TSTP Solution File: SWB097+1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWB097+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n024.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 08:32:18 EDT 2022

% Result   : Theorem 0.76s 0.75s
% Output   : Proof 0.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   44
% Syntax   : Number of formulae    :   88 (  20 unt;  15 typ;   0 def)
%            Number of atoms       :  692 (   0 equ)
%            Maximal formula atoms :   36 (   9 avg)
%            Number of connectives : 1200 ( 617   ~; 413   |;  92   &)
%                                         (  72 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :   36 (  36 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (   4   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   9 usr;   1 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;  11 con; 0-3 aty)
%            Number of variables   :  247 ( 219   !;  13   ?; 247   :)

% Comments : 
%------------------------------------------------------------------------------
tff(iext_type,type,
    iext: ( $i * $i * $i ) > $o ).

tff(uri_ex_w_type,type,
    uri_ex_w: $i ).

tff(uri_ex_p_type,type,
    uri_ex_p: $i ).

tff(icext_type,type,
    icext: ( $i * $i ) > $o ).

tff(uri_ex_c_type,type,
    uri_ex_c: $i ).

tff(uri_ex_z_type,type,
    uri_ex_z: $i ).

tff(tptp_fun_Y_42_type,type,
    tptp_fun_Y_42: ( $i * $i * $i ) > $i ).

tff(uri_owl_onClass_type,type,
    uri_owl_onClass: $i ).

tff(uri_owl_onProperty_type,type,
    uri_owl_onProperty: $i ).

tff(literal_typed_type,type,
    literal_typed: ( $i * $i ) > $i ).

tff(uri_xsd_nonNegativeInteger_type,type,
    uri_xsd_nonNegativeInteger: $i ).

tff(dat_str_1_type,type,
    dat_str_1: $i ).

tff(uri_owl_minQualifiedCardinality_type,type,
    uri_owl_minQualifiedCardinality: $i ).

tff(uri_ex_x_type,type,
    uri_ex_x: $i ).

tff(uri_rdf_type_type,type,
    uri_rdf_type: $i ).

tff(1,plain,
    ( iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
  <=> iext(uri_owl_onClass,uri_ex_z,uri_ex_c) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    ( iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
    & iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
    & iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
    & iext(uri_rdf_type,uri_ex_x,uri_ex_c)
    & iext(uri_ex_p,uri_ex_w,uri_ex_x) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',premise_rdfbased_sem_restrict_minqcr_inst_subj_one) ).

tff(3,plain,
    ( iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
    & iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
    & iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
    & iext(uri_rdf_type,uri_ex_x,uri_ex_c) ),
    inference(and_elim,[status(thm)],[2]) ).

tff(4,plain,
    ( iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
    & iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
    & iext(uri_owl_onClass,uri_ex_z,uri_ex_c) ),
    inference(and_elim,[status(thm)],[3]) ).

tff(5,plain,
    iext(uri_owl_onClass,uri_ex_z,uri_ex_c),
    inference(and_elim,[status(thm)],[4]) ).

tff(6,plain,
    iext(uri_owl_onClass,uri_ex_z,uri_ex_c),
    inference(modus_ponens,[status(thm)],[5,1]) ).

tff(7,plain,
    ( iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
  <=> iext(uri_owl_onProperty,uri_ex_z,uri_ex_p) ),
    inference(rewrite,[status(thm)],]) ).

tff(8,plain,
    ( iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
    & iext(uri_owl_onProperty,uri_ex_z,uri_ex_p) ),
    inference(and_elim,[status(thm)],[4]) ).

tff(9,plain,
    iext(uri_owl_onProperty,uri_ex_z,uri_ex_p),
    inference(and_elim,[status(thm)],[8]) ).

tff(10,plain,
    iext(uri_owl_onProperty,uri_ex_z,uri_ex_p),
    inference(modus_ponens,[status(thm)],[9,7]) ).

tff(11,plain,
    ( iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
  <=> iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ),
    inference(rewrite,[status(thm)],]) ).

tff(12,plain,
    iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)),
    inference(and_elim,[status(thm)],[8]) ).

tff(13,plain,
    iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)),
    inference(modus_ponens,[status(thm)],[12,11]) ).

tff(14,plain,
    ^ [Z: $i,P: $i,C: $i] :
      refl(
        ( ( ~ iext(uri_owl_onProperty,Z,P)
          | ~ iext(uri_owl_onClass,Z,C)
          | ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
          | ! [X: $i] :
              ~ ( ~ ( ~ icext(Z,X)
                    | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                        | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
                | ~ ( icext(Z,X)
                    | ! [Y: $i] :
                        ( ~ icext(C,Y)
                        | ~ iext(P,X,Y) ) ) ) )
      <=> ( ~ iext(uri_owl_onProperty,Z,P)
          | ~ iext(uri_owl_onClass,Z,C)
          | ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
          | ! [X: $i] :
              ~ ( ~ ( ~ icext(Z,X)
                    | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                        | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
                | ~ ( icext(Z,X)
                    | ! [Y: $i] :
                        ( ~ icext(C,Y)
                        | ~ iext(P,X,Y) ) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(15,plain,
    ( ! [Z: $i,P: $i,C: $i] :
        ( ~ iext(uri_owl_onProperty,Z,P)
        | ~ iext(uri_owl_onClass,Z,C)
        | ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
        | ! [X: $i] :
            ~ ( ~ ( ~ icext(Z,X)
                  | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                      | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
              | ~ ( icext(Z,X)
                  | ! [Y: $i] :
                      ( ~ icext(C,Y)
                      | ~ iext(P,X,Y) ) ) ) )
  <=> ! [Z: $i,P: $i,C: $i] :
        ( ~ iext(uri_owl_onProperty,Z,P)
        | ~ iext(uri_owl_onClass,Z,C)
        | ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
        | ! [X: $i] :
            ~ ( ~ ( ~ icext(Z,X)
                  | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                      | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
              | ~ ( icext(Z,X)
                  | ! [Y: $i] :
                      ( ~ icext(C,Y)
                      | ~ iext(P,X,Y) ) ) ) ) ),
    inference(quant_intro,[status(thm)],[14]) ).

