TSTP Solution File: SWB040+1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SWB040+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n026.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 08:32:05 EDT 2022

% Result   : Theorem 0.98s 0.88s
% Output   : Proof 0.98s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   67
% Syntax   : Number of formulae    :  146 (  32 unt;  10 typ;   0 def)
%            Number of atoms       : 1168 (   0 equ)
%            Maximal formula atoms :   20 (   8 avg)
%            Number of connectives : 1998 (1012   ~; 676   |; 144   &)
%                                         ( 140 <=>;  26  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :   46 (  46 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   4   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :   11 (  10 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :  383 ( 348   !;   0   ?; 383   :)

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

tff(tptp_fun_X_61_type,type,
    tptp_fun_X_61: ( $i * $i ) > $i ).

tff(uri_ex_n2_type,type,
    uri_ex_n2: $i ).

tff(uri_ex_n1_type,type,
    uri_ex_n1: $i ).

tff(uri_ex_c2_type,type,
    uri_ex_c2: $i ).

tff(ic_type,type,
    ic: $i > $o ).

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

tff(uri_owl_complementOf_type,type,
    uri_owl_complementOf: $i ).

tff(uri_ex_c1_type,type,
    uri_ex_c1: $i ).

tff(uri_rdfs_subClassOf_type,type,
    uri_rdfs_subClassOf: $i ).

tff(1,plain,
    ( iext(uri_owl_complementOf,uri_ex_n2,uri_ex_c2)
  <=> iext(uri_owl_complementOf,uri_ex_n2,uri_ex_c2) ),
    inference(rewrite,[status(thm)],]) ).

tff(2,axiom,
    ( iext(uri_owl_complementOf,uri_ex_n2,uri_ex_c2)
    & iext(uri_owl_complementOf,uri_ex_n1,uri_ex_c1)
    & iext(uri_rdfs_subClassOf,uri_ex_c1,uri_ex_c2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_rdfbased_sem_bool_tollens) ).

tff(3,plain,
    ( iext(uri_owl_complementOf,uri_ex_n2,uri_ex_c2)
    & iext(uri_owl_complementOf,uri_ex_n1,uri_ex_c1) ),
    inference(and_elim,[status(thm)],[2]) ).

tff(4,plain,
    iext(uri_owl_complementOf,uri_ex_n2,uri_ex_c2),
    inference(and_elim,[status(thm)],[3]) ).

tff(5,plain,
    iext(uri_owl_complementOf,uri_ex_n2,uri_ex_c2),
    inference(modus_ponens,[status(thm)],[4,1]) ).

tff(6,plain,
    ^ [Z: $i,C: $i] :
      refl(
        ( ( ~ iext(uri_owl_complementOf,Z,C)
          | ~ ( ~ ic(C)
              | ~ ic(Z)
              | ~ ! [X: $i] :
                    ( icext(Z,X)
                  <=> ~ icext(C,X) ) ) )
      <=> ( ~ iext(uri_owl_complementOf,Z,C)
          | ~ ( ~ ic(C)
              | ~ ic(Z)
              | ~ ! [X: $i] :
                    ( icext(Z,X)
                  <=> ~ icext(C,X) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(7,plain,
    ( ! [Z: $i,C: $i] :
        ( ~ iext(uri_owl_complementOf,Z,C)
        | ~ ( ~ ic(C)
            | ~ ic(Z)
            | ~ ! [X: $i] :
                  ( icext(Z,X)
                <=> ~ icext(C,X) ) ) )
  <=> ! [Z: $i,C: $i] :
        ( ~ iext(uri_owl_complementOf,Z,C)
        | ~ ( ~ ic(C)
            | ~ ic(Z)
            | ~ ! [X: $i] :
                  ( icext(Z,X)
                <=> ~ icext(C,X) ) ) ) ),
    inference(quant_intro,[status(thm)],[6]) ).

tff(8,plain,
    ^ [Z: $i,C: $i] :
      rewrite(
        ( ( ~ iext(uri_owl_complementOf,Z,C)
          | ~ ( ~ ic(C)
              | ~ ic(Z)
              | ~ ! [X: $i] :
                    ( icext(Z,X)
                  <=> ~ icext(C,X) ) ) )
      <=> ( ~ iext(uri_owl_complementOf,Z,C)
          | ~ ( ~ ic(C)
              | ~ ic(Z)
              | ~ ! [X: $i] :
                    ( icext(Z,X)
                  <=> ~ icext(C,X) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(9,plain,
    ( ! [Z: $i,C: $i] :
        ( ~ iext(uri_owl_complementOf,Z,C)
        | ~ ( ~ ic(C)
            | ~ ic(Z)
            | ~ ! [X: $i] :
                  ( icext(Z,X)
                <=> ~ icext(C,X) ) ) )
  <=> ! [Z: $i,C: $i] :
        ( ~ iext(uri_owl_complementOf,Z,C)
        | ~ ( ~ ic(C)
            | ~ ic(Z)
            | ~ ! [X: $i] :
                  ( icext(Z,X)
                <=> ~ icext(C,X) ) ) ) ),
    inference(quant_intro,[status(thm)],[8]) ).

tff(10,plain,
    ( ! [Z: $i,C: $i] :
        ( ~ iext(uri_owl_complementOf,Z,C)
        | ~ ( ~ ic(C)
            | ~ ic(Z)
            | ~ ! [X: $i] :
                  ( icext(Z,X)
                <=> ~ icext(C,X) ) ) )
  <=> ! [Z: $i,C: $i] :
        ( ~ iext(uri_owl_complementOf,Z,C)
        | ~ ( ~ ic(C)
            | ~ ic(Z)
            | ~ ! [X: $i] :
                  ( icext(Z,X)
                <=> ~ icext(C,X) ) ) ) ),
    inference(transitivity,[status(thm)],[9,7]) ).

tff(11,plain,
    ^ [Z: $i,C: $i] :
      rewrite(
        ( ( ~ iext(uri_owl_complementOf,Z,C)
          | ( ic(Z)
            & ic(C)
            & ! [X: $i] :
                ( icext(Z,X)
              <=> ~ icext(C,X) ) ) )
      <=> ( ~ iext(uri_owl_complementOf,Z,C)
          | ~ ( ~ ic(C)
              | ~ ic(Z)
              | ~ ! [X: $i] :
                    ( icext(Z,X)
                  <=> ~ icext(C,X) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(12,plain,
    ( ! [Z: $i,C: $i] :
        ( ~ iext(uri_owl_complementOf,Z,C)
        | ( ic(Z)
          & ic(C)
          & ! [X: $i] :
              ( icext(Z,X)
            <=> ~ icext(C,X) ) ) )
  <=> ! [Z: $i,C: $i] :
        ( ~ iext(uri_owl_complementOf,Z,C)
        | ~ ( ~ ic(C)
            | ~ ic(Z)
            | ~ ! [X: $i] :
                  ( icext(Z,X)
                <=> ~ icext(C,X) ) ) ) ),
    inference(quant_intro,[status(thm)],[11]) ).

tff(13,plain,
    ( ! [Z: $i,C: $i] :
        ( ~ iext(uri_owl_complementOf,Z,C)
        | ( ic(Z)
          & ic(C)
          & ! [X: $i] :
              ( icext(Z,X)
            <=> ~ icext(C,X) ) ) )
  <=> ! [Z: $i,C: $i] :
        ( ~ iext(uri_owl_complementOf,Z,C)
        | ( ic(Z)
          & ic(C)
          & ! [X: $i] :
              ( icext(Z,X)
            <=> ~ icext(C,X) ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(14,plain,
    ^ [Z: $i,C: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( ic(Z)
              & ic(C)
              & ! [X: $i] :
                  ( icext(Z,X)
                <=> ~ icext(C,X) ) )
          <=> ( ic(Z)
              & ic(C)
              & ! [X: $i] :
                  ( icext(Z,X)
                <=> ~ icext(C,X) ) ) )),
          ( ( iext(uri_owl_complementOf,Z,C)
           => ( ic(Z)
              & ic(C)
              & ! [X: $i] :
                  ( icext(Z,X)
                <=> ~ icext(C,X) ) ) )
        <=> ( iext(uri_owl_complementOf,Z,C)
           => ( ic(Z)
              & ic(C)
              & ! [X: $i] :
                  ( icext(Z,X)
                <=> ~ icext(C,X) ) ) ) )),
        rewrite(
          ( ( iext(uri_owl_complementOf,Z,C)
           => ( ic(Z)
              & ic(C)
              & ! [X: $i] :
                  ( icext(Z,X)
                <=> ~ icext(C,X) ) ) )
        <=> ( ~ iext(uri_owl_complementOf,Z,C)
            | ( ic(Z)
              & ic(C)
              & ! [X: $i] :
                  ( icext(Z,X)
                <=> ~ icext(C,X) ) ) ) )),
        ( ( iext(uri_owl_complementOf,Z,C)
         => ( ic(Z)
            & ic(C)
            & ! [X: $i] :
                ( icext(Z,X)
              <=> ~ icext(C,X) ) ) )
      <=> ( ~ iext(uri_owl_complementOf,Z,C)
          | ( ic(Z)
            & ic(C)
            & ! [X: $i] :
                ( icext(Z,X)
              <=> ~ icext(C,X) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(15,plain,
    ( ! [Z: $i,C: $i] :
        ( iext(uri_owl_complementOf,Z,C)
       => ( ic(Z)
          & ic(C)
          & ! [X: $i] :
              ( icext(Z,X)
            <=> ~ icext(C,X) ) ) )
  <=> ! [Z: $i,C: $i] :
        ( ~ iext(uri_owl_complementOf,Z,C)
        | ( ic(Z)
          & ic(C)
          & ! [X: $i] :
              ( icext(Z,X)
            <=> ~ icext(C,X) ) ) ) ),
    inference(quant_intro,[status(thm)],[14]) ).

