TSTP Solution File: LCL944^8 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : LCL944^8 : TPTP v8.2.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n011.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 May 21 00:08:45 EDT 2024

% Result   : Theorem 65.77s 15.19s
% Output   : Refutation 65.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  120
% Syntax   : Number of formulae    :  190 (  10 unt;  47 typ;   5 def)
%            Number of atoms       : 1627 (   5 equ;   0 cnn)
%            Maximal formula atoms :   36 (  11 avg)
%            Number of connectives : 3806 (   2   ~;   0   |;  31   &;3147   @)
%                                         (   0 <=>; 626  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (  13 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   76 (  76   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   48 (  46 usr;   2 con; 0-3 aty)
%            Number of variables   :  723 ( 165   ^ 556   !;   2   ?; 723   :)

% Comments : 
%------------------------------------------------------------------------------
thf(mworld_type,type,
    mworld: $tType ).

thf(mrel_type,type,
    mrel: mworld > mworld > $o ).

thf(mactual_type,type,
    mactual: mworld ).

thf(mlocal_type,type,
    mlocal: ( mworld > $o ) > $o ).

thf(mlocal_def,definition,
    ( mlocal
    = ( ^ [A: mworld > $o] : ( A @ mactual ) ) ) ).

thf(mand_type,type,
    mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(mand_def,definition,
    ( mand
    = ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
          ( ( A @ C )
          & ( B @ C ) ) ) ) ).

thf(mimplies_type,type,
    mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(mimplies_def,definition,
    ( mimplies
    = ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
          ( ( A @ C )
         => ( B @ C ) ) ) ) ).

thf(mbox_type,type,
    mbox: ( mworld > $o ) > mworld > $o ).

thf(mbox_def,definition,
    ( mbox
    = ( ^ [A: mworld > $o,B: mworld] :
        ! [C: mworld] :
          ( ( mrel @ B @ C )
         => ( A @ C ) ) ) ) ).

thf(eiw_di_type,type,
    eiw_di: $i > mworld > $o ).

thf(mforall_di_type,type,
    mforall_di: ( $i > mworld > $o ) > mworld > $o ).

thf(mforall_di_def,definition,
    ( mforall_di
    = ( ^ [A: $i > mworld > $o,B: mworld] :
        ! [C: $i] :
          ( ( eiw_di @ C @ B )
         => ( A @ C @ B ) ) ) ) ).

thf(r2_type,type,
    r2: mworld > $o ).

thf(r3_type,type,
    r3: mworld > $o ).

thf(r4_type,type,
    r4: mworld > $o ).

thf(r5_type,type,
    r5: mworld > $o ).

thf(equivalence_1_type,type,
    equivalence_1: mworld > $o ).

thf(equivalence_2_type,type,
    equivalence_2: mworld > $o ).

thf(cn2_type,type,
    cn2: mworld > $o ).

thf(cn1_type,type,
    cn1: mworld > $o ).

thf(cn3_type,type,
    cn3: mworld > $o ).

thf(kn2_type,type,
    kn2: mworld > $o ).

thf(kn1_type,type,
    kn1: mworld > $o ).

thf(kn3_type,type,
    kn3: mworld > $o ).

thf(equivalence_3_type,type,
    equivalence_3: mworld > $o ).

thf(op_implies_or_type,type,
    op_implies_or: mworld > $o ).

thf(op_and_type,type,
    op_and: mworld > $o ).

thf(and_2_type,type,
    and_2: mworld > $o ).

thf(and_3_type,type,
    and_3: mworld > $o ).

thf(and_1_type,type,
    and_1: mworld > $o ).

thf(implies_2_type,type,
    implies_2: mworld > $o ).

thf(implies_3_type,type,
    implies_3: mworld > $o ).

thf(op_implies_and_type,type,
    op_implies_and: mworld > $o ).

thf(implies_1_type,type,
    implies_1: mworld > $o ).

thf(substitution_of_equivalents_type,type,
    substitution_of_equivalents: mworld > $o ).

thf(op_or_type,type,
    op_or: mworld > $o ).

thf(modus_tollens_type,type,
    modus_tollens: mworld > $o ).

thf(or_1_type,type,
    or_1: mworld > $o ).

thf(or_2_type,type,
    or_2: mworld > $o ).

thf(or_3_type,type,
    or_3: mworld > $o ).

thf(op_equiv_type,type,
    op_equiv: mworld > $o ).

thf(modus_ponens_type,type,
    modus_ponens: mworld > $o ).

thf(r1_type,type,
    r1: mworld > $o ).

thf(qmltpeq_type,type,
    qmltpeq: $i > $i > mworld > $o ).

thf(is_a_theorem_type,type,
    is_a_theorem: $i > mworld > $o ).

thf(equiv_type,type,
    equiv: $i > $i > $i ).

thf(not_type,type,
    not: $i > $i ).

thf(or_type,type,
    or: $i > $i > $i ).

thf(and_type,type,
    and: $i > $i > $i ).

thf(implies_type,type,
    implies: $i > $i > $i ).

thf(51,axiom,
    mlocal @ ( mbox @ implies_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_2) ).

thf(448,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ( implies_2 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(44,axiom,
    ( mlocal
    @ ( mbox
      @ ( mimplies @ ( mbox @ op_equiv )
        @ ( mbox
          @ ( mforall_di
            @ ^ [A: $i] :
                ( mbox
                @ ( mforall_di
                  @ ^ [B: $i] : ( mbox @ ( qmltpeq @ ( equiv @ A @ B ) @ ( and @ ( implies @ A @ B ) @ ( implies @ B @ A ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_equiv_0) ).

thf(371,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ( ! [B: mworld] :
            ( ( mrel @ A @ B )
           => ( op_equiv @ B ) )
       => ! [B: mworld] :
            ( ( mrel @ A @ B )
           => ! [C: $i] :
                ( ( eiw_di @ C @ B )
               => ! [D: mworld] :
                    ( ( mrel @ B @ D )
                   => ! [E: $i] :
                        ( ( eiw_di @ E @ D )
                       => ! [F: mworld] :
                            ( ( mrel @ D @ F )
                           => ( qmltpeq @ ( equiv @ C @ E ) @ ( and @ ( implies @ C @ E ) @ ( implies @ E @ C ) ) @ F ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(33,axiom,
    ( mlocal
    @ ( mand
      @ ( mbox
        @ ( mimplies @ ( mbox @ r1 )
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( or @ A @ A ) @ A ) ) ) ) ) ) )
      @ ( mbox
        @ ( mimplies
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( or @ A @ A ) @ A ) ) ) ) )
          @ ( mbox @ r1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r1_0) ).

