SET007 Axioms: SET007+630.ax
%------------------------------------------------------------------------------
% File : SET007+630 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Function Spaces in the Category of Directed Suprema Preserving Maps
% 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 : waybel27 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 73 ( 2 unt; 0 def)
% Number of atoms : 988 ( 36 equ)
% Maximal formula atoms : 47 ( 13 avg)
% Number of connectives : 1021 ( 106 ~; 0 |; 691 &)
% ( 8 <=>; 216 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 11 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 51 ( 50 usr; 0 prp; 1-3 aty)
% Number of functors : 47 ( 47 usr; 4 con; 0-6 aty)
% Number of variables : 255 ( 246 !; 9 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(cc1_waybel27,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_xboole_0(A) )
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v1_waybel27(A)
& v2_waybel27(A)
& v3_waybel27(A) ) ) ).
fof(rc1_waybel27,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& v1_waybel27(A)
& v2_waybel27(A)
& v3_waybel27(A) ) ).
fof(fc1_waybel27,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_waybel27(A) )
=> ( v1_relat_1(k7_relat_1(A,B))
& v1_funct_1(k7_relat_1(A,B))
& v1_waybel27(k7_relat_1(A,B)) ) ) ).
fof(fc2_waybel27,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v2_waybel27(A) )
=> ( v1_relat_1(k7_relat_1(A,B))
& v1_funct_1(k7_relat_1(A,B))
& v2_waybel27(k7_relat_1(A,B)) ) ) ).
fof(rc2_waybel27,axiom,
! [A,B,C] :
? [D] :
( m1_pboole(D,k1_funct_2(A,k1_funct_2(B,C)))
& v1_relat_1(D)
& v1_funct_1(D)
& v1_waybel27(D) ) ).
fof(rc3_waybel27,axiom,
! [A,B,C] :
? [D] :
( m1_pboole(D,k1_funct_2(k2_zfmisc_1(A,B),C))
& v1_relat_1(D)
& v1_funct_1(D)
& v2_waybel27(D) ) ).
fof(cc2_waybel27,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_fraenkel(B) )
=> ! [C] :
( m1_relset_1(C,A,B)
=> ( ( v1_funct_1(C)
& v1_funct_2(C,A,B) )
=> ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& v1_funcop_1(C)
& v1_partfun1(C,A,B) ) ) ) ) ).
fof(fc3_waybel27,axiom,
! [A] :
( ( v1_monoid_0(A)
& l1_struct_0(A) )
=> v1_fraenkel(u1_struct_0(A)) ) ).
fof(fc4_waybel27,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k6_yellow_1(A,B))
& v1_orders_2(k6_yellow_1(A,B))
& v1_monoid_0(k6_yellow_1(A,B)) ) ) ).
fof(rc4_waybel27,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v1_orders_2(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& ~ v1_yellow_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v1_monoid_0(A) ) ).
fof(rc5_waybel27,axiom,
? [A] :
( l1_struct_0(A)
& ~ v3_struct_0(A)
& v1_monoid_0(A) ) ).
fof(cc3_waybel27,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_monoid_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_0(B,A)
=> ( ~ v3_struct_0(B)
=> ( ~ v3_struct_0(B)
& v1_monoid_0(B) ) ) ) ) ).
fof(fc5_waybel27,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) )
=> ( ~ v3_struct_0(k2_waybel27(A,B))
& v1_orders_2(k2_waybel27(A,B))
& v2_orders_2(k2_waybel27(A,B))
& v4_orders_2(k2_waybel27(A,B))
& ~ v1_yellow_3(k2_waybel27(A,B))
& v1_monoid_0(k2_waybel27(A,B)) ) ) ).
fof(fc6_waybel27,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k2_waybel27(A,B))
& v1_orders_2(k2_waybel27(A,B))
& v2_orders_2(k2_waybel27(A,B))
& v3_orders_2(k2_waybel27(A,B))
& v4_orders_2(k2_waybel27(A,B))
& ~ v1_yellow_3(k2_waybel27(A,B))
& v1_monoid_0(k2_waybel27(A,B)) ) ) ).
