SET007 Axioms: SET007+549.ax
%------------------------------------------------------------------------------
% File : SET007+549 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On the Composition of Non-parahalting Macro Instructions
% 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 : sfmastr1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 66 ( 0 unt; 0 def)
% Number of atoms : 471 ( 33 equ)
% Maximal formula atoms : 16 ( 7 avg)
% Number of connectives : 442 ( 37 ~; 13 |; 252 &)
% ( 3 <=>; 137 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 30 ( 29 usr; 0 prp; 1-3 aty)
% Number of functors : 82 ( 82 usr; 10 con; 0-4 aty)
% Number of variables : 161 ( 158 !; 3 ?)
% 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_sfmastr1,axiom,
! [A,B] :
( ( ~ v1_sf_mastr(A)
& m1_scmfsa_2(A)
& m1_scmfsa_2(B) )
=> ( v1_scmfsa6c(k8_scmfsa_2(A,B))
& v2_scmfsa6c(k8_scmfsa_2(A,B))
& v1_sfmastr1(k8_scmfsa_2(A,B)) ) ) ).
fof(fc2_sfmastr1,axiom,
! [A,B] :
( ( ~ v1_sf_mastr(A)
& m1_scmfsa_2(A)
& m1_scmfsa_2(B) )
=> ( v1_scmfsa6c(k9_scmfsa_2(A,B))
& v2_scmfsa6c(k9_scmfsa_2(A,B))
& v1_sfmastr1(k9_scmfsa_2(A,B)) ) ) ).
fof(fc3_sfmastr1,axiom,
! [A,B] :
( ( ~ v1_sf_mastr(A)
& m1_scmfsa_2(A)
& m1_scmfsa_2(B) )
=> ( v1_scmfsa6c(k10_scmfsa_2(A,B))
& v2_scmfsa6c(k10_scmfsa_2(A,B))
& v1_sfmastr1(k10_scmfsa_2(A,B)) ) ) ).
fof(fc4_sfmastr1,axiom,
! [A,B] :
( ( ~ v1_sf_mastr(A)
& m1_scmfsa_2(A)
& m1_scmfsa_2(B) )
=> ( v1_scmfsa6c(k11_scmfsa_2(A,B))
& v2_scmfsa6c(k11_scmfsa_2(A,B))
& v1_sfmastr1(k11_scmfsa_2(A,B)) ) ) ).
fof(rc1_sfmastr1,axiom,
? [A] :
( m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
& v1_scmfsa6c(A)
& v1_sfmastr1(A) ) ).
fof(fc5_sfmastr1,axiom,
! [A,B] :
( ( ~ v1_sf_mastr(A)
& m1_scmfsa_2(A)
& ~ v1_sf_mastr(B)
& m1_scmfsa_2(B) )
=> ( v1_scmfsa6c(k12_scmfsa_2(A,B))
& v2_scmfsa6c(k12_scmfsa_2(A,B))
& v1_sfmastr1(k12_scmfsa_2(A,B)) ) ) ).
fof(fc6_sfmastr1,axiom,
! [A] :
( m1_subset_1(A,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> v1_sfmastr1(k13_scmfsa_2(A)) ) ).
fof(fc7_sfmastr1,axiom,
! [A,B] :
( ( m1_scmfsa_2(A)
& m1_subset_1(B,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
=> v1_sfmastr1(k14_scmfsa_2(B,A)) ) ).
fof(fc8_sfmastr1,axiom,
! [A,B] :
( ( m1_scmfsa_2(A)
& m1_subset_1(B,u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
=> v1_sfmastr1(k15_scmfsa_2(B,A)) ) ).
fof(fc9_sfmastr1,axiom,
! [A,B,C] :
( ( m1_scmfsa_2(A)
& m2_scmfsa_2(B)
& ~ v1_sf_mastr(C)
& m1_scmfsa_2(C) )
=> ( v1_scmfsa6c(k16_scmfsa_2(C,A,B))
& v2_scmfsa6c(k16_scmfsa_2(C,A,B))
& v1_sfmastr1(k16_scmfsa_2(C,A,B)) ) ) ).
