SET007 Axioms: SET007+441.ax
%------------------------------------------------------------------------------
% File : SET007+441 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Minimal Signature for Partial Algebra
% 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 : pua2mss1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 102 ( 4 unt; 0 def)
% Number of atoms : 686 ( 67 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 653 ( 69 ~; 2 |; 302 &)
% ( 31 <=>; 249 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 53 ( 51 usr; 1 prp; 0-4 aty)
% Number of functors : 79 ( 79 usr; 16 con; 0-6 aty)
% Number of variables : 323 ( 295 !; 28 ?)
% 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_pua2mss1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B) )
=> ? [C] :
( m1_relset_1(C,A,B)
& ~ v1_xboole_0(C)
& v1_relat_1(C)
& v1_funct_1(C) ) ) ).
fof(cc1_pua2mss1,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( m1_finseq_1(B,A)
=> v2_relat_1(B) ) ) ).
fof(rc2_pua2mss1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A))
& ~ v1_xboole_0(B)
& v1_relat_1(B)
& v2_relat_1(B)
& v1_funct_1(B)
& v1_finset_1(B)
& v1_finseq_1(B)
& v4_unialg_1(B,A)
& v5_unialg_1(B,A) ) ) ).
fof(cc2_pua2mss1,axiom,
! [A] :
( l1_unialg_1(A)
=> ( v8_unialg_1(A)
=> ~ v3_struct_0(A) ) ) ).
fof(cc3_pua2mss1,axiom,
! [A,B] :
( m2_pua2mss1(B,A)
=> ( v2_relat_1(B)
& v2_funct_1(B) ) ) ).
fof(cc4_pua2mss1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_pua2mss1(B,A)
=> ( ~ v1_xboole_0(B)
& v2_relat_1(B)
& v2_funct_1(B) ) ) ) ).
fof(fc1_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ( v1_relat_1(k7_pua2mss1(A))
& v1_relat_2(k7_pua2mss1(A))
& v3_relat_2(k7_pua2mss1(A))
& v8_relat_2(k7_pua2mss1(A))
& v1_partfun1(k7_pua2mss1(A),u1_struct_0(A),u1_struct_0(A)) ) ) ).
fof(fc2_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ( v1_relat_1(k10_pua2mss1(A))
& v1_relat_2(k10_pua2mss1(A))
& v3_relat_2(k10_pua2mss1(A))
& v8_relat_2(k10_pua2mss1(A))
& v1_partfun1(k10_pua2mss1(A),u1_struct_0(A),u1_struct_0(A)) ) ) ).
fof(fc3_pua2mss1,axiom,
! [A,B] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A)
& m3_pua2mss1(B,A) )
=> ( ~ v3_struct_0(k12_pua2mss1(A,B))
& v1_msualg_1(k12_pua2mss1(A,B))
& ~ v2_msualg_1(k12_pua2mss1(A,B)) ) ) ).
fof(t1_pua2mss1,axiom,
! [A] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v2_relat_1(B)
& v1_funct_1(B) )
=> ( r1_tarski(k4_card_3(A),k4_card_3(B))
=> ( k1_relat_1(A) = k1_relat_1(B)
& ! [C] :
( r2_hidden(C,k1_relat_1(A))
=> r1_tarski(k1_funct_1(A,C),k1_funct_1(B,C)) ) ) ) ) ) ).
fof(t2_pua2mss1,axiom,
! [A] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v2_relat_1(B)
& v1_funct_1(B) )
=> ( k4_card_3(A) = k4_card_3(B)
=> A = B ) ) ) ).
fof(d1_pua2mss1,axiom,
! [A] :
( ( v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m1_subset_1(B,k4_finseq_1(u1_unialg_1(A)))
=> k2_pua2mss1(A,B) = k1_funct_1(u1_unialg_1(A),B) ) ) ).
fof(t3_pua2mss1,axiom,
! [A,B] :
( m1_eqrel_1(B,A)
=> ! [C,D,E] :
( ( r2_hidden(C,D)
& r2_hidden(D,B)
& r2_hidden(C,E)
& r2_hidden(E,B) )
=> D = E ) ) ).
fof(t4_pua2mss1,axiom,
! [A,B] :
( r1_setfam_1(A,B)
=> ! [C] :
( m2_finseq_1(C,A)
=> ? [D] :
( m2_finseq_1(D,B)
& r1_tarski(k4_card_3(C),k4_card_3(D)) ) ) ) ).
