SET007 Axioms: SET007+479.ax
%------------------------------------------------------------------------------
% File : SET007+479 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Conditional Branch 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 : scmfsa8b [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 57 ( 0 unt; 0 def)
% Number of atoms : 728 ( 95 equ)
% Maximal formula atoms : 28 ( 12 avg)
% Number of connectives : 723 ( 52 ~; 8 |; 394 &)
% ( 2 <=>; 267 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 12 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 26 ( 25 usr; 0 prp; 1-3 aty)
% Number of functors : 60 ( 60 usr; 13 con; 0-4 aty)
% Number of variables : 236 ( 236 !; 0 ?)
% 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_scmfsa8b,axiom,
! [A,B,C] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(A)
& v2_scmfsa6b(A)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(B)
& v2_scmfsa6b(B)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& ~ v1_sf_mastr(C)
& m1_scmfsa_2(C) )
=> ( ~ v1_xboole_0(k1_scmfsa8b(C,A,B))
& v1_relat_1(k1_scmfsa8b(C,A,B))
& v1_funct_1(k1_scmfsa8b(C,A,B))
& v1_finset_1(k1_scmfsa8b(C,A,B))
& v1_ami_3(k1_scmfsa8b(C,A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k1_scmfsa8b(C,A,B))
& v1_scmfsa6b(k1_scmfsa8b(C,A,B))
& v2_scmfsa6b(k1_scmfsa8b(C,A,B)) ) ) ).
fof(fc2_scmfsa8b,axiom,
! [A,B,C] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(A)
& v2_scmfsa6b(A)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(B)
& v2_scmfsa6b(B)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& ~ v1_sf_mastr(C)
& m1_scmfsa_2(C) )
=> ( ~ v1_xboole_0(k2_scmfsa8b(C,A,B))
& v1_relat_1(k2_scmfsa8b(C,A,B))
& v1_funct_1(k2_scmfsa8b(C,A,B))
& v1_finset_1(k2_scmfsa8b(C,A,B))
& v1_ami_3(k2_scmfsa8b(C,A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k2_scmfsa8b(C,A,B))
& v1_scmfsa6b(k2_scmfsa8b(C,A,B))
& v2_scmfsa6b(k2_scmfsa8b(C,A,B)) ) ) ).
fof(fc3_scmfsa8b,axiom,
! [A,B,C,D] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(A)
& v2_scmfsa6b(A)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(B)
& v2_scmfsa6b(B)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& ~ v1_sf_mastr(C)
& m1_scmfsa_2(C)
& ~ v1_sf_mastr(D)
& m1_scmfsa_2(D) )
=> ( ~ v1_xboole_0(k4_scmfsa8b(C,D,A,B))
& v1_relat_1(k4_scmfsa8b(C,D,A,B))
& v1_funct_1(k4_scmfsa8b(C,D,A,B))
& v1_finset_1(k4_scmfsa8b(C,D,A,B))
& v1_ami_3(k4_scmfsa8b(C,D,A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k4_scmfsa8b(C,D,A,B))
& v1_scmfsa6b(k4_scmfsa8b(C,D,A,B))
& v2_scmfsa6b(k4_scmfsa8b(C,D,A,B)) ) ) ).
fof(fc4_scmfsa8b,axiom,
! [A,B,C,D] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(A)
& v2_scmfsa6b(A)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(B)
& v2_scmfsa6b(B)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& ~ v1_sf_mastr(C)
& m1_scmfsa_2(C)
& ~ v1_sf_mastr(D)
& m1_scmfsa_2(D) )
=> ( ~ v1_xboole_0(k5_scmfsa8b(C,D,A,B))
& v1_relat_1(k5_scmfsa8b(C,D,A,B))
& v1_funct_1(k5_scmfsa8b(C,D,A,B))
& v1_finset_1(k5_scmfsa8b(C,D,A,B))
& v1_ami_3(k5_scmfsa8b(C,D,A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k5_scmfsa8b(C,D,A,B))
& v1_scmfsa6b(k5_scmfsa8b(C,D,A,B))
& v2_scmfsa6b(k5_scmfsa8b(C,D,A,B)) ) ) ).
