SET007 Axioms: SET007+104.ax
%------------------------------------------------------------------------------
% File : SET007+104 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Interpretation and Satisfiability in the First Order Logic
% 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 : valuat_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 102 ( 15 unt; 0 def)
% Number of atoms : 587 ( 90 equ)
% Maximal formula atoms : 21 ( 5 avg)
% Number of connectives : 578 ( 93 ~; 5 |; 124 &)
% ( 25 <=>; 331 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 9 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 1 prp; 0-4 aty)
% Number of functors : 57 ( 57 usr; 17 con; 0-4 aty)
% Number of variables : 350 ( 344 !; 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_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( ~ v1_xboole_0(k1_valuat_1(A))
& v1_fraenkel(k1_valuat_1(A)) ) ) ).
fof(rc1_valuat_1,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& v1_valuat_1(A) ) ).
fof(fc2_valuat_1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_valuat_1(A) )
=> v2_margrel1(k1_funct_1(A,B)) ) ).
fof(cc1_valuat_1,axiom,
! [A,B] :
( m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
=> v1_valuat_1(B) ) ).
fof(fc3_valuat_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_valuat_1(A) )
=> ( v1_relat_1(k3_valuat_1(A))
& v1_funct_1(k3_valuat_1(A))
& v1_valuat_1(k3_valuat_1(A)) ) ) ).
fof(fc4_valuat_1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_valuat_1(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_valuat_1(B) )
=> ( v1_relat_1(k4_valuat_1(A,B))
& v1_funct_1(k4_valuat_1(A,B))
& v1_valuat_1(k4_valuat_1(A,B)) ) ) ).
fof(d1_valuat_1,axiom,
! [A] : k1_valuat_1(A) = k1_funct_2(k2_qc_lang1,A) ).
fof(t1_valuat_1,axiom,
$true ).
fof(t2_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,k1_valuat_1(A))
=> ( v1_funct_1(B)
& v1_funct_2(B,k2_qc_lang1,A)
& m2_relset_1(B,k2_qc_lang1,A) ) ) ) ).
fof(d2_valuat_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v1_valuat_1(A)
<=> r1_tarski(k2_relat_1(A),k6_margrel1) ) ) ).
fof(d3_valuat_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_valuat_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( B = k3_valuat_1(A)
<=> ( k1_relat_1(B) = k1_relat_1(A)
& ! [C] :
( r2_hidden(C,k1_relat_1(A))
=> k1_funct_1(B,C) = k9_margrel1(k1_funct_1(A,C)) ) ) ) ) ) ).
fof(d4_valuat_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_valuat_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_valuat_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( C = k4_valuat_1(A,B)
<=> ( k1_relat_1(C) = k3_xboole_0(k1_relat_1(A),k1_relat_1(B))
& ! [D] :
( r2_hidden(D,k1_relat_1(C))
=> k1_funct_1(C,D) = k10_margrel1(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ) ) ).
fof(d5_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ( C = k5_valuat_1(A,B)
<=> ! [D] :
( m1_subset_1(D,A)
=> k8_funct_2(A,k6_margrel1,C,D) = k11_margrel1(k8_funct_2(A,k6_margrel1,B,D)) ) ) ) ) ) ).
fof(d6_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ( D = k6_valuat_1(A,B,C)
<=> ! [E] :
( m1_subset_1(E,A)
=> k8_funct_2(A,k6_margrel1,D,E) = k12_margrel1(k8_funct_2(A,k6_margrel1,B,E),k8_funct_2(A,k6_margrel1,C,E)) ) ) ) ) ) ) ).
fof(t3_valuat_1,axiom,
$true ).
fof(t4_valuat_1,axiom,
$true ).
fof(t5_valuat_1,axiom,
$true ).
fof(t6_valuat_1,axiom,
$true ).