thf(327,plain,
    ( ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( r1 @ B ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ( is_a_theorem @ ( implies @ ( or @ C @ C ) @ C ) @ D ) ) ) ) ) )
    & ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ( is_a_theorem @ ( implies @ ( or @ C @ C ) @ C ) @ D ) ) ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( r1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(49,axiom,
    ( mlocal
    @ ( mand
      @ ( mbox
        @ ( mimplies @ ( mbox @ r5 )
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] :
                        ( mbox
                        @ ( mforall_di
                          @ ^ [C: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ B @ C ) @ ( implies @ ( or @ A @ B ) @ ( or @ A @ C ) ) ) ) ) ) ) ) ) ) ) ) )
      @ ( mbox
        @ ( mimplies
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] :
                        ( mbox
                        @ ( mforall_di
                          @ ^ [C: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ B @ C ) @ ( implies @ ( or @ A @ B ) @ ( or @ A @ C ) ) ) ) ) ) ) ) ) ) )
          @ ( mbox @ r5 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r5_0) ).

thf(410,plain,
    ( ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( r5 @ B ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ! [G: $i] :
                                  ( ( eiw_di @ G @ F )
                                 => ! [H: mworld] :
                                      ( ( mrel @ F @ H )
                                     => ( is_a_theorem @ ( implies @ ( implies @ E @ G ) @ ( implies @ ( or @ C @ E ) @ ( or @ C @ G ) ) ) @ H ) ) ) ) ) ) ) ) ) )
    & ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ! [G: $i] :
                                  ( ( eiw_di @ G @ F )
                                 => ! [H: mworld] :
                                      ( ( mrel @ F @ H )
                                     => ( is_a_theorem @ ( implies @ ( implies @ E @ G ) @ ( implies @ ( or @ C @ E ) @ ( or @ C @ G ) ) ) @ H ) ) ) ) ) ) ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( r5 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(11,axiom,
    ( mlocal
    @ ( mand
      @ ( mbox
        @ ( mimplies @ ( mbox @ kn2 )
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) ) ) ) ) ) ) )
      @ ( mbox
        @ ( mimplies
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) ) ) ) ) )
          @ ( mbox @ kn2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kn2_0) ).

thf(138,plain,
    ( ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( kn2 @ B ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( is_a_theorem @ ( implies @ ( and @ C @ E ) @ C ) @ F ) ) ) ) ) ) ) )
    & ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( is_a_theorem @ ( implies @ ( and @ C @ E ) @ C ) @ F ) ) ) ) ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( kn2 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(54,axiom,
    mlocal @ ( mbox @ op_implies_and ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).

thf(468,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ( op_implies_and @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(41,axiom,
    ( mlocal
    @ ( mand
      @ ( mbox
        @ ( mimplies @ ( mbox @ cn2 )
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ A @ ( implies @ ( not @ A ) @ B ) ) ) ) ) ) ) ) ) )
      @ ( mbox
        @ ( mimplies
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ A @ ( implies @ ( not @ A ) @ B ) ) ) ) ) ) ) )
          @ ( mbox @ cn2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn2_0) ).

thf(352,plain,
    ( ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( cn2 @ B ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( is_a_theorem @ ( implies @ C @ ( implies @ ( not @ C ) @ E ) ) @ F ) ) ) ) ) ) ) )
    & ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( is_a_theorem @ ( implies @ C @ ( implies @ ( not @ C ) @ E ) ) @ F ) ) ) ) ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( cn2 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(9,axiom,
    ( mlocal
    @ ( mbox
      @ ( mforall_di
        @ ^ [A: $i] :
            ( mbox
            @ ( mforall_di
              @ ^ [B: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( and @ A @ C ) @ ( and @ B @ C ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_substitution_1) ).

thf(120,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ! [B: $i] :
          ( ( eiw_di @ B @ A )
         => ! [C: mworld] :
              ( ( mrel @ A @ C )
             => ! [D: $i] :
                  ( ( eiw_di @ D @ C )
                 => ! [E: mworld] :
                      ( ( mrel @ C @ E )
                     => ! [F: $i] :
                          ( ( eiw_di @ F @ E )
                         => ! [G: mworld] :
                              ( ( mrel @ E @ G )
                             => ( ! [H: mworld] :
                                    ( ( mrel @ G @ H )
                                   => ( qmltpeq @ B @ D @ H ) )
                               => ! [H: mworld] :
                                    ( ( mrel @ G @ H )
                                   => ( qmltpeq @ ( and @ B @ F ) @ ( and @ D @ F ) @ H ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(27,axiom,
    ( mlocal
    @ ( mand
      @ ( mbox
        @ ( mimplies @ ( mbox @ or_3 )
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] :
                        ( mbox
                        @ ( mforall_di
                          @ ^ [C: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ A @ C ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ ( or @ A @ B ) @ C ) ) ) ) ) ) ) ) ) ) ) ) )
      @ ( mbox
        @ ( mimplies
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] :
                        ( mbox
                        @ ( mforall_di
                          @ ^ [C: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ A @ C ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ ( or @ A @ B ) @ C ) ) ) ) ) ) ) ) ) ) )
          @ ( mbox @ or_3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_3_0) ).

thf(269,plain,
    ( ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( or_3 @ B ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ! [G: $i] :
                                  ( ( eiw_di @ G @ F )
                                 => ! [H: mworld] :
                                      ( ( mrel @ F @ H )
                                     => ( is_a_theorem @ ( implies @ ( implies @ C @ G ) @ ( implies @ ( implies @ E @ G ) @ ( implies @ ( or @ C @ E ) @ G ) ) ) @ H ) ) ) ) ) ) ) ) ) )
    & ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ! [G: $i] :
                                  ( ( eiw_di @ G @ F )
                                 => ! [H: mworld] :
                                      ( ( mrel @ F @ H )
                                     => ( is_a_theorem @ ( implies @ ( implies @ C @ G ) @ ( implies @ ( implies @ E @ G ) @ ( implies @ ( or @ C @ E ) @ G ) ) ) @ H ) ) ) ) ) ) ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( or_3 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(35,axiom,
    mlocal @ ( mbox @ or_1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_1) ).

thf(340,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ( or_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(12,axiom,
    ! [A: mworld] : ( mrel @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).

thf(153,plain,
    ! [A: mworld] : ( mrel @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(47,axiom,
    ( mlocal
    @ ( mbox
      @ ( mforall_di
        @ ^ [A: $i] :
            ( mbox
            @ ( mforall_di
              @ ^ [B: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( or @ C @ A ) @ ( or @ C @ B ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_substitution_2) ).

thf(404,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ! [B: $i] :
          ( ( eiw_di @ B @ A )
         => ! [C: mworld] :
              ( ( mrel @ A @ C )
             => ! [D: $i] :
                  ( ( eiw_di @ D @ C )
                 => ! [E: mworld] :
                      ( ( mrel @ C @ E )
                     => ! [F: $i] :
                          ( ( eiw_di @ F @ E )
                         => ! [G: mworld] :
                              ( ( mrel @ E @ G )
                             => ( ! [H: mworld] :
                                    ( ( mrel @ G @ H )
                                   => ( qmltpeq @ B @ D @ H ) )
                               => ! [H: mworld] :
                                    ( ( mrel @ G @ H )
                                   => ( qmltpeq @ ( or @ F @ B ) @ ( or @ F @ D ) @ H ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(28,axiom,
    ( mlocal
    @ ( mand
      @ ( mbox
        @ ( mimplies @ ( mbox @ modus_tollens )
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ ( not @ B ) @ ( not @ A ) ) @ ( implies @ A @ B ) ) ) ) ) ) ) ) ) )
      @ ( mbox
        @ ( mimplies
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ ( not @ B ) @ ( not @ A ) ) @ ( implies @ A @ B ) ) ) ) ) ) ) )
          @ ( mbox @ modus_tollens ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_tollens_0) ).

