SET007 Axioms: SET007+552.ax
%------------------------------------------------------------------------------
% File : SET007+552 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The For (going up) Macro Instruction
% 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 : sfmastr3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 65 ( 1 unt; 0 def)
% Number of atoms : 604 ( 78 equ)
% Maximal formula atoms : 18 ( 9 avg)
% Number of connectives : 589 ( 50 ~; 14 |; 243 &)
% ( 6 <=>; 276 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 12 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 39 ( 37 usr; 1 prp; 0-5 aty)
% Number of functors : 72 ( 72 usr; 11 con; 0-6 aty)
% Number of variables : 267 ( 265 !; 2 ?)
% 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_sfmastr3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& v5_membered(A) )
=> ( v1_xreal_0(k3_seq_4(A))
& v1_int_1(k3_seq_4(A))
& v1_xcmplx_0(k3_seq_4(A)) ) ) ).
fof(fc2_sfmastr3,axiom,
! [A,B,C,D] :
( ( ~ v1_sf_mastr(A)
& m1_scmfsa_2(A)
& m1_scmfsa_2(B)
& 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)
& 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) )
=> ( v1_relat_1(k5_scmfsa8b(A,B,C,D))
& v1_funct_1(k5_scmfsa8b(A,B,C,D))
& v1_finset_1(k5_scmfsa8b(A,B,C,D))
& v1_ami_3(k5_scmfsa8b(A,B,C,D),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k5_scmfsa8b(A,B,C,D))
& v1_scmfsa7b(k5_scmfsa8b(A,B,C,D)) ) ) ).
fof(fc3_sfmastr3,axiom,
! [A,B,C,D] :
( ( ~ v1_sf_mastr(A)
& m1_scmfsa_2(A)
& m1_scmfsa_2(B)
& m1_scmfsa_2(C)
& 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) )
=> ( v1_relat_1(k3_sfmastr3(A,B,C,D))
& v1_funct_1(k3_sfmastr3(A,B,C,D))
& v1_finset_1(k3_sfmastr3(A,B,C,D))
& v1_ami_3(k3_sfmastr3(A,B,C,D),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k3_sfmastr3(A,B,C,D))
& v1_scmfsa7b(k3_sfmastr3(A,B,C,D)) ) ) ).
fof(fc4_sfmastr3,axiom,
! [A,B,C,D] :
( ( m1_scmfsa_2(A)
& m1_scmfsa_2(B)
& ~ v1_sf_mastr(C)
& m1_scmfsa_2(C)
& m2_scmfsa_2(D) )
=> ( v1_relat_1(k4_sfmastr3(A,B,C,D))
& v1_funct_1(k4_sfmastr3(A,B,C,D))
& v1_finset_1(k4_sfmastr3(A,B,C,D))
& v1_ami_3(k4_sfmastr3(A,B,C,D),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k4_sfmastr3(A,B,C,D))
& v1_scmfsa7b(k4_sfmastr3(A,B,C,D)) ) ) ).
fof(fc5_sfmastr3,axiom,
! [A,B,C] :
( ( m2_scmfsa_2(A)
& m1_scmfsa_2(B)
& m1_scmfsa_2(C) )
=> ( v1_relat_1(k5_sfmastr3(A,B,C))
& v1_funct_1(k5_sfmastr3(A,B,C))
& ~ v1_xboole_0(k5_sfmastr3(A,B,C))
& v1_finset_1(k5_sfmastr3(A,B,C))
& v1_ami_3(k5_sfmastr3(A,B,C),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k5_sfmastr3(A,B,C))
& v1_scmfsa7b(k5_sfmastr3(A,B,C))
& v1_scmfsa6b(k5_sfmastr3(A,B,C))
& v2_scmfsa6b(k5_sfmastr3(A,B,C))
& v3_scmfsa6b(k5_sfmastr3(A,B,C)) ) ) ).
fof(t1_sfmastr3,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& v3_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> ( v1_funct_1(k2_funct_7(k2_funct_7(B,C,k1_funct_1(B,D)),D,k1_funct_1(B,C)))
& v1_funct_2(k2_funct_7(k2_funct_7(B,C,k1_funct_1(B,D)),D,k1_funct_1(B,C)),A,A)
& v3_funct_2(k2_funct_7(k2_funct_7(B,C,k1_funct_1(B,D)),D,k1_funct_1(B,C)),A,A)
& m2_relset_1(k2_funct_7(k2_funct_7(B,C,k1_funct_1(B,D)),D,k1_funct_1(B,C)),A,A) ) ) ) ) ).
