SET007 Axioms: SET007+476.ax
%------------------------------------------------------------------------------
% File : SET007+476 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On the Composition of Macro Instructions. Part III
% 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 : scmfsa6c [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 46 ( 0 unt; 0 def)
% Number of atoms : 305 ( 20 equ)
% Maximal formula atoms : 14 ( 6 avg)
% Number of connectives : 279 ( 20 ~; 0 |; 182 &)
% ( 3 <=>; 74 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 8 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 21 ( 20 usr; 0 prp; 1-3 aty)
% Number of functors : 53 ( 53 usr; 7 con; 0-4 aty)
% Number of variables : 102 ( 101 !; 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_scmfsa6c,axiom,
( v3_ami_1(k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa6c(k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
& v2_scmfsa6c(k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) ).
fof(rc1_scmfsa6c,axiom,
? [A] :
( m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
& v1_scmfsa6c(A)
& v2_scmfsa6c(A) ) ).
fof(fc2_scmfsa6c,axiom,
! [A] :
( ( v1_scmfsa6c(A)
& m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
=> ( ~ v1_xboole_0(k2_scmfsa6a(A))
& v1_relat_1(k2_scmfsa6a(A))
& v1_funct_1(k2_scmfsa6a(A))
& v1_finset_1(k2_scmfsa6a(A))
& v1_ami_3(k2_scmfsa6a(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k2_scmfsa6a(A))
& v1_scmfsa6b(k2_scmfsa6a(A))
& v2_scmfsa6b(k2_scmfsa6a(A)) ) ) ).
fof(fc3_scmfsa6c,axiom,
! [A] :
( ( v2_scmfsa6c(A)
& m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
=> ( ~ v1_xboole_0(k2_scmfsa6a(A))
& v1_relat_1(k2_scmfsa6a(A))
& v1_funct_1(k2_scmfsa6a(A))
& v1_finset_1(k2_scmfsa6a(A))
& v1_ami_3(k2_scmfsa6a(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k2_scmfsa6a(A))
& v1_scmfsa6b(k2_scmfsa6a(A))
& v3_scmfsa6b(k2_scmfsa6a(A)) ) ) ).
fof(fc4_scmfsa6c,axiom,
! [A,B] :
( ( m1_scmfsa_2(A)
& m1_scmfsa_2(B) )
=> v1_scmfsa6c(k8_scmfsa_2(A,B)) ) ).
fof(fc5_scmfsa6c,axiom,
! [A,B] :
( ( m1_scmfsa_2(A)
& m1_scmfsa_2(B) )
=> v1_scmfsa6c(k9_scmfsa_2(A,B)) ) ).
fof(fc6_scmfsa6c,axiom,
! [A,B] :
( ( m1_scmfsa_2(A)
& m1_scmfsa_2(B) )
=> v1_scmfsa6c(k10_scmfsa_2(A,B)) ) ).
fof(fc7_scmfsa6c,axiom,
! [A,B] :
( ( m1_scmfsa_2(A)
& m1_scmfsa_2(B) )
=> v1_scmfsa6c(k11_scmfsa_2(A,B)) ) ).
fof(fc8_scmfsa6c,axiom,
! [A,B] :
( ( m1_scmfsa_2(A)
& m1_scmfsa_2(B) )
=> v1_scmfsa6c(k12_scmfsa_2(A,B)) ) ).
fof(fc9_scmfsa6c,axiom,
! [A,B,C] :
( ( m1_scmfsa_2(A)
& m1_scmfsa_2(B)
& m2_scmfsa_2(C) )
=> v1_scmfsa6c(k16_scmfsa_2(B,A,C)) ) ).
fof(fc10_scmfsa6c,axiom,
! [A,B,C] :
( ( m1_scmfsa_2(A)
& m1_scmfsa_2(B)
& m2_scmfsa_2(C) )
=> ( v1_scmfsa6c(k17_scmfsa_2(B,A,C))
& v2_scmfsa6c(k17_scmfsa_2(B,A,C)) ) ) ).
fof(fc11_scmfsa6c,axiom,
! [A,B] :
( ( m1_scmfsa_2(A)
& m2_scmfsa_2(B) )
=> v1_scmfsa6c(k18_scmfsa_2(A,B)) ) ).
fof(fc12_scmfsa6c,axiom,
! [A,B] :
( ( m1_scmfsa_2(A)
& m2_scmfsa_2(B) )
=> ( v1_scmfsa6c(k19_scmfsa_2(A,B))
& v2_scmfsa6c(k19_scmfsa_2(A,B)) ) ) ).
fof(fc13_scmfsa6c,axiom,
! [A,B] :
( ( ~ v1_sf_mastr(A)
& m1_scmfsa_2(A)
& m1_scmfsa_2(B) )
=> ( v1_scmfsa6c(k8_scmfsa_2(A,B))
& v2_scmfsa6c(k8_scmfsa_2(A,B)) ) ) ).
