SET007 Axioms: SET007+551.ax
%------------------------------------------------------------------------------
% File : SET007+551 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Another Times 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 : sfmastr2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 37 ( 0 unt; 0 def)
% Number of atoms : 313 ( 50 equ)
% Maximal formula atoms : 14 ( 8 avg)
% Number of connectives : 306 ( 30 ~; 10 |; 126 &)
% ( 4 <=>; 136 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 10 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 21 ( 20 usr; 0 prp; 1-3 aty)
% Number of functors : 50 ( 50 usr; 8 con; 0-4 aty)
% Number of variables : 111 ( 111 !; 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_sfmastr2,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)
& m1_scmfsa_2(B) )
=> ( v1_relat_1(k1_sfmastr2(B,A))
& v1_funct_1(k1_sfmastr2(B,A))
& v1_ami_3(k1_sfmastr2(B,A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k1_sfmastr2(B,A))
& v1_scmfsa7b(k1_sfmastr2(B,A)) ) ) ).
fof(t1_sfmastr2,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)) )
=> ( r2_hidden(B,k2_sf_mastr(C))
| k20_scmfsa_2(k3_scmfsa6b(C,A),B) = k20_scmfsa_2(k1_scmfsa6c(A),B) ) ) ) ) ) ).
fof(t2_sfmastr2,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
=> ! [B] :
( m2_scmfsa_2(B)
=> ! [C] :
( ( v1_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)) )
=> ( r2_hidden(B,k4_sf_mastr(C))
| k21_scmfsa_2(k3_scmfsa6b(C,A),B) = k21_scmfsa_2(k1_scmfsa6c(A),B) ) ) ) ) ) ).
fof(t3_sfmastr2,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)) )
| v2_scmfsa6b(C) )
& ~ ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) != np__1
& v1_sf_mastr(B) )
& ~ r2_hidden(B,k2_sf_mastr(C))
& k20_scmfsa_2(k3_scmfsa6b(C,A),B) != k20_scmfsa_2(A,B) ) ) ) ) ).
fof(t4_sfmastr2,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) )
=> ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
=> ( r5_scmfsa7b(B,A)
<=> r5_scmfsa7b(B,k1_scmfsa6c(A)) ) ) ) ) ).
fof(t5_sfmastr2,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) )
=> ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
=> ( ( ( r5_scmfsa7b(B,A)
& r6_scmfsa7b(B,A) )
=> ( r5_scmfsa7b(B,k1_scmfsa6c(A))
& r6_scmfsa7b(B,k1_scmfsa6c(A)) ) )
& ( ( r5_scmfsa7b(B,k1_scmfsa6c(A))
& r6_scmfsa7b(B,k1_scmfsa6c(A)) )
=> ( r5_scmfsa7b(B,A)
& r6_scmfsa7b(B,A) ) ) ) ) ) ) ).
fof(t6_sfmastr2,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] :
( m1_subset_1(C,k1_zfmisc_1(k2_scmfsa_2))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k3_scmfsa_2))
=> ( k7_relat_1(A,k2_xboole_0(C,D)) = k7_relat_1(B,k2_xboole_0(C,D))
<=> ( ! [E] :
( m1_scmfsa_2(E)
=> ( r2_hidden(E,C)
=> k20_scmfsa_2(A,E) = k20_scmfsa_2(B,E) ) )
& ! [E] :
( m2_scmfsa_2(E)
=> ( r2_hidden(E,D)
=> k21_scmfsa_2(A,E) = k21_scmfsa_2(B,E) ) ) ) ) ) ) ) ) ).
fof(t7_sfmastr2,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] :
( m1_subset_1(C,k1_zfmisc_1(k2_scmfsa_2))
=> ( k7_relat_1(A,k2_xboole_0(C,k3_scmfsa_2)) = k7_relat_1(B,k2_xboole_0(C,k3_scmfsa_2))
<=> ( ! [D] :
( m1_scmfsa_2(D)
=> ( r2_hidden(D,C)
=> k20_scmfsa_2(A,D) = k20_scmfsa_2(B,D) ) )
& ! [D] :
( m2_scmfsa_2(D)
=> k21_scmfsa_2(A,D) = k21_scmfsa_2(B,D) ) ) ) ) ) ) ).