fof(t1_scmfsa8b,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> r2_hidden(k2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k1_relat_1(A)) ) ).
fof(t2_scmfsa8b,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_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> r2_hidden(B,k1_relat_1(A)) ) ) ).
fof(t3_scmfsa8b,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)))
=> ( r5_scmfsa7b(A,B)
=> r2_hidden(k5_scmfsa_2(np__0),k1_relat_1(A)) ) ) ) ).
fof(t4_scmfsa8b,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_struct_0(B,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [C] :
( m1_struct_0(C,k1_scmfsa_2,u2_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,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B)),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C)) = k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C)) ) ) ) ).
fof(t5_scmfsa8b,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) )
=> k7_relat_1(k1_scmfsa6c(A),k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(B)),k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) ) ) ).
fof(t6_scmfsa8b,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_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) )
=> ( ( k7_relat_1(A,k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(B,k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2))
& r5_scmfsa7b(C,A) )
=> r5_scmfsa7b(C,B) ) ) ) ) ).
fof(t7_scmfsa8b,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_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) )
=> ( k7_relat_1(A,k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(B,k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2))
=> r1_funct_7(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)))),k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0)))),u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) ) ) ) ) ).
fof(t8_scmfsa8b,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_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) )
=> ( ( k7_relat_1(A,k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(B,k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2))
& r5_scmfsa7b(C,A)
& r6_scmfsa7b(C,A) )
=> ( r5_scmfsa7b(C,B)
& r6_scmfsa7b(C,B) ) ) ) ) ) ).
fof(t9_scmfsa8b,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] :
( ( 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(B,k1_scmfsa6c(A))
<=> r5_scmfsa7b(B,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k3_scmfsa6a(C))) ) ) ) ) ).
fof(t10_scmfsa8b,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] :
( ( 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_struct_0(D,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ( r5_scmfsa7b(B,A)
<=> r5_scmfsa7b(B,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D)))) ) ) ) ) ) ).
fof(t11_scmfsa8b,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_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,C,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))),A)
& r5_scmfsa7b(C,A) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_tarski(k6_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k1_scmfsa_5(C,D)),B)
& k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B) = k5_scmfsa_2(D)
& k7_relat_1(A,k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(B,k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( k2_scmfsa_4(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,A),E)),D) = 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),E))
& k4_scmfsa_4(k8_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,A),E)),D) = k8_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),E))
& 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),E),k2_xboole_0(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,B),E),k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ) ) ) ).
fof(t12_scmfsa8b,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ! [B] :
( ( v1_scmfsa6c(B)
& v2_scmfsa6c(B)
& m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
=> ! [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) )
=> ! [D] :
( m1_scmfsa_2(D)
=> k20_scmfsa_2(k3_scmfsa6b(k5_scmfsa6a(B,C),A),D) = k20_scmfsa_2(k3_scmfsa6b(C,k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k1_scmfsa6c(A))),D) ) ) ) ) ).
fof(t13_scmfsa8b,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ! [B] :
( ( v1_scmfsa6c(B)
& v2_scmfsa6c(B)
& m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
=> ! [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) )
=> ! [D] :
( m2_scmfsa_2(D)
=> k21_scmfsa_2(k3_scmfsa6b(k5_scmfsa6a(B,C),A),D) = k21_scmfsa_2(k3_scmfsa6b(C,k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k1_scmfsa6c(A))),D) ) ) ) ) ).
fof(d1_scmfsa8b,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) )
=> k1_scmfsa8b(A,B,C) = k4_scmfsa6a(k4_scmfsa6a(k4_scmfsa6a(k5_scmfsa6a(k14_scmfsa_2(k5_scmfsa_2(k1_nat_1(k4_card_1(C),np__3)),A),C),k2_scmfsa8a(k5_scmfsa_2(k1_nat_1(k4_card_1(B),np__1)))),B),k5_scmfsa_4) ) ) ) ).
