SET007 Axioms: SET007+559.ax
%------------------------------------------------------------------------------
% File : SET007+559 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Kernel Projections and Quotient Lattices
% 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 : waybel20 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 58 ( 1 unt; 0 def)
% Number of atoms : 741 ( 26 equ)
% Maximal formula atoms : 33 ( 12 avg)
% Number of connectives : 763 ( 80 ~; 1 |; 474 &)
% ( 6 <=>; 202 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 11 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 49 ( 47 usr; 1 prp; 0-3 aty)
% Number of functors : 41 ( 41 usr; 1 con; 0-6 aty)
% Number of variables : 184 ( 180 !; 4 ?)
% 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_waybel20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
& ~ v1_xboole_0(B)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
& v11_quantal1(B)
& v5_orders_3(B,A,A)
& v22_waybel_0(B,A,A)
& v6_waybel_1(B,A)
& v8_waybel_1(B,A) ) ) ).
fof(t1_waybel20,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k6_partfun1(A)))
=> k1_funct_5(B) = k2_funct_5(B) ) ).
fof(t2_waybel20,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ( v3_relat_2(k3_funct_2(k2_zfmisc_1(A,A),k2_zfmisc_1(B,B),k16_funct_3(A,A,B,B,C,C),k6_partfun1(B)))
& v8_relat_2(k3_funct_2(k2_zfmisc_1(A,A),k2_zfmisc_1(B,B),k16_funct_3(A,A,B,B,C,C),k6_partfun1(B)))
& v1_partfun1(k3_funct_2(k2_zfmisc_1(A,A),k2_zfmisc_1(B,B),k16_funct_3(A,A,B,B,C,C),k6_partfun1(B)),A,A)
& m2_relset_1(k3_funct_2(k2_zfmisc_1(A,A),k2_zfmisc_1(B,B),k16_funct_3(A,A,B,B,C,C),k6_partfun1(B)),A,A) ) ) ) ) ).
fof(t3_waybel20,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( r1_tarski(k1_funct_5(k9_relat_1(k15_funct_3(A,B),C)),k9_relat_1(A,k1_funct_5(C)))
& r1_tarski(k2_funct_5(k9_relat_1(k15_funct_3(A,B),C)),k9_relat_1(B,k2_funct_5(C))) ) ) ) ).
fof(t4_waybel20,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( r1_tarski(C,k2_zfmisc_1(k1_relat_1(A),k1_relat_1(B)))
=> ( k1_funct_5(k9_relat_1(k15_funct_3(A,B),C)) = k9_relat_1(A,k1_funct_5(C))
& k2_funct_5(k9_relat_1(k15_funct_3(A,B),C)) = k9_relat_1(B,k2_funct_5(C)) ) ) ) ) ).
fof(t5_waybel20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ( r2_yellow_0(A,k1_xboole_0)
=> v2_yellow_0(A) ) ) ).
fof(t6_waybel20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ( r1_yellow_0(A,k1_xboole_0)
=> v1_yellow_0(A) ) ) ).
fof(t7_waybel20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B))))
=> ( r2_yellow_0(k3_yellow_3(A,B),C)
=> k2_yellow_0(k3_yellow_3(A,B),C) = k7_yellow_3(A,B,k2_yellow_0(A,k4_yellow_3(A,B,C)),k2_yellow_0(B,k5_yellow_3(A,B,C))) ) ) ) ) ).
fof(t8_waybel20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B))))
=> ( r1_yellow_0(k3_yellow_3(A,B),C)
=> k1_yellow_0(k3_yellow_3(A,B),C) = k7_yellow_3(A,B,k1_yellow_0(A,k4_yellow_3(A,B,C)),k1_yellow_0(B,k5_yellow_3(A,B,C))) ) ) ) ) ).
fof(t9_waybel20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_orders_2(C)
& l1_orders_2(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v4_orders_2(D)
& l1_orders_2(D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
& m2_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
=> ( ( v17_waybel_0(E,A,C)
& v17_waybel_0(F,B,D) )
=> v17_waybel_0(k1_waybel20(A,B,C,D,E,F),k3_yellow_3(A,B),k3_yellow_3(C,D)) ) ) ) ) ) ) ) ).