fof(fc10_sfmastr1,axiom,
! [A,B] :
( ( m2_scmfsa_2(A)
& ~ v1_sf_mastr(B)
& m1_scmfsa_2(B) )
=> ( v1_scmfsa6c(k18_scmfsa_2(B,A))
& v2_scmfsa6c(k18_scmfsa_2(B,A))
& v1_sfmastr1(k18_scmfsa_2(B,A)) ) ) ).
fof(fc11_sfmastr1,axiom,
! [A,B] :
( ( m2_scmfsa_2(A)
& m1_scmfsa_2(B) )
=> ( v1_scmfsa6c(k19_scmfsa_2(B,A))
& v2_scmfsa6c(k19_scmfsa_2(B,A))
& v1_sfmastr1(k19_scmfsa_2(B,A)) ) ) ).
fof(fc12_sfmastr1,axiom,
! [A,B,C] :
( ( m2_scmfsa_2(A)
& m1_scmfsa_2(B)
& m1_scmfsa_2(C) )
=> ( v1_scmfsa6c(k17_scmfsa_2(C,B,A))
& v2_scmfsa6c(k17_scmfsa_2(C,B,A))
& v1_sfmastr1(k17_scmfsa_2(C,B,A)) ) ) ).
fof(rc2_sfmastr1,axiom,
? [A] :
( m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
& v1_sfmastr1(A) ) ).
fof(fc13_sfmastr1,axiom,
! [A] :
( ( v1_sfmastr1(A)
& m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
=> ( v1_relat_1(k2_scmfsa6a(A))
& v1_funct_1(k2_scmfsa6a(A))
& v1_finset_1(k2_scmfsa6a(A))
& v1_ami_3(k2_scmfsa6a(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k2_scmfsa6a(A))
& v1_scmfsa7b(k2_scmfsa6a(A)) ) ) ).
fof(fc14_sfmastr1,axiom,
! [A,B] :
( ( v1_sfmastr1(A)
& m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
& v1_sfmastr1(B)
& m1_subset_1(B,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
=> ( v1_relat_1(k7_scmfsa6a(A,B))
& v1_funct_1(k7_scmfsa6a(A,B))
& v1_finset_1(k7_scmfsa6a(A,B))
& v1_ami_3(k7_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k7_scmfsa6a(A,B))
& v1_scmfsa7b(k7_scmfsa6a(A,B)) ) ) ).
fof(fc15_sfmastr1,axiom,
! [A,B] :
( ( v1_sfmastr1(A)
& m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
& v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(B)
& v1_scmfsa7b(B)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( v1_relat_1(k5_scmfsa6a(A,B))
& v1_funct_1(k5_scmfsa6a(A,B))
& v1_finset_1(k5_scmfsa6a(A,B))
& v1_ami_3(k5_scmfsa6a(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k5_scmfsa6a(A,B))
& v1_scmfsa7b(k5_scmfsa6a(A,B)) ) ) ).
fof(fc16_sfmastr1,axiom,
! [A,B] :
( ( v1_sfmastr1(A)
& m1_subset_1(A,u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
& v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(B)
& v1_scmfsa7b(B)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( v1_relat_1(k6_scmfsa6a(B,A))
& v1_funct_1(k6_scmfsa6a(B,A))
& v1_finset_1(k6_scmfsa6a(B,A))
& v1_ami_3(k6_scmfsa6a(B,A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k6_scmfsa6a(B,A))
& v1_scmfsa7b(k6_scmfsa6a(B,A)) ) ) ).
fof(fc17_sfmastr1,axiom,
! [A,B] :
( ( ~ v1_sf_mastr(A)
& m1_scmfsa_2(A)
& ~ v1_sf_mastr(B)
& m1_scmfsa_2(B) )
=> ( ~ v1_xboole_0(k2_scmfsa6c(A,B))
& v1_relat_1(k2_scmfsa6c(A,B))
& v1_funct_1(k2_scmfsa6c(A,B))
& v1_finset_1(k2_scmfsa6c(A,B))
& v1_ami_3(k2_scmfsa6c(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k2_scmfsa6c(A,B))
& v1_scmfsa6b(k2_scmfsa6c(A,B))
& v2_scmfsa6b(k2_scmfsa6c(A,B))
& v3_scmfsa6b(k2_scmfsa6c(A,B))
& v1_scmfsa7b(k2_scmfsa6c(A,B)) ) ) ).
