SET007 Axioms: SET007+450.ax
%------------------------------------------------------------------------------
% File : SET007+450 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : An Extension of SCM
% 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 : scmfsa_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 78 ( 18 unt; 0 def)
% Number of atoms : 311 ( 97 equ)
% Maximal formula atoms : 41 ( 3 avg)
% Number of connectives : 251 ( 18 ~; 0 |; 94 &)
% ( 15 <=>; 124 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 69 ( 69 usr; 23 con; 0-6 aty)
% Number of variables : 166 ( 119 !; 47 ?)
% 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_scmfsa_1,axiom,
~ v1_xboole_0(k2_scmfsa_1) ).
fof(fc2_scmfsa_1,axiom,
~ v1_xboole_0(k1_scmfsa_1) ).
fof(fc3_scmfsa_1,axiom,
~ v1_xboole_0(k3_scmfsa_1) ).
fof(fc4_scmfsa_1,axiom,
( ~ v1_xboole_0(k4_scmfsa_1)
& v1_relat_1(k4_scmfsa_1) ) ).
fof(d1_scmfsa_1,axiom,
k1_scmfsa_1 = k2_ami_2 ).
fof(d2_scmfsa_1,axiom,
k2_scmfsa_1 = k4_xboole_0(k4_numbers,k5_numbers) ).
fof(d3_scmfsa_1,axiom,
k3_scmfsa_1 = k3_ami_2 ).
fof(t1_scmfsa_1,axiom,
$true ).
fof(t2_scmfsa_1,axiom,
r1_tarski(k4_ami_2,k4_scmfsa_1) ).
fof(d5_scmfsa_1,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(k1_gr_cy_1(np__13),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k13_finseq_1(k4_numbers))),k4_numbers))),k4_scmfsa_1)
=> k5_scmfsa_1(A) = k1_mcart_1(A) ) ).
fof(t3_scmfsa_1,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(k1_gr_cy_1(np__13),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k13_finseq_1(k4_numbers))),k4_numbers))),k4_scmfsa_1)
=> ( r1_xreal_0(k5_scmfsa_1(A),np__8)
=> r2_hidden(A,k4_ami_2) ) ) ).
fof(t4_scmfsa_1,axiom,
r2_hidden(k4_tarski(np__0,k1_xboole_0),k4_scmfsa_1) ).
fof(d6_scmfsa_1,axiom,
k6_scmfsa_1 = k1_funct_4(k1_funct_4(k10_pboole(k4_numbers,k13_finseq_1(k4_numbers)),k5_ami_2),k5_relat_1(k7_relat_1(k5_ami_2,k3_ami_2),k3_cqc_lang(k4_ami_2,k4_scmfsa_1))) ).
fof(t5_scmfsa_1,axiom,
$true ).
fof(t6_scmfsa_1,axiom,
! [A,B] :
( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
=> ! [C] :
( m2_subset_1(C,k4_numbers,k1_scmfsa_1)
=> ! [D] :
( m2_subset_1(D,k4_numbers,k2_scmfsa_1)
=> ( r2_hidden(A,k2_tarski(np__9,np__10))
=> r2_hidden(k4_tarski(A,k3_finseq_4(k4_numbers,B,D,C)),k4_scmfsa_1) ) ) ) ) ).
fof(t7_scmfsa_1,axiom,
! [A,B] :
( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
=> ! [C] :
( m2_subset_1(C,k4_numbers,k2_scmfsa_1)
=> ( r2_hidden(A,k2_tarski(np__11,np__12))
=> r2_hidden(k4_tarski(A,k2_finseq_4(k4_numbers,B,C)),k4_scmfsa_1) ) ) ) ).
fof(t8_scmfsa_1,axiom,
k4_numbers = k2_xboole_0(k2_xboole_0(k2_xboole_0(k1_tarski(np__0),k1_scmfsa_1),k2_scmfsa_1),k3_scmfsa_1) ).
fof(t9_scmfsa_1,axiom,
k1_funct_1(k6_scmfsa_1,np__0) = k3_scmfsa_1 ).
fof(t10_scmfsa_1,axiom,
! [A] :
( m2_subset_1(A,k4_numbers,k1_scmfsa_1)
=> k8_funct_2(k4_numbers,k2_xboole_0(k2_tarski(k4_numbers,k13_finseq_1(k4_numbers)),k2_tarski(k4_scmfsa_1,k3_scmfsa_1)),k6_scmfsa_1,A) = k4_numbers ) ).