tff(16,plain,
    ^ [Z: $i,P: $i,C: $i] :
      rewrite(
        ( ( ~ iext(uri_owl_onProperty,Z,P)
          | ~ iext(uri_owl_onClass,Z,C)
          | ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
          | ! [X: $i] :
              ~ ( ~ ( ~ icext(Z,X)
                    | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                        | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
                | ~ ( icext(Z,X)
                    | ! [Y: $i] :
                        ( ~ icext(C,Y)
                        | ~ iext(P,X,Y) ) ) ) )
      <=> ( ~ iext(uri_owl_onProperty,Z,P)
          | ~ iext(uri_owl_onClass,Z,C)
          | ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
          | ! [X: $i] :
              ~ ( ~ ( ~ icext(Z,X)
                    | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                        | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
                | ~ ( icext(Z,X)
                    | ! [Y: $i] :
                        ( ~ icext(C,Y)
                        | ~ iext(P,X,Y) ) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(17,plain,
    ( ! [Z: $i,P: $i,C: $i] :
        ( ~ iext(uri_owl_onProperty,Z,P)
        | ~ iext(uri_owl_onClass,Z,C)
        | ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
        | ! [X: $i] :
            ~ ( ~ ( ~ icext(Z,X)
                  | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                      | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
              | ~ ( icext(Z,X)
                  | ! [Y: $i] :
                      ( ~ icext(C,Y)
                      | ~ iext(P,X,Y) ) ) ) )
  <=> ! [Z: $i,P: $i,C: $i] :
        ( ~ iext(uri_owl_onProperty,Z,P)
        | ~ iext(uri_owl_onClass,Z,C)
        | ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
        | ! [X: $i] :
            ~ ( ~ ( ~ icext(Z,X)
                  | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                      | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
              | ~ ( icext(Z,X)
                  | ! [Y: $i] :
                      ( ~ icext(C,Y)
                      | ~ iext(P,X,Y) ) ) ) ) ),
    inference(quant_intro,[status(thm)],[16]) ).

tff(18,plain,
    ( ! [Z: $i,P: $i,C: $i] :
        ( ~ iext(uri_owl_onProperty,Z,P)
        | ~ iext(uri_owl_onClass,Z,C)
        | ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
        | ! [X: $i] :
            ~ ( ~ ( ~ icext(Z,X)
                  | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                      | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
              | ~ ( icext(Z,X)
                  | ! [Y: $i] :
                      ( ~ icext(C,Y)
                      | ~ iext(P,X,Y) ) ) ) )
  <=> ! [Z: $i,P: $i,C: $i] :
        ( ~ iext(uri_owl_onProperty,Z,P)
        | ~ iext(uri_owl_onClass,Z,C)
        | ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
        | ! [X: $i] :
            ~ ( ~ ( ~ icext(Z,X)
                  | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                      | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
              | ~ ( icext(Z,X)
                  | ! [Y: $i] :
                      ( ~ icext(C,Y)
                      | ~ iext(P,X,Y) ) ) ) ) ),
    inference(transitivity,[status(thm)],[17,15]) ).