fof(t7_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_fraenkel(C,k2_qc_lang1,A,k2_valuat_1(A))
=> ! [D] :
( m2_fraenkel(D,k2_valuat_1(A),k6_margrel1,k1_fraenkel(k2_valuat_1(A),k6_margrel1))
=> ( k8_funct_2(k2_valuat_1(A),k6_margrel1,k7_valuat_1(A,B,D),C) = k7_margrel1
<=> ? [E] :
( m2_fraenkel(E,k2_qc_lang1,A,k2_valuat_1(A))
& k8_funct_2(k2_valuat_1(A),k6_margrel1,D,E) = k7_margrel1
& ! [F] :
( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
=> ( B != F
=> k8_funct_2(k2_qc_lang1,A,E,F) = k8_funct_2(k2_qc_lang1,A,C,F) ) ) ) ) ) ) ) ) ).
fof(t8_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_fraenkel(C,k2_qc_lang1,A,k2_valuat_1(A))
=> ! [D] :
( m2_fraenkel(D,k2_valuat_1(A),k6_margrel1,k1_fraenkel(k2_valuat_1(A),k6_margrel1))
=> ( k8_funct_2(k2_valuat_1(A),k6_margrel1,k7_valuat_1(A,B,D),C) = k8_margrel1
<=> ! [E] :
( m2_fraenkel(E,k2_qc_lang1,A,k2_valuat_1(A))
=> ( ! [F] :
( m2_subset_1(F,k1_qc_lang1,k2_qc_lang1)
=> ( B != F
=> k8_funct_2(k2_qc_lang1,A,E,F) = k8_funct_2(k2_qc_lang1,A,C,F) ) )
=> k8_funct_2(k2_valuat_1(A),k6_margrel1,D,E) = k8_margrel1 ) ) ) ) ) ) ) ).
fof(d8_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_cqc_lang(C,B)
& m1_qc_lang1(C,B) )
=> ! [D] :
( m2_fraenkel(D,k2_qc_lang1,A,k2_valuat_1(A))
=> ! [E] :
( m2_finseq_1(E,A)
=> ( E = k8_valuat_1(A,B,C,D)
<=> ( k3_finseq_1(E) = B
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,F)
& r1_xreal_0(F,B) )
=> k1_funct_1(E,F) = k1_funct_1(D,k1_funct_1(C,F)) ) ) ) ) ) ) ) ) ) ).
fof(d9_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_cqc_lang(C,B)
& m1_qc_lang1(C,B) )
=> ! [D] :
( m1_subset_1(D,k3_margrel1(A))
=> ! [E] :
( m2_fraenkel(E,k2_valuat_1(A),k6_margrel1,k1_fraenkel(k2_valuat_1(A),k6_margrel1))
=> ( E = k9_valuat_1(A,B,C,D)
<=> ! [F] :
( m2_fraenkel(F,k2_qc_lang1,A,k2_valuat_1(A))
=> ( ( r2_hidden(k8_valuat_1(A,B,C,F),D)
=> k8_funct_2(k2_valuat_1(A),k6_margrel1,E,F) = k8_margrel1 )
& ( ~ r2_hidden(k8_valuat_1(A,B,C,F),D)
=> k8_funct_2(k2_valuat_1(A),k6_margrel1,E,F) = k7_margrel1 ) ) ) ) ) ) ) ) ) ).
fof(d10_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_qc_lang1,k3_margrel1(A))
& m2_relset_1(B,k5_qc_lang1,k3_margrel1(A)) )
=> ( m1_valuat_1(B,A)
<=> ! [C] :
( m1_subset_1(C,k5_qc_lang1)
=> ! [D] :
( m1_subset_1(D,k3_margrel1(A))
=> ~ ( r1_margrel1(A,k8_funct_2(k5_qc_lang1,k3_margrel1(A),B,C),D)
& ~ r1_margrel1(A,D,k4_margrel1(A))
& k6_qc_lang1(C) != k5_margrel1(A,D) ) ) ) ) ) ) ).
