SET007 Axioms: SET007+623.ax
%------------------------------------------------------------------------------
% File : SET007+623 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Retracts and Inheritance
% 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 : yellow16 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 84 ( 1 unt; 0 def)
% Number of atoms : 974 ( 38 equ)
% Maximal formula atoms : 26 ( 11 avg)
% Number of connectives : 1028 ( 138 ~; 1 |; 581 &)
% ( 20 <=>; 288 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 10 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 66 ( 64 usr; 1 prp; 0-4 aty)
% Number of functors : 51 ( 51 usr; 15 con; 0-5 aty)
% Number of variables : 273 ( 260 !; 13 ?)
% 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_yellow16,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ? [C] :
( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_orders_3(C,A,B)
& v22_waybel_0(C,A,B) ) ) ).
fof(rc2_yellow16,axiom,
! [A] :
( l1_struct_0(A)
=> ? [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
& v1_relat_1(B)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v11_quantal1(B) ) ) ).
fof(cc1_yellow16,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_yellow16(A) )
=> ( v1_relat_1(A)
& v1_yellow_1(A)
& v5_waybel_3(A) ) ) ).
fof(fc1_yellow16,axiom,
! [A,B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ( v1_relat_1(k2_funcop_1(A,B))
& v1_funct_1(k2_funcop_1(A,B))
& v1_yellow_1(k2_funcop_1(A,B))
& v5_waybel_3(k2_funcop_1(A,B))
& v2_pralg_1(k2_funcop_1(A,B))
& v1_yellow16(k2_funcop_1(A,B)) ) ) ).
fof(rc3_yellow16,axiom,
! [A] :
? [B] :
( m1_pboole(B,A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_yellow_1(B)
& v4_waybel_3(B)
& v5_waybel_3(B)
& v2_pralg_1(B)
& v1_yellow16(B) ) ).
fof(fc2_yellow16,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v4_waybel_3(B)
& v1_yellow16(B)
& m1_pboole(B,A) )
=> ( ~ v3_struct_0(k5_yellow_1(A,B))
& v1_orders_2(k5_yellow_1(A,B))
& v2_orders_2(k5_yellow_1(A,B))
& v3_orders_2(k5_yellow_1(A,B))
& v4_orders_2(k5_yellow_1(A,B))
& v1_monoid_0(k5_yellow_1(A,B)) ) ) ).
fof(fc3_yellow16,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_yellow_1(A,B)))) )
=> ~ v1_xboole_0(k5_card_3(D,C)) ) ).
fof(fc4_yellow16,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& v1_yellow_1(B)
& v4_waybel_3(B)
& m1_pboole(B,A)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_yellow_1(A,B)))) )
=> ~ v1_xboole_0(k5_card_3(D,C)) ) ).
fof(fc5_yellow16,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B) )
=> ( ~ v3_struct_0(k6_yellow_1(B,A))
& v1_orders_2(k6_yellow_1(B,A))
& v2_orders_2(k6_yellow_1(B,A))
& v3_orders_2(k6_yellow_1(B,A))
& v4_orders_2(k6_yellow_1(B,A))
& v24_waybel_0(k6_yellow_1(B,A)) ) ) ).
fof(fc6_yellow16,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ~ v1_xboole_0(u1_pre_topc(A)) ) ).
fof(t1_yellow16,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> k5_relat_1(A,B) = k1_zf_fund1(A,B) ) ) ).
fof(t2_yellow16,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& m1_yellow_0(C,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,u1_struct_0(C))
& m2_relset_1(D,A,u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,u1_struct_0(C))
& m2_relset_1(E,A,u1_struct_0(C)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,A,u1_struct_0(B))
& m2_relset_1(F,A,u1_struct_0(B)) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,A,u1_struct_0(B))
& m2_relset_1(G,A,u1_struct_0(B)) )
=> ( ( F = D
& G = E
& r1_yellow_2(A,C,D,E) )
=> r1_yellow_2(A,B,F,G) ) ) ) ) ) ) ) ).
