SET007 Axioms: SET007+158.ax
%------------------------------------------------------------------------------
% File : SET007+158 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Similarity of Formulae
% 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_sim1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 94 ( 6 unt; 0 def)
% Number of atoms : 586 ( 90 equ)
% Maximal formula atoms : 31 ( 6 avg)
% Number of connectives : 526 ( 34 ~; 2 |; 169 &)
% ( 13 <=>; 308 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 8 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 34 ( 32 usr; 1 prp; 0-4 aty)
% Number of functors : 93 ( 93 usr; 25 con; 0-4 aty)
% Number of variables : 309 ( 303 !; 6 ?)
% 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_sim1,axiom,
! [A] :
( m1_subset_1(A,k7_cqc_lang)
=> ( ~ v1_xboole_0(k11_cqc_sim1(A))
& v1_membered(k11_cqc_sim1(A))
& v2_membered(k11_cqc_sim1(A))
& v3_membered(k11_cqc_sim1(A))
& v4_membered(k11_cqc_sim1(A))
& v5_membered(k11_cqc_sim1(A)) ) ) ).
fof(t1_cqc_sim1,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> k9_relat_1(k1_funct_4(C,k2_funcop_1(k1_tarski(A),B)),k1_tarski(A)) = k1_tarski(B) ) ).
fof(t2_cqc_sim1,axiom,
! [A,B,C,D,E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> r1_tarski(k9_relat_1(k1_funct_4(E,k2_funcop_1(B,D)),A),k2_xboole_0(k9_relat_1(E,A),k1_tarski(D))) ) ).
fof(t3_cqc_sim1,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] : k9_relat_1(k1_funct_4(C,k2_funcop_1(k1_tarski(A),B)),k4_xboole_0(D,k1_tarski(A))) = k9_relat_1(C,k4_xboole_0(D,k1_tarski(A))) ) ).
fof(t4_cqc_sim1,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ~ r2_hidden(B,k9_relat_1(C,k4_xboole_0(D,k1_tarski(A))))
=> k9_relat_1(k1_funct_4(C,k2_funcop_1(k1_tarski(A),B)),k4_xboole_0(D,k1_tarski(A))) = k4_xboole_0(k9_relat_1(k1_funct_4(C,k2_funcop_1(k1_tarski(A),B)),D),k1_tarski(B)) ) ) ).
fof(t5_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ~ ( v2_qc_lang1(A)
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B))
=> ! [D] :
( ( v1_cqc_lang(D,B)
& m1_qc_lang1(D,B) )
=> A != k8_cqc_lang(B,C,D) ) ) ) ) ) ).
fof(t6_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ~ ( v3_qc_lang1(A)
& ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> A != k10_cqc_lang(B) ) ) ) ).
fof(t7_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ~ ( v4_qc_lang1(A)
& ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> A != k11_cqc_lang(B,C) ) ) ) ) ).
fof(t8_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ~ ( v5_qc_lang1(A)
& ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> A != k15_cqc_lang(B,C) ) ) ) ) ).
fof(t10_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> r2_qc_lang2(A,k10_cqc_lang(A)) ) ).
fof(t11_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( r2_qc_lang2(A,k11_cqc_lang(A,B))
& r2_qc_lang2(B,k11_cqc_lang(A,B)) ) ) ) ).
fof(t12_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> r2_qc_lang2(A,k15_cqc_lang(B,A)) ) ) ).
fof(t13_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_cqc_lang(B,A)
& m1_qc_lang1(B,A) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(B)) )
=> r2_hidden(k1_funct_1(B,C),k2_qc_lang1) ) ) ) ) ).
fof(d1_cqc_sim1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k7_cqc_lang)
& m2_relset_1(B,A,k7_cqc_lang) )
=> ! [C] :
( m2_fraenkel(C,A,k7_cqc_lang,k1_fraenkel(A,k7_cqc_lang))
=> ( C = k1_cqc_sim1(A,B)
<=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
=> ( E = k8_funct_2(A,k7_cqc_lang,B,D)
=> k8_funct_2(A,k7_cqc_lang,C,D) = k10_cqc_lang(E) ) ) ) ) ) ) ) ).
fof(d2_cqc_sim1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang)
& m2_relset_1(A,k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang)
& m2_relset_1(B,k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_fraenkel(D,k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,k1_fraenkel(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang))
=> ( D = k2_cqc_sim1(A,B,C)
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_fraenkel(F,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1))
=> ! [G] :
( m2_subset_1(G,k8_qc_lang1,k7_cqc_lang)
=> ! [H] :
( m2_subset_1(H,k8_qc_lang1,k7_cqc_lang)
=> ( ( G = k8_funct_2(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,A,k1_domain_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1),E,F))
& H = k8_funct_2(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,B,k1_domain_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1),k1_nat_1(E,C),F)) )
=> k8_funct_2(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,D,k1_domain_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1),E,F)) = k11_cqc_lang(G,H) ) ) ) ) ) ) ) ) ) ) ).
fof(d3_cqc_sim1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang)
& m2_relset_1(A,k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang) )
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_fraenkel(C,k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,k1_fraenkel(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang))
=> ( C = k3_cqc_sim1(A,B)
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_fraenkel(E,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1))
=> ! [F] :
( m2_subset_1(F,k8_qc_lang1,k7_cqc_lang)
=> ( F = k1_funct_1(A,k4_tarski(k1_nat_1(D,np__1),k1_funct_4(E,k2_funcop_1(k23_qc_lang1(B),k2_qc_lang3(D)))))
=> k8_funct_2(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,C,k1_domain_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1),D,E)) = k15_cqc_lang(k2_qc_lang3(D),F) ) ) ) ) ) ) ) ) ).