fof(fc7_waybel27,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)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k2_waybel27(A,B))
& v1_orders_2(k2_waybel27(A,B))
& v2_orders_2(k2_waybel27(A,B))
& v3_orders_2(k2_waybel27(A,B))
& v4_orders_2(k2_waybel27(A,B))
& v1_yellow_0(k2_waybel27(A,B))
& v2_yellow_0(k2_waybel27(A,B))
& v3_yellow_0(k2_waybel27(A,B))
& v24_waybel_0(k2_waybel27(A,B))
& v25_waybel_0(k2_waybel27(A,B))
& ~ v1_yellow_3(k2_waybel27(A,B))
& v1_lattice3(k2_waybel27(A,B))
& v2_lattice3(k2_waybel27(A,B))
& v3_lattice3(k2_waybel27(A,B))
& v1_monoid_0(k2_waybel27(A,B)) ) ) ).
fof(d1_waybel27,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v1_waybel27(A)
<=> ( ! [B] :
( r2_hidden(B,k1_relat_1(A))
=> ( v1_relat_1(B)
& v1_funct_1(B)
& v1_funcop_1(B) ) )
& ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( r2_hidden(B,k1_relat_1(A))
=> k1_funct_1(A,B) = k4_funct_5(B) ) ) ) ) ) ).
fof(d2_waybel27,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v2_waybel27(A)
<=> ( ! [B] :
( r2_hidden(B,k1_relat_1(A))
=> ( v1_relat_1(B)
& v1_funct_1(B)
& v1_relat_1(k1_funct_5(B)) ) )
& ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( r2_hidden(B,k1_relat_1(A))
=> k1_funct_1(A,B) = k3_funct_5(B) ) ) ) ) ) ).
fof(d3_waybel27,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v3_waybel27(A)
<=> ( ! [B] :
( r2_hidden(B,k1_relat_1(A))
=> ( v1_relat_1(B)
& v1_funct_1(B)
& v1_funcop_1(B) ) )
& ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( r2_hidden(B,k1_relat_1(A))
=> k1_funct_1(A,B) = k10_funct_6(B) ) ) ) ) ) ).
fof(t1_waybel27,axiom,
! [A,B,C,D] :
~ ( r1_tarski(D,k1_funct_2(A,k1_funct_2(B,C)))
& ! [E] :
( m1_pboole(E,D)
=> ~ ( v1_waybel27(E)
& r1_tarski(k2_relat_1(E),k1_funct_2(k2_zfmisc_1(A,B),C)) ) ) ) ).
fof(t2_waybel27,axiom,
! [A,B,C,D] :
~ ( r1_tarski(D,k1_funct_2(k2_zfmisc_1(A,B),C))
& ! [E] :
( m1_pboole(E,D)
=> ~ ( v2_waybel27(E)
& ( ( B = k1_xboole_0
=> A = k1_xboole_0 )
=> r1_tarski(k2_relat_1(E),k1_funct_2(A,k1_funct_2(B,C))) ) ) ) ) ).
fof(t3_waybel27,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C,D] :
( ( v1_relat_1(D)
& v1_funct_1(D)
& v3_waybel27(D) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E)
& v3_waybel27(E) )
=> ( ( r1_tarski(k1_relat_1(D),k1_funct_2(A,k1_funct_2(B,C)))
& r1_tarski(k2_relat_1(D),k1_relat_1(E)) )
=> k5_relat_1(D,E) = k6_partfun1(k1_relat_1(D)) ) ) ) ) ) ).
fof(t4_waybel27,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B,C,D] :
( ( v1_relat_1(D)
& v1_funct_1(D)
& v1_waybel27(D) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E)
& v2_waybel27(E) )
=> ( ( r1_tarski(k1_relat_1(D),k1_funct_2(B,k1_funct_2(A,C)))
& r1_tarski(k2_relat_1(D),k1_relat_1(E)) )
=> k5_relat_1(D,E) = k6_partfun1(k1_relat_1(D)) ) ) ) ) ).
fof(t5_waybel27,axiom,
! [A,B,C,D] :
( ( v1_relat_1(D)
& v1_funct_1(D)
& v2_waybel27(D) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E)
& v1_waybel27(E) )
=> ( ( r1_tarski(k1_relat_1(D),k1_funct_2(k2_zfmisc_1(A,B),C))
& r1_tarski(k2_relat_1(D),k1_relat_1(E)) )
=> k5_relat_1(D,E) = k6_partfun1(k1_relat_1(D)) ) ) ) ).