tff(19,plain,
    ^ [Z: $i,P: $i,C: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              rewrite(
                ( ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
                  & iext(uri_owl_onProperty,Z,P)
                  & iext(uri_owl_onClass,Z,C) )
              <=> ~ ( ~ iext(uri_owl_onProperty,Z,P)
                    | ~ iext(uri_owl_onClass,Z,C)
                    | ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ) )),
              ( ~ ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
                  & iext(uri_owl_onProperty,Z,P)
                  & iext(uri_owl_onClass,Z,C) )
            <=> ~ ~ ( ~ iext(uri_owl_onProperty,Z,P)
                    | ~ iext(uri_owl_onClass,Z,C)
                    | ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ) )),
            rewrite(
              ( ~ ~ ( ~ iext(uri_owl_onProperty,Z,P)
                    | ~ iext(uri_owl_onClass,Z,C)
                    | ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) )
            <=> ( ~ iext(uri_owl_onProperty,Z,P)
                | ~ iext(uri_owl_onClass,Z,C)
                | ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ) )),
            ( ~ ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
                & iext(uri_owl_onProperty,Z,P)
                & iext(uri_owl_onClass,Z,C) )
          <=> ( ~ iext(uri_owl_onProperty,Z,P)
              | ~ iext(uri_owl_onClass,Z,C)
              | ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ) )),
          quant_intro(
            proof_bind(
              ^ [X: $i] :
                trans(
                  monotonicity(
                    rewrite(
                      ( ( ~ icext(Z,X)
                        | ( iext(P,X,tptp_fun_Y_42(X,C,P))
                          & icext(C,tptp_fun_Y_42(X,C,P)) ) )
                    <=> ( ~ icext(Z,X)
                        | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                            | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) ) )),
                    rewrite(
                      ( ( icext(Z,X)
                        | ! [Y: $i] :
                            ~ ( iext(P,X,Y)
                              & icext(C,Y) ) )
                    <=> ( icext(Z,X)
                        | ! [Y: $i] :
                            ( ~ icext(C,Y)
                            | ~ iext(P,X,Y) ) ) )),
                    ( ( ( ~ icext(Z,X)
                        | ( iext(P,X,tptp_fun_Y_42(X,C,P))
                          & icext(C,tptp_fun_Y_42(X,C,P)) ) )
                      & ( icext(Z,X)
                        | ! [Y: $i] :
                            ~ ( iext(P,X,Y)
                              & icext(C,Y) ) ) )
                  <=> ( ( ~ icext(Z,X)
                        | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                            | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
                      & ( icext(Z,X)
                        | ! [Y: $i] :
                            ( ~ icext(C,Y)
                            | ~ iext(P,X,Y) ) ) ) )),
                  rewrite(
                    ( ( ( ~ icext(Z,X)
                        | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                            | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
                      & ( icext(Z,X)
                        | ! [Y: $i] :
                            ( ~ icext(C,Y)
                            | ~ iext(P,X,Y) ) ) )
                  <=> ~ ( ~ ( ~ icext(Z,X)
                            | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                                | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
                        | ~ ( icext(Z,X)
                            | ! [Y: $i] :
                                ( ~ icext(C,Y)
                                | ~ iext(P,X,Y) ) ) ) )),
                  ( ( ( ~ icext(Z,X)
                      | ( iext(P,X,tptp_fun_Y_42(X,C,P))
                        & icext(C,tptp_fun_Y_42(X,C,P)) ) )
                    & ( icext(Z,X)
                      | ! [Y: $i] :
                          ~ ( iext(P,X,Y)
                            & icext(C,Y) ) ) )
                <=> ~ ( ~ ( ~ icext(Z,X)
                          | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                              | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
                      | ~ ( icext(Z,X)
                          | ! [Y: $i] :
                              ( ~ icext(C,Y)
                              | ~ iext(P,X,Y) ) ) ) ))),
            ( ! [X: $i] :
                ( ( ~ icext(Z,X)
                  | ( iext(P,X,tptp_fun_Y_42(X,C,P))
                    & icext(C,tptp_fun_Y_42(X,C,P)) ) )
                & ( icext(Z,X)
                  | ! [Y: $i] :
                      ~ ( iext(P,X,Y)
                        & icext(C,Y) ) ) )
          <=> ! [X: $i] :
                ~ ( ~ ( ~ icext(Z,X)
                      | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                          | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
                  | ~ ( icext(Z,X)
                      | ! [Y: $i] :
                          ( ~ icext(C,Y)
                          | ~ iext(P,X,Y) ) ) ) )),
          ( ( ~ ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
                & iext(uri_owl_onProperty,Z,P)
                & iext(uri_owl_onClass,Z,C) )
            | ! [X: $i] :
                ( ( ~ icext(Z,X)
                  | ( iext(P,X,tptp_fun_Y_42(X,C,P))
                    & icext(C,tptp_fun_Y_42(X,C,P)) ) )
                & ( icext(Z,X)
                  | ! [Y: $i] :
                      ~ ( iext(P,X,Y)
                        & icext(C,Y) ) ) ) )
        <=> ( ~ iext(uri_owl_onProperty,Z,P)
            | ~ iext(uri_owl_onClass,Z,C)
            | ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
            | ! [X: $i] :
                ~ ( ~ ( ~ icext(Z,X)
                      | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                          | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
                  | ~ ( icext(Z,X)
                      | ! [Y: $i] :
                          ( ~ icext(C,Y)
                          | ~ iext(P,X,Y) ) ) ) ) )),
        rewrite(
          ( ( ~ iext(uri_owl_onProperty,Z,P)
            | ~ iext(uri_owl_onClass,Z,C)
            | ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
            | ! [X: $i] :
                ~ ( ~ ( ~ icext(Z,X)
                      | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                          | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
                  | ~ ( icext(Z,X)
                      | ! [Y: $i] :
                          ( ~ icext(C,Y)
                          | ~ iext(P,X,Y) ) ) ) )
        <=> ( ~ iext(uri_owl_onProperty,Z,P)
            | ~ iext(uri_owl_onClass,Z,C)
            | ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
            | ! [X: $i] :
                ~ ( ~ ( ~ icext(Z,X)
                      | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                          | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
                  | ~ ( icext(Z,X)
                      | ! [Y: $i] :
                          ( ~ icext(C,Y)
                          | ~ iext(P,X,Y) ) ) ) ) )),
        ( ( ~ ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
              & iext(uri_owl_onProperty,Z,P)
              & iext(uri_owl_onClass,Z,C) )
          | ! [X: $i] :
              ( ( ~ icext(Z,X)
                | ( iext(P,X,tptp_fun_Y_42(X,C,P))
                  & icext(C,tptp_fun_Y_42(X,C,P)) ) )
              & ( icext(Z,X)
                | ! [Y: $i] :
                    ~ ( iext(P,X,Y)
                      & icext(C,Y) ) ) ) )
      <=> ( ~ iext(uri_owl_onProperty,Z,P)
          | ~ iext(uri_owl_onClass,Z,C)
          | ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
          | ! [X: $i] :
              ~ ( ~ ( ~ icext(Z,X)
                    | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                        | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
                | ~ ( icext(Z,X)
                    | ! [Y: $i] :
                        ( ~ icext(C,Y)
                        | ~ iext(P,X,Y) ) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(20,plain,
    ( ! [Z: $i,P: $i,C: $i] :
        ( ~ ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
            & iext(uri_owl_onProperty,Z,P)
            & iext(uri_owl_onClass,Z,C) )
        | ! [X: $i] :
            ( ( ~ icext(Z,X)
              | ( iext(P,X,tptp_fun_Y_42(X,C,P))
                & icext(C,tptp_fun_Y_42(X,C,P)) ) )
            & ( icext(Z,X)
              | ! [Y: $i] :
                  ~ ( iext(P,X,Y)
                    & icext(C,Y) ) ) ) )
  <=> ! [Z: $i,P: $i,C: $i] :
        ( ~ iext(uri_owl_onProperty,Z,P)
        | ~ iext(uri_owl_onClass,Z,C)
        | ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
        | ! [X: $i] :
            ~ ( ~ ( ~ icext(Z,X)
                  | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                      | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
              | ~ ( icext(Z,X)
                  | ! [Y: $i] :
                      ( ~ icext(C,Y)
                      | ~ iext(P,X,Y) ) ) ) ) ),
    inference(quant_intro,[status(thm)],[19]) ).