fof(t2_sfmastr3,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C] :
~ ( r2_hidden(B,k1_relat_1(A))
& r2_hidden(C,k1_relat_1(A))
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_relat_1(A),k1_relat_1(A))
& v3_funct_2(D,k1_relat_1(A),k1_relat_1(A))
& m2_relset_1(D,k1_relat_1(A),k1_relat_1(A)) )
=> k2_funct_7(k2_funct_7(A,B,k1_funct_1(A,C)),C,k1_funct_1(A,B)) != k5_relat_1(D,A) ) ) ) ).
fof(d1_sfmastr3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_finset_1(A)
& v2_membered(A) )
=> ! [B] :
( v1_xreal_0(B)
=> ( B = k3_seq_4(A)
<=> ( r2_hidden(B,A)
& ! [C] :
( v1_xreal_0(C)
=> ( r2_hidden(C,A)
=> r1_xreal_0(B,C) ) ) ) ) ) ) ).
fof(d2_sfmastr3,axiom,
$true ).
fof(d3_sfmastr3,axiom,
! [A] :
( m2_finseq_1(A,k4_numbers)
=> ! [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(B,C)
& r1_xreal_0(C,k3_finseq_1(A)) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( D = k1_sfmastr3(A,B,C)
<=> ? [E] :
( ~ v1_xboole_0(E)
& v1_finset_1(E)
& m1_subset_1(E,k1_zfmisc_1(k4_numbers))
& E = k2_relat_1(k2_graph_2(k4_numbers,A,B,C))
& k1_nat_1(D,np__1) = k1_nat_1(k5_finseq_4(k2_graph_2(k4_numbers,A,B,C),k3_seq_4(E)),B) ) ) ) ) ) ) ) ).
fof(t3_sfmastr3,axiom,
! [A] :
( m2_finseq_1(A,k4_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(B,C)
& r1_xreal_0(C,k3_finseq_1(A)) )
=> ( D = k1_sfmastr3(A,B,C)
<=> ( r1_xreal_0(B,D)
& r1_xreal_0(D,C)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(B,E)
& r1_xreal_0(E,C) )
=> r1_xreal_0(k1_funct_1(A,D),k1_funct_1(A,E)) ) )
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(B,E)
& ~ r1_xreal_0(D,E)
& r1_xreal_0(k1_funct_1(A,E),k1_funct_1(A,D)) ) ) ) ) ) ) ) ) ) ).
fof(t4_sfmastr3,axiom,
! [A] :
( m2_finseq_1(A,k4_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(B,k3_finseq_1(A)) )
=> k1_sfmastr3(A,B,B) = B ) ) ) ).
fof(d4_sfmastr3,axiom,
! [A] :
( m2_finseq_1(A,k4_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_sfmastr3(A,B,C)
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(B,D)
& r1_xreal_0(D,E)
& r1_xreal_0(E,C) )
=> r1_xreal_0(k1_funct_1(A,D),k1_funct_1(A,E)) ) ) ) ) ) ) ) ).
fof(d5_sfmastr3,axiom,
! [A] :
( m2_finseq_1(A,k4_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r2_sfmastr3(A,B)
<=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,B)
& r1_xreal_0(D,k3_finseq_1(A)) )
=> ( r1_xreal_0(D,B)
| r1_xreal_0(k1_funct_1(A,C),k1_funct_1(A,D)) ) ) ) ) ) ) ) ).
fof(t5_sfmastr3,axiom,
! [A] :
( m2_finseq_1(A,k4_numbers)
=> ! [B] :
( m2_finseq_1(B,k4_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
& D = k1_sfmastr3(A,k1_nat_1(C,np__1),k3_finseq_1(A))
& r2_sfmastr3(A,C)
& r1_sfmastr3(A,np__1,C)
& B = k2_funct_7(k2_funct_7(A,k1_nat_1(C,np__1),k1_funct_1(A,D)),D,k1_funct_1(A,k1_nat_1(C,np__1))) )
=> r1_sfmastr3(B,np__1,k1_nat_1(C,np__1)) ) ) ) ) ) ).