fof(fc18_sfmastr1,axiom,
! [A,B] :
( ( v1_ami_3(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(A)
& v1_scmfsa7b(A)
& m1_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& ~ v1_sf_mastr(B)
& m1_scmfsa_2(B) )
=> ( v1_relat_1(k2_scmfsa8c(B,A))
& v1_funct_1(k2_scmfsa8c(B,A))
& v1_finset_1(k2_scmfsa8c(B,A))
& v1_ami_3(k2_scmfsa8c(B,A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k2_scmfsa8c(B,A))
& v1_scmfsa7b(k2_scmfsa8c(B,A)) ) ) ).
fof(fc19_sfmastr1,axiom,
! [A,B] :
( ( v1_finset_1(A)
& m1_subset_1(A,k1_zfmisc_1(k2_scmfsa_2))
& m1_subset_1(B,k5_numbers) )
=> ~ v1_xboole_0(k1_funct_1(k5_sfmastr1(A),B)) ) ).
fof(fc20_sfmastr1,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(k2_scmfsa_2)) )
=> ~ v1_sf_mastr(k6_sfmastr1(A,B)) ) ).
fof(fc21_sfmastr1,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ~ v1_sf_mastr(k7_sfmastr1(A,B)) ) ).
fof(d1_sfmastr1,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))
=> ( v1_sfmastr1(A)
<=> v1_scmfsa7b(k2_scmfsa6a(A)) ) ) ).
fof(t1_sfmastr1,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) )
=> ( ~ r2_hidden(A,k2_sf_mastr(B))
=> r4_scmfsa7b(B,A) ) ) ) ).
fof(t2_sfmastr1,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) )
=> k7_relat_1(k17_ami_1(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,k5_scmfsa_2(np__0))),k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2)) = k1_xboole_0 ) ).
fof(t3_sfmastr1,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) )
=> ( ( r6_scmfsa7b(B,k1_scmfsa6c(A))
& r5_scmfsa7b(B,k1_scmfsa6c(A))
& r5_scmfsa7b(C,k3_scmfsa6b(B,A)) )
=> r5_scmfsa7b(k4_scmfsa6a(B,C),k1_scmfsa6c(A)) ) ) ) ) ).
fof(t4_sfmastr1,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) )
=> ( ( r6_scmfsa7b(B,k1_scmfsa6c(A))
& r6_scmfsa7b(C,k3_scmfsa6b(B,A))
& r5_scmfsa7b(B,k1_scmfsa6c(A))
& r5_scmfsa7b(C,k3_scmfsa6b(B,A)) )
=> r6_scmfsa7b(k4_scmfsa6a(B,C),k1_scmfsa6c(A)) ) ) ) ) ).
fof(t5_sfmastr1,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,A)
& r1_tarski(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,k5_scmfsa_2(np__0))),A)
& v9_ami_1(A,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(D,k2_scm_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,A))
=> r1_funct_7(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),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,k4_scmfsa6a(B,C))),D),u2_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) ) ) ) ) ) ) ).
fof(t6_sfmastr1,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)
& v1_scmfsa7b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( ( r6_scmfsa7b(C,k1_scmfsa6c(A))
& r6_scmfsa7b(B,k3_scmfsa6b(C,A))
& r5_scmfsa7b(C,k1_scmfsa6c(A))
& r5_scmfsa7b(B,k3_scmfsa6b(C,A)) )
=> 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,k3_scmfsa6a(k4_scmfsa6a(C,B)))) = k1_nat_1(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,k3_scmfsa6a(C))),np__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,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(C))),k3_scmfsa6a(B)))) ) ) ) ) ).
