SET007 Axioms: SET007+557.ax
%------------------------------------------------------------------------------
% File : SET007+557 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Bubble Sort on SCMFSA
% 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 : scmbsort [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 77 ( 10 unt; 0 def)
% Number of atoms : 492 ( 131 equ)
% Maximal formula atoms : 19 ( 6 avg)
% Number of connectives : 486 ( 71 ~; 12 |; 194 &)
% ( 5 <=>; 204 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 8 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 37 ( 35 usr; 1 prp; 0-4 aty)
% Number of functors : 98 ( 98 usr; 23 con; 0-7 aty)
% Number of variables : 206 ( 201 !; 5 ?)
% 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(t1_scmbsort,axiom,
$true ).
fof(t2_scmbsort,axiom,
$true ).
fof(t3_scmbsort,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) )
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> ( r4_scmfsa7b(A,C)
=> ( B = C
| r4_scmfsa7b(k2_scmfsa8c(B,A),C) ) ) ) ) ) ).
fof(t4_scmbsort,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C,D,E] : k1_funct_1(k1_funct_4(k1_funct_4(A,k3_cqc_lang(B,C)),k3_cqc_lang(E,D)),E) = D ) ).
fof(t5_scmbsort,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C] : k1_funct_1(k1_funct_4(k1_funct_4(A,k3_cqc_lang(B,C)),k3_cqc_lang(C,B)),B) = C ) ).
fof(t6_scmbsort,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C,D,E,F] :
~ ( F != E
& F != B
& k1_funct_1(k1_funct_4(k1_funct_4(A,k3_cqc_lang(B,C)),k3_cqc_lang(E,D)),F) != k1_funct_1(A,F) ) ) ).
fof(t7_scmbsort,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C,D] :
( ( k1_funct_1(A,C) = k1_funct_1(B,D)
& k1_funct_1(A,D) = k1_funct_1(B,C)
& r2_hidden(C,k1_relat_1(A))
& r2_hidden(D,k1_relat_1(A))
& k1_relat_1(A) = k1_relat_1(B)
& ! [E] :
( r2_hidden(E,k1_relat_1(A))
=> ( E = C
| E = D
| k1_funct_1(A,E) = k1_funct_1(B,E) ) ) )
=> r1_rfinseq(A,B) ) ) ) ).
fof(t8_scmbsort,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] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> k20_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k16_scmfsa_2(D,C,B),A),D) = k4_finseq_4(k5_numbers,k4_numbers,k21_scmfsa_2(A,B),k18_complex1(k20_scmfsa_2(A,C))) ) ) ) ) ).
fof(t9_scmbsort,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] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> k21_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k17_scmfsa_2(D,C,B),A),B) = k2_funct_7(k21_scmfsa_2(A,B),k18_complex1(k20_scmfsa_2(A,C)),k20_scmfsa_2(A,D)) ) ) ) ) ).
fof(t10_scmbsort,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_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m1_scmfsa_2(E)
=> ( C != k1_nat_1(D,np__1)
=> k20_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k16_scmfsa_2(k4_scmfsa_2(C),E,B),k1_scmfsa6c(A)),k4_scmfsa_2(k1_nat_1(D,np__1))) = k20_scmfsa_2(A,k4_scmfsa_2(k1_nat_1(D,np__1))) ) ) ) ) ) ) ).
fof(t11_scmbsort,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_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m1_scmfsa_2(D)
=> ( B != k1_nat_1(C,np__1)
=> k20_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(k4_scmfsa_2(B),D),k1_scmfsa6c(A)),k4_scmfsa_2(k1_nat_1(C,np__1))) = k20_scmfsa_2(A,k4_scmfsa_2(k1_nat_1(C,np__1))) ) ) ) ) ) ).
fof(t12_scmbsort,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] :
( ( ~ v1_sf_mastr(C)
& m1_scmfsa_2(C) )
=> ( k20_scmfsa_2(k3_scmfsa6b(k5_scmfsa_4,A),C) = k20_scmfsa_2(A,C)
& k21_scmfsa_2(k3_scmfsa6b(k5_scmfsa_4,A),B) = k21_scmfsa_2(A,B) ) ) ) ) ).
fof(t13_scmbsort,axiom,
! [A] :
( v4_ordinal2(A)
=> ~ ( r1_xreal_0(A,np__10)
& A != np__0
& A != np__1
& A != np__2
& A != np__3
& A != np__4
& A != np__5
& A != np__6
& A != np__7
& A != np__8
& A != np__9
& A != np__10 ) ) ).