fof(t11_scmfsa_1,axiom,
! [A] :
( m2_subset_1(A,k4_numbers,k3_scmfsa_1)
=> k8_funct_2(k4_numbers,k2_xboole_0(k2_tarski(k4_numbers,k13_finseq_1(k4_numbers)),k2_tarski(k4_scmfsa_1,k3_scmfsa_1)),k6_scmfsa_1,A) = k4_scmfsa_1 ) ).
fof(t12_scmfsa_1,axiom,
! [A] :
( m2_subset_1(A,k4_numbers,k2_scmfsa_1)
=> k8_funct_2(k4_numbers,k2_xboole_0(k2_tarski(k4_numbers,k13_finseq_1(k4_numbers)),k2_tarski(k4_scmfsa_1,k3_scmfsa_1)),k6_scmfsa_1,A) = k13_finseq_1(k4_numbers) ) ).
fof(t13_scmfsa_1,axiom,
( k3_scmfsa_1 != k4_numbers
& k4_scmfsa_1 != k4_numbers
& k3_scmfsa_1 != k4_scmfsa_1
& k3_scmfsa_1 != k13_finseq_1(k4_numbers)
& k4_scmfsa_1 != k13_finseq_1(k4_numbers) ) ).
fof(t14_scmfsa_1,axiom,
! [A] :
( v1_int_1(A)
=> ( k1_funct_1(k6_scmfsa_1,A) = k3_scmfsa_1
=> A = np__0 ) ) ).
fof(t15_scmfsa_1,axiom,
! [A] :
( v1_int_1(A)
=> ( k1_funct_1(k6_scmfsa_1,A) = k4_numbers
=> r2_hidden(A,k1_scmfsa_1) ) ) ).
fof(t16_scmfsa_1,axiom,
! [A] :
( v1_int_1(A)
=> ( k1_funct_1(k6_scmfsa_1,A) = k4_scmfsa_1
=> r2_hidden(A,k3_scmfsa_1) ) ) ).
fof(t17_scmfsa_1,axiom,
! [A] :
( v1_int_1(A)
=> ( k1_funct_1(k6_scmfsa_1,A) = k13_finseq_1(k4_numbers)
=> r2_hidden(A,k2_scmfsa_1) ) ) ).
fof(t18_scmfsa_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(k1_gr_cy_1(np__9),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers))),k4_ami_2)
=> m1_subset_1(k1_funct_4(k7_relat_1(A,k5_numbers),k3_finsop_1(k4_ami_2,k3_ami_2,B)),k4_card_3(k5_ami_2)) ) ) ).
fof(t19_scmfsa_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
=> ! [B] :
( m1_subset_1(B,k4_card_3(k5_ami_2))
=> m1_subset_1(k1_funct_4(k1_funct_4(A,B),k7_relat_1(A,k3_scmfsa_1)),k4_card_3(k6_scmfsa_1)) ) ) ).
fof(d7_scmfsa_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
=> ! [B] :
( m2_subset_1(B,k4_numbers,k3_scmfsa_1)
=> k7_scmfsa_1(A,B) = k1_funct_4(A,k3_cqc_lang(np__0,B)) ) ) ).
fof(d8_scmfsa_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
=> ! [B] :
( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
=> ! [C] :
( v1_int_1(C)
=> k8_scmfsa_1(A,B,C) = k1_funct_4(A,k3_cqc_lang(B,C)) ) ) ) ).
fof(d9_scmfsa_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
=> ! [B] :
( m2_subset_1(B,k4_numbers,k2_scmfsa_1)
=> ! [C] :
( m2_finseq_1(C,k4_numbers)
=> k9_scmfsa_1(A,B,C) = k1_funct_4(A,k3_cqc_lang(B,C)) ) ) ) ).
fof(d10_scmfsa_1,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(k1_gr_cy_1(np__13),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k13_finseq_1(k4_numbers))),k4_numbers))),k4_scmfsa_1)
=> ( ? [B] :
( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
& ? [C] :
( m2_subset_1(C,k4_numbers,k2_scmfsa_1)
& ? [D] :
( m2_subset_1(D,k4_numbers,k1_scmfsa_1)
& ? [E] :
( m2_subset_1(E,k5_numbers,k1_gr_cy_1(np__13))
& A = k4_tarski(E,k3_finseq_4(k4_numbers,B,C,D)) ) ) ) )
=> ! [B] :
( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
=> ( B = k12_scmfsa_1(A)
<=> ? [C] :
( m2_subset_1(C,k4_numbers,k1_scmfsa_1)
& ? [D] :
( m2_subset_1(D,k4_numbers,k2_scmfsa_1)
& ? [E] :
( m2_subset_1(E,k4_numbers,k1_scmfsa_1)
& k3_finseq_4(k4_numbers,C,D,E) = k2_mcart_1(A)
& B = C ) ) ) ) ) ) ) ).