tff(16,axiom,
    ! [Z: $i,C: $i] :
      ( iext(uri_owl_complementOf,Z,C)
     => ( ic(Z)
        & ic(C)
        & ! [X: $i] :
            ( icext(Z,X)
          <=> ~ icext(C,X) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',owl_bool_complementof_class) ).

tff(17,plain,
    ! [Z: $i,C: $i] :
      ( ~ iext(uri_owl_complementOf,Z,C)
      | ( ic(Z)
        & ic(C)
        & ! [X: $i] :
            ( icext(Z,X)
          <=> ~ icext(C,X) ) ) ),
    inference(modus_ponens,[status(thm)],[16,15]) ).

tff(18,plain,
    ! [Z: $i,C: $i] :
      ( ~ iext(uri_owl_complementOf,Z,C)
      | ( ic(Z)
        & ic(C)
        & ! [X: $i] :
            ( icext(Z,X)
          <=> ~ icext(C,X) ) ) ),
    inference(modus_ponens,[status(thm)],[17,13]) ).

tff(19,plain,
    ! [Z: $i,C: $i] :
      ( ~ iext(uri_owl_complementOf,Z,C)
      | ( ic(Z)
        & ic(C)
        & ! [X: $i] :
            ( icext(Z,X)
          <=> ~ icext(C,X) ) ) ),
    inference(skolemize,[status(sab)],[18]) ).

tff(20,plain,
    ! [Z: $i,C: $i] :
      ( ~ iext(uri_owl_complementOf,Z,C)
      | ~ ( ~ ic(C)
          | ~ ic(Z)
          | ~ ! [X: $i] :
                ( icext(Z,X)
              <=> ~ icext(C,X) ) ) ),
    inference(modus_ponens,[status(thm)],[19,12]) ).

tff(21,plain,
    ! [Z: $i,C: $i] :
      ( ~ iext(uri_owl_complementOf,Z,C)
      | ~ ( ~ ic(C)
          | ~ ic(Z)
          | ~ ! [X: $i] :
                ( icext(Z,X)
              <=> ~ icext(C,X) ) ) ),
    inference(modus_ponens,[status(thm)],[20,10]) ).

tff(22,plain,
    ( ( ~ ! [Z: $i,C: $i] :
            ( ~ iext(uri_owl_complementOf,Z,C)
            | ~ ( ~ ic(C)
                | ~ ic(Z)
                | ~ ! [X: $i] :
                      ( icext(Z,X)
                    <=> ~ icext(C,X) ) ) )
      | ~ iext(uri_owl_complementOf,uri_ex_n2,uri_ex_c2)
      | ~ ( ~ ic(uri_ex_c2)
          | ~ ic(uri_ex_n2)
          | ~ ! [X: $i] :
                ( icext(uri_ex_n2,X)
              <=> ~ icext(uri_ex_c2,X) ) ) )
  <=> ( ~ ! [Z: $i,C: $i] :
            ( ~ iext(uri_owl_complementOf,Z,C)
            | ~ ( ~ ic(C)
                | ~ ic(Z)
                | ~ ! [X: $i] :
                      ( icext(Z,X)
                    <=> ~ icext(C,X) ) ) )
      | ~ iext(uri_owl_complementOf,uri_ex_n2,uri_ex_c2)
      | ~ ( ~ ic(uri_ex_c2)
          | ~ ic(uri_ex_n2)
          | ~ ! [X: $i] :
                ( icext(uri_ex_n2,X)
              <=> ~ icext(uri_ex_c2,X) ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(23,plain,
    ( ~ ! [Z: $i,C: $i] :
          ( ~ iext(uri_owl_complementOf,Z,C)
          | ~ ( ~ ic(C)
              | ~ ic(Z)
              | ~ ! [X: $i] :
                    ( icext(Z,X)
                  <=> ~ icext(C,X) ) ) )
    | ~ iext(uri_owl_complementOf,uri_ex_n2,uri_ex_c2)
    | ~ ( ~ ic(uri_ex_c2)
        | ~ ic(uri_ex_n2)
        | ~ ! [X: $i] :
              ( icext(uri_ex_n2,X)
            <=> ~ icext(uri_ex_c2,X) ) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(24,plain,
    ( ~ ! [Z: $i,C: $i] :
          ( ~ iext(uri_owl_complementOf,Z,C)
          | ~ ( ~ ic(C)
              | ~ ic(Z)
              | ~ ! [X: $i] :
                    ( icext(Z,X)
                  <=> ~ icext(C,X) ) ) )
    | ~ iext(uri_owl_complementOf,uri_ex_n2,uri_ex_c2)
    | ~ ( ~ ic(uri_ex_c2)
        | ~ ic(uri_ex_n2)
        | ~ ! [X: $i] :
              ( icext(uri_ex_n2,X)
            <=> ~ icext(uri_ex_c2,X) ) ) ),
    inference(modus_ponens,[status(thm)],[23,22]) ).

tff(25,plain,
    ~ ( ~ ic(uri_ex_c2)
      | ~ ic(uri_ex_n2)
      | ~ ! [X: $i] :
            ( icext(uri_ex_n2,X)
          <=> ~ icext(uri_ex_c2,X) ) ),
    inference(unit_resolution,[status(thm)],[24,21,5]) ).

tff(26,plain,
    ( ~ ic(uri_ex_c2)
    | ~ ic(uri_ex_n2)
    | ~ ! [X: $i] :
          ( icext(uri_ex_n2,X)
        <=> ~ icext(uri_ex_c2,X) )
    | ! [X: $i] :
        ( icext(uri_ex_n2,X)
      <=> ~ icext(uri_ex_c2,X) ) ),
    inference(tautology,[status(thm)],]) ).

tff(27,plain,
    ! [X: $i] :
      ( icext(uri_ex_n2,X)
    <=> ~ icext(uri_ex_c2,X) ),
    inference(unit_resolution,[status(thm)],[26,25]) ).

tff(28,plain,
    ( ~ ! [X: $i] :
          ( icext(uri_ex_n2,X)
        <=> ~ icext(uri_ex_c2,X) )
    | ( icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
    <=> ~ icext(uri_ex_c2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(29,plain,
    ( icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
  <=> ~ icext(uri_ex_c2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ),
    inference(unit_resolution,[status(thm)],[28,27]) ).

tff(30,plain,
    ^ [C1: $i,C2: $i] :
      rewrite(
        ( ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
                | ~ ( ~ ic(C2)
                    | ~ ic(C1)
                    | ~ ! [X: $i] :
                          ( ~ icext(C1,X)
                          | icext(C2,X) ) ) )
            | ~ ( iext(uri_rdfs_subClassOf,C1,C2)
                | ~ ic(C2)
                | ~ ic(C1)
                | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
                    | icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
      <=> ~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
                | ~ ic(C2)
                | ~ ic(C1)
                | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
                    | icext(C2,tptp_fun_X_61(C2,C1)) ) )
            | ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
                | ~ ( ~ ic(C2)
                    | ~ ic(C1)
                    | ~ ! [X: $i] :
                          ( ~ icext(C1,X)
                          | icext(C2,X) ) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(31,plain,
    ( ! [C1: $i,C2: $i] :
        ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
              | ~ ( ~ ic(C2)
                  | ~ ic(C1)
                  | ~ ! [X: $i] :
                        ( ~ icext(C1,X)
                        | icext(C2,X) ) ) )
          | ~ ( iext(uri_rdfs_subClassOf,C1,C2)
              | ~ ic(C2)
              | ~ ic(C1)
              | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
                  | icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
  <=> ! [C1: $i,C2: $i] :
        ~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
              | ~ ic(C2)
              | ~ ic(C1)
              | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
                  | icext(C2,tptp_fun_X_61(C2,C1)) ) )
          | ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
              | ~ ( ~ ic(C2)
                  | ~ ic(C1)
                  | ~ ! [X: $i] :
                        ( ~ icext(C1,X)
                        | icext(C2,X) ) ) ) ) ),
    inference(quant_intro,[status(thm)],[30]) ).