fof(t5_pua2mss1,axiom,
! [A,B] :
( m1_eqrel_1(B,A)
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,C)
& m2_relset_1(D,B,C) )
=> ( ! [E] :
( r2_hidden(E,B)
=> r1_tarski(E,k1_funct_1(D,E)) )
=> ! [E] :
( m2_finseq_1(E,B)
=> ! [F] :
( m2_finseq_1(F,C)
=> ( r1_tarski(k4_card_3(E),k4_card_3(F))
<=> k1_partfun1(k5_numbers,B,B,C,E,D) = F ) ) ) ) ) ) ) ).
fof(t6_pua2mss1,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ~ ( r1_tarski(k2_relat_1(B),k3_tarski(A))
& ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ~ ( k1_relat_1(C) = k1_relat_1(B)
& r1_tarski(k2_relat_1(C),A)
& r2_hidden(B,k4_card_3(C)) ) ) ) ) ).
fof(t7_pua2mss1,axiom,
! [A,B] :
( m1_eqrel_1(B,A)
=> ! [C] :
( m2_finseq_1(C,A)
=> ? [D] :
( m2_finseq_1(D,B)
& r2_hidden(C,k4_card_3(D)) ) ) ) ).
fof(d2_pua2mss1,axiom,
! [A] : k3_pua2mss1(A) = k8_eqrel_1(A,k6_partfun1(A)) ).
fof(t14_pua2mss1,axiom,
! [A,B] :
( m2_finseq_1(B,k3_pua2mss1(A))
=> ? [C] :
( m2_finseq_1(C,A)
& k4_card_3(B) = k1_tarski(C) ) ) ).
fof(d3_pua2mss1,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( m2_pua2mss1(B,A)
<=> ( m1_eqrel_1(k2_relat_1(B),A)
& v2_funct_1(B) ) ) ) ).
fof(d4_pua2mss1,axiom,
! [A,B] :
( m2_pua2mss1(B,A)
=> ! [C] :
( r2_hidden(C,A)
=> ! [D] :
( D = k6_pua2mss1(A,B,C)
<=> ( r2_hidden(D,k1_relat_1(B))
& r2_hidden(C,k1_funct_1(B,D)) ) ) ) ) ).
fof(t15_pua2mss1,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v2_relat_1(B)
& v1_funct_1(B) )
=> ( ( k3_card_3(B) = A
& ! [C,D] :
( ( r2_hidden(C,k1_relat_1(B))
& r2_hidden(D,k1_relat_1(B)) )
=> ( C = D
| r1_xboole_0(k1_funct_1(B,C),k1_funct_1(B,D)) ) ) )
=> m2_pua2mss1(B,A) ) ) ).
fof(t16_pua2mss1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_eqrel_1(C,B)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,C)
& m2_relset_1(D,A,C) )
=> ( ( r1_tarski(C,k2_relat_1(D))
& v2_funct_1(D) )
=> m2_pua2mss1(D,B) ) ) ) ) ) ).
fof(d5_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( B = k7_pua2mss1(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(k4_tarski(C,D),B)
<=> ! [E] :
( m1_pua2mss1(E,k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),k1_pua2mss1(u1_struct_0(A),u1_unialg_1(A)))
=> ! [F] :
( ( v1_relat_1(F)
& v1_funct_1(F)
& v1_finseq_1(F) )
=> ! [G] :
( ( v1_relat_1(G)
& v1_funct_1(G)
& v1_finseq_1(G) )
=> ( r2_hidden(k7_finseq_1(k7_finseq_1(F,k12_finseq_1(u1_struct_0(A),C)),G),k4_relset_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),E))
<=> r2_hidden(k7_finseq_1(k7_finseq_1(F,k12_finseq_1(u1_struct_0(A),D)),G),k4_relset_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),E)) ) ) ) ) ) ) ) ) ) ) ).
