SET007 Axioms: SET007+222.ax
%------------------------------------------------------------------------------
% File : SET007+222 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Fano-Desargues Parallelity Spaces
% 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 : parsp_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 74 ( 11 unt; 0 def)
% Number of atoms : 872 ( 59 equ)
% Maximal formula atoms : 33 ( 11 avg)
% Number of connectives : 953 ( 155 ~; 20 |; 389 &)
% ( 5 <=>; 384 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 13 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 1 prp; 0-5 aty)
% Number of functors : 13 ( 13 usr; 0 con; 1-8 aty)
% Number of variables : 348 ( 342 !; 6 ?)
% 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(rc1_parsp_2,axiom,
? [A] :
( l1_parsp_1(A)
& ~ v3_struct_0(A)
& v1_parsp_1(A)
& v2_parsp_1(A)
& v1_parsp_2(A) ) ).
fof(t1_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ( ~ v3_struct_0(k9_parsp_1(A))
& v2_parsp_1(k9_parsp_1(A))
& l1_parsp_1(k9_parsp_1(A)) ) ) ).
fof(t2_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k9_parsp_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k9_parsp_1(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k9_parsp_1(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k9_parsp_1(A)))
=> ( r1_parsp_1(k9_parsp_1(A),B,C,D,E)
<=> ? [F] :
( m1_subset_1(F,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
& ? [G] :
( m1_subset_1(G,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
& ? [H] :
( m1_subset_1(H,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
& ? [I] :
( m1_subset_1(I,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
& k5_domain_1(u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),B,C,D,E) = k4_mcart_1(F,G,H,I)
& ~ ( ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ~ ( k10_group_1(A,J,k6_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F),k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G))) = k6_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),H),k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),I))
& k10_group_1(A,J,k6_rlvect_1(A,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F),k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G))) = k6_rlvect_1(A,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),H),k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),I))
& k10_group_1(A,J,k6_rlvect_1(A,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F),k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G))) = k6_rlvect_1(A,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),H),k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),I)) ) )
& ~ ( k6_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F),k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G)) = k1_rlvect_1(A)
& k6_rlvect_1(A,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F),k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G)) = k1_rlvect_1(A)
& k6_rlvect_1(A,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F),k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G)) = k1_rlvect_1(A) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t3_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k9_parsp_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k9_parsp_1(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k9_parsp_1(A)))
=> ! [E] :
( m1_subset_1(E,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
=> ! [F] :
( m1_subset_1(F,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
=> ! [G] :
( m1_subset_1(G,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
=> ( k5_domain_1(u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),B,C,B,D) = k4_mcart_1(E,F,E,G)
=> ( r1_parsp_1(k9_parsp_1(A),B,C,B,D)
| ( E != F
& E != G
& F != G ) ) ) ) ) ) ) ) ) ) ).
fof(t4_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k9_parsp_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k9_parsp_1(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k9_parsp_1(A)))
=> ! [E] :
( m1_subset_1(E,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
=> ! [F] :
( m1_subset_1(F,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
=> ! [G] :
( m1_subset_1(G,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ( ( k5_domain_1(u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),B,C,B,D) = k4_mcart_1(E,F,E,G)
& k10_group_1(A,H,k6_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E),k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F))) = k10_group_1(A,I,k6_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E),k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G)))
& k10_group_1(A,H,k6_rlvect_1(A,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E),k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F))) = k10_group_1(A,I,k6_rlvect_1(A,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E),k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G)))
& k10_group_1(A,H,k6_rlvect_1(A,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E),k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F))) = k10_group_1(A,I,k6_rlvect_1(A,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E),k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G))) )
=> ( r1_parsp_1(k9_parsp_1(A),B,C,B,D)
| ( H = k1_rlvect_1(A)
& I = k1_rlvect_1(A) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t5_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k9_parsp_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k9_parsp_1(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k9_parsp_1(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k9_parsp_1(A)))
=> ! [F] :
( m1_subset_1(F,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
=> ! [G] :
( m1_subset_1(G,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
=> ! [H] :
( m1_subset_1(H,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
=> ! [I] :
( m1_subset_1(I,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
=> ( ( r1_parsp_1(k9_parsp_1(A),B,C,D,E)
& r1_parsp_1(k9_parsp_1(A),B,D,C,E)
& k5_domain_1(u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),B,C,D,E) = k4_mcart_1(F,G,H,I) )
=> ( r1_parsp_1(k9_parsp_1(A),B,C,B,D)
| ( k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),I) = k6_rlvect_1(A,k4_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G),k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),H)),k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F))
& k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),I) = k6_rlvect_1(A,k4_rlvect_1(A,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G),k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),H)),k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F))
& k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),I) = k6_rlvect_1(A,k4_rlvect_1(A,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G),k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),H)),k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t6_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ~ ! [B] :
( m1_subset_1(B,u1_struct_0(k9_parsp_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k9_parsp_1(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k9_parsp_1(A)))
=> r1_parsp_1(k9_parsp_1(A),B,C,B,D) ) ) ) ) ).