fof(t3_yellow16,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_yellow_0(C,B)
& m1_yellow_0(C,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,u1_struct_0(C))
& m2_relset_1(D,A,u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,u1_struct_0(C))
& m2_relset_1(E,A,u1_struct_0(C)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,A,u1_struct_0(B))
& m2_relset_1(F,A,u1_struct_0(B)) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,A,u1_struct_0(B))
& m2_relset_1(G,A,u1_struct_0(B)) )
=> ( ( F = D
& G = E
& r1_yellow_2(A,B,F,G) )
=> r1_yellow_2(A,C,D,E) ) ) ) ) ) ) ) ).
fof(t4_yellow16,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( ( v11_quantal1(A)
& r1_tarski(k2_relat_1(B),k2_relat_1(A))
& r1_tarski(k2_relat_1(B),k1_relat_1(A)) )
=> k5_relat_1(B,A) = B ) ) ) ).
fof(t5_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& v4_waybel_0(B,A)
& m1_yellow_0(B,A) )
=> v24_waybel_0(B) ) ) ).
fof(t6_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( v11_quantal1(B)
& v22_waybel_0(B,A,A) )
=> v4_waybel_0(k2_yellow_2(A,A,B),A) ) ) ) ).
fof(t7_yellow16,axiom,
$true ).
fof(t8_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_struct_0(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ( k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),D,C) = k7_grcat_1(A)
=> k8_yellow_2(u1_struct_0(B),A,C) = u1_struct_0(A) ) ) ) ) ) ).
fof(t9_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_yellow_0(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),k1_yellow_9(A,B),C) = k7_grcat_1(B)
=> ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v11_quantal1(C)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) ) ) ) ) ) ).
fof(d1_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r1_yellow16(A,B,C)
<=> ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v22_waybel_0(C,B,A)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A))
& k7_relat_1(C,u1_struct_0(A)) = k7_grcat_1(A)
& v4_yellow_0(A,B)
& v4_waybel_0(A,B)
& m1_yellow_0(A,B) ) ) ) ) ) ).
fof(d2_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r2_yellow16(A,B,C)
<=> ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v22_waybel_0(C,B,A)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A))
& ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& v22_waybel_0(D,A,B)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B))
& k5_relat_1(D,C) = k7_grcat_1(A) ) ) ) ) ) ) ).
fof(d3_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ( r3_yellow16(A,B)
<=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A))
& r1_yellow16(A,B,C) ) ) ) ) ).
fof(d4_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ( r4_yellow16(A,B)
<=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A))
& r2_yellow16(A,B,C) ) ) ) ) ).
fof(t10_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r1_yellow16(A,B,C)
=> k5_relat_1(k1_yellow_9(B,A),C) = k7_grcat_1(A) ) ) ) ) ).
fof(t11_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r1_yellow16(A,B,C)
=> r2_yellow16(A,B,C) ) ) ) ) ).
fof(t12_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r1_yellow16(A,B,C)
=> k2_relat_1(C) = u1_struct_0(A) ) ) ) ) ).
fof(t13_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r2_yellow16(A,B,C)
=> k2_relat_1(C) = u1_struct_0(A) ) ) ) ) ).
fof(t14_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r1_yellow16(A,B,C)
=> ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
& v11_quantal1(C)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) ) ) ) ) ) ).
fof(t15_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( r1_yellow16(B,A,C)
=> k2_yellow_2(A,A,C) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) ) ) ) ) ).
fof(t16_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( r1_yellow16(B,A,C)
=> ( v22_waybel_0(C,A,A)
& v6_waybel_1(C,A) ) ) ) ) ) ).
fof(t17_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v23_waybel_0(C,A,B)
<=> ( v5_orders_3(C,A,B)
& ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& v5_orders_3(D,B,A)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A))
& k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),D,C) = k7_grcat_1(B)
& k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,D) = k7_grcat_1(A) ) ) ) ) ) ) ).
fof(t18_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ( r5_waybel_1(A,B)
<=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_orders_3(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& v5_orders_3(D,B,A)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A))
& k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),D,C) = k7_grcat_1(B)
& k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,D) = k7_grcat_1(A) ) ) ) ) ) ).
fof(t19_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& l1_orders_2(B) )
=> ( r5_waybel_1(A,B)
=> ( r4_yellow16(A,B)
& r4_yellow16(B,A) ) ) ) ) ).