fof(d4_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A))
=> ! [C] :
( ( v1_cqc_lang(C,A)
& m1_qc_lang1(C,A) )
=> ! [D] :
( m2_fraenkel(D,k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,k1_fraenkel(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang))
=> ( D = k5_cqc_sim1(A,B,C)
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_fraenkel(F,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1))
=> k8_funct_2(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,D,k1_domain_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1),E,F)) = k8_cqc_lang(A,B,k4_cqc_sim1(A,C,F)) ) ) ) ) ) ) ) ).
fof(d5_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( B = k6_cqc_sim1(A)
<=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,k7_cqc_lang,k5_numbers)
& m2_relset_1(C,k7_cqc_lang,k5_numbers)
& B = k1_recdef_1(k7_cqc_lang,C,A)
& k1_recdef_1(k7_cqc_lang,C,k9_cqc_lang) = np__0
& ! [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))
=> ( k1_recdef_1(k7_cqc_lang,C,k8_cqc_lang(G,I,H)) = np__0
& k1_recdef_1(k7_cqc_lang,C,k10_cqc_lang(D)) = k1_recdef_1(k7_cqc_lang,C,D)
& k1_recdef_1(k7_cqc_lang,C,k11_cqc_lang(D,E)) = k1_nat_1(k1_recdef_1(k7_cqc_lang,C,D),k1_recdef_1(k7_cqc_lang,C,E))
& k1_recdef_1(k7_cqc_lang,C,k15_cqc_lang(F,D)) = k1_nat_1(k1_recdef_1(k7_cqc_lang,C,D),np__1) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d6_cqc_sim1,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k7_cqc_lang,k1_fraenkel(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang))
& m2_relset_1(A,k7_cqc_lang,k1_fraenkel(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang)) )
=> ( A = k8_cqc_sim1
<=> ( k7_cqc_sim1(A,k9_cqc_lang) = k2_funcop_1(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k9_cqc_lang)
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_cqc_lang(C,B)
& m1_qc_lang1(C,B) )
=> ! [D] :
( m2_subset_1(D,k5_qc_lang1,k7_qc_lang1(B))
=> k7_cqc_sim1(A,k8_cqc_lang(B,D,C)) = k5_cqc_sim1(B,D,C) ) ) )
& ! [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)
=> ( k7_cqc_sim1(A,k10_cqc_lang(B)) = k1_cqc_sim1(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_sim1(A,B))
& k7_cqc_sim1(A,k11_cqc_lang(B,C)) = k2_cqc_sim1(k7_cqc_sim1(A,B),k7_cqc_sim1(A,C),k6_cqc_sim1(B))
& k7_cqc_sim1(A,k15_cqc_lang(D,B)) = k3_cqc_sim1(k7_cqc_sim1(A,B),D) ) ) ) ) ) ) ) ).
fof(d7_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_fraenkel(C,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1))
=> k9_cqc_sim1(A,B,C) = k8_funct_2(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,k7_cqc_sim1(k8_cqc_sim1,A),k1_domain_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1),B,C)) ) ) ) ).
fof(t14_cqc_sim1,axiom,
k6_cqc_sim1(k9_cqc_lang) = np__0 ).
fof(t15_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_cqc_lang(B,A)
& m1_qc_lang1(B,A) )
=> ! [C] :
( m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(A))
=> k6_cqc_sim1(k8_cqc_lang(A,C,B)) = np__0 ) ) ) ).
fof(t16_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> k6_cqc_sim1(k10_cqc_lang(A)) = k6_cqc_sim1(A) ) ).
fof(t17_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> k6_cqc_sim1(k11_cqc_lang(A,B)) = k1_nat_1(k6_cqc_sim1(A),k6_cqc_sim1(B)) ) ) ).
fof(t18_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> k6_cqc_sim1(k15_cqc_lang(B,A)) = k1_nat_1(k6_cqc_sim1(A),np__1) ) ) ).
fof(d8_cqc_sim1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(k5_numbers)) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( B = k10_cqc_sim1(A)
<=> ( r2_hidden(B,A)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(C,A)
=> r1_xreal_0(B,C) ) ) ) ) ) ) ).
fof(t19_cqc_sim1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(k5_numbers)) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k5_numbers)) )
=> ( r1_tarski(A,B)
=> r1_xreal_0(k10_cqc_sim1(B),k10_cqc_sim1(A)) ) ) ) ).
fof(t20_cqc_sim1,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> v1_finset_1(k24_qc_lang1(A)) ) ).
fof(d10_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> k12_cqc_sim1(A) = k10_cqc_sim1(k11_cqc_sim1(A)) ) ).
fof(t21_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ( k12_cqc_sim1(A) = np__0
<=> v6_qc_lang1(A) ) ) ).
fof(t22_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(k2_qc_lang3(B),k24_qc_lang1(A))
& r1_xreal_0(k12_cqc_sim1(A),B) ) ) ) ).
fof(t23_cqc_sim1,axiom,
k12_cqc_sim1(k9_cqc_lang) = np__0 ).
fof(t24_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> k12_cqc_sim1(k10_cqc_lang(A)) = k12_cqc_sim1(A) ) ).
fof(t25_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( r1_xreal_0(k12_cqc_sim1(A),k12_cqc_sim1(k11_cqc_lang(A,B)))
& r1_xreal_0(k12_cqc_sim1(B),k12_cqc_sim1(k11_cqc_lang(A,B))) ) ) ) ).
