SET007 Axioms: SET007+254.ax
%------------------------------------------------------------------------------
% File : SET007+254 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Desargues Theorem In Projective 3-Space
% Version : [Urb08] axioms.
% English :
% 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 : projdes1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 30 ( 5 unt; 0 def)
% Number of atoms : 518 ( 26 equ)
% Maximal formula atoms : 39 ( 17 avg)
% Number of connectives : 587 ( 99 ~; 22 |; 292 &)
% ( 2 <=>; 172 =>; 0 <=; 0 <~>)
% Maximal formula depth : 47 ( 17 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-5 aty)
% Number of functors : 1 ( 1 usr; 0 con; 1-1 aty)
% Number of variables : 160 ( 159 !; 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(cc1_projdes1,axiom,
! [A] :
( l1_collsp(A)
=> ( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& ~ v7_anproj_2(A) )
=> ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& v5_anproj_2(A)
& ~ v7_anproj_2(A) ) ) ) ).
fof(t1_projdes1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& ~ v7_anproj_2(A)
& l1_collsp(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))
=> ( r1_collsp(A,B,C,D)
=> ( r1_collsp(A,C,D,B)
& r1_collsp(A,D,B,C)
& r1_collsp(A,C,B,D)
& r1_collsp(A,B,D,C)
& r1_collsp(A,D,C,B) ) ) ) ) ) ) ).
fof(t2_projdes1,axiom,
$true ).
fof(t3_projdes1,axiom,
$true ).
fof(t4_projdes1,axiom,
$true ).
fof(t5_projdes1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& ~ v7_anproj_2(A)
& l1_collsp(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))
=> r1_collsp(A,B,C,D) ) ) ) ) ).
fof(t6_projdes1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& ~ v7_anproj_2(A)
& l1_collsp(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_collsp(A,B,C,D)
& r1_collsp(A,B,C,E)
& B != E
& r1_collsp(A,B,E,D) ) ) ) ) ) ) ).
fof(t7_projdes1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& ~ v7_anproj_2(A)
& l1_collsp(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_collsp(A,B,C,E)
& r1_collsp(A,B,D,E) )
=> ( r1_collsp(A,B,C,D)
| B = E ) ) ) ) ) ) ) ).
fof(t8_projdes1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& ~ v7_anproj_2(A)
& l1_collsp(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_collsp(A,B,C,D)
& r1_collsp(A,B,D,E)
& r1_collsp(A,C,D,F)
& D != E
& r1_collsp(A,G,E,F)
& r1_collsp(A,B,C,G)
& B != G
& F = D ) ) ) ) ) ) ) ) ).
fof(d1_projdes1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& ~ v7_anproj_2(A)
& l1_collsp(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_projdes1(A,B,C,D,E)
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(A))
& r1_collsp(A,B,C,F)
& r1_collsp(A,D,E,F) ) ) ) ) ) ) ) ).
fof(t9_projdes1,axiom,
$true ).
fof(t10_projdes1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& ~ v7_anproj_2(A)
& l1_collsp(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_collsp(A,B,C,D)
& ~ r1_collsp(A,C,D,E)
& ~ r1_collsp(A,D,E,B)
& ~ r1_collsp(A,E,B,C) )
=> r1_projdes1(A,B,C,D,E) ) ) ) ) ) ) ).
fof(t11_projdes1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& ~ v7_anproj_2(A)
& l1_collsp(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_projdes1(A,B,C,D,E)
=> ( r1_projdes1(A,C,D,E,B)
& r1_projdes1(A,D,E,B,C)
& r1_projdes1(A,E,B,C,D)
& r1_projdes1(A,C,B,D,E)
& r1_projdes1(A,D,C,E,B)
& r1_projdes1(A,E,D,B,C)
& r1_projdes1(A,B,E,C,D)
& r1_projdes1(A,B,D,E,C)
& r1_projdes1(A,C,E,B,D)
& r1_projdes1(A,D,B,C,E)
& r1_projdes1(A,E,C,D,B)
& r1_projdes1(A,D,B,E,C)
& r1_projdes1(A,E,C,B,D)
& r1_projdes1(A,B,D,C,E)
& r1_projdes1(A,C,E,D,B)
& r1_projdes1(A,B,C,E,D)
& r1_projdes1(A,B,E,D,C)
& r1_projdes1(A,C,D,B,E)
& r1_projdes1(A,C,B,E,D)
& r1_projdes1(A,D,C,B,E)
& r1_projdes1(A,D,E,C,B)
& r1_projdes1(A,E,B,D,C)
& r1_projdes1(A,E,D,C,B) ) ) ) ) ) ) ) ).
fof(t12_projdes1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& ~ v7_anproj_2(A)
& l1_collsp(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))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ( ( r1_projdes1(A,B,C,D,E)
& r1_projdes1(A,B,C,D,F)
& r1_projdes1(A,B,C,D,G)
& r1_projdes1(A,B,C,D,H) )
=> ( r1_collsp(A,B,C,D)
| r1_projdes1(A,E,F,G,H) ) ) ) ) ) ) ) ) ) ) ).
fof(t13_projdes1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& ~ v7_anproj_2(A)
& l1_collsp(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))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ( ( r1_projdes1(A,E,F,G,B)
& r1_projdes1(A,E,F,G,D)
& r1_projdes1(A,E,F,G,C)
& r1_projdes1(A,B,C,D,H) )
=> ( r1_collsp(A,B,C,D)
| r1_projdes1(A,E,F,G,H) ) ) ) ) ) ) ) ) ) ) ).
fof(t14_projdes1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& ~ v7_anproj_2(A)
& l1_collsp(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_collsp(A,B,C,D)
& r1_projdes1(A,E,F,G,B)
& r1_projdes1(A,E,F,G,C) )
=> ( B = C
| r1_projdes1(A,E,F,G,D) ) ) ) ) ) ) ) ) ) ).
