SET007 Axioms: SET007+79.ax
%------------------------------------------------------------------------------
% File : SET007+79 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : A Classical First Order Language
% 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 : cqc_lang [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 93 ( 23 unt; 0 def)
% Number of atoms : 502 ( 144 equ)
% Maximal formula atoms : 52 ( 5 avg)
% Number of connectives : 422 ( 13 ~; 1 |; 181 &)
% ( 18 <=>; 209 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 1 prp; 0-3 aty)
% Number of functors : 126 ( 126 usr; 42 con; 0-5 aty)
% Number of variables : 251 ( 236 !; 15 ?)
% 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_cqc_lang,axiom,
! [A,B] :
( v1_relat_1(k3_cqc_lang(A,B))
& v1_funct_1(k3_cqc_lang(A,B)) ) ).
fof(fc2_cqc_lang,axiom,
~ v1_xboole_0(k7_cqc_lang) ).
fof(rc1_cqc_lang,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ? [B] :
( m1_qc_lang1(B,A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B)
& v1_cqc_lang(B,A) ) ) ).
fof(d1_cqc_lang,axiom,
! [A,B,C,D] :
( ( A = B
=> k1_cqc_lang(A,B,C,D) = C )
& ( A != B
=> k1_cqc_lang(A,B,C,D) = D ) ) ).
fof(d2_cqc_lang,axiom,
! [A,B] : k3_cqc_lang(A,B) = k2_funcop_1(k1_tarski(A),B) ).
fof(t1_cqc_lang,axiom,
$true ).
fof(t2_cqc_lang,axiom,
$true ).
fof(t3_cqc_lang,axiom,
$true ).
fof(t4_cqc_lang,axiom,
$true ).
fof(t5_cqc_lang,axiom,
! [A,B] :
( k1_relat_1(k3_cqc_lang(A,B)) = k1_tarski(A)
& k2_relat_1(k3_cqc_lang(A,B)) = k1_tarski(B) ) ).
fof(t6_cqc_lang,axiom,
! [A,B] : k1_funct_1(k3_cqc_lang(A,B),A) = B ).
fof(t7_cqc_lang,axiom,
! [A] :
( r2_hidden(A,k1_qc_lang1)
<=> ~ ( ~ r2_hidden(A,k3_qc_lang1)
& ~ r2_hidden(A,k4_qc_lang1)
& ~ r2_hidden(A,k2_qc_lang1) ) ) ).
fof(d3_cqc_lang,axiom,
! [A] :
( m2_finseq_1(A,k1_qc_lang1)
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k4_qc_lang1,k1_qc_lang1) )
=> ! [C] :
( m2_finseq_1(C,k1_qc_lang1)
=> ( C = k4_cqc_lang(A,B)
<=> ( k3_finseq_1(C) = k3_finseq_1(A)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(A)) )
=> ( ( r2_hidden(k1_funct_1(A,D),k1_relat_1(B))
=> k1_funct_1(C,D) = k1_funct_1(B,k1_funct_1(A,D)) )
& ( ~ r2_hidden(k1_funct_1(A,D),k1_relat_1(B))
=> k1_funct_1(C,D) = k1_funct_1(A,D) ) ) ) ) ) ) ) ) ) ).
fof(t8_cqc_lang,axiom,
$true ).
fof(t9_cqc_lang,axiom,
$true ).
fof(t10_cqc_lang,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k4_qc_lang1)
=> ( v1_funct_1(k3_cqc_lang(B,A))
& m2_relset_1(k3_cqc_lang(B,A),k4_qc_lang1,k1_qc_lang1) ) ) ) ).
fof(t11_cqc_lang,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k4_qc_lang1)
=> ! [D] :
( m2_finseq_1(D,k1_qc_lang1)
=> ! [E] :
( m2_finseq_1(E,k1_qc_lang1)
=> ! [F] :
( ( v1_funct_1(F)
& m2_relset_1(F,k4_qc_lang1,k1_qc_lang1) )
=> ( ( F = k6_cqc_lang(C,B)
& D = k4_cqc_lang(E,F)
& r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(E)) )
=> ( ( k1_funct_1(E,A) = C
=> k1_funct_1(D,A) = B )
& ( k1_funct_1(E,A) != C
=> k1_funct_1(D,A) = k1_funct_1(E,A) ) ) ) ) ) ) ) ) ) ).
