TSTP Solution File: SET055^12 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SET055^12 : TPTP v8.2.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 03:01:11 EDT 2024

% Result   : Theorem 6.01s 2.32s
% Output   : Refutation 6.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  136
% Syntax   : Number of formulae    :  223 (  13 unt;  43 typ;   8 def)
%            Number of atoms       :  996 (  27 equ;   0 cnn)
%            Maximal formula atoms :   11 (   5 avg)
%            Number of connectives : 2612 (   8   ~;   4   |;  38   &;2320   @)
%                                         (   0 <=>; 242  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (  10 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   96 (  96   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   44 (  42 usr;   7 con; 0-3 aty)
%            Number of variables   :  416 ( 215   ^ 194   !;   7   ?; 416   :)

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

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(mnot_type,type,
    mnot: ( mworld > $o ) > mworld > $o ).

thf(mnot_def,definition,
    ( mnot
    = ( ^ [A: mworld > $o,B: mworld] :
          ~ ( A @ B ) ) ) ).

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(mor_type,type,
    mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(mor_def,definition,
    ( mor
    = ( ^ [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(mequiv_type,type,
    mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(mequiv_def,definition,
    ( mequiv
    = ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
          ( ( A @ C )
          = ( B @ 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(mexists_di_type,type,
    mexists_di: ( $i > mworld > $o ) > mworld > $o ).

thf(mexists_di_def,definition,
    ( mexists_di
    = ( ^ [A: $i > mworld > $o,B: mworld] :
        ? [C: $i] :
          ( ( eiw_di @ C @ B )
          & ( A @ C @ B ) ) ) ) ).

thf(universal_class_type,type,
    universal_class: $i ).

thf(identity_relation_type,type,
    identity_relation: $i ).

thf(successor_relation_type,type,
    successor_relation: $i ).

thf(element_relation_type,type,
    element_relation: $i ).

thf(null_class_type,type,
    null_class: $i ).

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

thf(inductive_type,type,
    inductive: $i > mworld > $o ).

thf(disjoint_type,type,
    disjoint: $i > $i > mworld > $o ).

thf(function_type,type,
    function: $i > mworld > $o ).

thf(member_type,type,
    member: $i > $i > mworld > $o ).

thf(subclass_type,type,
    subclass: $i > $i > mworld > $o ).

thf(singleton_type,type,
    singleton: $i > $i ).

thf(image_type,type,
    image: $i > $i > $i ).

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

thf(rotate_type,type,
    rotate: $i > $i ).

thf(unordered_pair_type,type,
    unordered_pair: $i > $i > $i ).

thf(successor_type,type,
    successor: $i > $i ).

thf(apply_type,type,
    apply: $i > $i > $i ).

thf(power_class_type,type,
    power_class: $i > $i ).

thf(range_of_type,type,
    range_of: $i > $i ).

thf(union_type,type,
    union: $i > $i > $i ).

thf(restrict_type,type,
    restrict: $i > $i > $i > $i ).

thf(second_type,type,
    second: $i > $i ).

thf(ordered_pair_type,type,
    ordered_pair: $i > $i > $i ).

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

thf(sum_class_type,type,
    sum_class: $i > $i ).

thf(compose_type,type,
    compose: $i > $i > $i ).

thf(intersection_type,type,
    intersection: $i > $i > $i ).

thf(cross_product_type,type,
    cross_product: $i > $i > $i ).

thf(complement_type,type,
    complement: $i > $i ).

thf(flip_type,type,
    flip: $i > $i ).

thf(first_type,type,
    first: $i > $i ).

thf(25,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] : ( subclass @ A @ universal_class ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).

thf(142,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ( subclass @ A @ universal_class @ mactual ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(45,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( inductive @ A ) ) @ ( inductive @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive_substitution_1) ).

thf(192,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( ( qmltpeq @ A @ B @ mactual )
              & ( inductive @ A @ mactual ) )
           => ( inductive @ B @ mactual ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(38,axiom,
    ( mlocal
    @ ( mexists_di
      @ ^ [A: $i] :
          ( mand @ ( member @ A @ universal_class )
          @ ( mand @ ( inductive @ A )
            @ ( mforall_di
              @ ^ [B: $i] : ( mimplies @ ( inductive @ B ) @ ( subclass @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infinity) ).