tff(32,plain,
    ^ [C1: $i,C2: $i] :
      refl(
        ( ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
                | ~ ( ~ ic(C2)
                    | ~ ic(C1)
                    | ~ ! [X: $i] :
                          ( ~ icext(C1,X)
                          | icext(C2,X) ) ) )
            | ~ ( iext(uri_rdfs_subClassOf,C1,C2)
                | ~ ic(C2)
                | ~ ic(C1)
                | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
                    | icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
      <=> ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
                | ~ ( ~ ic(C2)
                    | ~ ic(C1)
                    | ~ ! [X: $i] :
                          ( ~ icext(C1,X)
                          | icext(C2,X) ) ) )
            | ~ ( iext(uri_rdfs_subClassOf,C1,C2)
                | ~ ic(C2)
                | ~ ic(C1)
                | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
                    | icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(33,plain,
    ( ! [C1: $i,C2: $i] :
        ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
              | ~ ( ~ ic(C2)
                  | ~ ic(C1)
                  | ~ ! [X: $i] :
                        ( ~ icext(C1,X)
                        | icext(C2,X) ) ) )
          | ~ ( iext(uri_rdfs_subClassOf,C1,C2)
              | ~ ic(C2)
              | ~ ic(C1)
              | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
                  | icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
  <=> ! [C1: $i,C2: $i] :
        ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
              | ~ ( ~ ic(C2)
                  | ~ ic(C1)
                  | ~ ! [X: $i] :
                        ( ~ icext(C1,X)
                        | icext(C2,X) ) ) )
          | ~ ( iext(uri_rdfs_subClassOf,C1,C2)
              | ~ ic(C2)
              | ~ ic(C1)
              | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
                  | icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) ),
    inference(quant_intro,[status(thm)],[32]) ).

tff(34,plain,
    ^ [C1: $i,C2: $i] :
      rewrite(
        ( ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
                | ~ ( ~ ic(C2)
                    | ~ ic(C1)
                    | ~ ! [X: $i] :
                          ( ~ icext(C1,X)
                          | icext(C2,X) ) ) )
            | ~ ( iext(uri_rdfs_subClassOf,C1,C2)
                | ~ ic(C2)
                | ~ ic(C1)
                | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
                    | icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
      <=> ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
                | ~ ( ~ ic(C2)
                    | ~ ic(C1)
                    | ~ ! [X: $i] :
                          ( ~ icext(C1,X)
                          | icext(C2,X) ) ) )
            | ~ ( iext(uri_rdfs_subClassOf,C1,C2)
                | ~ ic(C2)
                | ~ ic(C1)
                | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
                    | icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(35,plain,
    ( ! [C1: $i,C2: $i] :
        ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
              | ~ ( ~ ic(C2)
                  | ~ ic(C1)
                  | ~ ! [X: $i] :
                        ( ~ icext(C1,X)
                        | icext(C2,X) ) ) )
          | ~ ( iext(uri_rdfs_subClassOf,C1,C2)
              | ~ ic(C2)
              | ~ ic(C1)
              | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
                  | icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
  <=> ! [C1: $i,C2: $i] :
        ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
              | ~ ( ~ ic(C2)
                  | ~ ic(C1)
                  | ~ ! [X: $i] :
                        ( ~ icext(C1,X)
                        | icext(C2,X) ) ) )
          | ~ ( iext(uri_rdfs_subClassOf,C1,C2)
              | ~ ic(C2)
              | ~ ic(C1)
              | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
                  | icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) ),
    inference(quant_intro,[status(thm)],[34]) ).

tff(36,plain,
    ( ! [C1: $i,C2: $i] :
        ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
              | ~ ( ~ ic(C2)
                  | ~ ic(C1)
                  | ~ ! [X: $i] :
                        ( ~ icext(C1,X)
                        | icext(C2,X) ) ) )
          | ~ ( iext(uri_rdfs_subClassOf,C1,C2)
              | ~ ic(C2)
              | ~ ic(C1)
              | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
                  | icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
  <=> ! [C1: $i,C2: $i] :
        ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
              | ~ ( ~ ic(C2)
                  | ~ ic(C1)
                  | ~ ! [X: $i] :
                        ( ~ icext(C1,X)
                        | icext(C2,X) ) ) )
          | ~ ( iext(uri_rdfs_subClassOf,C1,C2)
              | ~ ic(C2)
              | ~ ic(C1)
              | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
                  | icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) ),
    inference(transitivity,[status(thm)],[35,33]) ).

tff(37,plain,
    ^ [C1: $i,C2: $i] :
      trans(
        monotonicity(
          rewrite(
            ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
              | ( ic(C1)
                & ic(C2)
                & ! [X: $i] :
                    ( ~ icext(C1,X)
                    | icext(C2,X) ) ) )
          <=> ( ~ iext(uri_rdfs_subClassOf,C1,C2)
              | ~ ( ~ ic(C2)
                  | ~ ic(C1)
                  | ~ ! [X: $i] :
                        ( ~ icext(C1,X)
                        | icext(C2,X) ) ) ) )),
          rewrite(
            ( ( iext(uri_rdfs_subClassOf,C1,C2)
              | ~ ic(C2)
              | ~ ic(C1)
              | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
                  | icext(C2,tptp_fun_X_61(C2,C1)) ) )
          <=> ( iext(uri_rdfs_subClassOf,C1,C2)
              | ~ ic(C2)
              | ~ ic(C1)
              | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
                  | icext(C2,tptp_fun_X_61(C2,C1)) ) ) )),
          ( ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
              | ( ic(C1)
                & ic(C2)
                & ! [X: $i] :
                    ( ~ icext(C1,X)
                    | icext(C2,X) ) ) )
            & ( iext(uri_rdfs_subClassOf,C1,C2)
              | ~ ic(C2)
              | ~ ic(C1)
              | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
                  | icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
        <=> ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
              | ~ ( ~ ic(C2)
                  | ~ ic(C1)
                  | ~ ! [X: $i] :
                        ( ~ icext(C1,X)
                        | icext(C2,X) ) ) )
            & ( iext(uri_rdfs_subClassOf,C1,C2)
              | ~ ic(C2)
              | ~ ic(C1)
              | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
                  | icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) )),
        rewrite(
          ( ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
              | ~ ( ~ ic(C2)
                  | ~ ic(C1)
                  | ~ ! [X: $i] :
                        ( ~ icext(C1,X)
                        | icext(C2,X) ) ) )
            & ( iext(uri_rdfs_subClassOf,C1,C2)
              | ~ ic(C2)
              | ~ ic(C1)
              | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
                  | icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
        <=> ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
                  | ~ ( ~ ic(C2)
                      | ~ ic(C1)
                      | ~ ! [X: $i] :
                            ( ~ icext(C1,X)
                            | icext(C2,X) ) ) )
              | ~ ( iext(uri_rdfs_subClassOf,C1,C2)
                  | ~ ic(C2)
                  | ~ ic(C1)
                  | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
                      | icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) )),
        ( ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
            | ( ic(C1)
              & ic(C2)
              & ! [X: $i] :
                  ( ~ icext(C1,X)
                  | icext(C2,X) ) ) )
          & ( iext(uri_rdfs_subClassOf,C1,C2)
            | ~ ic(C2)
            | ~ ic(C1)
            | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
                | icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
      <=> ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
                | ~ ( ~ ic(C2)
                    | ~ ic(C1)
                    | ~ ! [X: $i] :
                          ( ~ icext(C1,X)
                          | icext(C2,X) ) ) )
            | ~ ( iext(uri_rdfs_subClassOf,C1,C2)
                | ~ ic(C2)
                | ~ ic(C1)
                | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
                    | icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(38,plain,
    ( ! [C1: $i,C2: $i] :
        ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
          | ( ic(C1)
            & ic(C2)
            & ! [X: $i] :
                ( ~ icext(C1,X)
                | icext(C2,X) ) ) )
        & ( iext(uri_rdfs_subClassOf,C1,C2)
          | ~ ic(C2)
          | ~ ic(C1)
          | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
              | icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
  <=> ! [C1: $i,C2: $i] :
        ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
              | ~ ( ~ ic(C2)
                  | ~ ic(C1)
                  | ~ ! [X: $i] :
                        ( ~ icext(C1,X)
                        | icext(C2,X) ) ) )
          | ~ ( iext(uri_rdfs_subClassOf,C1,C2)
              | ~ ic(C2)
              | ~ ic(C1)
              | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
                  | icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) ),
    inference(quant_intro,[status(thm)],[37]) ).