fof(t12_cqc_lang,axiom,
$true ).
fof(t13_cqc_lang,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
<=> ( k6_qc_lang3(A) = k1_xboole_0
& k5_qc_lang3(A) = k1_xboole_0 ) ) ) ).
fof(d5_cqc_lang,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_qc_lang1(B,A)
=> ( v1_cqc_lang(B,A)
<=> r1_tarski(k2_relat_1(B),k2_qc_lang1) ) ) ) ).
fof(t14_cqc_lang,axiom,
$true ).
fof(t16_cqc_lang,axiom,
m2_subset_1(k11_qc_lang1,k8_qc_lang1,k7_cqc_lang) ).
fof(t18_cqc_lang,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ( m2_subset_1(k12_qc_lang1(A),k8_qc_lang1,k7_cqc_lang)
<=> m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) ) ) ).
fof(t19_cqc_lang,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( m2_subset_1(k13_qc_lang1(A,B),k8_qc_lang1,k7_cqc_lang)
<=> ( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
& m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) ) ) ) ) ).
fof(t20_cqc_lang,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> m2_subset_1(k2_qc_lang2(A,B),k8_qc_lang1,k7_cqc_lang) ) ) ).
fof(t21_cqc_lang,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> m2_subset_1(k3_qc_lang2(A,B),k8_qc_lang1,k7_cqc_lang) ) ) ).
fof(t22_cqc_lang,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> m2_subset_1(k4_qc_lang2(A,B),k8_qc_lang1,k7_cqc_lang) ) ) ).
fof(t23_cqc_lang,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( m2_subset_1(k14_qc_lang1(A,B),k8_qc_lang1,k7_cqc_lang)
<=> m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) ) ) ) ).
fof(t24_cqc_lang,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> m2_subset_1(k5_qc_lang2(A,B),k8_qc_lang1,k7_cqc_lang) ) ) ).
fof(d6_cqc_lang,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m1_subset_1(C,k8_qc_lang1)
=> ( C = k17_cqc_lang(A,B)
<=> ? [D] :
( v1_funct_1(D)
& v1_funct_2(D,k8_qc_lang1,k8_qc_lang1)
& m2_relset_1(D,k8_qc_lang1,k8_qc_lang1)
& C = k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,A)
& ! [E] :
( m1_subset_1(E,k8_qc_lang1)
=> ( k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k9_cqc_lang) = k9_cqc_lang
& ( v2_qc_lang1(E)
=> k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,E) = k9_qc_lang1(k15_qc_lang1(E),k4_cqc_lang(k16_qc_lang1(E),k6_cqc_lang(k3_qc_lang3(np__0),B))) )
& ( v3_qc_lang1(E)
=> k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,E) = k12_qc_lang1(k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k17_qc_lang1(E))) )
& ( v4_qc_lang1(E)
=> k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,E) = k13_qc_lang1(k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k18_qc_lang1(E)),k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k19_qc_lang1(E))) )
& ( v5_qc_lang1(E)
=> k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,E) = k2_cqc_lang(k8_qc_lang1,k20_qc_lang1(E),B,E,k14_qc_lang1(k20_qc_lang1(E),k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k21_qc_lang1(E)))) ) ) ) ) ) ) ) ) ).
fof(t25_cqc_lang,axiom,
$true ).
fof(t26_cqc_lang,axiom,
$true ).
fof(t27_cqc_lang,axiom,
$true ).
fof(t28_cqc_lang,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> k17_cqc_lang(k9_cqc_lang,A) = k9_cqc_lang ) ).
fof(t29_cqc_lang,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( v2_qc_lang1(B)
=> k17_cqc_lang(B,A) = k9_qc_lang1(k15_qc_lang1(B),k4_cqc_lang(k16_qc_lang1(B),k6_cqc_lang(k3_qc_lang3(np__0),A))) ) ) ) ).
