%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : LCL230+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n029.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 04:55:32 EDT 2022

% Result   : Theorem 0.18s 0.37s
% Output   : Proof 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   23 (   4 unt;   3 typ;   0 def)
%            Number of atoms       :   76 (   0 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :   75 (  19   ~;  37   |;   0   &)
%                                         (  13 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   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  :    5 (   3 usr;   5 prp; 0-0 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :    0 (   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(q_type,type,
    q: $o ).

tff(p_type,type,
    p: $o ).

tff(r_type,type,
    r: $o ).

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

tff(2,plain,
    ( ~ $true
  <=> $false ),
    inference(rewrite,[status(thm)],]) ).

tff(3,plain,
    ( ( $false
      | $true )
  <=> $true ),
    inference(rewrite,[status(thm)],]) ).

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

tff(5,axiom,
    ~ ( ( ( p
          | q )
       => ( p
          | r ) )
     => ( p
        | ( q
         => r ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel5) ).

tff(6,plain,
    ~ ( p
      | r
      | ~ q
      | ~ ( p
          | r
          | ~ ( p
              | q ) ) ),
    inference(modus_ponens,[status(thm)],[5,4]) ).

tff(7,plain,
    q,
    inference(or_elim,[status(thm)],[6]) ).

tff(8,plain,
    ( q
  <=> $true ),
    inference(iff_true,[status(thm)],[7]) ).

tff(9,plain,
    ~ p,
    inference(or_elim,[status(thm)],[6]) ).

tff(10,plain,
    ( p
  <=> $false ),
    inference(iff_false,[status(thm)],[9]) ).

tff(11,plain,
    ( ( p
      | q )
  <=> ( $false
      | $true ) ),
    inference(monotonicity,[status(thm)],[10,8]) ).

tff(12,plain,
    ( ( p
      | q )
  <=> $true ),
    inference(transitivity,[status(thm)],[11,3]) ).

tff(13,plain,
    ( ~ ( p
        | q )
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[12]) ).

tff(14,plain,
    ( ~ ( p
        | q )
  <=> $false ),
    inference(transitivity,[status(thm)],[13,2]) ).

tff(15,plain,
    ~ r,
    inference(or_elim,[status(thm)],[6]) ).

tff(16,plain,
    ( r
  <=> $false ),
    inference(iff_false,[status(thm)],[15]) ).

tff(17,plain,
    ( ( p
      | r
      | ~ ( p
          | q ) )
  <=> ( $false
      | $false
      | $false ) ),
    inference(monotonicity,[status(thm)],[10,16,14]) ).

tff(18,plain,
    ( ( p
      | r
      | ~ ( p
          | q ) )
  <=> $false ),
    inference(transitivity,[status(thm)],[17,1]) ).

tff(19,plain,
    ( p
    | r
    | ~ ( p
        | q ) ),
    inference(or_elim,[status(thm)],[6]) ).

tff(20,plain,
    $false,
    inference(modus_ponens,[status(thm)],[19,18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LCL230+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33  % Computer : n029.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Thu Sep  1 19:25:13 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.33  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.33  Usage: tptp [options] [-file:]file
% 0.13/0.33    -h, -?       prints this message.
% 0.13/0.33    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.33    -m, -model   generate model.
% 0.13/0.33    -p, -proof   generate proof.
% 0.13/0.33    -c, -core    generate unsat core of named formulas.
% 0.13/0.33    -st, -statistics display statistics.
% 0.13/0.33    -t:timeout   set timeout (in second).
% 0.13/0.33    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.33    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.33    -<param>:<value> configuration parameter and value.
% 0.13/0.33    -o:<output-file> file to place output in.
% 0.18/0.37  % SZS status Theorem
% 0.18/0.37  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------