%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SET296-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n015.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 05:06:25 EDT 2022

% Result   : Unsatisfiable 0.19s 0.42s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   16 (   8 unt;   4 typ;   0 def)
%            Number of atoms       :   18 (  16 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   10 (   5   ~;   1   |;   0   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of FOOLs       :    1 (   1 fml;   0 var)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   1 con; 0-1 aty)
%            Number of variables   :   10 (   9   !;   0   ?;  10   :)

% Comments : 
%------------------------------------------------------------------------------
tff(range_of_type,type,
    range_of: $i > $i ).

tff(x_type,type,
    x: $i ).

tff(domain_of_type,type,
    domain_of: $i > $i ).

tff(inverse_type,type,
    inverse: $i > $i ).

tff(1,plain,
    ( ( domain_of(inverse(x)) != range_of(x) )
  <=> ( domain_of(inverse(x)) != range_of(x) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    domain_of(inverse(x)) != range_of(x),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_of_inverse_1) ).

tff(3,plain,
    domain_of(inverse(x)) != range_of(x),
    inference(modus_ponens,[status(thm)],[2,1]) ).

tff(4,plain,
    ^ [Z: $i] :
      refl(
        ( ( domain_of(inverse(Z)) = range_of(Z) )
      <=> ( domain_of(inverse(Z)) = range_of(Z) ) )),
    inference(bind,[status(th)],]) ).

tff(5,plain,
    ( ! [Z: $i] : ( domain_of(inverse(Z)) = range_of(Z) )
  <=> ! [Z: $i] : ( domain_of(inverse(Z)) = range_of(Z) ) ),
    inference(quant_intro,[status(thm)],[4]) ).

tff(6,plain,
    ( ! [Z: $i] : ( domain_of(inverse(Z)) = range_of(Z) )
  <=> ! [Z: $i] : ( domain_of(inverse(Z)) = range_of(Z) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(7,axiom,
    ! [Z: $i] : ( domain_of(inverse(Z)) = range_of(Z) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',range_of) ).

tff(8,plain,
    ! [Z: $i] : ( domain_of(inverse(Z)) = range_of(Z) ),
    inference(modus_ponens,[status(thm)],[7,6]) ).

tff(9,plain,
    ! [Z: $i] : ( domain_of(inverse(Z)) = range_of(Z) ),
    inference(skolemize,[status(sab)],[8]) ).

tff(10,plain,
    ! [Z: $i] : ( domain_of(inverse(Z)) = range_of(Z) ),
    inference(modus_ponens,[status(thm)],[9,5]) ).

tff(11,plain,
    ( ~ ! [Z: $i] : ( domain_of(inverse(Z)) = range_of(Z) )
    | ( domain_of(inverse(x)) = range_of(x) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(12,plain,
    $false,
    inference(unit_resolution,[status(thm)],[11,10,3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET296-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n015.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sat Sep  3 04:18:25 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34  Usage: tptp [options] [-file:]file
% 0.12/0.34    -h, -?       prints this message.
% 0.12/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.34    -m, -model   generate model.
% 0.12/0.34    -p, -proof   generate proof.
% 0.12/0.34    -c, -core    generate unsat core of named formulas.
% 0.12/0.34    -st, -statistics display statistics.
% 0.12/0.34    -t:timeout   set timeout (in second).
% 0.12/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34    -<param>:<value> configuration parameter and value.
% 0.12/0.34    -o:<output-file> file to place output in.
% 0.19/0.42  % SZS status Unsatisfiable
% 0.19/0.42  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------