fof(d11_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> k14_cqc_sim1(A) = k9_cqc_sim1(A,k12_cqc_sim1(A),k13_cqc_sim1(k2_qc_lang1)) ) ).
fof(t26_cqc_sim1,axiom,
k14_cqc_sim1(k9_cqc_lang) = k9_cqc_lang ).
fof(t27_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_cqc_lang(B,A)
& m1_qc_lang1(B,A) )
=> ! [C] :
( m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(A))
=> k14_cqc_sim1(k8_cqc_lang(A,C,B)) = k8_cqc_lang(A,C,B) ) ) ) ).
fof(t28_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ( v2_qc_lang1(A)
=> k14_cqc_sim1(A) = A ) ) ).
fof(t29_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> k14_cqc_sim1(k10_cqc_lang(A)) = k10_cqc_lang(k14_cqc_sim1(A)) ) ).
fof(t30_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( ( v3_qc_lang1(A)
& B = k17_qc_lang1(A) )
=> k14_cqc_sim1(A) = k10_cqc_lang(k14_cqc_sim1(B)) ) ) ) ).
fof(d12_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k4_zfmisc_1(k7_cqc_lang,k5_numbers,k5_finsub_1(k2_qc_lang1),k1_fraenkel(k2_qc_lang1,k2_qc_lang1))))
=> ( r1_cqc_sim1(A,B)
<=> ( r2_hidden(k4_mcart_1(A,k12_cqc_sim1(A),k1_setwiseo(k2_qc_lang1),k13_cqc_sim1(k2_qc_lang1)),B)
& ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m1_subset_1(E,k5_finsub_1(k2_qc_lang1))
=> ! [F] :
( m2_fraenkel(F,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1))
=> ( r2_hidden(k4_mcart_1(k10_cqc_lang(C),D,E,F),B)
=> r2_hidden(k4_mcart_1(C,D,E,F),B) ) ) ) ) )
& ! [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_numbers,k5_numbers)
=> ! [F] :
( m1_subset_1(F,k5_finsub_1(k2_qc_lang1))
=> ! [G] :
( m2_fraenkel(G,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1))
=> ( r2_hidden(k4_mcart_1(k11_cqc_lang(C,D),E,F,G),B)
=> ( r2_hidden(k4_mcart_1(C,E,F,G),B)
& r2_hidden(k4_mcart_1(D,k1_nat_1(E,k6_cqc_sim1(C)),F,G),B) ) ) ) ) ) ) )
& ! [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] :
( m1_subset_1(F,k5_finsub_1(k2_qc_lang1))
=> ! [G] :
( m2_fraenkel(G,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1))
=> ( r2_hidden(k4_mcart_1(k15_cqc_lang(D,C),E,F,G),B)
=> r2_hidden(k4_mcart_1(C,k1_nat_1(E,np__1),k2_xboole_0(F,k23_qc_lang1(D)),k1_funct_4(G,k2_funcop_1(k23_qc_lang1(D),k2_qc_lang3(E)))),B) ) ) ) ) ) ) ) ) ) ) ).
fof(d13_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k4_zfmisc_1(k7_cqc_lang,k5_numbers,k5_finsub_1(k2_qc_lang1),k1_fraenkel(k2_qc_lang1,k2_qc_lang1))))
=> ( B = k16_cqc_sim1(A)
<=> ( r1_cqc_sim1(A,B)
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k4_zfmisc_1(k7_cqc_lang,k5_numbers,k5_finsub_1(k2_qc_lang1),k1_fraenkel(k2_qc_lang1,k2_qc_lang1))))
=> ( r1_cqc_sim1(A,C)
=> r1_tarski(B,C) ) ) ) ) ) ) ).
fof(t31_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> r2_hidden(k4_mcart_1(A,k12_cqc_sim1(A),k1_setwiseo(k2_qc_lang1),k13_cqc_sim1(k2_qc_lang1)),k16_cqc_sim1(A)) ) ).
fof(t32_cqc_sim1,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_numbers,k5_numbers)
=> ! [D] :
( m1_subset_1(D,k5_finsub_1(k2_qc_lang1))
=> ! [E] :
( m2_fraenkel(E,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1))
=> ( r2_hidden(k4_mcart_1(k10_cqc_lang(B),C,D,E),k16_cqc_sim1(A))
=> r2_hidden(k4_mcart_1(B,C,D,E),k16_cqc_sim1(A)) ) ) ) ) ) ) ).
fof(t33_cqc_sim1,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,k8_qc_lang1,k7_cqc_lang)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m1_subset_1(E,k5_finsub_1(k2_qc_lang1))
=> ! [F] :
( m2_fraenkel(F,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1))
=> ( r2_hidden(k4_mcart_1(k11_cqc_lang(B,C),D,E,F),k16_cqc_sim1(A))
=> ( r2_hidden(k4_mcart_1(B,D,E,F),k16_cqc_sim1(A))
& r2_hidden(k4_mcart_1(C,k1_nat_1(D,k6_cqc_sim1(B)),E,F),k16_cqc_sim1(A)) ) ) ) ) ) ) ) ) ).
fof(t34_cqc_sim1,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] :
( m1_subset_1(E,k5_finsub_1(k2_qc_lang1))
=> ! [F] :
( m2_fraenkel(F,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1))
=> ( r2_hidden(k4_mcart_1(k15_cqc_lang(C,B),D,E,F),k16_cqc_sim1(A))
=> r2_hidden(k4_mcart_1(B,k1_nat_1(D,np__1),k5_setwiseo(k2_qc_lang1,E,k15_cqc_sim1(k2_qc_lang1,C)),k1_funct_4(F,k2_funcop_1(k15_cqc_sim1(k2_qc_lang1,C),k2_qc_lang3(D)))),k16_cqc_sim1(A)) ) ) ) ) ) ) ) ).