fof(t10_waybel20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_orders_2(C)
& v4_orders_2(C)
& l1_orders_2(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v2_orders_2(D)
& v4_orders_2(D)
& l1_orders_2(D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
& m2_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
=> ( ( v21_waybel_0(E,A,C)
& v21_waybel_0(F,B,D) )
=> v21_waybel_0(k1_waybel20(A,B,C,D,E,F),k3_yellow_3(A,B),k3_yellow_3(C,D)) ) ) ) ) ) ) ) ).
fof(t11_waybel20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_orders_2(C)
& l1_orders_2(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v4_orders_2(D)
& l1_orders_2(D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
& m2_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
=> ( ( v18_waybel_0(E,A,C)
& v18_waybel_0(F,B,D) )
=> v18_waybel_0(k1_waybel20(A,B,C,D,E,F),k3_yellow_3(A,B),k3_yellow_3(C,D)) ) ) ) ) ) ) ) ).
fof(t12_waybel20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_orders_2(C)
& v4_orders_2(C)
& l1_orders_2(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v2_orders_2(D)
& v4_orders_2(D)
& l1_orders_2(D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
& m2_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
=> ( ( v22_waybel_0(E,A,C)
& v22_waybel_0(F,B,D) )
=> v22_waybel_0(k1_waybel20(A,B,C,D,E,F),k3_yellow_3(A,B),k3_yellow_3(C,D)) ) ) ) ) ) ) ) ).
fof(t13_waybel20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A))))
=> ( ( r1_tarski(B,k6_partfun1(u1_struct_0(A)))
& r2_yellow_0(k3_yellow_3(A,A),B) )
=> r2_hidden(k2_yellow_0(k3_yellow_3(A,A),B),k6_partfun1(u1_struct_0(A))) ) ) ) ).
fof(t14_waybel20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A))))
=> ( ( r1_tarski(B,k6_partfun1(u1_struct_0(A)))
& r1_yellow_0(k3_yellow_3(A,A),B) )
=> r2_hidden(k1_yellow_0(k3_yellow_3(A,A),B),k6_partfun1(u1_struct_0(A))) ) ) ) ).
fof(t15_waybel20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ( ( r5_waybel_1(A,B)
& v2_orders_2(A) )
=> v2_orders_2(B) ) ) ) ).
fof(t16_waybel20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ( ( r5_waybel_1(A,B)
& v3_orders_2(A) )
=> v3_orders_2(B) ) ) ) ).
fof(t17_waybel20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ( ( r5_waybel_1(A,B)
& v4_orders_2(A) )
=> v4_orders_2(B) ) ) ) ).
fof(t18_waybel20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ( ( r5_waybel_1(A,B)
& v3_lattice3(A) )
=> v3_lattice3(B) ) ) ) ).
fof(t19_waybel20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(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)) )
=> ( v17_waybel_0(B,A,A)
=> v17_waybel_0(k2_waybel_1(A,A,B),A,k2_yellow_2(A,A,B)) ) ) ) ).
fof(t20_waybel20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(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)) )
=> ( v21_waybel_0(B,A,A)
=> v21_waybel_0(k2_waybel_1(A,A,B),A,k2_yellow_2(A,A,B)) ) ) ) ).
fof(t21_waybel20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(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)) )
=> ( v18_waybel_0(B,A,A)
=> v18_waybel_0(k2_waybel_1(A,A,B),A,k2_yellow_2(A,A,B)) ) ) ) ).
fof(t22_waybel20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(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)) )
=> ( v22_waybel_0(B,A,A)
=> v22_waybel_0(k2_waybel_1(A,A,B),A,k2_yellow_2(A,A,B)) ) ) ) ).
fof(t23_waybel20,axiom,
$true ).