fof(t6_sfmastr3,axiom,
! [A] :
( m2_finseq_1(A,k4_numbers)
=> ! [B] :
( m2_finseq_1(B,k4_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(A))
& D = k1_sfmastr3(A,k1_nat_1(C,np__1),k3_finseq_1(A))
& r2_sfmastr3(A,C)
& B = k2_funct_7(k2_funct_7(A,k1_nat_1(C,np__1),k1_funct_1(A,D)),D,k1_funct_1(A,k1_nat_1(C,np__1))) )
=> r2_sfmastr3(B,k1_nat_1(C,np__1)) ) ) ) ) ) ).
fof(t7_sfmastr3,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_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,k1_scmfsa6c(A))
& r6_scmfsa7b(C,k1_scmfsa6c(A))
& r4_scmfsa7b(C,B) )
=> k20_scmfsa_2(k3_scmfsa6b(C,A),B) = k20_scmfsa_2(k1_scmfsa6c(A),B) ) ) ) ) ).
fof(t8_sfmastr3,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(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(k3_scmfsa6b(k5_scmfsa_4,A),k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(A,k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2)) ) ) ).
fof(t9_sfmastr3,axiom,
! [A] :
( m1_scmfsa_2(A)
=> r2_scmfsa7b(k5_scmfsa_4,A) ) ).
fof(t10_sfmastr3,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> ( A != B
=> r1_scmfsa7b(k8_scmfsa_2(C,B),A) ) ) ) ) ).
fof(t11_sfmastr3,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] :
( m1_scmfsa_2(C)
=> ! [D] :
( m2_scmfsa_2(D)
=> k20_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k16_scmfsa_2(B,C,D),A),B) = k4_finseq_4(k5_numbers,k4_numbers,k21_scmfsa_2(A,D),k1_int_2(k20_scmfsa_2(A,C))) ) ) ) ) ).
fof(t12_sfmastr3,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_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> ! [D] :
( m2_scmfsa_2(D)
=> k21_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k17_scmfsa_2(C,B,D),A),D) = k2_funct_7(k21_scmfsa_2(A,D),k1_int_2(k20_scmfsa_2(A,B)),k20_scmfsa_2(A,C)) ) ) ) ) ).
fof(t13_sfmastr3,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) )
=> k2_sf_mastr(k5_scmfsa8b(A,B,C,D)) = k4_subset_1(k2_scmfsa_2,k4_subset_1(k2_scmfsa_2,k2_sfmastr1(A,B),k2_sf_mastr(C)),k2_sf_mastr(D)) ) ) ) ) ).
fof(t14_sfmastr3,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) )
=> ( r4_scmfsa7b(C,A)
=> r4_scmfsa7b(k2_scmfsa_9(B,C),A) ) ) ) ) ).
fof(t15_sfmastr3,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [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) )
=> ! [E] :
( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(E)
& m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( ( r4_scmfsa7b(D,A)
& r4_scmfsa7b(E,A) )
=> ( A = B
| r4_scmfsa7b(k5_scmfsa8b(B,C,D,E),A) ) ) ) ) ) ) ) ).
fof(d6_sfmastr3,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [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) )
=> ! [E] :
( m1_subset_1(E,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> k2_sfmastr3(A,B,C,D,E) = k5_scmfsa_9(k2_scmfsa6b(k2_scmfsa6b(E,k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(A,B,C),k2_sf_mastr(D))),k2_xcmplx_0(k6_xcmplx_0(k20_scmfsa_2(E,C),k20_scmfsa_2(E,B)),np__1)),A,k20_scmfsa_2(E,B)),k6_scmfsa6a(k6_scmfsa6a(D,k9_scmfsa_2(A,k4_scmfsa_2(np__0))),k10_scmfsa_2(k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(A,B,C),k2_sf_mastr(D))),k4_scmfsa_2(np__0))),k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(A,B,C),k2_sf_mastr(D)))) ) ) ) ) ) ).
fof(t16_sfmastr3,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] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ! [E] :
( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(E)
& m1_ami_1(E,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(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),np__0),k4_scmfsa_2(np__0)) = np__1 ) ) ) ) ) ) ).
fof(t17_sfmastr3,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] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ! [E] :
( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(E)
& m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),np__0),B) = k20_scmfsa_2(A,C) ) ) ) ) ) ).
fof(t18_sfmastr3,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] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ! [E] :
( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(E)
& m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( B != C
=> k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),np__0),C) = k20_scmfsa_2(A,C) ) ) ) ) ) ) ).