fof(t35_cqc_sim1,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_numbers,k5_numbers)
=> ! [D] :
( m2_fraenkel(D,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1))
=> ! [E] :
( m1_subset_1(E,k5_finsub_1(k2_qc_lang1))
=> ~ ( r2_hidden(k4_mcart_1(A,C,E,D),k16_cqc_sim1(B))
& k4_mcart_1(A,C,E,D) != k4_mcart_1(B,k12_cqc_sim1(B),k1_setwiseo(k2_qc_lang1),k13_cqc_sim1(k2_qc_lang1))
& ~ r2_hidden(k4_mcart_1(k10_cqc_lang(A),C,E,D),k16_cqc_sim1(B))
& ! [F] :
( m2_subset_1(F,k8_qc_lang1,k7_cqc_lang)
=> ~ r2_hidden(k4_mcart_1(k11_cqc_lang(A,F),C,E,D),k16_cqc_sim1(B)) )
& ! [F] :
( m2_subset_1(F,k8_qc_lang1,k7_cqc_lang)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ~ ( C = k1_nat_1(G,k6_cqc_sim1(F))
& r2_hidden(k4_mcart_1(k11_cqc_lang(F,A),G,E,D),k16_cqc_sim1(B)) ) ) )
& ! [F] :
( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ! [H] :
( m2_fraenkel(H,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1))
=> ~ ( k1_nat_1(G,np__1) = C
& k1_funct_4(H,k2_funcop_1(k15_cqc_sim1(k2_qc_lang1,F),k2_qc_lang3(G))) = D
& ( r2_hidden(k4_mcart_1(k15_cqc_lang(F,A),G,E,H),k16_cqc_sim1(B))
| r2_hidden(k4_mcart_1(k15_cqc_lang(F,A),G,k6_setwiseo(k2_qc_lang1,E,k15_cqc_sim1(k2_qc_lang1,F)),H),k16_cqc_sim1(B)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t36_cqc_sim1,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_numbers,k5_numbers)
=> ! [D] :
( m1_subset_1(D,k5_finsub_1(k2_qc_lang1))
=> ! [E] :
( m2_fraenkel(E,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1))
=> ( r2_hidden(k4_mcart_1(B,C,D,E),k16_cqc_sim1(A))
=> r2_qc_lang2(B,A) ) ) ) ) ) ) ).
fof(t37_cqc_sim1,axiom,
k16_cqc_sim1(k9_cqc_lang) = k1_tarski(k4_mcart_1(k9_cqc_lang,np__0,k1_setwiseo(k2_qc_lang1),k13_cqc_sim1(k2_qc_lang1))) ).
fof(t38_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_cqc_lang(B,A)
& m1_qc_lang1(B,A) )
=> ! [C] :
( m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(A))
=> k16_cqc_sim1(k8_cqc_lang(A,C,B)) = k1_tarski(k4_mcart_1(k8_cqc_lang(A,C,B),k12_cqc_sim1(k8_cqc_lang(A,C,B)),k1_setwiseo(k2_qc_lang1),k13_cqc_sim1(k2_qc_lang1))) ) ) ) ).
fof(t39_cqc_sim1,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_numbers,k5_numbers)
=> ! [D] :
( m1_subset_1(D,k5_finsub_1(k2_qc_lang1))
=> ! [E] :
( m2_fraenkel(E,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1))
=> ( r2_hidden(k4_mcart_1(B,C,D,E),k16_cqc_sim1(A))
=> r1_tarski(k24_qc_lang1(B),k2_xboole_0(k24_qc_lang1(A),D)) ) ) ) ) ) ) ).
fof(t40_cqc_sim1,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_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_fraenkel(E,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1))
=> ! [F] :
( m1_subset_1(F,k5_finsub_1(k2_qc_lang1))
=> ~ ( r2_hidden(k4_mcart_1(A,C,F,E),k16_cqc_sim1(B))
& r2_hidden(k2_qc_lang3(D),k8_setwiseo(k2_qc_lang1,k2_qc_lang1,E,F))
& r1_xreal_0(C,D) ) ) ) ) ) ) ) ).
fof(t41_cqc_sim1,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_numbers,k5_numbers)
=> ! [D] :
( m2_fraenkel(D,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1))
=> ! [E] :
( m1_subset_1(E,k5_finsub_1(k2_qc_lang1))
=> ~ ( r2_hidden(k4_mcart_1(A,C,E,D),k16_cqc_sim1(B))
& r2_hidden(k2_qc_lang3(C),k8_setwiseo(k2_qc_lang1,k2_qc_lang1,D,E)) ) ) ) ) ) ) ).
fof(t42_cqc_sim1,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_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_fraenkel(E,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1))
=> ! [F] :
( m1_subset_1(F,k5_finsub_1(k2_qc_lang1))
=> ~ ( r2_hidden(k4_mcart_1(A,C,F,E),k16_cqc_sim1(B))
& r2_hidden(k2_qc_lang3(D),k2_funct_2(k2_qc_lang1,k2_qc_lang1,E,k24_qc_lang1(B)))
& r1_xreal_0(C,D) ) ) ) ) ) ) ) ).