tff(39,plain,
    ^ [C1: $i,C2: $i] :
      rewrite(
        ( ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
            | ( ic(C1)
              & ic(C2)
              & ! [X: $i] :
                  ( ~ icext(C1,X)
                  | icext(C2,X) ) ) )
          & ( iext(uri_rdfs_subClassOf,C1,C2)
            | ~ ic(C1)
            | ~ ic(C2)
            | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
                | icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
      <=> ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
            | ( ic(C1)
              & ic(C2)
              & ! [X: $i] :
                  ( ~ icext(C1,X)
                  | icext(C2,X) ) ) )
          & ( iext(uri_rdfs_subClassOf,C1,C2)
            | ~ ic(C2)
            | ~ ic(C1)
            | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
                | icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(40,plain,
    ( ! [C1: $i,C2: $i] :
        ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
          | ( ic(C1)
            & ic(C2)
            & ! [X: $i] :
                ( ~ icext(C1,X)
                | icext(C2,X) ) ) )
        & ( iext(uri_rdfs_subClassOf,C1,C2)
          | ~ ic(C1)
          | ~ ic(C2)
          | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
              | icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
  <=> ! [C1: $i,C2: $i] :
        ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
          | ( ic(C1)
            & ic(C2)
            & ! [X: $i] :
                ( ~ icext(C1,X)
                | icext(C2,X) ) ) )
        & ( iext(uri_rdfs_subClassOf,C1,C2)
          | ~ ic(C2)
          | ~ ic(C1)
          | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
              | icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) ),
    inference(quant_intro,[status(thm)],[39]) ).

tff(41,plain,
    ( ! [C1: $i,C2: $i] :
        ( iext(uri_rdfs_subClassOf,C1,C2)
      <=> ( ic(C1)
          & ic(C2)
          & ! [X: $i] :
              ( ~ icext(C1,X)
              | icext(C2,X) ) ) )
  <=> ! [C1: $i,C2: $i] :
        ( iext(uri_rdfs_subClassOf,C1,C2)
      <=> ( ic(C1)
          & ic(C2)
          & ! [X: $i] :
              ( ~ icext(C1,X)
              | icext(C2,X) ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(42,plain,
    ^ [C1: $i,C2: $i] :
      rewrite(
        ( ( iext(uri_rdfs_subClassOf,C1,C2)
        <=> ( ic(C1)
            & ic(C2)
            & ! [X: $i] :
                ( icext(C1,X)
               => icext(C2,X) ) ) )
      <=> ( iext(uri_rdfs_subClassOf,C1,C2)
        <=> ( ic(C1)
            & ic(C2)
            & ! [X: $i] :
                ( ~ icext(C1,X)
                | icext(C2,X) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(43,plain,
    ( ! [C1: $i,C2: $i] :
        ( iext(uri_rdfs_subClassOf,C1,C2)
      <=> ( ic(C1)
          & ic(C2)
          & ! [X: $i] :
              ( icext(C1,X)
             => icext(C2,X) ) ) )
  <=> ! [C1: $i,C2: $i] :
        ( iext(uri_rdfs_subClassOf,C1,C2)
      <=> ( ic(C1)
          & ic(C2)
          & ! [X: $i] :
              ( ~ icext(C1,X)
              | icext(C2,X) ) ) ) ),
    inference(quant_intro,[status(thm)],[42]) ).

tff(44,axiom,
    ! [C1: $i,C2: $i] :
      ( iext(uri_rdfs_subClassOf,C1,C2)
    <=> ( ic(C1)
        & ic(C2)
        & ! [X: $i] :
            ( icext(C1,X)
           => icext(C2,X) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',owl_rdfsext_subclassof) ).

tff(45,plain,
    ! [C1: $i,C2: $i] :
      ( iext(uri_rdfs_subClassOf,C1,C2)
    <=> ( ic(C1)
        & ic(C2)
        & ! [X: $i] :
            ( ~ icext(C1,X)
            | icext(C2,X) ) ) ),
    inference(modus_ponens,[status(thm)],[44,43]) ).

tff(46,plain,
    ! [C1: $i,C2: $i] :
      ( iext(uri_rdfs_subClassOf,C1,C2)
    <=> ( ic(C1)
        & ic(C2)
        & ! [X: $i] :
            ( ~ icext(C1,X)
            | icext(C2,X) ) ) ),
    inference(modus_ponens,[status(thm)],[45,41]) ).

tff(47,plain,
    ! [C1: $i,C2: $i] :
      ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
        | ( ic(C1)
          & ic(C2)
          & ! [X: $i] :
              ( ~ icext(C1,X)
              | icext(C2,X) ) ) )
      & ( iext(uri_rdfs_subClassOf,C1,C2)
        | ~ ic(C1)
        | ~ ic(C2)
        | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
            | icext(C2,tptp_fun_X_61(C2,C1)) ) ) ),
    inference(skolemize,[status(sab)],[46]) ).

tff(48,plain,
    ! [C1: $i,C2: $i] :
      ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
        | ( ic(C1)
          & ic(C2)
          & ! [X: $i] :
              ( ~ icext(C1,X)
              | icext(C2,X) ) ) )
      & ( iext(uri_rdfs_subClassOf,C1,C2)
        | ~ ic(C2)
        | ~ ic(C1)
        | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
            | icext(C2,tptp_fun_X_61(C2,C1)) ) ) ),
    inference(modus_ponens,[status(thm)],[47,40]) ).

tff(49,plain,
    ! [C1: $i,C2: $i] :
      ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
            | ~ ( ~ ic(C2)
                | ~ ic(C1)
                | ~ ! [X: $i] :
                      ( ~ icext(C1,X)
                      | icext(C2,X) ) ) )
        | ~ ( iext(uri_rdfs_subClassOf,C1,C2)
            | ~ ic(C2)
            | ~ ic(C1)
            | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
                | icext(C2,tptp_fun_X_61(C2,C1)) ) ) ),
    inference(modus_ponens,[status(thm)],[48,38]) ).

tff(50,plain,
    ! [C1: $i,C2: $i] :
      ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
            | ~ ( ~ ic(C2)
                | ~ ic(C1)
                | ~ ! [X: $i] :
                      ( ~ icext(C1,X)
                      | icext(C2,X) ) ) )
        | ~ ( iext(uri_rdfs_subClassOf,C1,C2)
            | ~ ic(C2)
            | ~ ic(C1)
            | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
                | icext(C2,tptp_fun_X_61(C2,C1)) ) ) ),
    inference(modus_ponens,[status(thm)],[49,36]) ).

tff(51,plain,
    ! [C1: $i,C2: $i] :
      ~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
            | ~ ic(C2)
            | ~ ic(C1)
            | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
                | icext(C2,tptp_fun_X_61(C2,C1)) ) )
        | ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
            | ~ ( ~ ic(C2)
                | ~ ic(C1)
                | ~ ! [X: $i] :
                      ( ~ icext(C1,X)
                      | icext(C2,X) ) ) ) ),
    inference(modus_ponens,[status(thm)],[50,31]) ).

tff(52,plain,
    ( ~ ! [C1: $i,C2: $i] :
          ~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
                | ~ ic(C2)
                | ~ ic(C1)
                | ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
                    | icext(C2,tptp_fun_X_61(C2,C1)) ) )
            | ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
                | ~ ( ~ ic(C2)
                    | ~ ic(C1)
                    | ~ ! [X: $i] :
                          ( ~ icext(C1,X)
                          | icext(C2,X) ) ) ) )
    | ~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
            | ~ ic(uri_ex_n1)
            | ~ ic(uri_ex_n2)
            | ~ ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
                | icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) )
        | ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
            | ~ ( ~ ic(uri_ex_n1)
                | ~ ic(uri_ex_n2)
                | ~ ! [X: $i] :
                      ( ~ icext(uri_ex_n2,X)
                      | icext(uri_ex_n1,X) ) ) ) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(53,plain,
    ~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
          | ~ ic(uri_ex_n1)
          | ~ ic(uri_ex_n2)
          | ~ ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
              | icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) )
      | ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
          | ~ ( ~ ic(uri_ex_n1)
              | ~ ic(uri_ex_n2)
              | ~ ! [X: $i] :
                    ( ~ icext(uri_ex_n2,X)
                    | icext(uri_ex_n1,X) ) ) ) ),
    inference(unit_resolution,[status(thm)],[52,51]) ).

