SET007 Axioms: SET007+793.ax
%------------------------------------------------------------------------------
% File : SET007+793 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : SCMPDS Is Not Standard
% 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 : scmpds_9 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 54 ( 1 unt; 0 def)
% Number of atoms : 329 ( 41 equ)
% Maximal formula atoms : 12 ( 6 avg)
% Number of connectives : 305 ( 30 ~; 0 |; 163 &)
% ( 2 <=>; 110 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 37 ( 36 usr; 0 prp; 1-4 aty)
% Number of functors : 59 ( 59 usr; 8 con; 0-4 aty)
% Number of variables : 146 ( 145 !; 1 ?)
% 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(fc1_scmpds_9,axiom,
( ~ v3_struct_0(k1_scmpds_2)
& v1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& ~ v2_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v4_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v5_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v6_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v7_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v8_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v10_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v7_amistd_2(k1_scmpds_2,k1_tarski(k4_numbers)) ) ).
fof(fc2_scmpds_9,axiom,
! [A] :
( v1_int_1(A)
=> ( v1_xboole_0(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k4_scmpds_2(A)))
& v1_finset_1(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k4_scmpds_2(A)))
& v1_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k4_scmpds_2(A)))
& v2_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k4_scmpds_2(A)))
& v3_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k4_scmpds_2(A)))
& v4_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k4_scmpds_2(A)))
& v5_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k4_scmpds_2(A))) ) ) ).
fof(fc3_scmpds_9,axiom,
! [A] :
( m1_scmpds_2(A)
=> ( ~ v1_xboole_0(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k5_scmpds_2(A)))
& ~ v1_finset_1(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k5_scmpds_2(A)))
& ~ v1_realset1(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k5_scmpds_2(A))) ) ) ).
fof(fc4_scmpds_9,axiom,
! [A,B] :
( ( m1_scmpds_2(A)
& v1_int_1(B) )
=> ( v1_xboole_0(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k7_scmpds_2(A,B)))
& v1_finset_1(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k7_scmpds_2(A,B)))
& v1_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k7_scmpds_2(A,B)))
& v2_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k7_scmpds_2(A,B)))
& v3_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k7_scmpds_2(A,B)))
& v4_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k7_scmpds_2(A,B)))
& v5_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k7_scmpds_2(A,B))) ) ) ).
fof(fc5_scmpds_9,axiom,
! [A,B] :
( ( m1_scmpds_2(A)
& v1_int_1(B) )
=> ( v1_xboole_0(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_2(A,B)))
& v1_finset_1(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_2(A,B)))
& v1_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_2(A,B)))
& v2_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_2(A,B)))
& v3_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_2(A,B)))
& v4_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_2(A,B)))
& v5_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_2(A,B))) ) ) ).
fof(fc6_scmpds_9,axiom,
! [A,B,C] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& v1_int_1(C) )
=> ( v1_xboole_0(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_scmpds_2(A,B,C)))
& v1_finset_1(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_scmpds_2(A,B,C)))
& v1_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_scmpds_2(A,B,C)))
& v2_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_scmpds_2(A,B,C)))
& v3_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_scmpds_2(A,B,C)))
& v4_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_scmpds_2(A,B,C)))
& v5_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k11_scmpds_2(A,B,C))) ) ) ).
fof(fc7_scmpds_9,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& m1_scmpds_2(B)
& v1_int_1(C)
& v1_int_1(D) )
=> ( v1_xboole_0(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k17_scmpds_2(A,B,C,D)))
& v1_finset_1(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k17_scmpds_2(A,B,C,D)))
& v1_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k17_scmpds_2(A,B,C,D)))
& v2_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k17_scmpds_2(A,B,C,D)))
& v3_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k17_scmpds_2(A,B,C,D)))
& v4_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k17_scmpds_2(A,B,C,D)))
& v5_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k17_scmpds_2(A,B,C,D))) ) ) ).
fof(fc8_scmpds_9,axiom,
! [A,B,C] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& v1_int_1(C) )
=> ( v1_xboole_0(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k12_scmpds_2(A,B,C)))
& v1_finset_1(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k12_scmpds_2(A,B,C)))
& v1_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k12_scmpds_2(A,B,C)))
& v2_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k12_scmpds_2(A,B,C)))
& v3_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k12_scmpds_2(A,B,C)))
& v4_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k12_scmpds_2(A,B,C)))
& v5_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k12_scmpds_2(A,B,C))) ) ) ).