thf(288,plain,
    ( ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( modus_tollens @ B ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( is_a_theorem @ ( implies @ ( implies @ ( not @ E ) @ ( not @ C ) ) @ ( implies @ C @ E ) ) @ F ) ) ) ) ) ) ) )
    & ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( is_a_theorem @ ( implies @ ( implies @ ( not @ E ) @ ( not @ C ) ) @ ( implies @ C @ E ) ) @ F ) ) ) ) ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( modus_tollens @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(46,axiom,
    ( mlocal
    @ ( mand
      @ ( mbox
        @ ( mimplies @ ( mbox @ and_3 )
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ A @ ( implies @ B @ ( and @ A @ B ) ) ) ) ) ) ) ) ) ) )
      @ ( mbox
        @ ( mimplies
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ A @ ( implies @ B @ ( and @ A @ B ) ) ) ) ) ) ) ) )
          @ ( mbox @ and_3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_3_0) ).

thf(389,plain,
    ( ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( and_3 @ B ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( is_a_theorem @ ( implies @ C @ ( implies @ E @ ( and @ C @ E ) ) ) @ F ) ) ) ) ) ) ) )
    & ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( is_a_theorem @ ( implies @ C @ ( implies @ E @ ( and @ C @ E ) ) ) @ F ) ) ) ) ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( and_3 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(67,axiom,
    ( mlocal
    @ ( mbox
      @ ( mforall_di
        @ ^ [A: $i] :
            ( mbox
            @ ( mforall_di
              @ ^ [B: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( equiv @ C @ A ) @ ( equiv @ C @ B ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equiv_substitution_2) ).

thf(570,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ! [B: $i] :
          ( ( eiw_di @ B @ A )
         => ! [C: mworld] :
              ( ( mrel @ A @ C )
             => ! [D: $i] :
                  ( ( eiw_di @ D @ C )
                 => ! [E: mworld] :
                      ( ( mrel @ C @ E )
                     => ! [F: $i] :
                          ( ( eiw_di @ F @ E )
                         => ! [G: mworld] :
                              ( ( mrel @ E @ G )
                             => ( ! [H: mworld] :
                                    ( ( mrel @ G @ H )
                                   => ( qmltpeq @ B @ D @ H ) )
                               => ! [H: mworld] :
                                    ( ( mrel @ G @ H )
                                   => ( qmltpeq @ ( equiv @ F @ B ) @ ( equiv @ F @ D ) @ H ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(37,axiom,
    mlocal @ ( mbox @ and_3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_3) ).

thf(344,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ( and_3 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(14,axiom,
    ( mlocal
    @ ( mbox
      @ ( mforall_di
        @ ^ [A: $i] :
            ( mbox
            @ ( mforall_di
              @ ^ [B: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( equiv @ A @ C ) @ ( equiv @ B @ C ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equiv_substitution_1) ).

thf(157,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ! [B: $i] :
          ( ( eiw_di @ B @ A )
         => ! [C: mworld] :
              ( ( mrel @ A @ C )
             => ! [D: $i] :
                  ( ( eiw_di @ D @ C )
                 => ! [E: mworld] :
                      ( ( mrel @ C @ E )
                     => ! [F: $i] :
                          ( ( eiw_di @ F @ E )
                         => ! [G: mworld] :
                              ( ( mrel @ E @ G )
                             => ( ! [H: mworld] :
                                    ( ( mrel @ G @ H )
                                   => ( qmltpeq @ B @ D @ H ) )
                               => ! [H: mworld] :
                                    ( ( mrel @ G @ H )
                                   => ( qmltpeq @ ( equiv @ B @ F ) @ ( equiv @ D @ F ) @ H ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(23,axiom,
    ( mlocal
    @ ( mand
      @ ( mbox
        @ ( mimplies @ ( mbox @ cn1 )
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] :
                        ( mbox
                        @ ( mforall_di
                          @ ^ [C: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) ) ) ) ) ) ) ) ) ) )
      @ ( mbox
        @ ( mimplies
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] :
                        ( mbox
                        @ ( mforall_di
                          @ ^ [C: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) ) ) ) ) ) ) ) )
          @ ( mbox @ cn1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn1_0) ).

thf(211,plain,
    ( ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( cn1 @ B ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ! [G: $i] :
                                  ( ( eiw_di @ G @ F )
                                 => ! [H: mworld] :
                                      ( ( mrel @ F @ H )
                                     => ( is_a_theorem @ ( implies @ ( implies @ C @ E ) @ ( implies @ ( implies @ E @ G ) @ ( implies @ C @ G ) ) ) @ H ) ) ) ) ) ) ) ) ) )
    & ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ! [G: $i] :
                                  ( ( eiw_di @ G @ F )
                                 => ! [H: mworld] :
                                      ( ( mrel @ F @ H )
                                     => ( is_a_theorem @ ( implies @ ( implies @ C @ E ) @ ( implies @ ( implies @ E @ G ) @ ( implies @ C @ G ) ) ) @ H ) ) ) ) ) ) ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( cn1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(56,axiom,
    ( mlocal
    @ ( mbox
      @ ( mforall_di
        @ ^ [A: $i] :
            ( mbox
            @ ( mforall_di
              @ ^ [B: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ B @ C ) ) ) @ ( mbox @ ( qmltpeq @ A @ C ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).

thf(485,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ! [B: $i] :
          ( ( eiw_di @ B @ A )
         => ! [C: mworld] :
              ( ( mrel @ A @ C )
             => ! [D: $i] :
                  ( ( eiw_di @ D @ C )
                 => ! [E: mworld] :
                      ( ( mrel @ C @ E )
                     => ! [F: $i] :
                          ( ( eiw_di @ F @ E )
                         => ! [G: mworld] :
                              ( ( mrel @ E @ G )
                             => ( ( ! [H: mworld] :
                                      ( ( mrel @ G @ H )
                                     => ( qmltpeq @ B @ D @ H ) )
                                  & ! [H: mworld] :
                                      ( ( mrel @ G @ H )
                                     => ( qmltpeq @ D @ F @ H ) ) )
                               => ! [H: mworld] :
                                    ( ( mrel @ G @ H )
                                   => ( qmltpeq @ B @ F @ H ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(39,axiom,
    mlocal @ ( mbox @ op_and ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_and) ).

thf(348,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ( op_and @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(58,axiom,
    mlocal @ ( mbox @ or_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_2) ).

thf(492,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ( or_2 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(17,axiom,
    mlocal @ ( mbox @ substitution_of_equivalents ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents_1) ).

thf(164,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ( substitution_of_equivalents @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(53,axiom,
    ( mlocal
    @ ( mand
      @ ( mbox
        @ ( mimplies @ ( mbox @ implies_1 )
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ A @ ( implies @ B @ A ) ) ) ) ) ) ) ) ) )
      @ ( mbox
        @ ( mimplies
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ A @ ( implies @ B @ A ) ) ) ) ) ) ) )
          @ ( mbox @ implies_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_1_0) ).