fof(d11_scmfsa_1,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(k1_gr_cy_1(np__13),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k13_finseq_1(k4_numbers))),k4_numbers))),k4_scmfsa_1)
=> ( ? [B] :
( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
& ? [C] :
( m2_subset_1(C,k4_numbers,k2_scmfsa_1)
& ? [D] :
( m2_subset_1(D,k4_numbers,k1_scmfsa_1)
& ? [E] :
( m2_subset_1(E,k5_numbers,k1_gr_cy_1(np__13))
& A = k4_tarski(E,k3_finseq_4(k4_numbers,B,C,D)) ) ) ) )
=> ! [B] :
( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
=> ( B = k13_scmfsa_1(A)
<=> ? [C] :
( m2_subset_1(C,k4_numbers,k1_scmfsa_1)
& ? [D] :
( m2_subset_1(D,k4_numbers,k2_scmfsa_1)
& ? [E] :
( m2_subset_1(E,k4_numbers,k1_scmfsa_1)
& k3_finseq_4(k4_numbers,C,D,E) = k2_mcart_1(A)
& B = E ) ) ) ) ) ) ) ).
fof(d12_scmfsa_1,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(k1_gr_cy_1(np__13),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k13_finseq_1(k4_numbers))),k4_numbers))),k4_scmfsa_1)
=> ( ? [B] :
( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
& ? [C] :
( m2_subset_1(C,k4_numbers,k2_scmfsa_1)
& ? [D] :
( m2_subset_1(D,k4_numbers,k1_scmfsa_1)
& ? [E] :
( m2_subset_1(E,k5_numbers,k1_gr_cy_1(np__13))
& A = k4_tarski(E,k3_finseq_4(k4_numbers,B,C,D)) ) ) ) )
=> ! [B] :
( m2_subset_1(B,k4_numbers,k2_scmfsa_1)
=> ( B = k14_scmfsa_1(A)
<=> ? [C] :
( m2_subset_1(C,k4_numbers,k1_scmfsa_1)
& ? [D] :
( m2_subset_1(D,k4_numbers,k2_scmfsa_1)
& ? [E] :
( m2_subset_1(E,k4_numbers,k1_scmfsa_1)
& k3_finseq_4(k4_numbers,C,D,E) = k2_mcart_1(A)
& B = D ) ) ) ) ) ) ) ).
fof(d13_scmfsa_1,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(k1_gr_cy_1(np__13),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k13_finseq_1(k4_numbers))),k4_numbers))),k4_scmfsa_1)
=> ( ? [B] :
( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
& ? [C] :
( m2_subset_1(C,k4_numbers,k2_scmfsa_1)
& ? [D] :
( m2_subset_1(D,k5_numbers,k1_gr_cy_1(np__13))
& A = k4_tarski(D,k2_finseq_4(k4_numbers,B,C)) ) ) )
=> ! [B] :
( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
=> ( B = k15_scmfsa_1(A)
<=> ? [C] :
( m2_subset_1(C,k4_numbers,k1_scmfsa_1)
& ? [D] :
( m2_subset_1(D,k4_numbers,k2_scmfsa_1)
& k2_finseq_4(k4_numbers,C,D) = k2_mcart_1(A)
& B = C ) ) ) ) ) ) ).
fof(d14_scmfsa_1,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(k1_gr_cy_1(np__13),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k13_finseq_1(k4_numbers))),k4_numbers))),k4_scmfsa_1)
=> ( ? [B] :
( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
& ? [C] :
( m2_subset_1(C,k4_numbers,k2_scmfsa_1)
& ? [D] :
( m2_subset_1(D,k5_numbers,k1_gr_cy_1(np__13))
& A = k4_tarski(D,k2_finseq_4(k4_numbers,B,C)) ) ) )
=> ! [B] :
( m2_subset_1(B,k4_numbers,k2_scmfsa_1)
=> ( B = k16_scmfsa_1(A)
<=> ? [C] :
( m2_subset_1(C,k4_numbers,k1_scmfsa_1)
& ? [D] :
( m2_subset_1(D,k4_numbers,k2_scmfsa_1)
& k2_finseq_4(k4_numbers,C,D) = k2_mcart_1(A)
& B = D ) ) ) ) ) ) ).