fof(d2_scmfsa8b,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_scmfsa8b(A,B,C) = k4_scmfsa6a(k4_scmfsa6a(k4_scmfsa6a(k5_scmfsa6a(k15_scmfsa_2(k5_scmfsa_2(k1_nat_1(k4_card_1(C),np__3)),A),C),k2_scmfsa8a(k5_scmfsa_2(k1_nat_1(k4_card_1(B),np__1)))),B),k5_scmfsa_4) ) ) ) ).
fof(d3_scmfsa8b,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) )
=> k3_scmfsa8b(A,B,C) = k1_scmfsa8b(A,C,k2_scmfsa8b(A,C,B)) ) ) ) ).
fof(t14_scmfsa8b,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_card_1(k1_scmfsa8b(C,A,B)) = k1_nat_1(k1_nat_1(k4_card_1(A),k4_card_1(B)),np__4) ) ) ) ).
fof(t15_scmfsa8b,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_card_1(k2_scmfsa8b(C,A,B)) = k1_nat_1(k1_nat_1(k4_card_1(A),k4_card_1(B)),np__4) ) ) ) ).
fof(t16_scmfsa8b,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] :
( ( 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_sf_mastr(D)
& m1_scmfsa_2(D) )
=> ( ( k20_scmfsa_2(A,D) = np__0
& r5_scmfsa7b(B,A)
& r6_scmfsa7b(B,A) )
=> ( r5_scmfsa7b(k1_scmfsa8b(D,B,C),A)
& r6_scmfsa7b(k1_scmfsa8b(D,B,C),A) ) ) ) ) ) ) ).
fof(t17_scmfsa8b,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] :
( ( 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_sf_mastr(D)
& m1_scmfsa_2(D) )
=> ( ( k20_scmfsa_2(A,D) = np__0
& r5_scmfsa7b(B,k1_scmfsa6c(A))
& r6_scmfsa7b(B,k1_scmfsa6c(A)) )
=> k3_scmfsa6b(k1_scmfsa8b(D,B,C),A) = k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6b(B,A),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__3)))) ) ) ) ) ) ).
fof(t18_scmfsa8b,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] :
( ( 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_sf_mastr(D)
& m1_scmfsa_2(D) )
=> ( ( r5_scmfsa7b(C,A)
& r6_scmfsa7b(C,A) )
=> ( k20_scmfsa_2(A,D) = np__0
| ( r5_scmfsa7b(k1_scmfsa8b(D,B,C),A)
& r6_scmfsa7b(k1_scmfsa8b(D,B,C),A) ) ) ) ) ) ) ) ).
fof(t19_scmfsa8b,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] :
( ( ~ v1_sf_mastr(C)
& m1_scmfsa_2(C) )
=> ! [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( ( r5_scmfsa7b(B,k1_scmfsa6c(D))
& r6_scmfsa7b(B,k1_scmfsa6c(D)) )
=> ( k20_scmfsa_2(D,C) = np__0
| k3_scmfsa6b(k1_scmfsa8b(C,A,B),D) = k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6b(B,D),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(k1_nat_1(k1_nat_1(k4_card_1(A),k4_card_1(B)),np__3)))) ) ) ) ) ) ) ).
fof(t20_scmfsa8b,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)
& v2_scmfsa6b(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)
& v2_scmfsa6b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [D] :
( ( ~ v1_sf_mastr(D)
& m1_scmfsa_2(D) )
=> ( v2_scmfsa6b(k1_scmfsa8b(D,B,C))
& ( k20_scmfsa_2(A,D) = np__0
=> k3_scmfsa6b(k1_scmfsa8b(D,B,C),A) = k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6b(B,A),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__3)))) )
& ( k20_scmfsa_2(A,D) != np__0
=> k3_scmfsa6b(k1_scmfsa8b(D,B,C),A) = k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6b(C,A),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__3)))) ) ) ) ) ) ) ).
