SET007 Axioms: SET007+214.ax
%------------------------------------------------------------------------------
% File : SET007+214 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : 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_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 91 ( 24 unt; 0 def)
% Number of atoms : 925 ( 60 equ)
% Maximal formula atoms : 30 ( 10 avg)
% Number of connectives : 985 ( 151 ~; 4 |; 576 &)
% ( 11 <=>; 243 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 11 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 1 prp; 0-5 aty)
% Number of functors : 27 ( 27 usr; 0 con; 1-8 aty)
% Number of variables : 260 ( 235 !; 25 ?)
% 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_1,axiom,
? [A] :
( l1_parsp_1(A)
& v1_parsp_1(A) ) ).
fof(rc2_parsp_1,axiom,
? [A] :
( l1_parsp_1(A)
& ~ v3_struct_0(A) ) ).
fof(fc1_parsp_1,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) )
=> ~ v1_xboole_0(k5_parsp_1(A)) ) ).
fof(fc2_parsp_1,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) )
=> ~ v1_xboole_0(k6_parsp_1(A)) ) ).
fof(fc3_parsp_1,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))
& v1_parsp_1(k9_parsp_1(A)) ) ) ).
fof(rc3_parsp_1,axiom,
? [A] :
( l1_parsp_1(A)
& ~ v3_struct_0(A)
& v1_parsp_1(A)
& v2_parsp_1(A) ) ).
fof(d1_parsp_1,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] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
& m2_relset_1(B,k2_zfmisc_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) )
=> ( B = k1_parsp_1(A)
<=> ! [C] :
( m1_subset_1(C,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
=> k2_binop_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),B,C,D) = k4_domain_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k4_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C),k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D)),k4_rlvect_1(A,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C),k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D)),k4_rlvect_1(A,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C),k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D))) ) ) ) ) ) ).
fof(d2_parsp_1,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,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
=> k2_parsp_1(A,B,C) = k2_binop_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k1_parsp_1(A),B,C) ) ) ) ).
fof(t1_parsp_1,axiom,
$true ).
fof(t2_parsp_1,axiom,
$true ).
fof(t3_parsp_1,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,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
=> k2_parsp_1(A,B,C) = k4_domain_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k4_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B),k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C)),k4_rlvect_1(A,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B),k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C)),k4_rlvect_1(A,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B),k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C))) ) ) ) ).
fof(t4_parsp_1,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(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))
=> k2_parsp_1(A,k4_domain_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B,C,D),k4_domain_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E,F,G)) = k4_domain_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k4_rlvect_1(A,B,E),k4_rlvect_1(A,C,F),k4_rlvect_1(A,D,G)) ) ) ) ) ) ) ) ).
fof(d3_parsp_1,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] :
( ( v1_funct_1(B)
& v1_funct_2(B,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
& m2_relset_1(B,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) )
=> ( B = k3_parsp_1(A)
<=> ! [C] :
( m1_subset_1(C,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
=> k8_funct_2(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),B,C) = k4_domain_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k5_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C)),k5_rlvect_1(A,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C)),k5_rlvect_1(A,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C))) ) ) ) ) ).
fof(d4_parsp_1,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,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
=> k4_parsp_1(A,B) = k8_funct_2(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_parsp_1(A),B) ) ) ).
fof(t5_parsp_1,axiom,
$true ).
fof(t6_parsp_1,axiom,
$true ).
fof(t7_parsp_1,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,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
=> k4_parsp_1(A,B) = k4_domain_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k5_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B)),k5_rlvect_1(A,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B)),k5_rlvect_1(A,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B))) ) ) ).
fof(d5_parsp_1,axiom,
! [A,B] :
( m1_parsp_1(B,A)
<=> r1_tarski(B,k4_zfmisc_1(A,A,A,A)) ) ).
fof(d6_parsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(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_1(A,B,C,D,E)
<=> r2_hidden(k5_domain_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B,C,D,E),u1_parsp_1(A)) ) ) ) ) ) ) ).