thf(453,plain,
    ( ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( implies_1 @ B ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( is_a_theorem @ ( implies @ C @ ( implies @ E @ C ) ) @ F ) ) ) ) ) ) ) )
    & ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( is_a_theorem @ ( implies @ C @ ( implies @ E @ C ) ) @ F ) ) ) ) ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( implies_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(32,axiom,
    ( mlocal
    @ ( mand
      @ ( mbox
        @ ( mimplies @ ( mbox @ implies_2 )
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ A @ ( implies @ A @ B ) ) @ ( implies @ A @ B ) ) ) ) ) ) ) ) ) )
      @ ( mbox
        @ ( mimplies
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ A @ ( implies @ A @ B ) ) @ ( implies @ A @ B ) ) ) ) ) ) ) )
          @ ( mbox @ implies_2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_2_0) ).

thf(312,plain,
    ( ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( implies_2 @ B ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( is_a_theorem @ ( implies @ ( implies @ C @ ( implies @ C @ E ) ) @ ( implies @ C @ E ) ) @ F ) ) ) ) ) ) ) )
    & ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( is_a_theorem @ ( implies @ ( implies @ C @ ( implies @ C @ E ) ) @ ( implies @ C @ E ) ) @ F ) ) ) ) ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( implies_2 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(8,axiom,
    ( mlocal
    @ ( mbox
      @ ( mimplies @ ( mbox @ op_or )
        @ ( mbox
          @ ( mforall_di
            @ ^ [A: $i] :
                ( mbox
                @ ( mforall_di
                  @ ^ [B: $i] : ( mbox @ ( qmltpeq @ ( or @ A @ B ) @ ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_or_0) ).

thf(117,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ( ! [B: mworld] :
            ( ( mrel @ A @ B )
           => ( op_or @ B ) )
       => ! [B: mworld] :
            ( ( mrel @ A @ B )
           => ! [C: $i] :
                ( ( eiw_di @ C @ B )
               => ! [D: mworld] :
                    ( ( mrel @ B @ D )
                   => ! [E: $i] :
                        ( ( eiw_di @ E @ D )
                       => ! [F: mworld] :
                            ( ( mrel @ D @ F )
                           => ( qmltpeq @ ( or @ C @ E ) @ ( not @ ( and @ ( not @ C ) @ ( not @ E ) ) ) @ F ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(61,axiom,
    ( mlocal
    @ ( mbox
      @ ( mforall_di
        @ ^ [A: $i] :
            ( mbox
            @ ( mforall_di
              @ ^ [B: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( or @ A @ C ) @ ( or @ B @ C ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_substitution_1) ).

thf(534,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ! [B: $i] :
          ( ( eiw_di @ B @ A )
         => ! [C: mworld] :
              ( ( mrel @ A @ C )
             => ! [D: $i] :
                  ( ( eiw_di @ D @ C )
                 => ! [E: mworld] :
                      ( ( mrel @ C @ E )
                     => ! [F: $i] :
                          ( ( eiw_di @ F @ E )
                         => ! [G: mworld] :
                              ( ( mrel @ E @ G )
                             => ( ! [H: mworld] :
                                    ( ( mrel @ G @ H )
                                   => ( qmltpeq @ B @ D @ H ) )
                               => ! [H: mworld] :
                                    ( ( mrel @ G @ H )
                                   => ( qmltpeq @ ( or @ B @ F ) @ ( or @ D @ F ) @ H ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(15,axiom,
    mlocal @ ( mbox @ op_equiv ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_equiv) ).

thf(160,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ( op_equiv @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(1,conjecture,
    mlocal @ ( mbox @ r2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r2) ).

thf(2,negated_conjecture,
    ~ ( mlocal @ ( mbox @ r2 ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(70,plain,
    ~ ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( r2 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(50,axiom,
    ( mlocal
    @ ( mand
      @ ( mbox
        @ ( mimplies @ ( mbox @ r4 )
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] :
                        ( mbox
                        @ ( mforall_di
                          @ ^ [C: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( or @ A @ ( or @ B @ C ) ) @ ( or @ B @ ( or @ A @ C ) ) ) ) ) ) ) ) ) ) ) ) )
      @ ( mbox
        @ ( mimplies
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] :
                        ( mbox
                        @ ( mforall_di
                          @ ^ [C: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( or @ A @ ( or @ B @ C ) ) @ ( or @ B @ ( or @ A @ C ) ) ) ) ) ) ) ) ) ) )
          @ ( mbox @ r4 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r4_0) ).

thf(429,plain,
    ( ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( r4 @ B ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ! [G: $i] :
                                  ( ( eiw_di @ G @ F )
                                 => ! [H: mworld] :
                                      ( ( mrel @ F @ H )
                                     => ( is_a_theorem @ ( implies @ ( or @ C @ ( or @ E @ G ) ) @ ( or @ E @ ( or @ C @ G ) ) ) @ H ) ) ) ) ) ) ) ) ) )
    & ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ! [G: $i] :
                                  ( ( eiw_di @ G @ F )
                                 => ! [H: mworld] :
                                      ( ( mrel @ F @ H )
                                     => ( is_a_theorem @ ( implies @ ( or @ C @ ( or @ E @ G ) ) @ ( or @ E @ ( or @ C @ G ) ) ) @ H ) ) ) ) ) ) ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( r4 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(20,axiom,
    mlocal @ ( mbox @ equivalence_3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_3) ).

thf(192,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ( equivalence_3 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(48,axiom,
    ( mlocal
    @ ( mbox
      @ ( mforall_di
        @ ^ [A: $i] :
            ( mbox
            @ ( mforall_di
              @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ B @ A ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).

thf(407,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ! [B: $i] :
          ( ( eiw_di @ B @ A )
         => ! [C: mworld] :
              ( ( mrel @ A @ C )
             => ! [D: $i] :
                  ( ( eiw_di @ D @ C )
                 => ! [E: mworld] :
                      ( ( mrel @ C @ E )
                     => ( ! [F: mworld] :
                            ( ( mrel @ E @ F )
                           => ( qmltpeq @ B @ D @ F ) )
                       => ! [F: mworld] :
                            ( ( mrel @ E @ F )
                           => ( qmltpeq @ D @ B @ F ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(64,axiom,
    mlocal @ ( mbox @ modus_ponens ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_ponens) ).

thf(554,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ( modus_ponens @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(62,axiom,
    ( mlocal
    @ ( mand
      @ ( mbox
        @ ( mimplies @ ( mbox @ and_2 )
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ B ) ) ) ) ) ) ) ) )
      @ ( mbox
        @ ( mimplies
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ B ) ) ) ) ) ) )
          @ ( mbox @ and_2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_2_0) ).