fof(t43_cqc_sim1,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_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_fraenkel(E,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1))
=> ! [F] :
( m1_subset_1(F,k5_finsub_1(k2_qc_lang1))
=> ~ ( r2_hidden(k4_mcart_1(A,C,F,E),k16_cqc_sim1(B))
& r2_hidden(k2_qc_lang3(D),k2_funct_2(k2_qc_lang1,k2_qc_lang1,E,k24_qc_lang1(A)))
& r1_xreal_0(C,D) ) ) ) ) ) ) ) ).
fof(t44_cqc_sim1,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_numbers,k5_numbers)
=> ! [D] :
( m2_fraenkel(D,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1))
=> ! [E] :
( m1_subset_1(E,k5_finsub_1(k2_qc_lang1))
=> ~ ( r2_hidden(k4_mcart_1(A,C,E,D),k16_cqc_sim1(B))
& r2_hidden(k2_qc_lang3(C),k2_funct_2(k2_qc_lang1,k2_qc_lang1,D,k24_qc_lang1(A))) ) ) ) ) ) ) ).
fof(t45_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> k24_qc_lang1(A) = k24_qc_lang1(k14_cqc_sim1(A)) ) ).
fof(t46_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> k12_cqc_sim1(A) = k12_cqc_sim1(k14_cqc_sim1(A)) ) ).
fof(d14_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( r2_cqc_sim1(A,B)
<=> k14_cqc_sim1(A) = k14_cqc_sim1(B) ) ) ) ).
fof(t47_cqc_sim1,axiom,
$true ).
fof(t48_cqc_sim1,axiom,
$true ).
fof(t49_cqc_sim1,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,k8_qc_lang1,k7_cqc_lang)
=> ( ( r2_cqc_sim1(A,B)
& r2_cqc_sim1(B,C) )
=> r2_cqc_sim1(A,C) ) ) ) ) ).
fof(s1_cqc_sim1,axiom,
? [A] :
( v1_funct_1(A)
& v1_funct_2(A,k8_qc_lang1,f1_s1_cqc_sim1)
& m2_relset_1(A,k8_qc_lang1,f1_s1_cqc_sim1)
& k8_funct_2(k8_qc_lang1,f1_s1_cqc_sim1,A,k9_cqc_lang) = f2_s1_cqc_sim1
& ! [B] :
( m1_subset_1(B,k8_qc_lang1)
=> ( ( v2_qc_lang1(B)
=> k8_funct_2(k8_qc_lang1,f1_s1_cqc_sim1,A,B) = f3_s1_cqc_sim1(B) )
& ( v3_qc_lang1(B)
=> k8_funct_2(k8_qc_lang1,f1_s1_cqc_sim1,A,B) = f4_s1_cqc_sim1(k8_funct_2(k8_qc_lang1,f1_s1_cqc_sim1,A,k17_qc_lang1(B)),B) )
& ( v4_qc_lang1(B)
=> k8_funct_2(k8_qc_lang1,f1_s1_cqc_sim1,A,B) = f5_s1_cqc_sim1(k8_funct_2(k8_qc_lang1,f1_s1_cqc_sim1,A,k18_qc_lang1(B)),k8_funct_2(k8_qc_lang1,f1_s1_cqc_sim1,A,k19_qc_lang1(B)),B) )
& ( v5_qc_lang1(B)
=> k8_funct_2(k8_qc_lang1,f1_s1_cqc_sim1,A,B) = f6_s1_cqc_sim1(k8_funct_2(k8_qc_lang1,f1_s1_cqc_sim1,A,k21_qc_lang1(B)),B) ) ) ) ) ).
fof(s2_cqc_sim1,axiom,
? [A] :
( v1_funct_1(A)
& v1_funct_2(A,k7_cqc_lang,k1_fraenkel(f1_s2_cqc_sim1,f2_s2_cqc_sim1))
& m2_relset_1(A,k7_cqc_lang,k1_fraenkel(f1_s2_cqc_sim1,f2_s2_cqc_sim1))
& k8_funct_2(k7_cqc_lang,k1_fraenkel(f1_s2_cqc_sim1,f2_s2_cqc_sim1),A,k9_cqc_lang) = f3_s2_cqc_sim1
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_cqc_lang(C,B)
& m1_qc_lang1(C,B) )
=> ! [D] :
( m2_subset_1(D,k5_qc_lang1,k7_qc_lang1(B))
=> k8_funct_2(k7_cqc_lang,k1_fraenkel(f1_s2_cqc_sim1,f2_s2_cqc_sim1),A,k8_cqc_lang(B,D,C)) = f4_s2_cqc_sim1(B,D,C) ) ) )
& ! [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)
=> ( k8_funct_2(k7_cqc_lang,k1_fraenkel(f1_s2_cqc_sim1,f2_s2_cqc_sim1),A,k10_cqc_lang(B)) = f5_s2_cqc_sim1(k8_funct_2(k7_cqc_lang,k1_fraenkel(f1_s2_cqc_sim1,f2_s2_cqc_sim1),A,B),B)
& k8_funct_2(k7_cqc_lang,k1_fraenkel(f1_s2_cqc_sim1,f2_s2_cqc_sim1),A,k11_cqc_lang(B,C)) = f6_s2_cqc_sim1(k8_funct_2(k7_cqc_lang,k1_fraenkel(f1_s2_cqc_sim1,f2_s2_cqc_sim1),A,B),k8_funct_2(k7_cqc_lang,k1_fraenkel(f1_s2_cqc_sim1,f2_s2_cqc_sim1),A,C),B,C)
& k8_funct_2(k7_cqc_lang,k1_fraenkel(f1_s2_cqc_sim1,f2_s2_cqc_sim1),A,k15_cqc_lang(D,B)) = f7_s2_cqc_sim1(D,k8_funct_2(k7_cqc_lang,k1_fraenkel(f1_s2_cqc_sim1,f2_s2_cqc_sim1),A,B),B) ) ) ) ) ) ).