fof(t24_waybel20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_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))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v21_waybel_0(C,A,B)
=> v5_orders_3(C,A,B) ) ) ) ) ).
fof(t25_waybel20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(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)) )
=> ( v5_orders_3(C,A,B)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( v2_waybel_0(D,A)
=> v2_waybel_0(k4_pre_topc(A,B,C,D),B) ) ) ) ) ) ) ).
fof(t26_waybel20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_orders_2(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(C))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( ( v17_waybel_0(D,A,B)
& v17_waybel_0(E,B,C) )
=> v17_waybel_0(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C) ) ) ) ) ) ) ).
fof(t27_waybel20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_orders_2(C)
& v4_orders_2(C)
& l1_orders_2(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(C))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( ( v21_waybel_0(D,A,B)
& v21_waybel_0(E,B,C) )
=> v21_waybel_0(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C) ) ) ) ) ) ) ).
fof(t28_waybel20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_orders_2(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(C))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( ( v18_waybel_0(D,A,B)
& v18_waybel_0(E,B,C) )
=> v18_waybel_0(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C) ) ) ) ) ) ) ).
fof(t29_waybel20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_orders_2(C)
& v4_orders_2(C)
& l1_orders_2(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(C))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( ( v22_waybel_0(D,A,B)
& v22_waybel_0(E,B,C) )
=> v22_waybel_0(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C) ) ) ) ) ) ) ).
fof(t30_waybel20,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_yellow_1(B)
& v4_waybel_3(B)
& m1_pboole(B,A) )
=> ( ! [C] :
( m1_subset_1(C,A)
=> ( v4_orders_2(k3_waybel_3(A,B,C))
& v1_yellow_0(k3_waybel_3(A,B,C))
& l1_orders_2(k3_waybel_3(A,B,C)) ) )
=> v1_yellow_0(k5_yellow_1(A,B)) ) ) ) ).
fof(t31_waybel20,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_yellow_1(B)
& v4_waybel_3(B)
& m1_pboole(B,A) )
=> ( ! [C] :
( m1_subset_1(C,A)
=> ( v4_orders_2(k3_waybel_3(A,B,C))
& v2_yellow_0(k3_waybel_3(A,B,C))
& l1_orders_2(k3_waybel_3(A,B,C)) ) )
=> v2_yellow_0(k5_yellow_1(A,B)) ) ) ) ).
fof(t32_waybel20,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_yellow_1(B)
& v4_waybel_3(B)
& m1_pboole(B,A) )
=> ( ! [C] :
( m1_subset_1(C,A)
=> ( v4_orders_2(k3_waybel_3(A,B,C))
& v1_yellow_0(k3_waybel_3(A,B,C))
& l1_orders_2(k3_waybel_3(A,B,C)) ) )
=> ! [C] :
( m1_subset_1(C,A)
=> k4_waybel_3(A,B,k3_yellow_0(k5_yellow_1(A,B)),C) = k3_yellow_0(k3_waybel_3(A,B,C)) ) ) ) ) ).
fof(t33_waybel20,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_yellow_1(B)
& v4_waybel_3(B)
& m1_pboole(B,A) )
=> ( ! [C] :
( m1_subset_1(C,A)
=> ( v4_orders_2(k3_waybel_3(A,B,C))
& v2_yellow_0(k3_waybel_3(A,B,C))
& l1_orders_2(k3_waybel_3(A,B,C)) ) )
=> ! [C] :
( m1_subset_1(C,A)
=> k4_waybel_3(A,B,k4_yellow_0(k5_yellow_1(A,B)),C) = k4_yellow_0(k3_waybel_3(A,B,C)) ) ) ) ) ).
