TPTP Problem File: LAT361+1.p
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%------------------------------------------------------------------------------
% File : LAT361+1 : TPTP v8.2.0. Released v3.4.0.
% Domain : Lattice Theory
% Problem : Duality Based on Galois Connection - Part I T19
% Version : [Urb08] axioms : Especial.
% English :
% Refs : [Ban01] Bancerek (2001), Duality Based on the Galois Connectio
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : t19_waybel34 [Urb08]
% Status : Theorem
% Rating : 0.53 v8.2.0, 0.56 v7.5.0, 0.59 v7.4.0, 0.47 v7.3.0, 0.52 v7.2.0, 0.48 v7.1.0, 0.57 v6.4.0, 0.65 v6.3.0, 0.54 v6.2.0, 0.60 v6.1.0, 0.73 v6.0.0, 0.65 v5.5.0, 0.78 v5.4.0, 0.79 v5.3.0, 0.81 v5.2.0, 0.75 v5.1.0, 0.76 v5.0.0, 0.75 v4.1.0, 0.74 v4.0.1, 0.83 v3.7.0, 0.75 v3.5.0, 0.84 v3.4.0
% Syntax : Number of formulae : 137 ( 18 unt; 0 def)
% Number of atoms : 739 ( 20 equ)
% Maximal formula atoms : 17 ( 5 avg)
% Number of connectives : 703 ( 101 ~; 1 |; 449 &)
% ( 2 <=>; 150 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 58 ( 56 usr; 1 prp; 0-6 aty)
% Number of functors : 21 ( 21 usr; 1 con; 0-5 aty)
% Number of variables : 294 ( 261 !; 33 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : Normal version: includes the axioms (which may be theorems from
% other articles) and background that are possibly necessary.
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : The problem encoding is based on set theory.
%------------------------------------------------------------------------------
fof(t19_waybel34,conjecture,
! [A] :
( ~ v2_setfam_1(A)
=> ( k13_functor0(k5_waybel34(A),k4_waybel34(A),k5_waybel34(A),k7_waybel34(A),k6_waybel34(A)) = k12_functor0(k5_waybel34(A))
& k13_functor0(k4_waybel34(A),k5_waybel34(A),k4_waybel34(A),k6_waybel34(A),k7_waybel34(A)) = k12_functor0(k4_waybel34(A)) ) ) ).
fof(abstractness_v6_altcat_1,axiom,
! [A] :
( l2_altcat_1(A)
=> ( v6_altcat_1(A)
=> A = g2_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A)) ) ) ).
fof(abstractness_v9_functor0,axiom,
! [A,B,C] :
( ( l1_altcat_1(A)
& l1_altcat_1(B)
& l2_functor0(C,A,B) )
=> ( v9_functor0(C,A,B)
=> C = g2_functor0(A,B,u1_functor0(A,B,C),u2_functor0(A,B,C)) ) ) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( r2_hidden(A,B)
=> ~ r2_hidden(B,A) ) ).
fof(cc10_membered,axiom,
! [A] :
( v1_membered(A)
=> ! [B] :
( m1_subset_1(B,A)
=> v1_xcmplx_0(B) ) ) ).
fof(cc11_membered,axiom,
! [A] :
( v2_membered(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ( v1_xcmplx_0(B)
& v1_xreal_0(B) ) ) ) ).
fof(cc12_membered,axiom,
! [A] :
( v3_membered(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ( v1_xcmplx_0(B)
& v1_xreal_0(B)
& v1_rat_1(B) ) ) ) ).
fof(cc13_membered,axiom,
! [A] :
( v4_membered(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ( v1_xcmplx_0(B)
& v1_xreal_0(B)
& v1_int_1(B)
& v1_rat_1(B) ) ) ) ).
fof(cc14_membered,axiom,
! [A] :
( v5_membered(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ( v1_xcmplx_0(B)
& v4_ordinal2(B)
& v1_xreal_0(B)
& v1_int_1(B)
& v1_rat_1(B) ) ) ) ).
fof(cc15_membered,axiom,
! [A] :
( v1_xboole_0(A)
=> ( v1_membered(A)
& v2_membered(A)
& v3_membered(A)
& v4_membered(A)
& v5_membered(A) ) ) ).