fof(t19_sfmastr3,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] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ! [E] :
( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(E)
& m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( B != C
=> k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,D,C,E,A),np__0),C) = k20_scmfsa_2(A,C) ) ) ) ) ) ) ).
fof(t20_sfmastr3,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] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ! [E] :
( m1_scmfsa_2(E)
=> ! [F] :
( ( v1_ami_3(F,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(F)
& m1_ami_1(F,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( r2_hidden(C,k2_sf_mastr(F))
=> ( B = C
| k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,D,E,F,A),np__0),C) = k20_scmfsa_2(A,C) ) ) ) ) ) ) ) ) ).
fof(t21_sfmastr3,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] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ! [E] :
( m2_scmfsa_2(E)
=> ! [F] :
( ( v1_ami_3(F,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(F)
& m1_ami_1(F,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> k21_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,F,A),np__0),E) = k21_scmfsa_2(A,E) ) ) ) ) ) ) ).
fof(t22_sfmastr3,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] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ! [E] :
( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(E)
& m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
=> ! [F] :
( ( ~ v1_sf_mastr(F)
& m1_scmfsa_2(F) )
=> ( F = k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(B,C,D),k2_sf_mastr(E)))
=> k7_relat_1(k3_scmfsa6b(k6_scmfsa6a(k6_scmfsa6a(k7_scmfsa6a(k8_scmfsa_2(F,D),k10_scmfsa_2(F,C)),k9_scmfsa_2(F,k4_scmfsa_2(np__0))),k8_scmfsa_2(B,C)),A),k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k2_scmfsa6b(k2_scmfsa6b(A,F,k2_xcmplx_0(k6_xcmplx_0(k20_scmfsa_2(A,D),k20_scmfsa_2(A,C)),np__1)),B,k20_scmfsa_2(A,C)),k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ) ) ) ).
fof(d7_sfmastr3,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [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) )
=> ! [E] :
( m1_subset_1(E,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( r3_sfmastr3(A,B,C,D,E)
<=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(k2_xcmplx_0(k6_xcmplx_0(k20_scmfsa_2(E,C),k20_scmfsa_2(E,B)),np__1),F)
=> ( r5_scmfsa7b(D,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(A,B,C,D,E),F))
& r6_scmfsa7b(D,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(A,B,C,D,E),F)) ) ) ) ) ) ) ) ) ) ).
fof(t23_sfmastr3,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_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ! [E] :
( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(E)
& v2_scmfsa6b(E)
& m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> r3_sfmastr3(B,C,D,E,A) ) ) ) ) ) ).
fof(t24_sfmastr3,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] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ! [E] :
( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(E)
& v1_scmfsa7b(E)
& m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [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,k2_sfmastr3(B,C,D,E,A),F),k4_scmfsa_2(np__0)) = np__1
& r5_scmfsa7b(E,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),F))
& r6_scmfsa7b(E,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),F)) )
=> k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),k1_nat_1(F,np__1)),k4_scmfsa_2(np__0)) = np__1 ) ) ) ) ) ) ) ).
fof(t25_sfmastr3,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] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ! [E] :
( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(E)
& v1_scmfsa7b(E)
& m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
& r3_sfmastr3(B,C,D,E,A) )
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r1_xreal_0(F,k2_xcmplx_0(k6_xcmplx_0(k20_scmfsa_2(A,D),k20_scmfsa_2(A,C)),np__1))
=> ( k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),F),k4_scmfsa_2(np__0)) = np__1
& ( r4_scmfsa7b(E,B)
=> ( k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),F),B) = k2_xcmplx_0(F,k20_scmfsa_2(A,C))
& r1_xreal_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),F),B),k2_xcmplx_0(k20_scmfsa_2(A,D),np__1)) ) )
& k2_xcmplx_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),F),k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(B,C,D),k2_sf_mastr(E)))),F) = k2_xcmplx_0(k6_xcmplx_0(k20_scmfsa_2(A,D),k20_scmfsa_2(A,C)),np__1) ) ) ) ) ) ) ) ) ) ).