thf(173,plain,
    ? [A: $i] :
      ( ( eiw_di @ A @ mactual )
      & ( member @ A @ universal_class @ mactual )
      & ( inductive @ A @ mactual )
      & ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( inductive @ B @ mactual )
           => ( subclass @ A @ B @ mactual ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(70,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ A @ C ) @ ( unordered_pair @ B @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_substitution_1) ).

thf(244,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ( ( qmltpeq @ A @ B @ mactual )
               => ( qmltpeq @ ( unordered_pair @ A @ C ) @ ( unordered_pair @ B @ C ) @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(46,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ C @ A ) ) @ ( member @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_substitution_2) ).

thf(194,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ( ( ( qmltpeq @ A @ B @ mactual )
                  & ( member @ C @ A @ mactual ) )
               => ( member @ C @ B @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(79,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( apply @ C @ A ) @ ( apply @ C @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply_substitution_2) ).

thf(263,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ( ( qmltpeq @ A @ B @ mactual )
               => ( qmltpeq @ ( apply @ C @ A ) @ ( apply @ C @ B ) @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(20,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mequiv @ ( member @ A @ ( power_class @ B ) ) @ ( mand @ ( member @ A @ universal_class ) @ ( subclass @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class_defn) ).

thf(127,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( member @ A @ ( power_class @ B ) @ mactual )
            = ( ( member @ A @ universal_class @ mactual )
              & ( subclass @ A @ B @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(23,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( inverse @ A ) @ ( inverse @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_substitution_1) ).

thf(138,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( qmltpeq @ A @ B @ mactual )
           => ( qmltpeq @ ( inverse @ A ) @ ( inverse @ B ) @ mactual ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(8,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ B @ C ) ) @ ( qmltpeq @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).

thf(101,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ( ( ( qmltpeq @ A @ B @ mactual )
                  & ( qmltpeq @ B @ C @ mactual ) )
               => ( qmltpeq @ A @ C @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(65,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( ordered_pair @ C @ A ) @ ( ordered_pair @ C @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_substitution_2) ).

thf(234,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ( ( qmltpeq @ A @ B @ mactual )
               => ( qmltpeq @ ( ordered_pair @ C @ A ) @ ( ordered_pair @ C @ B ) @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(15,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mequiv @ ( disjoint @ A @ B )
              @ ( mforall_di
                @ ^ [C: $i] : ( mnot @ ( mand @ ( member @ C @ A ) @ ( member @ C @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_defn) ).

thf(115,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( disjoint @ A @ B @ mactual )
            = ( ! [C: $i] :
                  ( ( eiw_di @ C @ mactual )
                 => ~ ( ( member @ C @ A @ mactual )
                      & ( member @ C @ B @ mactual ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(17,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( image @ C @ A ) @ ( image @ C @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image_substitution_2) ).

thf(120,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ( ( qmltpeq @ A @ B @ mactual )
               => ( qmltpeq @ ( image @ C @ A ) @ ( image @ C @ B ) @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(82,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] : ( mimplies @ ( member @ A @ universal_class ) @ ( member @ ( sum_class @ A ) @ universal_class ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class_0) ).

thf(269,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ( ( member @ A @ universal_class @ mactual )
       => ( member @ ( sum_class @ A ) @ universal_class @ mactual ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(50,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] : ( subclass @ ( flip @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip_0) ).

thf(202,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ( subclass @ ( flip @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) @ mactual ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(57,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mequiv @ ( subclass @ A @ B )
              @ ( mforall_di
                @ ^ [C: $i] : ( mimplies @ ( member @ C @ A ) @ ( member @ C @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_defn) ).

thf(217,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( subclass @ A @ B @ mactual )
            = ( ! [C: $i] :
                  ( ( eiw_di @ C @ mactual )
                 => ( ( member @ C @ A @ mactual )
                   => ( member @ C @ B @ mactual ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(85,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mimplies @ ( mand @ ( member @ A @ universal_class ) @ ( function @ B ) ) @ ( member @ ( image @ B @ A ) @ universal_class ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replacement) ).

thf(276,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( ( member @ A @ universal_class @ mactual )
              & ( function @ B @ mactual ) )
           => ( member @ ( image @ B @ A ) @ universal_class @ mactual ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(12,axiom,
    mlocal @ ( subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation_defn1) ).