fof(t6_waybel27,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_funcop_1(A) )
=> ! [B,C] :
( r2_hidden(B,k1_relat_1(k10_funct_6(A)))
=> r1_tarski(k9_relat_1(k1_funct_1(k10_funct_6(A),B),C),k5_card_3(B,k9_relat_1(A,C))) ) ) ).
fof(t7_waybel27,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_funcop_1(A) )
=> ! [B,C] :
( ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( r2_hidden(D,k9_relat_1(A,C))
=> r2_hidden(B,k1_relat_1(D)) ) )
=> r1_tarski(k5_card_3(B,k9_relat_1(A,C)),k9_relat_1(k1_funct_1(k10_funct_6(A),B),C)) ) ) ).
fof(t8_waybel27,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( r1_tarski(k2_relat_1(C),k1_funct_2(A,B))
=> ! [D,E] :
( r2_hidden(D,A)
=> k9_relat_1(k1_funct_1(k10_funct_6(C),D),E) = k5_card_3(D,k9_relat_1(C,E)) ) ) ) ).
fof(t9_waybel27,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C] :
( r1_tarski(k2_zfmisc_1(C,k1_tarski(B)),k1_relat_1(A))
=> k5_card_3(B,k9_relat_1(k3_funct_5(A),C)) = k9_relat_1(A,k2_zfmisc_1(C,k1_tarski(B))) ) ) ).
fof(t10_waybel27,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] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(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)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(k2_yellow_2(B,B,C)))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(k2_yellow_2(B,B,C))) )
=> k1_partfun1(u1_struct_0(A),u1_struct_0(k2_yellow_2(B,B,C)),u1_struct_0(B),u1_struct_0(B),D,C) = D ) ) ) ) ).
fof(t11_waybel27,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) )
=> ( m1_yellow_0(B,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(A),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
=> ( ( v5_orders_3(D,A,B)
& D = E )
=> v5_orders_3(E,A,C) ) ) ) ) ) ) ) ).
fof(t12_waybel27,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) )
=> ( ( v4_yellow_0(B,C)
& m1_yellow_0(B,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(A),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) )
=> ( ( v5_orders_3(E,A,C)
& D = E )
=> v5_orders_3(D,A,B) ) ) ) ) ) ) ) ).
fof(t13_waybel27,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ( k3_funct_2(A,k2_tarski(np__0,np__1),k5_funct_3(B,A),k1_tarski(np__1)) = B
& k3_funct_2(A,k2_tarski(np__0,np__1),k5_funct_3(B,A),k1_tarski(np__0)) = k4_xboole_0(A,B) ) ) ).
fof(t14_waybel27,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k6_yellow_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k6_yellow_1(A,B)))
=> ( r1_orders_2(k6_yellow_1(A,B),C,D)
<=> ! [E] :
( m1_subset_1(E,A)
=> r1_orders_2(B,k1_waybel27(A,B,C,E),k1_waybel27(A,B,D,E)) ) ) ) ) ) ) ).
fof(t15_waybel27,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_orders_2(C) )
=> ( g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = g1_orders_2(u1_struct_0(C),u1_orders_2(C))
=> k6_yellow_1(A,B) = k6_yellow_1(A,C) ) ) ) ).
fof(t16_waybel27,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] :
( ( ~ v3_struct_0(D)
& v2_pre_topc(D)
& l1_pre_topc(D) )
=> ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))
& g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = g1_pre_topc(u1_struct_0(D),u1_pre_topc(D)) )
=> k1_waybel26(A,C) = k1_waybel26(B,D) ) ) ) ) ) ).
fof(t17_waybel27,axiom,
! [A] :
? [B] :
( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k3_yellow_1(A)),u1_struct_0(k6_yellow_1(A,k3_yellow_1(np__1))))
& m2_relset_1(B,u1_struct_0(k3_yellow_1(A)),u1_struct_0(k6_yellow_1(A,k3_yellow_1(np__1))))
& v23_waybel_0(B,k3_yellow_1(A),k6_yellow_1(A,k3_yellow_1(np__1)))
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> k1_funct_1(B,C) = k5_funct_3(C,A) ) ) ).
fof(t18_waybel27,axiom,
! [A] : r5_waybel_1(k3_yellow_1(A),k6_yellow_1(A,k3_yellow_1(np__1))) ).