fof(s3_cqc_sim1,axiom,
( ( k8_funct_2(k7_cqc_lang,k1_fraenkel(f1_s3_cqc_sim1,f2_s3_cqc_sim1),f3_s3_cqc_sim1,k9_cqc_lang) = f5_s3_cqc_sim1
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_cqc_lang(B,A)
& m1_qc_lang1(B,A) )
=> ! [C] :
( m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(A))
=> k8_funct_2(k7_cqc_lang,k1_fraenkel(f1_s3_cqc_sim1,f2_s3_cqc_sim1),f3_s3_cqc_sim1,k8_cqc_lang(A,C,B)) = f6_s3_cqc_sim1(A,C,B) ) ) )
& ! [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)
=> ( k8_funct_2(k7_cqc_lang,k1_fraenkel(f1_s3_cqc_sim1,f2_s3_cqc_sim1),f3_s3_cqc_sim1,k10_cqc_lang(A)) = f7_s3_cqc_sim1(k8_funct_2(k7_cqc_lang,k1_fraenkel(f1_s3_cqc_sim1,f2_s3_cqc_sim1),f3_s3_cqc_sim1,A),A)
& k8_funct_2(k7_cqc_lang,k1_fraenkel(f1_s3_cqc_sim1,f2_s3_cqc_sim1),f3_s3_cqc_sim1,k11_cqc_lang(A,B)) = f8_s3_cqc_sim1(k8_funct_2(k7_cqc_lang,k1_fraenkel(f1_s3_cqc_sim1,f2_s3_cqc_sim1),f3_s3_cqc_sim1,A),k8_funct_2(k7_cqc_lang,k1_fraenkel(f1_s3_cqc_sim1,f2_s3_cqc_sim1),f3_s3_cqc_sim1,B),A,B)
& k8_funct_2(k7_cqc_lang,k1_fraenkel(f1_s3_cqc_sim1,f2_s3_cqc_sim1),f3_s3_cqc_sim1,k15_cqc_lang(C,A)) = f9_s3_cqc_sim1(C,k8_funct_2(k7_cqc_lang,k1_fraenkel(f1_s3_cqc_sim1,f2_s3_cqc_sim1),f3_s3_cqc_sim1,A),A) ) ) ) )
& k8_funct_2(k7_cqc_lang,k1_fraenkel(f1_s3_cqc_sim1,f2_s3_cqc_sim1),f4_s3_cqc_sim1,k9_cqc_lang) = f5_s3_cqc_sim1
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_cqc_lang(B,A)
& m1_qc_lang1(B,A) )
=> ! [C] :
( m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(A))
=> k8_funct_2(k7_cqc_lang,k1_fraenkel(f1_s3_cqc_sim1,f2_s3_cqc_sim1),f4_s3_cqc_sim1,k8_cqc_lang(A,C,B)) = f6_s3_cqc_sim1(A,C,B) ) ) )
& ! [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)
=> ( k8_funct_2(k7_cqc_lang,k1_fraenkel(f1_s3_cqc_sim1,f2_s3_cqc_sim1),f4_s3_cqc_sim1,k10_cqc_lang(A)) = f7_s3_cqc_sim1(k8_funct_2(k7_cqc_lang,k1_fraenkel(f1_s3_cqc_sim1,f2_s3_cqc_sim1),f4_s3_cqc_sim1,A),A)
& k8_funct_2(k7_cqc_lang,k1_fraenkel(f1_s3_cqc_sim1,f2_s3_cqc_sim1),f4_s3_cqc_sim1,k11_cqc_lang(A,B)) = f8_s3_cqc_sim1(k8_funct_2(k7_cqc_lang,k1_fraenkel(f1_s3_cqc_sim1,f2_s3_cqc_sim1),f4_s3_cqc_sim1,A),k8_funct_2(k7_cqc_lang,k1_fraenkel(f1_s3_cqc_sim1,f2_s3_cqc_sim1),f4_s3_cqc_sim1,B),A,B)
& k8_funct_2(k7_cqc_lang,k1_fraenkel(f1_s3_cqc_sim1,f2_s3_cqc_sim1),f4_s3_cqc_sim1,k15_cqc_lang(C,A)) = f9_s3_cqc_sim1(C,k8_funct_2(k7_cqc_lang,k1_fraenkel(f1_s3_cqc_sim1,f2_s3_cqc_sim1),f4_s3_cqc_sim1,A),A) ) ) ) ) )
=> f3_s3_cqc_sim1 = f4_s3_cqc_sim1 ) ).
fof(s4_cqc_sim1,axiom,
( ( v1_finset_1(f2_s4_cqc_sim1)
& f2_s4_cqc_sim1 != k1_xboole_0
& r1_tarski(f2_s4_cqc_sim1,f1_s4_cqc_sim1)
& ! [A] :
( m1_subset_1(A,f1_s4_cqc_sim1)
=> ! [B] :
( m1_subset_1(B,f1_s4_cqc_sim1)
=> ( p1_s4_cqc_sim1(A,B)
| p1_s4_cqc_sim1(B,A) ) ) )
& ! [A] :
( m1_subset_1(A,f1_s4_cqc_sim1)
=> ! [B] :
( m1_subset_1(B,f1_s4_cqc_sim1)
=> ! [C] :
( m1_subset_1(C,f1_s4_cqc_sim1)
=> ( ( p1_s4_cqc_sim1(A,B)
& p1_s4_cqc_sim1(B,C) )
=> p1_s4_cqc_sim1(A,C) ) ) ) ) )
=> ? [A] :
( m1_subset_1(A,f1_s4_cqc_sim1)
& r2_hidden(A,f2_s4_cqc_sim1)
& ! [B] :
( m1_subset_1(B,f1_s4_cqc_sim1)
=> ( r2_hidden(B,f2_s4_cqc_sim1)
=> p1_s4_cqc_sim1(A,B) ) ) ) ) ).