fof(cc16_membered,axiom,
! [A] :
( v1_membered(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> v1_membered(B) ) ) ).
fof(cc17_membered,axiom,
! [A] :
( v2_membered(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ( v1_membered(B)
& v2_membered(B) ) ) ) ).
fof(cc18_membered,axiom,
! [A] :
( v3_membered(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ( v1_membered(B)
& v2_membered(B)
& v3_membered(B) ) ) ) ).
fof(cc19_membered,axiom,
! [A] :
( v4_membered(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ( v1_membered(B)
& v2_membered(B)
& v3_membered(B)
& v4_membered(B) ) ) ) ).
fof(cc1_finset_1,axiom,
! [A] :
( v1_xboole_0(A)
=> v1_finset_1(A) ) ).
fof(cc1_funct_1,axiom,
! [A] :
( v1_xboole_0(A)
=> v1_funct_1(A) ) ).
fof(cc1_functor0,axiom,
! [A,B,C,D,E] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B)
& m1_pboole(D,A)
& m1_pboole(E,B) )
=> ! [F] :
( m1_functor0(F,A,B,C,D,E)
=> v1_funcop_1(F) ) ) ).
fof(cc1_functor2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( m2_functor0(C,A,B)
=> ( v8_functor0(C,A,B)
& v12_functor0(C,A,B) ) ) ) ).
fof(cc1_membered,axiom,
! [A] :
( v5_membered(A)
=> v4_membered(A) ) ).
fof(cc1_relset_1,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> v1_relat_1(C) ) ).
fof(cc1_yellow21,axiom,
! [A] :
( l2_altcat_1(A)
=> ( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v3_yellow21(A) )
=> ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v1_altcat_2(A)
& v2_yellow21(A) ) ) ) ).
fof(cc20_membered,axiom,
! [A] :
( v5_membered(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ( v1_membered(B)
& v2_membered(B)
& v3_membered(B)
& v4_membered(B)
& v5_membered(B) ) ) ) ).
fof(cc2_finset_1,axiom,
! [A] :
( v1_finset_1(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> v1_finset_1(B) ) ) ).
fof(cc2_funct_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_xboole_0(A)
& v1_funct_1(A) )
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v2_funct_1(A) ) ) ).
fof(cc2_functor0,axiom,
! [A] :
( l2_altcat_1(A)
=> ( ( ~ v3_struct_0(A)
& v12_altcat_1(A) )
=> ( ~ v3_struct_0(A)
& v1_altcat_2(A) ) ) ) ).
fof(cc2_functor2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( m2_functor0(C,A,B)
=> ( v15_functor0(C,A,B)
=> ( v6_functor0(C,A,B)
& v8_functor0(C,A,B)
& v10_functor0(C,A,B)
& v12_functor0(C,A,B)
& v13_functor0(C,A,B) ) ) ) ) ).
fof(cc2_membered,axiom,
! [A] :
( v4_membered(A)
=> v3_membered(A) ) ).
fof(cc2_setfam_1,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ~ v1_xboole_0(A) ) ).
fof(cc2_yellow21,axiom,
! [A] :
( l2_altcat_1(A)
=> ( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow21(A) )
=> ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v9_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v1_altcat_2(A)
& v2_yellow18(A)
& v3_yellow18(A)
& v4_yellow18(A)
& v1_yellow21(A) ) ) ) ).
fof(cc3_functor0,axiom,
! [A,B] :
( ( l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_struct_0(B) )
=> ! [C] :
( l1_functor0(C,A,B)
=> ( v10_functor0(C,A,B)
=> v6_functor0(C,A,B) ) ) ) ).
fof(cc3_functor2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( m2_functor0(C,A,B)
=> ( ( v10_functor0(C,A,B)
& v13_functor0(C,A,B) )
=> ( v6_functor0(C,A,B)
& v8_functor0(C,A,B)
& v12_functor0(C,A,B)
& v15_functor0(C,A,B) ) ) ) ) ).
fof(cc3_membered,axiom,
! [A] :
( v3_membered(A)
=> v2_membered(A) ) ).
