%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SET899+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n016.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 05:08:33 EDT 2022

% Result   : Theorem 0.13s 0.56s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   12 (   2 unt;   4 typ;   0 def)
%            Number of atoms       :   32 (   0 equ)
%            Maximal formula atoms :    6 (   4 avg)
%            Number of connectives :   32 (   9   ~;  15   |;   0   &)
%                                         (   3 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 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  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   0 con; 1-2 aty)
%            Number of variables   :   27 (  24   !;   0   ?;  27   :)

% Comments : 
%------------------------------------------------------------------------------
tff(subset_type,type,
    subset: ( $i * $i ) > $o ).

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

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

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

tff(1,plain,
    ^ [A: $i,B: $i,C: $i] :
      rewrite(
        ( ( subset(A,B)
         => ( in(C,A)
            | subset(A,set_difference(B,singleton(C))) ) )
      <=> ( subset(A,set_difference(B,singleton(C)))
          | in(C,A)
          | ~ subset(A,B) ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [A: $i,B: $i,C: $i] :
        ( subset(A,B)
       => ( in(C,A)
          | subset(A,set_difference(B,singleton(C))) ) )
  <=> ! [A: $i,B: $i,C: $i] :
        ( subset(A,set_difference(B,singleton(C)))
        | in(C,A)
        | ~ subset(A,B) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( subset(A,B)
     => ( in(C,A)
        | subset(A,set_difference(B,singleton(C))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_zfmisc_1) ).

tff(4,plain,
    ! [A: $i,B: $i,C: $i] :
      ( subset(A,set_difference(B,singleton(C)))
      | in(C,A)
      | ~ subset(A,B) ),
    inference(modus_ponens,[status(thm)],[3,2]) ).

tff(5,plain,
    ( ~ ! [A: $i,B: $i,C: $i] :
          ( subset(A,B)
         => ( in(C,A)
            | subset(A,set_difference(B,singleton(C))) ) )
  <=> ~ ! [A: $i,B: $i,C: $i] :
          ( subset(A,set_difference(B,singleton(C)))
          | in(C,A)
          | ~ subset(A,B) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(6,axiom,
    ~ ! [A: $i,B: $i,C: $i] :
        ( subset(A,B)
       => ( in(C,A)
          | subset(A,set_difference(B,singleton(C))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_zfmisc_1) ).

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

tff(8,plain,
    $false,
    inference(unit_resolution,[status(thm)],[7,4]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.30  % Problem  : SET899+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.30  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.51  % Computer : n016.cluster.edu
% 0.13/0.51  % Model    : x86_64 x86_64
% 0.13/0.51  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.51  % Memory   : 8042.1875MB
% 0.13/0.51  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.51  % CPULimit : 300
% 0.13/0.51  % WCLimit  : 300
% 0.13/0.51  % DateTime : Sat Sep  3 08:52:07 EDT 2022
% 0.13/0.52  % CPUTime  : 
% 0.13/0.52  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.52  Usage: tptp [options] [-file:]file
% 0.13/0.52    -h, -?       prints this message.
% 0.13/0.52    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.52    -m, -model   generate model.
% 0.13/0.52    -p, -proof   generate proof.
% 0.13/0.52    -c, -core    generate unsat core of named formulas.
% 0.13/0.52    -st, -statistics display statistics.
% 0.13/0.52    -t:timeout   set timeout (in second).
% 0.13/0.52    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.52    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.52    -<param>:<value> configuration parameter and value.
% 0.13/0.52    -o:<output-file> file to place output in.
% 0.13/0.56  % SZS status Theorem
% 0.13/0.56  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------