fof(d6_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ! [C] :
( m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
=> ( C = k8_pua2mss1(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r2_hidden(k4_tarski(D,E),C)
<=> ( r2_hidden(k4_tarski(D,E),B)
& ! [F] :
( m1_pua2mss1(F,k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),k1_pua2mss1(u1_struct_0(A),u1_unialg_1(A)))
=> ! [G] :
( ( v1_relat_1(G)
& v1_funct_1(G)
& v1_finseq_1(G) )
=> ! [H] :
( ( v1_relat_1(H)
& v1_funct_1(H)
& v1_finseq_1(H) )
=> ( ( r2_hidden(k7_finseq_1(k7_finseq_1(G,k12_finseq_1(u1_struct_0(A),D)),H),k4_relset_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),F))
& r2_hidden(k7_finseq_1(k7_finseq_1(G,k12_finseq_1(u1_struct_0(A),E)),H),k4_relset_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),F)) )
=> r2_hidden(k4_tarski(k1_funct_1(F,k7_finseq_1(k7_finseq_1(G,k12_finseq_1(u1_struct_0(A),D)),H)),k1_funct_1(F,k7_finseq_1(k7_finseq_1(G,k12_finseq_1(u1_struct_0(A),E)),H))),B) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d7_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_relset_1(D,u1_struct_0(A),u1_struct_0(A))
=> ( D = k9_pua2mss1(A,B,C)
<=> ? [E] :
( m1_pboole(E,k5_numbers)
& D = k1_funct_1(E,C)
& k1_funct_1(E,np__0) = B
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m2_relset_1(G,u1_struct_0(A),u1_struct_0(A))
=> ( G = k1_funct_1(E,F)
=> k1_funct_1(E,k1_nat_1(F,np__1)) = k8_pua2mss1(A,G) ) ) ) ) ) ) ) ) ) ).
fof(t17_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( k9_pua2mss1(A,B,np__0) = B
& k9_pua2mss1(A,B,np__1) = k8_pua2mss1(A,B) ) ) ) ).
fof(t18_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
=> k9_pua2mss1(A,C,k1_nat_1(B,np__1)) = k8_pua2mss1(A,k9_pua2mss1(A,C,B)) ) ) ) ).
fof(t19_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_relset_1(D,u1_struct_0(A),u1_struct_0(A))
=> k9_pua2mss1(A,D,k1_nat_1(B,C)) = k9_pua2mss1(A,k9_pua2mss1(A,D,B),C) ) ) ) ) ).
fof(t20_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( 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)) )
=> ( r1_tarski(B,k7_pua2mss1(A))
=> ( v1_partfun1(k8_pua2mss1(A,B),u1_struct_0(A),u1_struct_0(A))
& v3_relat_2(k8_pua2mss1(A,B))
& v8_relat_2(k8_pua2mss1(A,B)) ) ) ) ) ).
fof(t21_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> r1_tarski(k8_pua2mss1(A,B),B) ) ) ).
fof(t22_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( 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)) )
=> ( r1_tarski(B,k7_pua2mss1(A))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( v1_partfun1(k9_pua2mss1(A,B,C),u1_struct_0(A),u1_struct_0(A))
& v3_relat_2(k9_pua2mss1(A,B,C))
& v8_relat_2(k9_pua2mss1(A,B,C)) ) ) ) ) ) ).
fof(d8_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( B = k10_pua2mss1(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(k4_tarski(C,D),B)
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> r2_hidden(k4_tarski(C,D),k9_pua2mss1(A,k7_pua2mss1(A),E)) ) ) ) ) ) ) ) ).
fof(t23_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> r1_tarski(k10_pua2mss1(A),k7_pua2mss1(A)) ) ).
fof(d9_pua2mss1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k3_finseq_2(A),A) )
=> ! [C] :
( m1_eqrel_1(C,A)
=> ( r1_pua2mss1(A,B,C)
<=> ! [D] :
( m2_finseq_1(D,C)
=> ? [E] :
( m2_subset_1(E,k1_zfmisc_1(A),C)
& r1_tarski(k9_relat_1(B,k4_card_3(D)),E) ) ) ) ) ) ) ).
fof(d10_pua2mss1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k3_finseq_2(A),A) )
=> ! [C] :
( m1_eqrel_1(C,A)
=> ( r2_pua2mss1(A,B,C)
<=> ( r1_pua2mss1(A,B,C)
& ! [D] :
( m2_finseq_1(D,C)
=> ( ~ r1_xboole_0(k4_card_3(D),k4_relset_1(k3_finseq_2(A),A,B))
=> r1_tarski(k4_card_3(D),k4_relset_1(k3_finseq_2(A),A,B)) ) ) ) ) ) ) ) ).
fof(t24_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m1_pua2mss1(B,k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),k1_pua2mss1(u1_struct_0(A),u1_unialg_1(A)))
=> r2_pua2mss1(u1_struct_0(A),B,k3_pua2mss1(u1_struct_0(A))) ) ) ).
