SET007 Axioms: SET007+233.ax


%------------------------------------------------------------------------------
% File     : SET007+233 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Classical and Non-classical Pasch Configuration
% Version  : [Urb08] axioms.
% English  : Classical and Non-classical Pasch Configuration in Ordered Affine
%            Planes

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : pasch [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   45 (   8 unit)
%            Number of atoms       :  490 (  15 equality)
%            Maximal formula depth :   24 (  14 average)
%            Number of connectives :  570 ( 125 ~  ;  16  |; 210  &)
%                                         (   6 <=>; 213 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   17 (   1 propositional; 0-5 arity)
%            Number of functors    :    1 (   0 constant; 1-1 arity)
%            Number of variables   :  200 (   0 singleton; 199 !;   1 ?)
%            Maximal term depth    :    2 (   1 average)
% SPC      : 

% Comments :  The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(d1_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ( v1_pasch(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( ( r1_diraf(A,C,F,B)
                                & r3_diraf(A,F,D,E)
                                & r2_diraf(A,C,D,E,B) )
                             => ( r3_diraf(A,F,C,D)
                                | r1_diraf(A,D,F,E) ) ) ) ) ) ) ) ) ) )).

fof(d2_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ( v2_pasch(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( ( r1_diraf(A,F,C,D)
                                & r3_diraf(A,F,B,E)
                                & r2_diraf(A,B,C,D,E) )
                             => ( r3_diraf(A,F,B,C)
                                | r1_diraf(A,F,B,E) ) ) ) ) ) ) ) ) ) )).

fof(d3_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ( v3_pasch(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ( ( r2_diraf(A,B,E,C,F)
                                    & r2_diraf(A,B,E,D,G)
                                    & r1_diraf(A,B,C,D)
                                    & r3_diraf(A,E,F,G) )
                                 => ( r3_diraf(A,B,C,E)
                                    | r1_diraf(A,E,F,G) ) ) ) ) ) ) ) ) ) ) )).

fof(d4_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ( v4_pasch(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ~ ( r1_diraf(A,B,C,E)
                                    & r1_diraf(A,C,F,D)
                                    & ~ r3_diraf(A,B,C,D)
                                    & ! [H] :
                                        ( m1_subset_1(H,u1_struct_0(A))
                                       => ~ ( r1_diraf(A,B,H,D)
                                            & r1_diraf(A,H,F,E) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d5_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ( v5_pasch(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ~ ( r1_diraf(A,B,C,E)
                                    & r1_diraf(A,B,F,D)
                                    & ~ r3_diraf(A,B,C,D)
                                    & ! [H] :
                                        ( m1_subset_1(H,u1_struct_0(A))
                                       => ~ ( r1_diraf(A,C,H,D)
                                            & r1_diraf(A,F,H,E) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d6_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ( v6_pasch(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ~ ( r2_analoaf(A,B,C,D,E)
                            & r2_analoaf(A,B,D,C,E)
                            & ~ r3_diraf(A,B,C,D)
                            & ! [F] :
                                ( m1_subset_1(F,u1_struct_0(A))
                               => ~ ( r1_diraf(A,B,F,E)
                                    & r1_diraf(A,C,F,D) ) ) ) ) ) ) ) ) ) )).

fof(t1_pasch,axiom,(
    $true )).

fof(t2_pasch,axiom,(
    $true )).

fof(t3_pasch,axiom,(
    $true )).

fof(t4_pasch,axiom,(
    $true )).

fof(t5_pasch,axiom,(
    $true )).

fof(t6_pasch,axiom,(
    $true )).

fof(t7_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ~ ( r2_analoaf(A,B,C,C,D)
                          & C != D
                          & B != C
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ~ ( r2_analoaf(A,E,C,C,F)
                                  & r2_diraf(A,E,B,D,F)
                                  & D != F
                                  & C != F ) ) ) ) ) ) ) ) )).