fof(d15_scmfsa_1,axiom,
! [A] :
( m2_subset_1(A,k4_numbers,k3_scmfsa_1)
=> ! [B] :
( m2_subset_1(B,k4_numbers,k3_scmfsa_1)
=> ( B = k17_scmfsa_1(A)
<=> ? [C] :
( m2_subset_1(C,k5_numbers,k3_ami_2)
& C = A
& B = k15_ami_2(C) ) ) ) ) ).
fof(d16_scmfsa_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
=> k18_scmfsa_1(A) = k1_funct_1(A,np__0) ) ).
fof(d17_scmfsa_1,axiom,
! [A] :
( m2_subset_1(A,k2_zfmisc_1(k1_gr_cy_1(np__13),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k13_finseq_1(k4_numbers))),k4_numbers))),k4_scmfsa_1)
=> ! [B] :
( m1_subset_1(B,k4_card_3(k6_scmfsa_1))
=> ! [C] :
( m1_subset_1(C,k4_card_3(k6_scmfsa_1))
=> ( ( r1_xreal_0(k5_scmfsa_1(A),np__8)
=> ( C = k19_scmfsa_1(A,B)
<=> ? [D] :
( m2_subset_1(D,k2_zfmisc_1(k1_gr_cy_1(np__9),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers))),k4_ami_2)
& ? [E] :
( m1_subset_1(E,k4_card_3(k5_ami_2))
& A = D
& E = k1_funct_4(k7_relat_1(B,k5_numbers),k3_finsop_1(k4_ami_2,k3_ami_2,D))
& C = k1_funct_4(k1_funct_4(B,k16_ami_2(D,E)),k7_relat_1(B,k3_scmfsa_1)) ) ) ) )
& ( k5_scmfsa_1(A) = np__9
=> ( C = k19_scmfsa_1(A,B)
<=> ? [D] :
( v1_int_1(D)
& ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& E = k1_int_2(k10_scmfsa_1(B,k13_scmfsa_1(A)))
& D = k4_finseq_4(k5_numbers,k4_numbers,k11_scmfsa_1(B,k14_scmfsa_1(A)),E)
& C = k7_scmfsa_1(k8_scmfsa_1(B,k12_scmfsa_1(A),D),k17_scmfsa_1(k18_scmfsa_1(B))) ) ) ) )
& ( k5_scmfsa_1(A) = np__10
=> ( C = k19_scmfsa_1(A,B)
<=> ? [D] :
( m2_finseq_1(D,k4_numbers)
& ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& E = k1_int_2(k10_scmfsa_1(B,k13_scmfsa_1(A)))
& D = k2_funct_7(k11_scmfsa_1(B,k14_scmfsa_1(A)),E,k10_scmfsa_1(B,k12_scmfsa_1(A)))
& C = k7_scmfsa_1(k9_scmfsa_1(B,k14_scmfsa_1(A),D),k17_scmfsa_1(k18_scmfsa_1(B))) ) ) ) )
& ( k5_scmfsa_1(A) = np__11
=> ( C = k19_scmfsa_1(A,B)
<=> C = k7_scmfsa_1(k8_scmfsa_1(B,k15_scmfsa_1(A),k3_finseq_1(k11_scmfsa_1(B,k16_scmfsa_1(A)))),k17_scmfsa_1(k18_scmfsa_1(B))) ) )
& ( k5_scmfsa_1(A) = np__12
=> ( C = k19_scmfsa_1(A,B)
<=> ? [D] :
( m2_finseq_1(D,k4_numbers)
& ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& E = k1_int_2(k10_scmfsa_1(B,k15_scmfsa_1(A)))
& D = k1_finsop_1(k5_numbers,E,np__0)
& C = k7_scmfsa_1(k9_scmfsa_1(B,k16_scmfsa_1(A),D),k17_scmfsa_1(k18_scmfsa_1(B))) ) ) ) )
& ~ ( ~ r1_xreal_0(k5_scmfsa_1(A),np__8)
& k5_scmfsa_1(A) != np__9
& k5_scmfsa_1(A) != np__10
& k5_scmfsa_1(A) != np__11
& k5_scmfsa_1(A) != np__12
& ~ ( C = k19_scmfsa_1(A,B)
<=> C = B ) ) ) ) ) ) ).