fof(t14_scmbsort,axiom,
! [A] :
( v4_ordinal2(A)
=> ~ ( r1_xreal_0(A,np__12)
& A != np__0
& A != np__1
& A != np__2
& A != np__3
& A != np__4
& A != np__5
& A != np__6
& A != np__7
& A != np__8
& A != np__9
& A != np__10
& A != np__11
& A != np__12 ) ) ).
fof(t15_scmbsort,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( k1_relat_1(A) = k1_relat_1(B)
& ! [D] :
( r2_hidden(D,C)
=> k1_funct_1(A,D) = k1_funct_1(B,D) ) )
=> k7_relat_1(A,C) = k7_relat_1(B,C) ) ) ) ).
fof(t16_scmbsort,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] :
( 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))
=> ! [C] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ( r2_hidden(B,k2_relat_1(A))
=> ( ( B != k8_scmfsa_2(C,D)
& B != k9_scmfsa_2(C,D)
& B != k10_scmfsa_2(C,D)
& B != k11_scmfsa_2(C,D)
& B != k12_scmfsa_2(C,D) )
| ( r2_hidden(C,k2_sf_mastr(A))
& r2_hidden(D,k2_sf_mastr(A)) ) ) ) ) ) ) ) ).
fof(t17_scmbsort,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] :
( 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))
=> ! [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))
=> ( r2_hidden(B,k2_relat_1(A))
=> ( ( B != k14_scmfsa_2(D,C)
& B != k15_scmfsa_2(D,C) )
| r2_hidden(C,k2_sf_mastr(A)) ) ) ) ) ) ) ).
fof(t18_scmbsort,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] :
( 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))
=> ! [C] :
( m2_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ! [E] :
( m1_scmfsa_2(E)
=> ( r2_hidden(B,k2_relat_1(A))
=> ( ( B != k16_scmfsa_2(D,E,C)
& B != k17_scmfsa_2(D,E,C) )
| ( r2_hidden(E,k2_sf_mastr(A))
& r2_hidden(D,k2_sf_mastr(A)) ) ) ) ) ) ) ) ) ).
fof(t19_scmbsort,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] :
( 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))
=> ! [C] :
( m2_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ! [E] :
( m1_scmfsa_2(E)
=> ( r2_hidden(B,k2_relat_1(A))
=> ( ( B != k16_scmfsa_2(D,E,C)
& B != k17_scmfsa_2(D,E,C) )
| r2_hidden(C,k4_sf_mastr(A)) ) ) ) ) ) ) ) ).
fof(t20_scmbsort,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] :
( 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))
=> ! [C] :
( m2_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ( r2_hidden(B,k2_relat_1(A))
=> ( ( B != k18_scmfsa_2(D,C)
& B != k19_scmfsa_2(D,C) )
| r2_hidden(D,k2_sf_mastr(A)) ) ) ) ) ) ) ).
fof(t21_scmbsort,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] :
( 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))
=> ! [C] :
( m2_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ( r2_hidden(B,k2_relat_1(A))
=> ( ( B != k18_scmfsa_2(D,C)
& B != k19_scmfsa_2(D,C) )
| r2_hidden(C,k4_sf_mastr(A)) ) ) ) ) ) ) ).
fof(t22_scmbsort,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( v1_setfam_1(B)
=> ! [C] :
( ( ~ v3_struct_0(C)
& ~ v2_ami_1(C,B)
& v5_ami_1(C,B)
& v7_ami_1(C,B)
& v8_ami_1(C,B)
& l1_ami_1(C,B) )
=> ! [D] :
( ( v1_ami_3(D,B,C)
& m1_ami_1(D,B,C) )
=> ! [E] :
( m1_subset_1(E,k4_card_3(u5_ami_1(B,C)))
=> ! [F] :
( m1_subset_1(F,k4_card_3(u5_ami_1(B,C)))
=> ( ( r1_tarski(D,E)
& r1_tarski(D,F) )
=> k7_relat_1(k11_ami_1(B,C,k10_ami_1(B,C,E),A),k1_relat_1(D)) = k7_relat_1(k11_ami_1(B,C,k10_ami_1(B,C,F),A),k1_relat_1(D)) ) ) ) ) ) ) ) ).