tff(54,plain,
    ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
        | ~ ic(uri_ex_n1)
        | ~ ic(uri_ex_n2)
        | ~ ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
            | icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) )
    | ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
        | ~ ( ~ ic(uri_ex_n1)
            | ~ ic(uri_ex_n2)
            | ~ ! [X: $i] :
                  ( ~ icext(uri_ex_n2,X)
                  | icext(uri_ex_n1,X) ) ) )
    | iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
    | ~ ic(uri_ex_n1)
    | ~ ic(uri_ex_n2)
    | ~ ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
        | icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) ),
    inference(tautology,[status(thm)],]) ).

tff(55,plain,
    ( iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
    | ~ ic(uri_ex_n1)
    | ~ ic(uri_ex_n2)
    | ~ ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
        | icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) ),
    inference(unit_resolution,[status(thm)],[54,53]) ).

tff(56,plain,
    ^ [X: $i,Y: $i] :
      refl(
        ( ( ~ iext(uri_owl_complementOf,X,Y)
          | ~ ( ~ ic(Y)
              | ~ ic(X) ) )
      <=> ( ~ iext(uri_owl_complementOf,X,Y)
          | ~ ( ~ ic(Y)
              | ~ ic(X) ) ) )),
    inference(bind,[status(th)],]) ).

tff(57,plain,
    ( ! [X: $i,Y: $i] :
        ( ~ iext(uri_owl_complementOf,X,Y)
        | ~ ( ~ ic(Y)
            | ~ ic(X) ) )
  <=> ! [X: $i,Y: $i] :
        ( ~ iext(uri_owl_complementOf,X,Y)
        | ~ ( ~ ic(Y)
            | ~ ic(X) ) ) ),
    inference(quant_intro,[status(thm)],[56]) ).

tff(58,plain,
    ^ [X: $i,Y: $i] :
      rewrite(
        ( ( ~ iext(uri_owl_complementOf,X,Y)
          | ( ic(X)
            & ic(Y) ) )
      <=> ( ~ iext(uri_owl_complementOf,X,Y)
          | ~ ( ~ ic(Y)
              | ~ ic(X) ) ) )),
    inference(bind,[status(th)],]) ).

tff(59,plain,
    ( ! [X: $i,Y: $i] :
        ( ~ iext(uri_owl_complementOf,X,Y)
        | ( ic(X)
          & ic(Y) ) )
  <=> ! [X: $i,Y: $i] :
        ( ~ iext(uri_owl_complementOf,X,Y)
        | ~ ( ~ ic(Y)
            | ~ ic(X) ) ) ),
    inference(quant_intro,[status(thm)],[58]) ).

tff(60,plain,
    ( ! [X: $i,Y: $i] :
        ( ~ iext(uri_owl_complementOf,X,Y)
        | ( ic(X)
          & ic(Y) ) )
  <=> ! [X: $i,Y: $i] :
        ( ~ iext(uri_owl_complementOf,X,Y)
        | ( ic(X)
          & ic(Y) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(61,plain,
    ^ [X: $i,Y: $i] :
      rewrite(
        ( ( iext(uri_owl_complementOf,X,Y)
         => ( ic(X)
            & ic(Y) ) )
      <=> ( ~ iext(uri_owl_complementOf,X,Y)
          | ( ic(X)
            & ic(Y) ) ) )),
    inference(bind,[status(th)],]) ).

tff(62,plain,
    ( ! [X: $i,Y: $i] :
        ( iext(uri_owl_complementOf,X,Y)
       => ( ic(X)
          & ic(Y) ) )
  <=> ! [X: $i,Y: $i] :
        ( ~ iext(uri_owl_complementOf,X,Y)
        | ( ic(X)
          & ic(Y) ) ) ),
    inference(quant_intro,[status(thm)],[61]) ).

tff(63,axiom,
    ! [X: $i,Y: $i] :
      ( iext(uri_owl_complementOf,X,Y)
     => ( ic(X)
        & ic(Y) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',owl_prop_complementof_ext) ).

tff(64,plain,
    ! [X: $i,Y: $i] :
      ( ~ iext(uri_owl_complementOf,X,Y)
      | ( ic(X)
        & ic(Y) ) ),
    inference(modus_ponens,[status(thm)],[63,62]) ).

tff(65,plain,
    ! [X: $i,Y: $i] :
      ( ~ iext(uri_owl_complementOf,X,Y)
      | ( ic(X)
        & ic(Y) ) ),
    inference(modus_ponens,[status(thm)],[64,60]) ).

tff(66,plain,
    ! [X: $i,Y: $i] :
      ( ~ iext(uri_owl_complementOf,X,Y)
      | ( ic(X)
        & ic(Y) ) ),
    inference(skolemize,[status(sab)],[65]) ).

tff(67,plain,
    ! [X: $i,Y: $i] :
      ( ~ iext(uri_owl_complementOf,X,Y)
      | ~ ( ~ ic(Y)
          | ~ ic(X) ) ),
    inference(modus_ponens,[status(thm)],[66,59]) ).

tff(68,plain,
    ! [X: $i,Y: $i] :
      ( ~ iext(uri_owl_complementOf,X,Y)
      | ~ ( ~ ic(Y)
          | ~ ic(X) ) ),
    inference(modus_ponens,[status(thm)],[67,57]) ).

tff(69,plain,
    ( ( ~ ! [X: $i,Y: $i] :
            ( ~ iext(uri_owl_complementOf,X,Y)
            | ~ ( ~ ic(Y)
                | ~ ic(X) ) )
      | ~ iext(uri_owl_complementOf,uri_ex_n2,uri_ex_c2)
      | ~ ( ~ ic(uri_ex_c2)
          | ~ ic(uri_ex_n2) ) )
  <=> ( ~ ! [X: $i,Y: $i] :
            ( ~ iext(uri_owl_complementOf,X,Y)
            | ~ ( ~ ic(Y)
                | ~ ic(X) ) )
      | ~ iext(uri_owl_complementOf,uri_ex_n2,uri_ex_c2)
      | ~ ( ~ ic(uri_ex_c2)
          | ~ ic(uri_ex_n2) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(70,plain,
    ( ~ ! [X: $i,Y: $i] :
          ( ~ iext(uri_owl_complementOf,X,Y)
          | ~ ( ~ ic(Y)
              | ~ ic(X) ) )
    | ~ iext(uri_owl_complementOf,uri_ex_n2,uri_ex_c2)
    | ~ ( ~ ic(uri_ex_c2)
        | ~ ic(uri_ex_n2) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(71,plain,
    ( ~ ! [X: $i,Y: $i] :
          ( ~ iext(uri_owl_complementOf,X,Y)
          | ~ ( ~ ic(Y)
              | ~ ic(X) ) )
    | ~ iext(uri_owl_complementOf,uri_ex_n2,uri_ex_c2)
    | ~ ( ~ ic(uri_ex_c2)
        | ~ ic(uri_ex_n2) ) ),
    inference(modus_ponens,[status(thm)],[70,69]) ).

tff(72,plain,
    ~ ( ~ ic(uri_ex_c2)
      | ~ ic(uri_ex_n2) ),
    inference(unit_resolution,[status(thm)],[71,68,5]) ).

tff(73,plain,
    ( ~ ic(uri_ex_c2)
    | ~ ic(uri_ex_n2)
    | ic(uri_ex_n2) ),
    inference(tautology,[status(thm)],]) ).

tff(74,plain,
    ic(uri_ex_n2),
    inference(unit_resolution,[status(thm)],[73,72]) ).

tff(75,plain,
    ( iext(uri_owl_complementOf,uri_ex_n1,uri_ex_c1)
  <=> iext(uri_owl_complementOf,uri_ex_n1,uri_ex_c1) ),
    inference(rewrite,[status(thm)],]) ).

tff(76,plain,
    iext(uri_owl_complementOf,uri_ex_n1,uri_ex_c1),
    inference(and_elim,[status(thm)],[3]) ).

tff(77,plain,
    iext(uri_owl_complementOf,uri_ex_n1,uri_ex_c1),
    inference(modus_ponens,[status(thm)],[76,75]) ).