fof(d1_sfmastr2,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) )
=> k1_sfmastr2(A,B) = k5_scmfsa6a(k8_scmfsa_2(k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(A),k2_sf_mastr(B))),A),k2_scmfsa_9(k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(A),k2_sf_mastr(B))),k6_scmfsa6a(B,k10_scmfsa_2(k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(A),k2_sf_mastr(B))),k4_scmfsa_2(np__0))))) ) ) ).
fof(t8_sfmastr2,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) )
=> r1_tarski(k4_subset_1(k2_scmfsa_2,k1_sfmastr1(A),k2_sf_mastr(B)),k2_sf_mastr(k1_sfmastr2(A,B))) ) ) ).
fof(t9_sfmastr2,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( ( v1_ami_3(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(B)
& m1_ami_1(B,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> k4_sf_mastr(k1_sfmastr2(A,B)) = k4_sf_mastr(B) ) ) ).
fof(d2_sfmastr2,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)
=> k2_sfmastr2(A,B,C) = k5_scmfsa_9(k4_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k8_scmfsa_2(k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(C),k2_sf_mastr(B))),C),k1_scmfsa6c(A)),k6_scmfsa6a(B,k10_scmfsa_2(k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(C),k2_sf_mastr(B))),k4_scmfsa_2(np__0))),k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(C),k2_sf_mastr(B)))) ) ) ) ).
fof(t10_sfmastr2,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)
& v1_scmfsa7b(C)
& m1_ami_1(C,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_sfmastr2(A,C,B),np__0),k4_scmfsa_2(np__0)) = np__1 ) ) ) ).
fof(t11_sfmastr2,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)
& v1_scmfsa7b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( ~ ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) != np__1
& v1_sf_mastr(B) )
=> k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),np__0),k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(B),k2_sf_mastr(C)))) = k20_scmfsa_2(A,B) ) ) ) ) ).
fof(t12_sfmastr2,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)
& v1_scmfsa7b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D),k4_scmfsa_2(np__0)) = np__1
& r5_scmfsa7b(C,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D))
& r6_scmfsa7b(C,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D)) )
=> ( k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),k1_nat_1(D,np__1)),k4_scmfsa_2(np__0)) = np__1
& ( ~ r1_xreal_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D),k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(B),k2_sf_mastr(C)))),np__0)
=> k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),k1_nat_1(D,np__1)),k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(B),k2_sf_mastr(C)))) = k6_xcmplx_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D),k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(B),k2_sf_mastr(C)))),np__1) ) ) ) ) ) ) ) ).
fof(t13_sfmastr2,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) )
=> ( ~ ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) != np__1
& v1_sf_mastr(B) )
=> k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),np__0),B) = k20_scmfsa_2(A,B) ) ) ) ) ).
fof(t14_sfmastr2,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] :
( m2_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) )
=> k21_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,D,B),np__0),C) = k21_scmfsa_2(A,C) ) ) ) ) ).
fof(d3_sfmastr2,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) )
=> ( r1_sfmastr2(A,B,C)
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(k20_scmfsa_2(A,B),D)
=> ( r5_scmfsa7b(C,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D))
& r6_scmfsa7b(C,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D)) ) ) ) ) ) ) ) ).
fof(t15_sfmastr2,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) )
=> ( v2_scmfsa6b(C)
=> r1_sfmastr2(A,B,C) ) ) ) ) ).
fof(t16_sfmastr2,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)
& v1_scmfsa7b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( r1_sfmastr2(A,B,C)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(D,k20_scmfsa_2(A,B))
=> k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D),k4_scmfsa_2(np__0)) = np__1 ) ) ) ) ) ) ).