fof(d18_scmfsa_1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k4_scmfsa_1,k1_fraenkel(k4_card_3(k6_scmfsa_1),k4_card_3(k6_scmfsa_1)))
& m2_relset_1(A,k4_scmfsa_1,k1_fraenkel(k4_card_3(k6_scmfsa_1),k4_card_3(k6_scmfsa_1))) )
=> ( A = k20_scmfsa_1
<=> ! [B] :
( m2_subset_1(B,k2_zfmisc_1(k1_gr_cy_1(np__13),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k13_finseq_1(k4_numbers))),k4_numbers))),k4_scmfsa_1)
=> ! [C] :
( m1_subset_1(C,k4_card_3(k6_scmfsa_1))
=> k8_funct_2(k4_card_3(k6_scmfsa_1),k4_card_3(k6_scmfsa_1),k1_cat_2(k4_scmfsa_1,k4_card_3(k6_scmfsa_1),k4_card_3(k6_scmfsa_1),k1_fraenkel(k4_card_3(k6_scmfsa_1),k4_card_3(k6_scmfsa_1)),A,B),C) = k19_scmfsa_1(B,C) ) ) ) ) ).
fof(t20_scmfsa_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
=> ! [B] :
( m2_subset_1(B,k4_numbers,k3_scmfsa_1)
=> k1_funct_1(k7_scmfsa_1(A,B),np__0) = B ) ) ).
fof(t21_scmfsa_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
=> ! [B] :
( m2_subset_1(B,k4_numbers,k3_scmfsa_1)
=> ! [C] :
( m2_subset_1(C,k4_numbers,k1_scmfsa_1)
=> k10_scmfsa_1(k7_scmfsa_1(A,B),C) = k10_scmfsa_1(A,C) ) ) ) ).
fof(t22_scmfsa_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
=> ! [B] :
( m2_subset_1(B,k4_numbers,k3_scmfsa_1)
=> ! [C] :
( m2_subset_1(C,k4_numbers,k2_scmfsa_1)
=> k11_scmfsa_1(k7_scmfsa_1(A,B),C) = k11_scmfsa_1(A,C) ) ) ) ).
fof(t23_scmfsa_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
=> ! [B] :
( m2_subset_1(B,k4_numbers,k3_scmfsa_1)
=> ! [C] :
( m2_subset_1(C,k4_numbers,k3_scmfsa_1)
=> k1_funct_1(k7_scmfsa_1(A,B),C) = k1_funct_1(A,C) ) ) ) ).
fof(t24_scmfsa_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
=> ! [B] :
( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
=> ! [C] :
( v1_int_1(C)
=> k1_funct_1(k8_scmfsa_1(A,B,C),np__0) = k1_funct_1(A,np__0) ) ) ) ).
fof(t25_scmfsa_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
=> ! [B] :
( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
=> ! [C] :
( v1_int_1(C)
=> k10_scmfsa_1(k8_scmfsa_1(A,B,C),B) = C ) ) ) ).
fof(t26_scmfsa_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
=> ! [B] :
( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( m2_subset_1(D,k4_numbers,k1_scmfsa_1)
=> ( D != B
=> k10_scmfsa_1(k8_scmfsa_1(A,B,C),D) = k10_scmfsa_1(A,D) ) ) ) ) ) ).
fof(t27_scmfsa_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
=> ! [B] :
( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( m2_subset_1(D,k4_numbers,k2_scmfsa_1)
=> k11_scmfsa_1(k8_scmfsa_1(A,B,C),D) = k11_scmfsa_1(A,D) ) ) ) ) ).
fof(t28_scmfsa_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
=> ! [B] :
( m2_subset_1(B,k4_numbers,k1_scmfsa_1)
=> ! [C] :
( v1_int_1(C)
=> ! [D] :
( m2_subset_1(D,k4_numbers,k3_scmfsa_1)
=> k1_funct_1(k8_scmfsa_1(A,B,C),D) = k1_funct_1(A,D) ) ) ) ) ).
