%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SEU161+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n003.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 07:27:53 EDT 2022

% Result   : Theorem 0.11s 0.39s
% Output   : Proof 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   11 (   2 unt;   3 typ;   0 def)
%            Number of atoms       :   22 (  10 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   22 (   9   ~;   5   |;   0   &)
%                                         (   3 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of FOOLs       :    1 (   1 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   3   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   0 con; 1-2 aty)
%            Number of variables   :   18 (  16   !;   0   ?;  18   :)

% Comments : 
%------------------------------------------------------------------------------
tff(set_union2_type,type,
    set_union2: ( $i * $i ) > $i ).

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

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

tff(1,plain,
    ( ~ ! [A: $i,B: $i] :
          ( in(A,B)
         => ( set_union2(singleton(A),B) = B ) )
  <=> ~ ! [A: $i,B: $i] :
          ( ~ in(A,B)
          | ( set_union2(singleton(A),B) = B ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    ~ ! [A: $i,B: $i] :
        ( in(A,B)
       => ( set_union2(singleton(A),B) = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_zfmisc_1) ).

tff(3,plain,
    ~ ! [A: $i,B: $i] :
        ( ~ in(A,B)
        | ( set_union2(singleton(A),B) = B ) ),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    ^ [A: $i,B: $i] :
      rewrite(
        ( ( in(A,B)
         => ( set_union2(singleton(A),B) = B ) )
      <=> ( ~ in(A,B)
          | ( set_union2(singleton(A),B) = B ) ) )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ! [A: $i,B: $i] :
        ( in(A,B)
       => ( set_union2(singleton(A),B) = B ) )
  <=> ! [A: $i,B: $i] :
        ( ~ in(A,B)
        | ( set_union2(singleton(A),B) = B ) ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,axiom,
    ! [A: $i,B: $i] :
      ( in(A,B)
     => ( set_union2(singleton(A),B) = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l23_zfmisc_1) ).

tff(7,plain,
    ! [A: $i,B: $i] :
      ( ~ in(A,B)
      | ( set_union2(singleton(A),B) = B ) ),
    inference(modus_ponens,[status(thm)],[6,5]) ).

tff(8,plain,
    $false,
    inference(unit_resolution,[status(thm)],[7,3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SEU161+2 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.33  % Computer : n003.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Sat Sep  3 09:47:25 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 0.11/0.33  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33  Usage: tptp [options] [-file:]file
% 0.11/0.33    -h, -?       prints this message.
% 0.11/0.33    -smt2        print SMT-LIB2 benchmark.
% 0.11/0.33    -m, -model   generate model.
% 0.11/0.33    -p, -proof   generate proof.
% 0.11/0.33    -c, -core    generate unsat core of named formulas.
% 0.11/0.33    -st, -statistics display statistics.
% 0.11/0.33    -t:timeout   set timeout (in second).
% 0.11/0.33    -smt2status  display status in smt2 format instead of SZS.
% 0.11/0.33    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33    -<param>:<value> configuration parameter and value.
% 0.11/0.33    -o:<output-file> file to place output in.
% 0.11/0.39  % SZS status Theorem
% 0.11/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------