fof(t7_sfmastr1,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)
& v1_scmfsa7b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( ( r6_scmfsa7b(C,k1_scmfsa6c(A))
& r6_scmfsa7b(B,k3_scmfsa6b(C,A))
& r5_scmfsa7b(C,k1_scmfsa6c(A))
& r5_scmfsa7b(B,k3_scmfsa6b(C,A)) )
=> k3_scmfsa6b(k4_scmfsa6a(C,B),A) = k8_ami_5(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6b(B,k3_scmfsa6b(C,A)),k12_ami_3(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_scmfsa_4(k6_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k3_scmfsa6b(B,k3_scmfsa6b(C,A))),k4_card_1(C)))) ) ) ) ) ).
fof(t8_sfmastr1,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)
& v1_scmfsa7b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [D] :
( m1_scmfsa_2(D)
=> ~ ( ( v2_scmfsa6b(C)
| ( r6_scmfsa7b(C,k1_scmfsa6c(A))
& r5_scmfsa7b(C,k1_scmfsa6c(A)) ) )
& ( v2_scmfsa6b(B)
| ( r6_scmfsa7b(B,k3_scmfsa6b(C,A))
& r5_scmfsa7b(B,k3_scmfsa6b(C,A)) ) )
& k20_scmfsa_2(k3_scmfsa6b(k4_scmfsa6a(C,B),A),D) != k20_scmfsa_2(k3_scmfsa6b(B,k3_scmfsa6b(C,A)),D) ) ) ) ) ) ).
fof(t9_sfmastr1,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)
& v1_scmfsa7b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [D] :
( m2_scmfsa_2(D)
=> ~ ( ( v2_scmfsa6b(C)
| ( r6_scmfsa7b(C,k1_scmfsa6c(A))
& r5_scmfsa7b(C,k1_scmfsa6c(A)) ) )
& ( v2_scmfsa6b(B)
| ( r6_scmfsa7b(B,k3_scmfsa6b(C,A))
& r5_scmfsa7b(B,k3_scmfsa6b(C,A)) ) )
& k21_scmfsa_2(k3_scmfsa6b(k4_scmfsa6a(C,B),A),D) != k21_scmfsa_2(k3_scmfsa6b(B,k3_scmfsa6b(C,A)),D) ) ) ) ) ) ).
fof(t10_sfmastr1,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)
& v1_scmfsa7b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ~ ( ( v2_scmfsa6b(C)
| ( r6_scmfsa7b(C,k1_scmfsa6c(A))
& r5_scmfsa7b(C,k1_scmfsa6c(A)) ) )
& ( v2_scmfsa6b(B)
| ( r6_scmfsa7b(B,k3_scmfsa6b(C,A))
& r5_scmfsa7b(B,k3_scmfsa6b(C,A)) ) )
& k7_relat_1(k3_scmfsa6b(k4_scmfsa6a(C,B),A),k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2)) != k7_relat_1(k3_scmfsa6b(B,k3_scmfsa6b(C,A)),k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ).
fof(t11_sfmastr1,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)
& v1_scmfsa7b(B)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( ( v2_scmfsa6b(B)
| ( r5_scmfsa7b(B,k1_scmfsa6c(A))
& r6_scmfsa7b(B,k1_scmfsa6c(A)) ) )
=> k7_relat_1(k1_scmfsa6c(k3_scmfsa6b(B,A)),k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k3_scmfsa6b(B,A),k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ).
fof(t12_sfmastr1,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)
& v1_scmfsa7b(B)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [C] :
( ( v1_scmfsa6c(C)
& m2_subset_1(C,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
=> ! [D] :
( m1_scmfsa_2(D)
=> ( ( v2_scmfsa6b(B)
| ( r6_scmfsa7b(B,k1_scmfsa6c(A))
& r5_scmfsa7b(B,k1_scmfsa6c(A)) ) )
=> k20_scmfsa_2(k3_scmfsa6b(k6_scmfsa6a(B,C),A),D) = k20_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k3_scmfsa6b(B,A)),D) ) ) ) ) ) ).
fof(t13_sfmastr1,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)
& v1_scmfsa7b(B)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [C] :
( ( v1_scmfsa6c(C)
& m2_subset_1(C,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
=> ! [D] :
( m2_scmfsa_2(D)
=> ( ( v2_scmfsa6b(B)
| ( r6_scmfsa7b(B,k1_scmfsa6c(A))
& r5_scmfsa7b(B,k1_scmfsa6c(A)) ) )
=> k21_scmfsa_2(k3_scmfsa6b(k6_scmfsa6a(B,C),A),D) = k21_scmfsa_2(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k3_scmfsa6b(B,A)),D) ) ) ) ) ) ).
