%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN045-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n014.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 : Thu Sep 29 23:53:18 EDT 2022

% Result   : Unsatisfiable 0.20s 0.39s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   27 (   4 unt;   3 typ;   0 def)
%            Number of atoms       :   56 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   46 (  14   ~;  15   |;   0   &)
%                                         (  17 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 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(r_type,type,
    r: $o ).

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

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

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

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

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

tff(4,axiom,
    ~ p,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).

tff(5,plain,
    ( p
  <=> $false ),
    inference(iff_false,[status(thm)],[4]) ).

tff(6,plain,
    ( ( p
      | r )
  <=> ( $false
      | r ) ),
    inference(monotonicity,[status(thm)],[5]) ).

tff(7,plain,
    ( ( p
      | r )
  <=> r ),
    inference(transitivity,[status(thm)],[6,3]) ).

tff(8,axiom,
    ( p
    | r ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).

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

tff(10,plain,
    ( r
  <=> $true ),
    inference(iff_true,[status(thm)],[9]) ).

tff(11,plain,
    ( ~ r
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[10]) ).

tff(12,plain,
    ( ~ r
  <=> $false ),
    inference(transitivity,[status(thm)],[11,2]) ).

tff(13,plain,
    ( ( $false
      | q )
  <=> q ),
    inference(rewrite,[status(thm)],]) ).

tff(14,plain,
    ( ( p
      | q )
  <=> ( $false
      | q ) ),
    inference(monotonicity,[status(thm)],[5]) ).

tff(15,plain,
    ( ( p
      | q )
  <=> q ),
    inference(transitivity,[status(thm)],[14,13]) ).

tff(16,axiom,
    ( p
    | q ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).

tff(17,plain,
    q,
    inference(modus_ponens,[status(thm)],[16,15]) ).

tff(18,plain,
    ( q
  <=> $true ),
    inference(iff_true,[status(thm)],[17]) ).

tff(19,plain,
    ( ~ q
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[18]) ).

tff(20,plain,
    ( ~ q
  <=> $false ),
    inference(transitivity,[status(thm)],[19,2]) ).

tff(21,plain,
    ( ( ~ q
      | ~ r )
  <=> ( $false
      | $false ) ),
    inference(monotonicity,[status(thm)],[20,12]) ).

tff(22,plain,
    ( ( ~ q
      | ~ r )
  <=> $false ),
    inference(transitivity,[status(thm)],[21,1]) ).

tff(23,axiom,
    ( ~ q
    | ~ r ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).

tff(24,plain,
    $false,
    inference(modus_ponens,[status(thm)],[23,22]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SYN045-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n014.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
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Mon Sep  5 01:17:14 EDT 2022
% 0.13/0.35  % 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.
% 0.20/0.39  % SZS status Unsatisfiable
% 0.20/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------