tff(21,plain,
    ( ! [Z: $i,P: $i,C: $i] :
        ( ~ ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
            & iext(uri_owl_onProperty,Z,P)
            & iext(uri_owl_onClass,Z,C) )
        | ! [X: $i] :
            ( icext(Z,X)
          <=> ? [Y: $i] :
                ( iext(P,X,Y)
                & icext(C,Y) ) ) )
  <=> ! [Z: $i,P: $i,C: $i] :
        ( ~ ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
            & iext(uri_owl_onProperty,Z,P)
            & iext(uri_owl_onClass,Z,C) )
        | ! [X: $i] :
            ( icext(Z,X)
          <=> ? [Y: $i] :
                ( iext(P,X,Y)
                & icext(C,Y) ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(22,plain,
    ^ [Z: $i,P: $i,C: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
              & iext(uri_owl_onProperty,Z,P)
              & iext(uri_owl_onClass,Z,C) )
          <=> ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
              & iext(uri_owl_onProperty,Z,P)
              & iext(uri_owl_onClass,Z,C) ) )),
          ( ( ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
              & iext(uri_owl_onProperty,Z,P)
              & iext(uri_owl_onClass,Z,C) )
           => ! [X: $i] :
                ( icext(Z,X)
              <=> ? [Y: $i] :
                    ( iext(P,X,Y)
                    & icext(C,Y) ) ) )
        <=> ( ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
              & iext(uri_owl_onProperty,Z,P)
              & iext(uri_owl_onClass,Z,C) )
           => ! [X: $i] :
                ( icext(Z,X)
              <=> ? [Y: $i] :
                    ( iext(P,X,Y)
                    & icext(C,Y) ) ) ) )),
        rewrite(
          ( ( ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
              & iext(uri_owl_onProperty,Z,P)
              & iext(uri_owl_onClass,Z,C) )
           => ! [X: $i] :
                ( icext(Z,X)
              <=> ? [Y: $i] :
                    ( iext(P,X,Y)
                    & icext(C,Y) ) ) )
        <=> ( ~ ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
                & iext(uri_owl_onProperty,Z,P)
                & iext(uri_owl_onClass,Z,C) )
            | ! [X: $i] :
                ( icext(Z,X)
              <=> ? [Y: $i] :
                    ( iext(P,X,Y)
                    & icext(C,Y) ) ) ) )),
        ( ( ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
            & iext(uri_owl_onProperty,Z,P)
            & iext(uri_owl_onClass,Z,C) )
         => ! [X: $i] :
              ( icext(Z,X)
            <=> ? [Y: $i] :
                  ( iext(P,X,Y)
                  & icext(C,Y) ) ) )
      <=> ( ~ ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
              & iext(uri_owl_onProperty,Z,P)
              & iext(uri_owl_onClass,Z,C) )
          | ! [X: $i] :
              ( icext(Z,X)
            <=> ? [Y: $i] :
                  ( iext(P,X,Y)
                  & icext(C,Y) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(23,plain,
    ( ! [Z: $i,P: $i,C: $i] :
        ( ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
          & iext(uri_owl_onProperty,Z,P)
          & iext(uri_owl_onClass,Z,C) )
       => ! [X: $i] :
            ( icext(Z,X)
          <=> ? [Y: $i] :
                ( iext(P,X,Y)
                & icext(C,Y) ) ) )
  <=> ! [Z: $i,P: $i,C: $i] :
        ( ~ ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
            & iext(uri_owl_onProperty,Z,P)
            & iext(uri_owl_onClass,Z,C) )
        | ! [X: $i] :
            ( icext(Z,X)
          <=> ? [Y: $i] :
                ( iext(P,X,Y)
                & icext(C,Y) ) ) ) ),
    inference(quant_intro,[status(thm)],[22]) ).

tff(24,axiom,
    ! [Z: $i,P: $i,C: $i] :
      ( ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
        & iext(uri_owl_onProperty,Z,P)
        & iext(uri_owl_onClass,Z,C) )
     => ! [X: $i] :
          ( icext(Z,X)
        <=> ? [Y: $i] :
              ( iext(P,X,Y)
              & icext(C,Y) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',owl_restrict_minqcr_object_001) ).

tff(25,plain,
    ! [Z: $i,P: $i,C: $i] :
      ( ~ ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
          & iext(uri_owl_onProperty,Z,P)
          & iext(uri_owl_onClass,Z,C) )
      | ! [X: $i] :
          ( icext(Z,X)
        <=> ? [Y: $i] :
              ( iext(P,X,Y)
              & icext(C,Y) ) ) ),
    inference(modus_ponens,[status(thm)],[24,23]) ).

tff(26,plain,
    ! [Z: $i,P: $i,C: $i] :
      ( ~ ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
          & iext(uri_owl_onProperty,Z,P)
          & iext(uri_owl_onClass,Z,C) )
      | ! [X: $i] :
          ( icext(Z,X)
        <=> ? [Y: $i] :
              ( iext(P,X,Y)
              & icext(C,Y) ) ) ),
    inference(modus_ponens,[status(thm)],[25,21]) ).

