SET007 Axioms: SET007+477.ax
%------------------------------------------------------------------------------
% File : SET007+477 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Constant Assignment Macro Instructions of SCMFSA. Part II
% 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 : scmfsa7b [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 50 ( 1 unt; 0 def)
% Number of atoms : 303 ( 52 equ)
% Maximal formula atoms : 18 ( 6 avg)
% Number of connectives : 303 ( 50 ~; 0 |; 125 &)
% ( 11 <=>; 117 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 8 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 32 ( 31 usr; 0 prp; 1-3 aty)
% Number of functors : 62 ( 62 usr; 8 con; 0-4 aty)
% Number of variables : 112 ( 109 !; 3 ?)
% 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_scmfsa7b,axiom,
! [A] :
( m1_finseq_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ( v1_relat_1(k1_scmfsa_7(A))
& v1_funct_1(k1_scmfsa_7(A))
& v1_finset_1(k1_scmfsa_7(A))
& v1_ami_3(k1_scmfsa_7(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k1_scmfsa_7(A)) ) ) ).
fof(fc2_scmfsa7b,axiom,
! [A,B] :
( ( m1_scmfsa_2(A)
& v1_int_1(B) )
=> ( v1_relat_1(k2_scmfsa_7(A,B))
& v1_funct_1(k2_scmfsa_7(A,B))
& v1_finset_1(k2_scmfsa_7(A,B))
& v1_ami_3(k2_scmfsa_7(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k2_scmfsa_7(A,B)) ) ) ).
fof(fc3_scmfsa7b,axiom,
! [A,B] :
( ( m1_scmfsa_2(A)
& v1_int_1(B) )
=> ( v1_relat_1(k2_scmfsa_7(A,B))
& v1_funct_1(k2_scmfsa_7(A,B))
& ~ v1_xboole_0(k2_scmfsa_7(A,B))
& v1_finset_1(k2_scmfsa_7(A,B))
& v1_ami_3(k2_scmfsa_7(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k2_scmfsa_7(A,B))
& v1_scmfsa6b(k2_scmfsa_7(A,B))
& v2_scmfsa6b(k2_scmfsa_7(A,B)) ) ) ).
fof(fc4_scmfsa7b,axiom,
! [A,B] :
( ( m2_scmfsa_2(A)
& m1_finseq_1(B,k4_numbers) )
=> ( v1_relat_1(k5_scmfsa_7(A,B))
& v1_funct_1(k5_scmfsa_7(A,B))
& v1_finset_1(k5_scmfsa_7(A,B))
& v1_ami_3(k5_scmfsa_7(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k5_scmfsa_7(A,B)) ) ) ).
fof(fc5_scmfsa7b,axiom,
! [A,B] :
( ( m2_scmfsa_2(A)
& m1_finseq_1(B,k4_numbers) )
=> ( v1_relat_1(k5_scmfsa_7(A,B))
& v1_funct_1(k5_scmfsa_7(A,B))
& ~ v1_xboole_0(k5_scmfsa_7(A,B))
& v1_finset_1(k5_scmfsa_7(A,B))
& v1_ami_3(k5_scmfsa_7(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k5_scmfsa_7(A,B))
& v1_scmfsa6b(k5_scmfsa_7(A,B))
& v2_scmfsa6b(k5_scmfsa_7(A,B)) ) ) ).
fof(rc1_scmfsa7b,axiom,
? [A] :
( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_relat_1(A)
& v1_funct_1(A)
& v1_finset_1(A)
& v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(A)
& v1_scmfsa7b(A)
& v2_scmfsa7b(A) ) ).
fof(rc2_scmfsa7b,axiom,
? [A] :
( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finset_1(A)
& v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(A)
& v1_scmfsa6b(A)
& v2_scmfsa6b(A)
& v1_scmfsa7b(A) ) ).
fof(fc6_scmfsa7b,axiom,
( v1_relat_1(k5_scmfsa_4)
& v1_funct_1(k5_scmfsa_4)
& ~ v1_xboole_0(k5_scmfsa_4)
& v1_finset_1(k5_scmfsa_4)
& v1_ami_3(k5_scmfsa_4,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k5_scmfsa_4)
& v1_scmfsa6b(k5_scmfsa_4)
& v2_scmfsa6b(k5_scmfsa_4)
& v1_scmfsa7b(k5_scmfsa_4) ) ).