fof(t14_sfmastr1,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)
& v1_scmfsa7b(B)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [C] :
( ( v1_scmfsa6c(C)
& m2_subset_1(C,k2_zfmisc_1(u3_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers))),u1_struct_0(k1_scmfsa_2)))),u4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)) )
=> ( ( v2_scmfsa6b(B)
| ( r6_scmfsa7b(B,k1_scmfsa6c(A))
& r5_scmfsa7b(B,k1_scmfsa6c(A)) ) )
=> k7_relat_1(k3_scmfsa6b(k6_scmfsa6a(B,C),A),k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k3_scmfsa6b(B,A)),k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ).
fof(t15_sfmastr1,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_scmfsa6c(C)
& v1_sfmastr1(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)
=> ( ( v2_scmfsa6b(B)
| ( r6_scmfsa7b(B,k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k1_scmfsa6c(A)))
& r5_scmfsa7b(B,k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k1_scmfsa6c(A))) ) )
=> k20_scmfsa_2(k3_scmfsa6b(k5_scmfsa6a(C,B),A),D) = k20_scmfsa_2(k3_scmfsa6b(B,k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k1_scmfsa6c(A))),D) ) ) ) ) ) ).
fof(t16_sfmastr1,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_scmfsa6c(C)
& v1_sfmastr1(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] :
( m2_scmfsa_2(D)
=> ( ( v2_scmfsa6b(B)
| ( r6_scmfsa7b(B,k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k1_scmfsa6c(A)))
& r5_scmfsa7b(B,k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k1_scmfsa6c(A))) ) )
=> k21_scmfsa_2(k3_scmfsa6b(k5_scmfsa6a(C,B),A),D) = k21_scmfsa_2(k3_scmfsa6b(B,k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k1_scmfsa6c(A))),D) ) ) ) ) ) ).
fof(t17_sfmastr1,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_scmfsa6c(C)
& v1_sfmastr1(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)) )
=> ( ( v2_scmfsa6b(B)
| ( r6_scmfsa7b(B,k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k1_scmfsa6c(A)))
& r5_scmfsa7b(B,k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k1_scmfsa6c(A))) ) )
=> k7_relat_1(k3_scmfsa6b(k5_scmfsa6a(C,B),A),k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2)) = k7_relat_1(k3_scmfsa6b(B,k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,C,k1_scmfsa6c(A))),k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ).
fof(t18_sfmastr1,axiom,
! [A] :
( ( v1_finset_1(A)
& m1_subset_1(A,k1_zfmisc_1(k2_scmfsa_2)) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ~ r2_hidden(np__0,k8_funct_2(k5_numbers,k1_zfmisc_1(k5_numbers),k5_sfmastr1(A),B))
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(C,k8_funct_2(k5_numbers,k1_zfmisc_1(k5_numbers),k5_sfmastr1(A),B))
& r2_hidden(k4_scmfsa_2(C),A) ) ) ) ) ) ).
fof(t19_sfmastr1,axiom,
! [A] :
( ( v1_finset_1(A)
& m1_subset_1(A,k1_zfmisc_1(k2_scmfsa_2)) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ r1_xreal_0(k10_cqc_sim1(k8_funct_2(k5_numbers,k1_zfmisc_1(k5_numbers),k5_sfmastr1(A),k1_nat_1(B,np__1))),k10_cqc_sim1(k8_funct_2(k5_numbers,k1_zfmisc_1(k5_numbers),k5_sfmastr1(A),B))) ) ) ).
fof(t20_sfmastr1,axiom,
! [A] :
( ( v1_finset_1(A)
& m1_subset_1(A,k1_zfmisc_1(k2_scmfsa_2)) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(C,B)
& r1_xreal_0(k10_cqc_sim1(k8_funct_2(k5_numbers,k1_zfmisc_1(k5_numbers),k5_sfmastr1(A),C)),k10_cqc_sim1(k8_funct_2(k5_numbers,k1_zfmisc_1(k5_numbers),k5_sfmastr1(A),B))) ) ) ) ) ).