fof(t20_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_orders_3(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& v5_orders_3(D,B,A)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ~ ( k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),D,C) = k7_grcat_1(B)
& ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(A))
& v6_waybel_1(E,A)
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(A)) )
=> ~ ( E = k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,D)
& k2_partfun1(u1_struct_0(A),u1_struct_0(A),E,u1_struct_0(k2_yellow_2(A,A,E))) = k7_grcat_1(k2_yellow_2(A,A,E))
& r5_waybel_1(B,k2_yellow_2(A,A,E)) ) ) ) ) ) ) ) ).
fof(t21_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ~ ( r2_yellow16(B,A,C)
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& v22_waybel_0(D,A,A)
& v6_waybel_1(D,A)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
=> ~ ( r1_yellow16(k2_yellow_2(A,A,D),A,D)
& r5_waybel_1(B,k2_yellow_2(A,A,D)) ) ) ) ) ) ) ).
fof(t22_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ( r3_yellow16(B,A)
=> v24_waybel_0(B) ) ) ) ).
fof(t23_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ( r3_yellow16(B,A)
=> v3_lattice3(B) ) ) ) ).
fof(t24_yellow16,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ( r3_yellow16(B,A)
=> v3_waybel_3(B) ) ) ) ).
fof(t25_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ( r4_yellow16(B,A)
=> v24_waybel_0(B) ) ) ) ).
fof(t26_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ( r4_yellow16(B,A)
=> v3_lattice3(B) ) ) ) ).
fof(t27_yellow16,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ( r4_yellow16(B,A)
=> v3_waybel_3(B) ) ) ) ).
fof(t28_yellow16,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( ( v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( m1_yellow_0(C,B)
=> ( v4_yellow_0(C,B)
<=> ( v4_yellow_0(C,A)
& m1_yellow_0(C,A) ) ) ) ) ) ).
fof(t29_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& v4_waybel_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_waybel_0(C,B)
& m1_yellow_0(C,B) )
=> ( v4_waybel_0(C,A)
& m1_yellow_0(C,A) ) ) ) ) ).
fof(t30_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& v4_waybel_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_yellow_0(C,A)
& v4_waybel_0(C,A)
& m1_yellow_0(C,A) )
=> ( m1_yellow_0(B,C)
=> ( v4_yellow_0(B,C)
& v4_waybel_0(B,C)
& m1_yellow_0(B,C) ) ) ) ) ) ).
fof(d5_yellow16,axiom,
! [A] :
( v1_relat_1(A)
=> ( v1_yellow16(A)
<=> ! [B] :
( r2_hidden(B,k2_relat_1(A))
=> ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) ) ) ) ) ).
fof(t31_yellow16,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v4_waybel_3(B)
& v1_yellow16(B)
& m1_pboole(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k5_yellow_1(A,B)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k5_yellow_1(A,B))))
=> ( r2_lattice3(k5_yellow_1(A,B),D,C)
<=> ! [E] :
( m1_subset_1(E,A)
=> r2_lattice3(k6_waybel_3(A,B,E),k5_waybel_3(A,B,E,D),k7_waybel_3(A,B,C,E)) ) ) ) ) ) ) ).
fof(t32_yellow16,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v4_waybel_3(B)
& v1_yellow16(B)
& m1_pboole(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k5_yellow_1(A,B)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k5_yellow_1(A,B))))
=> ( r1_lattice3(k5_yellow_1(A,B),D,C)
<=> ! [E] :
( m1_subset_1(E,A)
=> r1_lattice3(k6_waybel_3(A,B,E),k5_waybel_3(A,B,E,D),k7_waybel_3(A,B,C,E)) ) ) ) ) ) ) ).
fof(t33_yellow16,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v4_waybel_3(B)
& v1_yellow16(B)
& m1_pboole(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_yellow_1(A,B))))
=> ( r1_yellow_0(k5_yellow_1(A,B),C)
<=> ! [D] :
( m1_subset_1(D,A)
=> r1_yellow_0(k2_yellow16(A,B,D),k5_waybel_3(A,B,D,C)) ) ) ) ) ) ).
fof(t34_yellow16,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v4_waybel_3(B)
& v1_yellow16(B)
& m1_pboole(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_yellow_1(A,B))))
=> ( r2_yellow_0(k5_yellow_1(A,B),C)
<=> ! [D] :
( m1_subset_1(D,A)
=> r2_yellow_0(k2_yellow16(A,B,D),k5_waybel_3(A,B,D,C)) ) ) ) ) ) ).