fof(t34_waybel20,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_yellow_1(B)
& v4_waybel_3(B)
& v5_waybel_3(B)
& m1_pboole(B,A) )
=> ( ! [C] :
( m1_subset_1(C,A)
=> ( v2_orders_2(k6_waybel_3(A,B,C))
& v3_orders_2(k6_waybel_3(A,B,C))
& v4_orders_2(k6_waybel_3(A,B,C))
& v1_lattice3(k6_waybel_3(A,B,C))
& v2_lattice3(k6_waybel_3(A,B,C))
& v3_lattice3(k6_waybel_3(A,B,C))
& v3_waybel_3(k6_waybel_3(A,B,C))
& l1_orders_2(k6_waybel_3(A,B,C)) ) )
=> v3_waybel_3(k5_yellow_1(A,B)) ) ) ) ).
fof(t35_waybel20,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] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& v3_waybel_3(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_waybel16(C,A,B)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A))))
=> ( D = k5_pre_topc(k3_yellow_3(A,A),k3_yellow_3(B,B),k1_waybel20(A,A,B,B,C,C),k6_partfun1(u1_struct_0(B)))
=> ( ~ v3_struct_0(k5_yellow_0(k3_yellow_3(A,A),D))
& v4_yellow_0(k5_yellow_0(k3_yellow_3(A,A),D),k3_yellow_3(A,A))
& v7_yellow_0(k5_yellow_0(k3_yellow_3(A,A),D),k3_yellow_3(A,A))
& v4_waybel_0(k5_yellow_0(k3_yellow_3(A,A),D),k3_yellow_3(A,A))
& m1_yellow_0(k5_yellow_0(k3_yellow_3(A,A),D),k3_yellow_3(A,A)) ) ) ) ) ) ) ).
fof(d1_waybel20,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A))))
=> ( ( v3_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> k2_waybel20(A,B) = B ) ) ) ).
fof(d2_waybel20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A))))
=> ( v1_waybel20(B,A)
<=> ( v3_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
& ~ v3_struct_0(k5_yellow_0(k3_yellow_3(A,A),B))
& v4_yellow_0(k5_yellow_0(k3_yellow_3(A,A),B),k3_yellow_3(A,A))
& v7_yellow_0(k5_yellow_0(k3_yellow_3(A,A),B),k3_yellow_3(A,A))
& v4_waybel_0(k5_yellow_0(k3_yellow_3(A,A),B),k3_yellow_3(A,A))
& m1_yellow_0(k5_yellow_0(k3_yellow_3(A,A),B),k3_yellow_3(A,A)) ) ) ) ) ).
fof(t36_waybel20,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
=> ( v1_waybel20(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r2_hidden(k7_yellow_3(A,A,k2_yellow_0(A,k6_eqrel_1(u1_struct_0(A),k2_waybel20(A,B),C)),C),B) ) ) ) ) ).
fof(d3_waybel20,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
=> ( v1_waybel20(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v8_waybel_1(C,A)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( C = k3_waybel20(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_waybel_0(A,A,C,D) = k2_yellow_0(A,k6_eqrel_1(u1_struct_0(A),k2_waybel20(A,B),D)) ) ) ) ) ) ) ).
fof(t37_waybel20,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
=> ( v1_waybel20(B,A)
=> ( v22_waybel_0(k3_waybel20(A,B),A,A)
& B = k5_pre_topc(k3_yellow_3(A,A),k3_yellow_3(A,A),k1_waybel20(A,A,A,A,k3_waybel20(A,B),k3_waybel20(A,B)),k6_partfun1(u1_struct_0(A))) ) ) ) ) ).
fof(t39_waybel20,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] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A))))
=> ( ( v3_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( ! [C] :
( ( v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_lattice3(C)
& v2_lattice3(C)
& v3_lattice3(C)
& v3_waybel_3(C)
& l1_orders_2(C) )
=> ~ ( u1_struct_0(C) = k8_eqrel_1(u1_struct_0(A),k2_waybel20(A,B))
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) )
=> ( ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k1_waybel_0(A,C,D,E) = k6_eqrel_1(u1_struct_0(A),k2_waybel20(A,B),E) )
=> m1_waybel16(D,A,C) ) ) ) )
| ( ~ v3_struct_0(k5_yellow_0(k3_yellow_3(A,A),B))
& v4_yellow_0(k5_yellow_0(k3_yellow_3(A,A),B),k3_yellow_3(A,A))
& v7_yellow_0(k5_yellow_0(k3_yellow_3(A,A),B),k3_yellow_3(A,A))
& v4_waybel_0(k5_yellow_0(k3_yellow_3(A,A),B),k3_yellow_3(A,A))
& m1_yellow_0(k5_yellow_0(k3_yellow_3(A,A),B),k3_yellow_3(A,A)) ) ) ) ) ) ).