fof(d11_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_valuat_1(B,A)
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ! [D] :
( m2_fraenkel(D,k2_valuat_1(A),k6_margrel1,k1_fraenkel(k2_valuat_1(A),k6_margrel1))
=> ( D = k12_valuat_1(A,B,C)
<=> ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,k7_cqc_lang,k1_fraenkel(k2_valuat_1(A),k6_margrel1))
& m2_relset_1(E,k7_cqc_lang,k1_fraenkel(k2_valuat_1(A),k6_margrel1))
& D = k10_valuat_1(A,E,C)
& k10_valuat_1(A,E,k9_cqc_lang) = k1_margrel1(k6_margrel1,k2_valuat_1(A),k8_margrel1)
& ! [F] :
( m2_subset_1(F,k8_qc_lang1,k7_cqc_lang)
=> ! [G] :
( m2_subset_1(G,k8_qc_lang1,k7_cqc_lang)
=> ! [H] :
( m2_subset_1(H,k1_qc_lang1,k2_qc_lang1)
=> ! [I] :
( m2_subset_1(I,k1_numbers,k5_numbers)
=> ! [J] :
( ( v1_cqc_lang(J,I)
& m1_qc_lang1(J,I) )
=> ! [K] :
( m2_subset_1(K,k5_qc_lang1,k7_qc_lang1(I))
=> ( k10_valuat_1(A,E,k8_cqc_lang(I,K,J)) = k9_valuat_1(A,I,J,k11_valuat_1(A,I,B,K))
& k10_valuat_1(A,E,k10_cqc_lang(F)) = k5_valuat_1(k2_valuat_1(A),k10_valuat_1(A,E,F))
& k10_valuat_1(A,E,k11_cqc_lang(F,G)) = k6_valuat_1(k2_valuat_1(A),k10_valuat_1(A,E,F),k10_valuat_1(A,E,G))
& k10_valuat_1(A,E,k15_cqc_lang(H,F)) = k7_valuat_1(A,H,k10_valuat_1(A,E,F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t9_valuat_1,axiom,
$true ).
fof(t10_valuat_1,axiom,
$true ).
fof(t11_valuat_1,axiom,
$true ).
fof(t12_valuat_1,axiom,
$true ).
fof(t13_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_valuat_1(B,A)
=> k12_valuat_1(A,B,k9_cqc_lang) = k1_margrel1(k6_margrel1,k2_valuat_1(A),k8_margrel1) ) ) ).
fof(t14_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
=> ! [C] :
( m1_valuat_1(C,A)
=> k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,C,k9_cqc_lang),B) = k8_margrel1 ) ) ) ).
fof(t15_valuat_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_cqc_lang(C,A)
& m1_qc_lang1(C,A) )
=> ! [D] :
( m1_valuat_1(D,B)
=> ! [E] :
( m2_subset_1(E,k5_qc_lang1,k7_qc_lang1(A))
=> k12_valuat_1(B,D,k8_cqc_lang(A,E,C)) = k9_valuat_1(B,A,C,k11_valuat_1(B,A,D,E)) ) ) ) ) ) ).
fof(t16_valuat_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m2_fraenkel(C,k2_qc_lang1,B,k2_valuat_1(B))
=> ! [D] :
( ( v1_cqc_lang(D,A)
& m1_qc_lang1(D,A) )
=> ! [E] :
( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
=> ! [F] :
( m1_valuat_1(F,B)
=> ! [G] :
( m2_subset_1(G,k5_qc_lang1,k7_qc_lang1(A))
=> ! [H] :
( m1_subset_1(H,k3_margrel1(B))
=> ( ( E = k8_cqc_lang(A,G,D)
& r1_margrel1(B,H,k11_valuat_1(B,A,F,G)) )
=> ( r2_hidden(k8_valuat_1(B,A,D,C),H)
<=> k8_funct_2(k2_valuat_1(B),k6_margrel1,k12_valuat_1(B,F,E),C) = k8_margrel1 ) ) ) ) ) ) ) ) ) ) ).
fof(t17_valuat_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m2_fraenkel(C,k2_qc_lang1,B,k2_valuat_1(B))
=> ! [D] :
( ( v1_cqc_lang(D,A)
& m1_qc_lang1(D,A) )
=> ! [E] :
( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
=> ! [F] :
( m1_valuat_1(F,B)
=> ! [G] :
( m2_subset_1(G,k5_qc_lang1,k7_qc_lang1(A))
=> ! [H] :
( m1_subset_1(H,k3_margrel1(B))
=> ( ( E = k8_cqc_lang(A,G,D)
& r1_margrel1(B,H,k11_valuat_1(B,A,F,G)) )
=> ( ~ r2_hidden(k8_valuat_1(B,A,D,C),H)
<=> k8_funct_2(k2_valuat_1(B),k6_margrel1,k12_valuat_1(B,F,E),C) = k7_margrel1 ) ) ) ) ) ) ) ) ) ) ).