fof(t35_yellow16,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v4_waybel_3(B)
& v1_yellow16(B)
& m1_pboole(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_yellow_1(A,B))))
=> ( r1_yellow_0(k5_yellow_1(A,B),C)
=> ! [D] :
( m1_subset_1(D,A)
=> k7_waybel_3(A,B,k1_yellow_0(k5_yellow_1(A,B),C),D) = k1_yellow_0(k3_waybel_3(A,B,D),k5_waybel_3(A,B,D,C)) ) ) ) ) ) ).
fof(t36_yellow16,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v4_waybel_3(B)
& v1_yellow16(B)
& m1_pboole(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_yellow_1(A,B))))
=> ( r2_yellow_0(k5_yellow_1(A,B),C)
=> ! [D] :
( m1_subset_1(D,A)
=> k7_waybel_3(A,B,k2_yellow_0(k5_yellow_1(A,B),C),D) = k2_yellow_0(k3_waybel_3(A,B,D),k5_waybel_3(A,B,D,C)) ) ) ) ) ) ).
fof(t37_yellow16,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_yellow_1(B)
& v4_waybel_3(B)
& v5_waybel_3(B)
& m1_pboole(B,A) )
=> ! [C] :
( ( v1_waybel_0(C,k5_yellow_1(A,B))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_yellow_1(A,B)))) )
=> ! [D] :
( m1_subset_1(D,A)
=> v1_waybel_0(k5_waybel_3(A,B,D,C),k3_waybel_3(A,B,D)) ) ) ) ) ).
fof(t38_yellow16,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_yellow_1(B)
& v4_waybel_3(B)
& m1_pboole(B,A) )
=> ! [C] :
( ( v1_yellow_1(C)
& v4_waybel_3(C)
& m1_pboole(C,A) )
=> ( ! [D] :
( m1_subset_1(D,A)
=> m1_yellow_0(k3_waybel_3(A,C,D),k3_waybel_3(A,B,D)) )
=> m1_yellow_0(k5_yellow_1(A,C),k5_yellow_1(A,B)) ) ) ) ) ).
fof(t39_yellow16,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_yellow_1(B)
& v4_waybel_3(B)
& m1_pboole(B,A) )
=> ! [C] :
( ( v1_yellow_1(C)
& v4_waybel_3(C)
& m1_pboole(C,A) )
=> ( ! [D] :
( m1_subset_1(D,A)
=> ( v4_yellow_0(k3_waybel_3(A,C,D),k3_waybel_3(A,B,D))
& m1_yellow_0(k3_waybel_3(A,C,D),k3_waybel_3(A,B,D)) ) )
=> ( v4_yellow_0(k5_yellow_1(A,C),k5_yellow_1(A,B))
& m1_yellow_0(k5_yellow_1(A,C),k5_yellow_1(A,B)) ) ) ) ) ) ).
fof(t40_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_yellow_0(B,A) )
=> ! [C] : m1_yellow_0(k6_yellow_1(C,B),k6_yellow_1(C,A)) ) ) ).
fof(t41_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( v4_yellow_0(k6_yellow_1(C,B),k6_yellow_1(C,A))
& m1_yellow_0(k6_yellow_1(C,B),k6_yellow_1(C,A)) ) ) ) ).
fof(d6_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( r5_yellow16(A,B,C)
<=> ( r1_yellow_0(B,C)
=> r2_hidden(k1_yellow_0(B,C),u1_struct_0(A)) ) ) ) ) ).
fof(d7_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( r6_yellow16(A,B,C)
<=> ( r2_yellow_0(B,C)
=> r2_hidden(k2_yellow_0(B,C),u1_struct_0(A)) ) ) ) ) ).
fof(t42_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ( r5_yellow16(B,A,C)
<=> ( r1_yellow_0(A,C)
=> ( r1_yellow_0(B,C)
& k1_yellow_0(B,C) = k1_yellow_0(A,C) ) ) ) ) ) ) ).
fof(t43_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ( r6_yellow16(B,A,C)
<=> ( r2_yellow_0(A,C)
=> ( r2_yellow_0(B,C)
& k2_yellow_0(B,C) = k2_yellow_0(A,C) ) ) ) ) ) ) ).