fof(t30_cqc_lang,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(A))
=> ! [D] :
( m1_qc_lang1(D,A)
=> k17_cqc_lang(k9_qc_lang1(C,D),B) = k9_qc_lang1(C,k5_cqc_lang(A,D,k6_cqc_lang(k3_qc_lang3(np__0),B))) ) ) ) ) ).
fof(t31_cqc_lang,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( v3_qc_lang1(B)
=> k17_cqc_lang(B,A) = k12_qc_lang1(k17_cqc_lang(k17_qc_lang1(B),A)) ) ) ) ).
fof(t32_cqc_lang,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> k17_cqc_lang(k12_qc_lang1(B),A) = k12_qc_lang1(k17_cqc_lang(B,A)) ) ) ).
fof(t33_cqc_lang,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( v4_qc_lang1(B)
=> k17_cqc_lang(B,A) = k13_qc_lang1(k17_cqc_lang(k18_qc_lang1(B),A),k17_cqc_lang(k19_qc_lang1(B),A)) ) ) ) ).
fof(t34_cqc_lang,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ! [C] :
( m1_subset_1(C,k8_qc_lang1)
=> k17_cqc_lang(k13_qc_lang1(B,C),A) = k13_qc_lang1(k17_cqc_lang(B,A),k17_cqc_lang(C,A)) ) ) ) ).
fof(t35_cqc_lang,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( ( v5_qc_lang1(B)
& k20_qc_lang1(B) = A )
=> k17_cqc_lang(B,A) = B ) ) ) ).
fof(t36_cqc_lang,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( v5_qc_lang1(B)
=> ( k20_qc_lang1(B) = A
| k17_cqc_lang(B,A) = k14_qc_lang1(k20_qc_lang1(B),k17_cqc_lang(k21_qc_lang1(B),A)) ) ) ) ) ).
fof(t37_cqc_lang,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> k17_cqc_lang(k14_qc_lang1(A,B),A) = k14_qc_lang1(A,B) ) ) ).
fof(t38_cqc_lang,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m1_subset_1(C,k8_qc_lang1)
=> ( A != B
=> k17_cqc_lang(k14_qc_lang1(A,C),B) = k14_qc_lang1(A,k17_cqc_lang(C,B)) ) ) ) ) ).
fof(t39_cqc_lang,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( k5_qc_lang3(B) = k1_xboole_0
=> k17_cqc_lang(B,A) = B ) ) ) ).
fof(t40_cqc_lang,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> k17_cqc_lang(B,A) = B ) ) ).
fof(t41_cqc_lang,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> k6_qc_lang3(k17_cqc_lang(B,A)) = k6_qc_lang3(B) ) ) ).
fof(t42_cqc_lang,axiom,
! [A,B,C] : k9_funct_2(A,B,C) = k3_cqc_lang(k4_tarski(A,B),C) ).
fof(t43_cqc_lang,axiom,
! [A,B,C] : k1_binop_1(k9_funct_2(A,B,C),A,B) = C ).
fof(s1_cqc_lang,axiom,
( ! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( ( v1_cqc_lang(E,D)
& m1_qc_lang1(E,D) )
=> ! [F] :
( m2_subset_1(F,k5_qc_lang1,k7_qc_lang1(D))
=> ( p1_s1_cqc_lang(k9_cqc_lang)
& p1_s1_cqc_lang(k8_cqc_lang(D,F,E))
& ( p1_s1_cqc_lang(A)
=> p1_s1_cqc_lang(k10_cqc_lang(A)) )
& ( ( p1_s1_cqc_lang(A)
& p1_s1_cqc_lang(B) )
=> p1_s1_cqc_lang(k11_cqc_lang(A,B)) )
& ( p1_s1_cqc_lang(A)
=> p1_s1_cqc_lang(k15_cqc_lang(C,A)) ) ) ) ) ) ) ) )
=> ! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> p1_s1_cqc_lang(A) ) ) ).