fof(cc4_functor0,axiom,
! [A,B] :
( ( l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_struct_0(B) )
=> ! [C] :
( l1_functor0(C,A,B)
=> ( v11_functor0(C,A,B)
=> v6_functor0(C,A,B) ) ) ) ).
fof(cc4_functor2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( m2_functor0(C,A,B)
=> ( v16_functor0(C,A,B)
=> ( v6_functor0(C,A,B)
& v8_functor0(C,A,B)
& v11_functor0(C,A,B)
& v12_functor0(C,A,B)
& v14_functor0(C,A,B) ) ) ) ) ).
fof(cc4_membered,axiom,
! [A] :
( v2_membered(A)
=> v1_membered(A) ) ).
fof(cc5_functor0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( m2_functor0(C,A,B)
=> ( v15_functor0(C,A,B)
=> v6_functor0(C,A,B) ) ) ) ).
fof(cc5_functor2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( m2_functor0(C,A,B)
=> ( ( v11_functor0(C,A,B)
& v14_functor0(C,A,B) )
=> ( v6_functor0(C,A,B)
& v8_functor0(C,A,B)
& v12_functor0(C,A,B)
& v16_functor0(C,A,B) ) ) ) ) ).
fof(cc6_functor0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( m2_functor0(C,A,B)
=> ( v16_functor0(C,A,B)
=> v6_functor0(C,A,B) ) ) ) ).
fof(dt_g2_altcat_1,axiom,
! [A,B,C] :
( ( m1_pboole(B,k2_zfmisc_1(A,A))
& m3_pboole(C,k3_zfmisc_1(A,A,A),k3_altcat_1(A,B,B),k2_altcat_1(A,B)) )
=> ( v6_altcat_1(g2_altcat_1(A,B,C))
& l2_altcat_1(g2_altcat_1(A,B,C)) ) ) ).
fof(dt_g2_functor0,axiom,
! [A,B,C,D] :
( ( l1_altcat_1(A)
& l1_altcat_1(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))
& m1_functor0(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),C,u1_altcat_1(A),u1_altcat_1(B)) )
=> ( v9_functor0(g2_functor0(A,B,C,D),A,B)
& l2_functor0(g2_functor0(A,B,C,D),A,B) ) ) ).
fof(dt_k11_functor0,axiom,
! [A] :
( l1_altcat_1(A)
=> ( v9_functor0(k11_functor0(A),A,A)
& l2_functor0(k11_functor0(A),A,A) ) ) ).
fof(dt_k12_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( v9_functor0(k12_functor0(A),A,A)
& v15_functor0(k12_functor0(A),A,A)
& m2_functor0(k12_functor0(A),A,A) ) ) ).
fof(dt_k13_functor0,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A)
& ~ v3_struct_0(B)
& v1_altcat_2(B)
& l1_altcat_1(B)
& ~ v3_struct_0(C)
& v1_altcat_2(C)
& l1_altcat_1(C)
& v8_functor0(D,A,B)
& l2_functor0(D,A,B)
& l2_functor0(E,B,C) )
=> ( v9_functor0(k13_functor0(A,B,C,D,E),A,C)
& l2_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) ).
fof(dt_k15_functor0,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A)
& ~ v3_struct_0(B)
& l1_altcat_1(B)
& l2_functor0(C,A,B) )
=> ( v9_functor0(k15_functor0(A,B,C),B,A)
& l2_functor0(k15_functor0(A,B,C),B,A) ) ) ).
fof(dt_k1_xboole_0,axiom,
$true ).
fof(dt_k1_zfmisc_1,axiom,
$true ).
fof(dt_k2_altcat_1,axiom,
! [A,B] :
( m1_pboole(B,k2_zfmisc_1(A,A))
=> m1_pboole(k2_altcat_1(A,B),k3_zfmisc_1(A,A,A)) ) ).
fof(dt_k2_zfmisc_1,axiom,
$true ).
fof(dt_k3_altcat_1,axiom,
! [A,B,C] :
( ( m1_pboole(B,k2_zfmisc_1(A,A))
& m1_pboole(C,k2_zfmisc_1(A,A)) )
=> m1_pboole(k3_altcat_1(A,B,C),k3_zfmisc_1(A,A,A)) ) ).