fof(fc14_scmfsa6c,axiom,
! [A,B] :
( ( ~ v1_sf_mastr(A)
& m1_scmfsa_2(A)
& m1_scmfsa_2(B) )
=> ( v1_scmfsa6c(k9_scmfsa_2(A,B))
& v2_scmfsa6c(k9_scmfsa_2(A,B)) ) ) ).
fof(fc15_scmfsa6c,axiom,
! [A,B] :
( ( ~ v1_sf_mastr(A)
& m1_scmfsa_2(A)
& m1_scmfsa_2(B) )
=> ( v1_scmfsa6c(k10_scmfsa_2(A,B))
& v2_scmfsa6c(k10_scmfsa_2(A,B)) ) ) ).
fof(fc16_scmfsa6c,axiom,
! [A,B] :
( ( ~ v1_sf_mastr(A)
& m1_scmfsa_2(A)
& m1_scmfsa_2(B) )
=> ( v1_scmfsa6c(k11_scmfsa_2(A,B))
& v2_scmfsa6c(k11_scmfsa_2(A,B)) ) ) ).
fof(fc17_scmfsa6c,axiom,
! [A,B] :
( ( ~ v1_sf_mastr(A)
& m1_scmfsa_2(A)
& ~ v1_sf_mastr(B)
& m1_scmfsa_2(B) )
=> ( v1_scmfsa6c(k12_scmfsa_2(A,B))
& v2_scmfsa6c(k12_scmfsa_2(A,B)) ) ) ).
fof(fc18_scmfsa6c,axiom,
! [A,B,C] :
( ( m1_scmfsa_2(A)
& m2_scmfsa_2(B)
& ~ v1_sf_mastr(C)
& m1_scmfsa_2(C) )
=> ( v1_scmfsa6c(k16_scmfsa_2(C,A,B))
& v2_scmfsa6c(k16_scmfsa_2(C,A,B)) ) ) ).
fof(fc19_scmfsa6c,axiom,
! [A,B] :
( ( m2_scmfsa_2(A)
& ~ v1_sf_mastr(B)
& m1_scmfsa_2(B) )
=> ( v1_scmfsa6c(k18_scmfsa_2(B,A))
& v2_scmfsa6c(k18_scmfsa_2(B,A)) ) ) ).
fof(fc20_scmfsa6c,axiom,
! [A,B] :
( ( v1_scmfsa6c(A)
& m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
& v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(B)
& v2_scmfsa6b(B)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( ~ v1_xboole_0(k5_scmfsa6a(A,B))
& v1_relat_1(k5_scmfsa6a(A,B))
& v1_funct_1(k5_scmfsa6a(A,B))
& v1_finset_1(k5_scmfsa6a(A,B))
& v1_ami_3(k5_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k5_scmfsa6a(A,B))
& v1_scmfsa6b(k5_scmfsa6a(A,B))
& v2_scmfsa6b(k5_scmfsa6a(A,B)) ) ) ).
fof(fc21_scmfsa6c,axiom,
! [A,B] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(A)
& v2_scmfsa6b(A)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa6c(B)
& m1_subset_1(B,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
=> ( ~ v1_xboole_0(k6_scmfsa6a(A,B))
& v1_relat_1(k6_scmfsa6a(A,B))
& v1_funct_1(k6_scmfsa6a(A,B))
& v1_finset_1(k6_scmfsa6a(A,B))
& v1_ami_3(k6_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k6_scmfsa6a(A,B))
& v1_scmfsa6b(k6_scmfsa6a(A,B))
& v2_scmfsa6b(k6_scmfsa6a(A,B)) ) ) ).
fof(fc22_scmfsa6c,axiom,
! [A,B] :
( ( v1_scmfsa6c(A)
& m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
& v1_scmfsa6c(B)
& m1_subset_1(B,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
=> ( ~ v1_xboole_0(k7_scmfsa6a(A,B))
& v1_relat_1(k7_scmfsa6a(A,B))
& v1_funct_1(k7_scmfsa6a(A,B))
& v1_finset_1(k7_scmfsa6a(A,B))
& v1_ami_3(k7_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k7_scmfsa6a(A,B))
& v1_scmfsa6b(k7_scmfsa6a(A,B))
& v2_scmfsa6b(k7_scmfsa6a(A,B)) ) ) ).
fof(fc23_scmfsa6c,axiom,
! [A,B] :
( ( v2_scmfsa6c(A)
& m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
& v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(B)
& v3_scmfsa6b(B)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( v1_relat_1(k5_scmfsa6a(A,B))
& v1_funct_1(k5_scmfsa6a(A,B))
& v1_finset_1(k5_scmfsa6a(A,B))
& v1_ami_3(k5_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k5_scmfsa6a(A,B))
& v1_scmfsa6b(k5_scmfsa6a(A,B))
& v3_scmfsa6b(k5_scmfsa6a(A,B)) ) ) ).