fof(t23_scmbsort,axiom,
! [A] :
( m1_ami_1(A,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] :
~ ( r1_tarski(k1_relat_1(A),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2))
& r2_hidden(C,k2_xboole_0(k2_xboole_0(k1_relat_1(A),k4_sf_mastr(B)),k2_sf_mastr(B)))
& ~ m1_scmfsa_2(C)
& ~ m2_scmfsa_2(C) ) ) ) ).
fof(t24_scmbsort,axiom,
$true ).
fof(t25_scmbsort,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [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)
& m1_ami_1(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [E] :
( m1_subset_1(E,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ! [F] :
( m1_subset_1(F,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( ( r1_xreal_0(B,A)
& r1_tarski(D,E)
& r1_tarski(D,F)
& r1_tarski(k1_relat_1(C),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2))
& ! [G] :
( m2_subset_1(G,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,E),G)),k1_relat_1(D))
& 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,F),G)),k1_relat_1(D)) ) )
& k1_funct_1(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,E),B),k2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) = k1_funct_1(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,F),B),k2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
& k7_relat_1(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,E),B),k2_xboole_0(k2_xboole_0(k1_relat_1(C),k4_sf_mastr(D)),k2_sf_mastr(D))) = k7_relat_1(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,F),B),k2_xboole_0(k2_xboole_0(k1_relat_1(C),k4_sf_mastr(D)),k2_sf_mastr(D))) )
=> ( k1_funct_1(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,E),A),k2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) = k1_funct_1(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,F),A),k2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
& k7_relat_1(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,E),A),k2_xboole_0(k2_xboole_0(k1_relat_1(C),k4_sf_mastr(D)),k2_sf_mastr(D))) = k7_relat_1(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,F),A),k2_xboole_0(k2_xboole_0(k1_relat_1(C),k4_sf_mastr(D)),k2_sf_mastr(D))) ) ) ) ) ) ) ) ) ).
fof(t26_scmbsort,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ! [E] :
( m1_subset_1(E,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( ( r1_xreal_0(B,A)
& r1_tarski(C,D)
& r1_tarski(C,E)
& ! [F] :
( m2_subset_1(F,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,D),F)),k1_relat_1(C))
& 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,E),F)),k1_relat_1(C)) ) )
& k1_funct_1(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,D),B),k2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) = k1_funct_1(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,E),B),k2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
& k7_relat_1(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,D),B),k2_xboole_0(k4_sf_mastr(C),k2_sf_mastr(C))) = k7_relat_1(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,E),B),k2_xboole_0(k4_sf_mastr(C),k2_sf_mastr(C))) )
=> ( k1_funct_1(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,D),A),k2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) = k1_funct_1(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,E),A),k2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
& k7_relat_1(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,D),A),k2_xboole_0(k4_sf_mastr(C),k2_sf_mastr(C))) = k7_relat_1(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,E),A),k2_xboole_0(k4_sf_mastr(C),k2_sf_mastr(C))) ) ) ) ) ) ) ) ).
fof(t27_scmbsort,axiom,
$true ).
fof(t28_scmbsort,axiom,
$true ).
fof(t29_scmbsort,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) )
=> ! [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)
=> ( k2_sf_mastr(k1_scmfsa8b(C,A,B)) = k2_xboole_0(k2_xboole_0(k1_struct_0(k1_scmfsa_2,C),k2_sf_mastr(A)),k2_sf_mastr(B))
& k2_sf_mastr(k2_scmfsa8b(C,A,B)) = k2_xboole_0(k2_xboole_0(k1_struct_0(k1_scmfsa_2,C),k2_sf_mastr(A)),k2_sf_mastr(B)) ) ) ) ) ).
fof(t30_scmbsort,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) )
=> ! [B] :
( m1_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> k2_sf_mastr(k1_scmfsa8a(A,B)) = k2_sf_mastr(A) ) ) ).
fof(t31_scmbsort,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [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) )
=> k2_sf_mastr(k2_scmfsa8c(A,B)) = k2_xboole_0(k2_sf_mastr(B),k2_struct_0(k1_scmfsa_2,A,k4_scmfsa_2(np__0))) ) ) ).
fof(t32_scmbsort,axiom,
! [A,B,C] : k2_xboole_0(k2_tarski(B,A),k2_tarski(C,A)) = k1_enumset1(A,B,C) ).