thf(110,plain,
    subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ) @ mactual,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(47,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] : ( mimplies @ ( member @ C @ ( cross_product @ A @ B ) ) @ ( qmltpeq @ C @ ( ordered_pair @ ( first @ C ) @ ( second @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cross_product_0) ).

thf(196,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ( ( member @ C @ ( cross_product @ A @ B ) @ mactual )
               => ( qmltpeq @ C @ ( ordered_pair @ ( first @ C ) @ ( second @ C ) ) @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(31,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] :
                  ( mforall_di
                  @ ^ [D: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( restrict @ C @ A @ D ) @ ( restrict @ C @ B @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restrict_substitution_2) ).

thf(157,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ! [D: $i] :
                  ( ( eiw_di @ D @ mactual )
                 => ( ( qmltpeq @ A @ B @ mactual )
                   => ( qmltpeq @ ( restrict @ C @ A @ D ) @ ( restrict @ C @ B @ D ) @ mactual ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(29,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mequiv @ ( member @ ( ordered_pair @ A @ B ) @ element_relation ) @ ( mand @ ( member @ B @ universal_class ) @ ( member @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation_defn) ).

thf(152,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( member @ ( ordered_pair @ A @ B ) @ element_relation @ mactual )
            = ( ( member @ B @ universal_class @ mactual )
              & ( member @ A @ B @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(62,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( qmltpeq @ ( image @ B @ A ) @ ( range_of @ ( restrict @ B @ A @ universal_class ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image_defn) ).

thf(228,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( qmltpeq @ ( image @ B @ A ) @ ( range_of @ ( restrict @ B @ A @ universal_class ) ) @ mactual ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(78,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( cross_product @ A @ C ) @ ( cross_product @ B @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cross_product_substitution_1) ).

thf(261,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ( ( qmltpeq @ A @ B @ mactual )
               => ( qmltpeq @ ( cross_product @ A @ C ) @ ( cross_product @ B @ C ) @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(34,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] : ( mnot @ ( member @ A @ null_class ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_defn) ).

thf(164,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ~ ( member @ A @ null_class @ mactual ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(10,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] :
                  ( mforall_di
                  @ ^ [D: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( restrict @ A @ C @ D ) @ ( restrict @ B @ C @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restrict_substitution_1) ).

thf(106,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ! [D: $i] :
                  ( ( eiw_di @ D @ mactual )
                 => ( ( qmltpeq @ A @ B @ mactual )
                   => ( qmltpeq @ ( restrict @ A @ C @ D ) @ ( restrict @ B @ C @ D ) @ mactual ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(67,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] : ( qmltpeq @ A @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).

thf(238,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ( qmltpeq @ A @ A @ mactual ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(80,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] : ( qmltpeq @ ( singleton @ A ) @ ( unordered_pair @ A @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set_defn) ).

thf(265,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ( qmltpeq @ ( singleton @ A ) @ ( unordered_pair @ A @ A ) @ mactual ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(52,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ C @ A ) @ ( unordered_pair @ C @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_substitution_2) ).

thf(206,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ( ( qmltpeq @ A @ B @ mactual )
               => ( qmltpeq @ ( unordered_pair @ C @ A ) @ ( unordered_pair @ C @ B ) @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(72,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] : ( qmltpeq @ ( successor @ A ) @ ( union @ A @ ( singleton @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_defn) ).

thf(248,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ( qmltpeq @ ( successor @ A ) @ ( union @ A @ ( singleton @ A ) ) @ mactual ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(58,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( compose @ A @ C ) @ ( compose @ B @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_substitution_1) ).

thf(220,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ( ( qmltpeq @ A @ B @ mactual )
               => ( qmltpeq @ ( compose @ A @ C ) @ ( compose @ B @ C ) @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(4,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_substitution_1) ).

thf(92,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( qmltpeq @ A @ B @ mactual )
           => ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) @ mactual ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(74,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).

thf(252,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( qmltpeq @ A @ B @ mactual )
           => ( qmltpeq @ B @ A @ mactual ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(6,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( member @ ( unordered_pair @ A @ B ) @ universal_class ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_0) ).

thf(97,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( member @ ( unordered_pair @ A @ B ) @ universal_class @ mactual ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(60,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( sum_class @ A ) @ ( sum_class @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class_substitution_1) ).

thf(224,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( qmltpeq @ A @ B @ mactual )
           => ( qmltpeq @ ( sum_class @ A ) @ ( sum_class @ B ) @ mactual ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(43,axiom,
    ! [A: mworld] :
    ? [B: $i] : ( eiw_di @ B @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eiw_di_nonempty) ).

