteger0(W0)
      | ~ ( ( sdtasdt0(W0,sz00) != sz00 )
          | ( sz00 != sdtasdt0(sz00,W0) ) ) ),
    inference(modus_ponens,[status(thm)],[40,30]) ).

tff(42,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ aInteger0(W0)
            | ~ ( ( sdtasdt0(W0,sz00) != sz00 )
                | ( sz00 != sdtasdt0(sz00,W0) ) ) )
      | ~ aInteger0(xq)
      | ~ ( ( sdtasdt0(xq,sz00) != sz00 )
          | ( sz00 != sdtasdt0(sz00,xq) ) ) )
  <=> ( ~ ! [W0: $i] :
            ( ~ aInteger0(W0)
            | ~ ( ( sdtasdt0(W0,sz00) != sz00 )
                | ( sz00 != sdtasdt0(sz00,W0) ) ) )
      | ~ aInteger0(xq)
      | ~ ( ( sdtasdt0(xq,sz00) != sz00 )
          | ( sz00 != sdtasdt0(sz00,xq) ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(43,plain,
    ( ~ ! [W0: $i] :
          ( ~ aInteger0(W0)
          | ~ ( ( sdtasdt0(W0,sz00) != sz00 )
              | ( sz00 != sdtasdt0(sz00,W0) ) ) )
    | ~ aInteger0(xq)
    | ~ ( ( sdtasdt0(xq,sz00) != sz00 )
        | ( sz00 != sdtasdt0(sz00,xq) ) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(44,plain,
    ( ~ ! [W0: $i] :
          ( ~ aInteger0(W0)
          | ~ ( ( sdtasdt0(W0,sz00) != sz00 )
              | ( sz00 != sdtasdt0(sz00,W0) ) ) )
    | ~ aInteger0(xq)
    | ~ ( ( sdtasdt0(xq,sz00) != sz00 )
        | ( sz00 != sdtasdt0(sz00,xq) ) ) ),
    inference(modus_ponens,[status(thm)],[43,42]) ).

tff(45,plain,
    ~ ( ( sdtasdt0(xq,sz00) != sz00 )
      | ( sz00 != sdtasdt0(sz00,xq) ) ),
    inference(unit_resolution,[status(thm)],[44,41,28]) ).

tff(46,plain,
    ( ( sdtasdt0(xq,sz00) != sz00 )
    | ( sz00 != sdtasdt0(sz00,xq) )
    | ( sdtasdt0(xq,sz00) = sz00 ) ),
    inference(tautology,[status(thm)],]) ).

tff(47,plain,
    sdtasdt0(xq,sz00) = sz00,
    inference(unit_resolution,[status(thm)],[46,45]) ).

tff(48,plain,
    sdtasdt0(xq,sz00) = sdtpldt0(xa,smndt0(xa)),
    inference(transitivity,[status(thm)],[47,25]) ).

tff(49,plain,
    ^ [W0: $i] :
      refl(
        ( ( ~ aInteger0(W0)
          | ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) )
      <=> ( ~ aInteger0(W0)
          | ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) ) )),
    inference(bind,[status(th)],]) ).

tff(50,plain,
    ( ! [W0: $i] :
        ( ~ aInteger0(W0)
        | ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) )
  <=> ! [W0: $i] :
        ( ~ aInteger0(W0)
        | ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) ) ),
    inference(quant_intro,[status(thm)],[49]) ).

tff(51,plain,
    ^ [W0: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( aInteger0(W0)
              & ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) )
          <=> ~ ( ~ aInteger0(W0)
                | ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) ) )),
          ( ~ ( aInteger0(W0)
              & ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) )
        <=> ~ ~ ( ~ aInteger0(W0)
                | ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) ) )),
        rewrite(
          ( ~ ~ ( ~ aInteger0(W0)
                | ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) )
        <=> ( ~ aInteger0(W0)
            | ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) ) )),
        ( ~ ( aInteger0(W0)
            & ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) )
      <=> ( ~ aInteger0(W0)
          | ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) ) )),
    inference(bind,[status(th)],]) ).

tff(52,plain,
    ( ! [W0: $i] :
        ~ ( aInteger0(W0)
          & ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) )
  <=> ! [W0: $i] :
        ( ~ aInteger0(W0)
        | ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) ) ),
    inference(quant_intro,[status(thm)],[51]) ).

tff(53,plain,
    ( ~ ? [W0: $i] :
          ( aInteger0(W0)
          & ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) )
  <=> ~ ? [W0: $i] :
          ( aInteger0(W0)
          & ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(54,axiom,
    ~ ( ? [W0: $i] :
          ( aInteger0(W0)
          & ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) )
      | aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
      | sdteqdtlpzmzozddtrp0(xa,xa,xq) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

tff(55,plain,
    ~ ( ? [W0: $i] :
          ( aInteger0(W0)
          & ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) )
      | aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa))) ),
    inference(or_elim,[status(thm)],[54]) ).