fof(dt_k3_zfmisc_1,axiom,
$true ).
fof(dt_k4_waybel34,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( ~ v3_struct_0(k4_waybel34(A))
& v2_altcat_1(k4_waybel34(A))
& v6_altcat_1(k4_waybel34(A))
& v11_altcat_1(k4_waybel34(A))
& v12_altcat_1(k4_waybel34(A))
& v2_yellow21(k4_waybel34(A))
& l2_altcat_1(k4_waybel34(A)) ) ) ).
fof(dt_k5_waybel34,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( ~ v3_struct_0(k5_waybel34(A))
& v2_altcat_1(k5_waybel34(A))
& v6_altcat_1(k5_waybel34(A))
& v11_altcat_1(k5_waybel34(A))
& v12_altcat_1(k5_waybel34(A))
& v2_yellow21(k5_waybel34(A))
& l2_altcat_1(k5_waybel34(A)) ) ) ).
fof(dt_k6_waybel34,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ( v9_functor0(k6_waybel34(A),k4_waybel34(A),k5_waybel34(A))
& v16_functor0(k6_waybel34(A),k4_waybel34(A),k5_waybel34(A))
& m2_functor0(k6_waybel34(A),k4_waybel34(A),k5_waybel34(A)) ) ) ).
fof(dt_k7_waybel34,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ( v9_functor0(k7_waybel34(A),k5_waybel34(A),k4_waybel34(A))
& v16_functor0(k7_waybel34(A),k5_waybel34(A),k4_waybel34(A))
& m2_functor0(k7_waybel34(A),k5_waybel34(A),k4_waybel34(A)) ) ) ).
fof(dt_l1_altcat_1,axiom,
! [A] :
( l1_altcat_1(A)
=> l1_struct_0(A) ) ).
fof(dt_l1_functor0,axiom,
$true ).
fof(dt_l1_struct_0,axiom,
$true ).
fof(dt_l2_altcat_1,axiom,
! [A] :
( l2_altcat_1(A)
=> l1_altcat_1(A) ) ).
fof(dt_l2_functor0,axiom,
! [A,B] :
( ( l1_altcat_1(A)
& l1_altcat_1(B) )
=> ! [C] :
( l2_functor0(C,A,B)
=> l1_functor0(C,A,B) ) ) ).
fof(dt_m1_functor0,axiom,
! [A,B,C,D,E] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B)
& m1_pboole(D,A)
& m1_pboole(E,B) )
=> ! [F] :
( m1_functor0(F,A,B,C,D,E)
=> m1_pboole(F,A) ) ) ).
fof(dt_m1_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ( v1_relat_1(B)
& v1_funct_1(B) ) ) ).
fof(dt_m1_relset_1,axiom,
$true ).
fof(dt_m1_subset_1,axiom,
$true ).
fof(dt_m2_functor0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ! [C] :
( m2_functor0(C,A,B)
=> l2_functor0(C,A,B) ) ) ).
fof(dt_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
=> m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ).
fof(dt_m3_pboole,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> ! [D] :
( m3_pboole(D,A,B,C)
=> m1_pboole(D,A) ) ) ).
fof(dt_u1_altcat_1,axiom,
! [A] :
( l1_altcat_1(A)
=> m1_pboole(u1_altcat_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) ) ).
fof(dt_u1_functor0,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& l1_struct_0(B)
& l1_functor0(C,A,B) )
=> ( v1_funct_1(u1_functor0(A,B,C))
& v1_funct_2(u1_functor0(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))
& m2_relset_1(u1_functor0(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))) ) ) ).
fof(dt_u1_struct_0,axiom,
$true ).
fof(dt_u2_altcat_1,axiom,
! [A] :
( l2_altcat_1(A)
=> m3_pboole(u2_altcat_1(A),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_altcat_1(u1_struct_0(A),u1_altcat_1(A),u1_altcat_1(A)),k2_altcat_1(u1_struct_0(A),u1_altcat_1(A))) ) ).
fof(dt_u2_functor0,axiom,
! [A,B,C] :
( ( l1_altcat_1(A)
& l1_altcat_1(B)
& l2_functor0(C,A,B) )
=> m1_functor0(u2_functor0(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_functor0(A,B,C),u1_altcat_1(A),u1_altcat_1(B)) ) ).