fof(t33_scmbsort,axiom,
$true ).
fof(t34_scmbsort,axiom,
$true ).
fof(t35_scmbsort,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) )
=> ! [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)
=> ( k4_sf_mastr(k1_scmfsa8b(C,A,B)) = k1_finsub_1(k1_zfmisc_1(k3_scmfsa_2),k4_sf_mastr(A),k4_sf_mastr(B))
& k4_sf_mastr(k2_scmfsa8b(C,A,B)) = k1_finsub_1(k1_zfmisc_1(k3_scmfsa_2),k4_sf_mastr(A),k4_sf_mastr(B)) ) ) ) ) ).
fof(t36_scmbsort,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) )
=> ! [B] :
( m1_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> k4_sf_mastr(k1_scmfsa8a(A,B)) = k4_sf_mastr(A) ) ) ).
fof(t37_scmbsort,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [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) )
=> k4_sf_mastr(k2_scmfsa8c(A,B)) = k4_sf_mastr(B) ) ) ).
fof(t38_scmbsort,axiom,
! [A] :
( m2_finseq_1(A,k4_numbers)
=> m2_finseq_1(A,k1_numbers) ) ).
fof(t39_scmbsort,axiom,
! [A] :
( m2_finseq_1(A,k4_numbers)
=> ? [B] :
( m2_finseq_1(B,k1_numbers)
& r1_rfinseq(A,B)
& m2_finseq_1(B,k4_numbers)
& v1_rfinseq(B) ) ) ).
fof(t40_scmbsort,axiom,
k1_relat_1(k1_funct_4(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)))) = k2_struct_0(k1_scmfsa_2,k4_scmfsa_2(np__0),k2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ).
fof(t41_scmbsort,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) )
=> k1_relat_1(k3_scmfsa6a(A)) = k2_xboole_0(k1_relat_1(A),k2_struct_0(k1_scmfsa_2,k4_scmfsa_2(np__0),k2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) ) ).
fof(t42_scmbsort,axiom,
! [A] :
( m2_finseq_1(A,k4_numbers)
=> ! [B] :
( m2_scmfsa_2(B)
=> ! [C] :
( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> k1_relat_1(k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6a(C),k1_scmbsort(B,A))) = k2_xboole_0(k1_relat_1(C),k1_enumset1(k4_scmfsa_2(np__0),k2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),B)) ) ) ) ).
fof(t43_scmbsort,axiom,
! [A] :
( m1_struct_0(A,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> k2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) != A ) ).
fof(t44_scmbsort,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [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) )
=> k4_card_1(k2_scmfsa8c(A,B)) = k1_nat_1(k4_card_1(B),np__12) ) ) ).
fof(t45_scmbsort,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] :
( 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))
=> ! [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))
=> k4_card_1(k6_scmfsa6a(k7_scmfsa6a(A,B),C)) = np__6 ) ) ) ).
fof(t46_scmbsort,axiom,
! [A] :
( m2_finseq_1(A,k4_numbers)
=> ! [B] :
( m2_scmfsa_2(B)
=> ! [C] :
( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> r1_xboole_0(k1_relat_1(k3_scmfsa6a(C)),k1_relat_1(k1_scmbsort(B,A))) ) ) ) ).
fof(t47_scmbsort,axiom,
! [A] :
( m2_finseq_1(A,k4_numbers)
=> ! [B] :
( m2_scmfsa_2(B)
=> ! [C] :
( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> r3_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6a(C),k1_scmbsort(B,A)),k5_scmfsa_2(np__0)) ) ) ) ).
fof(t48_scmbsort,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) )
=> ! [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] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [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))
=> ( D = k1_funct_1(B,k5_scmfsa_2(C))
=> ( r1_xreal_0(k4_card_1(B),C)
| k1_funct_1(k4_scmfsa6a(A,B),k5_scmfsa_2(k1_nat_1(k4_card_1(A),C))) = k4_scmfsa_4(D,k4_card_1(A)) ) ) ) ) ) ) ).
fof(t49_scmbsort,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] :
( m2_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ! [E] :
( m1_struct_0(E,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ~ ( ~ ( A != k8_scmfsa_2(C,D)
& A != k9_scmfsa_2(C,D)
& A != k10_scmfsa_2(C,D)
& A != k11_scmfsa_2(C,D)
& A != k12_scmfsa_2(C,D)
& A != k13_scmfsa_2(E)
& A != k14_scmfsa_2(E,C)
& A != k15_scmfsa_2(E,C)
& A != k16_scmfsa_2(D,C,B)
& A != k17_scmfsa_2(D,C,B)
& A != k18_scmfsa_2(C,B)
& A != k19_scmfsa_2(C,B) )
& A = k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ) ) ) ) ).