fof(t25_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m1_pua2mss1(B,k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),k1_pua2mss1(u1_struct_0(A),u1_unialg_1(A)))
=> r2_pua2mss1(u1_struct_0(A),B,k8_eqrel_1(u1_struct_0(A),k10_pua2mss1(A))) ) ) ).
fof(d11_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m1_eqrel_1(B,u1_struct_0(A))
=> ( m3_pua2mss1(B,A)
<=> ! [C] :
( m1_pua2mss1(C,k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),k1_pua2mss1(u1_struct_0(A),u1_unialg_1(A)))
=> r2_pua2mss1(u1_struct_0(A),C,B) ) ) ) ) ).
fof(d12_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m2_pua2mss1(B,u1_struct_0(A))
=> ( m4_pua2mss1(B,A)
<=> m3_pua2mss1(k4_pua2mss1(u1_struct_0(A),B),A) ) ) ) ).
fof(t26_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> m3_pua2mss1(k8_eqrel_1(u1_struct_0(A),k10_pua2mss1(A)),A) ) ).
fof(t27_pua2mss1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_eqrel_1(B,A)
=> ! [C] :
( m2_finseq_1(C,B)
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D)
& v1_finseq_1(D) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E)
& v1_finseq_1(E) )
=> ! [F,G] :
( r2_hidden(k7_finseq_1(k7_finseq_1(D,k9_finseq_1(F)),E),k4_card_3(C))
=> ( ! [H] :
( m2_subset_1(H,k1_zfmisc_1(A),B)
=> ~ ( r2_hidden(F,H)
& r2_hidden(G,H) ) )
| r2_hidden(k7_finseq_1(k7_finseq_1(D,k9_finseq_1(G)),E),k4_card_3(C)) ) ) ) ) ) ) ) ).
fof(t28_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m3_pua2mss1(B,A)
=> r1_setfam_1(B,k8_eqrel_1(u1_struct_0(A),k10_pua2mss1(A))) ) ) ).
fof(d13_pua2mss1,axiom,
! [A] :
( l1_msualg_1(A)
=> ! [B] :
( l1_msualg_1(B)
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( r3_pua2mss1(A,B,C,D)
<=> ( k1_relat_1(C) = u1_struct_0(A)
& k1_relat_1(D) = u1_msualg_1(A)
& r1_tarski(k2_relat_1(C),u1_struct_0(B))
& r1_tarski(k2_relat_1(D),u1_msualg_1(B))
& k5_relat_1(u3_msualg_1(A),C) = k5_relat_1(D,u3_msualg_1(B))
& ! [E,F] :
( ( v1_relat_1(F)
& v1_funct_1(F) )
=> ( ( r2_hidden(E,u1_msualg_1(A))
& F = k1_funct_1(u2_msualg_1(A),E) )
=> k5_relat_1(F,C) = k1_funct_1(u2_msualg_1(B),k1_funct_1(D,E)) ) ) ) ) ) ) ) ) ).
fof(t29_pua2mss1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> r3_pua2mss1(A,A,k6_partfun1(u1_struct_0(A)),k6_partfun1(u1_msualg_1(A))) ) ).
fof(t30_pua2mss1,axiom,
! [A] :
( l1_msualg_1(A)
=> ! [B] :
( l1_msualg_1(B)
=> ! [C] :
( l1_msualg_1(C)
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ! [F] :
( ( v1_relat_1(F)
& v1_funct_1(F) )
=> ! [G] :
( ( v1_relat_1(G)
& v1_funct_1(G) )
=> ( ( r3_pua2mss1(A,B,D,F)
& r3_pua2mss1(B,C,E,G) )
=> r3_pua2mss1(A,C,k5_relat_1(D,E),k5_relat_1(F,G)) ) ) ) ) ) ) ) ) ).
fof(d14_pua2mss1,axiom,
! [A] :
( l1_msualg_1(A)
=> ! [B] :
( l1_msualg_1(B)
=> ( r4_pua2mss1(A,B)
<=> ? [C] :
( v1_relat_1(C)
& v1_funct_1(C)
& ? [D] :
( v1_relat_1(D)
& v1_funct_1(D)
& r3_pua2mss1(B,A,C,D)
& k2_relat_1(C) = u1_struct_0(A)
& k2_relat_1(D) = u1_msualg_1(A) ) ) ) ) ) ).