fof(t26_sfmastr3,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] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ! [E] :
( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(E)
& v1_scmfsa7b(E)
& m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
& r3_sfmastr3(B,C,D,E,A) )
=> ! [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,k2_sfmastr3(B,C,D,E,A),F),k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(B,C,D),k2_sf_mastr(E)))),np__0)
& r1_xreal_0(k2_xcmplx_0(k6_xcmplx_0(k20_scmfsa_2(A,D),k20_scmfsa_2(A,C)),np__1),F) )
& ~ ( ~ r1_xreal_0(k2_xcmplx_0(k6_xcmplx_0(k20_scmfsa_2(A,D),k20_scmfsa_2(A,C)),np__1),F)
& r1_xreal_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),F),k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(B,C,D),k2_sf_mastr(E)))),np__0) ) ) ) ) ) ) ) ) ) ).
fof(t27_sfmastr3,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] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ! [E] :
( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(E)
& v1_scmfsa7b(E)
& m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
& r3_sfmastr3(B,C,D,E,A) )
=> ( r1_xreal_0(k2_xcmplx_0(k6_xcmplx_0(k20_scmfsa_2(A,D),k20_scmfsa_2(A,C)),np__1),F)
| k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),k1_nat_1(F,np__1)),k2_xboole_0(k4_subset_1(k2_scmfsa_2,k3_sfmastr1(B,C,D),k2_sf_mastr(E)),k3_scmfsa_2)) = k7_relat_1(k3_scmfsa6b(k6_scmfsa6a(E,k9_scmfsa_2(B,k4_scmfsa_2(np__0))),k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr3(B,C,D,E,A),F)),k2_xboole_0(k4_subset_1(k2_scmfsa_2,k3_sfmastr1(B,C,D),k2_sf_mastr(E)),k3_scmfsa_2)) ) ) ) ) ) ) ) ) ).
fof(d8_sfmastr3,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [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) )
=> k3_sfmastr3(A,B,C,D) = k4_scmfsa6a(k6_scmfsa6a(k6_scmfsa6a(k7_scmfsa6a(k8_scmfsa_2(k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(A,B,C),k2_sf_mastr(D))),C),k10_scmfsa_2(k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(A,B,C),k2_sf_mastr(D))),B)),k9_scmfsa_2(k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(A,B,C),k2_sf_mastr(D))),k4_scmfsa_2(np__0))),k8_scmfsa_2(A,B)),k2_scmfsa_9(k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(A,B,C),k2_sf_mastr(D))),k6_scmfsa6a(k6_scmfsa6a(D,k9_scmfsa_2(A,k4_scmfsa_2(np__0))),k10_scmfsa_2(k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(A,B,C),k2_sf_mastr(D))),k4_scmfsa_2(np__0))))) ) ) ) ) ).
fof(t28_sfmastr3,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [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_tarski(k4_subset_1(k2_scmfsa_2,k3_sfmastr1(A,B,C),k2_sf_mastr(D)),k2_sf_mastr(k3_sfmastr3(A,B,C,D))) ) ) ) ) ).
fof(t29_sfmastr3,axiom,
! [A] :
( ( ~ v1_sf_mastr(A)
& m1_scmfsa_2(A) )
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ! [E] :
( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(E)
& m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( r4_scmfsa7b(E,B)
=> ( A = B
| B = k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k3_sfmastr1(A,C,D),k2_sf_mastr(E)))
| r4_scmfsa7b(k3_sfmastr3(A,C,D,E),B) ) ) ) ) ) ) ) ).
fof(t30_sfmastr3,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] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ! [E] :
( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(E)
& m1_ami_1(E,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,C),k20_scmfsa_2(A,D))
| ( ! [F] :
( m1_scmfsa_2(F)
=> ( r2_hidden(F,k4_subset_1(k2_scmfsa_2,k2_sfmastr1(C,D),k2_sf_mastr(E)))
=> ( F = B
| k20_scmfsa_2(k3_scmfsa6b(k3_sfmastr3(B,C,D,E),A),F) = k20_scmfsa_2(A,F) ) ) )
& ! [F] :
( m2_scmfsa_2(F)
=> k21_scmfsa_2(k3_scmfsa6b(k3_sfmastr3(B,C,D,E),A),F) = k21_scmfsa_2(A,F) ) ) ) ) ) ) ) ) ) ).
fof(t31_sfmastr3,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] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ! [E] :
( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(E)
& v1_scmfsa7b(E)
& m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
& F = k2_xcmplx_0(k6_xcmplx_0(k20_scmfsa_2(A,C),k20_scmfsa_2(A,D)),np__1) )
=> ( ( ~ r3_sfmastr3(B,D,C,E,A)
& ~ v2_scmfsa6b(E) )
| k7_relat_1(k3_scmfsa6b(k3_sfmastr3(B,D,C,E),A),k4_subset_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,k2_sfmastr3(B,D,C,E,A),F),k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ) ) ) ).
