%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SEU165+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n029.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 07:27:55 EDT 2022

% Result   : Theorem 0.22s 0.41s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    6
% Syntax   : Number of formulae    :    8 (   1 unt;   3 typ;   0 def)
%            Number of atoms       :   16 (   0 equ)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :   15 (   4   ~;   0   |;   5   &)
%                                         (   6 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   0 con; 2-2 aty)
%            Number of variables   :   20 (  20   !;   0   ?;  20   :)

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

tff(cartesian_product2_type,type,
    cartesian_product2: ( $i * $i ) > $i ).

tff(ordered_pair_type,type,
    ordered_pair: ( $i * $i ) > $i ).

tff(1,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( in(ordered_pair(A,B),cartesian_product2(C,D))
    <=> ( in(A,C)
        & in(B,D) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).

tff(2,plain,
    ( ~ ! [A: $i,B: $i,C: $i,D: $i] :
          ( in(ordered_pair(A,B),cartesian_product2(C,D))
        <=> ( in(A,C)
            & in(B,D) ) )
  <=> ~ ! [A: $i,B: $i,C: $i,D: $i] :
          ( in(ordered_pair(A,B),cartesian_product2(C,D))
        <=> ( in(A,C)
            & in(B,D) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(3,axiom,
    ~ ! [A: $i,B: $i,C: $i,D: $i] :
        ( in(ordered_pair(A,B),cartesian_product2(C,D))
      <=> ( in(A,C)
          & in(B,D) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).

tff(4,plain,
    ~ ! [A: $i,B: $i,C: $i,D: $i] :
        ( in(ordered_pair(A,B),cartesian_product2(C,D))
      <=> ( in(A,C)
          & in(B,D) ) ),
    inference(modus_ponens,[status(thm)],[3,2]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem  : SEU165+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.15  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.37  % Computer : n029.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 : Sat Sep  3 09:58:15 EDT 2022
% 0.15/0.37  % CPUTime  : 
% 0.15/0.37  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.37  Usage: tptp [options] [-file:]file
% 0.15/0.37    -h, -?       prints this message.
% 0.15/0.37    -smt2        print SMT-LIB2 benchmark.
% 0.15/0.37    -m, -model   generate model.
% 0.15/0.37    -p, -proof   generate proof.
% 0.15/0.37    -c, -core    generate unsat core of named formulas.
% 0.15/0.37    -st, -statistics display statistics.
% 0.15/0.37    -t:timeout   set timeout (in second).
% 0.15/0.37    -smt2status  display status in smt2 format instead of SZS.
% 0.15/0.37    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.37    -<param>:<value> configuration parameter and value.
% 0.15/0.37    -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
%------------------------------------------------------------------------------