fof(t21_scmfsa8b,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)
& v2_scmfsa6b(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)
& v2_scmfsa6b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [D] :
( ( ~ v1_sf_mastr(D)
& m1_scmfsa_2(D) )
=> ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6b(k1_scmfsa8b(D,B,C),A)) = k5_scmfsa_2(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__3))
& ( k20_scmfsa_2(A,D) = np__0
=> ( ! [E] :
( m1_scmfsa_2(E)
=> k20_scmfsa_2(k3_scmfsa6b(k1_scmfsa8b(D,B,C),A),E) = k20_scmfsa_2(k3_scmfsa6b(B,A),E) )
& ! [E] :
( m2_scmfsa_2(E)
=> k21_scmfsa_2(k3_scmfsa6b(k1_scmfsa8b(D,B,C),A),E) = k21_scmfsa_2(k3_scmfsa6b(B,A),E) ) ) )
& ( k20_scmfsa_2(A,D) != np__0
=> ( ! [E] :
( m1_scmfsa_2(E)
=> k20_scmfsa_2(k3_scmfsa6b(k1_scmfsa8b(D,B,C),A),E) = k20_scmfsa_2(k3_scmfsa6b(C,A),E) )
& ! [E] :
( m2_scmfsa_2(E)
=> k21_scmfsa_2(k3_scmfsa6b(k1_scmfsa8b(D,B,C),A),E) = k21_scmfsa_2(k3_scmfsa6b(C,A),E) ) ) ) ) ) ) ) ) ).
fof(t22_scmfsa8b,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] :
( ( 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_sf_mastr(D)
& m1_scmfsa_2(D) )
=> ( ( r5_scmfsa7b(B,A)
& r6_scmfsa7b(B,A) )
=> ( r1_xreal_0(k20_scmfsa_2(A,D),np__0)
| ( r5_scmfsa7b(k2_scmfsa8b(D,B,C),A)
& r6_scmfsa7b(k2_scmfsa8b(D,B,C),A) ) ) ) ) ) ) ) ).
fof(t23_scmfsa8b,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] :
( ( ~ v1_sf_mastr(C)
& m1_scmfsa_2(C) )
=> ! [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( ( r5_scmfsa7b(A,k1_scmfsa6c(D))
& r6_scmfsa7b(A,k1_scmfsa6c(D)) )
=> ( r1_xreal_0(k20_scmfsa_2(D,C),np__0)
| k3_scmfsa6b(k2_scmfsa8b(C,A,B),D) = k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6b(A,D),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(k1_nat_1(k1_nat_1(k4_card_1(A),k4_card_1(B)),np__3)))) ) ) ) ) ) ) ).
fof(t24_scmfsa8b,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] :
( ( 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_sf_mastr(D)
& m1_scmfsa_2(D) )
=> ( ( r1_xreal_0(k20_scmfsa_2(A,D),np__0)
& r5_scmfsa7b(C,A)
& r6_scmfsa7b(C,A) )
=> ( r5_scmfsa7b(k2_scmfsa8b(D,B,C),A)
& r6_scmfsa7b(k2_scmfsa8b(D,B,C),A) ) ) ) ) ) ) ).
fof(t25_scmfsa8b,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] :
( ( ~ v1_sf_mastr(C)
& m1_scmfsa_2(C) )
=> ! [D] :
( m1_subset_1(D,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ( ( r1_xreal_0(k20_scmfsa_2(D,C),np__0)
& r5_scmfsa7b(B,k1_scmfsa6c(D))
& r6_scmfsa7b(B,k1_scmfsa6c(D)) )
=> k3_scmfsa6b(k2_scmfsa8b(C,A,B),D) = k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6b(B,D),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(k1_nat_1(k1_nat_1(k4_card_1(A),k4_card_1(B)),np__3)))) ) ) ) ) ) ).
fof(t26_scmfsa8b,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)
& v2_scmfsa6b(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)
& v2_scmfsa6b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [D] :
( ( ~ v1_sf_mastr(D)
& m1_scmfsa_2(D) )
=> ( v2_scmfsa6b(k2_scmfsa8b(D,B,C))
& ( ~ r1_xreal_0(k20_scmfsa_2(A,D),np__0)
=> k3_scmfsa6b(k2_scmfsa8b(D,B,C),A) = k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6b(B,A),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__3)))) )
& ( r1_xreal_0(k20_scmfsa_2(A,D),np__0)
=> k3_scmfsa6b(k2_scmfsa8b(D,B,C),A) = k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6b(C,A),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__3)))) ) ) ) ) ) ) ).