fof(fc9_scmpds_9,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& m1_scmpds_2(B)
& v1_int_1(C)
& v1_int_1(D) )
=> ( v1_xboole_0(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k13_scmpds_2(A,B,C,D)))
& v1_finset_1(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k13_scmpds_2(A,B,C,D)))
& v1_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k13_scmpds_2(A,B,C,D)))
& v2_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k13_scmpds_2(A,B,C,D)))
& v3_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k13_scmpds_2(A,B,C,D)))
& v4_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k13_scmpds_2(A,B,C,D)))
& v5_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k13_scmpds_2(A,B,C,D))) ) ) ).
fof(fc10_scmpds_9,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& m1_scmpds_2(B)
& v1_int_1(C)
& v1_int_1(D) )
=> ( v1_xboole_0(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k14_scmpds_2(A,B,C,D)))
& v1_finset_1(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k14_scmpds_2(A,B,C,D)))
& v1_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k14_scmpds_2(A,B,C,D)))
& v2_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k14_scmpds_2(A,B,C,D)))
& v3_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k14_scmpds_2(A,B,C,D)))
& v4_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k14_scmpds_2(A,B,C,D)))
& v5_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k14_scmpds_2(A,B,C,D))) ) ) ).
fof(fc11_scmpds_9,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& m1_scmpds_2(B)
& v1_int_1(C)
& v1_int_1(D) )
=> ( v1_xboole_0(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k15_scmpds_2(A,B,C,D)))
& v1_finset_1(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k15_scmpds_2(A,B,C,D)))
& v1_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k15_scmpds_2(A,B,C,D)))
& v2_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k15_scmpds_2(A,B,C,D)))
& v3_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k15_scmpds_2(A,B,C,D)))
& v4_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k15_scmpds_2(A,B,C,D)))
& v5_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k15_scmpds_2(A,B,C,D))) ) ) ).
fof(fc12_scmpds_9,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& m1_scmpds_2(B)
& v1_int_1(C)
& v1_int_1(D) )
=> ( v1_xboole_0(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k16_scmpds_2(A,B,C,D)))
& v1_finset_1(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k16_scmpds_2(A,B,C,D)))
& v1_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k16_scmpds_2(A,B,C,D)))
& v2_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k16_scmpds_2(A,B,C,D)))
& v3_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k16_scmpds_2(A,B,C,D)))
& v4_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k16_scmpds_2(A,B,C,D)))
& v5_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k16_scmpds_2(A,B,C,D))) ) ) ).
fof(fc13_scmpds_9,axiom,
! [A,B,C] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& v1_int_1(C) )
=> ( v1_xboole_0(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_scmpds_2(A,B,C)))
& v1_finset_1(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_scmpds_2(A,B,C)))
& v1_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_scmpds_2(A,B,C)))
& v2_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_scmpds_2(A,B,C)))
& v3_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_scmpds_2(A,B,C)))
& v4_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_scmpds_2(A,B,C)))
& v5_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k8_scmpds_2(A,B,C))) ) ) ).
fof(fc14_scmpds_9,axiom,
! [A,B,C] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& v1_int_1(C) )
=> ( v1_xboole_0(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_2(A,B,C)))
& v1_finset_1(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_2(A,B,C)))
& v1_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_2(A,B,C)))
& v2_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_2(A,B,C)))
& v3_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_2(A,B,C)))
& v4_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_2(A,B,C)))
& v5_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k9_scmpds_2(A,B,C))) ) ) ).
fof(fc15_scmpds_9,axiom,
! [A,B,C] :
( ( m1_scmpds_2(A)
& v1_int_1(B)
& v1_int_1(C) )
=> ( v1_xboole_0(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_scmpds_2(A,B,C)))
& v1_finset_1(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_scmpds_2(A,B,C)))
& v1_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_scmpds_2(A,B,C)))
& v2_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_scmpds_2(A,B,C)))
& v3_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_scmpds_2(A,B,C)))
& v4_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_scmpds_2(A,B,C)))
& v5_membered(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k10_scmpds_2(A,B,C))) ) ) ).
fof(fc16_scmpds_9,axiom,
( ~ v3_struct_0(k1_scmpds_2)
& v1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& ~ v2_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v4_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v5_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v6_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v7_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v8_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v10_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& ~ v3_amistd_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v7_amistd_2(k1_scmpds_2,k1_tarski(k4_numbers)) ) ).