tff(27,plain,
    ! [Z: $i,P: $i,C: $i] :
      ( ~ ( iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
          & iext(uri_owl_onProperty,Z,P)
          & iext(uri_owl_onClass,Z,C) )
      | ! [X: $i] :
          ( ( ~ icext(Z,X)
            | ( iext(P,X,tptp_fun_Y_42(X,C,P))
              & icext(C,tptp_fun_Y_42(X,C,P)) ) )
          & ( icext(Z,X)
            | ! [Y: $i] :
                ~ ( iext(P,X,Y)
                  & icext(C,Y) ) ) ) ),
    inference(skolemize,[status(sab)],[26]) ).

tff(28,plain,
    ! [Z: $i,P: $i,C: $i] :
      ( ~ iext(uri_owl_onProperty,Z,P)
      | ~ iext(uri_owl_onClass,Z,C)
      | ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
      | ! [X: $i] :
          ~ ( ~ ( ~ icext(Z,X)
                | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                    | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
            | ~ ( icext(Z,X)
                | ! [Y: $i] :
                    ( ~ icext(C,Y)
                    | ~ iext(P,X,Y) ) ) ) ),
    inference(modus_ponens,[status(thm)],[27,20]) ).

tff(29,plain,
    ! [Z: $i,P: $i,C: $i] :
      ( ~ iext(uri_owl_onProperty,Z,P)
      | ~ iext(uri_owl_onClass,Z,C)
      | ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
      | ! [X: $i] :
          ~ ( ~ ( ~ icext(Z,X)
                | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                    | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
            | ~ ( icext(Z,X)
                | ! [Y: $i] :
                    ( ~ icext(C,Y)
                    | ~ iext(P,X,Y) ) ) ) ),
    inference(modus_ponens,[status(thm)],[28,18]) ).

tff(30,plain,
    ( ( ~ ! [Z: $i,P: $i,C: $i] :
            ( ~ iext(uri_owl_onProperty,Z,P)
            | ~ iext(uri_owl_onClass,Z,C)
            | ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
            | ! [X: $i] :
                ~ ( ~ ( ~ icext(Z,X)
                      | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                          | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
                  | ~ ( icext(Z,X)
                      | ! [Y: $i] :
                          ( ~ icext(C,Y)
                          | ~ iext(P,X,Y) ) ) ) )
      | ~ iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
      | ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
      | ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
      | ! [X: $i] :
          ~ ( ~ ( ~ icext(uri_ex_z,X)
                | ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
                    | ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p)) ) )
            | ~ ( icext(uri_ex_z,X)
                | ! [Y: $i] :
                    ( ~ icext(uri_ex_c,Y)
                    | ~ iext(uri_ex_p,X,Y) ) ) ) )
  <=> ( ~ ! [Z: $i,P: $i,C: $i] :
            ( ~ iext(uri_owl_onProperty,Z,P)
            | ~ iext(uri_owl_onClass,Z,C)
            | ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
            | ! [X: $i] :
                ~ ( ~ ( ~ icext(Z,X)
                      | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                          | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
                  | ~ ( icext(Z,X)
                      | ! [Y: $i] :
                          ( ~ icext(C,Y)
                          | ~ iext(P,X,Y) ) ) ) )
      | ~ iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
      | ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
      | ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
      | ! [X: $i] :
          ~ ( ~ ( ~ icext(uri_ex_z,X)
                | ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
                    | ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p)) ) )
            | ~ ( icext(uri_ex_z,X)
                | ! [Y: $i] :
                    ( ~ icext(uri_ex_c,Y)
                    | ~ iext(uri_ex_p,X,Y) ) ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(31,plain,
    ( ( ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
      | ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
      | ~ iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
      | ! [X: $i] :
          ~ ( ~ ( ~ icext(uri_ex_z,X)
                | ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
                    | ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p)) ) )
            | ~ ( icext(uri_ex_z,X)
                | ! [Y: $i] :
                    ( ~ icext(uri_ex_c,Y)
                    | ~ iext(uri_ex_p,X,Y) ) ) ) )
  <=> ( ~ iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
      | ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
      | ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
      | ! [X: $i] :
          ~ ( ~ ( ~ icext(uri_ex_z,X)
                | ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
                    | ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p)) ) )
            | ~ ( icext(uri_ex_z,X)
                | ! [Y: $i] :
                    ( ~ icext(uri_ex_c,Y)
                    | ~ iext(uri_ex_p,X,Y) ) ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(32,plain,
    ( ( ~ ! [Z: $i,P: $i,C: $i] :
            ( ~ iext(uri_owl_onProperty,Z,P)
            | ~ iext(uri_owl_onClass,Z,C)
            | ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
            | ! [X: $i] :
                ~ ( ~ ( ~ icext(Z,X)
                      | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                          | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
                  | ~ ( icext(Z,X)
                      | ! [Y: $i] :
                          ( ~ icext(C,Y)
                          | ~ iext(P,X,Y) ) ) ) )
      | ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
      | ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
      | ~ iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
      | ! [X: $i] :
          ~ ( ~ ( ~ icext(uri_ex_z,X)
                | ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
                    | ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p)) ) )
            | ~ ( icext(uri_ex_z,X)
                | ! [Y: $i] :
                    ( ~ icext(uri_ex_c,Y)
                    | ~ iext(uri_ex_p,X,Y) ) ) ) )
  <=> ( ~ ! [Z: $i,P: $i,C: $i] :
            ( ~ iext(uri_owl_onProperty,Z,P)
            | ~ iext(uri_owl_onClass,Z,C)
            | ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
            | ! [X: $i] :
                ~ ( ~ ( ~ icext(Z,X)
                      | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                          | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
                  | ~ ( icext(Z,X)
                      | ! [Y: $i] :
                          ( ~ icext(C,Y)
                          | ~ iext(P,X,Y) ) ) ) )
      | ~ iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
      | ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
      | ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
      | ! [X: $i] :
          ~ ( ~ ( ~ icext(uri_ex_z,X)
                | ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
                    | ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p)) ) )
            | ~ ( icext(uri_ex_z,X)
                | ! [Y: $i] :
                    ( ~ icext(uri_ex_c,Y)
                    | ~ iext(uri_ex_p,X,Y) ) ) ) ) ),
    inference(monotonicity,[status(thm)],[31]) ).