fof(t27_scmfsa8b,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)
& v2_scmfsa6b(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)
& v2_scmfsa6b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [D] :
( ( ~ v1_sf_mastr(D)
& m1_scmfsa_2(D) )
=> ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6b(k2_scmfsa8b(D,B,C),A)) = k5_scmfsa_2(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__3))
& ( ~ r1_xreal_0(k20_scmfsa_2(A,D),np__0)
=> ( ! [E] :
( m1_scmfsa_2(E)
=> k20_scmfsa_2(k3_scmfsa6b(k2_scmfsa8b(D,B,C),A),E) = k20_scmfsa_2(k3_scmfsa6b(B,A),E) )
& ! [E] :
( m2_scmfsa_2(E)
=> k21_scmfsa_2(k3_scmfsa6b(k2_scmfsa8b(D,B,C),A),E) = k21_scmfsa_2(k3_scmfsa6b(B,A),E) ) ) )
& ( r1_xreal_0(k20_scmfsa_2(A,D),np__0)
=> ( ! [E] :
( m1_scmfsa_2(E)
=> k20_scmfsa_2(k3_scmfsa6b(k2_scmfsa8b(D,B,C),A),E) = k20_scmfsa_2(k3_scmfsa6b(C,A),E) )
& ! [E] :
( m2_scmfsa_2(E)
=> k21_scmfsa_2(k3_scmfsa6b(k2_scmfsa8b(D,B,C),A),E) = k21_scmfsa_2(k3_scmfsa6b(C,A),E) ) ) ) ) ) ) ) ) ).
fof(t28_scmfsa8b,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] :
( ( 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_sf_mastr(D)
& m1_scmfsa_2(D) )
=> ( ( r5_scmfsa7b(B,A)
& r6_scmfsa7b(B,A) )
=> ( r1_xreal_0(np__0,k20_scmfsa_2(A,D))
| ( r5_scmfsa7b(k3_scmfsa8b(D,B,C),A)
& r6_scmfsa7b(k3_scmfsa8b(D,B,C),A) ) ) ) ) ) ) ) ).
fof(t29_scmfsa8b,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] :
( ( 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_sf_mastr(D)
& m1_scmfsa_2(D) )
=> ( ( r5_scmfsa7b(B,k1_scmfsa6c(A))
& r6_scmfsa7b(B,k1_scmfsa6c(A)) )
=> ( r1_xreal_0(np__0,k20_scmfsa_2(A,D))
| k3_scmfsa6b(k3_scmfsa8b(D,B,C),A) = k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6b(B,A),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(k1_nat_1(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),k4_card_1(C)),np__7)))) ) ) ) ) ) ) ).
fof(t30_scmfsa8b,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] :
( ( 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_sf_mastr(D)
& m1_scmfsa_2(D) )
=> ( ( k20_scmfsa_2(A,D) = np__0
& r5_scmfsa7b(C,A)
& r6_scmfsa7b(C,A) )
=> ( r5_scmfsa7b(k3_scmfsa8b(D,B,C),A)
& r6_scmfsa7b(k3_scmfsa8b(D,B,C),A) ) ) ) ) ) ) ).
fof(t31_scmfsa8b,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] :
( ( 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_sf_mastr(D)
& m1_scmfsa_2(D) )
=> ( ( k20_scmfsa_2(A,D) = np__0
& r5_scmfsa7b(C,k1_scmfsa6c(A))
& r6_scmfsa7b(C,k1_scmfsa6c(A)) )
=> k3_scmfsa6b(k3_scmfsa8b(D,B,C),A) = k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6b(C,A),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(k1_nat_1(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),k4_card_1(C)),np__7)))) ) ) ) ) ) ).
fof(t32_scmfsa8b,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] :
( ( 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_sf_mastr(D)
& m1_scmfsa_2(D) )
=> ( ( r5_scmfsa7b(C,A)
& r6_scmfsa7b(C,A) )
=> ( r1_xreal_0(k20_scmfsa_2(A,D),np__0)
| ( r5_scmfsa7b(k3_scmfsa8b(D,B,C),A)
& r6_scmfsa7b(k3_scmfsa8b(D,B,C),A) ) ) ) ) ) ) ) ).
