SET007 Axioms: SET007+550.ax
%------------------------------------------------------------------------------
% File : SET007+550 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The While 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 : scmfsa9a [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 60 ( 5 unt; 0 def)
% Number of atoms : 517 ( 75 equ)
% Maximal formula atoms : 18 ( 8 avg)
% Number of connectives : 536 ( 79 ~; 13 |; 224 &)
% ( 7 <=>; 213 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 10 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 36 ( 34 usr; 1 prp; 0-3 aty)
% Number of functors : 74 ( 74 usr; 13 con; 0-4 aty)
% Number of variables : 186 ( 180 !; 6 ?)
% 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_scmfsa9a,axiom,
! [A] :
( v4_ordinal2(A)
=> ( ~ ( ~ v1_abian(A)
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> A != k1_nat_1(k2_nat_1(np__2,B),np__1) ) )
& ~ ( ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& A = k1_nat_1(k2_nat_1(np__2,B),np__1) )
& v1_abian(A) ) ) ) ).
fof(t2_scmfsa9a,axiom,
$true ).
fof(t3_scmfsa9a,axiom,
$true ).
fof(t4_scmfsa9a,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ~ ( ~ r1_xreal_0(A,np__0)
& ~ r1_xreal_0(B,np__1)
& r1_xreal_0(A,k5_int_1(A,B)) ) ) ) ).
fof(t5_scmfsa9a,axiom,
$true ).
fof(t6_scmfsa9a,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_setfam_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& ~ v2_ami_1(B,A)
& v4_ami_1(B,A)
& v5_ami_1(B,A)
& v8_ami_1(B,A)
& l1_ami_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k4_card_3(u5_ami_1(A,B)))
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( k8_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),D)) = k5_ami_1(A,B)
=> k11_ami_1(A,B,k10_ami_1(A,B,C),k2_scm_1(A,B,C)) = k11_ami_1(A,B,k10_ami_1(A,B,C),D) ) ) ) ) ) ).
fof(t7_scmfsa9a,axiom,
! [A] :
( m1_struct_0(A,k1_scmfsa_2,u2_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))
=> k2_sf_mastr(k14_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,B)) = k1_sf_mastr(B) ) ) ).
fof(t8_scmfsa9a,axiom,
! [A] :
( m1_struct_0(A,k1_scmfsa_2,u2_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))
=> k4_sf_mastr(k14_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,B)) = k3_sf_mastr(B) ) ) ).
fof(t9_scmfsa9a,axiom,
k2_sf_mastr(k5_scmfsa_4) = k1_xboole_0 ).
fof(t10_scmfsa9a,axiom,
k4_sf_mastr(k5_scmfsa_4) = k1_xboole_0 ).
fof(t11_scmfsa9a,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_sf_mastr(k2_scmfsa8a(A)) = k1_xboole_0 ) ).
fof(t12_scmfsa9a,axiom,
! [A] :
( m1_struct_0(A,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> k4_sf_mastr(k2_scmfsa8a(A)) = k1_xboole_0 ) ).
fof(t13_scmfsa9a,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) )
=> ! [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) )
=> k2_sf_mastr(k1_scmfsa8b(A,B,C)) = k1_finsub_1(k1_zfmisc_1(k2_scmfsa_2),k1_finsub_1(k1_zfmisc_1(k2_scmfsa_2),k1_sfmastr1(A),k2_sf_mastr(B)),k2_sf_mastr(C)) ) ) ) ).
fof(t14_scmfsa9a,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)) ) ) ) ).
fof(t15_scmfsa9a,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) )
=> ! [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) )
=> k2_sf_mastr(k2_scmfsa8b(A,B,C)) = k1_finsub_1(k1_zfmisc_1(k2_scmfsa_2),k1_finsub_1(k1_zfmisc_1(k2_scmfsa_2),k1_sfmastr1(A),k2_sf_mastr(B)),k2_sf_mastr(C)) ) ) ) ).