fof(t32_sfmastr3,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] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ! [E] :
( ( v1_ami_3(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(E)
& v1_scmfsa7b(E)
& m1_ami_1(E,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
=> ( ( ~ r3_sfmastr3(B,C,D,E,A)
& ~ v2_scmfsa6b(E) )
| ( r5_scmfsa7b(k3_sfmastr3(B,C,D,E),A)
& r6_scmfsa7b(k3_sfmastr3(B,C,D,E),A) ) ) ) ) ) ) ) ) ).
fof(d9_sfmastr3,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> ! [D] :
( m2_scmfsa_2(D)
=> k4_sfmastr3(A,B,C,D) = k5_scmfsa6a(k8_scmfsa_2(C,A),k3_sfmastr3(k6_sfmastr1(np__3,k3_sfmastr1(A,B,C)),A,B,k4_scmfsa6a(k7_scmfsa6a(k16_scmfsa_2(k6_sfmastr1(np__1,k3_sfmastr1(A,B,C)),k6_sfmastr1(np__3,k3_sfmastr1(A,B,C)),D),k16_scmfsa_2(k6_sfmastr1(np__2,k3_sfmastr1(A,B,C)),C,D)),k5_scmfsa8b(k6_sfmastr1(np__2,k3_sfmastr1(A,B,C)),k6_sfmastr1(np__1,k3_sfmastr1(A,B,C)),k2_scmfsa6a(k8_scmfsa_2(C,k6_sfmastr1(np__3,k3_sfmastr1(A,B,C)))),k5_scmfsa_4)))) ) ) ) ) ).
fof(t33_sfmastr3,axiom,
! [A] :
( ( ~ v1_sf_mastr(A)
& m1_scmfsa_2(A) )
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> ! [D] :
( m2_scmfsa_2(D)
=> ( A != B
=> r4_scmfsa7b(k4_sfmastr3(B,C,A,D),B) ) ) ) ) ) ).
fof(t34_sfmastr3,axiom,
! [A] :
( ( ~ v1_sf_mastr(A)
& m1_scmfsa_2(A) )
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> ! [D] :
( m2_scmfsa_2(D)
=> r1_tarski(k3_sfmastr1(B,C,A),k2_sf_mastr(k4_sfmastr3(B,C,A,D))) ) ) ) ) ).
fof(t35_sfmastr3,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] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ! [E] :
( m2_scmfsa_2(E)
=> ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
=> ( r5_scmfsa7b(k4_sfmastr3(C,D,B,E),A)
& r6_scmfsa7b(k4_sfmastr3(C,D,B,E),A) ) ) ) ) ) ) ) ).
fof(t36_sfmastr3,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] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ! [E] :
( m2_scmfsa_2(E)
=> ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
=> ( C = B
| D = B
| ( k21_scmfsa_2(k3_scmfsa6b(k4_sfmastr3(C,D,B,E),A),E) = k21_scmfsa_2(A,E)
& k20_scmfsa_2(k3_scmfsa6b(k4_sfmastr3(C,D,B,E),A),C) = k20_scmfsa_2(A,C)
& k20_scmfsa_2(k3_scmfsa6b(k4_sfmastr3(C,D,B,E),A),D) = k20_scmfsa_2(A,D) ) ) ) ) ) ) ) ) ).
fof(t37_sfmastr3,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] :
( m1_scmfsa_2(C)
=> ! [D] :
( m1_scmfsa_2(D)
=> ! [E] :
( m2_scmfsa_2(E)
=> ( ( r1_xreal_0(np__1,k20_scmfsa_2(A,C))
& r1_xreal_0(k20_scmfsa_2(A,C),k20_scmfsa_2(A,D))
& r1_xreal_0(k20_scmfsa_2(A,D),k3_finseq_1(k21_scmfsa_2(A,E)))
& k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1 )
=> ( C = B
| D = B
| k20_scmfsa_2(k3_scmfsa6b(k4_sfmastr3(C,D,B,E),A),B) = k1_sfmastr3(k21_scmfsa_2(A,E),k1_int_2(k20_scmfsa_2(A,C)),k1_int_2(k20_scmfsa_2(A,D))) ) ) ) ) ) ) ) ).