fof(t50_scmbsort,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) )
=> ! [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] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [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))
=> ( ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k4_scmfsa_4(D,E) = D )
& C = k4_card_1(A) )
=> ( D = k5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
| ( k1_funct_1(k4_scmfsa6a(k6_scmfsa6a(A,D),B),k5_scmfsa_2(C)) = D
& k1_funct_1(k4_scmfsa6a(k6_scmfsa6a(A,D),B),k5_scmfsa_2(k1_nat_1(C,np__1))) = k13_scmfsa_2(k5_scmfsa_2(k1_nat_1(k4_card_1(A),np__2))) ) ) ) ) ) ) ) ).
fof(t51_scmbsort,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(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)
& m1_ami_1(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( E = k4_card_1(C)
=> ( k1_funct_1(k4_scmfsa6a(k6_scmfsa6a(C,k8_scmfsa_2(A,B)),D),k5_scmfsa_2(E)) = k8_scmfsa_2(A,B)
& k1_funct_1(k4_scmfsa6a(k6_scmfsa6a(C,k8_scmfsa_2(A,B)),D),k5_scmfsa_2(k1_nat_1(E,np__1))) = k13_scmfsa_2(k5_scmfsa_2(k1_nat_1(k4_card_1(C),np__2))) ) ) ) ) ) ) ) ).
fof(t52_scmbsort,axiom,
! [A] :
( m2_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( ( v1_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(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)
& m1_ami_1(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( E = k4_card_1(C)
=> ( k1_funct_1(k4_scmfsa6a(k6_scmfsa6a(C,k18_scmfsa_2(B,A)),D),k5_scmfsa_2(E)) = k18_scmfsa_2(B,A)
& k1_funct_1(k4_scmfsa6a(k6_scmfsa6a(C,k18_scmfsa_2(B,A)),D),k5_scmfsa_2(k1_nat_1(E,np__1))) = k13_scmfsa_2(k5_scmfsa_2(k1_nat_1(k4_card_1(C),np__2))) ) ) ) ) ) ) ) ).
fof(t53_scmbsort,axiom,
! [A] :
( m2_finseq_1(A,k4_numbers)
=> ! [B] :
( m2_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)))
=> ! [D] :
( ( v1_ami_3(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(D)
& m1_ami_1(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( r1_tarski(k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6a(D),k1_scmbsort(B,A)),C)
=> r1_tarski(D,C) ) ) ) ) ) ).
fof(t54_scmbsort,axiom,
! [A] :
( m2_finseq_1(A,k4_numbers)
=> ! [B] :
( m2_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)))
=> ! [D] :
( ( v1_ami_3(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(D)
& m1_ami_1(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( r1_tarski(k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6a(D),k1_scmbsort(B,A)),C)
=> ( k21_scmfsa_2(C,B) = A
& k20_scmfsa_2(C,k4_scmfsa_2(np__0)) = np__1 ) ) ) ) ) ) ).
fof(t55_scmbsort,axiom,
! [A] :
( m2_scmfsa_2(A)
=> ! [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)))
=> r1_tarski(k1_enumset1(B,k2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),A),k1_relat_1(C)) ) ) ) ).
fof(t56_scmbsort,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) )
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> r1_tarski(k2_xboole_0(k4_sf_mastr(A),k2_sf_mastr(A)),k1_relat_1(B)) ) ) ).
fof(t57_scmbsort,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] :
( m2_scmfsa_2(C)
=> k21_scmfsa_2(k12_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,k3_scmfsa6a(B))),C) = k21_scmfsa_2(k3_scmfsa6b(B,A),C) ) ) ) ).