fof(t18_valuat_1,axiom,
$true ).
fof(t19_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m1_valuat_1(C,A)
=> k12_valuat_1(A,C,k10_cqc_lang(B)) = k5_valuat_1(k2_valuat_1(A),k12_valuat_1(A,C,B)) ) ) ) ).
fof(t20_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ! [D] :
( m1_valuat_1(D,A)
=> k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,D,k10_cqc_lang(C)),B) = k11_margrel1(k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,D,C),B)) ) ) ) ) ).
fof(t21_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ! [D] :
( m1_valuat_1(D,A)
=> k12_valuat_1(A,D,k11_cqc_lang(B,C)) = k6_valuat_1(k2_valuat_1(A),k12_valuat_1(A,D,B),k12_valuat_1(A,D,C)) ) ) ) ) ).
fof(t22_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ! [E] :
( m1_valuat_1(E,A)
=> k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,E,k11_cqc_lang(C,D)),B) = k12_margrel1(k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,E,C),B),k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,E,D),B)) ) ) ) ) ) ).
fof(t23_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ! [D] :
( m1_valuat_1(D,A)
=> k12_valuat_1(A,D,k15_cqc_lang(B,C)) = k7_valuat_1(A,B,k12_valuat_1(A,D,C)) ) ) ) ) ).
fof(t24_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ! [D] :
( m1_valuat_1(D,A)
=> k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,D,k11_cqc_lang(C,k10_cqc_lang(C))),B) = k7_margrel1 ) ) ) ) ).
fof(t25_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ! [D] :
( m1_valuat_1(D,A)
=> k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,D,k10_cqc_lang(k11_cqc_lang(C,k10_cqc_lang(C)))),B) = k8_margrel1 ) ) ) ) ).
fof(d12_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m1_valuat_1(C,A)
=> ! [D] :
( m2_fraenkel(D,k2_qc_lang1,A,k2_valuat_1(A))
=> ( r1_valuat_1(A,B,C,D)
<=> k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,C,B),D) = k8_margrel1 ) ) ) ) ) ).
fof(t26_valuat_1,axiom,
$true ).
fof(t27_valuat_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m2_fraenkel(C,k2_qc_lang1,B,k2_valuat_1(B))
=> ! [D] :
( ( v1_cqc_lang(D,A)
& m1_qc_lang1(D,A) )
=> ! [E] :
( m1_valuat_1(E,B)
=> ! [F] :
( m2_subset_1(F,k5_qc_lang1,k7_qc_lang1(A))
=> ( r1_valuat_1(B,k8_cqc_lang(A,F,D),E,C)
<=> k8_funct_2(k2_valuat_1(B),k6_margrel1,k9_valuat_1(B,A,D,k11_valuat_1(B,A,E,F)),C) = k8_margrel1 ) ) ) ) ) ) ) ).
fof(t28_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ! [D] :
( m1_valuat_1(D,A)
=> ( r1_valuat_1(A,k10_cqc_lang(C),D,B)
<=> ~ r1_valuat_1(A,C,D,B) ) ) ) ) ) ).
fof(t29_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ! [E] :
( m1_valuat_1(E,A)
=> ( r1_valuat_1(A,k11_cqc_lang(C,D),E,B)
<=> ( r1_valuat_1(A,C,E,B)
& r1_valuat_1(A,D,E,B) ) ) ) ) ) ) ) ).
fof(t30_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_fraenkel(C,k2_qc_lang1,A,k2_valuat_1(A))
=> ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ! [E] :
( m1_valuat_1(E,A)
=> ( r1_valuat_1(A,k15_cqc_lang(B,D),E,C)
<=> k8_funct_2(k2_valuat_1(A),k6_margrel1,k7_valuat_1(A,B,k12_valuat_1(A,E,D)),C) = k8_margrel1 ) ) ) ) ) ) ).