fof(t19_waybel27,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& l1_orders_2(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v4_yellow_0(D,k6_yellow_1(B,k6_yellow_1(A,C)))
& m1_yellow_0(D,k6_yellow_1(B,k6_yellow_1(A,C))) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v4_yellow_0(E,k6_yellow_1(A,k6_yellow_1(B,C)))
& m1_yellow_0(E,k6_yellow_1(A,k6_yellow_1(B,C))) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(D),u1_struct_0(E))
& m2_relset_1(F,u1_struct_0(D),u1_struct_0(E)) )
=> ( v3_waybel27(F)
=> v5_orders_3(F,D,E) ) ) ) ) ) ) ) ).
fof(t20_waybel27,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& l1_orders_2(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v4_yellow_0(D,k6_yellow_1(A,k6_yellow_1(B,C)))
& m1_yellow_0(D,k6_yellow_1(A,k6_yellow_1(B,C))) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v4_yellow_0(E,k6_yellow_1(k2_zfmisc_1(A,B),C))
& m1_yellow_0(E,k6_yellow_1(k2_zfmisc_1(A,B),C)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(D),u1_struct_0(E))
& m2_relset_1(F,u1_struct_0(D),u1_struct_0(E)) )
=> ( v1_waybel27(F)
=> v5_orders_3(F,D,E) ) ) ) ) ) ) ) ).
fof(t21_waybel27,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& l1_orders_2(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v4_yellow_0(D,k6_yellow_1(A,k6_yellow_1(B,C)))
& m1_yellow_0(D,k6_yellow_1(A,k6_yellow_1(B,C))) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v4_yellow_0(E,k6_yellow_1(k2_zfmisc_1(A,B),C))
& m1_yellow_0(E,k6_yellow_1(k2_zfmisc_1(A,B),C)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(E),u1_struct_0(D))
& m2_relset_1(F,u1_struct_0(E),u1_struct_0(D)) )
=> ( v2_waybel27(F)
=> v5_orders_3(F,E,D) ) ) ) ) ) ) ) ).
fof(d4_waybel27,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_orders_2(C)
& l1_orders_2(C) )
=> ( C = k2_waybel27(A,B)
<=> ( v4_yellow_0(C,k6_yellow_1(u1_struct_0(A),B))
& m1_yellow_0(C,k6_yellow_1(u1_struct_0(A),B))
& ! [D] :
( r2_hidden(D,u1_struct_0(C))
<=> ( 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)) ) ) ) ) ) ) ) ).
fof(t22_waybel27,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> r1_tarski(u1_struct_0(k2_waybel27(A,B)),k1_funct_2(u1_struct_0(A),u1_struct_0(B))) ) ) ).
fof(t23_waybel27,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_waybel27(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k2_waybel27(A,B)))
=> ( r3_orders_2(k2_waybel27(A,B),C,D)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> r3_orders_2(B,k3_waybel27(A,B,C,E),k3_waybel27(A,B,D,E)) ) ) ) ) ) ) ).
fof(t24_waybel27,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(B) )
=> k2_waybel27(A,B) = k2_waybel17(A,B) ) ) ).
fof(t25_waybel27,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(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) )
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
& g1_orders_2(u1_struct_0(C),u1_orders_2(C)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D)) )
=> k2_waybel27(A,C) = k2_waybel27(B,D) ) ) ) ) ) ).
fof(t26_waybel27,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] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B) )
=> ( v8_yellow_0(k2_waybel27(A,B),k6_yellow_1(u1_struct_0(A),B))
& m1_yellow_0(k2_waybel27(A,B),k6_yellow_1(u1_struct_0(A),B)) ) ) ) ).
fof(t27_waybel27,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] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_waybel27(A,B))))
=> k1_yellow_0(k2_waybel27(A,B),C) = k1_yellow_0(k6_yellow_1(u1_struct_0(A),B),C) ) ) ) ).