fof(t31_pua2mss1,axiom,
! [A] :
( l1_msualg_1(A)
=> ! [B] :
( l1_msualg_1(B)
=> ! [C] :
( l1_msualg_1(C)
=> ( ( r4_pua2mss1(A,B)
& r4_pua2mss1(B,C) )
=> r4_pua2mss1(A,C) ) ) ) ) ).
fof(d16_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( l3_msualg_1(C,B)
=> ! [D] :
( m2_pua2mss1(D,u1_msualg_1(B))
=> ( r6_pua2mss1(A,B,C,D)
<=> ( m4_pua2mss1(u4_msualg_1(B,C),A)
& k1_relat_1(D) = k4_finseq_1(u1_unialg_1(A))
& ! [E] :
( m1_subset_1(E,k4_finseq_1(u1_unialg_1(A)))
=> m2_pua2mss1(k7_relat_1(u5_msualg_1(B,C),k1_funct_1(D,E)),k2_pua2mss1(A,E)) ) ) ) ) ) ) ) ).
fof(d17_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ( r7_pua2mss1(A,B)
<=> ? [C] :
( l3_msualg_1(C,B)
& ? [D] :
( m2_pua2mss1(D,u1_msualg_1(B))
& r6_pua2mss1(A,B,C,D) ) ) ) ) ) ).
fof(t32_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m3_pua2mss1(B,A)
=> r7_pua2mss1(A,k12_pua2mss1(A,B)) ) ) ).
fof(t33_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ! [C] :
( l3_msualg_1(C,B)
=> ! [D] :
( m2_pua2mss1(D,u1_msualg_1(B))
=> ( r6_pua2mss1(A,B,C,D)
=> ! [E] :
( m1_subset_1(E,k4_finseq_1(u1_unialg_1(A)))
=> ! [F] :
( m2_finseq_1(F,k2_relat_1(u4_msualg_1(B,C)))
=> ~ ( r1_tarski(k4_card_3(F),k4_relset_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),k2_pua2mss1(A,E)))
& ! [G] :
( m1_subset_1(G,u1_msualg_1(B))
=> ~ ( k5_relat_1(k1_msualg_1(B,G),u4_msualg_1(B,C)) = F
& r2_hidden(G,k1_funct_1(D,E)) ) ) ) ) ) ) ) ) ) ) ).
fof(t34_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m3_pua2mss1(B,A)
=> ( B = k8_eqrel_1(u1_struct_0(A),k10_pua2mss1(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& ~ v2_msualg_1(C)
& l1_msualg_1(C) )
=> ( r7_pua2mss1(A,C)
=> r5_pua2mss1(k12_pua2mss1(A,B),C) ) ) ) ) ) ).
fof(s1_pua2mss1,axiom,
? [A] :
( m2_relset_1(A,f1_s1_pua2mss1,f2_s1_pua2mss1)
& ? [B] :
( m1_pboole(B,k5_numbers)
& A = k1_funct_1(B,f3_s1_pua2mss1)
& k1_funct_1(B,np__0) = f4_s1_pua2mss1
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_relset_1(D,f1_s1_pua2mss1,f2_s1_pua2mss1)
=> ( D = k1_funct_1(B,C)
=> k1_funct_1(B,k1_nat_1(C,np__1)) = f5_s1_pua2mss1(D,C) ) ) ) ) ) ).
fof(s2_pua2mss1,axiom,
! [A] :
( m2_relset_1(A,f1_s2_pua2mss1,f2_s2_pua2mss1)
=> ! [B] :
( m2_relset_1(B,f1_s2_pua2mss1,f2_s2_pua2mss1)
=> ( ( ! [C] :
( m1_subset_1(C,f1_s2_pua2mss1)
=> ! [D] :
( m1_subset_1(D,f2_s2_pua2mss1)
=> ( r2_hidden(k4_tarski(C,D),A)
<=> p1_s2_pua2mss1(C,D) ) ) )
& ! [C] :
( m1_subset_1(C,f1_s2_pua2mss1)
=> ! [D] :
( m1_subset_1(D,f2_s2_pua2mss1)
=> ( r2_hidden(k4_tarski(C,D),B)
<=> p1_s2_pua2mss1(C,D) ) ) ) )
=> A = B ) ) ) ).
