%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN000+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n023.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 23:53:04 EDT 2022

% Result   : Theorem 0.23s 0.42s
% Output   : Proof 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   22 (  16 unt;   2 typ;   0 def)
%            Number of atoms       :   29 (   0 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   27 (  22   ~;   1   |;   0   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :    4 (   4 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    1 (   1   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    1 (   1 usr;   1 con; 0-0 aty)
%            Number of variables   :   18 (   5   !;  11   ?;  18   :)

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

tff(h_type,type,
    h: $i ).

tff(1,plain,
    ^ [X: $i] :
      refl(
        ( ~ p(X)
      <=> ~ p(X) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [X: $i] : ~ p(X)
  <=> ! [X: $i] : ~ p(X) ),
    inference(quant_intro,[status(thm)],[1]) ).

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

tff(4,axiom,
    ~ ? [X: $i] : p(X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',role_conjecture) ).

tff(5,plain,
    ~ ? [X: $i] : p(X),
    inference(modus_ponens,[status(thm)],[4,3]) ).

tff(6,plain,
    ~ ? [X: $i] : p(X),
    inference(modus_ponens,[status(thm)],[5,3]) ).

tff(7,plain,
    ~ ? [X: $i] : p(X),
    inference(modus_ponens,[status(thm)],[6,3]) ).

tff(8,plain,
    ~ ? [X: $i] : p(X),
    inference(modus_ponens,[status(thm)],[7,3]) ).

tff(9,plain,
    ~ ? [X: $i] : p(X),
    inference(modus_ponens,[status(thm)],[8,3]) ).

tff(10,plain,
    ~ ? [X: $i] : p(X),
    inference(modus_ponens,[status(thm)],[9,3]) ).

tff(11,plain,
    ~ ? [X: $i] : p(X),
    inference(modus_ponens,[status(thm)],[10,3]) ).

tff(12,plain,
    ~ ? [X: $i] : p(X),
    inference(modus_ponens,[status(thm)],[11,3]) ).

tff(13,plain,
    ^ [X: $i] : refl($oeq(~ p(X),~ p(X))),
    inference(bind,[status(th)],]) ).

tff(14,plain,
    ! [X: $i] : ~ p(X),
    inference(nnf-neg,[status(sab)],[12,13]) ).

tff(15,plain,
    ! [X: $i] : ~ p(X),
    inference(modus_ponens,[status(thm)],[14,2]) ).

tff(16,plain,
    ( p(h)
  <=> p(h) ),
    inference(rewrite,[status(thm)],]) ).

tff(17,axiom,
    p(h),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',role_hypothesis) ).

tff(18,plain,
    p(h),
    inference(modus_ponens,[status(thm)],[17,16]) ).

tff(19,plain,
    ( ~ ! [X: $i] : ~ p(X)
    | ~ p(h) ),
    inference(quant_inst,[status(thm)],]) ).

tff(20,plain,
    $false,
    inference(unit_resolution,[status(thm)],[19,18,15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : SYN000+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.15  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.37  % Computer : n023.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Mon Sep  5 01:00:02 EDT 2022
% 0.15/0.37  % CPUTime  : 
% 0.15/0.38  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.38  Usage: tptp [options] [-file:]file
% 0.15/0.38    -h, -?       prints this message.
% 0.15/0.38    -smt2        print SMT-LIB2 benchmark.
% 0.15/0.38    -m, -model   generate model.
% 0.15/0.38    -p, -proof   generate proof.
% 0.15/0.38    -c, -core    generate unsat core of named formulas.
% 0.15/0.38    -st, -statistics display statistics.
% 0.15/0.38    -t:timeout   set timeout (in second).
% 0.15/0.38    -smt2status  display status in smt2 format instead of SZS.
% 0.15/0.38    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.38    -<param>:<value> configuration parameter and value.
% 0.15/0.38    -o:<output-file> file to place output in.
% 0.23/0.42  % SZS status Theorem
% 0.23/0.42  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------