fof(d5_waybel27,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(B))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
=> ( v22_waybel_0(E,A,B)
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(C),u1_struct_0(D))
& m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
=> ( v22_waybel_0(F,C,D)
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(k2_waybel27(B,C)),u1_struct_0(k2_waybel27(A,D)))
& m2_relset_1(G,u1_struct_0(k2_waybel27(B,C)),u1_struct_0(k2_waybel27(A,D))) )
=> ( G = k4_waybel27(A,B,C,D,E,F)
<=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,u1_struct_0(B),u1_struct_0(C))
& v22_waybel_0(H,B,C)
& m2_relset_1(H,u1_struct_0(B),u1_struct_0(C)) )
=> k1_funct_1(G,H) = k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(D),E,k7_funct_2(u1_struct_0(B),u1_struct_0(C),u1_struct_0(D),H,F)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t28_waybel27,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] :
( ( ~ v3_struct_0(C)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& l1_orders_2(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v2_orders_2(D)
& v3_orders_2(D)
& v4_orders_2(D)
& l1_orders_2(D) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v2_orders_2(E)
& v3_orders_2(E)
& v4_orders_2(E)
& l1_orders_2(E) )
=> ! [F] :
( ( ~ v3_struct_0(F)
& v2_orders_2(F)
& v3_orders_2(F)
& v4_orders_2(F)
& l1_orders_2(F) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(B),u1_struct_0(C))
& v22_waybel_0(G,B,C)
& m2_relset_1(G,u1_struct_0(B),u1_struct_0(C)) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,u1_struct_0(A),u1_struct_0(B))
& v22_waybel_0(H,A,B)
& m2_relset_1(H,u1_struct_0(A),u1_struct_0(B)) )
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(D),u1_struct_0(E))
& v22_waybel_0(I,D,E)
& m2_relset_1(I,u1_struct_0(D),u1_struct_0(E)) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(E),u1_struct_0(F))
& v22_waybel_0(J,E,F)
& m2_relset_1(J,u1_struct_0(E),u1_struct_0(F)) )
=> k7_funct_2(u1_struct_0(k2_waybel27(C,D)),u1_struct_0(k2_waybel27(B,E)),u1_struct_0(k2_waybel27(A,F)),k4_waybel27(B,C,D,E,G,I),k4_waybel27(A,B,E,F,H,J)) = k4_waybel27(A,C,D,F,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),H,G),k7_funct_2(u1_struct_0(D),u1_struct_0(E),u1_struct_0(F),I,J)) ) ) ) ) ) ) ) ) ) ) ).
fof(t29_waybel27,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) )
=> k4_waybel27(A,A,B,B,k7_grcat_1(A),k7_grcat_1(B)) = k7_grcat_1(k2_waybel27(A,B)) ) ) ).
fof(t30_waybel27,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] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_lattice3(C)
& v2_lattice3(C)
& v3_lattice3(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v2_orders_2(D)
& v3_orders_2(D)
& v4_orders_2(D)
& v1_lattice3(D)
& v2_lattice3(D)
& v3_lattice3(D)
& l1_orders_2(D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
& v22_waybel_0(E,A,B)
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(C),u1_struct_0(D))
& v22_waybel_0(F,C,D)
& m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
=> v22_waybel_0(k4_waybel27(A,B,C,D,E,F),k2_waybel27(B,C),k2_waybel27(A,D)) ) ) ) ) ) ) ).
fof(t31_waybel27,axiom,
v4_waybel11(k1_waybel25(k9_waybel18)) ).
fof(t32_waybel27,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A) )
=> k1_waybel26(A,k9_waybel18) = k2_waybel27(A,k3_yellow_1(np__1)) ) ).
fof(t33_waybel27,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_funct_1(B)
& v1_funct_2(B,u1_struct_0(k2_waybel27(A,k3_yellow_1(np__1))),u1_struct_0(k2_yellow_1(k5_waybel11(A))))
& m2_relset_1(B,u1_struct_0(k2_waybel27(A,k3_yellow_1(np__1))),u1_struct_0(k2_yellow_1(k5_waybel11(A))))
& v23_waybel_0(B,k2_waybel27(A,k3_yellow_1(np__1)),k2_yellow_1(k5_waybel11(A)))
& ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(k3_yellow_1(np__1)))
& v22_waybel_0(C,A,k3_yellow_1(np__1))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(k3_yellow_1(np__1))) )
=> k1_funct_1(B,C) = k5_pre_topc(A,k3_yellow_1(np__1),C,k1_tarski(np__1)) ) ) ) ).
fof(t34_waybel27,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) )
=> r5_waybel_1(k2_waybel27(A,k3_yellow_1(np__1)),k2_yellow_1(k5_waybel11(A))) ) ).