fof(fc24_scmfsa6c,axiom,
! [A,B] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(A)
& v3_scmfsa6b(A)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v2_scmfsa6c(B)
& m1_subset_1(B,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
=> ( v1_relat_1(k6_scmfsa6a(A,B))
& v1_funct_1(k6_scmfsa6a(A,B))
& v1_finset_1(k6_scmfsa6a(A,B))
& v1_ami_3(k6_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k6_scmfsa6a(A,B))
& v1_scmfsa6b(k6_scmfsa6a(A,B))
& v3_scmfsa6b(k6_scmfsa6a(A,B)) ) ) ).
fof(fc25_scmfsa6c,axiom,
! [A,B] :
( ( v2_scmfsa6c(A)
& m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
& v2_scmfsa6c(B)
& m1_subset_1(B,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
=> ( v1_relat_1(k7_scmfsa6a(A,B))
& v1_funct_1(k7_scmfsa6a(A,B))
& v1_finset_1(k7_scmfsa6a(A,B))
& v1_ami_3(k7_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k7_scmfsa6a(A,B))
& v1_scmfsa6b(k7_scmfsa6a(A,B))
& v3_scmfsa6b(k7_scmfsa6a(A,B)) ) ) ).
fof(fc26_scmfsa6c,axiom,
! [A,B] :
( ( m1_scmfsa_2(A)
& m1_scmfsa_2(B) )
=> ( ~ v1_xboole_0(k2_scmfsa6c(A,B))
& v1_relat_1(k2_scmfsa6c(A,B))
& v1_funct_1(k2_scmfsa6c(A,B))
& v1_finset_1(k2_scmfsa6c(A,B))
& v1_ami_3(k2_scmfsa6c(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k2_scmfsa6c(A,B))
& v1_scmfsa6b(k2_scmfsa6c(A,B))
& v2_scmfsa6b(k2_scmfsa6c(A,B)) ) ) ).
fof(fc27_scmfsa6c,axiom,
! [A,B] :
( ( ~ v1_sf_mastr(A)
& m1_scmfsa_2(A)
& ~ v1_sf_mastr(B)
& m1_scmfsa_2(B) )
=> ( ~ v1_xboole_0(k2_scmfsa6c(A,B))
& v1_relat_1(k2_scmfsa6c(A,B))
& v1_funct_1(k2_scmfsa6c(A,B))
& v1_finset_1(k2_scmfsa6c(A,B))
& v1_ami_3(k2_scmfsa6c(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k2_scmfsa6c(A,B))
& v1_scmfsa6b(k2_scmfsa6c(A,B))
& v2_scmfsa6b(k2_scmfsa6c(A,B))
& v3_scmfsa6b(k2_scmfsa6c(A,B)) ) ) ).
fof(t1_scmfsa6c,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ! [C] :
( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(C)
& v2_scmfsa6b(C)
& v3_scmfsa6b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [D] :
( ( v1_ami_3(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(D)
& v2_scmfsa6b(D)
& m1_ami_1(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> k20_scmfsa_2(k3_scmfsa6b(k4_scmfsa6a(C,D),B),A) = k20_scmfsa_2(k3_scmfsa6b(D,k3_scmfsa6b(C,B)),A) ) ) ) ) ).
fof(t2_scmfsa6c,axiom,
! [A] :
( m2_scmfsa_2(A)
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ! [C] :
( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(C)
& v2_scmfsa6b(C)
& v3_scmfsa6b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [D] :
( ( v1_ami_3(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(D)
& v2_scmfsa6b(D)
& m1_ami_1(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> k21_scmfsa_2(k3_scmfsa6b(k4_scmfsa6a(C,D),B),A) = k21_scmfsa_2(k3_scmfsa6b(D,k3_scmfsa6b(C,B)),A) ) ) ) ) ).
fof(d1_scmfsa6c,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))
=> ( v1_scmfsa6c(A)
<=> v2_scmfsa6b(k2_scmfsa6a(A)) ) ) ).
fof(d2_scmfsa6c,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))
=> ( v2_scmfsa6c(A)
<=> v3_scmfsa6b(k2_scmfsa6a(A)) ) ) ).
fof(d3_scmfsa6c,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> k1_scmfsa6c(A) = k1_funct_4(k1_funct_4(A,k3_cqc_lang(k4_scmfsa_2(np__0),np__1)),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))) ) ).
