%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN400+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n010.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 23:55:10 EDT 2022

% Result   : Theorem 0.14s 0.39s
% Output   : Proof 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   10 (   1 unt;   1 typ;   0 def)
%            Number of atoms       :   23 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   19 (   5   ~;   0   |;   0   &)
%                                         (  14 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   4 avg)
%            Maximal term depth    :    0 (   0 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   3 prp; 0-0 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :    6 (   6   !;   0   ?;   6   :)

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

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

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

tff(3,plain,
    ( ! [X: $i] : p
  <=> p ),
    inference(elim_unused_vars,[status(thm)],]) ).

tff(4,plain,
    ( ( ! [X: $i] : p
    <=> p )
  <=> ( p
    <=> p ) ),
    inference(monotonicity,[status(thm)],[3]) ).

tff(5,plain,
    ( ( ! [X: $i] : p
    <=> p )
  <=> $true ),
    inference(transitivity,[status(thm)],[4,2]) ).

tff(6,plain,
    ( ~ ( ! [X: $i] : p
      <=> p )
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[5]) ).

tff(7,plain,
    ( ~ ( ! [X: $i] : p
      <=> p )
  <=> $false ),
    inference(transitivity,[status(thm)],[6,1]) ).

tff(8,axiom,
    ~ ( ! [X: $i] : p
    <=> p ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kalish227) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SYN400+1 : TPTP v8.1.0. Released v2.0.0.
% 0.08/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35  % Computer : n010.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon Sep  5 03:01:27 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35  Usage: tptp [options] [-file:]file
% 0.14/0.35    -h, -?       prints this message.
% 0.14/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.14/0.35    -m, -model   generate model.
% 0.14/0.35    -p, -proof   generate proof.
% 0.14/0.35    -c, -core    generate unsat core of named formulas.
% 0.14/0.35    -st, -statistics display statistics.
% 0.14/0.35    -t:timeout   set timeout (in second).
% 0.14/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.14/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35    -<param>:<value> configuration parameter and value.
% 0.14/0.35    -o:<output-file> file to place output in.
% 0.14/0.39  % SZS status Theorem
% 0.14/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------