fof(d3_sfmastr1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(k2_scmfsa_2)) )
=> k6_sfmastr1(A,B) = k4_scmfsa_2(k10_cqc_sim1(k8_funct_2(k5_numbers,k1_zfmisc_1(k5_numbers),k5_sfmastr1(B),A))) ) ) ).
fof(t21_sfmastr1,axiom,
! [A] :
( ( v1_finset_1(A)
& m1_subset_1(A,k1_zfmisc_1(k2_scmfsa_2)) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ r2_hidden(k6_sfmastr1(B,A),A) ) ) ).
fof(t22_sfmastr1,axiom,
! [A] :
( ( v1_finset_1(A)
& m1_subset_1(A,k1_zfmisc_1(k2_scmfsa_2)) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( B != C
& k6_sfmastr1(B,A) = k6_sfmastr1(C,A) ) ) ) ) ).
fof(d4_sfmastr1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> k7_sfmastr1(A,B) = k6_sfmastr1(A,k2_sf_mastr(B)) ) ) ).
fof(t23_sfmastr1,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> ( r2_hidden(A,k2_sf_mastr(k2_scmfsa6c(A,B)))
& r2_hidden(B,k2_sf_mastr(k2_scmfsa6c(A,B))) ) ) ) ).
fof(d5_sfmastr1,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> k8_sfmastr1(A,B) = k6_scmfsa6a(k4_scmfsa6a(k6_scmfsa6a(k6_scmfsa6a(k7_scmfsa6a(k8_scmfsa_2(k6_sfmastr1(np__2,k2_sf_mastr(k2_scmfsa6c(B,k6_sfmastr1(np__1,k2_sfmastr1(A,B))))),A),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__1,k2_sf_mastr(k2_scmfsa6c(B,k6_sfmastr1(np__1,k2_sfmastr1(A,B))))),k6_sfmastr1(np__2,k2_sf_mastr(k2_scmfsa6c(B,k6_sfmastr1(np__1,k2_sfmastr1(A,B))))))),k2_scmfsa8c(k6_sfmastr1(np__1,k2_sf_mastr(k2_scmfsa6c(B,k6_sfmastr1(np__1,k2_sfmastr1(A,B))))),k5_scmfsa6a(k9_scmfsa_2(B,k6_sfmastr1(np__1,k2_sfmastr1(A,B))),k2_scmfsa6c(B,k6_sfmastr1(np__1,k2_sfmastr1(A,B)))))),k8_scmfsa_2(A,k6_sfmastr1(np__2,k2_sf_mastr(k2_scmfsa6c(B,k6_sfmastr1(np__1,k2_sfmastr1(A,B))))))) ) ) ).
fof(t24_sfmastr1,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(k8_sfmastr1(B,C),A),C) = k3_pre_ff(D)
& k20_scmfsa_2(k3_scmfsa6b(k8_sfmastr1(B,C),A),B) = k20_scmfsa_2(A,B) ) ) ) ) ) ) ) ).
fof(dt_k1_sfmastr1,axiom,
! [A] :
( m1_scmfsa_2(A)
=> m1_subset_1(k1_sfmastr1(A),k1_zfmisc_1(k2_scmfsa_2)) ) ).
fof(redefinition_k1_sfmastr1,axiom,
! [A] :
( m1_scmfsa_2(A)
=> k1_sfmastr1(A) = k1_tarski(A) ) ).
fof(dt_k2_sfmastr1,axiom,
! [A,B] :
( ( m1_scmfsa_2(A)
& m1_scmfsa_2(B) )
=> m1_subset_1(k2_sfmastr1(A,B),k1_zfmisc_1(k2_scmfsa_2)) ) ).
fof(commutativity_k2_sfmastr1,axiom,
! [A,B] :
( ( m1_scmfsa_2(A)
& m1_scmfsa_2(B) )
=> k2_sfmastr1(A,B) = k2_sfmastr1(B,A) ) ).