thf(188,plain,
    ! [A: mworld] :
    ? [B: $i] : ( eiw_di @ B @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(36,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_substitution_1) ).

thf(169,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ( ( qmltpeq @ A @ B @ mactual )
               => ( qmltpeq @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(76,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] : ( mequiv @ ( inductive @ A ) @ ( mand @ ( member @ null_class @ A ) @ ( subclass @ ( image @ successor_relation @ A ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive_defn) ).

thf(256,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ( ( inductive @ A @ mactual )
        = ( ( member @ null_class @ A @ mactual )
          & ( subclass @ ( image @ successor_relation @ A ) @ A @ mactual ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(19,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mequiv @ ( member @ B @ ( complement @ A ) ) @ ( mand @ ( member @ B @ universal_class ) @ ( mnot @ ( member @ B @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_0) ).

thf(124,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( member @ B @ ( complement @ A ) @ mactual )
            = ( ( member @ B @ universal_class @ mactual )
              & ~ ( member @ B @ A @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(55,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( ordered_pair @ A @ C ) @ ( ordered_pair @ B @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_substitution_1) ).

thf(212,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ( ( qmltpeq @ A @ B @ mactual )
               => ( qmltpeq @ ( ordered_pair @ A @ C ) @ ( ordered_pair @ B @ C ) @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(35,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] : ( mequiv @ ( member @ C @ ( union @ A @ B ) ) @ ( mor @ ( member @ C @ A ) @ ( member @ C @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).

thf(166,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ( ( member @ C @ ( union @ A @ B ) @ mactual )
                = ( ( member @ C @ A @ mactual )
                  | ( member @ C @ B @ mactual ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(33,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] : ( mequiv @ ( member @ A @ ( unordered_pair @ B @ C ) ) @ ( mand @ ( member @ A @ universal_class ) @ ( mor @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ A @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_defn) ).

thf(161,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ( ( member @ A @ ( unordered_pair @ B @ C ) @ mactual )
                = ( ( member @ A @ universal_class @ mactual )
                  & ( ( qmltpeq @ A @ B @ mactual )
                    | ( qmltpeq @ A @ C @ mactual ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(40,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] : ( mequiv @ ( member @ C @ ( intersection @ A @ B ) ) @ ( mand @ ( member @ C @ A ) @ ( member @ C @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_0) ).

thf(180,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ( ( member @ C @ ( intersection @ A @ B ) @ mactual )
                = ( ( member @ C @ A @ mactual )
                  & ( member @ C @ B @ mactual ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(28,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] :
                  ( mforall_di
                  @ ^ [D: $i] : ( mequiv @ ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( flip @ D ) ) @ ( mand @ ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) @ ( member @ ( ordered_pair @ ( ordered_pair @ B @ A ) @ C ) @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip_defn) ).

thf(149,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ! [D: $i] :
                  ( ( eiw_di @ D @ mactual )
                 => ( ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( flip @ D ) @ mactual )
                    = ( ( member @ ( ordered_pair @ ( ordered_pair @ A @ B ) @ C ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) @ mactual )
                      & ( member @ ( ordered_pair @ ( ordered_pair @ B @ A ) @ C ) @ D @ mactual ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(16,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( function @ A ) ) @ ( function @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function_substitution_1) ).

thf(118,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( ( qmltpeq @ A @ B @ mactual )
              & ( function @ A @ mactual ) )
           => ( function @ B @ mactual ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(51,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] : ( subclass @ ( rotate @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate_0) ).

thf(204,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ( subclass @ ( rotate @ A ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) @ mactual ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(77,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] :
                  ( mforall_di
                  @ ^ [D: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( restrict @ C @ D @ A ) @ ( restrict @ C @ D @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restrict_substitution_3) ).

thf(259,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ! [D: $i] :
                  ( ( eiw_di @ D @ mactual )
                 => ( ( qmltpeq @ A @ B @ mactual )
                   => ( qmltpeq @ ( restrict @ C @ D @ A ) @ ( restrict @ C @ D @ B ) @ mactual ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(26,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( qmltpeq @ ( apply @ A @ B ) @ ( sum_class @ ( image @ A @ ( singleton @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply_defn) ).