fof(existence_l1_altcat_1,axiom,
? [A] : l1_altcat_1(A) ).
fof(existence_l1_functor0,axiom,
! [A,B] :
( ( l1_struct_0(A)
& l1_struct_0(B) )
=> ? [C] : l1_functor0(C,A,B) ) ).
fof(existence_l1_struct_0,axiom,
? [A] : l1_struct_0(A) ).
fof(existence_l2_altcat_1,axiom,
? [A] : l2_altcat_1(A) ).
fof(existence_l2_functor0,axiom,
! [A,B] :
( ( l1_altcat_1(A)
& l1_altcat_1(B) )
=> ? [C] : l2_functor0(C,A,B) ) ).
fof(existence_m1_functor0,axiom,
! [A,B,C,D,E] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B)
& m1_pboole(D,A)
& m1_pboole(E,B) )
=> ? [F] : m1_functor0(F,A,B,C,D,E) ) ).
fof(existence_m1_pboole,axiom,
! [A] :
? [B] : m1_pboole(B,A) ).
fof(existence_m1_relset_1,axiom,
! [A,B] :
? [C] : m1_relset_1(C,A,B) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : m1_subset_1(B,A) ).
fof(existence_m2_functor0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ? [C] : m2_functor0(C,A,B) ) ).
fof(existence_m2_relset_1,axiom,
! [A,B] :
? [C] : m2_relset_1(C,A,B) ).
fof(existence_m3_pboole,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> ? [D] : m3_pboole(D,A,B,C) ) ).
fof(fc13_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A) )
=> ( v8_functor0(k11_functor0(A),A,A)
& v9_functor0(k11_functor0(A),A,A)
& v10_functor0(k11_functor0(A),A,A) ) ) ).
fof(fc14_finset_1,axiom,
! [A,B] :
( ( v1_finset_1(A)
& v1_finset_1(B) )
=> v1_finset_1(k2_zfmisc_1(A,B)) ) ).
fof(fc14_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( v8_functor0(k11_functor0(A),A,A)
& v9_functor0(k11_functor0(A),A,A)
& v10_functor0(k11_functor0(A),A,A)
& v12_functor0(k11_functor0(A),A,A)
& v13_functor0(k11_functor0(A),A,A) ) ) ).
fof(fc15_finset_1,axiom,
! [A,B,C] :
( ( v1_finset_1(A)
& v1_finset_1(B)
& v1_finset_1(C) )
=> v1_finset_1(k3_zfmisc_1(A,B,C)) ) ).
fof(fc15_functor0,axiom,
! [A] :
( l1_altcat_1(A)
=> ( v9_functor0(k11_functor0(A),A,A)
& v21_functor0(k11_functor0(A),A,A) ) ) ).
fof(fc16_functor0,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A)
& ~ v3_struct_0(B)
& v1_altcat_2(B)
& l1_altcat_1(B)
& ~ v3_struct_0(C)
& v1_altcat_2(C)
& l1_altcat_1(C)
& v8_functor0(D,A,B)
& v10_functor0(D,A,B)
& l2_functor0(D,A,B)
& v10_functor0(E,B,C)
& l2_functor0(E,B,C) )
=> ( v9_functor0(k13_functor0(A,B,C,D,E),A,C)
& v10_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) ).
fof(fc17_functor0,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A)
& ~ v3_struct_0(B)
& v1_altcat_2(B)
& l1_altcat_1(B)
& ~ v3_struct_0(C)
& v1_altcat_2(C)
& l1_altcat_1(C)
& v8_functor0(D,A,B)
& v11_functor0(D,A,B)
& l2_functor0(D,A,B)
& v10_functor0(E,B,C)
& l2_functor0(E,B,C) )
=> ( v9_functor0(k13_functor0(A,B,C,D,E),A,C)
& v11_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) ).
fof(fc18_functor0,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A)
& ~ v3_struct_0(B)
& v1_altcat_2(B)
& l1_altcat_1(B)
& ~ v3_struct_0(C)
& v1_altcat_2(C)
& l1_altcat_1(C)
& v8_functor0(D,A,B)
& v10_functor0(D,A,B)
& l2_functor0(D,A,B)
& v11_functor0(E,B,C)
& l2_functor0(E,B,C) )
=> ( v9_functor0(k13_functor0(A,B,C,D,E),A,C)
& v11_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) ).