tff(33,plain,
    ( ( ~ ! [Z: $i,P: $i,C: $i] :
            ( ~ iext(uri_owl_onProperty,Z,P)
            | ~ iext(uri_owl_onClass,Z,C)
            | ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
            | ! [X: $i] :
                ~ ( ~ ( ~ icext(Z,X)
                      | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                          | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
                  | ~ ( icext(Z,X)
                      | ! [Y: $i] :
                          ( ~ icext(C,Y)
                          | ~ iext(P,X,Y) ) ) ) )
      | ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
      | ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
      | ~ iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
      | ! [X: $i] :
          ~ ( ~ ( ~ icext(uri_ex_z,X)
                | ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
                    | ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p)) ) )
            | ~ ( icext(uri_ex_z,X)
                | ! [Y: $i] :
                    ( ~ icext(uri_ex_c,Y)
                    | ~ iext(uri_ex_p,X,Y) ) ) ) )
  <=> ( ~ ! [Z: $i,P: $i,C: $i] :
            ( ~ iext(uri_owl_onProperty,Z,P)
            | ~ iext(uri_owl_onClass,Z,C)
            | ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
            | ! [X: $i] :
                ~ ( ~ ( ~ icext(Z,X)
                      | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                          | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
                  | ~ ( icext(Z,X)
                      | ! [Y: $i] :
                          ( ~ icext(C,Y)
                          | ~ iext(P,X,Y) ) ) ) )
      | ~ iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
      | ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
      | ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
      | ! [X: $i] :
          ~ ( ~ ( ~ icext(uri_ex_z,X)
                | ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
                    | ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p)) ) )
            | ~ ( icext(uri_ex_z,X)
                | ! [Y: $i] :
                    ( ~ icext(uri_ex_c,Y)
                    | ~ iext(uri_ex_p,X,Y) ) ) ) ) ),
    inference(transitivity,[status(thm)],[32,30]) ).

tff(34,plain,
    ( ~ ! [Z: $i,P: $i,C: $i] :
          ( ~ iext(uri_owl_onProperty,Z,P)
          | ~ iext(uri_owl_onClass,Z,C)
          | ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
          | ! [X: $i] :
              ~ ( ~ ( ~ icext(Z,X)
                    | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                        | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
                | ~ ( icext(Z,X)
                    | ! [Y: $i] :
                        ( ~ icext(C,Y)
                        | ~ iext(P,X,Y) ) ) ) )
    | ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
    | ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
    | ~ iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
    | ! [X: $i] :
        ~ ( ~ ( ~ icext(uri_ex_z,X)
              | ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
                  | ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p)) ) )
          | ~ ( icext(uri_ex_z,X)
              | ! [Y: $i] :
                  ( ~ icext(uri_ex_c,Y)
                  | ~ iext(uri_ex_p,X,Y) ) ) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(35,plain,
    ( ~ ! [Z: $i,P: $i,C: $i] :
          ( ~ iext(uri_owl_onProperty,Z,P)
          | ~ iext(uri_owl_onClass,Z,C)
          | ~ iext(uri_owl_minQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
          | ! [X: $i] :
              ~ ( ~ ( ~ icext(Z,X)
                    | ~ ( ~ iext(P,X,tptp_fun_Y_42(X,C,P))
                        | ~ icext(C,tptp_fun_Y_42(X,C,P)) ) )
                | ~ ( icext(Z,X)
                    | ! [Y: $i] :
                        ( ~ icext(C,Y)
                        | ~ iext(P,X,Y) ) ) ) )
    | ~ iext(uri_owl_minQualifiedCardinality,uri_ex_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
    | ~ iext(uri_owl_onProperty,uri_ex_z,uri_ex_p)
    | ~ iext(uri_owl_onClass,uri_ex_z,uri_ex_c)
    | ! [X: $i] :
        ~ ( ~ ( ~ icext(uri_ex_z,X)
              | ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
                  | ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p)) ) )
          | ~ ( icext(uri_ex_z,X)
              | ! [Y: $i] :
                  ( ~ icext(uri_ex_c,Y)
                  | ~ iext(uri_ex_p,X,Y) ) ) ) ),
    inference(modus_ponens,[status(thm)],[34,33]) ).

tff(36,plain,
    ! [X: $i] :
      ~ ( ~ ( ~ icext(uri_ex_z,X)
            | ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
                | ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p)) ) )
        | ~ ( icext(uri_ex_z,X)
            | ! [Y: $i] :
                ( ~ icext(uri_ex_c,Y)
                | ~ iext(uri_ex_p,X,Y) ) ) ),
    inference(unit_resolution,[status(thm)],[35,29,13,10,6]) ).