fof(t33_scmfsa8b,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] :
( ( 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_sf_mastr(D)
& m1_scmfsa_2(D) )
=> ( ( r5_scmfsa7b(C,k1_scmfsa6c(A))
& r6_scmfsa7b(C,k1_scmfsa6c(A)) )
=> ( r1_xreal_0(k20_scmfsa_2(A,D),np__0)
| k3_scmfsa6b(k3_scmfsa8b(D,B,C),A) = k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6b(C,A),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(k1_nat_1(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),k4_card_1(C)),np__7)))) ) ) ) ) ) ) ).
fof(t34_scmfsa8b,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)
& v2_scmfsa6b(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)
& v2_scmfsa6b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [D] :
( ( ~ v1_sf_mastr(D)
& m1_scmfsa_2(D) )
=> ( v2_scmfsa6b(k3_scmfsa8b(D,B,C))
& ( ~ r1_xreal_0(np__0,k20_scmfsa_2(A,D))
=> k3_scmfsa6b(k3_scmfsa8b(D,B,C),A) = k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6b(B,A),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(k1_nat_1(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),k4_card_1(C)),np__7)))) )
& ( r1_xreal_0(np__0,k20_scmfsa_2(A,D))
=> k3_scmfsa6b(k3_scmfsa8b(D,B,C),A) = k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6b(C,A),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(k1_nat_1(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),k4_card_1(C)),np__7)))) ) ) ) ) ) ) ).
fof(d4_scmfsa8b,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) )
=> k4_scmfsa8b(A,B,C,D) = k5_scmfsa6a(k10_scmfsa_2(A,B),k1_scmfsa8b(A,C,D)) ) ) ) ) ).
fof(d5_scmfsa8b,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) )
=> k5_scmfsa8b(A,B,C,D) = k5_scmfsa6a(k10_scmfsa_2(A,B),k2_scmfsa8b(A,C,D)) ) ) ) ) ).
fof(t35_scmfsa8b,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) )
=> k7_relat_1(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))),k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k3_scmfsa6b(B,A),k2_xboole_0(k2_scmfsa_2,k3_scmfsa_2)) ) ) ).
fof(t36_scmfsa8b,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ! [B] :
( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(B)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [C] :
( m1_scmfsa_2(C)
=> r1_funct_7(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))),k3_scmfsa6b(B,A),u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) ) ) ).
fof(t37_scmfsa8b,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] :
( m2_subset_1(C,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ! [D] :
( m1_scmfsa_2(D)
=> ( ( ! [E] :
( m1_scmfsa_2(E)
=> ( D != E
=> k20_scmfsa_2(A,E) = k20_scmfsa_2(B,E) ) )
& ! [E] :
( m2_scmfsa_2(E)
=> k21_scmfsa_2(A,E) = k21_scmfsa_2(B,E) )
& r1_scmfsa7b(C,D)
& k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A) = k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B) )
=> ( ! [E] :
( m1_scmfsa_2(E)
=> ( D != E
=> k20_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,A),E) = k20_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,B),E) ) )
& ! [E] :
( m2_scmfsa_2(E)
=> k21_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,A),E) = k21_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,B),E) )
& k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,A)) = k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,B)) ) ) ) ) ) ) ).
fof(t38_scmfsa8b,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_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_scmfsa_2(D)
=> ( ( r2_scmfsa7b(C,D)
& ! [E] :
( m1_scmfsa_2(E)
=> ( D != E
=> k20_scmfsa_2(A,E) = k20_scmfsa_2(B,E) ) )
& ! [E] :
( m2_scmfsa_2(E)
=> k21_scmfsa_2(A,E) = k21_scmfsa_2(B,E) )
& r5_scmfsa7b(C,A)
& r6_scmfsa7b(C,A) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ! [F] :
( m1_scmfsa_2(F)
=> ( D != F
=> k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),E),F) = k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,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))))),E),F) ) )
& ! [F] :
( m2_scmfsa_2(F)
=> k21_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),E),F) = k21_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),E),F) )
& k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,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))))),E)) = k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),E))
& k8_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,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))))),E)) = k8_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k10_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k5_scmfsa_2(np__0))))),E)) ) ) ) ) ) ) ) ).