fof(fc17_scmpds_9,axiom,
( ~ v3_struct_0(k1_scmpds_2)
& v1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& ~ v2_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v4_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v5_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v6_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v7_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v8_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v10_ami_1(k1_scmpds_2,k1_tarski(k4_numbers))
& ~ v3_amistd_1(k1_scmpds_2,k1_tarski(k4_numbers))
& ~ v4_amistd_1(k1_scmpds_2,k1_tarski(k4_numbers))
& v7_amistd_2(k1_scmpds_2,k1_tarski(k4_numbers)) ) ).
fof(t1_scmpds_9,axiom,
! [A] :
( v1_xreal_0(A)
=> r1_xreal_0(np__0,k2_xcmplx_0(A,k18_complex1(A))) ) ).
fof(t2_scmpds_9,axiom,
! [A] :
( v1_xreal_0(A)
=> r1_xreal_0(np__0,k2_xcmplx_0(k4_xcmplx_0(A),k18_complex1(A))) ) ).
fof(t3_scmpds_9,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( k18_complex1(A) = k18_complex1(B)
& A != B
& A != k4_xcmplx_0(B) ) ) ) ).
fof(t4_scmpds_9,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v4_ordinal2(B)
=> ~ ( ~ r1_xreal_0(B,A)
& A != np__0
& v1_int_1(k7_xcmplx_0(A,B)) ) ) ) ).
fof(t6_scmpds_9,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C,D] :
( B != D
=> k1_funct_1(k1_funct_4(A,k3_cqc_lang(B,C)),D) = k1_funct_1(A,D) ) ) ).
fof(t7_scmpds_9,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C,D,E] :
( B != C
=> ( k1_funct_1(k1_funct_4(A,k4_funct_4(B,C,D,E)),B) = D
& k1_funct_1(k1_funct_4(A,k4_funct_4(B,C,D,E)),C) = E ) ) ) ).
fof(d1_scmpds_9,axiom,
! [A] :
( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [B] :
( v4_ordinal2(B)
=> ( B = k2_scmpds_9(A)
<=> k16_ami_3(B) = A ) ) ) ).
fof(t8_scmpds_9,axiom,
! [A] :
( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> A = k1_nat_1(k2_nat_1(np__2,k3_scmpds_9(A)),np__2) ) ).
fof(t9_scmpds_9,axiom,
! [A] :
( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [B] :
( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ~ ( A != B
& k3_scmpds_9(A) = k3_scmpds_9(B) ) ) ) ).
fof(t10_scmpds_9,axiom,
! [A] :
( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [B] :
( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ~ ( A != B
& k18_scmpds_2(A) = k18_scmpds_2(B) ) ) ) ).
fof(t11_scmpds_9,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B))
=> ! [D] :
( m1_struct_0(D,B,u2_ami_1(A,B))
=> r1_tarski(k2_amistd_1(A,B,C),k1_amistd_1(A,B,D,C)) ) ) ) ) ).
fof(t12_scmpds_9,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [B] :
( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ( ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)))
=> ( ( k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C) = B
& k13_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C,B) = A )
=> k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A,C),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,C)) ) )
=> k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,B,A) = k1_struct_0(k1_scmpds_2,k18_scmpds_2(B)) ) ) ) ).
fof(t13_scmpds_9,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ( ! [B] :
( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,B,A) = k1_struct_0(k1_scmpds_2,k18_scmpds_2(B)) )
=> v1_xboole_0(k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,A)) ) ) ).
fof(t14_scmpds_9,axiom,
! [A] :
( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [B] :
( v1_int_1(B)
=> k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,A,k4_scmpds_2(B)) = k1_tarski(k1_nat_1(k2_nat_1(np__2,k1_int_2(k2_xcmplx_0(B,k3_scmpds_9(A)))),np__2)) ) ) ).
fof(t16_scmpds_9,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [C] :
( v1_int_1(C)
=> k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,B,k7_scmpds_2(A,C)) = k1_struct_0(k1_scmpds_2,k18_scmpds_2(B)) ) ) ) ).
fof(t17_scmpds_9,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [C] :
( v1_int_1(C)
=> k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,B,k6_scmpds_2(A,C)) = k1_struct_0(k1_scmpds_2,k18_scmpds_2(B)) ) ) ) ).
fof(t18_scmpds_9,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( v1_int_1(D)
=> k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,B,k11_scmpds_2(A,C,D)) = k1_struct_0(k1_scmpds_2,k18_scmpds_2(B)) ) ) ) ) ).
fof(t19_scmpds_9,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,C,k17_scmpds_2(A,B,D,E)) = k1_struct_0(k1_scmpds_2,k18_scmpds_2(C)) ) ) ) ) ) ).