fof(s2_cqc_lang,axiom,
? [A] :
( v1_funct_1(A)
& v1_funct_2(A,k7_cqc_lang,f1_s2_cqc_lang)
& m2_relset_1(A,k7_cqc_lang,f1_s2_cqc_lang)
& k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k9_cqc_lang) = f2_s2_cqc_lang
& ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ! [D] :
( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( ( v1_cqc_lang(F,E)
& m1_qc_lang1(F,E) )
=> ! [G] :
( m2_subset_1(G,k5_qc_lang1,k7_qc_lang1(E))
=> ( k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k8_cqc_lang(E,G,F)) = f3_s2_cqc_lang(E,G,F)
& k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k10_cqc_lang(B)) = f4_s2_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,B))
& k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k11_cqc_lang(B,C)) = f5_s2_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,B),k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,C))
& k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k15_cqc_lang(D,B)) = f6_s2_cqc_lang(D,k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,B)) ) ) ) ) ) ) ) ) ).
fof(s3_cqc_lang,axiom,
( ( k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k9_cqc_lang) = f4_s3_cqc_lang
& ! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( ( v1_cqc_lang(E,D)
& m1_qc_lang1(E,D) )
=> ! [F] :
( m2_subset_1(F,k5_qc_lang1,k7_qc_lang1(D))
=> ( k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k8_cqc_lang(D,F,E)) = f5_s3_cqc_lang(D,F,E)
& k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k10_cqc_lang(A)) = f6_s3_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,A))
& k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k11_cqc_lang(A,B)) = f7_s3_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,A),k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,B))
& k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k15_cqc_lang(C,A)) = f8_s3_cqc_lang(C,k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,A)) ) ) ) ) ) ) )
& k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k9_cqc_lang) = f4_s3_cqc_lang
& ! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( ( v1_cqc_lang(E,D)
& m1_qc_lang1(E,D) )
=> ! [F] :
( m2_subset_1(F,k5_qc_lang1,k7_qc_lang1(D))
=> ( k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k8_cqc_lang(D,F,E)) = f5_s3_cqc_lang(D,F,E)
& k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k10_cqc_lang(A)) = f6_s3_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,A))
& k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k11_cqc_lang(A,B)) = f7_s3_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,A),k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,B))
& k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k15_cqc_lang(C,A)) = f8_s3_cqc_lang(C,k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,A)) ) ) ) ) ) ) ) )
=> f2_s3_cqc_lang = f3_s3_cqc_lang ) ).
fof(s4_cqc_lang,axiom,
( ? [A] :
( m1_subset_1(A,f1_s4_cqc_lang)
& ? [B] :
( v1_funct_1(B)
& v1_funct_2(B,k7_cqc_lang,f1_s4_cqc_lang)
& m2_relset_1(B,k7_cqc_lang,f1_s4_cqc_lang)
& A = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,f2_s4_cqc_lang)
& k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k9_cqc_lang) = f3_s4_cqc_lang
& ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ! [E] :
( m2_subset_1(E,k1_qc_lang1,k2_qc_lang1)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( ( v1_cqc_lang(G,F)
& m1_qc_lang1(G,F) )
=> ! [H] :
( m2_subset_1(H,k5_qc_lang1,k7_qc_lang1(F))
=> ( k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k8_cqc_lang(F,H,G)) = f4_s4_cqc_lang(F,H,G)
& k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k10_cqc_lang(C)) = f5_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,C))
& k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k11_cqc_lang(C,D)) = f6_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,C),k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,D))
& k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k15_cqc_lang(E,C)) = f7_s4_cqc_lang(E,k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,C)) ) ) ) ) ) ) ) ) )
& ! [A] :
( m1_subset_1(A,f1_s4_cqc_lang)
=> ! [B] :
( m1_subset_1(B,f1_s4_cqc_lang)
=> ~ ( ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,k7_cqc_lang,f1_s4_cqc_lang)
& m2_relset_1(C,k7_cqc_lang,f1_s4_cqc_lang)
& A = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,f2_s4_cqc_lang)
& k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k9_cqc_lang) = f3_s4_cqc_lang
& ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ! [E] :
( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