thf(144,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( qmltpeq @ ( apply @ A @ B ) @ ( sum_class @ ( image @ A @ ( singleton @ B ) ) ) @ mactual ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(66,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subclass @ A @ C ) ) @ ( subclass @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_substitution_1) ).

thf(236,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ( ( ( qmltpeq @ A @ B @ mactual )
                  & ( subclass @ A @ C @ mactual ) )
               => ( subclass @ B @ C @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(32,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( range_of @ A ) @ ( range_of @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_of_substitution_1) ).

thf(159,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( qmltpeq @ A @ B @ mactual )
           => ( qmltpeq @ ( range_of @ A ) @ ( range_of @ B ) @ mactual ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(63,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] : ( qmltpeq @ ( inverse @ A ) @ ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_defn) ).

thf(230,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ( qmltpeq @ ( inverse @ A ) @ ( domain_of @ ( flip @ ( cross_product @ A @ universal_class ) ) ) @ mactual ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(83,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( subclass @ ( compose @ B @ A ) @ ( cross_product @ universal_class @ universal_class ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_defn1) ).

thf(271,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( subclass @ ( compose @ B @ A ) @ ( cross_product @ universal_class @ universal_class ) @ mactual ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(53,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( disjoint @ A @ C ) ) @ ( disjoint @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_substitution_1) ).

thf(208,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ( ( ( qmltpeq @ A @ B @ mactual )
                  & ( disjoint @ A @ C @ mactual ) )
               => ( disjoint @ B @ C @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(9,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mequiv @ ( qmltpeq @ A @ B ) @ ( mand @ ( subclass @ A @ B ) @ ( subclass @ B @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality) ).

thf(103,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( qmltpeq @ A @ B @ mactual )
            = ( ( subclass @ A @ B @ mactual )
              & ( subclass @ B @ A @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(24,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] : ( qmltpeq @ ( range_of @ A ) @ ( domain_of @ ( inverse @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_of_defn) ).

thf(140,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ( qmltpeq @ ( range_of @ A ) @ ( domain_of @ ( inverse @ A ) ) @ mactual ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(68,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( power_class @ A ) @ ( power_class @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class_substitution_1) ).

thf(240,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( qmltpeq @ A @ B @ mactual )
           => ( qmltpeq @ ( power_class @ A ) @ ( power_class @ B ) @ mactual ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(30,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( image @ A @ C ) @ ( image @ B @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image_substitution_1) ).

thf(155,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ( ( qmltpeq @ A @ B @ mactual )
               => ( qmltpeq @ ( image @ A @ C ) @ ( image @ B @ C ) @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(48,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ C @ A ) @ ( union @ C @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_substitution_2) ).

thf(198,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ( ( qmltpeq @ A @ B @ mactual )
               => ( qmltpeq @ ( union @ C @ A ) @ ( union @ C @ B ) @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(11,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( cross_product @ C @ A ) @ ( cross_product @ C @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cross_product_substitution_2) ).

thf(108,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ( ( qmltpeq @ A @ B @ mactual )
               => ( qmltpeq @ ( cross_product @ C @ A ) @ ( cross_product @ C @ B ) @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(21,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mimplies @ ( mnot @ ( qmltpeq @ A @ null_class ) )
          @ ( mexists_di
            @ ^ [B: $i] : ( mand @ ( member @ B @ universal_class ) @ ( mand @ ( member @ B @ A ) @ ( disjoint @ B @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity) ).

thf(130,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ( ~ ( qmltpeq @ A @ null_class @ mactual )
       => ? [B: $i] :
            ( ( eiw_di @ B @ mactual )
            & ( member @ B @ universal_class @ mactual )
            & ( member @ B @ A @ mactual )
            & ( disjoint @ B @ A @ mactual ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(86,axiom,
    ( mlocal
    @ ( mexists_di
      @ ^ [A: $i] :
          ( mand @ ( function @ A )
          @ ( mforall_di
            @ ^ [B: $i] : ( mimplies @ ( member @ B @ universal_class ) @ ( mor @ ( qmltpeq @ B @ null_class ) @ ( member @ ( apply @ A @ B ) @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice) ).

thf(278,plain,
    ? [A: $i] :
      ( ( eiw_di @ A @ mactual )
      & ( function @ A @ mactual )
      & ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( member @ B @ universal_class @ mactual )
           => ( ( qmltpeq @ B @ null_class @ mactual )
              | ( member @ ( apply @ A @ B ) @ B @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(22,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mequiv @ ( member @ B @ ( domain_of @ A ) ) @ ( mand @ ( member @ B @ universal_class ) @ ( mnot @ ( qmltpeq @ ( restrict @ A @ ( singleton @ B ) @ universal_class ) @ null_class ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_of_0) ).