tff(56,plain,
    ~ ? [W0: $i] :
        ( aInteger0(W0)
        & ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) ),
    inference(or_elim,[status(thm)],[55]) ).

tff(57,plain,
    ~ ? [W0: $i] :
        ( aInteger0(W0)
        & ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) ),
    inference(modus_ponens,[status(thm)],[56,53]) ).

tff(58,plain,
    ~ ? [W0: $i] :
        ( aInteger0(W0)
        & ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) ),
    inference(modus_ponens,[status(thm)],[57,53]) ).

tff(59,plain,
    ~ ? [W0: $i] :
        ( aInteger0(W0)
        & ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) ),
    inference(modus_ponens,[status(thm)],[58,53]) ).

tff(60,plain,
    ~ ? [W0: $i] :
        ( aInteger0(W0)
        & ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) ),
    inference(modus_ponens,[status(thm)],[59,53]) ).

tff(61,plain,
    ~ ? [W0: $i] :
        ( aInteger0(W0)
        & ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) ),
    inference(modus_ponens,[status(thm)],[60,53]) ).

tff(62,plain,
    ~ ? [W0: $i] :
        ( aInteger0(W0)
        & ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) ),
    inference(modus_ponens,[status(thm)],[61,53]) ).

tff(63,plain,
    ~ ? [W0: $i] :
        ( aInteger0(W0)
        & ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) ),
    inference(modus_ponens,[status(thm)],[62,53]) ).

tff(64,plain,
    ^ [W0: $i] :
      refl(
        $oeq(
          ~ ( aInteger0(W0)
            & ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) ),
          ~ ( aInteger0(W0)
            & ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) ))),
    inference(bind,[status(th)],]) ).

tff(65,plain,
    ! [W0: $i] :
      ~ ( aInteger0(W0)
        & ( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ) ),
    inference(nnf-neg,[status(sab)],[63,64]) ).

tff(66,plain,
    ! [W0: $i] :
      ( ~ aInteger0(W0)
      | ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) ),
    inference(modus_ponens,[status(thm)],[65,52]) ).

tff(67,plain,
    ! [W0: $i] :
      ( ~ aInteger0(W0)
      | ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) ),
    inference(modus_ponens,[status(thm)],[66,50]) ).

tff(68,plain,
    ( aInteger0(sz00)
  <=> aInteger0(sz00) ),
    inference(rewrite,[status(thm)],]) ).

tff(69,axiom,
    aInteger0(sz00),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).

tff(70,plain,
    aInteger0(sz00),
    inference(modus_ponens,[status(thm)],[69,68]) ).

tff(71,plain,
    ( ( ~ ! [W0: $i] :
            ( ~ aInteger0(W0)
            | ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) )
      | ~ aInteger0(sz00)
      | ( sdtasdt0(xq,sz00) != sdtpldt0(xa,smndt0(xa)) ) )
  <=> ( ~ ! [W0: $i] :
            ( ~ aInteger0(W0)
            | ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) )
      | ~ aInteger0(sz00)
      | ( sdtasdt0(xq,sz00) != sdtpldt0(xa,smndt0(xa)) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(72,plain,
    ( ~ ! [W0: $i] :
          ( ~ aInteger0(W0)
          | ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) )
    | ~ aInteger0(sz00)
    | ( sdtasdt0(xq,sz00) != sdtpldt0(xa,smndt0(xa)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(73,plain,
    ( ~ ! [W0: $i] :
          ( ~ aInteger0(W0)
          | ( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa)) ) )
    | ~ aInteger0(sz00)
    | ( sdtasdt0(xq,sz00) != sdtpldt0(xa,smndt0(xa)) ) ),
    inference(modus_ponens,[status(thm)],[72,71]) ).

tff(74,plain,
    sdtasdt0(xq,sz00) != sdtpldt0(xa,smndt0(xa)),
    inference(unit_resolution,[status(thm)],[73,70,67]) ).

tff(75,plain,
    $false,
    inference(unit_resolution,[status(thm)],[74,48]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM423+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n022.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Fri Sep  2 10:18:10 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35  Usage: tptp [options] [-file:]file
% 0.13/0.35    -h, -?       prints this message.
% 0.13/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.35    -m, -model   generate model.
% 0.13/0.35    -p, -proof   generate proof.
% 0.13/0.35    -c, -core    generate unsat core of named formulas.
% 0.13/0.35    -st, -statistics display statistics.
% 0.13/0.35    -t:timeout   set timeout (in second).
% 0.13/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35    -<param>:<value> configuration parameter and value.
% 0.13/0.35    -o:<output-file> file to place output in.
% 0.20/0.40  % SZS status Theorem
% 0.20/0.40  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------