fof(t39_scmfsa8b,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] :
( ( 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_struct_0(D,k1_scmfsa_2,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ( ( ( r5_scmfsa7b(B,A)
& r6_scmfsa7b(B,A) )
=> ( r5_scmfsa7b(B,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D))))
& r6_scmfsa7b(B,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D)))) ) )
& ( ( r5_scmfsa7b(B,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D))))
& r6_scmfsa7b(B,k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A,k17_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,B,k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,D)))) )
=> ( r5_scmfsa7b(B,A)
& r6_scmfsa7b(B,A) ) ) ) ) ) ) ) ).
fof(t40_scmfsa8b,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_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_scmfsa_2(D)
=> ( ( r2_scmfsa7b(C,D)
& ! [E] :
( m1_scmfsa_2(E)
=> ( D != E
=> k20_scmfsa_2(A,E) = k20_scmfsa_2(B,E) ) )
& ! [E] :
( m2_scmfsa_2(E)
=> k21_scmfsa_2(A,E) = k21_scmfsa_2(B,E) )
& r5_scmfsa7b(C,A)
& r6_scmfsa7b(C,A) )
=> ( r5_scmfsa7b(C,B)
& r6_scmfsa7b(C,B) ) ) ) ) ) ) ).
fof(t41_scmfsa8b,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_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_scmfsa_2(D)
=> ( ( ! [E] :
( ( ~ v1_sf_mastr(E)
& m1_scmfsa_2(E) )
=> ( D != E
=> k20_scmfsa_2(A,E) = k20_scmfsa_2(B,E) ) )
& ! [E] :
( m2_scmfsa_2(E)
=> k21_scmfsa_2(A,E) = k21_scmfsa_2(B,E) )
& r2_scmfsa7b(C,D)
& r5_scmfsa7b(C,k1_scmfsa6c(A))
& r6_scmfsa7b(C,k1_scmfsa6c(A)) )
=> ( ! [E] :
( m1_scmfsa_2(E)
=> ( D != E
=> k20_scmfsa_2(k3_scmfsa6b(C,A),E) = k20_scmfsa_2(k3_scmfsa6b(C,B),E) ) )
& ! [E] :
( m2_scmfsa_2(E)
=> k21_scmfsa_2(k3_scmfsa6b(C,A),E) = k21_scmfsa_2(k3_scmfsa6b(C,B),E) )
& k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6b(C,A)) = k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6b(C,B)) ) ) ) ) ) ) ).
fof(t42_scmfsa8b,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)
& v2_scmfsa6b(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)
& v2_scmfsa6b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [D] :
( ( ~ v1_sf_mastr(D)
& m1_scmfsa_2(D) )
=> ! [E] :
( ( ~ v1_sf_mastr(E)
& m1_scmfsa_2(E) )
=> ( ( r2_scmfsa7b(B,D)
& r2_scmfsa7b(C,D) )
=> ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6b(k4_scmfsa8b(D,E,B,C),A)) = k5_scmfsa_2(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__5))
& ( k20_scmfsa_2(A,D) = k20_scmfsa_2(A,E)
=> ( ! [F] :
( m1_scmfsa_2(F)
=> ( D != F
=> k20_scmfsa_2(k3_scmfsa6b(k4_scmfsa8b(D,E,B,C),A),F) = k20_scmfsa_2(k3_scmfsa6b(B,A),F) ) )
& ! [F] :
( m2_scmfsa_2(F)
=> k21_scmfsa_2(k3_scmfsa6b(k4_scmfsa8b(D,E,B,C),A),F) = k21_scmfsa_2(k3_scmfsa6b(B,A),F) ) ) )
& ( k20_scmfsa_2(A,D) != k20_scmfsa_2(A,E)
=> ( ! [F] :
( m1_scmfsa_2(F)
=> ( D != F
=> k20_scmfsa_2(k3_scmfsa6b(k4_scmfsa8b(D,E,B,C),A),F) = k20_scmfsa_2(k3_scmfsa6b(C,A),F) ) )
& ! [F] :
( m2_scmfsa_2(F)
=> k21_scmfsa_2(k3_scmfsa6b(k4_scmfsa8b(D,E,B,C),A),F) = k21_scmfsa_2(k3_scmfsa6b(C,A),F) ) ) ) ) ) ) ) ) ) ) ).