fof(t7_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k9_parsp_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k9_parsp_1(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k9_parsp_1(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k9_parsp_1(A)))
=> ( ( r1_parsp_1(k9_parsp_1(A),B,C,D,E)
& r1_parsp_1(k9_parsp_1(A),D,B,C,E)
& r1_parsp_1(k9_parsp_1(A),D,C,B,E) )
=> ( k4_rlvect_1(A,k2_group_1(A),k2_group_1(A)) = k1_rlvect_1(A)
| r1_parsp_1(k9_parsp_1(A),D,B,D,C) ) ) ) ) ) ) ) ).
fof(t8_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k9_parsp_1(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k9_parsp_1(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k9_parsp_1(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k9_parsp_1(A)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k9_parsp_1(A)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k9_parsp_1(A)))
=> ( ( r1_parsp_1(k9_parsp_1(A),B,C,D,F)
& r1_parsp_1(k9_parsp_1(A),B,C,E,G)
& r1_parsp_1(k9_parsp_1(A),B,D,C,F)
& r1_parsp_1(k9_parsp_1(A),B,E,C,G) )
=> ( r1_parsp_1(k9_parsp_1(A),B,C,B,D)
| r1_parsp_1(k9_parsp_1(A),B,C,B,E)
| r1_parsp_1(k9_parsp_1(A),D,E,F,G) ) ) ) ) ) ) ) ) ) ).
fof(d1_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& l1_parsp_1(A) )
=> ( v1_parsp_2(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_parsp_1(A,B,C,B,D) ) ) )
& ! [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_parsp_1(A,C,D,B,E)
& r1_parsp_1(A,B,C,D,E)
& r1_parsp_1(A,B,D,C,E) )
=> r1_parsp_1(A,B,C,B,D) ) ) ) ) )
& ! [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_parsp_1(A,B,E,C,F)
& r1_parsp_1(A,B,E,D,G)
& r1_parsp_1(A,B,C,E,F)
& r1_parsp_1(A,B,D,E,G) )
=> ( r1_parsp_1(A,B,E,B,C)
| r1_parsp_1(A,B,E,B,D)
| r1_parsp_1(A,C,D,F,G) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t9_parsp_2,axiom,
$true ).
fof(t10_parsp_2,axiom,
$true ).
fof(t11_parsp_2,axiom,
$true ).
fof(t12_parsp_2,axiom,
$true ).
fof(t13_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( B != C
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r1_parsp_1(A,B,C,B,D) ) ) ) ) ) ).
fof(d2_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D)
<=> r1_parsp_1(A,B,C,B,D) ) ) ) ) ) ).
fof(t14_parsp_2,axiom,
$true ).
fof(t15_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D)
=> ( r1_parsp_2(A,B,D,C)
& r1_parsp_2(A,D,C,B)
& r1_parsp_2(A,C,B,D)
& r1_parsp_2(A,C,D,B)
& r1_parsp_2(A,D,B,C) ) ) ) ) ) ) ).
fof(t16_parsp_2,axiom,
$true ).
fof(t17_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D)
& r1_parsp_1(A,B,C,E,F)
& r1_parsp_1(A,B,D,E,G)
& E != F
& E != G
& r1_parsp_2(A,E,F,G) ) ) ) ) ) ) ) ) ).
fof(t18_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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))
=> ( ~ ( B != C
& C != D
& D != B )
=> r1_parsp_2(A,B,C,D) ) ) ) ) ) ).
fof(t19_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D)
& r1_parsp_2(A,B,C,E)
& r1_parsp_2(A,B,C,F) )
=> ( B = C
| r1_parsp_2(A,D,E,F) ) ) ) ) ) ) ) ) ).
fof(t20_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( B != C
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r1_parsp_2(A,B,C,D) ) ) ) ) ) ).
fof(t21_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D)
& r1_parsp_2(A,B,C,E) )
=> r1_parsp_1(A,B,C,D,E) ) ) ) ) ) ) ).
fof(t22_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D)
& r1_parsp_1(A,B,C,D,E)
& r1_parsp_2(A,B,C,E) ) ) ) ) ) ) ).
fof(t23_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D)
& r1_parsp_1(A,B,C,D,E)
& D != E
& r1_parsp_2(A,B,C,F)
& r1_parsp_2(A,D,E,F) ) ) ) ) ) ) ) ).