fof(t17_sfmastr2,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)
& v1_scmfsa7b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( r1_sfmastr2(A,B,C)
=> ( ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) != np__1
& v1_sf_mastr(B) )
| ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(D,k20_scmfsa_2(A,B))
=> k2_xcmplx_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D),k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(B),k2_sf_mastr(C)))),D) = k20_scmfsa_2(A,B) ) ) ) ) ) ) ) ).
fof(t18_sfmastr2,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)
& v1_scmfsa7b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( ( r1_sfmastr2(A,B,C)
& r1_xreal_0(np__0,k20_scmfsa_2(A,B)) )
=> ( ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) != np__1
& v1_sf_mastr(B) )
| ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(k20_scmfsa_2(A,B),D)
=> ( k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D),k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(B),k2_sf_mastr(C)))) = np__0
& k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D),k4_scmfsa_2(np__0)) = np__1 ) ) ) ) ) ) ) ) ).
fof(t19_sfmastr2,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) )
=> ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
=> k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),np__0),k2_xboole_0(k2_sf_mastr(C),k3_scmfsa_2)) = k7_relat_1(A,k2_xboole_0(k2_sf_mastr(C),k3_scmfsa_2)) ) ) ) ) ).
fof(t20_sfmastr2,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)
& v1_scmfsa7b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D),k4_scmfsa_2(np__0)) = np__1
& r6_scmfsa7b(C,k1_scmfsa6c(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D)))
& r5_scmfsa7b(C,k1_scmfsa6c(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D))) )
=> ( r1_xreal_0(k20_scmfsa_2(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D),k6_sfmastr1(np__1,k4_subset_1(k2_scmfsa_2,k1_sfmastr1(B),k2_sf_mastr(C)))),np__0)
| k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),k1_nat_1(D,np__1)),k2_xboole_0(k2_sf_mastr(C),k3_scmfsa_2)) = k7_relat_1(k3_scmfsa6b(C,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D)),k2_xboole_0(k2_sf_mastr(C),k3_scmfsa_2)) ) ) ) ) ) ) ).
fof(t21_sfmastr2,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)
& v1_scmfsa7b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( ( r1_sfmastr2(A,B,C)
| v2_scmfsa6b(C) )
& ~ r1_xreal_0(k20_scmfsa_2(A,B),D)
& ~ ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) != np__1
& v1_sf_mastr(B) )
& k7_relat_1(k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),k1_nat_1(D,np__1)),k2_xboole_0(k2_sf_mastr(C),k3_scmfsa_2)) != k7_relat_1(k3_scmfsa6b(C,k11_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2,k2_sfmastr2(A,C,B),D)),k2_xboole_0(k2_sf_mastr(C),k3_scmfsa_2)) ) ) ) ) ) ).
fof(t22_sfmastr2,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) )
=> ( ( r1_xreal_0(k20_scmfsa_2(A,B),np__0)
& k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1 )
=> k7_relat_1(k3_scmfsa6b(k1_sfmastr2(B,C),A),k2_xboole_0(k2_sf_mastr(C),k3_scmfsa_2)) = k7_relat_1(A,k2_xboole_0(k2_sf_mastr(C),k3_scmfsa_2)) ) ) ) ) ).
fof(t23_sfmastr2,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)
& v1_scmfsa7b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( k20_scmfsa_2(A,B) = D
=> ( ( ~ r1_sfmastr2(A,B,C)
& ~ v2_scmfsa6b(C) )
| ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) != np__1
& v1_sf_mastr(B) )
| k7_relat_1(k3_scmfsa6b(k1_sfmastr2(B,C),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_sfmastr2(A,C,B),D),k4_subset_1(u1_struct_0(k1_scmfsa_2),k2_scmfsa_2,k3_scmfsa_2)) ) ) ) ) ) ) ).