fof(cc1_scmfsa7b,axiom,
! [A] :
( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
=> ( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(A)
& v1_scmfsa6b(A)
& v1_scmfsa7b(A) )
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finset_1(A)
& v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(A)
& v1_scmfsa6b(A)
& v3_scmfsa6b(A) ) ) ) ).
fof(fc7_scmfsa7b,axiom,
! [A,B] :
( ( ~ v1_sf_mastr(A)
& m1_scmfsa_2(A)
& v1_int_1(B) )
=> ( v1_relat_1(k2_scmfsa_7(A,B))
& v1_funct_1(k2_scmfsa_7(A,B))
& ~ v1_xboole_0(k2_scmfsa_7(A,B))
& v1_finset_1(k2_scmfsa_7(A,B))
& v1_ami_3(k2_scmfsa_7(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k2_scmfsa_7(A,B))
& v1_scmfsa6b(k2_scmfsa_7(A,B))
& v2_scmfsa6b(k2_scmfsa_7(A,B))
& v3_scmfsa6b(k2_scmfsa_7(A,B))
& v1_scmfsa7b(k2_scmfsa_7(A,B)) ) ) ).
fof(fc8_scmfsa7b,axiom,
! [A,B] :
( ( ~ v1_sf_mastr(A)
& m1_scmfsa_2(A)
& v1_int_1(B) )
=> ( v1_relat_1(k2_scmfsa_7(A,B))
& v1_funct_1(k2_scmfsa_7(A,B))
& ~ v1_xboole_0(k2_scmfsa_7(A,B))
& v1_finset_1(k2_scmfsa_7(A,B))
& v1_ami_3(k2_scmfsa_7(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k2_scmfsa_7(A,B))
& v1_scmfsa6b(k2_scmfsa_7(A,B))
& v2_scmfsa6b(k2_scmfsa_7(A,B))
& v3_scmfsa6b(k2_scmfsa_7(A,B))
& v1_scmfsa7b(k2_scmfsa_7(A,B)) ) ) ).
fof(t2_scmfsa7b,axiom,
! [A] :
( m2_finseq_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> k2_relat_1(k1_scmfsa_7(A)) = k2_relat_1(A) ) ).
fof(t3_scmfsa7b,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> k1_scmfsa_7(k13_binarith(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),A)) = k14_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0),A) ) ).
fof(t4_scmfsa7b,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> k1_relat_1(k2_scmfsa6a(A)) = k2_tarski(k5_scmfsa_2(np__0),k5_scmfsa_2(np__1)) ) ).
fof(t5_scmfsa7b,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> k2_scmfsa6a(A) = k1_scmfsa_7(k2_finseq_4(u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),A,k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) ) ).
fof(t6_scmfsa7b,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> k4_card_1(k2_scmfsa6a(A)) = np__2 ) ).
fof(t7_scmfsa7b,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ( ( A = k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
=> k1_funct_1(k1_scmfsa6a(k2_scmfsa6a(A)),k5_scmfsa_2(np__0)) = k13_scmfsa_2(k5_scmfsa_2(np__2)) )
& ( A != k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
=> k1_funct_1(k1_scmfsa6a(k2_scmfsa6a(A)),k5_scmfsa_2(np__0)) = A ) ) ) ).
fof(t8_scmfsa7b,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> k1_funct_1(k1_scmfsa6a(k2_scmfsa6a(A)),k5_scmfsa_2(np__1)) = k13_scmfsa_2(k5_scmfsa_2(np__2)) ) ).
fof(t9_scmfsa7b,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ! [B] :
( ( ~ v1_sf_mastr(B)
& m1_scmfsa_2(B) )
=> ! [C] :
( v1_int_1(C)
=> ( k20_scmfsa_2(k3_scmfsa6b(k2_scmfsa_7(B,C),A),B) = C
& ! [D] :
( ( ~ v1_sf_mastr(D)
& m1_scmfsa_2(D) )
=> ( D != B
=> k20_scmfsa_2(k3_scmfsa6b(k2_scmfsa_7(B,C),A),D) = k20_scmfsa_2(A,D) ) )
& ! [D] :
( m2_scmfsa_2(D)
=> k21_scmfsa_2(k3_scmfsa6b(k2_scmfsa_7(B,C),A),D) = k21_scmfsa_2(A,D) ) ) ) ) ) ).