fof(t24_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D)
& r1_parsp_2(A,B,C,E)
& r1_parsp_2(A,B,D,E)
& B != E ) ) ) ) ) ) ).
fof(t25_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D)
& r1_parsp_2(A,B,C,E)
& r1_parsp_2(A,B,D,F) )
=> ( B = C
| B = D
| r1_parsp_1(A,C,D,E,F) ) ) ) ) ) ) ) ) ).
fof(t26_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,F)
& r1_parsp_2(A,B,C,G)
& r1_parsp_2(A,D,E,F)
& r1_parsp_2(A,D,E,G) )
=> ( r1_parsp_1(A,B,C,D,E)
| F = G ) ) ) ) ) ) ) ) ) ).
fof(t27_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D)
& r1_parsp_1(A,B,C,D,E) )
=> ( B = C
| r1_parsp_1(A,B,D,C,E) ) ) ) ) ) ) ) ).
fof(t28_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D)
& r1_parsp_1(A,B,C,D,E) )
=> ( B = C
| r1_parsp_1(A,D,C,D,E) ) ) ) ) ) ) ) ).
fof(t29_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,E)
& r1_parsp_2(A,B,D,F)
& r1_parsp_2(A,B,D,G)
& r1_parsp_1(A,C,D,E,F)
& r1_parsp_1(A,C,D,E,G) )
=> ( r1_parsp_2(A,B,C,D)
| F = G ) ) ) ) ) ) ) ) ) ).
fof(t30_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D)
& r1_parsp_2(A,B,C,E) )
=> ( B = C
| r1_parsp_2(A,B,D,E) ) ) ) ) ) ) ) ).
fof(t31_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D)
& r1_parsp_2(A,B,D,E) )
=> ( B = D
| r1_parsp_2(A,C,D,E) ) ) ) ) ) ) ) ).
fof(d3_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D,E)
<=> ( ~ r1_parsp_2(A,B,C,D)
& r1_parsp_1(A,B,C,D,E)
& r1_parsp_1(A,B,D,C,E) ) ) ) ) ) ) ) ).
fof(t32_parsp_2,axiom,
$true ).
fof(t33_parsp_2,axiom,
$true ).
fof(t34_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D,E)
=> ( B != C
& C != D
& D != B
& B != E
& C != E
& D != E ) ) ) ) ) ) ) ).
fof(t35_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D,E)
=> ( ~ r1_parsp_2(A,B,C,D)
& ~ r1_parsp_2(A,C,B,E)
& ~ r1_parsp_2(A,D,E,B)
& ~ r1_parsp_2(A,E,D,C) ) ) ) ) ) ) ) ).
fof(t36_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D,E)
=> ( ~ r1_parsp_2(A,B,C,D)
& ~ r1_parsp_2(A,C,B,E)
& ~ r1_parsp_2(A,D,E,B)
& ~ r1_parsp_2(A,E,D,C)
& ~ r1_parsp_2(A,B,D,C)
& ~ r1_parsp_2(A,C,B,D)
& ~ r1_parsp_2(A,C,D,B)
& ~ r1_parsp_2(A,D,B,C)
& ~ r1_parsp_2(A,D,C,B)
& ~ r1_parsp_2(A,C,E,B)
& ~ r1_parsp_2(A,B,C,E)
& ~ r1_parsp_2(A,B,E,C)
& ~ r1_parsp_2(A,E,B,C)
& ~ r1_parsp_2(A,E,C,B)
& ~ r1_parsp_2(A,D,B,E)
& ~ r1_parsp_2(A,B,D,E)
& ~ r1_parsp_2(A,B,E,D)
& ~ r1_parsp_2(A,E,B,D)
& ~ r1_parsp_2(A,E,D,B)
& ~ r1_parsp_2(A,E,C,D)
& ~ r1_parsp_2(A,C,D,E)
& ~ r1_parsp_2(A,C,E,D)
& ~ r1_parsp_2(A,D,C,E)
& ~ r1_parsp_2(A,D,E,C) ) ) ) ) ) ) ) ).
fof(t37_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D,E)
& r1_parsp_2(A,B,C,F)
& r1_parsp_2(A,D,E,F) ) ) ) ) ) ) ) ).
fof(t38_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D,E)
=> r2_parsp_2(A,B,D,C,E) ) ) ) ) ) ) ).
fof(t39_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D,E)
=> r2_parsp_2(A,D,E,B,C) ) ) ) ) ) ) ).
fof(t40_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D,E)
=> r2_parsp_2(A,C,B,E,D) ) ) ) ) ) ) ).