fof(t20_scmpds_9,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( v1_int_1(D)
=> k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,B,k12_scmpds_2(A,C,D)) = k1_struct_0(k1_scmpds_2,k18_scmpds_2(B)) ) ) ) ) ).
fof(t21_scmpds_9,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,C,k13_scmpds_2(A,B,D,E)) = k1_struct_0(k1_scmpds_2,k18_scmpds_2(C)) ) ) ) ) ) ).
fof(t22_scmpds_9,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,C,k14_scmpds_2(A,B,D,E)) = k1_struct_0(k1_scmpds_2,k18_scmpds_2(C)) ) ) ) ) ) ).
fof(t23_scmpds_9,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,C,k15_scmpds_2(A,B,D,E)) = k1_struct_0(k1_scmpds_2,k18_scmpds_2(C)) ) ) ) ) ) ).
fof(t24_scmpds_9,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( m1_scmpds_2(B)
=> ! [C] :
( m1_struct_0(C,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,C,k16_scmpds_2(A,B,D,E)) = k1_struct_0(k1_scmpds_2,k18_scmpds_2(C)) ) ) ) ) ) ).
fof(t25_scmpds_9,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( v1_int_1(D)
=> k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,B,k8_scmpds_2(A,C,D)) = k2_tarski(k18_scmpds_2(B),k1_nat_1(k1_int_2(k3_xcmplx_0(np__2,k2_xcmplx_0(D,k3_scmpds_9(B)))),np__2)) ) ) ) ) ).
fof(t26_scmpds_9,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( v1_int_1(D)
=> k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,B,k9_scmpds_2(A,C,D)) = k2_tarski(k18_scmpds_2(B),k1_nat_1(k1_int_2(k3_xcmplx_0(np__2,k2_xcmplx_0(D,k3_scmpds_9(B)))),np__2)) ) ) ) ) ).
fof(t27_scmpds_9,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( v1_int_1(D)
=> k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,B,k10_scmpds_2(A,C,D)) = k2_tarski(k18_scmpds_2(B),k1_nat_1(k1_int_2(k3_xcmplx_0(np__2,k2_xcmplx_0(D,k3_scmpds_9(B)))),np__2)) ) ) ) ) ).
fof(t29_scmpds_9,axiom,
! [A] :
( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> k3_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2) ) ).
fof(t30_scmpds_9,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_struct_0(C,B,u2_ami_1(A,B))
=> ! [D] :
( m1_struct_0(D,B,u2_ami_1(A,B))
=> ( k3_amistd_1(A,B,C) = u2_ami_1(A,B)
=> r1_amistd_1(A,B,C,D) ) ) ) ) ) ).
fof(dt_k1_scmpds_9,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& m1_scmpds_2(B)
& v1_int_1(C)
& v1_int_1(D) )
=> m1_ami_1(k1_scmpds_9(A,B,C,D),k1_tarski(k4_numbers),k1_scmpds_2) ) ).
fof(redefinition_k1_scmpds_9,axiom,
! [A,B,C,D] :
( ( m1_scmpds_2(A)
& m1_scmpds_2(B)
& v1_int_1(C)
& v1_int_1(D) )
=> k1_scmpds_9(A,B,C,D) = k4_funct_4(A,B,C,D) ) ).
fof(dt_k2_scmpds_9,axiom,
! [A] :
( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> v4_ordinal2(k2_scmpds_9(A)) ) ).
fof(dt_k3_scmpds_9,axiom,
! [A] :
( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> m2_subset_1(k3_scmpds_9(A),k1_numbers,k5_numbers) ) ).
fof(redefinition_k3_scmpds_9,axiom,
! [A] :
( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> k3_scmpds_9(A) = k2_scmpds_9(A) ) ).
fof(t5_scmpds_9,axiom,
~ v1_finset_1(a_0_0_scmpds_9) ).
fof(t15_scmpds_9,axiom,
! [A] :
( m1_scmpds_2(A)
=> ! [B] :
( m1_struct_0(B,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))
=> k1_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,B,k5_scmpds_2(A)) = a_0_0_scmpds_9 ) ) ).
fof(t28_scmpds_9,axiom,
! [A] :
( m1_scmpds_2(A)
=> k2_amistd_1(k1_tarski(k4_numbers),k1_scmpds_2,k5_scmpds_2(A)) = a_0_0_scmpds_9 ) ).
fof(fraenkel_a_0_0_scmpds_9,axiom,
! [A] :
( r2_hidden(A,a_0_0_scmpds_9)
<=> ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& A = k2_nat_1(np__2,B)
& ~ r1_xreal_0(B,np__1) ) ) ).
%------------------------------------------------------------------------------