fof(d4_waybel20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v8_waybel_1(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> k4_waybel20(A,B) = k5_pre_topc(k3_yellow_3(A,A),k3_yellow_3(A,A),k1_waybel20(A,A,A,A,B,B),k6_partfun1(u1_struct_0(A))) ) ) ).
fof(t40_waybel20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v8_waybel_1(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v3_relat_2(k4_waybel20(A,B))
& v8_relat_2(k4_waybel20(A,B))
& v1_partfun1(k4_waybel20(A,B),u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(k4_waybel20(A,B),u1_struct_0(A),u1_struct_0(A)) ) ) ) ).
fof(t41_waybel20,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] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v22_waybel_0(B,A,A)
& v8_waybel_1(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> v1_waybel20(k4_waybel20(A,B),A) ) ) ).
fof(d5_waybel20,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] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
=> ( v1_waybel20(B,A)
=> ! [C] :
( ( v1_orders_2(C)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_lattice3(C)
& v2_lattice3(C)
& v3_lattice3(C)
& v3_waybel_3(C)
& l1_orders_2(C) )
=> ( C = k5_waybel20(A,B)
<=> ( u1_struct_0(C) = k8_eqrel_1(u1_struct_0(A),k2_waybel20(A,B))
& ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ( r3_orders_2(C,D,E)
<=> r3_orders_2(A,k2_yellow_0(A,D),k2_yellow_0(A,E)) ) ) ) ) ) ) ) ) ) ).
fof(t42_waybel20,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] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
=> ( v1_waybel20(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k5_waybel20(A,B)))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& C = k6_eqrel_1(u1_struct_0(A),k2_waybel20(A,B),D) ) ) ) ) ) ).
fof(t43_waybel20,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] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
=> ( v1_waybel20(B,A)
=> B = k4_waybel20(A,k3_waybel20(A,B)) ) ) ) ).
fof(t44_waybel20,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] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v22_waybel_0(B,A,A)
& v8_waybel_1(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> B = k3_waybel20(A,k4_waybel20(A,B)) ) ) ).
fof(t45_waybel20,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] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v6_waybel_1(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v17_waybel_0(B,A,A)
=> ( v2_orders_2(k2_yellow_2(A,A,B))
& v3_orders_2(k2_yellow_2(A,A,B))
& v4_orders_2(k2_yellow_2(A,A,B))
& v1_lattice3(k2_yellow_2(A,A,B))
& v2_lattice3(k2_yellow_2(A,A,B))
& v3_waybel_3(k2_yellow_2(A,A,B))
& l1_orders_2(k2_yellow_2(A,A,B))
& v7_yellow_0(k2_yellow_2(A,A,B),A) ) ) ) ) ).
fof(dt_k1_waybel20,axiom,
! [A,B,C,D,E,F] :
( ( l1_orders_2(A)
& l1_orders_2(B)
& l1_orders_2(C)
& l1_orders_2(D)
& v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
& m1_relset_1(E,u1_struct_0(A),u1_struct_0(C))
& v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
& m1_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
=> ( v1_funct_1(k1_waybel20(A,B,C,D,E,F))
& v1_funct_2(k1_waybel20(A,B,C,D,E,F),u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(k3_yellow_3(C,D)))
& m2_relset_1(k1_waybel20(A,B,C,D,E,F),u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(k3_yellow_3(C,D))) ) ) ).