fof(d10_sfmastr3,axiom,
! [A] :
( m2_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> k5_sfmastr3(A,B,C) = k6_scmfsa6a(k6_scmfsa6a(k7_scmfsa6a(k16_scmfsa_2(k6_sfmastr1(np__1,k2_sfmastr1(B,C)),B,A),k16_scmfsa_2(k6_sfmastr1(np__2,k2_sfmastr1(B,C)),C,A)),k17_scmfsa_2(k6_sfmastr1(np__2,k2_sfmastr1(B,C)),B,A)),k17_scmfsa_2(k6_sfmastr1(np__1,k2_sfmastr1(B,C)),C,A)) ) ) ) ).
fof(t38_sfmastr3,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> ! [D] :
( m2_scmfsa_2(D)
=> ~ ( A != k6_sfmastr1(np__1,k2_sfmastr1(B,C))
& A != k6_sfmastr1(np__2,k2_sfmastr1(B,C))
& ~ r4_scmfsa7b(k5_sfmastr3(D,B,C),A) ) ) ) ) ) ).
fof(t39_sfmastr3,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_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> ! [D] :
( m2_scmfsa_2(D)
=> ( ( r1_xreal_0(np__1,k20_scmfsa_2(A,B))
& r1_xreal_0(k20_scmfsa_2(A,B),k3_finseq_1(k21_scmfsa_2(A,D)))
& r1_xreal_0(np__1,k20_scmfsa_2(A,C))
& r1_xreal_0(k20_scmfsa_2(A,C),k3_finseq_1(k21_scmfsa_2(A,D)))
& k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1 )
=> k21_scmfsa_2(k3_scmfsa6b(k5_sfmastr3(D,B,C),A),D) = k2_funct_7(k2_funct_7(k21_scmfsa_2(A,D),k20_scmfsa_2(A,B),k1_funct_1(k21_scmfsa_2(A,D),k20_scmfsa_2(A,C))),k20_scmfsa_2(A,C),k1_funct_1(k21_scmfsa_2(A,D),k20_scmfsa_2(A,B))) ) ) ) ) ) ).
fof(t40_sfmastr3,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_scmfsa_2(B)
=> ! [C] :
( m1_scmfsa_2(C)
=> ! [D] :
( m2_scmfsa_2(D)
=> ( ( r1_xreal_0(np__1,k20_scmfsa_2(A,B))
& r1_xreal_0(k20_scmfsa_2(A,B),k3_finseq_1(k21_scmfsa_2(A,D)))
& r1_xreal_0(np__1,k20_scmfsa_2(A,C))
& r1_xreal_0(k20_scmfsa_2(A,C),k3_finseq_1(k21_scmfsa_2(A,D)))
& k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1 )
=> ( k1_funct_1(k21_scmfsa_2(k3_scmfsa6b(k5_sfmastr3(D,B,C),A),D),k20_scmfsa_2(A,B)) = k1_funct_1(k21_scmfsa_2(A,D),k20_scmfsa_2(A,C))
& k1_funct_1(k21_scmfsa_2(k3_scmfsa6b(k5_sfmastr3(D,B,C),A),D),k20_scmfsa_2(A,C)) = k1_funct_1(k21_scmfsa_2(A,D),k20_scmfsa_2(A,B)) ) ) ) ) ) ) ).
fof(t41_sfmastr3,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m2_scmfsa_2(C)
=> r1_tarski(k2_sfmastr1(A,B),k2_sf_mastr(k5_sfmastr3(C,A,B))) ) ) ) ).
fof(t42_sfmastr3,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ! [C] :
( m2_scmfsa_2(C)
=> k4_sf_mastr(k5_sfmastr3(C,A,B)) = k1_tarski(C) ) ) ) ).