thf(135,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( member @ B @ ( domain_of @ A ) @ mactual )
            = ( ( member @ B @ universal_class @ mactual )
              & ~ ( qmltpeq @ ( restrict @ A @ ( singleton @ B ) @ universal_class ) @ null_class @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(61,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( flip @ A ) @ ( flip @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip_substitution_1) ).

thf(226,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( qmltpeq @ A @ B @ mactual )
           => ( qmltpeq @ ( flip @ A ) @ ( flip @ B ) @ mactual ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(81,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( domain_of @ A ) @ ( domain_of @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_of_substitution_1) ).

thf(267,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( qmltpeq @ A @ B @ mactual )
           => ( qmltpeq @ ( domain_of @ A ) @ ( domain_of @ B ) @ mactual ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(73,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] : ( qmltpeq @ ( restrict @ B @ A @ C ) @ ( intersection @ B @ ( cross_product @ A @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restrict_defn) ).

thf(250,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ( qmltpeq @ ( restrict @ B @ A @ C ) @ ( intersection @ B @ ( cross_product @ A @ C ) ) @ mactual ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(7,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ C @ A ) @ ( intersection @ C @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_substitution_2) ).

thf(99,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ( ( qmltpeq @ A @ B @ mactual )
               => ( qmltpeq @ ( intersection @ C @ A ) @ ( intersection @ C @ B ) @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(1,conjecture,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] : ( qmltpeq @ A @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_0) ).

thf(2,negated_conjecture,
    ~ ( mlocal
      @ ( mforall_di
        @ ^ [A: $i] : ( qmltpeq @ A @ A ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(87,plain,
    ~ ! [A: $i] :
        ( ( eiw_di @ A @ mactual )
       => ( qmltpeq @ A @ A @ mactual ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(42,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( second @ A ) @ ( second @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',second_substitution_1) ).

thf(186,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( qmltpeq @ A @ B @ mactual )
           => ( qmltpeq @ ( second @ A ) @ ( second @ B ) @ mactual ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(14,axiom,
    mlocal @ ( subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation_0) ).

thf(114,plain,
    subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ) @ mactual,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(37,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( complement @ A ) @ ( complement @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_substitution_1) ).

thf(171,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( qmltpeq @ A @ B @ mactual )
           => ( qmltpeq @ ( complement @ A ) @ ( complement @ B ) @ mactual ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(71,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( disjoint @ C @ A ) ) @ ( disjoint @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_substitution_2) ).

thf(246,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ( ( ( qmltpeq @ A @ B @ mactual )
                  & ( disjoint @ C @ A @ mactual ) )
               => ( disjoint @ C @ B @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(56,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] :
                  ( mforall_di
                  @ ^ [D: $i] : ( mequiv @ ( member @ ( ordered_pair @ ( ordered_pair @ B @ C ) @ D ) @ ( rotate @ A ) ) @ ( mand @ ( member @ ( ordered_pair @ ( ordered_pair @ B @ C ) @ D ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) @ ( member @ ( ordered_pair @ ( ordered_pair @ C @ D ) @ B ) @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate_defn) ).

thf(214,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ! [D: $i] :
                  ( ( eiw_di @ D @ mactual )
                 => ( ( member @ ( ordered_pair @ ( ordered_pair @ B @ C ) @ D ) @ ( rotate @ A ) @ mactual )
                    = ( ( member @ ( ordered_pair @ ( ordered_pair @ B @ C ) @ D ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) @ mactual )
                      & ( member @ ( ordered_pair @ ( ordered_pair @ C @ D ) @ B ) @ A @ mactual ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(27,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] : ( mequiv @ ( function @ A ) @ ( mand @ ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) ) @ ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function_defn) ).

thf(146,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ( ( function @ A @ mactual )
        = ( ( subclass @ A @ ( cross_product @ universal_class @ universal_class ) @ mactual )
          & ( subclass @ ( compose @ A @ ( inverse @ A ) ) @ identity_relation @ mactual ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(44,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( first @ A ) @ ( first @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',first_substitution_1) ).