tff(78,plain,
    ( ( ~ ! [X: $i,Y: $i] :
            ( ~ iext(uri_owl_complementOf,X,Y)
            | ~ ( ~ ic(Y)
                | ~ ic(X) ) )
      | ~ iext(uri_owl_complementOf,uri_ex_n1,uri_ex_c1)
      | ~ ( ~ ic(uri_ex_c1)
          | ~ ic(uri_ex_n1) ) )
  <=> ( ~ ! [X: $i,Y: $i] :
            ( ~ iext(uri_owl_complementOf,X,Y)
            | ~ ( ~ ic(Y)
                | ~ ic(X) ) )
      | ~ iext(uri_owl_complementOf,uri_ex_n1,uri_ex_c1)
      | ~ ( ~ ic(uri_ex_c1)
          | ~ ic(uri_ex_n1) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(79,plain,
    ( ~ ! [X: $i,Y: $i] :
          ( ~ iext(uri_owl_complementOf,X,Y)
          | ~ ( ~ ic(Y)
              | ~ ic(X) ) )
    | ~ iext(uri_owl_complementOf,uri_ex_n1,uri_ex_c1)
    | ~ ( ~ ic(uri_ex_c1)
        | ~ ic(uri_ex_n1) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(80,plain,
    ( ~ ! [X: $i,Y: $i] :
          ( ~ iext(uri_owl_complementOf,X,Y)
          | ~ ( ~ ic(Y)
              | ~ ic(X) ) )
    | ~ iext(uri_owl_complementOf,uri_ex_n1,uri_ex_c1)
    | ~ ( ~ ic(uri_ex_c1)
        | ~ ic(uri_ex_n1) ) ),
    inference(modus_ponens,[status(thm)],[79,78]) ).

tff(81,plain,
    ~ ( ~ ic(uri_ex_c1)
      | ~ ic(uri_ex_n1) ),
    inference(unit_resolution,[status(thm)],[80,68,77]) ).

tff(82,plain,
    ( ~ ic(uri_ex_c1)
    | ~ ic(uri_ex_n1)
    | ic(uri_ex_n1) ),
    inference(tautology,[status(thm)],]) ).

tff(83,plain,
    ic(uri_ex_n1),
    inference(unit_resolution,[status(thm)],[82,81]) ).

tff(84,plain,
    ( ~ iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
  <=> ~ iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1) ),
    inference(rewrite,[status(thm)],]) ).

tff(85,axiom,
    ~ iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conclusion_rdfbased_sem_bool_tollens) ).

tff(86,plain,
    ~ iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1),
    inference(modus_ponens,[status(thm)],[85,84]) ).

tff(87,plain,
    ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
        | ~ ic(uri_ex_n1)
        | ~ ic(uri_ex_n2)
        | ~ ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
            | icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) )
    | iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
    | ~ ic(uri_ex_n1)
    | ~ ic(uri_ex_n2)
    | ~ ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
        | icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) ),
    inference(tautology,[status(thm)],]) ).

tff(88,plain,
    ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_n2,uri_ex_n1)
        | ~ ic(uri_ex_n1)
        | ~ ic(uri_ex_n2)
        | ~ ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
            | icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) )
    | ~ ic(uri_ex_n1)
    | ~ ic(uri_ex_n2)
    | ~ ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
        | icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) ),
    inference(unit_resolution,[status(thm)],[87,86]) ).

tff(89,plain,
    ~ ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
      | icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ),
    inference(unit_resolution,[status(thm)],[88,83,74,55]) ).

tff(90,plain,
    ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
    | icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
    | icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ),
    inference(tautology,[status(thm)],]) ).

tff(91,plain,
    icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)),
    inference(unit_resolution,[status(thm)],[90,89]) ).

tff(92,plain,
    ( ~ ( icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
      <=> ~ icext(uri_ex_c2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) )
    | ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
    | ~ icext(uri_ex_c2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ),
    inference(tautology,[status(thm)],]) ).

tff(93,plain,
    ( ~ ( icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
      <=> ~ icext(uri_ex_c2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) )
    | ~ icext(uri_ex_c2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ),
    inference(unit_resolution,[status(thm)],[92,91]) ).

tff(94,plain,
    ~ icext(uri_ex_c2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)),
    inference(unit_resolution,[status(thm)],[93,29]) ).

tff(95,plain,
    ( ( ~ ! [Z: $i,C: $i] :
            ( ~ iext(uri_owl_complementOf,Z,C)
            | ~ ( ~ ic(C)
                | ~ ic(Z)
                | ~ ! [X: $i] :
                      ( icext(Z,X)
                    <=> ~ icext(C,X) ) ) )
      | ~ iext(uri_owl_complementOf,uri_ex_n1,uri_ex_c1)
      | ~ ( ~ ic(uri_ex_c1)
          | ~ ic(uri_ex_n1)
          | ~ ! [X: $i] :
                ( icext(uri_ex_n1,X)
              <=> ~ icext(uri_ex_c1,X) ) ) )
  <=> ( ~ ! [Z: $i,C: $i] :
            ( ~ iext(uri_owl_complementOf,Z,C)
            | ~ ( ~ ic(C)
                | ~ ic(Z)
                | ~ ! [X: $i] :
                      ( icext(Z,X)
                    <=> ~ icext(C,X) ) ) )
      | ~ iext(uri_owl_complementOf,uri_ex_n1,uri_ex_c1)
      | ~ ( ~ ic(uri_ex_c1)
          | ~ ic(uri_ex_n1)
          | ~ ! [X: $i] :
                ( icext(uri_ex_n1,X)
              <=> ~ icext(uri_ex_c1,X) ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(96,plain,
    ( ~ ! [Z: $i,C: $i] :
          ( ~ iext(uri_owl_complementOf,Z,C)
          | ~ ( ~ ic(C)
              | ~ ic(Z)
              | ~ ! [X: $i] :
                    ( icext(Z,X)
                  <=> ~ icext(C,X) ) ) )
    | ~ iext(uri_owl_complementOf,uri_ex_n1,uri_ex_c1)
    | ~ ( ~ ic(uri_ex_c1)
        | ~ ic(uri_ex_n1)
        | ~ ! [X: $i] :
              ( icext(uri_ex_n1,X)
            <=> ~ icext(uri_ex_c1,X) ) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(97,plain,
    ( ~ ! [Z: $i,C: $i] :
          ( ~ iext(uri_owl_complementOf,Z,C)
          | ~ ( ~ ic(C)
              | ~ ic(Z)
              | ~ ! [X: $i] :
                    ( icext(Z,X)
                  <=> ~ icext(C,X) ) ) )
    | ~ iext(uri_owl_complementOf,uri_ex_n1,uri_ex_c1)
    | ~ ( ~ ic(uri_ex_c1)
        | ~ ic(uri_ex_n1)
        | ~ ! [X: $i] :
              ( icext(uri_ex_n1,X)
            <=> ~ icext(uri_ex_c1,X) ) ) ),
    inference(modus_ponens,[status(thm)],[96,95]) ).

tff(98,plain,
    ~ ( ~ ic(uri_ex_c1)
      | ~ ic(uri_ex_n1)
      | ~ ! [X: $i] :
            ( icext(uri_ex_n1,X)
          <=> ~ icext(uri_ex_c1,X) ) ),
    inference(unit_resolution,[status(thm)],[97,21,77]) ).

tff(99,plain,
    ( ~ ic(uri_ex_c1)
    | ~ ic(uri_ex_n1)
    | ~ ! [X: $i] :
          ( icext(uri_ex_n1,X)
        <=> ~ icext(uri_ex_c1,X) )
    | ! [X: $i] :
        ( icext(uri_ex_n1,X)
      <=> ~ icext(uri_ex_c1,X) ) ),
    inference(tautology,[status(thm)],]) ).

tff(100,plain,
    ! [X: $i] :
      ( icext(uri_ex_n1,X)
    <=> ~ icext(uri_ex_c1,X) ),
    inference(unit_resolution,[status(thm)],[99,98]) ).

tff(101,plain,
    ( ~ ! [X: $i] :
          ( icext(uri_ex_n1,X)
        <=> ~ icext(uri_ex_c1,X) )
    | ( icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
    <=> ~ icext(uri_ex_c1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(102,plain,
    ( icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
  <=> ~ icext(uri_ex_c1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ),
    inference(unit_resolution,[status(thm)],[101,100]) ).

tff(103,plain,
    ( ~ icext(uri_ex_n2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
    | icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
    | ~ icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ),
    inference(tautology,[status(thm)],]) ).

tff(104,plain,
    ~ icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)),
    inference(unit_resolution,[status(thm)],[103,89]) ).

tff(105,plain,
    ( ~ ( icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
      <=> ~ icext(uri_ex_c1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) )
    | icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
    | icext(uri_ex_c1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ),
    inference(tautology,[status(thm)],]) ).