fof(t16_scmfsa9a,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) )
=> ! [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) )
=> k4_sf_mastr(k2_scmfsa8b(A,B,C)) = k1_finsub_1(k1_zfmisc_1(k3_scmfsa_2),k4_sf_mastr(B),k4_sf_mastr(C)) ) ) ) ).
fof(t17_scmfsa9a,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(k1_scmfsa_9(A,B)) = k1_finsub_1(k1_zfmisc_1(k2_scmfsa_2),k1_sfmastr1(A),k2_sf_mastr(B)) ) ) ).
fof(t18_scmfsa9a,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(k1_scmfsa_9(A,B)) = k4_sf_mastr(B) ) ) ).
fof(d1_scmfsa9a,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_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_scmfsa9a(A,B,C)
<=> ! [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,k4_scmfsa_9(A,C,B),D),B) = np__0
=> ( r5_scmfsa7b(C,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),D))
& r6_scmfsa7b(C,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),D)) ) ) ) ) ) ) ) ).
fof(d2_scmfsa9a,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_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) )
=> ( r2_scmfsa9a(A,B,C)
<=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers)
& m2_relset_1(D,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(k8_funct_2(k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers,D,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),E)),k8_funct_2(k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers,D,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),k1_nat_1(E,np__1))))
& k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),E),B) = np__0 ) ) ) ) ) ) ) ).
fof(t19_scmfsa9a,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_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(C)
& v2_scmfsa6b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> r1_scmfsa9a(A,B,C) ) ) ) ).
fof(t20_scmfsa9a,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_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_scmfsa9a(A,B,C)
& r2_scmfsa9a(A,B,C) )
=> ( r6_scmfsa7b(k1_scmfsa_9(B,C),A)
& r5_scmfsa7b(k1_scmfsa_9(B,C),A) ) ) ) ) ) ).
fof(t21_scmfsa9a,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_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(C)
& v2_scmfsa6b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( r2_scmfsa9a(A,B,C)
=> ( r6_scmfsa7b(k1_scmfsa_9(B,C),A)
& r5_scmfsa7b(k1_scmfsa_9(B,C),A) ) ) ) ) ) ).
fof(t22_scmfsa9a,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_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_tarski(k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa_9(B,C),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))),A)
=> ( k20_scmfsa_2(A,B) = np__0
| ( k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = np__4
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> 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,A),D),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ) ) ).
fof(t23_scmfsa9a,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_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) )
=> ( ( r5_scmfsa7b(C,A)
& r6_scmfsa7b(C,A)
& k20_scmfsa_2(A,B) = np__0 )
=> 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,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,k1_scmfsa_9(B,C),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),k1_nat_1(k2_scm_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,C,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),np__3)),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_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,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,C,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),k2_scm_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,C,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0)))))),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ).
fof(t24_scmfsa9a,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_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] :
( 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,k4_scmfsa_9(A,C,B),D),B) != np__0
=> k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),k1_nat_1(D,np__1)),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),D),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ).
fof(t25_scmfsa9a,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_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] :
( 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,k4_scmfsa_9(A,C,B),D),B) = np__0
& k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),D),k4_scmfsa_2(np__0)) = np__1 )
=> ( ( ~ ( r6_scmfsa7b(C,k1_scmfsa6c(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),D)))
& r5_scmfsa7b(C,k1_scmfsa6c(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),D))) )
& ~ v2_scmfsa6b(C) )
| k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),k1_nat_1(D,np__1)),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k3_scmfsa6b(C,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),D)),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ) ).
fof(t26_scmfsa9a,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_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(C)
& v1_scmfsa7b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
=> ( ( ~ r1_scmfsa9a(A,B,C)
& ~ v2_scmfsa6b(C) )
| ! [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,k4_scmfsa_9(A,C,B),D),k4_scmfsa_2(np__0)) = np__1 ) ) ) ) ) ) ).
fof(t27_scmfsa9a,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)))
=> ! [C] :
( ( ~ v1_sf_mastr(C)
& m1_scmfsa_2(C) )
=> ! [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_scmfsa9a(A,C,D)
& k7_relat_1(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(B,k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,D,C),E),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(B,D,C),E),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ) ).