fof(d7_parsp_1,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) )
=> k5_parsp_1(A) = k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)) ) ).
fof(d8_parsp_1,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) )
=> k6_parsp_1(A) = k4_zfmisc_1(k5_parsp_1(A),k5_parsp_1(A),k5_parsp_1(A),k5_parsp_1(A)) ) ).
fof(d9_parsp_1,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] :
( B = k7_parsp_1(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ( r2_hidden(C,k6_parsp_1(A))
& ? [D] :
( m1_subset_1(D,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(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)))
& C = k5_domain_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),D,E,F,G)
& k6_rlvect_1(A,k10_group_1(A,k6_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D),k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E)),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))),k10_group_1(A,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,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D),k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E)))) = k1_rlvect_1(A)
& k6_rlvect_1(A,k10_group_1(A,k6_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D),k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E)),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))),k10_group_1(A,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,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D),k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E)))) = k1_rlvect_1(A)
& k6_rlvect_1(A,k10_group_1(A,k6_rlvect_1(A,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D),k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E)),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))),k10_group_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)),k6_rlvect_1(A,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D),k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E)))) = k1_rlvect_1(A) ) ) ) ) ) ) ) ) ).
fof(t8_parsp_1,axiom,
$true ).
fof(t9_parsp_1,axiom,
$true ).
fof(t10_parsp_1,axiom,
$true ).
fof(t11_parsp_1,axiom,
$true ).
fof(t12_parsp_1,axiom,
$true ).
fof(t13_parsp_1,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) )
=> r1_tarski(k7_parsp_1(A),k4_zfmisc_1(k5_parsp_1(A),k5_parsp_1(A),k5_parsp_1(A),k5_parsp_1(A))) ) ).
fof(d10_parsp_1,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) )
=> k8_parsp_1(A) = k7_parsp_1(A) ) ).
fof(d11_parsp_1,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) )
=> k9_parsp_1(A) = g1_parsp_1(k5_parsp_1(A),k8_parsp_1(A)) ) ).
fof(t14_parsp_1,axiom,
$true ).
fof(t15_parsp_1,axiom,
$true ).
fof(t16_parsp_1,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) )
=> u1_struct_0(k9_parsp_1(A)) = k5_parsp_1(A) ) ).
fof(t17_parsp_1,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) )
=> u1_parsp_1(k9_parsp_1(A)) = k8_parsp_1(A) ) ).
fof(t18_parsp_1,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)
<=> r2_hidden(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),k8_parsp_1(A)) ) ) ) ) ) ) ).
fof(t19_parsp_1,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)))
=> ( r2_hidden(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),k8_parsp_1(A))
<=> ( r2_hidden(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),k6_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)))
& 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) = k5_domain_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),F,G,H,I)
& k6_rlvect_1(A,k10_group_1(A,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,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,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)),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,k10_group_1(A,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,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))),k10_group_1(A,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)),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)
& k6_rlvect_1(A,k10_group_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)),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))),k10_group_1(A,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)),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(t20_parsp_1,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)
<=> ( r2_hidden(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),k6_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)))
& 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) = k5_domain_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),F,G,H,I)
& k6_rlvect_1(A,k10_group_1(A,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,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,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)),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,k10_group_1(A,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,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))),k10_group_1(A,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)),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)
& k6_rlvect_1(A,k10_group_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)),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))),k10_group_1(A,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)),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(t21_parsp_1,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) )
=> u1_struct_0(k9_parsp_1(A)) = k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)) ) ).
fof(t22_parsp_1,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)))
=> r2_hidden(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),k6_parsp_1(A)) ) ) ) ) ) ).
fof(t23_parsp_1,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) = k5_domain_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),F,G,H,I)
& k6_rlvect_1(A,k10_group_1(A,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,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,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)),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,k10_group_1(A,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,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))),k10_group_1(A,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)),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)
& k6_rlvect_1(A,k10_group_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)),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))),k10_group_1(A,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)),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(t24_parsp_1,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)))
=> r1_parsp_1(k9_parsp_1(A),B,C,C,B) ) ) ) ).