fof(t8_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ~ ( r2_analoaf(A,B,C,B,D)
                          & B != D
                          & C != B
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ~ ( r2_analoaf(A,B,E,B,F)
                                  & r2_diraf(A,E,C,D,F)
                                  & D != F ) ) ) ) ) ) ) ) )).

fof(t9_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ~ ( r2_diraf(A,B,C,B,D)
                          & B != C
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ~ ( r2_diraf(A,B,E,B,F)
                                  & r2_diraf(A,E,C,D,F) ) ) ) ) ) ) ) ) )).

fof(t10_pasch,axiom,(
    $true )).

fof(t11_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ( ( r3_diraf(A,B,D,E)
                                  & r3_diraf(A,B,C,F)
                                  & r3_diraf(A,B,C,G)
                                  & r2_diraf(A,C,D,E,F)
                                  & r2_diraf(A,C,D,E,G) )
                               => ( r3_diraf(A,B,C,D)
                                  | F = G ) ) ) ) ) ) ) ) ) )).

fof(t12_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r2_diraf(A,B,C,D,E)
                              & r2_diraf(A,B,C,D,F)
                              & r2_diraf(A,B,D,C,E)
                              & r2_diraf(A,B,D,C,F) )
                           => ( r3_diraf(A,B,C,D)
                              | E = F ) ) ) ) ) ) ) ) )).

fof(t13_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r1_diraf(A,C,B,E)
                              & r3_diraf(A,B,D,F)
                              & r2_diraf(A,C,D,F,E) )
                           => ( r3_diraf(A,B,C,D)
                              | r1_diraf(A,D,B,F) ) ) ) ) ) ) ) ) )).

fof(t14_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => v1_pasch(A) ) )).

fof(t15_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r1_diraf(A,B,C,D)
                              & r3_diraf(A,B,E,F)
                              & r2_diraf(A,E,C,D,F) )
                           => ( r3_diraf(A,B,E,C)
                              | r1_diraf(A,B,E,F) ) ) ) ) ) ) ) ) )).

fof(t16_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => v2_pasch(A) ) )).

fof(t17_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ( ( r2_diraf(A,B,D,C,E)
                                  & r2_diraf(A,B,D,F,G)
                                  & r1_diraf(A,B,C,F)
                                  & r3_diraf(A,D,E,G) )
                               => ( r3_diraf(A,B,C,D)
                                  | r1_diraf(A,D,E,G) ) ) ) ) ) ) ) ) ) )).

fof(t18_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => v3_pasch(A) ) )).

fof(t19_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r2_analoaf(A,C,B,B,E)
                              & r2_analoaf(A,D,B,B,F)
                              & r2_diraf(A,C,D,E,F) )
                           => ( r3_diraf(A,B,C,D)
                              | r2_analoaf(A,C,D,F,E) ) ) ) ) ) ) ) ) )).

fof(t20_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r2_analoaf(A,B,C,B,E)
                              & r2_analoaf(A,B,D,B,F)
                              & r2_diraf(A,C,D,E,F) )
                           => ( r3_diraf(A,B,C,D)
                              | r2_analoaf(A,C,D,E,F) ) ) ) ) ) ) ) ) )).

fof(t21_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r2_diraf(A,B,C,D,E)
                          & r2_diraf(A,B,D,C,E) )
                       => ( r3_diraf(A,B,C,D)
                          | ( r2_analoaf(A,B,C,D,E)
                            & r2_analoaf(A,B,D,C,E) ) ) ) ) ) ) ) ) )).

fof(t22_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r1_diraf(A,B,C,D)
                              & r2_analoaf(A,C,E,D,F)
                              & r2_analoaf(A,B,E,B,F) )
                           => ( r3_diraf(A,B,F,D)
                              | B = C
                              | r1_diraf(A,B,E,F) ) ) ) ) ) ) ) ) )).

fof(t23_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r1_diraf(A,B,C,D)
                              & r2_analoaf(A,E,C,F,D)
                              & r2_analoaf(A,B,E,B,F) )
                           => ( r3_diraf(A,B,D,F)
                              | B = E
                              | r1_diraf(A,B,E,F) ) ) ) ) ) ) ) ) )).