fof(s3_pua2mss1,axiom,
! [A] :
( m2_relset_1(A,f1_s3_pua2mss1,f2_s3_pua2mss1)
=> ! [B] :
( m2_relset_1(B,f1_s3_pua2mss1,f2_s3_pua2mss1)
=> ~ ( ? [C] :
( m1_pboole(C,k5_numbers)
& A = k1_funct_1(C,f3_s3_pua2mss1)
& k1_funct_1(C,np__0) = f4_s3_pua2mss1
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_relset_1(E,f1_s3_pua2mss1,f2_s3_pua2mss1)
=> ( E = k1_funct_1(C,D)
=> k1_funct_1(C,k1_nat_1(D,np__1)) = f5_s3_pua2mss1(E,D) ) ) ) )
& ? [C] :
( m1_pboole(C,k5_numbers)
& B = k1_funct_1(C,f3_s3_pua2mss1)
& k1_funct_1(C,np__0) = f4_s3_pua2mss1
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_relset_1(E,f1_s3_pua2mss1,f2_s3_pua2mss1)
=> ( E = k1_funct_1(C,D)
=> k1_funct_1(C,k1_nat_1(D,np__1)) = f5_s3_pua2mss1(E,D) ) ) ) )
& A != B ) ) ) ).
fof(s4_pua2mss1,axiom,
( ( p1_s4_pua2mss1(f1_s4_pua2mss1)
& k3_finseq_1(f1_s4_pua2mss1) = k3_finseq_1(f2_s4_pua2mss1)
& ! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ! [C,D] :
( ( p1_s4_pua2mss1(k7_finseq_1(k7_finseq_1(A,k9_finseq_1(C)),B))
& p2_s4_pua2mss1(C,D) )
=> p1_s4_pua2mss1(k7_finseq_1(k7_finseq_1(A,k9_finseq_1(D)),B)) ) ) )
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( r2_hidden(A,k4_finseq_1(f1_s4_pua2mss1))
=> p2_s4_pua2mss1(k1_funct_1(f1_s4_pua2mss1,A),k1_funct_1(f2_s4_pua2mss1,A)) ) ) )
=> p1_s4_pua2mss1(f2_s4_pua2mss1) ) ).
fof(dt_m1_pua2mss1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(k4_partfun1(A,B))) )
=> ! [D] :
( m1_pua2mss1(D,A,B,C)
=> ( v1_funct_1(D)
& m2_relset_1(D,A,B) ) ) ) ).
fof(existence_m1_pua2mss1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(k4_partfun1(A,B))) )
=> ? [D] : m1_pua2mss1(D,A,B,C) ) ).
fof(redefinition_m1_pua2mss1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(k4_partfun1(A,B))) )
=> ! [D] :
( m1_pua2mss1(D,A,B,C)
<=> m1_subset_1(D,C) ) ) ).
fof(dt_m2_pua2mss1,axiom,
! [A,B] :
( m2_pua2mss1(B,A)
=> ( v1_relat_1(B)
& v1_funct_1(B) ) ) ).
fof(existence_m2_pua2mss1,axiom,
! [A] :
? [B] : m2_pua2mss1(B,A) ).
fof(dt_m3_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m3_pua2mss1(B,A)
=> m1_eqrel_1(B,u1_struct_0(A)) ) ) ).
fof(existence_m3_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ? [B] : m3_pua2mss1(B,A) ) ).
fof(dt_m4_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m4_pua2mss1(B,A)
=> m2_pua2mss1(B,u1_struct_0(A)) ) ) ).
fof(existence_m4_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ? [B] : m4_pua2mss1(B,A) ) ).
fof(reflexivity_r5_pua2mss1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> r5_pua2mss1(A,A) ) ).
fof(redefinition_r5_pua2mss1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A)
& ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& l1_msualg_1(B) )
=> ( r5_pua2mss1(A,B)
<=> r4_pua2mss1(A,B) ) ) ).
fof(dt_k1_pua2mss1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)) )
=> m1_subset_1(k1_pua2mss1(A,B),k1_zfmisc_1(k4_partfun1(k3_finseq_2(A),A))) ) ).
fof(redefinition_k1_pua2mss1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)) )
=> k1_pua2mss1(A,B) = k2_relat_1(B) ) ).
fof(dt_k2_pua2mss1,axiom,
! [A,B] :
( ( v8_unialg_1(A)
& l1_unialg_1(A)
& m1_subset_1(B,k4_finseq_1(u1_unialg_1(A))) )
=> m1_pua2mss1(k2_pua2mss1(A,B),k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),k1_pua2mss1(u1_struct_0(A),u1_unialg_1(A))) ) ).