fof(t25_parsp_1,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,D,D) ) ) ) ) ).
fof(t26_parsp_1,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,E)
& r1_parsp_1(k9_parsp_1(A),B,C,F,G)
& ~ r1_parsp_1(k9_parsp_1(A),D,E,F,G)
& B != C ) ) ) ) ) ) ) ) ).
fof(t27_parsp_1,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)
=> r1_parsp_1(k9_parsp_1(A),C,B,C,D) ) ) ) ) ) ).
fof(t28_parsp_1,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),B,D,C,E) ) ) ) ) ) ).
fof(d12_parsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_parsp_1(A) )
=> ( v2_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))
=> ( r1_parsp_1(A,B,C,C,B)
& r1_parsp_1(A,B,C,D,D)
& ~ ( r1_parsp_1(A,B,C,F,G)
& r1_parsp_1(A,B,C,H,I)
& ~ r1_parsp_1(A,F,G,H,I)
& B != C )
& ( r1_parsp_1(A,B,C,B,D)
=> r1_parsp_1(A,C,B,C,D) )
& ? [J] :
( m1_subset_1(J,u1_struct_0(A))
& r1_parsp_1(A,B,C,D,J)
& r1_parsp_1(A,B,D,C,J) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t29_parsp_1,axiom,
$true ).
fof(t30_parsp_1,axiom,
$true ).
fof(t31_parsp_1,axiom,
$true ).
fof(t32_parsp_1,axiom,
$true ).
fof(t33_parsp_1,axiom,
$true ).
fof(t34_parsp_1,axiom,
$true ).
fof(t35_parsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(A)
& l1_parsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_parsp_1(A,B,C,B,C) ) ) ) ).
fof(t36_parsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(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_1(A,B,C,D,E)
=> r1_parsp_1(A,D,E,B,C) ) ) ) ) ) ) ).
fof(t37_parsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(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_1(A,B,B,C,D) ) ) ) ) ).
fof(t38_parsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(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_1(A,B,C,D,E)
=> r1_parsp_1(A,C,B,D,E) ) ) ) ) ) ) ).
fof(t39_parsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(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_1(A,B,C,D,E)
=> r1_parsp_1(A,B,C,E,D) ) ) ) ) ) ) ).
fof(t40_parsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(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_1(A,B,C,D,E)
=> ( r1_parsp_1(A,C,B,D,E)
& r1_parsp_1(A,B,C,E,D)
& r1_parsp_1(A,C,B,E,D)
& r1_parsp_1(A,D,E,B,C)
& r1_parsp_1(A,E,D,B,C)
& r1_parsp_1(A,D,E,C,B)
& r1_parsp_1(A,E,D,C,B) ) ) ) ) ) ) ) ).
fof(t41_parsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(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_1(A,B,C,B,D)
=> ( r1_parsp_1(A,B,D,B,C)
& r1_parsp_1(A,C,B,B,D)
& r1_parsp_1(A,B,C,D,B)
& r1_parsp_1(A,B,D,C,B)
& r1_parsp_1(A,C,B,D,B)
& r1_parsp_1(A,D,B,B,C)
& r1_parsp_1(A,D,B,C,B)
& r1_parsp_1(A,C,B,C,D)
& r1_parsp_1(A,B,C,C,D)
& r1_parsp_1(A,C,B,D,C)
& r1_parsp_1(A,C,D,C,B)
& r1_parsp_1(A,B,C,D,C)
& r1_parsp_1(A,D,C,C,B)
& r1_parsp_1(A,C,D,B,C)
& r1_parsp_1(A,D,C,B,C)
& r1_parsp_1(A,D,B,D,C)
& r1_parsp_1(A,B,D,D,C)
& r1_parsp_1(A,D,B,C,D)
& r1_parsp_1(A,B,D,C,D)
& r1_parsp_1(A,D,C,D,B)
& r1_parsp_1(A,C,D,D,B)
& r1_parsp_1(A,D,C,B,D)
& r1_parsp_1(A,C,D,B,D) ) ) ) ) ) ) ).