fof(t10_scmfsa7b,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ! [B] :
( m2_scmfsa_2(B)
=> ! [C] :
( m2_finseq_1(C,k4_numbers)
=> ( k21_scmfsa_2(k3_scmfsa6b(k5_scmfsa_7(B,C),A),B) = C
& ! [D] :
( ( ~ v1_sf_mastr(D)
& m1_scmfsa_2(D) )
=> ~ ( D != k4_scmfsa_2(np__1)
& D != k4_scmfsa_2(np__2)
& k20_scmfsa_2(k3_scmfsa6b(k5_scmfsa_7(B,C),A),D) != k20_scmfsa_2(A,D) ) )
& ! [D] :
( m2_scmfsa_2(D)
=> ( D != B
=> k21_scmfsa_2(k3_scmfsa6b(k5_scmfsa_7(B,C),A),D) = k21_scmfsa_2(A,D) ) ) ) ) ) ) ).
fof(d1_scmfsa7b,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [B] :
( m1_scmfsa_2(B)
=> ( r1_scmfsa7b(A,B)
<=> ! [C] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_struct_0(D,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [E] :
( m2_scmfsa_2(E)
=> ( k8_scmfsa_2(C,B) != A
& k9_scmfsa_2(C,B) != A
& k10_scmfsa_2(C,B) != A
& k11_scmfsa_2(C,B) != A
& k12_scmfsa_2(C,B) != A
& k12_scmfsa_2(B,C) != A
& k14_scmfsa_2(D,B) != A
& k15_scmfsa_2(D,B) != A
& k16_scmfsa_2(C,B,E) != A
& k17_scmfsa_2(B,C,E) != A
& k17_scmfsa_2(C,B,E) != A
& k19_scmfsa_2(B,E) != A ) ) ) ) ) ) ) ).
fof(d2_scmfsa7b,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [B] :
( m1_scmfsa_2(B)
=> ( r2_scmfsa7b(A,B)
<=> ! [C] :
( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ( r2_hidden(C,k2_relat_1(A))
=> r1_scmfsa7b(C,B) ) ) ) ) ) ).
fof(d3_scmfsa7b,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [B] :
( m1_scmfsa_2(B)
=> ( r3_scmfsa7b(A,B)
<=> ! [C] :
( m1_scmfsa_2(C)
=> ! [D] :
( m2_scmfsa_2(D)
=> ( k8_scmfsa_2(B,C) != A
& k9_scmfsa_2(B,C) != A
& k10_scmfsa_2(B,C) != A
& k11_scmfsa_2(B,C) != A
& k12_scmfsa_2(B,C) != A
& k12_scmfsa_2(C,B) != A
& k16_scmfsa_2(B,C,D) != A
& k18_scmfsa_2(B,D) != A ) ) ) ) ) ) ).
fof(d4_scmfsa7b,axiom,
! [A] :
( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
=> ! [B] :
( m1_scmfsa_2(B)
=> ( r4_scmfsa7b(A,B)
<=> ! [C] :
( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ( r2_hidden(C,k2_relat_1(A))
=> r3_scmfsa7b(C,B) ) ) ) ) ) ).
fof(d5_scmfsa7b,axiom,
! [A] :
( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
=> ( v1_scmfsa7b(A)
<=> r4_scmfsa7b(A,k4_scmfsa_2(np__0)) ) ) ).
fof(d6_scmfsa7b,axiom,
! [A] :
( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
=> ( v2_scmfsa7b(A)
<=> ~ r2_hidden(k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k2_relat_1(A)) ) ) ).
fof(t11_scmfsa7b,axiom,
! [A] :
( m1_scmfsa_2(A)
=> r3_scmfsa7b(k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),A) ) ).
fof(t12_scmfsa7b,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> ( A != B
=> r3_scmfsa7b(k8_scmfsa_2(B,C),A) ) ) ) ) ).
fof(t13_scmfsa7b,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> ( A != B
=> r3_scmfsa7b(k9_scmfsa_2(B,C),A) ) ) ) ) ).
fof(t14_scmfsa7b,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> ( A != B
=> r3_scmfsa7b(k10_scmfsa_2(B,C),A) ) ) ) ) ).