fof(dt_k3_pua2mss1,axiom,
! [A] : m1_eqrel_1(k3_pua2mss1(A),A) ).
fof(dt_k4_pua2mss1,axiom,
! [A,B] :
( m2_pua2mss1(B,A)
=> m1_eqrel_1(k4_pua2mss1(A,B),A) ) ).
fof(redefinition_k4_pua2mss1,axiom,
! [A,B] :
( m2_pua2mss1(B,A)
=> k4_pua2mss1(A,B) = k2_relat_1(B) ) ).
fof(dt_k5_pua2mss1,axiom,
! [A,B] :
( m1_eqrel_1(B,A)
=> m2_pua2mss1(k5_pua2mss1(A,B),A) ) ).
fof(redefinition_k5_pua2mss1,axiom,
! [A,B] :
( m1_eqrel_1(B,A)
=> k5_pua2mss1(A,B) = k6_relat_1(B) ) ).
fof(dt_k6_pua2mss1,axiom,
$true ).
fof(dt_k7_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> m2_relset_1(k7_pua2mss1(A),u1_struct_0(A),u1_struct_0(A)) ) ).
fof(dt_k8_pua2mss1,axiom,
! [A,B] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> m2_relset_1(k8_pua2mss1(A,B),u1_struct_0(A),u1_struct_0(A)) ) ).
fof(dt_k9_pua2mss1,axiom,
! [A,B,C] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
& m1_subset_1(C,k5_numbers) )
=> m2_relset_1(k9_pua2mss1(A,B,C),u1_struct_0(A),u1_struct_0(A)) ) ).
fof(dt_k10_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> m2_relset_1(k10_pua2mss1(A),u1_struct_0(A),u1_struct_0(A)) ) ).
fof(dt_k11_pua2mss1,axiom,
! [A,B] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A)
& m4_pua2mss1(B,A) )
=> m3_pua2mss1(k11_pua2mss1(A,B),A) ) ).
fof(redefinition_k11_pua2mss1,axiom,
! [A,B] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A)
& m4_pua2mss1(B,A) )
=> k11_pua2mss1(A,B) = k2_relat_1(B) ) ).
fof(dt_k12_pua2mss1,axiom,
! [A,B] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A)
& m3_pua2mss1(B,A) )
=> ( v1_msualg_1(k12_pua2mss1(A,B))
& l1_msualg_1(k12_pua2mss1(A,B)) ) ) ).
fof(dt_k13_pua2mss1,axiom,
! [A,B,C] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A)
& m3_pua2mss1(B,A)
& m1_subset_1(C,u1_msualg_1(k12_pua2mss1(A,B))) )
=> m1_subset_1(k13_pua2mss1(A,B,C),k4_finseq_1(u1_unialg_1(A))) ) ).
fof(redefinition_k13_pua2mss1,axiom,
! [A,B,C] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A)
& m3_pua2mss1(B,A)
& m1_subset_1(C,u1_msualg_1(k12_pua2mss1(A,B))) )
=> k13_pua2mss1(A,B,C) = k1_mcart_1(C) ) ).
fof(dt_k14_pua2mss1,axiom,
! [A,B,C] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A)
& m3_pua2mss1(B,A)
& m1_subset_1(C,u1_msualg_1(k12_pua2mss1(A,B))) )
=> m2_finseq_2(k14_pua2mss1(A,B,C),B,k3_finseq_2(B)) ) ).
fof(redefinition_k14_pua2mss1,axiom,
! [A,B,C] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A)
& m3_pua2mss1(B,A)
& m1_subset_1(C,u1_msualg_1(k12_pua2mss1(A,B))) )
=> k14_pua2mss1(A,B,C) = k2_mcart_1(C) ) ).
fof(t8_pua2mss1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_eqrel_1(C,A)
=> ! [D] :
( m1_eqrel_1(D,B)
=> m1_eqrel_1(a_4_0_pua2mss1(A,B,C,D),k2_zfmisc_1(A,B)) ) ) ) ) ).
fof(t9_pua2mss1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_eqrel_1(B,A)
=> m1_eqrel_1(a_2_0_pua2mss1(A,B),k3_finseq_2(A)) ) ) ).
fof(t10_pua2mss1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_eqrel_1(C,A)
=> m1_eqrel_1(a_3_0_pua2mss1(A,B,C),k4_finseq_2(B,A)) ) ) ) ).