fof(t44_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& v4_waybel_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( ~ v1_xboole_0(C)
=> ( v4_waybel_0(k6_yellow_1(C,B),k6_yellow_1(C,A))
& m1_yellow_0(k6_yellow_1(C,B),k6_yellow_1(C,A)) ) ) ) ) ).
fof(t45_yellow16,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& l1_orders_2(B) )
=> v24_waybel_0(k6_yellow_1(A,B)) ) ) ).
fof(t46_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v3_borsuk_1(C,A,B)
=> k8_yellow_2(u1_struct_0(A),B,C) = u1_struct_0(B) ) ) ) ) ).
fof(t47_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v3_borsuk_1(C,A,B)
=> v11_quantal1(C) ) ) ) ) ).
fof(t48_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v3_pre_topc(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_funct_1(k5_funct_3(B,u1_struct_0(A)))
& v1_funct_2(k5_funct_3(B,u1_struct_0(A)),u1_struct_0(A),u1_struct_0(k9_waybel18))
& v5_pre_topc(k5_funct_3(B,u1_struct_0(A)),A,k9_waybel18)
& m2_relset_1(k5_funct_3(B,u1_struct_0(A)),u1_struct_0(A),u1_struct_0(k9_waybel18)) ) ) ) ).
fof(t49_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ! [D] :
( ( v3_pre_topc(D,A)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r2_hidden(C,D)
=> r2_hidden(B,D) ) )
=> ( v1_funct_1(k5_funct_4(u1_struct_0(A),np__0,np__1,C,B))
& v1_funct_2(k5_funct_4(u1_struct_0(A),np__0,np__1,C,B),u1_struct_0(k9_waybel18),u1_struct_0(A))
& v5_pre_topc(k5_funct_4(u1_struct_0(A),np__0,np__1,C,B),k9_waybel18,A)
& m2_relset_1(k5_funct_4(u1_struct_0(A),np__0,np__1,C,B),u1_struct_0(k9_waybel18),u1_struct_0(A)) ) ) ) ) ) ).
fof(t50_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v3_pre_topc(D,A)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r2_hidden(B,D)
=> ( r2_hidden(C,D)
| k7_funct_2(k2_tarski(np__0,np__1),u1_struct_0(A),k2_tarski(np__0,np__1),k5_funct_4(u1_struct_0(A),np__0,np__1,C,B),k5_funct_3(D,u1_struct_0(A))) = k7_grcat_1(k9_waybel18) ) ) ) ) ) ) ).
fof(t51_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_yellow_9(D,k3_yellow_1(np__1))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(D))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(D)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(A),u1_struct_0(D))
& m2_relset_1(F,u1_struct_0(A),u1_struct_0(D)) )
=> ( ( E = k5_funct_3(B,u1_struct_0(A))
& F = k5_funct_3(C,u1_struct_0(A)) )
=> ( r1_tarski(B,C)
<=> r1_yellow_2(u1_struct_0(A),D,E,F) ) ) ) ) ) ) ) ) ).
fof(t52_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_yellow_0(C,k6_yellow_1(B,A))
& m1_yellow_0(C,k6_yellow_1(B,A)) )
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(C))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& D = k1_borsuk_1(u1_struct_0(A),B,E) ) )
=> r5_waybel_1(A,C) ) ) ) ) ).
fof(t53_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( r1_t_0topsp(A,B)
<=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& v5_pre_topc(D,B,A)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A))
& k4_borsuk_1(B,A,B,D,C) = k7_grcat_1(B)
& k4_borsuk_1(A,B,A,C,D) = k7_grcat_1(A) ) ) ) ) ) ).
fof(t54_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_pre_topc(C)
& l1_pre_topc(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(F,u1_struct_0(B),u1_struct_0(C)) )
=> ( ( k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),E,D) = k7_grcat_1(B)
& v3_tops_2(F,B,C) )
=> k7_funct_2(u1_struct_0(C),u1_struct_0(A),u1_struct_0(C),k7_funct_2(u1_struct_0(C),u1_struct_0(B),u1_struct_0(A),k2_tops_2(B,C,F),E),k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,F)) = k7_grcat_1(C) ) ) ) ) ) ) ) ).