fof(t24_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ~ ( ~ r3_diraf(A,B,C,D)
                              & r2_analoaf(A,B,D,B,E)
                              & r2_analoaf(A,D,C,E,F)
                              & r3_diraf(A,C,B,F)
                              & B != F
                              & r1_diraf(A,C,B,F) ) ) ) ) ) ) ) )).

fof(t25_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ~ ( r2_analoaf(A,B,C,B,D)
                          & C != B
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ~ ( r2_analoaf(A,B,E,B,F)
                                  & r2_analoaf(A,C,E,D,F) ) ) ) ) ) ) ) ) )).

fof(t26_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ~ ( r1_diraf(A,B,C,D)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ~ ( r1_diraf(A,B,F,E)
                                  & r2_analoaf(A,D,E,C,F) ) ) ) ) ) ) ) ) )).

fof(t27_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ~ ( B != C
                          & r1_diraf(A,B,C,D)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ~ ( r1_diraf(A,B,E,F)
                                  & r2_analoaf(A,C,E,D,F) ) ) ) ) ) ) ) ) )).

fof(t28_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ~ ( ~ r3_diraf(A,B,C,D)
                          & r1_diraf(A,B,E,D)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ~ ( r1_diraf(A,B,F,C)
                                  & r2_analoaf(A,C,D,F,E) ) ) ) ) ) ) ) ) )).

fof(t29_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ? [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                      & r2_analoaf(A,B,E,C,D)
                      & r2_analoaf(A,B,C,E,D) ) ) ) ) ) )).

fof(t30_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ~ ( r2_analoaf(A,B,C,D,E)
                          & ~ r3_diraf(A,B,C,D)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ~ ( r1_diraf(A,B,F,E)
                                  & r1_diraf(A,C,F,D) ) ) ) ) ) ) ) ) )).

fof(t31_pasch,axiom,(
    $true )).

fof(t32_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => v6_pasch(A) ) )).

fof(t33_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ~ ( r2_diraf(A,B,C,D,E)
                          & r2_diraf(A,B,D,C,E)
                          & ~ r3_diraf(A,B,C,D)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ~ ( r3_diraf(A,F,B,E)
                                  & r3_diraf(A,F,C,D) ) ) ) ) ) ) ) ) )).

fof(t34_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ~ ( r2_diraf(A,B,C,D,E)
                              & r2_diraf(A,B,D,C,E)
                              & ~ r3_diraf(A,B,C,D)
                              & r3_diraf(A,F,B,E)
                              & r3_diraf(A,F,C,D)
                              & r3_diraf(A,F,B,C) ) ) ) ) ) ) ) )).

fof(t35_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ~ ( r1_diraf(A,B,C,D)
                              & r1_diraf(A,C,E,F)
                              & ~ r3_diraf(A,B,C,F)
                              & ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ~ ( r1_diraf(A,B,G,F)
                                      & r1_diraf(A,G,E,D) ) ) ) ) ) ) ) ) ) )).

fof(t36_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => v4_pasch(A) ) )).

fof(t37_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ~ ( r1_diraf(A,B,C,D)
                              & r1_diraf(A,B,E,F)
                              & ~ r3_diraf(A,B,C,F)
                              & ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ~ ( r1_diraf(A,C,G,F)
                                      & r1_diraf(A,E,G,D) ) ) ) ) ) ) ) ) ) )).

fof(t38_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => v5_pasch(A) ) )).

fof(t39_pasch,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ( ( r1_diraf(A,B,C,D)
                                  & r2_analoaf(A,B,C,E,F)
                                  & r3_diraf(A,E,F,G)
                                  & r2_analoaf(A,B,E,C,F)
                                  & r2_analoaf(A,B,E,D,G) )
                               => ( r3_diraf(A,B,C,E)
                                  | r1_diraf(A,E,F,G) ) ) ) ) ) ) ) ) ) )).
%------------------------------------------------------------------------------