%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : LCL680+1.001 : TPTP v8.1.0. Released v4.0.0.
% 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 : Sun Sep 18 04:57:50 EDT 2022

% Result   : Theorem 0.22s 0.41s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   13 (   2 unt;   1 typ;   0 def)
%            Number of atoms       :   42 (   0 equ)
%            Maximal formula atoms :    3 (   3 avg)
%            Number of connectives :   56 (  33   ~;  10   |;   0   &)
%                                         (  13 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :    7 (   7 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    1 (   1   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   2 prp; 0-3 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   10 (   0   !;   9   ?;  10   :)

% Comments : 
%------------------------------------------------------------------------------
tff(p1_type,type,
    p1: $i > $o ).

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

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

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

tff(4,plain,
    ^ [X: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( ~ p1(X)
              | p1(X) )
          <=> $true )),
          ( ~ ( ~ p1(X)
              | p1(X) )
        <=> ~ $true )),
        rewrite(
          ( ~ $true
        <=> $false )),
        ( ~ ( ~ p1(X)
            | p1(X) )
      <=> $false )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ? [X: $i] :
        ~ ( ~ p1(X)
          | p1(X) )
  <=> ? [X: $i] : $false ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,plain,
    ( ? [X: $i] :
        ~ ( ~ p1(X)
          | p1(X) )
  <=> $false ),
    inference(transitivity,[status(thm)],[5,3]) ).

tff(7,plain,
    ( ~ ? [X: $i] :
          ~ ( ~ p1(X)
            | p1(X) )
  <=> ~ $false ),
    inference(monotonicity,[status(thm)],[6]) ).

tff(8,plain,
    ( ~ ? [X: $i] :
          ~ ( ~ p1(X)
            | p1(X) )
  <=> $true ),
    inference(transitivity,[status(thm)],[7,2]) ).

tff(9,plain,
    ( ~ ~ ? [X: $i] :
            ~ ( ~ p1(X)
              | p1(X) )
  <=> ~ $true ),
    inference(monotonicity,[status(thm)],[8]) ).

tff(10,plain,
    ( ~ ~ ? [X: $i] :
            ~ ( ~ p1(X)
              | p1(X) )
  <=> $false ),
    inference(transitivity,[status(thm)],[9,1]) ).

tff(11,axiom,
    ~ ~ ? [X: $i] :
          ~ ( ~ p1(X)
            | p1(X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main) ).

tff(12,plain,
    $false,
    inference(modus_ponens,[status(thm)],[11,10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : LCL680+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.14  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35  % Computer : n022.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 : Fri Sep  2 00:08:40 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.36  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36  Usage: tptp [options] [-file:]file
% 0.14/0.36    -h, -?       prints this message.
% 0.14/0.36    -smt2        print SMT-LIB2 benchmark.
% 0.14/0.36    -m, -model   generate model.
% 0.14/0.36    -p, -proof   generate proof.
% 0.14/0.36    -c, -core    generate unsat core of named formulas.
% 0.14/0.36    -st, -statistics display statistics.
% 0.14/0.36    -t:timeout   set timeout (in second).
% 0.14/0.36    -smt2status  display status in smt2 format instead of SZS.
% 0.14/0.36    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36    -<param>:<value> configuration parameter and value.
% 0.14/0.36    -o:<output-file> file to place output in.
% 0.22/0.41  % SZS status Theorem
% 0.22/0.41  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------