fof(redefinition_k1_waybel20,axiom,
! [A,B,C,D,E,F] :
( ( l1_orders_2(A)
& l1_orders_2(B)
& l1_orders_2(C)
& l1_orders_2(D)
& v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(C))
& m1_relset_1(E,u1_struct_0(A),u1_struct_0(C))
& v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(B),u1_struct_0(D))
& m1_relset_1(F,u1_struct_0(B),u1_struct_0(D)) )
=> k1_waybel20(A,B,C,D,E,F) = k15_funct_3(E,F) ) ).
fof(dt_k2_waybel20,axiom,
! [A,B] :
( ( l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
=> ( v3_relat_2(k2_waybel20(A,B))
& v8_relat_2(k2_waybel20(A,B))
& v1_partfun1(k2_waybel20(A,B),u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(k2_waybel20(A,B),u1_struct_0(A),u1_struct_0(A)) ) ) ).
fof(dt_k3_waybel20,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
=> ( v1_funct_1(k3_waybel20(A,B))
& v1_funct_2(k3_waybel20(A,B),u1_struct_0(A),u1_struct_0(A))
& v8_waybel_1(k3_waybel20(A,B),A)
& m2_relset_1(k3_waybel20(A,B),u1_struct_0(A),u1_struct_0(A)) ) ) ).
fof(dt_k4_waybel20,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v8_waybel_1(B,A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( ~ v1_xboole_0(k4_waybel20(A,B))
& m1_subset_1(k4_waybel20(A,B),k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) ) ) ).
fof(dt_k5_waybel20,axiom,
! [A,B] :
( ( 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)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) )
=> ( v1_orders_2(k5_waybel20(A,B))
& v2_orders_2(k5_waybel20(A,B))
& v3_orders_2(k5_waybel20(A,B))
& v4_orders_2(k5_waybel20(A,B))
& v1_lattice3(k5_waybel20(A,B))
& v2_lattice3(k5_waybel20(A,B))
& v3_lattice3(k5_waybel20(A,B))
& v3_waybel_3(k5_waybel20(A,B))
& l1_orders_2(k5_waybel20(A,B)) ) ) ).
fof(t38_waybel20,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] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A))))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v8_waybel_1(C,A)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ~ ( v22_waybel_0(C,A,A)
& B = k5_pre_topc(k3_yellow_3(A,A),k3_yellow_3(A,A),k1_waybel20(A,A,A,A,C,C),k6_partfun1(u1_struct_0(A)))
& ! [D] :
( ( v1_orders_2(D)
& v2_orders_2(D)
& v3_orders_2(D)
& v4_orders_2(D)
& v1_lattice3(D)
& v2_lattice3(D)
& v3_lattice3(D)
& v3_waybel_3(D)
& l1_orders_2(D) )
=> ~ ( u1_struct_0(D) = k8_eqrel_1(u1_struct_0(A),k2_waybel20(A,B))
& u1_orders_2(D) = a_3_0_waybel20(A,B,C)
& ! [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] :
( m1_subset_1(F,u1_struct_0(A))
=> k1_waybel_0(A,D,E,F) = k6_eqrel_1(u1_struct_0(A),k2_waybel20(A,B),F) )
=> m1_waybel16(E,A,D) ) ) ) ) ) ) ) ) ).
fof(fraenkel_a_3_0_waybel20,axiom,
! [A,B,C,D] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& v3_waybel_3(B)
& l1_orders_2(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,B))))
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(B))
& v8_waybel_1(D,B)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(B)) )
=> ( r2_hidden(A,a_3_0_waybel20(B,C,D))
<=> ? [E,F] :
( m1_subset_1(E,u1_struct_0(B))
& m1_subset_1(F,u1_struct_0(B))
& A = k1_domain_1(k1_zfmisc_1(u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B)),k6_eqrel_1(u1_struct_0(B),k2_waybel20(B,C),E),k6_eqrel_1(u1_struct_0(B),k2_waybel20(B,C),F))
& r3_orders_2(B,k1_waybel_0(B,B,D,E),k1_waybel_0(B,B,D,F)) ) ) ) ).
%------------------------------------------------------------------------------