fof(t31_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_fraenkel(C,k2_qc_lang1,A,k2_valuat_1(A))
=> ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ! [E] :
( m1_valuat_1(E,A)
=> ( r1_valuat_1(A,k15_cqc_lang(B,D),E,C)
<=> ! [F] :
( m2_fraenkel(F,k2_qc_lang1,A,k2_valuat_1(A))
=> ( ! [G] :
( m2_subset_1(G,k1_qc_lang1,k2_qc_lang1)
=> ( B != G
=> k8_funct_2(k2_qc_lang1,A,F,G) = k8_funct_2(k2_qc_lang1,A,C,G) ) )
=> k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,E,D),F) = k8_margrel1 ) ) ) ) ) ) ) ) ).
fof(t32_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m1_valuat_1(C,A)
=> k12_valuat_1(A,C,k10_cqc_lang(k10_cqc_lang(B))) = k12_valuat_1(A,C,B) ) ) ) ).
fof(t33_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m1_valuat_1(C,A)
=> k12_valuat_1(A,C,k11_cqc_lang(B,B)) = k12_valuat_1(A,C,B) ) ) ) ).
fof(t34_valuat_1,axiom,
$true ).
fof(t35_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ! [E] :
( m1_valuat_1(E,A)
=> ( r1_valuat_1(A,k12_cqc_lang(C,D),E,B)
<=> ( k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,E,C),B) = k7_margrel1
| k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,E,D),B) = k8_margrel1 ) ) ) ) ) ) ) ).
fof(t36_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ! [E] :
( m1_valuat_1(E,A)
=> ( r1_valuat_1(A,k12_cqc_lang(C,D),E,B)
<=> ( r1_valuat_1(A,C,E,B)
=> r1_valuat_1(A,D,E,B) ) ) ) ) ) ) ) ).
fof(t37_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_fraenkel(C,k2_qc_lang1,A,k2_valuat_1(A))
=> ! [D] :
( m2_fraenkel(D,k2_valuat_1(A),k6_margrel1,k1_fraenkel(k2_valuat_1(A),k6_margrel1))
=> ( k8_funct_2(k2_valuat_1(A),k6_margrel1,k7_valuat_1(A,B,D),C) = k8_margrel1
=> k8_funct_2(k2_valuat_1(A),k6_margrel1,D,C) = k8_margrel1 ) ) ) ) ) ).
fof(d13_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_valuat_1(B,A)
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ( r2_valuat_1(A,B,C)
<=> ! [D] :
( m2_fraenkel(D,k2_qc_lang1,A,k2_valuat_1(A))
=> r1_valuat_1(A,C,B,D) ) ) ) ) ) ).
fof(t38_valuat_1,axiom,
$true ).
fof(t39_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ! [D] :
( m1_valuat_1(D,A)
=> ( ~ r2_hidden(B,k24_qc_lang1(C))
=> ! [E] :
( m2_fraenkel(E,k2_qc_lang1,A,k2_valuat_1(A))
=> ! [F] :
( m2_fraenkel(F,k2_qc_lang1,A,k2_valuat_1(A))
=> ( ! [G] :
( m2_subset_1(G,k1_qc_lang1,k2_qc_lang1)
=> ( B != G
=> k8_funct_2(k2_qc_lang1,A,F,G) = k8_funct_2(k2_qc_lang1,A,E,G) ) )
=> k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,D,C),E) = k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,D,C),F) ) ) ) ) ) ) ) ) ).
fof(t40_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_fraenkel(C,k2_qc_lang1,A,k2_valuat_1(A))
=> ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ! [E] :
( m1_valuat_1(E,A)
=> ( r1_valuat_1(A,D,E,C)
=> ( r2_hidden(B,k24_qc_lang1(D))
| ! [F] :
( m2_fraenkel(F,k2_qc_lang1,A,k2_valuat_1(A))
=> ( ! [G] :
( m2_subset_1(G,k1_qc_lang1,k2_qc_lang1)
=> ( B != G
=> k8_funct_2(k2_qc_lang1,A,F,G) = k8_funct_2(k2_qc_lang1,A,C,G) ) )
=> r1_valuat_1(A,D,E,F) ) ) ) ) ) ) ) ) ) ).