thf(537,plain,
    ( ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( and_2 @ B ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( is_a_theorem @ ( implies @ ( and @ C @ E ) @ E ) @ F ) ) ) ) ) ) ) )
    & ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( is_a_theorem @ ( implies @ ( and @ C @ E ) @ E ) @ F ) ) ) ) ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( and_2 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(3,axiom,
    ! [A: mworld] :
    ? [B: $i] : ( eiw_di @ B @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eiw_di_nonempty) ).

thf(73,plain,
    ! [A: mworld] :
    ? [B: $i] : ( eiw_di @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(26,axiom,
    ( mlocal
    @ ( mbox
      @ ( mimplies @ ( mbox @ op_and )
        @ ( mbox
          @ ( mforall_di
            @ ^ [A: $i] :
                ( mbox
                @ ( mforall_di
                  @ ^ [B: $i] : ( mbox @ ( qmltpeq @ ( and @ A @ B ) @ ( not @ ( or @ ( not @ A ) @ ( not @ B ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_and_0) ).

thf(266,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ( ! [B: mworld] :
            ( ( mrel @ A @ B )
           => ( op_and @ B ) )
       => ! [B: mworld] :
            ( ( mrel @ A @ B )
           => ! [C: $i] :
                ( ( eiw_di @ C @ B )
               => ! [D: mworld] :
                    ( ( mrel @ B @ D )
                   => ! [E: $i] :
                        ( ( eiw_di @ E @ D )
                       => ! [F: mworld] :
                            ( ( mrel @ D @ F )
                           => ( qmltpeq @ ( and @ C @ E ) @ ( not @ ( or @ ( not @ C ) @ ( not @ E ) ) ) @ F ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(18,axiom,
    ( mlocal
    @ ( mand
      @ ( mbox
        @ ( mimplies @ ( mbox @ or_1 )
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ A @ ( or @ A @ B ) ) ) ) ) ) ) ) ) )
      @ ( mbox
        @ ( mimplies
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ A @ ( or @ A @ B ) ) ) ) ) ) ) )
          @ ( mbox @ or_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_1_0) ).

thf(166,plain,
    ( ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( or_1 @ B ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( is_a_theorem @ ( implies @ C @ ( or @ C @ E ) ) @ F ) ) ) ) ) ) ) )
    & ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( is_a_theorem @ ( implies @ C @ ( or @ C @ E ) ) @ F ) ) ) ) ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( or_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(68,axiom,
    mlocal @ ( mbox @ and_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_2) ).

thf(573,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ( and_2 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(19,axiom,
    ( mlocal
    @ ( mand
      @ ( mbox
        @ ( mimplies @ ( mbox @ cn3 )
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ ( not @ A ) @ A ) @ A ) ) ) ) ) ) )
      @ ( mbox
        @ ( mimplies
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ ( not @ A ) @ A ) @ A ) ) ) ) )
          @ ( mbox @ cn3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn3_0) ).

thf(181,plain,
    ( ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( cn3 @ B ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ( is_a_theorem @ ( implies @ ( implies @ ( not @ C ) @ C ) @ C ) @ D ) ) ) ) ) )
    & ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ( is_a_theorem @ ( implies @ ( implies @ ( not @ C ) @ C ) @ C ) @ D ) ) ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( cn3 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(40,axiom,
    mlocal @ ( mbox @ op_equiv ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_equiv) ).

thf(350,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ( op_equiv @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(24,axiom,
    ( mlocal
    @ ( mand
      @ ( mbox
        @ ( mimplies @ ( mbox @ equivalence_2 )
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ ( implies @ B @ A ) ) ) ) ) ) ) ) ) )
      @ ( mbox
        @ ( mimplies
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ ( implies @ B @ A ) ) ) ) ) ) ) )
          @ ( mbox @ equivalence_2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_2_0) ).

thf(230,plain,
    ( ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( equivalence_2 @ B ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( is_a_theorem @ ( implies @ ( equiv @ C @ E ) @ ( implies @ E @ C ) ) @ F ) ) ) ) ) ) ) )
    & ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( is_a_theorem @ ( implies @ ( equiv @ C @ E ) @ ( implies @ E @ C ) ) @ F ) ) ) ) ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( equivalence_2 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(66,axiom,
    ( mlocal
    @ ( mbox
      @ ( mforall_di
        @ ^ [A: $i] :
            ( mbox
            @ ( mforall_di
              @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( not @ A ) @ ( not @ B ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_substitution_1) ).

thf(567,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ! [B: $i] :
          ( ( eiw_di @ B @ A )
         => ! [C: mworld] :
              ( ( mrel @ A @ C )
             => ! [D: $i] :
                  ( ( eiw_di @ D @ C )
                 => ! [E: mworld] :
                      ( ( mrel @ C @ E )
                     => ( ! [F: mworld] :
                            ( ( mrel @ E @ F )
                           => ( qmltpeq @ B @ D @ F ) )
                       => ! [F: mworld] :
                            ( ( mrel @ E @ F )
                           => ( qmltpeq @ ( not @ B ) @ ( not @ D ) @ F ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(25,axiom,
    ( mlocal
    @ ( mand
      @ ( mbox
        @ ( mimplies @ ( mbox @ substitution_of_equivalents )
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( is_a_theorem @ ( equiv @ A @ B ) ) ) @ ( mbox @ ( qmltpeq @ A @ B ) ) ) ) ) ) ) ) ) )
      @ ( mbox
        @ ( mimplies
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( is_a_theorem @ ( equiv @ A @ B ) ) ) @ ( mbox @ ( qmltpeq @ A @ B ) ) ) ) ) ) ) )
          @ ( mbox @ substitution_of_equivalents ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents_0) ).

thf(245,plain,
    ( ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( substitution_of_equivalents @ B ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( ! [G: mworld] :
                                    ( ( mrel @ F @ G )
                                   => ( is_a_theorem @ ( equiv @ C @ E ) @ G ) )
                               => ! [G: mworld] :
                                    ( ( mrel @ F @ G )
                                   => ( qmltpeq @ C @ E @ G ) ) ) ) ) ) ) ) ) )
    & ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( ! [G: mworld] :
                                    ( ( mrel @ F @ G )
                                   => ( is_a_theorem @ ( equiv @ C @ E ) @ G ) )
                               => ! [G: mworld] :
                                    ( ( mrel @ F @ G )
                                   => ( qmltpeq @ C @ E @ G ) ) ) ) ) ) ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( substitution_of_equivalents @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(60,axiom,
    ( mlocal
    @ ( mand
      @ ( mbox
        @ ( mimplies @ ( mbox @ modus_ponens )
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( is_a_theorem @ A ) ) @ ( mbox @ ( is_a_theorem @ ( implies @ A @ B ) ) ) ) @ ( mbox @ ( is_a_theorem @ B ) ) ) ) ) ) ) ) ) )
      @ ( mbox
        @ ( mimplies
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( is_a_theorem @ A ) ) @ ( mbox @ ( is_a_theorem @ ( implies @ A @ B ) ) ) ) @ ( mbox @ ( is_a_theorem @ B ) ) ) ) ) ) ) )
          @ ( mbox @ modus_ponens ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_ponens_0) ).

