SET007 Axioms: SET007+233.ax
%------------------------------------------------------------------------------
% File : SET007+233 : TPTP v8.2.0. 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 unt; 0 def)
% Number of atoms : 490 ( 15 equ)
% Maximal formula atoms : 17 ( 10 avg)
% Number of connectives : 570 ( 125 ~; 16 |; 210 &)
% ( 6 <=>; 213 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 14 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-5 aty)
% Number of functors : 1 ( 1 usr; 0 con; 1-1 aty)
% Number of variables : 200 ( 199 !; 1 ?)
% 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) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------