tff(37,plain,
    ( ~ ! [X: $i] :
          ~ ( ~ ( ~ icext(uri_ex_z,X)
                | ~ ( ~ iext(uri_ex_p,X,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p))
                    | ~ icext(uri_ex_c,tptp_fun_Y_42(X,uri_ex_c,uri_ex_p)) ) )
            | ~ ( icext(uri_ex_z,X)
                | ! [Y: $i] :
                    ( ~ icext(uri_ex_c,Y)
                    | ~ iext(uri_ex_p,X,Y) ) ) )
    | ~ ( ~ ( ~ icext(uri_ex_z,uri_ex_w)
            | ~ ( ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p))
                | ~ icext(uri_ex_c,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p)) ) )
        | ~ ( icext(uri_ex_z,uri_ex_w)
            | ! [Y: $i] :
                ( ~ icext(uri_ex_c,Y)
                | ~ iext(uri_ex_p,uri_ex_w,Y) ) ) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(38,plain,
    ~ ( ~ ( ~ icext(uri_ex_z,uri_ex_w)
          | ~ ( ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p))
              | ~ icext(uri_ex_c,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p)) ) )
      | ~ ( icext(uri_ex_z,uri_ex_w)
          | ! [Y: $i] :
              ( ~ icext(uri_ex_c,Y)
              | ~ iext(uri_ex_p,uri_ex_w,Y) ) ) ),
    inference(unit_resolution,[status(thm)],[37,36]) ).

tff(39,plain,
    ( ~ ( ~ icext(uri_ex_z,uri_ex_w)
        | ~ ( ~ iext(uri_ex_p,uri_ex_w,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p))
            | ~ icext(uri_ex_c,tptp_fun_Y_42(uri_ex_w,uri_ex_c,uri_ex_p)) ) )
    | ~ ( icext(uri_ex_z,uri_ex_w)
        | ! [Y: $i] :
            ( ~ icext(uri_ex_c,Y)
            | ~ iext(uri_ex_p,uri_ex_w,Y) ) )
    | icext(uri_ex_z,uri_ex_w)
    | ! [Y: $i] :
        ( ~ icext(uri_ex_c,Y)
        | ~ iext(uri_ex_p,uri_ex_w,Y) ) ),
    inference(tautology,[status(thm)],]) ).

tff(40,plain,
    ( icext(uri_ex_z,uri_ex_w)
    | ! [Y: $i] :
        ( ~ icext(uri_ex_c,Y)
        | ~ iext(uri_ex_p,uri_ex_w,Y) ) ),
    inference(unit_resolution,[status(thm)],[39,38]) ).

tff(41,plain,
    ^ [X: $i,C: $i] :
      refl(
        ( ( iext(uri_rdf_type,X,C)
        <=> icext(C,X) )
      <=> ( iext(uri_rdf_type,X,C)
        <=> icext(C,X) ) )),
    inference(bind,[status(th)],]) ).

tff(42,plain,
    ( ! [X: $i,C: $i] :
        ( iext(uri_rdf_type,X,C)
      <=> icext(C,X) )
  <=> ! [X: $i,C: $i] :
        ( iext(uri_rdf_type,X,C)
      <=> icext(C,X) ) ),
    inference(quant_intro,[status(thm)],[41]) ).

tff(43,plain,
    ( ! [X: $i,C: $i] :
        ( iext(uri_rdf_type,X,C)
      <=> icext(C,X) )
  <=> ! [X: $i,C: $i] :
        ( iext(uri_rdf_type,X,C)
      <=> icext(C,X) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(44,axiom,
    ! [X: $i,C: $i] :
      ( iext(uri_rdf_type,X,C)
    <=> icext(C,X) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax',rdfs_cext_def) ).

tff(45,plain,
    ! [X: $i,C: $i] :
      ( iext(uri_rdf_type,X,C)
    <=> icext(C,X) ),
    inference(modus_ponens,[status(thm)],[44,43]) ).

tff(46,plain,
    ! [X: $i,C: $i] :
      ( iext(uri_rdf_type,X,C)
    <=> icext(C,X) ),
    inference(skolemize,[status(sab)],[45]) ).

tff(47,plain,
    ! [X: $i,C: $i] :
      ( iext(uri_rdf_type,X,C)
    <=> icext(C,X) ),
    inference(modus_ponens,[status(thm)],[46,42]) ).

tff(48,plain,
    ( ~ ! [X: $i,C: $i] :
          ( iext(uri_rdf_type,X,C)
        <=> icext(C,X) )
    | ( iext(uri_rdf_type,uri_ex_w,uri_ex_z)
    <=> icext(uri_ex_z,uri_ex_w) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(49,plain,
    ( iext(uri_rdf_type,uri_ex_w,uri_ex_z)
  <=> icext(uri_ex_z,uri_ex_w) ),
    inference(unit_resolution,[status(thm)],[48,47]) ).

tff(50,plain,
    ( ~ iext(uri_rdf_type,uri_ex_w,uri_ex_z)
  <=> ~ iext(uri_rdf_type,uri_ex_w,uri_ex_z) ),
    inference(rewrite,[status(thm)],]) ).

tff(51,axiom,
    ~ iext(uri_rdf_type,uri_ex_w,uri_ex_z),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conclusion_rdfbased_sem_restrict_minqcr_inst_subj_one) ).

tff(52,plain,
    ~ iext(uri_rdf_type,uri_ex_w,uri_ex_z),
    inference(modus_ponens,[status(thm)],[51,50]) ).

tff(53,plain,
    ( ~ ( iext(uri_rdf_type,uri_ex_w,uri_ex_z)
      <=> icext(uri_ex_z,uri_ex_w) )
    | iext(uri_rdf_type,uri_ex_w,uri_ex_z)
    | ~ icext(uri_ex_z,uri_ex_w) ),
    inference(tautology,[status(thm)],]) ).

tff(54,plain,
    ( ~ ( iext(uri_rdf_type,uri_ex_w,uri_ex_z)
      <=> icext(uri_ex_z,uri_ex_w) )
    | ~ icext(uri_ex_z,uri_ex_w) ),
    inference(unit_resolution,[status(thm)],[53,52]) ).