fof(t42_parsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(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))
=> ( ~ ( B != C
& D != E
& ~ ( B = D
& C = E )
& ~ ( B = E
& C = D ) )
=> r1_parsp_1(A,B,C,D,E) ) ) ) ) ) ) ).
fof(t43_parsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(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_1(A,D,E,B,C)
& r1_parsp_1(A,B,C,F,G) )
=> ( B = C
| r1_parsp_1(A,D,E,F,G) ) ) ) ) ) ) ) ) ) ).
fof(t44_parsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(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_1(A,B,C,B,D)
=> ( B != C
& C != D
& D != B ) ) ) ) ) ) ).
fof(t45_parsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(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_1(A,B,C,D,E)
=> ( B != C
& D != E ) ) ) ) ) ) ) ).
fof(t46_parsp_1,axiom,
$true ).
fof(t47_parsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(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_1(A,B,C,B,D)
=> ( ~ r1_parsp_1(A,B,D,B,C)
& ~ r1_parsp_1(A,C,B,B,D)
& ~ r1_parsp_1(A,B,C,D,B)
& ~ r1_parsp_1(A,B,D,C,B)
& ~ r1_parsp_1(A,C,B,D,B)
& ~ r1_parsp_1(A,D,B,B,C)
& ~ r1_parsp_1(A,D,B,C,B)
& ~ r1_parsp_1(A,C,B,C,D)
& ~ r1_parsp_1(A,B,C,C,D)
& ~ r1_parsp_1(A,C,B,D,C)
& ~ r1_parsp_1(A,C,D,C,B)
& ~ r1_parsp_1(A,C,B,D,C)
& ~ r1_parsp_1(A,D,C,C,B)
& ~ r1_parsp_1(A,C,D,B,C)
& ~ r1_parsp_1(A,D,C,B,C)
& ~ r1_parsp_1(A,D,B,D,C)
& ~ r1_parsp_1(A,B,D,D,C)
& ~ r1_parsp_1(A,D,B,C,D)
& ~ r1_parsp_1(A,B,D,C,D)
& ~ r1_parsp_1(A,D,C,D,B)
& ~ r1_parsp_1(A,C,D,D,B)
& ~ r1_parsp_1(A,D,C,B,D)
& ~ r1_parsp_1(A,C,D,B,D) ) ) ) ) ) ) ).
fof(t48_parsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(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))
=> ~ ( ~ r1_parsp_1(A,B,C,D,E)
& r1_parsp_1(A,B,C,F,G)
& r1_parsp_1(A,D,E,H,I)
& F != G
& H != I
& r1_parsp_1(A,F,G,H,I) ) ) ) ) ) ) ) ) ) ) ).
fof(t49_parsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(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_1(A,B,C,B,D)
& r1_parsp_1(A,B,C,E,F)
& r1_parsp_1(A,B,D,E,G)
& r1_parsp_1(A,C,D,F,G)
& E != F
& r1_parsp_1(A,E,F,E,G) ) ) ) ) ) ) ) ) ).
fof(t50_parsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(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_1(A,B,D,E,F)
& r1_parsp_1(A,C,D,E,F) )
=> ( r1_parsp_1(A,B,C,B,D)
| E = F ) ) ) ) ) ) ) ) ).
fof(t51_parsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(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_1(A,B,D,B,E)
& r1_parsp_1(A,C,D,C,E) )
=> ( r1_parsp_1(A,B,C,B,D)
| D = E ) ) ) ) ) ) ) ).