=> ! [F] :
( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ! [H] :
( ( v1_cqc_lang(H,G)
& m1_qc_lang1(H,G) )
=> ! [I] :
( m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G))
=> ( k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s4_cqc_lang(G,I,H)
& k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k10_cqc_lang(D)) = f5_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D))
& k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k11_cqc_lang(D,E)) = f6_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,E))
& k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k15_cqc_lang(F,D)) = f7_s4_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D)) ) ) ) ) ) ) ) )
& ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,k7_cqc_lang,f1_s4_cqc_lang)
& m2_relset_1(C,k7_cqc_lang,f1_s4_cqc_lang)
& B = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,f2_s4_cqc_lang)
& k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k9_cqc_lang) = f3_s4_cqc_lang
& ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ! [E] :
( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
=> ! [F] :
( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ! [H] :
( ( v1_cqc_lang(H,G)
& m1_qc_lang1(H,G) )
=> ! [I] :
( m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G))
=> ( k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s4_cqc_lang(G,I,H)
& k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k10_cqc_lang(D)) = f5_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D))
& k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k11_cqc_lang(D,E)) = f6_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,E))
& k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k15_cqc_lang(F,D)) = f7_s4_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D)) ) ) ) ) ) ) ) )
& A != B ) ) ) ) ).
fof(s5_cqc_lang,axiom,
( ! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m1_subset_1(B,f1_s5_cqc_lang)
=> ( B = f2_s5_cqc_lang(A)
<=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,k7_cqc_lang,f1_s5_cqc_lang)
& m2_relset_1(C,k7_cqc_lang,f1_s5_cqc_lang)
& B = k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,A)
& k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k9_cqc_lang) = f3_s5_cqc_lang
& ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ! [E] :
( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
=> ! [F] :
( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ! [H] :
( ( v1_cqc_lang(H,G)
& m1_qc_lang1(H,G) )
=> ! [I] :
( m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G))
=> ( k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s5_cqc_lang(G,I,H)
& k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k10_cqc_lang(D)) = f5_s5_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,D))
& k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k11_cqc_lang(D,E)) = f6_s5_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,E))
& k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k15_cqc_lang(F,D)) = f7_s5_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,D)) ) ) ) ) ) ) ) ) ) ) )
=> f2_s5_cqc_lang(k9_cqc_lang) = f3_s5_cqc_lang ) ).
fof(s6_cqc_lang,axiom,
( ! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m1_subset_1(B,f1_s6_cqc_lang)
=> ( B = f3_s6_cqc_lang(A)
<=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,k7_cqc_lang,f1_s6_cqc_lang)
& m2_relset_1(C,k7_cqc_lang,f1_s6_cqc_lang)
& B = k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,A)
& k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k9_cqc_lang) = f2_s6_cqc_lang
& ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ! [E] :
( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
=> ! [F] :
( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ! [H] :
( ( v1_cqc_lang(H,G)
& m1_qc_lang1(H,G) )
=> ! [I] :
( m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G))
=> ( k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s6_cqc_lang(G,I,H)
& k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k10_cqc_lang(D)) = f8_s6_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,D))
& k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k11_cqc_lang(D,E)) = f9_s6_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,E))
& k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k15_cqc_lang(F,D)) = f10_s6_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,D)) ) ) ) ) ) ) ) ) ) ) )
=> f3_s6_cqc_lang(k8_cqc_lang(f5_s6_cqc_lang,f6_s6_cqc_lang,f7_s6_cqc_lang)) = f4_s6_cqc_lang(f5_s6_cqc_lang,f6_s6_cqc_lang,f7_s6_cqc_lang) ) ).