fof(t55_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_pre_topc(C)
& l1_pre_topc(C) )
=> ( ( r1_waybel18(B,A)
& r1_t_0topsp(B,C) )
=> r1_waybel18(C,A) ) ) ) ) ).
fof(t56_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> v5_pre_topc(k1_yellow_9(A,B),B,A) ) ) ).
fof(t57_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v3_borsuk_1(C,A,B)
=> k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),k1_yellow_9(A,B),C) = k7_grcat_1(B) ) ) ) ) ).
fof(t58_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ( r1_borsuk_1(A,B)
=> r1_waybel18(B,A) ) ) ) ).
fof(t59_yellow16,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B) )
=> ( r1_waybel18(A,B)
<=> ? [C] :
( ~ v3_struct_0(C)
& m1_pre_topc(C,B)
& r1_borsuk_1(B,C)
& r1_t_0topsp(C,A) ) ) ) ) ).
fof(s1_yellow16,axiom,
( ( ! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_yellow_1(f1_s1_yellow16,f3_s1_yellow16))))
=> ( p1_s1_yellow16(A,k5_yellow_1(f1_s1_yellow16,f3_s1_yellow16))
=> ! [B] :
( m1_subset_1(B,f1_s1_yellow16)
=> p1_s1_yellow16(k5_waybel_3(f1_s1_yellow16,f3_s1_yellow16,B,A),k2_yellow16(f1_s1_yellow16,f3_s1_yellow16,B)) ) ) )
& ! [A] :
( m1_subset_1(A,f1_s1_yellow16)
=> ( v4_yellow_0(k2_yellow16(f1_s1_yellow16,f3_s1_yellow16,A),k2_yellow16(f1_s1_yellow16,f2_s1_yellow16,A))
& m1_yellow_0(k2_yellow16(f1_s1_yellow16,f3_s1_yellow16,A),k2_yellow16(f1_s1_yellow16,f2_s1_yellow16,A)) ) )
& ! [A] :
( m1_subset_1(A,f1_s1_yellow16)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow16(f1_s1_yellow16,f3_s1_yellow16,A))))
=> ( p1_s1_yellow16(B,k2_yellow16(f1_s1_yellow16,f3_s1_yellow16,A))
=> r5_yellow16(k2_yellow16(f1_s1_yellow16,f3_s1_yellow16,A),k2_yellow16(f1_s1_yellow16,f2_s1_yellow16,A),B) ) ) ) )
=> ! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_yellow_1(f1_s1_yellow16,f3_s1_yellow16))))
=> ( p1_s1_yellow16(A,k5_yellow_1(f1_s1_yellow16,f3_s1_yellow16))
=> r5_yellow16(k5_yellow_1(f1_s1_yellow16,f3_s1_yellow16),k5_yellow_1(f1_s1_yellow16,f2_s1_yellow16),A) ) ) ) ).
fof(s2_yellow16,axiom,
( ( ! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k6_yellow_1(f1_s2_yellow16,f3_s2_yellow16))))
=> ( p1_s2_yellow16(A,k6_yellow_1(f1_s2_yellow16,f3_s2_yellow16))
=> ! [B] :
( m1_subset_1(B,f1_s2_yellow16)
=> p1_s2_yellow16(k1_yellow16(f1_s2_yellow16,f3_s2_yellow16,B,A),f3_s2_yellow16) ) ) )
& ! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(f3_s2_yellow16)))
=> ( p1_s2_yellow16(A,f3_s2_yellow16)
=> r5_yellow16(f3_s2_yellow16,f2_s2_yellow16,A) ) ) )
=> ! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k6_yellow_1(f1_s2_yellow16,f3_s2_yellow16))))
=> ( p1_s2_yellow16(A,k6_yellow_1(f1_s2_yellow16,f3_s2_yellow16))
=> r5_yellow16(k6_yellow_1(f1_s2_yellow16,f3_s2_yellow16),k6_yellow_1(f1_s2_yellow16,f2_s2_yellow16),A) ) ) ) ).