fof(t29_scmfsa_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
=> ! [B] :
( m2_subset_1(B,k4_numbers,k2_scmfsa_1)
=> ! [C] :
( m2_finseq_1(C,k4_numbers)
=> k11_scmfsa_1(k9_scmfsa_1(A,B,C),B) = C ) ) ) ).
fof(t30_scmfsa_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
=> ! [B] :
( m2_subset_1(B,k4_numbers,k2_scmfsa_1)
=> ! [C] :
( m2_finseq_1(C,k4_numbers)
=> ! [D] :
( m2_subset_1(D,k4_numbers,k2_scmfsa_1)
=> ( D != B
=> k11_scmfsa_1(k9_scmfsa_1(A,B,C),D) = k11_scmfsa_1(A,D) ) ) ) ) ) ).
fof(t31_scmfsa_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
=> ! [B] :
( m2_subset_1(B,k4_numbers,k2_scmfsa_1)
=> ! [C] :
( m2_finseq_1(C,k4_numbers)
=> ! [D] :
( m2_subset_1(D,k4_numbers,k1_scmfsa_1)
=> k10_scmfsa_1(k9_scmfsa_1(A,B,C),D) = k10_scmfsa_1(A,D) ) ) ) ) ).
fof(t32_scmfsa_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
=> ! [B] :
( m2_subset_1(B,k4_numbers,k2_scmfsa_1)
=> ! [C] :
( m2_finseq_1(C,k4_numbers)
=> ! [D] :
( m2_subset_1(D,k4_numbers,k3_scmfsa_1)
=> k1_funct_1(k9_scmfsa_1(A,B,C),D) = k1_funct_1(A,D) ) ) ) ) ).
fof(dt_k1_scmfsa_1,axiom,
m1_subset_1(k1_scmfsa_1,k1_zfmisc_1(k4_numbers)) ).
fof(dt_k2_scmfsa_1,axiom,
m1_subset_1(k2_scmfsa_1,k1_zfmisc_1(k4_numbers)) ).
fof(dt_k3_scmfsa_1,axiom,
m1_subset_1(k3_scmfsa_1,k1_zfmisc_1(k4_numbers)) ).
fof(dt_k4_scmfsa_1,axiom,
m1_subset_1(k4_scmfsa_1,k1_zfmisc_1(k2_zfmisc_1(k1_gr_cy_1(np__13),k13_finseq_1(k2_xboole_0(k3_tarski(k2_tarski(k4_numbers,k13_finseq_1(k4_numbers))),k4_numbers))))) ).
fof(dt_k5_scmfsa_1,axiom,
! [A] :
( m1_subset_1(A,k4_scmfsa_1)
=> m2_subset_1(k5_scmfsa_1(A),k1_numbers,k5_numbers) ) ).
fof(dt_k6_scmfsa_1,axiom,
( v1_funct_1(k6_scmfsa_1)
& v1_funct_2(k6_scmfsa_1,k4_numbers,k2_xboole_0(k2_tarski(k4_numbers,k13_finseq_1(k4_numbers)),k2_tarski(k4_scmfsa_1,k3_scmfsa_1)))
& m2_relset_1(k6_scmfsa_1,k4_numbers,k2_xboole_0(k2_tarski(k4_numbers,k13_finseq_1(k4_numbers)),k2_tarski(k4_scmfsa_1,k3_scmfsa_1))) ) ).
fof(dt_k7_scmfsa_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
& m1_subset_1(B,k3_scmfsa_1) )
=> m1_subset_1(k7_scmfsa_1(A,B),k4_card_3(k6_scmfsa_1)) ) ).
fof(dt_k8_scmfsa_1,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
& m1_subset_1(B,k1_scmfsa_1)
& v1_int_1(C) )
=> m1_subset_1(k8_scmfsa_1(A,B,C),k4_card_3(k6_scmfsa_1)) ) ).
fof(dt_k9_scmfsa_1,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
& m1_subset_1(B,k2_scmfsa_1)
& m1_finseq_1(C,k4_numbers) )
=> m1_subset_1(k9_scmfsa_1(A,B,C),k4_card_3(k6_scmfsa_1)) ) ).
fof(dt_k10_scmfsa_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
& m1_subset_1(B,k1_scmfsa_1) )
=> v1_int_1(k10_scmfsa_1(A,B)) ) ).
fof(redefinition_k10_scmfsa_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
& m1_subset_1(B,k1_scmfsa_1) )
=> k10_scmfsa_1(A,B) = k1_funct_1(A,B) ) ).