fof(s7_cqc_lang,axiom,
( ! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m1_subset_1(B,f1_s7_cqc_lang)
=> ( B = f2_s7_cqc_lang(A)
<=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,k7_cqc_lang,f1_s7_cqc_lang)
& m2_relset_1(C,k7_cqc_lang,f1_s7_cqc_lang)
& B = k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,A)
& k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k9_cqc_lang) = f3_s7_cqc_lang
& ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ! [E] :
( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
=> ! [F] :
( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ! [H] :
( ( v1_cqc_lang(H,G)
& m1_qc_lang1(H,G) )
=> ! [I] :
( m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G))
=> ( k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s7_cqc_lang(G,I,H)
& k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k10_cqc_lang(D)) = f5_s7_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,D))
& k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k11_cqc_lang(D,E)) = f7_s7_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,E))
& k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k15_cqc_lang(F,D)) = f8_s7_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,D)) ) ) ) ) ) ) ) ) ) ) )
=> f2_s7_cqc_lang(k10_cqc_lang(f6_s7_cqc_lang)) = f5_s7_cqc_lang(f2_s7_cqc_lang(f6_s7_cqc_lang)) ) ).
fof(s8_cqc_lang,axiom,
( ! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m1_subset_1(B,f1_s8_cqc_lang)
=> ( B = f2_s8_cqc_lang(A)
<=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,k7_cqc_lang,f1_s8_cqc_lang)
& m2_relset_1(C,k7_cqc_lang,f1_s8_cqc_lang)
& B = k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,A)
& k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k9_cqc_lang) = f3_s8_cqc_lang
& ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ! [E] :
( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
=> ! [F] :
( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ! [H] :
( ( v1_cqc_lang(H,G)
& m1_qc_lang1(H,G) )
=> ! [I] :
( m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G))
=> ( k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s8_cqc_lang(G,I,H)
& k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k10_cqc_lang(D)) = f5_s8_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,D))
& k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k11_cqc_lang(D,E)) = f6_s8_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,E))
& k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k15_cqc_lang(F,D)) = f9_s8_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,D)) ) ) ) ) ) ) ) ) ) ) )
=> f2_s8_cqc_lang(k11_cqc_lang(f7_s8_cqc_lang,f8_s8_cqc_lang)) = f6_s8_cqc_lang(f2_s8_cqc_lang(f7_s8_cqc_lang),f2_s8_cqc_lang(f8_s8_cqc_lang)) ) ).
fof(s9_cqc_lang,axiom,
( ! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m1_subset_1(B,f1_s9_cqc_lang)
=> ( B = f2_s9_cqc_lang(A)
<=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,k7_cqc_lang,f1_s9_cqc_lang)
& m2_relset_1(C,k7_cqc_lang,f1_s9_cqc_lang)
& B = k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,A)
& k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k9_cqc_lang) = f3_s9_cqc_lang
& ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ! [E] :
( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
=> ! [F] :
( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ! [H] :
( ( v1_cqc_lang(H,G)
& m1_qc_lang1(H,G) )
=> ! [I] :
( m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G))
=> ( k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s9_cqc_lang(G,I,H)
& k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k10_cqc_lang(D)) = f5_s9_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,D))
& k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k11_cqc_lang(D,E)) = f6_s9_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,E))
& k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k15_cqc_lang(F,D)) = f7_s9_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,D)) ) ) ) ) ) ) ) ) ) ) )
=> f2_s9_cqc_lang(k15_cqc_lang(f8_s9_cqc_lang,f9_s9_cqc_lang)) = f7_s9_cqc_lang(f8_s9_cqc_lang,f2_s9_cqc_lang(f9_s9_cqc_lang)) ) ).
fof(dt_k1_cqc_lang,axiom,
$true ).
fof(dt_k2_cqc_lang,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(D,A)
& m1_subset_1(E,A) )
=> m1_subset_1(k2_cqc_lang(A,B,C,D,E),A) ) ).
fof(redefinition_k2_cqc_lang,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(D,A)
& m1_subset_1(E,A) )
=> k2_cqc_lang(A,B,C,D,E) = k1_cqc_lang(B,C,D,E) ) ).
fof(dt_k3_cqc_lang,axiom,
$true ).
fof(dt_k4_cqc_lang,axiom,
! [A,B] :
( ( m1_finseq_1(A,k1_qc_lang1)
& v1_funct_1(B)
& m1_relset_1(B,k4_qc_lang1,k1_qc_lang1) )
=> m2_finseq_1(k4_cqc_lang(A,B),k1_qc_lang1) ) ).