fof(s3_yellow16,axiom,
( ( ! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_yellow_1(f1_s3_yellow16,f3_s3_yellow16))))
=> ( p1_s3_yellow16(A,k5_yellow_1(f1_s3_yellow16,f3_s3_yellow16))
=> ! [B] :
( m1_subset_1(B,f1_s3_yellow16)
=> p1_s3_yellow16(k5_waybel_3(f1_s3_yellow16,f3_s3_yellow16,B,A),k2_yellow16(f1_s3_yellow16,f3_s3_yellow16,B)) ) ) )
& ! [A] :
( m1_subset_1(A,f1_s3_yellow16)
=> ( v4_yellow_0(k2_yellow16(f1_s3_yellow16,f3_s3_yellow16,A),k2_yellow16(f1_s3_yellow16,f2_s3_yellow16,A))
& m1_yellow_0(k2_yellow16(f1_s3_yellow16,f3_s3_yellow16,A),k2_yellow16(f1_s3_yellow16,f2_s3_yellow16,A)) ) )
& ! [A] :
( m1_subset_1(A,f1_s3_yellow16)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow16(f1_s3_yellow16,f3_s3_yellow16,A))))
=> ( p1_s3_yellow16(B,k2_yellow16(f1_s3_yellow16,f3_s3_yellow16,A))
=> r6_yellow16(k2_yellow16(f1_s3_yellow16,f3_s3_yellow16,A),k2_yellow16(f1_s3_yellow16,f2_s3_yellow16,A),B) ) ) ) )
=> ! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_yellow_1(f1_s3_yellow16,f3_s3_yellow16))))
=> ( p1_s3_yellow16(A,k5_yellow_1(f1_s3_yellow16,f3_s3_yellow16))
=> r6_yellow16(k5_yellow_1(f1_s3_yellow16,f3_s3_yellow16),k5_yellow_1(f1_s3_yellow16,f2_s3_yellow16),A) ) ) ) ).
fof(s4_yellow16,axiom,
( ( ! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k6_yellow_1(f1_s4_yellow16,f3_s4_yellow16))))
=> ( p1_s4_yellow16(A,k6_yellow_1(f1_s4_yellow16,f3_s4_yellow16))
=> ! [B] :
( m1_subset_1(B,f1_s4_yellow16)
=> p1_s4_yellow16(k1_yellow16(f1_s4_yellow16,f3_s4_yellow16,B,A),f3_s4_yellow16) ) ) )
& ! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(f3_s4_yellow16)))
=> ( p1_s4_yellow16(A,f3_s4_yellow16)
=> r6_yellow16(f3_s4_yellow16,f2_s4_yellow16,A) ) ) )
=> ! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k6_yellow_1(f1_s4_yellow16,f3_s4_yellow16))))
=> ( p1_s4_yellow16(A,k6_yellow_1(f1_s4_yellow16,f3_s4_yellow16))
=> r6_yellow16(k6_yellow_1(f1_s4_yellow16,f3_s4_yellow16),k6_yellow_1(f1_s4_yellow16,f2_s4_yellow16),A) ) ) ) ).
fof(dt_k1_yellow16,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& l1_orders_2(B)
& m1_subset_1(C,A)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k6_yellow_1(A,B)))) )
=> m1_subset_1(k1_yellow16(A,B,C,D),k1_zfmisc_1(u1_struct_0(B))) ) ).
fof(redefinition_k1_yellow16,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& l1_orders_2(B)
& m1_subset_1(C,A)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k6_yellow_1(A,B)))) )
=> k1_yellow16(A,B,C,D) = k5_card_3(C,D) ) ).
fof(dt_k2_yellow16,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v4_waybel_3(B)
& v1_yellow16(B)
& m1_pboole(B,A)
& m1_subset_1(C,A) )
=> ( ~ v3_struct_0(k2_yellow16(A,B,C))
& v2_orders_2(k2_yellow16(A,B,C))
& v3_orders_2(k2_yellow16(A,B,C))
& v4_orders_2(k2_yellow16(A,B,C))
& l1_orders_2(k2_yellow16(A,B,C)) ) ) ).
fof(redefinition_k2_yellow16,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v4_waybel_3(B)
& v1_yellow16(B)
& m1_pboole(B,A)
& m1_subset_1(C,A) )
=> k2_yellow16(A,B,C) = k1_funct_1(B,C) ) ).
%------------------------------------------------------------------------------