fof(t11_pua2mss1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( r1_tarski(B,A)
=> ! [C] :
( m1_eqrel_1(C,A)
=> m1_eqrel_1(a_3_1_pua2mss1(A,B,C),B) ) ) ) ).
fof(t12_pua2mss1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( m1_eqrel_1(B,k1_relat_1(A))
=> m1_eqrel_1(a_2_1_pua2mss1(A,B),A) ) ) ).
fof(t13_pua2mss1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> k3_pua2mss1(A) = a_1_0_pua2mss1(A) ) ).
fof(d15_pua2mss1,axiom,
! [A] :
( ( v6_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m3_pua2mss1(B,A)
=> ! [C] :
( ( v1_msualg_1(C)
& l1_msualg_1(C) )
=> ( C = k12_pua2mss1(A,B)
<=> ( u1_struct_0(C) = B
& u1_msualg_1(C) = a_2_2_pua2mss1(A,B)
& ! [D] :
( m1_subset_1(D,k4_finseq_1(u1_unialg_1(A)))
=> ! [E] :
( m2_finseq_2(E,B,k3_finseq_2(B))
=> ( ~ r2_subset_1(k4_card_3(E),k4_relset_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),k2_pua2mss1(A,D)))
=> ( k1_funct_1(u2_msualg_1(C),k4_tarski(D,E)) = E
& r1_tarski(k9_relat_1(k2_pua2mss1(A,D),k4_card_3(E)),k1_funct_1(u3_msualg_1(C),k4_tarski(D,E))) ) ) ) ) ) ) ) ) ) ).
fof(fraenkel_a_4_0_pua2mss1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& m1_eqrel_1(D,B)
& m1_eqrel_1(E,C) )
=> ( r2_hidden(A,a_4_0_pua2mss1(B,C,D,E))
<=> ? [F,G] :
( m2_subset_1(F,k1_zfmisc_1(B),D)
& m2_subset_1(G,k1_zfmisc_1(C),E)
& A = k12_mcart_1(B,C,F,G) ) ) ) ).
fof(fraenkel_a_2_0_pua2mss1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& m1_eqrel_1(C,B) )
=> ( r2_hidden(A,a_2_0_pua2mss1(B,C))
<=> ? [D] :
( m2_finseq_2(D,C,k3_finseq_2(C))
& A = k4_card_3(D) ) ) ) ).
fof(fraenkel_a_3_0_pua2mss1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& m2_subset_1(C,k1_numbers,k5_numbers)
& m1_eqrel_1(D,B) )
=> ( r2_hidden(A,a_3_0_pua2mss1(B,C,D))
<=> ? [E] :
( m2_finseq_2(E,D,k4_finseq_2(C,D))
& A = k4_card_3(E) ) ) ) ).
fof(fraenkel_a_3_1_pua2mss1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(B)
& m1_eqrel_1(D,B) )
=> ( r2_hidden(A,a_3_1_pua2mss1(B,C,D))
<=> ? [E] :
( m2_subset_1(E,k1_zfmisc_1(B),D)
& A = k3_xboole_0(E,C)
& ~ r1_xboole_0(E,C) ) ) ) ).
fof(fraenkel_a_2_1_pua2mss1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& v1_relat_1(B)
& v1_funct_1(B)
& m1_eqrel_1(C,k1_relat_1(B)) )
=> ( r2_hidden(A,a_2_1_pua2mss1(B,C))
<=> ? [D] :
( m2_subset_1(D,k1_zfmisc_1(k1_relat_1(B)),C)
& A = k7_relat_1(B,D) ) ) ) ).
fof(fraenkel_a_1_0_pua2mss1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ( r2_hidden(A,a_1_0_pua2mss1(B))
<=> ? [C] :
( m1_subset_1(C,B)
& A = k1_tarski(C) ) ) ) ).
fof(fraenkel_a_2_2_pua2mss1,axiom,
! [A,B,C] :
( ( v6_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B)
& m3_pua2mss1(C,B) )
=> ( r2_hidden(A,a_2_2_pua2mss1(B,C))
<=> ? [D,E] :
( m1_subset_1(D,k4_finseq_1(u1_unialg_1(B)))
& m2_finseq_2(E,C,k3_finseq_2(C))
& A = k4_tarski(D,E)
& ~ r2_subset_1(k4_card_3(E),k4_relset_1(k3_finseq_2(u1_struct_0(B)),u1_struct_0(B),k2_pua2mss1(B,D))) ) ) ) ).
%------------------------------------------------------------------------------