tff(106,plain,
    ( ~ ( icext(uri_ex_n1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
      <=> ~ icext(uri_ex_c1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) )
    | icext(uri_ex_c1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ),
    inference(unit_resolution,[status(thm)],[105,104]) ).

tff(107,plain,
    icext(uri_ex_c1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)),
    inference(unit_resolution,[status(thm)],[106,102]) ).

tff(108,plain,
    ( iext(uri_rdfs_subClassOf,uri_ex_c1,uri_ex_c2)
  <=> iext(uri_rdfs_subClassOf,uri_ex_c1,uri_ex_c2) ),
    inference(rewrite,[status(thm)],]) ).

tff(109,plain,
    iext(uri_rdfs_subClassOf,uri_ex_c1,uri_ex_c2),
    inference(and_elim,[status(thm)],[2]) ).

tff(110,plain,
    iext(uri_rdfs_subClassOf,uri_ex_c1,uri_ex_c2),
    inference(modus_ponens,[status(thm)],[109,108]) ).

tff(111,plain,
    ^ [C: $i,D: $i] :
      refl(
        ( ( ~ iext(uri_rdfs_subClassOf,C,D)
          | ~ ( ~ ic(D)
              | ~ ic(C)
              | ~ ! [X: $i] :
                    ( ~ icext(C,X)
                    | icext(D,X) ) ) )
      <=> ( ~ iext(uri_rdfs_subClassOf,C,D)
          | ~ ( ~ ic(D)
              | ~ ic(C)
              | ~ ! [X: $i] :
                    ( ~ icext(C,X)
                    | icext(D,X) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(112,plain,
    ( ! [C: $i,D: $i] :
        ( ~ iext(uri_rdfs_subClassOf,C,D)
        | ~ ( ~ ic(D)
            | ~ ic(C)
            | ~ ! [X: $i] :
                  ( ~ icext(C,X)
                  | icext(D,X) ) ) )
  <=> ! [C: $i,D: $i] :
        ( ~ iext(uri_rdfs_subClassOf,C,D)
        | ~ ( ~ ic(D)
            | ~ ic(C)
            | ~ ! [X: $i] :
                  ( ~ icext(C,X)
                  | icext(D,X) ) ) ) ),
    inference(quant_intro,[status(thm)],[111]) ).

tff(113,plain,
    ^ [C: $i,D: $i] :
      rewrite(
        ( ( ~ iext(uri_rdfs_subClassOf,C,D)
          | ~ ( ~ ic(D)
              | ~ ic(C)
              | ~ ! [X: $i] :
                    ( ~ icext(C,X)
                    | icext(D,X) ) ) )
      <=> ( ~ iext(uri_rdfs_subClassOf,C,D)
          | ~ ( ~ ic(D)
              | ~ ic(C)
              | ~ ! [X: $i] :
                    ( ~ icext(C,X)
                    | icext(D,X) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(114,plain,
    ( ! [C: $i,D: $i] :
        ( ~ iext(uri_rdfs_subClassOf,C,D)
        | ~ ( ~ ic(D)
            | ~ ic(C)
            | ~ ! [X: $i] :
                  ( ~ icext(C,X)
                  | icext(D,X) ) ) )
  <=> ! [C: $i,D: $i] :
        ( ~ iext(uri_rdfs_subClassOf,C,D)
        | ~ ( ~ ic(D)
            | ~ ic(C)
            | ~ ! [X: $i] :
                  ( ~ icext(C,X)
                  | icext(D,X) ) ) ) ),
    inference(quant_intro,[status(thm)],[113]) ).

tff(115,plain,
    ( ! [C: $i,D: $i] :
        ( ~ iext(uri_rdfs_subClassOf,C,D)
        | ~ ( ~ ic(D)
            | ~ ic(C)
            | ~ ! [X: $i] :
                  ( ~ icext(C,X)
                  | icext(D,X) ) ) )
  <=> ! [C: $i,D: $i] :
        ( ~ iext(uri_rdfs_subClassOf,C,D)
        | ~ ( ~ ic(D)
            | ~ ic(C)
            | ~ ! [X: $i] :
                  ( ~ icext(C,X)
                  | icext(D,X) ) ) ) ),
    inference(transitivity,[status(thm)],[114,112]) ).

tff(116,plain,
    ^ [C: $i,D: $i] :
      rewrite(
        ( ( ~ iext(uri_rdfs_subClassOf,C,D)
          | ( ic(C)
            & ic(D)
            & ! [X: $i] :
                ( ~ icext(C,X)
                | icext(D,X) ) ) )
      <=> ( ~ iext(uri_rdfs_subClassOf,C,D)
          | ~ ( ~ ic(D)
              | ~ ic(C)
              | ~ ! [X: $i] :
                    ( ~ icext(C,X)
                    | icext(D,X) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(117,plain,
    ( ! [C: $i,D: $i] :
        ( ~ iext(uri_rdfs_subClassOf,C,D)
        | ( ic(C)
          & ic(D)
          & ! [X: $i] :
              ( ~ icext(C,X)
              | icext(D,X) ) ) )
  <=> ! [C: $i,D: $i] :
        ( ~ iext(uri_rdfs_subClassOf,C,D)
        | ~ ( ~ ic(D)
            | ~ ic(C)
            | ~ ! [X: $i] :
                  ( ~ icext(C,X)
                  | icext(D,X) ) ) ) ),
    inference(quant_intro,[status(thm)],[116]) ).

tff(118,plain,
    ( ! [C: $i,D: $i] :
        ( ~ iext(uri_rdfs_subClassOf,C,D)
        | ( ic(C)
          & ic(D)
          & ! [X: $i] :
              ( ~ icext(C,X)
              | icext(D,X) ) ) )
  <=> ! [C: $i,D: $i] :
        ( ~ iext(uri_rdfs_subClassOf,C,D)
        | ( ic(C)
          & ic(D)
          & ! [X: $i] :
              ( ~ icext(C,X)
              | icext(D,X) ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(119,plain,
    ^ [C: $i,D: $i] :
      trans(
        monotonicity(
          trans(
            monotonicity(
              quant_intro(
                proof_bind(
                  ^ [X: $i] :
                    rewrite(
                      ( ( icext(C,X)
                       => icext(D,X) )
                    <=> ( ~ icext(C,X)
                        | icext(D,X) ) ))),
                ( ! [X: $i] :
                    ( icext(C,X)
                   => icext(D,X) )
              <=> ! [X: $i] :
                    ( ~ icext(C,X)
                    | icext(D,X) ) )),
              ( ( ic(C)
                & ic(D)
                & ! [X: $i] :
                    ( icext(C,X)
                   => icext(D,X) ) )
            <=> ( ic(C)
                & ic(D)
                & ! [X: $i] :
                    ( ~ icext(C,X)
                    | icext(D,X) ) ) )),
            rewrite(
              ( ( ic(C)
                & ic(D)
                & ! [X: $i] :
                    ( ~ icext(C,X)
                    | icext(D,X) ) )
            <=> ( ic(C)
                & ic(D)
                & ! [X: $i] :
                    ( ~ icext(C,X)
                    | icext(D,X) ) ) )),
            ( ( ic(C)
              & ic(D)
              & ! [X: $i] :
                  ( icext(C,X)
                 => icext(D,X) ) )
          <=> ( ic(C)
              & ic(D)
              & ! [X: $i] :
                  ( ~ icext(C,X)
                  | icext(D,X) ) ) )),
          ( ( iext(uri_rdfs_subClassOf,C,D)
           => ( ic(C)
              & ic(D)
              & ! [X: $i] :
                  ( icext(C,X)
                 => icext(D,X) ) ) )
        <=> ( iext(uri_rdfs_subClassOf,C,D)
           => ( ic(C)
              & ic(D)
              & ! [X: $i] :
                  ( ~ icext(C,X)
                  | icext(D,X) ) ) ) )),
        rewrite(
          ( ( iext(uri_rdfs_subClassOf,C,D)
           => ( ic(C)
              & ic(D)
              & ! [X: $i] :
                  ( ~ icext(C,X)
                  | icext(D,X) ) ) )
        <=> ( ~ iext(uri_rdfs_subClassOf,C,D)
            | ( ic(C)
              & ic(D)
              & ! [X: $i] :
                  ( ~ icext(C,X)
                  | icext(D,X) ) ) ) )),
        ( ( iext(uri_rdfs_subClassOf,C,D)
         => ( ic(C)
            & ic(D)
            & ! [X: $i] :
                ( icext(C,X)
               => icext(D,X) ) ) )
      <=> ( ~ iext(uri_rdfs_subClassOf,C,D)
          | ( ic(C)
            & ic(D)
            & ! [X: $i] :
                ( ~ icext(C,X)
                | icext(D,X) ) ) ) )),
    inference(bind,[status(th)],]) ).