thf(509,plain,
    ( ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( modus_ponens @ B ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( ( ! [G: mworld] :
                                      ( ( mrel @ F @ G )
                                     => ( is_a_theorem @ C @ G ) )
                                  & ! [G: mworld] :
                                      ( ( mrel @ F @ G )
                                     => ( is_a_theorem @ ( implies @ C @ E ) @ G ) ) )
                               => ! [G: mworld] :
                                    ( ( mrel @ F @ G )
                                   => ( is_a_theorem @ E @ G ) ) ) ) ) ) ) ) ) )
    & ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( ( ! [G: mworld] :
                                      ( ( mrel @ F @ G )
                                     => ( is_a_theorem @ C @ G ) )
                                  & ! [G: mworld] :
                                      ( ( mrel @ F @ G )
                                     => ( is_a_theorem @ ( implies @ C @ E ) @ G ) ) )
                               => ! [G: mworld] :
                                    ( ( mrel @ F @ G )
                                   => ( is_a_theorem @ E @ G ) ) ) ) ) ) ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( modus_ponens @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(7,axiom,
    ( mlocal
    @ ( mand
      @ ( mbox
        @ ( mimplies @ ( mbox @ implies_3 )
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] :
                        ( mbox
                        @ ( mforall_di
                          @ ^ [C: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) ) ) ) ) ) ) ) ) ) )
      @ ( mbox
        @ ( mimplies
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] :
                        ( mbox
                        @ ( mforall_di
                          @ ^ [C: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ C ) @ ( implies @ A @ C ) ) ) ) ) ) ) ) ) ) )
          @ ( mbox @ implies_3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_3_0) ).

thf(98,plain,
    ( ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( implies_3 @ B ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ! [G: $i] :
                                  ( ( eiw_di @ G @ F )
                                 => ! [H: mworld] :
                                      ( ( mrel @ F @ H )
                                     => ( is_a_theorem @ ( implies @ ( implies @ C @ E ) @ ( implies @ ( implies @ E @ G ) @ ( implies @ C @ G ) ) ) @ H ) ) ) ) ) ) ) ) ) )
    & ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ! [G: $i] :
                                  ( ( eiw_di @ G @ F )
                                 => ! [H: mworld] :
                                      ( ( mrel @ F @ H )
                                     => ( is_a_theorem @ ( implies @ ( implies @ C @ E ) @ ( implies @ ( implies @ E @ G ) @ ( implies @ C @ G ) ) ) @ H ) ) ) ) ) ) ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( implies_3 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(29,axiom,
    ( mlocal
    @ ( mbox
      @ ( mforall_di
        @ ^ [A: $i] :
            ( mbox
            @ ( mforall_di
              @ ^ [B: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( implies @ A @ C ) @ ( implies @ B @ C ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_substitution_1) ).

thf(303,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ! [B: $i] :
          ( ( eiw_di @ B @ A )
         => ! [C: mworld] :
              ( ( mrel @ A @ C )
             => ! [D: $i] :
                  ( ( eiw_di @ D @ C )
                 => ! [E: mworld] :
                      ( ( mrel @ C @ E )
                     => ! [F: $i] :
                          ( ( eiw_di @ F @ E )
                         => ! [G: mworld] :
                              ( ( mrel @ E @ G )
                             => ( ! [H: mworld] :
                                    ( ( mrel @ G @ H )
                                   => ( qmltpeq @ B @ D @ H ) )
                               => ! [H: mworld] :
                                    ( ( mrel @ G @ H )
                                   => ( qmltpeq @ ( implies @ B @ F ) @ ( implies @ D @ F ) @ H ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(59,axiom,
    ( mlocal
    @ ( mand
      @ ( mbox
        @ ( mimplies @ ( mbox @ equivalence_1 )
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ ( implies @ A @ B ) ) ) ) ) ) ) ) ) )
      @ ( mbox
        @ ( mimplies
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( equiv @ A @ B ) @ ( implies @ A @ B ) ) ) ) ) ) ) )
          @ ( mbox @ equivalence_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_1_0) ).

thf(494,plain,
    ( ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( equivalence_1 @ B ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( is_a_theorem @ ( implies @ ( equiv @ C @ E ) @ ( implies @ C @ E ) ) @ F ) ) ) ) ) ) ) )
    & ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( is_a_theorem @ ( implies @ ( equiv @ C @ E ) @ ( implies @ C @ E ) ) @ F ) ) ) ) ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( equivalence_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(13,axiom,
    mlocal @ ( mbox @ implies_3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_3) ).

thf(155,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ( implies_3 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(42,axiom,
    ( mlocal
    @ ( mbox
      @ ( mforall_di
        @ ^ [A: $i] : ( mbox @ ( qmltpeq @ A @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).

thf(367,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ! [B: $i] :
          ( ( eiw_di @ B @ A )
         => ! [C: mworld] :
              ( ( mrel @ A @ C )
             => ( qmltpeq @ B @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(63,axiom,
    mlocal @ ( mbox @ op_implies_or ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_implies_or) ).

thf(552,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ( op_implies_or @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(30,axiom,
    ( mlocal
    @ ( mbox
      @ ( mforall_di
        @ ^ [A: $i] :
            ( mbox
            @ ( mforall_di
              @ ^ [B: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( and @ C @ A ) @ ( and @ C @ B ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_substitution_2) ).

thf(306,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ! [B: $i] :
          ( ( eiw_di @ B @ A )
         => ! [C: mworld] :
              ( ( mrel @ A @ C )
             => ! [D: $i] :
                  ( ( eiw_di @ D @ C )
                 => ! [E: mworld] :
                      ( ( mrel @ C @ E )
                     => ! [F: $i] :
                          ( ( eiw_di @ F @ E )
                         => ! [G: mworld] :
                              ( ( mrel @ E @ G )
                             => ( ! [H: mworld] :
                                    ( ( mrel @ G @ H )
                                   => ( qmltpeq @ B @ D @ H ) )
                               => ! [H: mworld] :
                                    ( ( mrel @ G @ H )
                                   => ( qmltpeq @ ( and @ F @ B ) @ ( and @ F @ D ) @ H ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(5,axiom,
    ( mlocal
    @ ( mbox
      @ ( mimplies @ ( mbox @ op_implies_and )
        @ ( mbox
          @ ( mforall_di
            @ ^ [A: $i] :
                ( mbox
                @ ( mforall_di
                  @ ^ [B: $i] : ( mbox @ ( qmltpeq @ ( implies @ A @ B ) @ ( not @ ( and @ A @ ( not @ B ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_and_0) ).

thf(80,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ( ! [B: mworld] :
            ( ( mrel @ A @ B )
           => ( op_implies_and @ B ) )
       => ! [B: mworld] :
            ( ( mrel @ A @ B )
           => ! [C: $i] :
                ( ( eiw_di @ C @ B )
               => ! [D: mworld] :
                    ( ( mrel @ B @ D )
                   => ! [E: $i] :
                        ( ( eiw_di @ E @ D )
                       => ! [F: mworld] :
                            ( ( mrel @ D @ F )
                           => ( qmltpeq @ ( implies @ C @ E ) @ ( not @ ( and @ C @ ( not @ E ) ) ) @ F ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(57,axiom,
    mlocal @ ( mbox @ equivalence_1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_1) ).