fof(d3_scmfsa9a,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_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) )
=> ( r2_scmfsa9a(A,B,C)
=> ( ( ~ r1_scmfsa9a(A,B,C)
& ~ v2_scmfsa6b(C) )
| ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( D = k1_scmfsa9a(A,B,C)
<=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& D = E
& k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),E),B) != np__0
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),F),B) != np__0
=> r1_xreal_0(E,F) ) )
& 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,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,k1_scmfsa_9(B,C),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),k2_scm_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,k1_scmfsa_9(B,C),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0)))))),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(A,C,B),E),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ) ) ) ).
fof(t28_scmfsa9a,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_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) )
=> ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
=> ( k20_scmfsa_2(A,B) = np__0
| k7_relat_1(k3_scmfsa6b(k1_scmfsa_9(B,C),A),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ).
fof(t29_scmfsa9a,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_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) )
=> ( r2_scmfsa9a(k1_scmfsa6c(A),B,C)
=> ( ( ~ r1_scmfsa9a(k1_scmfsa6c(A),B,C)
& ~ v2_scmfsa6b(C) )
| k7_relat_1(k3_scmfsa6b(k1_scmfsa_9(B,C),A),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_scmfsa_9(k1_scmfsa6c(A),C,B),k1_scmfsa9a(k1_scmfsa6c(A),B,C)),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ).
fof(t30_scmfsa9a,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_scmfsa_9(A,B)) = k1_finsub_1(k1_zfmisc_1(k2_scmfsa_2),k1_sfmastr1(A),k2_sf_mastr(B)) ) ) ).
fof(t31_scmfsa9a,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_scmfsa_9(A,B)) = k4_sf_mastr(B) ) ) ).
fof(d4_scmfsa9a,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_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_scmfsa9a(A,B,C)
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),D),B),np__0)
=> ( r5_scmfsa7b(C,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),D))
& r6_scmfsa7b(C,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),D)) ) ) ) ) ) ) ) ).
fof(d5_scmfsa9a,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_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) )
=> ( r4_scmfsa9a(A,B,C)
<=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers)
& m2_relset_1(D,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(k8_funct_2(k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers,D,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),E)),k8_funct_2(k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers,D,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),k1_nat_1(E,np__1))))
& ~ r1_xreal_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),E),B),np__0) ) ) ) ) ) ) ) ).
fof(t32_scmfsa9a,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_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(C)
& v2_scmfsa6b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> r3_scmfsa9a(A,B,C) ) ) ) ).
fof(t33_scmfsa9a,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_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_scmfsa9a(A,B,C)
& r4_scmfsa9a(A,B,C) )
=> ( r6_scmfsa7b(k2_scmfsa_9(B,C),A)
& r5_scmfsa7b(k2_scmfsa_9(B,C),A) ) ) ) ) ) ).
fof(t34_scmfsa9a,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_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(C)
& v2_scmfsa6b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( r4_scmfsa9a(A,B,C)
=> ( r6_scmfsa7b(k2_scmfsa_9(B,C),A)
& r5_scmfsa7b(k2_scmfsa_9(B,C),A) ) ) ) ) ) ).
fof(t35_scmfsa9a,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_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_tarski(k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_scmfsa_9(B,C),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))),A)
& r1_xreal_0(k20_scmfsa_2(A,B),np__0) )
=> ( k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = np__4
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> 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,A),D),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ) ).
fof(t36_scmfsa9a,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_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) )
=> ( ( r5_scmfsa7b(C,A)
& r6_scmfsa7b(C,A) )
=> ( r1_xreal_0(k20_scmfsa_2(A,B),np__0)
| 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,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,k2_scmfsa_9(B,C),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),k1_nat_1(k2_scm_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,C,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),np__3)),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_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,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,C,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),k2_scm_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,C,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0)))))),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ).
fof(t37_scmfsa9a,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_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] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),D),B),np__0)
=> k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),k1_nat_1(D,np__1)),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),D),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ).