fof(d1_scmbsort,axiom,
! [A] :
( m2_scmfsa_2(A)
=> ! [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) )
=> ( B = k2_scmbsort(A)
<=> B = k4_scmfsa6a(k6_scmfsa6a(k6_scmfsa6a(k6_scmfsa6a(k6_scmfsa6a(k7_scmfsa6a(k8_scmfsa_2(k4_scmfsa_2(np__2),k4_scmfsa_2(np__0)),k8_scmfsa_2(k4_scmfsa_2(np__3),k4_scmfsa_2(np__0))),k8_scmfsa_2(k4_scmfsa_2(np__4),k4_scmfsa_2(np__0))),k8_scmfsa_2(k4_scmfsa_2(np__5),k4_scmfsa_2(np__0))),k8_scmfsa_2(k4_scmfsa_2(np__6),k4_scmfsa_2(np__0))),k18_scmfsa_2(k4_scmfsa_2(np__1),A)),k2_scmfsa8c(k4_scmfsa_2(np__1),k4_scmfsa6a(k6_scmfsa6a(k7_scmfsa6a(k8_scmfsa_2(k4_scmfsa_2(np__2),k4_scmfsa_2(np__1)),k10_scmfsa_2(k4_scmfsa_2(np__2),k4_scmfsa_2(np__0))),k18_scmfsa_2(k4_scmfsa_2(np__3),A)),k2_scmfsa8c(k4_scmfsa_2(np__2),k4_scmfsa6a(k6_scmfsa6a(k6_scmfsa6a(k6_scmfsa6a(k7_scmfsa6a(k8_scmfsa_2(k4_scmfsa_2(np__4),k4_scmfsa_2(np__3)),k10_scmfsa_2(k4_scmfsa_2(np__3),k4_scmfsa_2(np__0))),k16_scmfsa_2(k4_scmfsa_2(np__5),k4_scmfsa_2(np__3),A)),k16_scmfsa_2(k4_scmfsa_2(np__6),k4_scmfsa_2(np__4),A)),k10_scmfsa_2(k4_scmfsa_2(np__6),k4_scmfsa_2(np__5))),k2_scmfsa8b(k4_scmfsa_2(np__6),k6_scmfsa6a(k7_scmfsa6a(k16_scmfsa_2(k4_scmfsa_2(np__6),k4_scmfsa_2(np__4),A),k17_scmfsa_2(k4_scmfsa_2(np__6),k4_scmfsa_2(np__3),A)),k17_scmfsa_2(k4_scmfsa_2(np__5),k4_scmfsa_2(np__4),A)),k5_scmfsa_4)))))) ) ) ) ).
fof(d2_scmbsort,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) )
=> ( A = k3_scmbsort
<=> A = k2_scmbsort(k6_scmfsa_2(np__0)) ) ) ).
fof(t58_scmbsort,axiom,
! [A] :
( m2_scmfsa_2(A)
=> k2_sf_mastr(k2_scmbsort(A)) = k5_enumset1(k4_scmfsa_2(np__0),k4_scmfsa_2(np__1),k4_scmfsa_2(np__2),k4_scmfsa_2(np__3),k4_scmfsa_2(np__4),k4_scmfsa_2(np__5),k4_scmfsa_2(np__6)) ) ).
fof(t59_scmbsort,axiom,
! [A] :
( m2_scmfsa_2(A)
=> k4_sf_mastr(k2_scmbsort(A)) = k1_struct_0(k1_scmfsa_2,A) ) ).
fof(d3_scmbsort,axiom,
! [A] :
( ( v1_funct_1(A)
& m2_relset_1(A,k14_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k14_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
=> ( A = k4_scmbsort
<=> ! [B] :
( m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
=> ! [C] :
( m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
=> ( r2_hidden(k4_tarski(B,C),A)
<=> ? [D] :
( m2_finseq_1(D,k4_numbers)
& ? [E] :
( m2_finseq_1(E,k1_numbers)
& r1_rfinseq(D,E)
& m2_finseq_1(E,k4_numbers)
& v1_rfinseq(E)
& B = k1_scmbsort(k6_scmfsa_2(np__0),D)
& C = k3_cqc_lang(k6_scmfsa_2(np__0),E) ) ) ) ) ) ) ) ).
fof(t60_scmbsort,axiom,
! [A] :
( r2_hidden(A,k1_relat_1(k4_scmbsort))
<=> ? [B] :
( m2_finseq_1(B,k4_numbers)
& A = k1_scmbsort(k6_scmfsa_2(np__0),B) ) ) ).