fof(fc19_functor0,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A)
& ~ v3_struct_0(B)
& v1_altcat_2(B)
& l1_altcat_1(B)
& ~ v3_struct_0(C)
& v1_altcat_2(C)
& l1_altcat_1(C)
& v8_functor0(D,A,B)
& v11_functor0(D,A,B)
& l2_functor0(D,A,B)
& v11_functor0(E,B,C)
& l2_functor0(E,B,C) )
=> ( v9_functor0(k13_functor0(A,B,C,D,E),A,C)
& v10_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) ).
fof(fc1_struct_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ~ v1_xboole_0(u1_struct_0(A)) ) ).
fof(fc20_functor0,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A)
& ~ v3_struct_0(B)
& v1_altcat_2(B)
& l1_altcat_1(B)
& ~ v3_struct_0(C)
& v1_altcat_2(C)
& l1_altcat_1(C)
& v8_functor0(D,A,B)
& l2_functor0(D,A,B)
& v8_functor0(E,B,C)
& l2_functor0(E,B,C) )
=> ( v8_functor0(k13_functor0(A,B,C,D,E),A,C)
& v9_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) ).
fof(fc21_functor0,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B)
& ~ v3_struct_0(C)
& v12_altcat_1(C)
& l2_altcat_1(C)
& v6_functor0(D,A,B)
& v8_functor0(D,A,B)
& v12_functor0(D,A,B)
& l2_functor0(D,A,B)
& v12_functor0(E,B,C)
& l2_functor0(E,B,C) )
=> ( v9_functor0(k13_functor0(A,B,C,D,E),A,C)
& v12_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) ).
fof(fc5_waybel34,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ( ~ v3_struct_0(k4_waybel34(A))
& v2_altcat_1(k4_waybel34(A))
& v6_altcat_1(k4_waybel34(A))
& v9_altcat_1(k4_waybel34(A))
& v11_altcat_1(k4_waybel34(A))
& v12_altcat_1(k4_waybel34(A))
& v1_altcat_2(k4_waybel34(A))
& v2_yellow18(k4_waybel34(A))
& v3_yellow18(k4_waybel34(A))
& v4_yellow18(k4_waybel34(A))
& v1_yellow21(k4_waybel34(A))
& v2_yellow21(k4_waybel34(A))
& v3_yellow21(k4_waybel34(A)) ) ) ).
fof(fc6_membered,axiom,
( v1_xboole_0(k1_xboole_0)
& v1_membered(k1_xboole_0)
& v2_membered(k1_xboole_0)
& v3_membered(k1_xboole_0)
& v4_membered(k1_xboole_0)
& v5_membered(k1_xboole_0) ) ).
fof(fc6_waybel34,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ( ~ v3_struct_0(k5_waybel34(A))
& v2_altcat_1(k5_waybel34(A))
& v6_altcat_1(k5_waybel34(A))
& v9_altcat_1(k5_waybel34(A))
& v11_altcat_1(k5_waybel34(A))
& v12_altcat_1(k5_waybel34(A))
& v1_altcat_2(k5_waybel34(A))
& v2_yellow18(k5_waybel34(A))
& v3_yellow18(k5_waybel34(A))
& v4_yellow18(k5_waybel34(A))
& v1_yellow21(k5_waybel34(A))
& v2_yellow21(k5_waybel34(A))
& v3_yellow21(k5_waybel34(A)) ) ) ).
fof(fc7_functor0,axiom,
! [A,B,C] :
( ( l1_altcat_1(A)
& l1_altcat_1(B)
& l2_functor0(C,A,B) )
=> ( v1_relat_1(u2_functor0(A,B,C))
& v1_funct_1(u2_functor0(A,B,C))
& v1_funcop_1(u2_functor0(A,B,C)) ) ) ).