fof(t15_projdes1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& ~ v7_anproj_2(A)
& l1_collsp(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))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ~ ( ~ r1_collsp(A,B,C,D)
& r1_projdes1(A,B,C,D,E)
& r1_projdes1(A,B,C,D,F)
& r1_projdes1(A,B,C,D,G)
& r1_projdes1(A,B,C,D,H)
& ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ~ ( r1_collsp(A,E,F,I)
& r1_collsp(A,G,H,I) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t16_projdes1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& ~ v7_anproj_2(A)
& l1_collsp(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_projdes1(A,B,C,D,E) ) ) ) ) ) ).
fof(t17_projdes1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& ~ v7_anproj_2(A)
& l1_collsp(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))
=> ~ ( ~ r1_collsp(A,B,C,D)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> r1_projdes1(A,B,C,D,E) ) ) ) ) ) ) ).
fof(t18_projdes1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& ~ v7_anproj_2(A)
& l1_collsp(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
& B != D
& C != D
& B != E
& C != E
& E != D )
=> r1_projdes1(A,B,C,D,E) ) ) ) ) ) ) ).
fof(t19_projdes1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& ~ v7_anproj_2(A)
& l1_collsp(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_projdes1(A,B,C,D,E)
& r1_collsp(A,E,B,F)
& B != F
& r1_projdes1(A,B,C,D,F) ) ) ) ) ) ) ) ).
fof(t20_projdes1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& ~ v7_anproj_2(A)
& l1_collsp(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))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ( ( r1_projdes1(A,B,C,D,H)
& r1_projdes1(A,B,C,D,I)
& r1_projdes1(A,B,C,D,J)
& r1_projdes1(A,E,F,G,H)
& r1_projdes1(A,E,F,G,I)
& r1_projdes1(A,E,F,G,J) )
=> ( r1_collsp(A,B,C,D)
| r1_collsp(A,E,F,G)
| r1_projdes1(A,B,C,D,E)
| r1_collsp(A,H,I,J) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t21_projdes1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& ~ v7_anproj_2(A)
& l1_collsp(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))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(A))
=> ( ( r1_collsp(A,D,B,C)
& r1_collsp(A,B,E,I)
& r1_collsp(A,C,G,I)
& r1_collsp(A,E,F,J)
& r1_collsp(A,G,H,J)
& r1_collsp(A,B,F,K)
& r1_collsp(A,C,H,K) )
=> ( B = C
| r1_projdes1(A,B,E,F,D)
| r1_collsp(A,C,G,H)
| r1_collsp(A,I,J,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t22_projdes1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& ~ v7_anproj_2(A)
& l1_collsp(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_projdes1(A,B,C,D,E)
& r1_projdes1(A,B,C,D,F)
& ~ r1_collsp(A,B,C,F)
& r1_projdes1(A,B,C,E,F) ) ) ) ) ) ) ) ).
fof(t23_projdes1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& ~ v7_anproj_2(A)
& l1_collsp(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))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ( ( r1_collsp(A,E,B,F)
& r1_collsp(A,E,C,G)
& r1_collsp(A,E,D,H) )
=> ( r1_projdes1(A,B,C,D,E)
| E = F
| E = G
| E = H
| ( ~ r1_collsp(A,F,G,H)
& ~ r1_projdes1(A,F,G,H,E) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t24_projdes1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& ~ v7_anproj_2(A)
& l1_collsp(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))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(A))
=> ! [L] :
( m1_subset_1(L,u1_struct_0(A))
=> ! [M] :
( m1_subset_1(M,u1_struct_0(A))
=> ~ ( r1_projdes1(A,B,C,D,E)
& ~ r1_projdes1(A,B,C,D,F)
& ~ r1_projdes1(A,B,C,F,E)
& ~ r1_projdes1(A,C,D,F,E)
& ~ r1_projdes1(A,B,D,F,E)
& r1_collsp(A,E,F,G)
& r1_collsp(A,E,B,H)
& r1_collsp(A,E,C,I)
& r1_collsp(A,E,D,J)
& r1_collsp(A,B,F,K)
& r1_collsp(A,H,G,K)
& r1_collsp(A,C,F,L)
& r1_collsp(A,I,G,L)
& r1_collsp(A,D,F,M)
& E != H
& E != G
& F != G
& E != I
& r1_collsp(A,K,L,M) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d2_projdes1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& ~ v7_anproj_2(A)
& l1_collsp(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_projdes1(A,B,C,D,E)
<=> ( ~ r1_collsp(A,C,D,E)
& ~ r1_collsp(A,B,C,D)
& ~ r1_collsp(A,B,D,E)
& ~ r1_collsp(A,B,E,C) ) ) ) ) ) ) ) ).
fof(t25_projdes1,axiom,
$true ).
fof(t26_projdes1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& ~ v7_anproj_2(A)
& l1_collsp(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))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(A))
=> ( ( r1_collsp(A,B,C,F)
& r1_collsp(A,B,D,G)
& r1_collsp(A,B,E,H)
& r1_collsp(A,C,D,I)
& r1_collsp(A,F,G,I)
& r1_collsp(A,D,E,J)
& r1_collsp(A,G,H,J)
& r1_collsp(A,C,E,K)
& r1_collsp(A,F,H,K) )
=> ( r1_collsp(A,B,C,D)
| r1_collsp(A,B,D,E)
| r1_collsp(A,B,C,E)
| C = F
| D = G
| B = F
| B = G
| B = H
| r1_collsp(A,J,K,I) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t27_projdes1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& ~ v7_anproj_2(A)
& l1_collsp(A) )
=> v5_anproj_2(A) ) ).
%------------------------------------------------------------------------------