fof(t38_scmfsa9a,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_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] :
( 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,k5_scmfsa_9(A,C,B),D),k4_scmfsa_2(np__0)) = np__1
=> ( ( ~ ( r6_scmfsa7b(C,k1_scmfsa6c(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),D)))
& r5_scmfsa7b(C,k1_scmfsa6c(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),D))) )
& ~ v2_scmfsa6b(C) )
| r1_xreal_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),D),B),np__0)
| k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),k1_nat_1(D,np__1)),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k3_scmfsa6b(C,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),D)),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ) ).
fof(t39_scmfsa9a,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_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(C)
& v1_scmfsa7b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
=> ( ( ~ r3_scmfsa9a(A,B,C)
& ~ v2_scmfsa6b(C) )
| ! [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,k5_scmfsa_9(A,C,B),D),k4_scmfsa_2(np__0)) = np__1 ) ) ) ) ) ) ).
fof(t40_scmfsa9a,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)))
=> ! [C] :
( ( ~ v1_sf_mastr(C)
& m1_scmfsa_2(C) )
=> ! [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) )
=> ( ( r3_scmfsa9a(A,C,D)
& k7_relat_1(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(B,k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,D,C),E),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(B,D,C),E),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ) ).
fof(d6_scmfsa9a,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_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) )
=> ( r4_scmfsa9a(A,B,C)
=> ( ( ~ r3_scmfsa9a(A,B,C)
& ~ v2_scmfsa6b(C) )
| ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( D = k2_scmfsa9a(A,B,C)
<=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& D = E
& r1_xreal_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),E),B),np__0)
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r1_xreal_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),F),B),np__0)
=> r1_xreal_0(E,F) ) )
& 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,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,k2_scmfsa_9(B,C),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),k2_scm_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,k2_scmfsa_9(B,C),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0)))))),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),E),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ) ) ) ).
fof(t41_scmfsa9a,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_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) )
=> ( ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
& r1_xreal_0(k20_scmfsa_2(A,B),np__0) )
=> k7_relat_1(k3_scmfsa6b(k2_scmfsa_9(B,C),A),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ).
fof(t42_scmfsa9a,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_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) )
=> ( r4_scmfsa9a(k1_scmfsa6c(A),B,C)
=> ( ( ~ r3_scmfsa9a(k1_scmfsa6c(A),B,C)
& ~ v2_scmfsa6b(C) )
| k7_relat_1(k3_scmfsa6b(k2_scmfsa_9(B,C),A),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(k1_scmfsa6c(A),C,B),k2_scmfsa9a(k1_scmfsa6c(A),B,C)),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ).
fof(t43_scmfsa9a,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_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] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),D),B),np__0)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_xreal_0(D,E)
=> k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),E),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),D),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ) ) ).
fof(t44_scmfsa9a,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)))
=> ! [C] :
( ( ~ v1_sf_mastr(C)
& m1_scmfsa_2(C) )
=> ! [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) )
=> ( ( k7_relat_1(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(B,k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2))
& r3_scmfsa9a(A,C,D) )
=> r3_scmfsa9a(B,C,D) ) ) ) ) ) ).
fof(t45_scmfsa9a,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_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(C)
& v1_scmfsa7b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
& r3_scmfsa9a(A,B,C)
& r4_scmfsa9a(A,B,C) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(D,k2_scmfsa9a(A,B,C))
& r1_xreal_0(E,k2_scmfsa9a(A,B,C)) )
=> ( D = E
| ( k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),D) != k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),E)
& k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),D),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) != k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),E),k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ) ) ) ) ).
fof(d7_scmfsa9a,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers)
& m2_relset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers) )
=> ( v1_scmfsa9a(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] :
( 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,k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(C,k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2))
=> k8_funct_2(k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers,A,B) = k8_funct_2(k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers,A,C) ) ) ) ) ) ).
