%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : ARI093_1 : TPTP v8.1.0. Released v5.0.0.
% 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 : Tue Sep  6 17:00:36 EDT 2022

% Result   : Theorem 0.06s 0.29s
% Output   : Proof 0.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    4
% Syntax   : Number of formulae    :    9 (   3 unt;   0 typ;   0 def)
%            Number of atoms       :   25 (  10 equ)
%            Maximal formula atoms :    2 (   2 avg)
%            Number of connectives :   14 (   5   ~;   0   |;   0   &)
%                                         (   9 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :    7 (   7 fml;   0 var)
%            Number arithmetic     :   24 (   0 atm;   8 fun;   8 num;   8 var)
%            Number of types       :    1 (   0 usr;   1 ari)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   3 usr;   2 prp; 0-3 aty)
%            Number of functors    :    2 (   0 usr;   1 con; 0-2 aty)
%            Number of variables   :    8 (   0   !;   7   ?;   8   :)

% Comments : 
%------------------------------------------------------------------------------
tff(1,plain,
    ( ~ $true
  <=> $false ),
    inference(rewrite,[status(thm)],]) ).

tff(2,plain,
    ( ? [X: $int] : $true
  <=> $true ),
    inference(elim_unused_vars,[status(thm)],]) ).

tff(3,plain,
    ^ [X: $int] :
      trans(
        monotonicity(rewrite(( $difference(X,0) = X )),
          ( ( $difference(X,0) = X )
        <=> ( X = X ) )),
        rewrite(
          ( ( X = X )
        <=> $true )),
        ( ( $difference(X,0) = X )
      <=> $true )),
    inference(bind,[status(th)],]) ).

tff(4,plain,
    ( ? [X: $int] : ( $difference(X,0) = X )
  <=> ? [X: $int] : $true ),
    inference(quant_intro,[status(thm)],[3]) ).

tff(5,plain,
    ( ? [X: $int] : ( $difference(X,0) = X )
  <=> $true ),
    inference(transitivity,[status(thm)],[4,2]) ).

tff(6,plain,
    ( ~ ? [X: $int] : ( $difference(X,0) = X )
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[5]) ).

tff(7,plain,
    ( ~ ? [X: $int] : ( $difference(X,0) = X )
  <=> $false ),
    inference(transitivity,[status(thm)],[6,1]) ).

tff(8,axiom,
    ~ ? [X: $int] : ( $difference(X,0) = X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diff_zero_identity) ).

tff(9,plain,
    $false,
    inference(modus_ponens,[status(thm)],[8,7]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06  % Problem  : ARI093_1 : TPTP v8.1.0. Released v5.0.0.
% 0.00/0.07  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.06/0.25  % Computer : n022.cluster.edu
% 0.06/0.25  % Model    : x86_64 x86_64
% 0.06/0.25  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25  % Memory   : 8042.1875MB
% 0.06/0.25  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25  % CPULimit : 300
% 0.06/0.25  % WCLimit  : 300
% 0.06/0.25  % DateTime : Mon Aug 29 21:50:26 EDT 2022
% 0.06/0.25  % CPUTime  : 
% 0.06/0.26  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.06/0.26  Usage: tptp [options] [-file:]file
% 0.06/0.26    -h, -?       prints this message.
% 0.06/0.26    -smt2        print SMT-LIB2 benchmark.
% 0.06/0.26    -m, -model   generate model.
% 0.06/0.26    -p, -proof   generate proof.
% 0.06/0.26    -c, -core    generate unsat core of named formulas.
% 0.06/0.26    -st, -statistics display statistics.
% 0.06/0.26    -t:timeout   set timeout (in second).
% 0.06/0.26    -smt2status  display status in smt2 format instead of SZS.
% 0.06/0.26    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.06/0.26    -<param>:<value> configuration parameter and value.
% 0.06/0.26    -o:<output-file> file to place output in.
% 0.06/0.29  % SZS status Theorem
% 0.06/0.29  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------