fof(fc7_waybel34,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ( v6_functor0(k6_waybel34(A),k4_waybel34(A),k5_waybel34(A))
& v8_functor0(k6_waybel34(A),k4_waybel34(A),k5_waybel34(A))
& v9_functor0(k6_waybel34(A),k4_waybel34(A),k5_waybel34(A))
& v11_functor0(k6_waybel34(A),k4_waybel34(A),k5_waybel34(A))
& v12_functor0(k6_waybel34(A),k4_waybel34(A),k5_waybel34(A))
& v14_functor0(k6_waybel34(A),k4_waybel34(A),k5_waybel34(A))
& v16_functor0(k6_waybel34(A),k4_waybel34(A),k5_waybel34(A))
& v21_functor0(k6_waybel34(A),k4_waybel34(A),k5_waybel34(A)) ) ) ).
fof(fc8_waybel34,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ( v6_functor0(k7_waybel34(A),k5_waybel34(A),k4_waybel34(A))
& v8_functor0(k7_waybel34(A),k5_waybel34(A),k4_waybel34(A))
& v9_functor0(k7_waybel34(A),k5_waybel34(A),k4_waybel34(A))
& v11_functor0(k7_waybel34(A),k5_waybel34(A),k4_waybel34(A))
& v12_functor0(k7_waybel34(A),k5_waybel34(A),k4_waybel34(A))
& v14_functor0(k7_waybel34(A),k5_waybel34(A),k4_waybel34(A))
& v16_functor0(k7_waybel34(A),k5_waybel34(A),k4_waybel34(A))
& v21_functor0(k7_waybel34(A),k5_waybel34(A),k4_waybel34(A)) ) ) ).
fof(free_g2_altcat_1,axiom,
! [A,B,C] :
( ( m1_pboole(B,k2_zfmisc_1(A,A))
& m3_pboole(C,k3_zfmisc_1(A,A,A),k3_altcat_1(A,B,B),k2_altcat_1(A,B)) )
=> ! [D,E,F] :
( g2_altcat_1(A,B,C) = g2_altcat_1(D,E,F)
=> ( A = D
& B = E
& C = F ) ) ) ).
fof(free_g2_functor0,axiom,
! [A,B,C,D] :
( ( l1_altcat_1(A)
& l1_altcat_1(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))
& m1_functor0(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),C,u1_altcat_1(A),u1_altcat_1(B)) )
=> ! [E,F,G,H] :
( g2_functor0(A,B,C,D) = g2_functor0(E,F,G,H)
=> ( A = E
& B = F
& C = G
& D = H ) ) ) ).
fof(rc10_functor0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ? [C] :
( m2_functor0(C,A,B)
& v8_functor0(C,A,B)
& v9_functor0(C,A,B)
& v15_functor0(C,A,B)
& v16_functor0(C,A,B) ) ) ).
fof(rc11_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A) )
=> ? [B] :
( l2_functor0(B,A,A)
& v8_functor0(B,A,A)
& v10_functor0(B,A,A) ) ) ).
fof(rc1_finset_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_finset_1(A) ) ).
fof(rc1_funct_1,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A) ) ).
fof(rc1_membered,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_membered(A)
& v2_membered(A)
& v3_membered(A)
& v4_membered(A)
& v5_membered(A) ) ).
fof(rc1_yellow21,axiom,
? [A] :
( l2_altcat_1(A)
& ~ v3_struct_0(A)
& v2_altcat_1(A)
& v6_altcat_1(A)
& v9_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v1_altcat_2(A)
& v2_yellow18(A)
& v3_yellow18(A)
& v4_yellow18(A)
& v1_yellow21(A)
& v2_yellow21(A)
& v3_yellow21(A) ) ).
fof(rc2_funct_1,axiom,
? [A] :
( v1_relat_1(A)
& v1_xboole_0(A)
& v1_funct_1(A) ) ).
fof(rc2_setfam_1,axiom,
? [A] : ~ v2_setfam_1(A) ).
fof(rc3_finset_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(B)
& v1_finset_1(B) ) ) ).
fof(rc3_funct_1,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& v2_funct_1(A) ) ).
fof(rc3_functor0,axiom,
! [A,B] :
( ( l1_altcat_1(A)
& l1_altcat_1(B) )
=> ? [C] :
( l2_functor0(C,A,B)
& v9_functor0(C,A,B) ) ) ).
