%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SET925+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n013.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 : Tue Sep 20 05:08:39 EDT 2022

% Result   : Theorem 0.17s 0.36s
% Output   : Proof 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    7
% Syntax   : Number of formulae    :    9 (   1 unt;   4 typ;   0 def)
%            Number of atoms       :   11 (   5 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   10 (   4   ~;   0   |;   0   &)
%                                         (   6 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   3   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-2 aty)
%            Number of variables   :   10 (  10   !;   0   ?;  10   :)

% Comments : 
%------------------------------------------------------------------------------
tff(in_type,type,
    in: ( $i * $i ) > $o ).

tff(empty_set_type,type,
    empty_set: $i ).

tff(set_difference_type,type,
    set_difference: ( $i * $i ) > $i ).

tff(singleton_type,type,
    singleton: $i > $i ).

tff(1,axiom,
    ! [A: $i,B: $i] :
      ( ( set_difference(singleton(A),B) = empty_set )
    <=> in(A,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1) ).

tff(2,plain,
    ( ~ ! [A: $i,B: $i] :
          ( ( set_difference(singleton(A),B) = empty_set )
        <=> in(A,B) )
  <=> ~ ! [A: $i,B: $i] :
          ( ( set_difference(singleton(A),B) = empty_set )
        <=> in(A,B) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(3,axiom,
    ~ ! [A: $i,B: $i] :
        ( ( set_difference(singleton(A),B) = empty_set )
      <=> in(A,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_zfmisc_1) ).

tff(4,plain,
    ~ ! [A: $i,B: $i] :
        ( ( set_difference(singleton(A),B) = empty_set )
      <=> in(A,B) ),
    inference(modus_ponens,[status(thm)],[3,2]) ).

tff(5,plain,
    $false,
    inference(unit_resolution,[status(thm)],[4,1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SET925+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32  % Computer : n013.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Sat Sep  3 08:30:47 EDT 2022
% 0.11/0.32  % CPUTime  : 
% 0.11/0.32  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.32  Usage: tptp [options] [-file:]file
% 0.11/0.32    -h, -?       prints this message.
% 0.11/0.32    -smt2        print SMT-LIB2 benchmark.
% 0.11/0.32    -m, -model   generate model.
% 0.11/0.32    -p, -proof   generate proof.
% 0.11/0.32    -c, -core    generate unsat core of named formulas.
% 0.11/0.32    -st, -statistics display statistics.
% 0.11/0.32    -t:timeout   set timeout (in second).
% 0.11/0.32    -smt2status  display status in smt2 format instead of SZS.
% 0.11/0.32    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.32    -<param>:<value> configuration parameter and value.
% 0.11/0.32    -o:<output-file> file to place output in.
% 0.17/0.36  % SZS status Theorem
% 0.17/0.36  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------