fof(t61_scmbsort,axiom,
! [A] :
( m2_finseq_1(A,k4_numbers)
=> ? [B] :
( m2_finseq_1(B,k1_numbers)
& r1_rfinseq(A,B)
& v1_rfinseq(B)
& m2_finseq_1(B,k4_numbers)
& k1_funct_1(k4_scmbsort,k1_scmbsort(k6_scmfsa_2(np__0),A)) = k3_cqc_lang(k6_scmfsa_2(np__0),B) ) ) ).
fof(t62_scmbsort,axiom,
! [A] :
( m2_scmfsa_2(A)
=> k4_card_1(k2_scmbsort(A)) = np__63 ) ).
fof(t63_scmbsort,axiom,
! [A] :
( m2_scmfsa_2(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(np__63,B)
=> r2_hidden(k5_scmfsa_2(B),k1_relat_1(k2_scmbsort(A))) ) ) ) ).
fof(t64_scmbsort,axiom,
( v3_scm_halt(k2_scmbsort(k6_scmfsa_2(np__0)))
& v2_scm_halt(k2_scmbsort(k6_scmfsa_2(np__0))) ) ).
fof(t65_scmbsort,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( r1_rfinseq(k21_scmfsa_2(A,k6_scmfsa_2(np__0)),k21_scmfsa_2(k3_scmfsa6b(k2_scmbsort(k6_scmfsa_2(np__0)),A),k6_scmfsa_2(np__0)))
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(C,k3_finseq_1(k21_scmfsa_2(A,k6_scmfsa_2(np__0)))) )
=> ( r1_xreal_0(C,B)
| ! [D] :
( v1_int_1(D)
=> ! [E] :
( v1_int_1(E)
=> ( ( D = k2_seq_1(k5_numbers,k4_numbers,k21_scmfsa_2(k3_scmfsa6b(k2_scmbsort(k6_scmfsa_2(np__0)),A),k6_scmfsa_2(np__0)),B)
& E = k2_seq_1(k5_numbers,k4_numbers,k21_scmfsa_2(k3_scmfsa6b(k2_scmbsort(k6_scmfsa_2(np__0)),A),k6_scmfsa_2(np__0)),C) )
=> r1_xreal_0(E,D) ) ) ) ) ) ) ) ) ) ).
fof(t66_scmbsort,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ! [C] :
( m2_finseq_1(C,k4_numbers)
=> ( r1_tarski(k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6a(k3_scmbsort),k1_scmbsort(k6_scmfsa_2(np__0),C)),B)
=> 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,B),A)),k1_relat_1(k3_scmbsort)) ) ) ) ) ).
fof(t67_scmbsort,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_finseq_1(B,k4_numbers)
=> ~ ( r1_tarski(k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6a(k3_scmbsort),k1_scmbsort(k6_scmfsa_2(np__0),B)),A)
& ! [C] :
( m2_finseq_1(C,k1_numbers)
=> ~ ( r1_rfinseq(B,C)
& v1_rfinseq(C)
& m2_finseq_1(C,k4_numbers)
& k21_scmfsa_2(k12_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A),k6_scmfsa_2(np__0)) = C ) ) ) ) ) ).
fof(t68_scmbsort,axiom,
! [A] :
( m2_finseq_1(A,k4_numbers)
=> v11_ami_1(k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6a(k3_scmbsort),k1_scmbsort(k6_scmfsa_2(np__0),A)),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ).
fof(t69_scmbsort,axiom,
r1_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6a(k3_scmbsort),k4_scmbsort) ).
fof(dt_k1_scmbsort,axiom,
! [A,B] :
( ( m2_scmfsa_2(A)
& m1_finseq_1(B,k4_numbers) )
=> m1_ami_1(k1_scmbsort(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ).
fof(redefinition_k1_scmbsort,axiom,
! [A,B] :
( ( m2_scmfsa_2(A)
& m1_finseq_1(B,k4_numbers) )
=> k1_scmbsort(A,B) = k3_cqc_lang(A,B) ) ).
fof(dt_k2_scmbsort,axiom,
! [A] :
( m2_scmfsa_2(A)
=> ( v1_ami_3(k2_scmbsort(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k2_scmbsort(A))
& m1_ami_1(k2_scmbsort(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ).
fof(dt_k3_scmbsort,axiom,
( v1_ami_3(k3_scmbsort,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k3_scmbsort)
& m1_ami_1(k3_scmbsort,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ).
fof(dt_k4_scmbsort,axiom,
( v1_funct_1(k4_scmbsort)
& m2_relset_1(k4_scmbsort,k14_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k14_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) ).
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