fof(rc3_setfam_1,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ? [B] :
( m1_subset_1(B,A)
& ~ v1_xboole_0(B) ) ) ).
fof(rc3_struct_0,axiom,
? [A] :
( l1_struct_0(A)
& ~ v3_struct_0(A) ) ).
fof(rc4_finset_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(B)
& v1_finset_1(B) ) ) ).
fof(rc4_functor0,axiom,
! [A,B] :
( ( l1_altcat_1(A)
& l1_altcat_1(B) )
=> ? [C] :
( l2_functor0(C,A,B)
& v10_functor0(C,A,B) ) ) ).
fof(rc5_functor0,axiom,
! [A,B] :
( ( l1_altcat_1(A)
& l1_altcat_1(B) )
=> ? [C] :
( l2_functor0(C,A,B)
& v11_functor0(C,A,B) ) ) ).
fof(rc5_struct_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B) ) ) ).
fof(rc6_functor0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A)
& ~ v3_struct_0(B)
& v1_altcat_2(B)
& l1_altcat_1(B) )
=> ? [C] :
( l2_functor0(C,A,B)
& v8_functor0(C,A,B)
& v10_functor0(C,A,B)
& v11_functor0(C,A,B) ) ) ).
fof(rc7_functor0,axiom,
? [A] :
( l2_altcat_1(A)
& ~ v3_struct_0(A)
& v1_altcat_2(A) ) ).
fof(rc8_functor0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_altcat_1(A)
& ~ v3_struct_0(B)
& v1_altcat_2(B)
& l1_altcat_1(B) )
=> ? [C] :
( l2_functor0(C,A,B)
& v6_functor0(C,A,B)
& v8_functor0(C,A,B) ) ) ).
fof(rc9_functor0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& ~ v3_struct_0(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ? [C] :
( l2_functor0(C,A,B)
& v6_functor0(C,A,B)
& v8_functor0(C,A,B)
& v9_functor0(C,A,B)
& v12_functor0(C,A,B) ) ) ).
fof(redefinition_k12_functor0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> k12_functor0(A) = k11_functor0(A) ) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
<=> m1_relset_1(C,A,B) ) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : r1_tarski(A,A) ).
fof(t18_waybel34,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ( k15_functor0(k4_waybel34(A),k5_waybel34(A),k6_waybel34(A)) = k7_waybel34(A)
& k15_functor0(k5_waybel34(A),k4_waybel34(A),k7_waybel34(A)) = k6_waybel34(A) ) ) ).
fof(t1_subset,axiom,
! [A,B] :
( r2_hidden(A,B)
=> m1_subset_1(A,B) ) ).
fof(t21_functor1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v12_altcat_1(A)
& v1_altcat_2(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v12_altcat_1(B)
& v1_altcat_2(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( v8_functor0(C,A,B)
& l2_functor0(C,A,B) )
=> ( v21_functor0(C,A,B)
=> ! [D] :
( ( v8_functor0(D,B,A)
& l2_functor0(D,B,A) )
=> ( g2_functor0(B,A,u1_functor0(B,A,D),u2_functor0(B,A,D)) = k15_functor0(A,B,C)
=> k13_functor0(B,A,B,D,C) = k12_functor0(B) ) ) ) ) ) ) ).
fof(t2_subset,axiom,
! [A,B] :
( m1_subset_1(A,B)
=> ( v1_xboole_0(B)
| r2_hidden(A,B) ) ) ).
fof(t3_subset,axiom,
! [A,B] :
( m1_subset_1(A,k1_zfmisc_1(B))
<=> r1_tarski(A,B) ) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( r2_hidden(A,B)
& m1_subset_1(B,k1_zfmisc_1(C)) )
=> m1_subset_1(A,C) ) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( r2_hidden(A,B)
& m1_subset_1(B,k1_zfmisc_1(C))
& v1_xboole_0(C) ) ).
fof(t6_boole,axiom,
! [A] :
( v1_xboole_0(A)
=> A = k1_xboole_0 ) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( r2_hidden(A,B)
& v1_xboole_0(B) ) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( v1_xboole_0(A)
& A != B
& v1_xboole_0(B) ) ).
%------------------------------------------------------------------------------