thf(190,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( qmltpeq @ A @ B @ mactual )
           => ( qmltpeq @ ( first @ A ) @ ( first @ B ) @ mactual ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(41,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mequiv @ ( member @ A @ ( sum_class @ B ) )
              @ ( mexists_di
                @ ^ [C: $i] : ( mand @ ( member @ A @ C ) @ ( member @ C @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class_defn) ).

thf(183,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( member @ A @ ( sum_class @ B ) @ mactual )
            = ( ? [C: $i] :
                  ( ( eiw_di @ C @ mactual )
                  & ( member @ A @ C @ mactual )
                  & ( member @ C @ B @ mactual ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(84,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mequiv @ ( member @ ( ordered_pair @ A @ B ) @ successor_relation ) @ ( mand @ ( member @ A @ universal_class ) @ ( mand @ ( member @ B @ universal_class ) @ ( qmltpeq @ ( successor @ A ) @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation_defn2) ).

thf(273,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( member @ ( ordered_pair @ A @ B ) @ successor_relation @ mactual )
            = ( ( member @ A @ universal_class @ mactual )
              & ( member @ B @ universal_class @ mactual )
              & ( qmltpeq @ ( successor @ A ) @ B @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(54,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( rotate @ A ) @ ( rotate @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate_substitution_1) ).

thf(210,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( qmltpeq @ A @ B @ mactual )
           => ( qmltpeq @ ( rotate @ A ) @ ( rotate @ B ) @ mactual ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(69,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( qmltpeq @ ( ordered_pair @ A @ B ) @ ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_defn) ).

thf(242,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( qmltpeq @ ( ordered_pair @ A @ B ) @ ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ ( singleton @ B ) ) ) @ mactual ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(5,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] :
                  ( mforall_di
                  @ ^ [D: $i] : ( mequiv @ ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) ) @ ( mand @ ( member @ A @ C ) @ ( member @ B @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cross_product_defn) ).

thf(94,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ! [D: $i] :
                  ( ( eiw_di @ D @ mactual )
                 => ( ( member @ ( ordered_pair @ A @ B ) @ ( cross_product @ C @ D ) @ mactual )
                    = ( ( member @ A @ C @ mactual )
                      & ( member @ B @ D @ mactual ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(49,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( successor @ A ) @ ( successor @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_substitution_1) ).

thf(200,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ( ( qmltpeq @ A @ B @ mactual )
           => ( qmltpeq @ ( successor @ A ) @ ( successor @ B ) @ mactual ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(39,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ A @ C ) ) @ ( member @ B @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_substitution_1) ).

thf(178,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ( ( ( qmltpeq @ A @ B @ mactual )
                  & ( member @ A @ C @ mactual ) )
               => ( member @ B @ C @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(75,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( compose @ C @ A ) @ ( compose @ C @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_substitution_2) ).

thf(254,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ( ( qmltpeq @ A @ B @ mactual )
               => ( qmltpeq @ ( compose @ C @ A ) @ ( compose @ C @ B ) @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(18,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subclass @ C @ A ) ) @ ( subclass @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_substitution_2) ).

thf(122,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ( ( ( qmltpeq @ A @ B @ mactual )
                  & ( subclass @ C @ A @ mactual ) )
               => ( subclass @ C @ B @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(59,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( apply @ A @ C ) @ ( apply @ B @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply_substitution_1) ).

thf(222,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ( ( qmltpeq @ A @ B @ mactual )
               => ( qmltpeq @ ( apply @ A @ C ) @ ( apply @ B @ C ) @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(64,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ A @ C ) @ ( union @ B @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_substitution_1) ).

thf(232,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ( ( qmltpeq @ A @ B @ mactual )
               => ( qmltpeq @ ( union @ A @ C ) @ ( union @ B @ C ) @ mactual ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(3,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] : ( mimplies @ ( member @ A @ universal_class ) @ ( member @ ( power_class @ A ) @ universal_class ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class_0) ).

thf(90,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ( ( member @ A @ universal_class @ mactual )
       => ( member @ ( power_class @ A ) @ universal_class @ mactual ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(13,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mforall_di
              @ ^ [C: $i] :
                  ( mforall_di
                  @ ^ [D: $i] : ( mequiv @ ( member @ ( ordered_pair @ C @ D ) @ ( compose @ B @ A ) ) @ ( mand @ ( member @ C @ universal_class ) @ ( member @ D @ ( image @ B @ ( image @ B @ ( singleton @ C ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_defn2) ).