fof(t41_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D,E)
=> ( r2_parsp_2(A,B,D,C,E)
& r2_parsp_2(A,D,E,B,C)
& r2_parsp_2(A,C,B,E,D)
& r2_parsp_2(A,D,B,E,C)
& r2_parsp_2(A,E,C,D,B)
& r2_parsp_2(A,C,E,B,D)
& r2_parsp_2(A,E,D,C,B) ) ) ) ) ) ) ) ).
fof(t42_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ r2_parsp_2(A,B,C,D,E) ) ) ) ) ) ) ).
fof(t43_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D,E)
& r2_parsp_2(A,B,C,D,F) )
=> E = F ) ) ) ) ) ) ) ).
fof(t44_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D,E)
& r1_parsp_1(A,B,E,C,D) ) ) ) ) ) ) ).
fof(t45_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D,E)
& r2_parsp_2(A,B,C,E,D) ) ) ) ) ) ) ).
fof(t46_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( B != C
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r1_parsp_2(A,B,C,D)
& D != B
& D != C ) ) ) ) ) ) ).
fof(t47_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D,E)
& r2_parsp_2(A,B,C,F,G) )
=> r1_parsp_1(A,D,F,E,G) ) ) ) ) ) ) ) ) ).
fof(t48_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,E,F,B,C)
& r2_parsp_2(A,E,F,D,G) )
=> ( r1_parsp_2(A,B,C,D)
| r2_parsp_2(A,B,C,D,G) ) ) ) ) ) ) ) ) ) ).
fof(t49_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D)
& r2_parsp_2(A,B,E,C,F)
& r2_parsp_2(A,B,E,D,G) )
=> ( C = D
| r2_parsp_2(A,C,F,D,G) ) ) ) ) ) ) ) ) ) ).
fof(t50_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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))
=> ( ( r2_parsp_2(A,B,C,D,E)
& r2_parsp_2(A,B,C,F,G)
& r2_parsp_2(A,D,E,H,I) )
=> r1_parsp_1(A,F,H,G,I) ) ) ) ) ) ) ) ) ) ) ).
fof(t51_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( B != C
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ r2_parsp_2(A,B,C,D,E) ) ) ) ) ) ) ).
fof(t52_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( B != C
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ r2_parsp_2(A,B,D,E,C) ) ) ) ) ) ) ).
fof(d4_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D,E)
<=> ~ ( ~ ( B = C
& D = E )
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ~ ( r2_parsp_2(A,F,G,B,C)
& r2_parsp_2(A,F,G,D,E) ) ) ) ) ) ) ) ) ) ) ).
fof(t53_parsp_2,axiom,
$true ).
fof(t54_parsp_2,axiom,
$true ).
fof(t55_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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))
=> ( r3_parsp_2(A,B,B,C,D)
=> C = D ) ) ) ) ) ).
fof(t56_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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))
=> ( r3_parsp_2(A,B,C,D,D)
=> B = C ) ) ) ) ) ).
fof(t57_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_parsp_2(A,B,C,C,B)
=> B = C ) ) ) ) ).
fof(t58_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D,E)
=> r1_parsp_1(A,B,C,D,E) ) ) ) ) ) ) ).
fof(t59_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D,E)
=> r1_parsp_1(A,B,D,C,E) ) ) ) ) ) ) ).
fof(t60_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D,E)
=> ( r1_parsp_2(A,B,C,D)
| r2_parsp_2(A,B,C,D,E) ) ) ) ) ) ) ) ).
fof(t61_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D,E)
=> r3_parsp_2(A,B,C,D,E) ) ) ) ) ) ) ).
fof(t62_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D,E)
& r1_parsp_2(A,B,C,D)
& r2_parsp_2(A,F,G,B,C) )
=> r2_parsp_2(A,F,G,D,E) ) ) ) ) ) ) ) ) ).
fof(t63_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D,E)
& r3_parsp_2(A,B,C,D,F) )
=> E = F ) ) ) ) ) ) ) ).
fof(t64_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D,E) ) ) ) ) ) ).
fof(t65_parsp_2,axiom,
$true ).
fof(t66_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r3_parsp_2(A,B,C,B,C) ) ) ) ).
fof(t67_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D,E)
& r3_parsp_2(A,B,C,F,G) )
=> r3_parsp_2(A,D,E,F,G) ) ) ) ) ) ) ) ) ).
fof(t68_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D,E)
=> r3_parsp_2(A,D,E,B,C) ) ) ) ) ) ) ).
fof(t69_parsp_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& v1_parsp_2(A)
& l1_parsp_1(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_parsp_2(A,B,C,D,E)
=> r3_parsp_2(A,C,B,E,D) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------