fof(t35_waybel27,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] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_lattice3(C)
& v2_lattice3(C)
& v3_lattice3(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v2_orders_2(D)
& v3_orders_2(D)
& v4_orders_2(D)
& v1_lattice3(D)
& v2_lattice3(D)
& v3_lattice3(D)
& l1_orders_2(D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(C),u1_struct_0(D))
& m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
=> ( ( v23_waybel_0(E,A,B)
& v23_waybel_0(F,C,D) )
=> v23_waybel_0(k4_waybel27(A,B,C,D,E,F),k2_waybel27(B,C),k2_waybel27(A,D)) ) ) ) ) ) ) ) ).
fof(t36_waybel27,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] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_lattice3(C)
& v2_lattice3(C)
& v3_lattice3(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v2_orders_2(D)
& v3_orders_2(D)
& v4_orders_2(D)
& v1_lattice3(D)
& v2_lattice3(D)
& v3_lattice3(D)
& l1_orders_2(D) )
=> ( ( r5_waybel_1(A,B)
& r5_waybel_1(C,D) )
=> r5_waybel_1(k2_waybel27(B,C),k2_waybel27(A,D)) ) ) ) ) ) ).
fof(t37_waybel27,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] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(B))
& v22_waybel_0(C,B,B)
& v6_waybel_1(C,B)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) )
=> k2_yellow_2(k2_waybel27(A,B),k2_waybel27(A,B),k4_waybel27(A,A,B,B,k7_grcat_1(A),C)) = k2_waybel27(A,k2_yellow_2(B,B,C)) ) ) ) ).
fof(t38_waybel27,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(k6_yellow_1(A,C)))
& v22_waybel_0(D,B,k6_yellow_1(A,C))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(k6_yellow_1(A,C))) )
=> ! [E] :
( m1_subset_1(E,A)
=> ( v1_funct_1(k1_funct_1(k10_funct_6(D),E))
& v1_funct_2(k1_funct_1(k10_funct_6(D),E),u1_struct_0(B),u1_struct_0(C))
& v22_waybel_0(k1_funct_1(k10_funct_6(D),E),B,C)
& m2_relset_1(k1_funct_1(k10_funct_6(D),E),u1_struct_0(B),u1_struct_0(C)) ) ) ) ) ) ) ).
fof(t39_waybel27,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(k6_yellow_1(A,C)))
& v22_waybel_0(D,B,k6_yellow_1(A,C))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(k6_yellow_1(A,C))) )
=> ( v1_funct_1(k10_funct_6(D))
& v1_funct_2(k10_funct_6(D),A,u1_struct_0(k2_waybel27(B,C)))
& m2_relset_1(k10_funct_6(D),A,u1_struct_0(k2_waybel27(B,C))) ) ) ) ) ) ).
fof(t40_waybel27,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,u1_struct_0(k2_waybel27(B,C)))
& m2_relset_1(D,A,u1_struct_0(k2_waybel27(B,C))) )
=> ( v1_funct_1(k10_funct_6(D))
& v1_funct_2(k10_funct_6(D),u1_struct_0(B),u1_struct_0(k6_yellow_1(A,C)))
& v22_waybel_0(k10_funct_6(D),B,k6_yellow_1(A,C))
& m2_relset_1(k10_funct_6(D),u1_struct_0(B),u1_struct_0(k6_yellow_1(A,C))) ) ) ) ) ) ).
fof(t41_waybel27,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& l1_orders_2(C) )
=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k2_waybel27(B,k6_yellow_1(A,C))),u1_struct_0(k6_yellow_1(A,k2_waybel27(B,C))))
& m2_relset_1(D,u1_struct_0(k2_waybel27(B,k6_yellow_1(A,C))),u1_struct_0(k6_yellow_1(A,k2_waybel27(B,C))))
& v3_waybel27(D)
& v23_waybel_0(D,k2_waybel27(B,k6_yellow_1(A,C)),k6_yellow_1(A,k2_waybel27(B,C))) ) ) ) ) ).
fof(t42_waybel27,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& l1_orders_2(C) )
=> r5_waybel_1(k2_waybel27(B,k6_yellow_1(A,C)),k6_yellow_1(A,k2_waybel27(B,C))) ) ) ) ).
fof(t43_waybel27,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) )
=> v3_waybel_3(k2_waybel27(A,B)) ) ) ).