fof(t43_scmfsa8b,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)
& v2_scmfsa6b(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)
& v2_scmfsa6b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [D] :
( ( ~ v1_sf_mastr(D)
& m1_scmfsa_2(D) )
=> ! [E] :
( ( ~ v1_sf_mastr(E)
& m1_scmfsa_2(E) )
=> ( ( r2_scmfsa7b(B,D)
& r2_scmfsa7b(C,D) )
=> ( k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6b(k5_scmfsa8b(D,E,B,C),A)) = k5_scmfsa_2(k1_nat_1(k1_nat_1(k4_card_1(B),k4_card_1(C)),np__5))
& ( ~ r1_xreal_0(k20_scmfsa_2(A,D),k20_scmfsa_2(A,E))
=> ( ! [F] :
( m1_scmfsa_2(F)
=> ( D != F
=> k20_scmfsa_2(k3_scmfsa6b(k5_scmfsa8b(D,E,B,C),A),F) = k20_scmfsa_2(k3_scmfsa6b(B,A),F) ) )
& ! [F] :
( m2_scmfsa_2(F)
=> k21_scmfsa_2(k3_scmfsa6b(k5_scmfsa8b(D,E,B,C),A),F) = k21_scmfsa_2(k3_scmfsa6b(B,A),F) ) ) )
& ( r1_xreal_0(k20_scmfsa_2(A,D),k20_scmfsa_2(A,E))
=> ( ! [F] :
( m1_scmfsa_2(F)
=> ( D != F
=> k20_scmfsa_2(k3_scmfsa6b(k5_scmfsa8b(D,E,B,C),A),F) = k20_scmfsa_2(k3_scmfsa6b(C,A),F) ) )
& ! [F] :
( m2_scmfsa_2(F)
=> k21_scmfsa_2(k3_scmfsa6b(k5_scmfsa8b(D,E,B,C),A),F) = k21_scmfsa_2(k3_scmfsa6b(C,A),F) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k1_scmfsa8b,axiom,
! [A,B,C] :
( ( m1_scmfsa_2(A)
& 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)
& 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) )
=> ( v1_ami_3(k1_scmfsa8b(A,B,C),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k1_scmfsa8b(A,B,C))
& m1_ami_1(k1_scmfsa8b(A,B,C),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ).
fof(dt_k2_scmfsa8b,axiom,
! [A,B,C] :
( ( m1_scmfsa_2(A)
& 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)
& 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) )
=> ( v1_ami_3(k2_scmfsa8b(A,B,C),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k2_scmfsa8b(A,B,C))
& m1_ami_1(k2_scmfsa8b(A,B,C),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ).
fof(dt_k3_scmfsa8b,axiom,
! [A,B,C] :
( ( m1_scmfsa_2(A)
& 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)
& 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) )
=> ( v1_ami_3(k3_scmfsa8b(A,B,C),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k3_scmfsa8b(A,B,C))
& m1_ami_1(k3_scmfsa8b(A,B,C),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ).
fof(dt_k4_scmfsa8b,axiom,
! [A,B,C,D] :
( ( 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)
& 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)
& m1_ami_1(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( v1_ami_3(k4_scmfsa8b(A,B,C,D),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k4_scmfsa8b(A,B,C,D))
& m1_ami_1(k4_scmfsa8b(A,B,C,D),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ).
fof(dt_k5_scmfsa8b,axiom,
! [A,B,C,D] :
( ( 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)
& 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)
& m1_ami_1(D,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( 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))
& m1_ami_1(k5_scmfsa8b(A,B,C,D),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ).
%------------------------------------------------------------------------------