%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : LCL181+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n006.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 04:55:15 EDT 2022

% Result   : Theorem 0.15s 0.41s
% Output   : Proof 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   12 (   1 unt;   2 typ;   0 def)
%            Number of atoms       :   43 (   0 equ)
%            Maximal formula atoms :    8 (   4 avg)
%            Number of connectives :   50 (  17   ~;   6   |;   0   &)
%                                         (  15 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :    0 (   0 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   4 prp; 0-0 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :    0 (   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(p_type,type,
    p: $o ).

tff(q_type,type,
    q: $o ).

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

tff(2,plain,
    ( ( ( p
        | q )
    <=> ( p
        | q ) )
  <=> $true ),
    inference(rewrite,[status(thm)],]) ).

tff(3,plain,
    ( ( ~ q
     => p )
  <=> ( p
      | q ) ),
    inference(rewrite,[status(thm)],]) ).

tff(4,plain,
    ( ( ~ p
     => q )
  <=> ( p
      | q ) ),
    inference(rewrite,[status(thm)],]) ).

tff(5,plain,
    ( ( ( ~ p
       => q )
    <=> ( ~ q
       => p ) )
  <=> ( ( p
        | q )
    <=> ( p
        | q ) ) ),
    inference(monotonicity,[status(thm)],[4,3]) ).

tff(6,plain,
    ( ( ( ~ p
       => q )
    <=> ( ~ q
       => p ) )
  <=> $true ),
    inference(transitivity,[status(thm)],[5,2]) ).

tff(7,plain,
    ( ~ ( ( ~ p
         => q )
      <=> ( ~ q
         => p ) )
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[6]) ).

tff(8,plain,
    ( ~ ( ( ~ p
         => q )
      <=> ( ~ q
         => p ) )
  <=> $false ),
    inference(transitivity,[status(thm)],[7,1]) ).

tff(9,axiom,
    ~ ( ( ~ p
       => q )
    <=> ( ~ q
       => p ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel4) ).

tff(10,plain,
    $false,
    inference(modus_ponens,[status(thm)],[9,8]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : LCL181+1 : TPTP v8.1.0. Released v2.0.0.
% 0.08/0.15  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.36  % Computer : n006.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Sep  1 18:30:39 EDT 2022
% 0.15/0.36  % CPUTime  : 
% 0.15/0.37  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.37  Usage: tptp [options] [-file:]file
% 0.15/0.37    -h, -?       prints this message.
% 0.15/0.37    -smt2        print SMT-LIB2 benchmark.
% 0.15/0.37    -m, -model   generate model.
% 0.15/0.37    -p, -proof   generate proof.
% 0.15/0.37    -c, -core    generate unsat core of named formulas.
% 0.15/0.37    -st, -statistics display statistics.
% 0.15/0.37    -t:timeout   set timeout (in second).
% 0.15/0.37    -smt2status  display status in smt2 format instead of SZS.
% 0.15/0.37    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.37    -<param>:<value> configuration parameter and value.
% 0.15/0.37    -o:<output-file> file to place output in.
% 0.15/0.41  % SZS status Theorem
% 0.15/0.41  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------