fof(t15_scmfsa7b,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> ( A != B
=> r3_scmfsa7b(k11_scmfsa_2(B,C),A) ) ) ) ) ).
fof(t16_scmfsa7b,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> ~ ( A != B
& A != C
& ~ r3_scmfsa7b(k12_scmfsa_2(B,C),A) ) ) ) ) ).
fof(t17_scmfsa7b,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> r3_scmfsa7b(k13_scmfsa_2(B),A) ) ) ).
fof(t18_scmfsa7b,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_struct_0(C,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> r3_scmfsa7b(k14_scmfsa_2(C,B),A) ) ) ) ).
fof(t19_scmfsa7b,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_struct_0(C,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> r3_scmfsa7b(k15_scmfsa_2(C,B),A) ) ) ) ).
fof(t20_scmfsa7b,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> ! [D] :
( m2_scmfsa_2(D)
=> ( A != B
=> r3_scmfsa7b(k16_scmfsa_2(B,C,D),A) ) ) ) ) ) ).
fof(t21_scmfsa7b,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> ! [D] :
( m2_scmfsa_2(D)
=> r3_scmfsa7b(k17_scmfsa_2(B,C,D),A) ) ) ) ) ).
fof(t22_scmfsa7b,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m2_scmfsa_2(C)
=> ( A != B
=> r3_scmfsa7b(k18_scmfsa_2(B,C),A) ) ) ) ) ).
fof(t23_scmfsa7b,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m2_scmfsa_2(C)
=> r3_scmfsa7b(k19_scmfsa_2(B,C),A) ) ) ) ).
fof(d7_scmfsa7b,axiom,
! [A] :
( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( r5_scmfsa7b(A,B)
<=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r2_hidden(k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),C)),k1_relat_1(A)) ) ) ) ) ).
fof(d8_scmfsa7b,axiom,
! [A] :
( m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( r6_scmfsa7b(A,B)
<=> v9_ami_1(k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0)))),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ) ).
fof(t24_scmfsa7b,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(A)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( v1_scmfsa6b(A)
<=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> r5_scmfsa7b(A,B) ) ) ) ).
fof(t25_scmfsa7b,axiom,
! [A] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(A)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( v2_scmfsa6b(A)
<=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> r6_scmfsa7b(A,B) ) ) ) ).
fof(t26_scmfsa7b,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( r3_scmfsa7b(A,B)
=> k20_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,C),B) = k20_scmfsa_2(C,B) ) ) ) ) ).
fof(t27_scmfsa7b,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ! [B] :
( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(B)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [C] :
( m1_scmfsa_2(C)
=> ( ( r4_scmfsa7b(B,C)
& r5_scmfsa7b(B,A) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),D),C) = k20_scmfsa_2(A,C) ) ) ) ) ) ).
fof(t28_scmfsa7b,axiom,
r4_scmfsa7b(k5_scmfsa_4,k4_scmfsa_2(np__0)) ).
fof(t29_scmfsa7b,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( v1_int_1(B)
=> r1_tarski(k2_relat_1(k3_scmfsa_7(A,B)),k1_enumset1(k8_scmfsa_2(A,k4_scmfsa_2(np__0)),k9_scmfsa_2(A,k4_scmfsa_2(np__0)),k10_scmfsa_2(A,k4_scmfsa_2(np__0)))) ) ) ).
fof(t30_scmfsa7b,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( v1_int_1(B)
=> r1_tarski(k2_relat_1(k2_scmfsa_7(A,B)),k2_enumset1(k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k8_scmfsa_2(A,k4_scmfsa_2(np__0)),k9_scmfsa_2(A,k4_scmfsa_2(np__0)),k10_scmfsa_2(A,k4_scmfsa_2(np__0)))) ) ) ).
fof(t1_scmfsa7b,axiom,
! [A] :
( m2_finseq_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> k1_relat_1(k1_scmfsa_7(A)) = a_1_0_scmfsa7b(A) ) ).
fof(fraenkel_a_1_0_scmfsa7b,axiom,
! [A,B] :
( m2_finseq_1(B,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ( r2_hidden(A,a_1_0_scmfsa7b(B))
<=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& A = k5_scmfsa_2(C)
& ~ r1_xreal_0(k3_finseq_1(B),C) ) ) ) ).
%------------------------------------------------------------------------------