fof(t3_scmfsa6c,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa6c(A)) = k5_scmfsa_2(np__0)
& k20_scmfsa_2(k1_scmfsa6c(A),k4_scmfsa_2(np__0)) = np__1
& ! [B] :
( ( ~ v1_sf_mastr(B)
& m1_scmfsa_2(B) )
=> k20_scmfsa_2(k1_scmfsa6c(A),B) = k20_scmfsa_2(A,B) )
& ! [B] :
( m2_scmfsa_2(B)
=> k21_scmfsa_2(k1_scmfsa6c(A),B) = k21_scmfsa_2(A,B) )
& ! [B] :
( m1_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> k13_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa6c(A),B) = k13_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,B) ) ) ) ).
fof(t4_scmfsa6c,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] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( r1_funct_7(A,B,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
<=> k7_relat_1(A,k4_subset_1(u1_struct_0(k1_scmfsa_2),k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2),k1_struct_0(k1_scmfsa_2,k2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))) = k7_relat_1(B,k4_subset_1(u1_struct_0(k1_scmfsa_2),k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2),k1_struct_0(k1_scmfsa_2,k2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))) ) ) ) ).
fof(t5_scmfsa6c,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_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( k7_relat_1(B,k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(C,k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2))
=> k7_relat_1(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,B),k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,C),k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ).
fof(t6_scmfsa6c,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_scmfsa6c(B)
& m2_subset_1(B,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_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k1_scmfsa6c(A)) = k3_scmfsa6b(k2_scmfsa6a(B),A) ) ) ).
fof(t7_scmfsa6c,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ! [C] :
( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(C)
& v2_scmfsa6b(C)
& v3_scmfsa6b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [D] :
( ( v1_scmfsa6c(D)
& m2_subset_1(D,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)) )
=> k20_scmfsa_2(k3_scmfsa6b(k6_scmfsa6a(C,D),B),A) = k20_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D,k3_scmfsa6b(C,B)),A) ) ) ) ) ).
fof(t8_scmfsa6c,axiom,
! [A] :
( m2_scmfsa_2(A)
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ! [C] :
( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(C)
& v2_scmfsa6b(C)
& v3_scmfsa6b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [D] :
( ( v1_scmfsa6c(D)
& m2_subset_1(D,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)) )
=> k21_scmfsa_2(k3_scmfsa6b(k6_scmfsa6a(C,D),B),A) = k21_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D,k3_scmfsa6b(C,B)),A) ) ) ) ) ).
fof(t9_scmfsa6c,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ! [C] :
( ( v1_scmfsa6c(C)
& v2_scmfsa6c(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)) )
=> ! [D] :
( ( v1_scmfsa6c(D)
& m2_subset_1(D,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)) )
=> k20_scmfsa_2(k3_scmfsa6b(k7_scmfsa6a(C,D),B),A) = k20_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D,k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k1_scmfsa6c(B))),A) ) ) ) ) ).
fof(t10_scmfsa6c,axiom,
! [A] :
( m2_scmfsa_2(A)
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ! [C] :
( ( v1_scmfsa6c(C)
& v2_scmfsa6c(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)) )
=> ! [D] :
( ( v1_scmfsa6c(D)
& m2_subset_1(D,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)) )
=> k21_scmfsa_2(k3_scmfsa6b(k7_scmfsa6a(C,D),B),A) = k21_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D,k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k1_scmfsa6c(B))),A) ) ) ) ) ).
fof(d4_scmfsa6c,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> k2_scmfsa6c(A,B) = k6_scmfsa6a(k7_scmfsa6a(k8_scmfsa_2(k6_sf_mastr(k2_scmfsa6a(k8_scmfsa_2(A,B))),A),k8_scmfsa_2(A,B)),k8_scmfsa_2(B,k6_sf_mastr(k2_scmfsa6a(k8_scmfsa_2(A,B))))) ) ) ).
fof(t11_scmfsa6c,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_sf_mastr(C)
& m1_scmfsa_2(C) )
=> ( k20_scmfsa_2(k3_scmfsa6b(k2_scmfsa6c(B,C),A),B) = k20_scmfsa_2(A,C)
& k20_scmfsa_2(k3_scmfsa6b(k2_scmfsa6c(B,C),A),C) = k20_scmfsa_2(A,B) ) ) ) ) ).
fof(t12_scmfsa6c,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> k4_sf_mastr(k2_scmfsa6c(A,B)) = k1_xboole_0 ) ) ).
fof(dt_k1_scmfsa6c,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> m1_subset_1(k1_scmfsa6c(A),k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) ) ).
fof(dt_k2_scmfsa6c,axiom,
! [A,B] :
( ( m1_scmfsa_2(A)
& m1_scmfsa_2(B) )
=> ( v1_ami_3(k2_scmfsa6c(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k2_scmfsa6c(A,B))
& m1_ami_1(k2_scmfsa6c(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ).
%------------------------------------------------------------------------------