fof(s5_cqc_sim1,axiom,
( ( p1_s5_cqc_sim1(k9_cqc_lang)
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_cqc_lang(B,A)
& m1_qc_lang1(B,A) )
=> ! [C] :
( m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(A))
=> p1_s5_cqc_sim1(k8_cqc_lang(A,C,B)) ) ) )
& ! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ( p1_s5_cqc_sim1(A)
=> p1_s5_cqc_sim1(k10_cqc_lang(A)) ) )
& ! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( ( p1_s5_cqc_sim1(A)
& p1_s5_cqc_sim1(B) )
=> p1_s5_cqc_sim1(k11_cqc_lang(A,B)) ) ) )
& ! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ( p1_s5_cqc_sim1(A)
=> p1_s5_cqc_sim1(k15_cqc_lang(B,A)) ) ) ) )
=> ! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> p1_s5_cqc_sim1(A) ) ) ).
fof(s6_cqc_sim1,axiom,
( ( p1_s6_cqc_sim1(f1_s6_cqc_sim1,k12_cqc_sim1(f1_s6_cqc_sim1),k1_setwiseo(k2_qc_lang1),k13_cqc_sim1(k2_qc_lang1))
& ! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k5_finsub_1(k2_qc_lang1))
=> ! [D] :
( m2_fraenkel(D,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1))
=> ( ( r2_hidden(k4_mcart_1(k10_cqc_lang(A),B,C,D),k16_cqc_sim1(f1_s6_cqc_sim1))
& p1_s6_cqc_sim1(k10_cqc_lang(A),B,C,D) )
=> p1_s6_cqc_sim1(A,B,C,D) ) ) ) ) )
& ! [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_numbers,k5_numbers)
=> ! [D] :
( m1_subset_1(D,k5_finsub_1(k2_qc_lang1))
=> ! [E] :
( m2_fraenkel(E,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1))
=> ( ( r2_hidden(k4_mcart_1(k11_cqc_lang(A,B),C,D,E),k16_cqc_sim1(f1_s6_cqc_sim1))
& p1_s6_cqc_sim1(k11_cqc_lang(A,B),C,D,E) )
=> ( p1_s6_cqc_sim1(A,C,D,E)
& p1_s6_cqc_sim1(B,k1_nat_1(C,k6_cqc_sim1(A)),D,E) ) ) ) ) ) ) )
& ! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m1_subset_1(D,k5_finsub_1(k2_qc_lang1))
=> ! [E] :
( m2_fraenkel(E,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1))
=> ( ( r2_hidden(k4_mcart_1(k15_cqc_lang(B,A),C,D,E),k16_cqc_sim1(f1_s6_cqc_sim1))
& p1_s6_cqc_sim1(k15_cqc_lang(B,A),C,D,E) )
=> p1_s6_cqc_sim1(A,k1_nat_1(C,np__1),k5_setwiseo(k2_qc_lang1,D,k15_cqc_sim1(k2_qc_lang1,B)),k1_funct_4(E,k2_funcop_1(k15_cqc_sim1(k2_qc_lang1,B),k2_qc_lang3(C)))) ) ) ) ) ) ) )
=> ! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k5_finsub_1(k2_qc_lang1))
=> ! [D] :
( m2_fraenkel(D,k2_qc_lang1,k2_qc_lang1,k1_fraenkel(k2_qc_lang1,k2_qc_lang1))
=> ( r2_hidden(k4_mcart_1(A,B,C,D),k16_cqc_sim1(f1_s6_cqc_sim1))
=> p1_s6_cqc_sim1(A,B,C,D) ) ) ) ) ) ) ).
fof(symmetry_r2_cqc_sim1,axiom,
! [A,B] :
( ( m1_subset_1(A,k7_cqc_lang)
& m1_subset_1(B,k7_cqc_lang) )
=> ( r2_cqc_sim1(A,B)
=> r2_cqc_sim1(B,A) ) ) ).
fof(reflexivity_r2_cqc_sim1,axiom,
! [A,B] :
( ( m1_subset_1(A,k7_cqc_lang)
& m1_subset_1(B,k7_cqc_lang) )
=> r2_cqc_sim1(A,A) ) ).
fof(dt_k1_cqc_sim1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& v1_funct_2(B,A,k7_cqc_lang)
& m1_relset_1(B,A,k7_cqc_lang) )
=> m2_fraenkel(k1_cqc_sim1(A,B),A,k7_cqc_lang,k1_fraenkel(A,k7_cqc_lang)) ) ).
fof(dt_k2_cqc_sim1,axiom,
! [A,B,C] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang)
& m1_relset_1(A,k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang)
& v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang)
& m1_relset_1(B,k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang)
& m1_subset_1(C,k5_numbers) )
=> m2_fraenkel(k2_cqc_sim1(A,B,C),k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,k1_fraenkel(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang)) ) ).