tff(120,plain,
    ( ! [C: $i,D: $i] :
        ( iext(uri_rdfs_subClassOf,C,D)
       => ( ic(C)
          & ic(D)
          & ! [X: $i] :
              ( icext(C,X)
             => icext(D,X) ) ) )
  <=> ! [C: $i,D: $i] :
        ( ~ iext(uri_rdfs_subClassOf,C,D)
        | ( ic(C)
          & ic(D)
          & ! [X: $i] :
              ( ~ icext(C,X)
              | icext(D,X) ) ) ) ),
    inference(quant_intro,[status(thm)],[119]) ).

tff(121,axiom,
    ! [C: $i,D: $i] :
      ( iext(uri_rdfs_subClassOf,C,D)
     => ( ic(C)
        & ic(D)
        & ! [X: $i] :
            ( icext(C,X)
           => icext(D,X) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',rdfs_subclassof_main) ).

tff(122,plain,
    ! [C: $i,D: $i] :
      ( ~ iext(uri_rdfs_subClassOf,C,D)
      | ( ic(C)
        & ic(D)
        & ! [X: $i] :
            ( ~ icext(C,X)
            | icext(D,X) ) ) ),
    inference(modus_ponens,[status(thm)],[121,120]) ).

tff(123,plain,
    ! [C: $i,D: $i] :
      ( ~ iext(uri_rdfs_subClassOf,C,D)
      | ( ic(C)
        & ic(D)
        & ! [X: $i] :
            ( ~ icext(C,X)
            | icext(D,X) ) ) ),
    inference(modus_ponens,[status(thm)],[122,118]) ).

tff(124,plain,
    ! [C: $i,D: $i] :
      ( ~ iext(uri_rdfs_subClassOf,C,D)
      | ( ic(C)
        & ic(D)
        & ! [X: $i] :
            ( ~ icext(C,X)
            | icext(D,X) ) ) ),
    inference(skolemize,[status(sab)],[123]) ).

tff(125,plain,
    ! [C: $i,D: $i] :
      ( ~ iext(uri_rdfs_subClassOf,C,D)
      | ~ ( ~ ic(D)
          | ~ ic(C)
          | ~ ! [X: $i] :
                ( ~ icext(C,X)
                | icext(D,X) ) ) ),
    inference(modus_ponens,[status(thm)],[124,117]) ).

tff(126,plain,
    ! [C: $i,D: $i] :
      ( ~ iext(uri_rdfs_subClassOf,C,D)
      | ~ ( ~ ic(D)
          | ~ ic(C)
          | ~ ! [X: $i] :
                ( ~ icext(C,X)
                | icext(D,X) ) ) ),
    inference(modus_ponens,[status(thm)],[125,115]) ).

tff(127,plain,
    ( ( ~ ! [C: $i,D: $i] :
            ( ~ iext(uri_rdfs_subClassOf,C,D)
            | ~ ( ~ ic(D)
                | ~ ic(C)
                | ~ ! [X: $i] :
                      ( ~ icext(C,X)
                      | icext(D,X) ) ) )
      | ~ iext(uri_rdfs_subClassOf,uri_ex_c1,uri_ex_c2)
      | ~ ( ~ ic(uri_ex_c2)
          | ~ ic(uri_ex_c1)
          | ~ ! [X: $i] :
                ( ~ icext(uri_ex_c1,X)
                | icext(uri_ex_c2,X) ) ) )
  <=> ( ~ ! [C: $i,D: $i] :
            ( ~ iext(uri_rdfs_subClassOf,C,D)
            | ~ ( ~ ic(D)
                | ~ ic(C)
                | ~ ! [X: $i] :
                      ( ~ icext(C,X)
                      | icext(D,X) ) ) )
      | ~ iext(uri_rdfs_subClassOf,uri_ex_c1,uri_ex_c2)
      | ~ ( ~ ic(uri_ex_c2)
          | ~ ic(uri_ex_c1)
          | ~ ! [X: $i] :
                ( ~ icext(uri_ex_c1,X)
                | icext(uri_ex_c2,X) ) ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(128,plain,
    ( ~ ! [C: $i,D: $i] :
          ( ~ iext(uri_rdfs_subClassOf,C,D)
          | ~ ( ~ ic(D)
              | ~ ic(C)
              | ~ ! [X: $i] :
                    ( ~ icext(C,X)
                    | icext(D,X) ) ) )
    | ~ iext(uri_rdfs_subClassOf,uri_ex_c1,uri_ex_c2)
    | ~ ( ~ ic(uri_ex_c2)
        | ~ ic(uri_ex_c1)
        | ~ ! [X: $i] :
              ( ~ icext(uri_ex_c1,X)
              | icext(uri_ex_c2,X) ) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(129,plain,
    ( ~ ! [C: $i,D: $i] :
          ( ~ iext(uri_rdfs_subClassOf,C,D)
          | ~ ( ~ ic(D)
              | ~ ic(C)
              | ~ ! [X: $i] :
                    ( ~ icext(C,X)
                    | icext(D,X) ) ) )
    | ~ iext(uri_rdfs_subClassOf,uri_ex_c1,uri_ex_c2)
    | ~ ( ~ ic(uri_ex_c2)
        | ~ ic(uri_ex_c1)
        | ~ ! [X: $i] :
              ( ~ icext(uri_ex_c1,X)
              | icext(uri_ex_c2,X) ) ) ),
    inference(modus_ponens,[status(thm)],[128,127]) ).

tff(130,plain,
    ~ ( ~ ic(uri_ex_c2)
      | ~ ic(uri_ex_c1)
      | ~ ! [X: $i] :
            ( ~ icext(uri_ex_c1,X)
            | icext(uri_ex_c2,X) ) ),
    inference(unit_resolution,[status(thm)],[129,126,110]) ).

tff(131,plain,
    ( ~ ic(uri_ex_c2)
    | ~ ic(uri_ex_c1)
    | ~ ! [X: $i] :
          ( ~ icext(uri_ex_c1,X)
          | icext(uri_ex_c2,X) )
    | ! [X: $i] :
        ( ~ icext(uri_ex_c1,X)
        | icext(uri_ex_c2,X) ) ),
    inference(tautology,[status(thm)],]) ).

tff(132,plain,
    ! [X: $i] :
      ( ~ icext(uri_ex_c1,X)
      | icext(uri_ex_c2,X) ),
    inference(unit_resolution,[status(thm)],[131,130]) ).

tff(133,plain,
    ( ( ~ ! [X: $i] :
            ( ~ icext(uri_ex_c1,X)
            | icext(uri_ex_c2,X) )
      | ~ icext(uri_ex_c1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
      | icext(uri_ex_c2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) )
  <=> ( ~ ! [X: $i] :
            ( ~ icext(uri_ex_c1,X)
            | icext(uri_ex_c2,X) )
      | ~ icext(uri_ex_c1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
      | icext(uri_ex_c2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(134,plain,
    ( ~ ! [X: $i] :
          ( ~ icext(uri_ex_c1,X)
          | icext(uri_ex_c2,X) )
    | ~ icext(uri_ex_c1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
    | icext(uri_ex_c2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ),
    inference(quant_inst,[status(thm)],]) ).

tff(135,plain,
    ( ~ ! [X: $i] :
          ( ~ icext(uri_ex_c1,X)
          | icext(uri_ex_c2,X) )
    | ~ icext(uri_ex_c1,tptp_fun_X_61(uri_ex_n1,uri_ex_n2))
    | icext(uri_ex_c2,tptp_fun_X_61(uri_ex_n1,uri_ex_n2)) ),
    inference(modus_ponens,[status(thm)],[134,133]) ).

tff(136,plain,
    $false,
    inference(unit_resolution,[status(thm)],[135,132,107,94]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWB040+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n026.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sat Sep  3 20:16:24 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35  Usage: tptp [options] [-file:]file
% 0.13/0.35    -h, -?       prints this message.
% 0.13/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.35    -m, -model   generate model.
% 0.13/0.35    -p, -proof   generate proof.
% 0.13/0.35    -c, -core    generate unsat core of named formulas.
% 0.13/0.35    -st, -statistics display statistics.
% 0.13/0.35    -t:timeout   set timeout (in second).
% 0.13/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35    -<param>:<value> configuration parameter and value.
% 0.13/0.35    -o:<output-file> file to place output in.
% 0.98/0.88  % SZS status Theorem
% 0.98/0.88  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------