fof(dt_k5_cqc_lang,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_qc_lang1(B,A)
& v1_funct_1(C)
& m1_relset_1(C,k4_qc_lang1,k1_qc_lang1) )
=> m1_qc_lang1(k5_cqc_lang(A,B,C),A) ) ).
fof(redefinition_k5_cqc_lang,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_qc_lang1(B,A)
& v1_funct_1(C)
& m1_relset_1(C,k4_qc_lang1,k1_qc_lang1) )
=> k5_cqc_lang(A,B,C) = k4_cqc_lang(B,C) ) ).
fof(dt_k6_cqc_lang,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_qc_lang1)
& m1_subset_1(B,k2_qc_lang1) )
=> ( v1_funct_1(k6_cqc_lang(A,B))
& m2_relset_1(k6_cqc_lang(A,B),k4_qc_lang1,k1_qc_lang1) ) ) ).
fof(redefinition_k6_cqc_lang,axiom,
! [A,B] :
( ( m1_subset_1(A,k4_qc_lang1)
& m1_subset_1(B,k2_qc_lang1) )
=> k6_cqc_lang(A,B) = k3_cqc_lang(A,B) ) ).
fof(dt_k7_cqc_lang,axiom,
m1_subset_1(k7_cqc_lang,k1_zfmisc_1(k8_qc_lang1)) ).
fof(dt_k8_cqc_lang,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k7_qc_lang1(A))
& v1_cqc_lang(C,A)
& m1_qc_lang1(C,A) )
=> m2_subset_1(k8_cqc_lang(A,B,C),k8_qc_lang1,k7_cqc_lang) ) ).
fof(redefinition_k8_cqc_lang,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k7_qc_lang1(A))
& v1_cqc_lang(C,A)
& m1_qc_lang1(C,A) )
=> k8_cqc_lang(A,B,C) = k9_qc_lang1(B,C) ) ).
fof(dt_k9_cqc_lang,axiom,
m2_subset_1(k9_cqc_lang,k8_qc_lang1,k7_cqc_lang) ).
fof(redefinition_k9_cqc_lang,axiom,
k9_cqc_lang = k11_qc_lang1 ).
fof(dt_k10_cqc_lang,axiom,
! [A] :
( m1_subset_1(A,k7_cqc_lang)
=> m2_subset_1(k10_cqc_lang(A),k8_qc_lang1,k7_cqc_lang) ) ).
fof(redefinition_k10_cqc_lang,axiom,
! [A] :
( m1_subset_1(A,k7_cqc_lang)
=> k10_cqc_lang(A) = k12_qc_lang1(A) ) ).
fof(dt_k11_cqc_lang,axiom,
! [A,B] :
( ( m1_subset_1(A,k7_cqc_lang)
& m1_subset_1(B,k7_cqc_lang) )
=> m2_subset_1(k11_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang) ) ).
fof(redefinition_k11_cqc_lang,axiom,
! [A,B] :
( ( m1_subset_1(A,k7_cqc_lang)
& m1_subset_1(B,k7_cqc_lang) )
=> k11_cqc_lang(A,B) = k13_qc_lang1(A,B) ) ).
fof(dt_k12_cqc_lang,axiom,
! [A,B] :
( ( m1_subset_1(A,k7_cqc_lang)
& m1_subset_1(B,k7_cqc_lang) )
=> m2_subset_1(k12_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang) ) ).
fof(redefinition_k12_cqc_lang,axiom,
! [A,B] :
( ( m1_subset_1(A,k7_cqc_lang)
& m1_subset_1(B,k7_cqc_lang) )
=> k12_cqc_lang(A,B) = k2_qc_lang2(A,B) ) ).
fof(dt_k13_cqc_lang,axiom,
! [A,B] :
( ( m1_subset_1(A,k7_cqc_lang)
& m1_subset_1(B,k7_cqc_lang) )
=> m2_subset_1(k13_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang) ) ).