fof(d11_sfmastr3,axiom,
! [A] :
( m2_scmfsa_2(A)
=> k6_sfmastr3(A) = k5_scmfsa6a(k18_scmfsa_2(k7_sfmastr1(np__1,k5_sfmastr3(A,k6_sfmastr1(np__1,k1_subset_1(k2_scmfsa_2)),k6_sfmastr1(np__2,k1_subset_1(k2_scmfsa_2)))),A),k3_sfmastr3(k6_sfmastr1(np__1,k1_subset_1(k2_scmfsa_2)),k4_scmfsa_2(np__0),k7_sfmastr1(np__1,k5_sfmastr3(A,k6_sfmastr1(np__1,k1_subset_1(k2_scmfsa_2)),k6_sfmastr1(np__2,k1_subset_1(k2_scmfsa_2)))),k4_scmfsa6a(k4_sfmastr3(k6_sfmastr1(np__1,k1_subset_1(k2_scmfsa_2)),k7_sfmastr1(np__1,k5_sfmastr3(A,k6_sfmastr1(np__1,k1_subset_1(k2_scmfsa_2)),k6_sfmastr1(np__2,k1_subset_1(k2_scmfsa_2)))),k6_sfmastr1(np__2,k1_subset_1(k2_scmfsa_2)),A),k5_sfmastr3(A,k6_sfmastr1(np__1,k1_subset_1(k2_scmfsa_2)),k6_sfmastr1(np__2,k1_subset_1(k2_scmfsa_2)))))) ) ).
fof(t43_sfmastr3,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_subset_1(C,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( C = k3_scmfsa6b(k6_sfmastr3(B),A)
=> ( r1_sfmastr3(k21_scmfsa_2(C,B),np__1,k3_finseq_1(k21_scmfsa_2(C,B)))
& ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_1(k21_scmfsa_2(A,B)),k4_finseq_1(k21_scmfsa_2(A,B)))
& v3_funct_2(D,k4_finseq_1(k21_scmfsa_2(A,B)),k4_finseq_1(k21_scmfsa_2(A,B)))
& m2_relset_1(D,k4_finseq_1(k21_scmfsa_2(A,B)),k4_finseq_1(k21_scmfsa_2(A,B)))
& k21_scmfsa_2(C,B) = k1_partfun1(k4_finseq_1(k21_scmfsa_2(A,B)),k4_finseq_1(k21_scmfsa_2(A,B)),k5_numbers,k4_numbers,D,k21_scmfsa_2(A,B)) ) ) ) ) ) ) ).
fof(dt_k1_sfmastr3,axiom,
! [A,B,C] :
( ( m1_finseq_1(A,k4_numbers)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,k5_numbers) )
=> m2_subset_1(k1_sfmastr3(A,B,C),k1_numbers,k5_numbers) ) ).
fof(dt_k2_sfmastr3,axiom,
! [A,B,C,D,E] :
( ( m1_scmfsa_2(A)
& m1_scmfsa_2(B)
& m1_scmfsa_2(C)
& 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)
& m1_subset_1(E,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) )
=> ( v1_funct_1(k2_sfmastr3(A,B,C,D,E))
& v1_funct_2(k2_sfmastr3(A,B,C,D,E),k5_numbers,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
& m2_relset_1(k2_sfmastr3(A,B,C,D,E),k5_numbers,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) ) ) ).
fof(dt_k3_sfmastr3,axiom,
! [A,B,C,D] :
( ( m1_scmfsa_2(A)
& m1_scmfsa_2(B)
& m1_scmfsa_2(C)
& 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) )
=> ( v1_ami_3(k3_sfmastr3(A,B,C,D),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k3_sfmastr3(A,B,C,D))
& m1_ami_1(k3_sfmastr3(A,B,C,D),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ).
fof(dt_k4_sfmastr3,axiom,
! [A,B,C,D] :
( ( m1_scmfsa_2(A)
& m1_scmfsa_2(B)
& m1_scmfsa_2(C)
& m2_scmfsa_2(D) )
=> ( v1_ami_3(k4_sfmastr3(A,B,C,D),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k4_sfmastr3(A,B,C,D))
& m1_ami_1(k4_sfmastr3(A,B,C,D),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ).
fof(dt_k5_sfmastr3,axiom,
! [A,B,C] :
( ( m2_scmfsa_2(A)
& m1_scmfsa_2(B)
& m1_scmfsa_2(C) )
=> ( v1_ami_3(k5_sfmastr3(A,B,C),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k5_sfmastr3(A,B,C))
& m1_ami_1(k5_sfmastr3(A,B,C),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ).
fof(dt_k6_sfmastr3,axiom,
! [A] :
( m2_scmfsa_2(A)
=> ( v1_ami_3(k6_sfmastr3(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k6_sfmastr3(A))
& m1_ami_1(k6_sfmastr3(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ).
%------------------------------------------------------------------------------