fof(dt_k3_cqc_sim1,axiom,
! [A,B] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang)
& m1_relset_1(A,k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang)
& m1_subset_1(B,k2_qc_lang1) )
=> m2_fraenkel(k3_cqc_sim1(A,B),k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,k1_fraenkel(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang)) ) ).
fof(dt_k4_cqc_sim1,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& v1_cqc_lang(B,A)
& m1_qc_lang1(B,A)
& m1_subset_1(C,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)) )
=> ( v1_cqc_lang(k4_cqc_sim1(A,B,C),A)
& m1_qc_lang1(k4_cqc_sim1(A,B,C),A) ) ) ).
fof(redefinition_k4_cqc_sim1,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& v1_cqc_lang(B,A)
& m1_qc_lang1(B,A)
& m1_subset_1(C,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)) )
=> k4_cqc_sim1(A,B,C) = k5_relat_1(B,C) ) ).
fof(dt_k5_cqc_sim1,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_fraenkel(k5_cqc_sim1(A,B,C),k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,k1_fraenkel(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang)) ) ).
fof(dt_k6_cqc_sim1,axiom,
! [A] :
( m1_subset_1(A,k7_cqc_lang)
=> m2_subset_1(k6_cqc_sim1(A),k1_numbers,k5_numbers) ) ).
fof(dt_k7_cqc_sim1,axiom,
! [A,B] :
( ( v1_funct_1(A)
& v1_funct_2(A,k7_cqc_lang,k1_fraenkel(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang))
& m1_relset_1(A,k7_cqc_lang,k1_fraenkel(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang))
& m1_subset_1(B,k7_cqc_lang) )
=> m2_fraenkel(k7_cqc_sim1(A,B),k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang,k1_fraenkel(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang)) ) ).
fof(redefinition_k7_cqc_sim1,axiom,
! [A,B] :
( ( v1_funct_1(A)
& v1_funct_2(A,k7_cqc_lang,k1_fraenkel(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang))
& m1_relset_1(A,k7_cqc_lang,k1_fraenkel(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang))
& m1_subset_1(B,k7_cqc_lang) )
=> k7_cqc_sim1(A,B) = k1_funct_1(A,B) ) ).
fof(dt_k8_cqc_sim1,axiom,
( v1_funct_1(k8_cqc_sim1)
& v1_funct_2(k8_cqc_sim1,k7_cqc_lang,k1_fraenkel(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang))
& m2_relset_1(k8_cqc_sim1,k7_cqc_lang,k1_fraenkel(k2_zfmisc_1(k5_numbers,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)),k7_cqc_lang)) ) ).
fof(dt_k9_cqc_sim1,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k7_cqc_lang)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,k1_fraenkel(k2_qc_lang1,k2_qc_lang1)) )
=> m2_subset_1(k9_cqc_sim1(A,B,C),k8_qc_lang1,k7_cqc_lang) ) ).
fof(dt_k10_cqc_sim1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(k5_numbers)) )
=> m2_subset_1(k10_cqc_sim1(A),k1_numbers,k5_numbers) ) ).
fof(dt_k11_cqc_sim1,axiom,
! [A] :
( m1_subset_1(A,k7_cqc_lang)
=> m1_subset_1(k11_cqc_sim1(A),k1_zfmisc_1(k5_numbers)) ) ).
fof(dt_k12_cqc_sim1,axiom,
! [A] :
( m1_subset_1(A,k7_cqc_lang)
=> m2_subset_1(k12_cqc_sim1(A),k1_numbers,k5_numbers) ) ).
fof(dt_k13_cqc_sim1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> m2_fraenkel(k13_cqc_sim1(A),A,A,k1_fraenkel(A,A)) ) ).
fof(redefinition_k13_cqc_sim1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> k13_cqc_sim1(A) = k6_relat_1(A) ) ).
fof(dt_k14_cqc_sim1,axiom,
! [A] :
( m1_subset_1(A,k7_cqc_lang)
=> m2_subset_1(k14_cqc_sim1(A),k8_qc_lang1,k7_cqc_lang) ) ).
fof(dt_k15_cqc_sim1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A) )
=> m1_subset_1(k15_cqc_sim1(A,B),k5_finsub_1(A)) ) ).
fof(redefinition_k15_cqc_sim1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,A) )
=> k15_cqc_sim1(A,B) = k1_tarski(B) ) ).
fof(dt_k16_cqc_sim1,axiom,
! [A] :
( m1_subset_1(A,k7_cqc_lang)
=> m1_subset_1(k16_cqc_sim1(A),k1_zfmisc_1(k4_zfmisc_1(k7_cqc_lang,k5_numbers,k5_finsub_1(k2_qc_lang1),k1_fraenkel(k2_qc_lang1,k2_qc_lang1)))) ) ).
fof(t9_cqc_sim1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> k2_relat_1(A) = a_1_0_cqc_sim1(A) ) ).
fof(d9_cqc_sim1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> k11_cqc_sim1(A) = a_1_1_cqc_sim1(A) ) ).
fof(fraenkel_a_1_0_cqc_sim1,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( r2_hidden(A,a_1_0_cqc_sim1(B))
<=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& A = k1_funct_1(B,C)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(B)) ) ) ) ).
fof(fraenkel_a_1_1_cqc_sim1,axiom,
! [A,B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( r2_hidden(A,a_1_1_cqc_sim1(B))
<=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& A = C
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(C,D)
& r2_hidden(k2_qc_lang3(D),k24_qc_lang1(B)) ) ) ) ) ) ).
%------------------------------------------------------------------------------