thf(111,plain,
    ! [A: $i] :
      ( ( eiw_di @ A @ mactual )
     => ! [B: $i] :
          ( ( eiw_di @ B @ mactual )
         => ! [C: $i] :
              ( ( eiw_di @ C @ mactual )
             => ! [D: $i] :
                  ( ( eiw_di @ D @ mactual )
                 => ( ( member @ ( ordered_pair @ C @ D ) @ ( compose @ B @ A ) @ mactual )
                    = ( ( member @ C @ universal_class @ mactual )
                      & ( member @ D @ ( image @ B @ ( image @ B @ ( singleton @ C ) ) ) @ mactual ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(282,plain,
    $false,
    inference(e,[status(thm)],[142,192,173,244,194,263,127,138,101,234,115,120,269,202,217,276,110,196,157,152,228,261,164,106,238,265,206,248,220,92,252,97,224,188,169,256,124,212,166,161,180,149,118,204,259,144,236,159,230,271,208,103,140,240,155,198,108,130,278,135,226,267,250,99,87,186,114,171,246,214,146,190,183,273,210,242,94,200,178,254,122,222,232,90,111]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET055^12 : TPTP v8.2.0. Released v8.1.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n015.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Mon May 20 12:18:24 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.96/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.67/1.05  % [INFO] 	 Parsing done (185ms). 
% 1.67/1.06  % [INFO] 	 Running in sequential loop mode. 
% 2.20/1.27  % [INFO] 	 eprover registered as external prover. 
% 2.33/1.27  % [INFO] 	 cvc4 registered as external prover. 
% 2.33/1.27  % [INFO] 	 Scanning for conjecture ... 
% 2.60/1.37  % [INFO] 	 Found a conjecture (or negated_conjecture) and 85 axioms. Running axiom selection ... 
% 2.60/1.43  % [INFO] 	 Axiom selection finished. Selected 84 axioms (removed 1 axioms). 
% 3.01/1.50  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 3.01/1.51  % [INFO] 	 Type checking passed. 
% 3.01/1.51  % [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 ... 
% 6.01/2.31  % External prover 'e' found a proof!
% 6.01/2.31  % [INFO] 	 Killing All external provers ... 
% 6.01/2.32  % Time passed: 1782ms (effective reasoning time: 1249ms)
% 6.01/2.32  % 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)>
% 6.01/2.32  % Axioms used in derivation (84): sum_class_defn, flip_defn, compose_defn1, member_substitution_1, image_defn, function_defn, domain_of_substitution_1, compose_substitution_2, element_relation_defn, range_of_substitution_1, restrict_substitution_3, unordered_pair_defn, successor_substitution_1, successor_relation_defn1, power_class_defn, cross_product_substitution_2, first_substitution_1, inverse_defn, disjoint_substitution_2, replacement, apply_substitution_2, singleton_set_defn, element_relation_0, intersection_substitution_1, flip_substitution_1, cross_product_defn, rotate_0, function_substitution_1, complement_0, sum_class_substitution_1, extensionality, cross_product_0, domain_of_0, unordered_pair_substitution_2, intersection_0, infinity, intersection_substitution_2, image_substitution_1, ordered_pair_substitution_1, power_class_substitution_1, disjoint_substitution_1, sum_class_0, union_substitution_2, subclass_substitution_1, reflexivity, inductive_substitution_1, restrict_substitution_2, null_class_defn, unordered_pair_substitution_1, complement_substitution_1, subclass_defn, rotate_substitution_1, image_substitution_2, eiw_di_nonempty, subclass_substitution_2, power_class_0, compose_defn2, restrict_defn, flip_0, union_substitution_1, ordered_pair_substitution_2, choice, disjoint_defn, compose_substitution_1, unordered_pair_0, apply_defn, regularity, restrict_substitution_1, second_substitution_1, successor_defn, ordered_pair_defn, class_elements_are_sets, range_of_defn, transitivity, union_defn, successor_relation_defn2, cross_product_substitution_1, rotate_defn, member_substitution_2, inductive_defn, inverse_substitution_1, apply_substitution_1, singleton_substitution_1, symmetry
% 6.01/2.32  % No. of inferences in proof: 172
% 6.01/2.32  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1782 ms resp. 1249 ms w/o parsing
% 6.51/2.41  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.51/2.42  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------