tff(55,plain,
    ~ icext(uri_ex_z,uri_ex_w),
    inference(unit_resolution,[status(thm)],[54,49]) ).

tff(56,plain,
    ( ~ ( icext(uri_ex_z,uri_ex_w)
        | ! [Y: $i] :
            ( ~ icext(uri_ex_c,Y)
            | ~ iext(uri_ex_p,uri_ex_w,Y) ) )
    | icext(uri_ex_z,uri_ex_w)
    | ! [Y: $i] :
        ( ~ icext(uri_ex_c,Y)
        | ~ iext(uri_ex_p,uri_ex_w,Y) ) ),
    inference(tautology,[status(thm)],]) ).

tff(57,plain,
    ( ~ ( icext(uri_ex_z,uri_ex_w)
        | ! [Y: $i] :
            ( ~ icext(uri_ex_c,Y)
            | ~ iext(uri_ex_p,uri_ex_w,Y) ) )
    | ! [Y: $i] :
        ( ~ icext(uri_ex_c,Y)
        | ~ iext(uri_ex_p,uri_ex_w,Y) ) ),
    inference(unit_resolution,[status(thm)],[56,55]) ).

tff(58,plain,
    ! [Y: $i] :
      ( ~ icext(uri_ex_c,Y)
      | ~ iext(uri_ex_p,uri_ex_w,Y) ),
    inference(unit_resolution,[status(thm)],[57,40]) ).

tff(59,plain,
    ( ~ ! [X: $i,C: $i] :
          ( iext(uri_rdf_type,X,C)
        <=> icext(C,X) )
    | ( iext(uri_rdf_type,uri_ex_x,uri_ex_c)
    <=> icext(uri_ex_c,uri_ex_x) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(60,plain,
    ( iext(uri_rdf_type,uri_ex_x,uri_ex_c)
  <=> icext(uri_ex_c,uri_ex_x) ),
    inference(unit_resolution,[status(thm)],[59,47]) ).

tff(61,plain,
    ( iext(uri_rdf_type,uri_ex_x,uri_ex_c)
  <=> iext(uri_rdf_type,uri_ex_x,uri_ex_c) ),
    inference(rewrite,[status(thm)],]) ).

tff(62,plain,
    iext(uri_rdf_type,uri_ex_x,uri_ex_c),
    inference(and_elim,[status(thm)],[3]) ).

tff(63,plain,
    iext(uri_rdf_type,uri_ex_x,uri_ex_c),
    inference(modus_ponens,[status(thm)],[62,61]) ).

tff(64,plain,
    ( ~ ( iext(uri_rdf_type,uri_ex_x,uri_ex_c)
      <=> icext(uri_ex_c,uri_ex_x) )
    | ~ iext(uri_rdf_type,uri_ex_x,uri_ex_c)
    | icext(uri_ex_c,uri_ex_x) ),
    inference(tautology,[status(thm)],]) ).

tff(65,plain,
    ( ~ ( iext(uri_rdf_type,uri_ex_x,uri_ex_c)
      <=> icext(uri_ex_c,uri_ex_x) )
    | icext(uri_ex_c,uri_ex_x) ),
    inference(unit_resolution,[status(thm)],[64,63]) ).

tff(66,plain,
    icext(uri_ex_c,uri_ex_x),
    inference(unit_resolution,[status(thm)],[65,60]) ).

tff(67,plain,
    ( iext(uri_ex_p,uri_ex_w,uri_ex_x)
  <=> iext(uri_ex_p,uri_ex_w,uri_ex_x) ),
    inference(rewrite,[status(thm)],]) ).

tff(68,plain,
    iext(uri_ex_p,uri_ex_w,uri_ex_x),
    inference(and_elim,[status(thm)],[2]) ).

tff(69,plain,
    iext(uri_ex_p,uri_ex_w,uri_ex_x),
    inference(modus_ponens,[status(thm)],[68,67]) ).

tff(70,plain,
    ( ( ~ ! [Y: $i] :
            ( ~ icext(uri_ex_c,Y)
            | ~ iext(uri_ex_p,uri_ex_w,Y) )
      | ~ icext(uri_ex_c,uri_ex_x)
      | ~ iext(uri_ex_p,uri_ex_w,uri_ex_x) )
  <=> ( ~ ! [Y: $i] :
            ( ~ icext(uri_ex_c,Y)
            | ~ iext(uri_ex_p,uri_ex_w,Y) )
      | ~ icext(uri_ex_c,uri_ex_x)
      | ~ iext(uri_ex_p,uri_ex_w,uri_ex_x) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(71,plain,
    ( ~ ! [Y: $i] :
          ( ~ icext(uri_ex_c,Y)
          | ~ iext(uri_ex_p,uri_ex_w,Y) )
    | ~ icext(uri_ex_c,uri_ex_x)
    | ~ iext(uri_ex_p,uri_ex_w,uri_ex_x) ),
    inference(quant_inst,[status(thm)],]) ).

tff(72,plain,
    ( ~ ! [Y: $i] :
          ( ~ icext(uri_ex_c,Y)
          | ~ iext(uri_ex_p,uri_ex_w,Y) )
    | ~ icext(uri_ex_c,uri_ex_x)
    | ~ iext(uri_ex_p,uri_ex_w,uri_ex_x) ),
    inference(modus_ponens,[status(thm)],[71,70]) ).

tff(73,plain,
    $false,
    inference(unit_resolution,[status(thm)],[72,69,66,58]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SWB097+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n024.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 20:28:48 EDT 2022
% 0.12/0.33  % 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.
% 0.76/0.75  % SZS status Theorem
% 0.76/0.75  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------