fof(t44_waybel27,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_waybel_8(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_waybel_8(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B) )
=> v2_waybel_8(k2_waybel27(A,B)) ) ) ).
fof(t45_waybel27,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] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_lattice3(C)
& v2_lattice3(C)
& v3_lattice3(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(k2_waybel27(B,C)))
& v22_waybel_0(D,A,k2_waybel27(B,C))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(k2_waybel27(B,C))) )
=> ( v1_funct_1(k4_funct_5(D))
& v1_funct_2(k4_funct_5(D),u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
& v22_waybel_0(k4_funct_5(D),k3_yellow_3(A,B),C)
& m2_relset_1(k4_funct_5(D),u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C)) ) ) ) ) ) ).
fof(t46_waybel27,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] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_lattice3(C)
& v2_lattice3(C)
& v3_lattice3(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
& v22_waybel_0(D,k3_yellow_3(A,B),C)
& m2_relset_1(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C)) )
=> ( v1_funct_1(k3_funct_5(D))
& v1_funct_2(k3_funct_5(D),u1_struct_0(A),u1_struct_0(k2_waybel27(B,C)))
& v22_waybel_0(k3_funct_5(D),A,k2_waybel27(B,C))
& m2_relset_1(k3_funct_5(D),u1_struct_0(A),u1_struct_0(k2_waybel27(B,C))) ) ) ) ) ) ).
fof(t47_waybel27,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] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_lattice3(C)
& v2_lattice3(C)
& v3_lattice3(C)
& l1_orders_2(C) )
=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k2_waybel27(A,k2_waybel27(B,C))),u1_struct_0(k2_waybel27(k3_yellow_3(A,B),C)))
& m2_relset_1(D,u1_struct_0(k2_waybel27(A,k2_waybel27(B,C))),u1_struct_0(k2_waybel27(k3_yellow_3(A,B),C)))
& v1_waybel27(D)
& v23_waybel_0(D,k2_waybel27(A,k2_waybel27(B,C)),k2_waybel27(k3_yellow_3(A,B),C)) ) ) ) ) ).
fof(dt_k1_waybel27,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& l1_orders_2(B)
& m1_subset_1(C,u1_struct_0(k6_yellow_1(A,B)))
& m1_subset_1(D,A) )
=> m1_subset_1(k1_waybel27(A,B,C,D),u1_struct_0(B)) ) ).
fof(redefinition_k1_waybel27,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& l1_orders_2(B)
& m1_subset_1(C,u1_struct_0(k6_yellow_1(A,B)))
& m1_subset_1(D,A) )
=> k1_waybel27(A,B,C,D) = k1_funct_1(C,D) ) ).
fof(dt_k2_waybel27,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) )
=> ( v1_orders_2(k2_waybel27(A,B))
& l1_orders_2(k2_waybel27(A,B)) ) ) ).
fof(dt_k3_waybel27,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B)
& m1_subset_1(C,u1_struct_0(k2_waybel27(A,B)))
& m1_subset_1(D,u1_struct_0(A)) )
=> m1_subset_1(k3_waybel27(A,B,C,D),u1_struct_0(B)) ) ).
fof(redefinition_k3_waybel27,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B)
& m1_subset_1(C,u1_struct_0(k2_waybel27(A,B)))
& m1_subset_1(D,u1_struct_0(A)) )
=> k3_waybel27(A,B,C,D) = k1_funct_1(C,D) ) ).
fof(dt_k4_waybel27,axiom,
! [A,B,C,D,E,F] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B)
& ~ v3_struct_0(C)
& v2_orders_2(C)
& v4_orders_2(C)
& l1_orders_2(C)
& ~ v3_struct_0(D)
& v2_orders_2(D)
& v4_orders_2(D)
& l1_orders_2(D)
& v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(E,u1_struct_0(A),u1_struct_0(B))
& v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(C),u1_struct_0(D))
& m1_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
=> ( v1_funct_1(k4_waybel27(A,B,C,D,E,F))
& v1_funct_2(k4_waybel27(A,B,C,D,E,F),u1_struct_0(k2_waybel27(B,C)),u1_struct_0(k2_waybel27(A,D)))
& m2_relset_1(k4_waybel27(A,B,C,D,E,F),u1_struct_0(k2_waybel27(B,C)),u1_struct_0(k2_waybel27(A,D))) ) ) ).
%------------------------------------------------------------------------------