fof(t52_parsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(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))
=> ( ( r1_parsp_1(A,B,C,E,F)
& r1_parsp_1(A,B,D,E,G)
& r1_parsp_1(A,B,D,E,H)
& r1_parsp_1(A,C,D,F,G)
& r1_parsp_1(A,C,D,F,H) )
=> ( r1_parsp_1(A,B,C,B,D)
| G = H ) ) ) ) ) ) ) ) ) ) ).
fof(t53_parsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(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_1(A,B,C,B,D)
& r1_parsp_1(A,B,C,B,E) )
=> r1_parsp_1(A,B,C,D,E) ) ) ) ) ) ) ).
fof(t54_parsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(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 ) )
=> ! [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,B,C,D,E) ) ) ) ) ) ) ).
fof(t55_parsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(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) ) ) )
=> ! [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,B,C,D,E) ) ) ) ) ) ) ).
fof(t56_parsp_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_parsp_1(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_1(A,B,C,B,D)
& E != F
& r1_parsp_1(A,E,F,E,B)
& r1_parsp_1(A,E,F,E,C)
& r1_parsp_1(A,E,F,E,D) ) ) ) ) ) ) ) ).
fof(dt_m1_parsp_1,axiom,
$true ).
fof(existence_m1_parsp_1,axiom,
! [A] :
? [B] : m1_parsp_1(B,A) ).
fof(dt_l1_parsp_1,axiom,
! [A] :
( l1_parsp_1(A)
=> l1_struct_0(A) ) ).
fof(existence_l1_parsp_1,axiom,
? [A] : l1_parsp_1(A) ).
fof(abstractness_v1_parsp_1,axiom,
! [A] :
( l1_parsp_1(A)
=> ( v1_parsp_1(A)
=> A = g1_parsp_1(u1_struct_0(A),u1_parsp_1(A)) ) ) ).
fof(dt_k1_parsp_1,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) )
=> ( v1_funct_1(k1_parsp_1(A))
& v1_funct_2(k1_parsp_1(A),k2_zfmisc_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
& m2_relset_1(k1_parsp_1(A),k2_zfmisc_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) ) ) ).
fof(dt_k2_parsp_1,axiom,
! [A,B,C] :
( ( ~ 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)
& m1_subset_1(B,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
& m1_subset_1(C,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) )
=> m1_subset_1(k2_parsp_1(A,B,C),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) ) ).
fof(dt_k3_parsp_1,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) )
=> ( v1_funct_1(k3_parsp_1(A))
& v1_funct_2(k3_parsp_1(A),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
& m2_relset_1(k3_parsp_1(A),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) ) ) ).
fof(dt_k4_parsp_1,axiom,
! [A,B] :
( ( ~ 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)
& m1_subset_1(B,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) )
=> m1_subset_1(k4_parsp_1(A,B),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) ) ).
fof(dt_k5_parsp_1,axiom,
$true ).
fof(dt_k6_parsp_1,axiom,
$true ).
fof(dt_k7_parsp_1,axiom,
$true ).
fof(dt_k8_parsp_1,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) )
=> m1_parsp_1(k8_parsp_1(A),k5_parsp_1(A)) ) ).
fof(dt_k9_parsp_1,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) )
=> l1_parsp_1(k9_parsp_1(A)) ) ).
fof(dt_u1_parsp_1,axiom,
! [A] :
( l1_parsp_1(A)
=> m1_parsp_1(u1_parsp_1(A),u1_struct_0(A)) ) ).
fof(dt_g1_parsp_1,axiom,
! [A,B] :
( m1_parsp_1(B,A)
=> ( v1_parsp_1(g1_parsp_1(A,B))
& l1_parsp_1(g1_parsp_1(A,B)) ) ) ).
fof(free_g1_parsp_1,axiom,
! [A,B] :
( m1_parsp_1(B,A)
=> ! [C,D] :
( g1_parsp_1(A,B) = g1_parsp_1(C,D)
=> ( A = C
& B = D ) ) ) ).
%------------------------------------------------------------------------------