fof(t24_sfmastr2,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)
& v1_scmfsa7b(C)
& m1_ami_1(C,k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) )
=> ( k20_scmfsa_2(A,k4_scmfsa_2(np__0)) = np__1
=> ( ( ~ r1_sfmastr2(A,B,C)
& ~ v2_scmfsa6b(C) )
| ( r5_scmfsa7b(k1_sfmastr2(B,C),A)
& r6_scmfsa7b(k1_sfmastr2(B,C),A) ) ) ) ) ) ) ).
fof(d4_sfmastr2,axiom,
! [A] :
( ( ~ v1_sf_mastr(A)
& m1_scmfsa_2(A) )
=> k3_sfmastr2(A) = k1_sfmastr2(A,k6_scmfsa6a(k1_scmfsa_9(A,k2_scmfsa6a(k8_scmfsa_2(A,A))),k10_scmfsa_2(A,k4_scmfsa_2(np__0)))) ) ).
fof(t25_sfmastr2,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) )
=> ( r1_xreal_0(k20_scmfsa_2(A,B),np__0)
=> k20_scmfsa_2(k3_scmfsa6b(k3_sfmastr2(B),A),B) = k20_scmfsa_2(A,B) ) ) ) ).
fof(t26_sfmastr2,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) )
=> ( r1_xreal_0(np__0,k20_scmfsa_2(A,B))
=> k20_scmfsa_2(k3_scmfsa6b(k3_sfmastr2(B),A),B) = np__0 ) ) ) ).
fof(d5_sfmastr2,axiom,
! [A] :
( m1_scmfsa_2(A)
=> ! [B] :
( m1_scmfsa_2(B)
=> k4_sfmastr2(A,B) = k6_scmfsa6a(k4_scmfsa6a(k6_scmfsa6a(k7_scmfsa6a(k8_scmfsa_2(k7_sfmastr1(np__1,k1_sfmastr2(A,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)))))),A),k10_scmfsa_2(B,B)),k8_scmfsa_2(k6_sfmastr1(np__1,k2_sfmastr1(A,B)),k4_scmfsa_2(np__0))),k1_sfmastr2(A,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,k7_sfmastr1(np__1,k1_sfmastr2(A,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)))))))) ) ) ).
fof(t27_sfmastr2,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(k4_sfmastr2(B,C),A),C) = k3_pre_ff(D)
& k20_scmfsa_2(k3_scmfsa6b(k4_sfmastr2(B,C),A),B) = k20_scmfsa_2(A,B) ) ) ) ) ) ) ) ).
fof(dt_k1_sfmastr2,axiom,
! [A,B] :
( ( 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(k1_sfmastr2(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k1_sfmastr2(A,B))
& m1_ami_1(k1_sfmastr2(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ).
fof(dt_k2_sfmastr2,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
& v1_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)
& m1_scmfsa_2(C) )
=> ( v1_funct_1(k2_sfmastr2(A,B,C))
& v1_funct_2(k2_sfmastr2(A,B,C),k5_numbers,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)))
& m2_relset_1(k2_sfmastr2(A,B,C),k5_numbers,k4_card_3(u5_ami_1(k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2))) ) ) ).
fof(dt_k3_sfmastr2,axiom,
! [A] :
( ( ~ v1_sf_mastr(A)
& m1_scmfsa_2(A) )
=> ( v1_ami_3(k3_sfmastr2(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k3_sfmastr2(A))
& m1_ami_1(k3_sfmastr2(A),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ).
fof(dt_k4_sfmastr2,axiom,
! [A,B] :
( ( m1_scmfsa_2(A)
& m1_scmfsa_2(B) )
=> ( v1_ami_3(k4_sfmastr2(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2)
& v1_scmfsa_4(k4_sfmastr2(A,B))
& m1_ami_1(k4_sfmastr2(A,B),k2_tarski(k4_numbers,k3_finseq_2(k4_numbers)),k1_scmfsa_2) ) ) ).
%------------------------------------------------------------------------------