fof(redefinition_k13_cqc_lang,axiom,
! [A,B] :
( ( m1_subset_1(A,k7_cqc_lang)
& m1_subset_1(B,k7_cqc_lang) )
=> k13_cqc_lang(A,B) = k3_qc_lang2(A,B) ) ).
fof(dt_k14_cqc_lang,axiom,
! [A,B] :
( ( m1_subset_1(A,k7_cqc_lang)
& m1_subset_1(B,k7_cqc_lang) )
=> m2_subset_1(k14_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang) ) ).
fof(redefinition_k14_cqc_lang,axiom,
! [A,B] :
( ( m1_subset_1(A,k7_cqc_lang)
& m1_subset_1(B,k7_cqc_lang) )
=> k14_cqc_lang(A,B) = k4_qc_lang2(A,B) ) ).
fof(dt_k15_cqc_lang,axiom,
! [A,B] :
( ( m1_subset_1(A,k2_qc_lang1)
& m1_subset_1(B,k7_cqc_lang) )
=> m2_subset_1(k15_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang) ) ).
fof(redefinition_k15_cqc_lang,axiom,
! [A,B] :
( ( m1_subset_1(A,k2_qc_lang1)
& m1_subset_1(B,k7_cqc_lang) )
=> k15_cqc_lang(A,B) = k14_qc_lang1(A,B) ) ).
fof(dt_k16_cqc_lang,axiom,
! [A,B] :
( ( m1_subset_1(A,k2_qc_lang1)
& m1_subset_1(B,k7_cqc_lang) )
=> m2_subset_1(k16_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang) ) ).
fof(redefinition_k16_cqc_lang,axiom,
! [A,B] :
( ( m1_subset_1(A,k2_qc_lang1)
& m1_subset_1(B,k7_cqc_lang) )
=> k16_cqc_lang(A,B) = k5_qc_lang2(A,B) ) ).
fof(dt_k17_cqc_lang,axiom,
! [A,B] :
( ( m1_subset_1(A,k8_qc_lang1)
& m1_subset_1(B,k2_qc_lang1) )
=> m1_subset_1(k17_cqc_lang(A,B),k8_qc_lang1) ) ).
fof(d4_cqc_lang,axiom,
k7_cqc_lang = a_0_0_cqc_lang ).
fof(t15_cqc_lang,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_qc_lang1(B,A)
=> ( ( v1_cqc_lang(B,A)
& m1_qc_lang1(B,A) )
<=> ( a_2_0_cqc_lang(A,B) = k1_xboole_0
& a_2_1_cqc_lang(A,B) = k1_xboole_0 ) ) ) ) ).
fof(t17_cqc_lang,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A))
=> ! [C] :
( m1_qc_lang1(C,A)
=> ( m2_subset_1(k9_qc_lang1(B,C),k8_qc_lang1,k7_cqc_lang)
<=> ( a_2_0_cqc_lang(A,C) = k1_xboole_0
& a_2_1_cqc_lang(A,C) = k1_xboole_0 ) ) ) ) ) ).
fof(fraenkel_a_0_0_cqc_lang,axiom,
! [A] :
( r2_hidden(A,a_0_0_cqc_lang)
<=> ? [B] :
( m1_subset_1(B,k8_qc_lang1)
& A = B
& k6_qc_lang3(B) = k1_xboole_0
& k5_qc_lang3(B) = k1_xboole_0 ) ) ).
fof(fraenkel_a_2_0_cqc_lang,axiom,
! [A,B,C] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& m1_qc_lang1(C,B) )
=> ( r2_hidden(A,a_2_0_cqc_lang(B,C))
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& A = k1_funct_1(C,D)
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(C))
& r2_hidden(k1_funct_1(C,D),k4_qc_lang1) ) ) ) ).
fof(fraenkel_a_2_1_cqc_lang,axiom,
! [A,B,C] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& m1_qc_lang1(C,B) )
=> ( r2_hidden(A,a_2_1_cqc_lang(B,C))
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& A = k1_funct_1(C,D)
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(C))
& r2_hidden(k1_funct_1(C,D),k3_qc_lang1) ) ) ) ).
%------------------------------------------------------------------------------