fof(t46_scmfsa9a,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_ami_3(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(C)
& v1_scmfsa7b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ~ ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
& r3_scmfsa9a(A,B,C)
& r4_scmfsa9a(A,B,C)
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers)
& m2_relset_1(D,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers) )
=> ~ ( v1_scmfsa9a(D)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(k8_funct_2(k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers,D,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),E)),k8_funct_2(k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)),k5_numbers,D,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),k1_nat_1(E,np__1))))
& ~ r1_xreal_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_9(A,C,B),E),B),np__0) ) ) ) ) ) ) ) ) ).
fof(t47_scmfsa9a,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)))
=> ! [C] :
( ( ~ v1_sf_mastr(C)
& m1_scmfsa_2(C) )
=> ! [D] :
( ( v1_ami_3(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(D)
& v1_scmfsa7b(D)
& m1_ami_1(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
& k7_relat_1(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(B,k1_finsub_1(k1_zfmisc_1(u1_struct_0(k1_scmfsa_2)),k2_scmfsa_2,k3_scmfsa_2))
& r3_scmfsa9a(A,C,D)
& r4_scmfsa9a(A,C,D) )
=> r4_scmfsa9a(B,C,D) ) ) ) ) ) ).
fof(d8_scmfsa9a,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> k3_scmfsa9a(A,B) = k4_scmfsa6a(k6_scmfsa6a(k7_scmfsa6a(k10_scmfsa_2(B,B),k8_scmfsa_2(k6_sfmastr1(np__1,k2_sfmastr1(A,B)),k4_scmfsa_2(np__0))),k8_scmfsa_2(k6_sfmastr1(np__2,k2_sfmastr1(A,B)),A)),k2_scmfsa_9(k6_sfmastr1(np__2,k2_sfmastr1(A,B)),k4_scmfsa6a(k6_scmfsa6a(k2_scmfsa_7(k6_sfmastr1(np__3,k2_sfmastr1(A,B)),np__2),k12_scmfsa_2(k6_sfmastr1(np__2,k2_sfmastr1(A,B)),k6_sfmastr1(np__3,k2_sfmastr1(A,B)))),k1_scmfsa8b(k6_sfmastr1(np__3,k2_sfmastr1(A,B)),k2_scmfsa6a(k9_scmfsa_2(k6_sfmastr1(np__1,k2_sfmastr1(A,B)),B)),k2_scmfsa6a(k9_scmfsa_2(B,k6_sfmastr1(np__1,k2_sfmastr1(A,B)))))))) ) ) ).
fof(t48_scmfsa9a,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) )
=> ( B != C
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( D = k20_scmfsa_2(A,B)
=> ( k20_scmfsa_2(k3_scmfsa6b(k3_scmfsa9a(B,C),A),C) = k5_pre_ff(D)
& k20_scmfsa_2(k3_scmfsa6b(k3_scmfsa9a(B,C),A),B) = D ) ) ) ) ) ) ) ).
fof(s1_scmfsa9a,axiom,
( ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(f1_s1_scmfsa9a(A),f1_s1_scmfsa9a(k1_nat_1(A,np__1)))
& ~ p1_s1_scmfsa9a(A) ) )
=> ? [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
& p1_s1_scmfsa9a(A)
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( p1_s1_scmfsa9a(B)
=> r1_xreal_0(A,B) ) ) ) ) ).
fof(dt_k1_scmfsa9a,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
& ~ v1_sf_mastr(B)
& m1_scmfsa_2(B)
& 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) )
=> m2_subset_1(k1_scmfsa9a(A,B,C),k1_numbers,k5_numbers) ) ).
fof(dt_k2_scmfsa9a,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
& ~ v1_sf_mastr(B)
& m1_scmfsa_2(B)
& 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) )
=> m2_subset_1(k2_scmfsa9a(A,B,C),k1_numbers,k5_numbers) ) ).
fof(dt_k3_scmfsa9a,axiom,
! [A,B] :
( ( m1_scmfsa_2(A)
& m1_scmfsa_2(B) )
=> ( v1_ami_3(k3_scmfsa9a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k3_scmfsa9a(A,B))
& m1_ami_1(k3_scmfsa9a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ).
%------------------------------------------------------------------------------