fof(dt_k11_scmfsa_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
& m1_subset_1(B,k2_scmfsa_1) )
=> m2_finseq_1(k11_scmfsa_1(A,B),k4_numbers) ) ).
fof(redefinition_k11_scmfsa_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
& m1_subset_1(B,k2_scmfsa_1) )
=> k11_scmfsa_1(A,B) = k1_funct_1(A,B) ) ).
fof(dt_k12_scmfsa_1,axiom,
! [A] :
( m1_subset_1(A,k4_scmfsa_1)
=> m2_subset_1(k12_scmfsa_1(A),k4_numbers,k1_scmfsa_1) ) ).
fof(dt_k13_scmfsa_1,axiom,
! [A] :
( m1_subset_1(A,k4_scmfsa_1)
=> m2_subset_1(k13_scmfsa_1(A),k4_numbers,k1_scmfsa_1) ) ).
fof(dt_k14_scmfsa_1,axiom,
! [A] :
( m1_subset_1(A,k4_scmfsa_1)
=> m2_subset_1(k14_scmfsa_1(A),k4_numbers,k2_scmfsa_1) ) ).
fof(dt_k15_scmfsa_1,axiom,
! [A] :
( m1_subset_1(A,k4_scmfsa_1)
=> m2_subset_1(k15_scmfsa_1(A),k4_numbers,k1_scmfsa_1) ) ).
fof(dt_k16_scmfsa_1,axiom,
! [A] :
( m1_subset_1(A,k4_scmfsa_1)
=> m2_subset_1(k16_scmfsa_1(A),k4_numbers,k2_scmfsa_1) ) ).
fof(dt_k17_scmfsa_1,axiom,
! [A] :
( m1_subset_1(A,k3_scmfsa_1)
=> m2_subset_1(k17_scmfsa_1(A),k4_numbers,k3_scmfsa_1) ) ).
fof(dt_k18_scmfsa_1,axiom,
! [A] :
( m1_subset_1(A,k4_card_3(k6_scmfsa_1))
=> m2_subset_1(k18_scmfsa_1(A),k4_numbers,k3_scmfsa_1) ) ).
fof(dt_k19_scmfsa_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_scmfsa_1)
& m1_subset_1(B,k4_card_3(k6_scmfsa_1)) )
=> m1_subset_1(k19_scmfsa_1(A,B),k4_card_3(k6_scmfsa_1)) ) ).
fof(dt_k20_scmfsa_1,axiom,
( v1_funct_1(k20_scmfsa_1)
& v1_funct_2(k20_scmfsa_1,k4_scmfsa_1,k1_fraenkel(k4_card_3(k6_scmfsa_1),k4_card_3(k6_scmfsa_1)))
& m2_relset_1(k20_scmfsa_1,k4_scmfsa_1,k1_fraenkel(k4_card_3(k6_scmfsa_1),k4_card_3(k6_scmfsa_1))) ) ).
fof(d4_scmfsa_1,axiom,
k4_scmfsa_1 = k2_xboole_0(k2_xboole_0(k4_ami_2,a_0_0_scmfsa_1),a_0_1_scmfsa_1) ).
fof(fraenkel_a_0_0_scmfsa_1,axiom,
! [A] :
( r2_hidden(A,a_0_0_scmfsa_1)
<=> ? [B,C,D,E] :
( m2_subset_1(B,k5_numbers,k1_gr_cy_1(np__13))
& m2_subset_1(C,k4_numbers,k1_scmfsa_1)
& m2_subset_1(D,k4_numbers,k1_scmfsa_1)
& m2_subset_1(E,k4_numbers,k2_scmfsa_1)
& A = k4_tarski(B,k3_finseq_4(k4_numbers,C,E,D))
& r2_hidden(B,k2_tarski(np__9,np__10)) ) ) ).
fof(fraenkel_a_0_1_scmfsa_1,axiom,
! [A] :
( r2_hidden(A,a_0_1_scmfsa_1)
<=> ? [B,C,D] :
( m2_subset_1(B,k5_numbers,k1_gr_cy_1(np__13))
& m2_subset_1(C,k4_numbers,k1_scmfsa_1)
& m2_subset_1(D,k4_numbers,k2_scmfsa_1)
& A = k4_tarski(B,k2_finseq_4(k4_numbers,C,D))
& r2_hidden(B,k2_tarski(np__11,np__12)) ) ) ).
%------------------------------------------------------------------------------