thf(490,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ( equivalence_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(16,axiom,
    mlocal @ ( mbox @ modus_tollens ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_tollens) ).

thf(162,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ( modus_tollens @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(45,axiom,
    ( mlocal
    @ ( mand
      @ ( mbox
        @ ( mimplies @ ( mbox @ or_2 )
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) ) ) ) ) ) ) ) )
      @ ( mbox
        @ ( mimplies
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) ) ) ) ) ) )
          @ ( mbox @ or_2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_2_0) ).

thf(374,plain,
    ( ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( or_2 @ B ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( is_a_theorem @ ( implies @ E @ ( or @ C @ E ) ) @ F ) ) ) ) ) ) ) )
    & ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( is_a_theorem @ ( implies @ E @ ( or @ C @ E ) ) @ F ) ) ) ) ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( or_2 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(22,axiom,
    mlocal @ ( mbox @ equivalence_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_2) ).

thf(209,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ( equivalence_2 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(21,axiom,
    ( mlocal
    @ ( mand
      @ ( mbox
        @ ( mimplies @ ( mbox @ and_1 )
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) ) ) ) ) ) ) )
      @ ( mbox
        @ ( mimplies
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) ) ) ) ) )
          @ ( mbox @ and_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_1_0) ).

thf(194,plain,
    ( ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( and_1 @ B ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( is_a_theorem @ ( implies @ ( and @ C @ E ) @ C ) @ F ) ) ) ) ) ) ) )
    & ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( is_a_theorem @ ( implies @ ( and @ C @ E ) @ C ) @ F ) ) ) ) ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( and_1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(36,axiom,
    mlocal @ ( mbox @ implies_1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_1) ).

thf(342,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ( implies_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(10,axiom,
    ( mlocal
    @ ( mand
      @ ( mbox
        @ ( mimplies @ ( mbox @ r3 )
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( or @ A @ B ) @ ( or @ B @ A ) ) ) ) ) ) ) ) ) )
      @ ( mbox
        @ ( mimplies
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( or @ A @ B ) @ ( or @ B @ A ) ) ) ) ) ) ) )
          @ ( mbox @ r3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_0) ).

thf(123,plain,
    ( ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( r3 @ B ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( is_a_theorem @ ( implies @ ( or @ C @ E ) @ ( or @ E @ C ) ) @ F ) ) ) ) ) ) ) )
    & ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( is_a_theorem @ ( implies @ ( or @ C @ E ) @ ( or @ E @ C ) ) @ F ) ) ) ) ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( r3 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(34,axiom,
    mlocal @ ( mbox @ op_or ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).

thf(338,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ( op_or @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(55,axiom,
    ( mlocal
    @ ( mand
      @ ( mbox
        @ ( mimplies @ ( mbox @ r2 )
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) ) ) ) ) ) ) ) )
      @ ( mbox
        @ ( mimplies
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) ) ) ) ) ) )
          @ ( mbox @ r2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_0) ).

thf(470,plain,
    ( ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( r2 @ B ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( is_a_theorem @ ( implies @ E @ ( or @ C @ E ) ) @ F ) ) ) ) ) ) ) )
    & ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( is_a_theorem @ ( implies @ E @ ( or @ C @ E ) ) @ F ) ) ) ) ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( r2 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(52,axiom,
    ( mlocal
    @ ( mbox
      @ ( mimplies @ ( mbox @ op_implies_or )
        @ ( mbox
          @ ( mforall_di
            @ ^ [A: $i] :
                ( mbox
                @ ( mforall_di
                  @ ^ [B: $i] : ( mbox @ ( qmltpeq @ ( implies @ A @ B ) @ ( or @ ( not @ A ) @ B ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_or_0) ).

thf(450,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ( ! [B: mworld] :
            ( ( mrel @ A @ B )
           => ( op_implies_or @ B ) )
       => ! [B: mworld] :
            ( ( mrel @ A @ B )
           => ! [C: $i] :
                ( ( eiw_di @ C @ B )
               => ! [D: mworld] :
                    ( ( mrel @ B @ D )
                   => ! [E: $i] :
                        ( ( eiw_di @ E @ D )
                       => ! [F: mworld] :
                            ( ( mrel @ D @ F )
                           => ( qmltpeq @ ( implies @ C @ E ) @ ( or @ ( not @ C ) @ E ) @ F ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(65,axiom,
    ( mlocal
    @ ( mand
      @ ( mbox
        @ ( mimplies @ ( mbox @ kn1 )
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] : ( mbox @ ( is_a_theorem @ ( implies @ A @ ( and @ A @ A ) ) ) ) ) ) ) )
      @ ( mbox
        @ ( mimplies
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] : ( mbox @ ( is_a_theorem @ ( implies @ A @ ( and @ A @ A ) ) ) ) ) )
          @ ( mbox @ kn1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kn1_0) ).

thf(556,plain,
    ( ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( kn1 @ B ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ( is_a_theorem @ ( implies @ C @ ( and @ C @ C ) ) @ D ) ) ) ) ) )
    & ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ( is_a_theorem @ ( implies @ C @ ( and @ C @ C ) ) @ D ) ) ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( kn1 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(4,axiom,
    ( mlocal
    @ ( mbox
      @ ( mforall_di
        @ ^ [A: $i] :
            ( mbox
            @ ( mforall_di
              @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( is_a_theorem @ A ) ) ) @ ( mbox @ ( is_a_theorem @ B ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',is_a_theorem_substitution_1) ).

thf(75,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ! [B: $i] :
          ( ( eiw_di @ B @ A )
         => ! [C: mworld] :
              ( ( mrel @ A @ C )
             => ! [D: $i] :
                  ( ( eiw_di @ D @ C )
                 => ! [E: mworld] :
                      ( ( mrel @ C @ E )
                     => ( ( ! [F: mworld] :
                              ( ( mrel @ E @ F )
                             => ( qmltpeq @ B @ D @ F ) )
                          & ! [F: mworld] :
                              ( ( mrel @ E @ F )
                             => ( is_a_theorem @ B @ F ) ) )
                       => ! [F: mworld] :
                            ( ( mrel @ E @ F )
                           => ( is_a_theorem @ D @ F ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(38,axiom,
    mlocal @ ( mbox @ and_1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_1) ).

thf(346,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ( and_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(69,axiom,
    ( mlocal
    @ ( mand
      @ ( mbox
        @ ( mimplies @ ( mbox @ kn3 )
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] :
                        ( mbox
                        @ ( mforall_di
                          @ ^ [C: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( not @ ( and @ B @ C ) ) @ ( not @ ( and @ C @ A ) ) ) ) ) ) ) ) ) ) ) ) ) )
      @ ( mbox
        @ ( mimplies
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] :
                        ( mbox
                        @ ( mforall_di
                          @ ^ [C: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( not @ ( and @ B @ C ) ) @ ( not @ ( and @ C @ A ) ) ) ) ) ) ) ) ) ) ) )
          @ ( mbox @ kn3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kn3_0) ).