fof(redefinition_k2_sfmastr1,axiom,
! [A,B] :
( ( m1_scmfsa_2(A)
& m1_scmfsa_2(B) )
=> k2_sfmastr1(A,B) = k2_tarski(A,B) ) ).
fof(dt_k3_sfmastr1,axiom,
! [A,B,C] :
( ( m1_scmfsa_2(A)
& m1_scmfsa_2(B)
& m1_scmfsa_2(C) )
=> m1_subset_1(k3_sfmastr1(A,B,C),k1_zfmisc_1(k2_scmfsa_2)) ) ).
fof(redefinition_k3_sfmastr1,axiom,
! [A,B,C] :
( ( m1_scmfsa_2(A)
& m1_scmfsa_2(B)
& m1_scmfsa_2(C) )
=> k3_sfmastr1(A,B,C) = k1_enumset1(A,B,C) ) ).
fof(dt_k4_sfmastr1,axiom,
! [A,B,C,D] :
( ( m1_scmfsa_2(A)
& m1_scmfsa_2(B)
& m1_scmfsa_2(C)
& m1_scmfsa_2(D) )
=> m1_subset_1(k4_sfmastr1(A,B,C,D),k1_zfmisc_1(k2_scmfsa_2)) ) ).
fof(redefinition_k4_sfmastr1,axiom,
! [A,B,C,D] :
( ( m1_scmfsa_2(A)
& m1_scmfsa_2(B)
& m1_scmfsa_2(C)
& m1_scmfsa_2(D) )
=> k4_sfmastr1(A,B,C,D) = k2_enumset1(A,B,C,D) ) ).
fof(dt_k5_sfmastr1,axiom,
! [A] :
( ( v1_finset_1(A)
& m1_subset_1(A,k1_zfmisc_1(k2_scmfsa_2)) )
=> ( v1_funct_1(k5_sfmastr1(A))
& v1_funct_2(k5_sfmastr1(A),k5_numbers,k1_zfmisc_1(k5_numbers))
& m2_relset_1(k5_sfmastr1(A),k5_numbers,k1_zfmisc_1(k5_numbers)) ) ) ).
fof(dt_k6_sfmastr1,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(k2_scmfsa_2)) )
=> m1_scmfsa_2(k6_sfmastr1(A,B)) ) ).
fof(dt_k7_sfmastr1,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> m1_scmfsa_2(k7_sfmastr1(A,B)) ) ).
fof(dt_k8_sfmastr1,axiom,
! [A,B] :
( ( m1_scmfsa_2(A)
& m1_scmfsa_2(B) )
=> ( v1_ami_3(k8_sfmastr1(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k8_sfmastr1(A,B))
& m1_ami_1(k8_sfmastr1(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ).
fof(d2_sfmastr1,axiom,
! [A] :
( ( v1_finset_1(A)
& m1_subset_1(A,k1_zfmisc_1(k2_scmfsa_2)) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_zfmisc_1(k5_numbers))
& m2_relset_1(B,k5_numbers,k1_zfmisc_1(k5_numbers)) )
=> ( B = k5_sfmastr1(A)
<=> ( k8_funct_2(k5_numbers,k1_zfmisc_1(k5_numbers),B,np__0) = a_1_0_sfmastr1(A)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(k5_numbers)) )
=> ( k8_funct_2(k5_numbers,k1_zfmisc_1(k5_numbers),B,C) = D
=> k8_funct_2(k5_numbers,k1_zfmisc_1(k5_numbers),B,k1_nat_1(C,np__1)) = k4_xboole_0(D,k15_cqc_sim1(k5_numbers,k10_cqc_sim1(D))) ) ) )
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ v1_finset_1(k8_funct_2(k5_numbers,k1_zfmisc_1(k5_numbers),B,C)) ) ) ) ) ) ).
fof(fraenkel_a_1_0_sfmastr1,axiom,
! [A,B] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(k2_scmfsa_2)) )
=> ( r2_hidden(A,a_1_0_sfmastr1(B))
<=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& A = C
& ~ r2_hidden(k4_scmfsa_2(C),B)
& C != np__0 ) ) ) ).
%------------------------------------------------------------------------------