thf(575,plain,
    ( ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( kn3 @ B ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ! [G: $i] :
                                  ( ( eiw_di @ G @ F )
                                 => ! [H: mworld] :
                                      ( ( mrel @ F @ H )
                                     => ( is_a_theorem @ ( implies @ ( implies @ C @ E ) @ ( implies @ ( not @ ( and @ E @ G ) ) @ ( not @ ( and @ G @ C ) ) ) ) @ H ) ) ) ) ) ) ) ) ) )
    & ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ! [G: $i] :
                                  ( ( eiw_di @ G @ F )
                                 => ! [H: mworld] :
                                      ( ( mrel @ F @ H )
                                     => ( is_a_theorem @ ( implies @ ( implies @ C @ E ) @ ( implies @ ( not @ ( and @ E @ G ) ) @ ( not @ ( and @ G @ C ) ) ) ) @ H ) ) ) ) ) ) ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( kn3 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(43,axiom,
    mlocal @ ( mbox @ or_3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_3) ).

thf(369,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ( or_3 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(6,axiom,
    ( mlocal
    @ ( mand
      @ ( mbox
        @ ( mimplies @ ( mbox @ equivalence_3 )
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ A ) @ ( equiv @ A @ B ) ) ) ) ) ) ) ) ) ) )
      @ ( mbox
        @ ( mimplies
          @ ( mbox
            @ ( mforall_di
              @ ^ [A: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [B: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( implies @ B @ A ) @ ( equiv @ A @ B ) ) ) ) ) ) ) ) )
          @ ( mbox @ equivalence_3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_3_0) ).

thf(83,plain,
    ( ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( equivalence_3 @ B ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( is_a_theorem @ ( implies @ ( implies @ C @ E ) @ ( implies @ ( implies @ E @ C ) @ ( equiv @ C @ E ) ) ) @ F ) ) ) ) ) ) ) )
    & ! [A: mworld] :
        ( ( mrel @ mactual @ A )
       => ( ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ! [C: $i] :
                  ( ( eiw_di @ C @ B )
                 => ! [D: mworld] :
                      ( ( mrel @ B @ D )
                     => ! [E: $i] :
                          ( ( eiw_di @ E @ D )
                         => ! [F: mworld] :
                              ( ( mrel @ D @ F )
                             => ( is_a_theorem @ ( implies @ ( implies @ C @ E ) @ ( implies @ ( implies @ E @ C ) @ ( equiv @ C @ E ) ) ) @ F ) ) ) ) ) )
         => ! [B: mworld] :
              ( ( mrel @ A @ B )
             => ( equivalence_3 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(31,axiom,
    ( mlocal
    @ ( mbox
      @ ( mforall_di
        @ ^ [A: $i] :
            ( mbox
            @ ( mforall_di
              @ ^ [B: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( implies @ C @ A ) @ ( implies @ C @ B ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_substitution_2) ).

thf(309,plain,
    ! [A: mworld] :
      ( ( mrel @ mactual @ A )
     => ! [B: $i] :
          ( ( eiw_di @ B @ A )
         => ! [C: mworld] :
              ( ( mrel @ A @ C )
             => ! [D: $i] :
                  ( ( eiw_di @ D @ C )
                 => ! [E: mworld] :
                      ( ( mrel @ C @ E )
                     => ! [F: $i] :
                          ( ( eiw_di @ F @ E )
                         => ! [G: mworld] :
                              ( ( mrel @ E @ G )
                             => ( ! [H: mworld] :
                                    ( ( mrel @ G @ H )
                                   => ( qmltpeq @ B @ D @ H ) )
                               => ! [H: mworld] :
                                    ( ( mrel @ G @ H )
                                   => ( qmltpeq @ ( implies @ F @ B ) @ ( implies @ F @ D ) @ H ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(4491,plain,
    $false,
    inference(e,[status(thm)],[448,371,327,410,138,468,352,120,269,340,153,404,288,389,570,344,157,211,485,348,492,164,453,312,117,534,160,70,429,192,407,554,537,73,266,166,573,181,350,230,567,245,509,98,303,494,155,367,552,306,80,490,162,374,209,194,342,123,338,470,450,556,75,346,575,369,83,309]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem  : LCL944^8 : TPTP v8.2.0. Released v8.1.0.
% 0.05/0.12  % Command  : run_Leo-III %s %d
% 0.12/0.32  % Computer : n011.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Mon May 20 03:30:23 EDT 2024
% 0.12/0.32  % CPUTime  : 
% 0.81/0.80  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.42/1.00  % [INFO] 	 Parsing done (198ms). 
% 1.42/1.01  % [INFO] 	 Running in sequential loop mode. 
% 2.12/1.26  % [INFO] 	 eprover registered as external prover. 
% 2.12/1.26  % [INFO] 	 cvc4 registered as external prover. 
% 2.12/1.26  % [INFO] 	 Scanning for conjecture ... 
% 2.46/1.38  % [INFO] 	 Found a conjecture (or negated_conjecture) and 67 axioms. Running axiom selection ... 
% 2.77/1.46  % [INFO] 	 Axiom selection finished. Selected 67 axioms (removed 0 axioms). 
% 3.16/1.57  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 3.16/1.58  % [INFO] 	 Type checking passed. 
% 3.16/1.58  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 65.77/15.18  % External prover 'e' found a proof!
% 65.77/15.18  % [INFO] 	 Killing All external provers ... 
% 65.77/15.18  % Time passed: 14740ms (effective reasoning time: 14172ms)
% 65.77/15.18  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 65.77/15.19  % Axioms used in derivation (67): implies_2_0, equiv_substitution_1, principia_op_and, equivalence_2_0, kn1_0, implies_3_0, op_and_0, substitution_of_equivalents_1, r3_0, equiv_substitution_2, or_substitution_2, implies_substitution_2, r4_0, op_equiv_0, op_implies_or_0, hilbert_implies_1, hilbert_and_3, hilbert_op_implies_and, op_implies_and_0, substitution_of_equivalents_0, mrel_reflexive, and_substitution_2, or_1_0, cn3_0, and_3_0, cn2_0, modus_ponens_0, hilbert_or_1, kn2_0, principia_op_equiv, reflexivity, modus_tollens_0, hilbert_or_2, hilbert_implies_2, equivalence_3_0, or_2_0, hilbert_and_2, not_substitution_1, hilbert_modus_tollens, hilbert_op_or, implies_1_0, hilbert_equivalence_2, hilbert_equivalence_3, cn1_0, eiw_di_nonempty, hilbert_modus_ponens, hilbert_implies_3, is_a_theorem_substitution_1, and_substitution_1, hilbert_and_1, and_2_0, op_or_0, hilbert_equivalence_1, hilbert_or_3, and_1_0, transitivity, r1_0, r2_0, or_substitution_1, r5_0, implies_substitution_1, kn3_0, equivalence_1_0, hilbert_op_equiv, or_3_0, symmetry, principia_op_implies_or
% 65.77/15.19  % No. of inferences in proof: 138
% 65.77/15.19  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 14740 ms resp. 14172 ms w/o parsing
% 65.94/15.31  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 65.94/15.31  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------