fof(t41_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_fraenkel(C,k2_qc_lang1,A,k2_valuat_1(A))
=> ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ! [E] :
( m1_valuat_1(E,A)
=> ( r1_valuat_1(A,k15_cqc_lang(B,D),E,C)
<=> ! [F] :
( m2_fraenkel(F,k2_qc_lang1,A,k2_valuat_1(A))
=> ( ! [G] :
( m2_subset_1(G,k1_qc_lang1,k2_qc_lang1)
=> ( B != G
=> k8_funct_2(k2_qc_lang1,A,F,G) = k8_funct_2(k2_qc_lang1,A,C,G) ) )
=> r1_valuat_1(A,D,E,F) ) ) ) ) ) ) ) ) ).
fof(t42_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ! [E] :
( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
=> ! [F] :
( m1_valuat_1(F,A)
=> ! [G] :
( m1_subset_1(G,k8_qc_lang1)
=> ( ( D = k17_cqc_lang(G,B)
& E = k17_cqc_lang(G,C) )
=> ( B = C
| ! [H] :
( m2_fraenkel(H,k2_qc_lang1,A,k2_valuat_1(A))
=> ( k8_funct_2(k2_qc_lang1,A,H,B) = k8_funct_2(k2_qc_lang1,A,H,C)
=> k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,F,D),H) = k8_funct_2(k2_valuat_1(A),k6_margrel1,k12_valuat_1(A,F,E),H) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t43_valuat_1,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
& ~ r2_hidden(A,k24_qc_lang1(C))
& r2_hidden(A,k24_qc_lang1(k17_cqc_lang(C,B))) ) ) ) ) ).
fof(t44_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
=> ! [C] :
( m1_valuat_1(C,A)
=> r1_valuat_1(A,k9_cqc_lang,C,B) ) ) ) ).
fof(t45_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ! [E] :
( m1_valuat_1(E,A)
=> r1_valuat_1(A,k12_cqc_lang(k11_cqc_lang(C,D),k11_cqc_lang(D,C)),E,B) ) ) ) ) ) ).
fof(t46_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ! [D] :
( m1_valuat_1(D,A)
=> r1_valuat_1(A,k12_cqc_lang(k12_cqc_lang(k10_cqc_lang(C),C),C),D,B) ) ) ) ) ).
fof(t47_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ! [E] :
( m1_valuat_1(E,A)
=> r1_valuat_1(A,k12_cqc_lang(C,k12_cqc_lang(k10_cqc_lang(C),D)),E,B) ) ) ) ) ) ).
fof(t48_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
=> ! [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,k8_qc_lang1,k7_cqc_lang)
=> ! [F] :
( m1_valuat_1(F,A)
=> r1_valuat_1(A,k12_cqc_lang(k12_cqc_lang(C,D),k12_cqc_lang(k10_cqc_lang(k11_cqc_lang(D,E)),k10_cqc_lang(k11_cqc_lang(C,E)))),F,B) ) ) ) ) ) ) ).
fof(t49_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,k2_qc_lang1,A,k2_valuat_1(A))
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ! [E] :
( m1_valuat_1(E,A)
=> ( ( r1_valuat_1(A,C,E,B)
& r1_valuat_1(A,k12_cqc_lang(C,D),E,B) )
=> r1_valuat_1(A,D,E,B) ) ) ) ) ) ) ).
fof(t50_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_fraenkel(C,k2_qc_lang1,A,k2_valuat_1(A))
=> ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ! [E] :
( m1_valuat_1(E,A)
=> r1_valuat_1(A,k12_cqc_lang(k15_cqc_lang(B,D),D),E,C) ) ) ) ) ) ).
fof(t51_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_valuat_1(B,A)
=> r2_valuat_1(A,B,k9_cqc_lang) ) ) ).
fof(t52_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ! [D] :
( m1_valuat_1(D,A)
=> r2_valuat_1(A,D,k12_cqc_lang(k11_cqc_lang(B,C),k11_cqc_lang(C,B))) ) ) ) ) ).
fof(t53_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m1_valuat_1(C,A)
=> r2_valuat_1(A,C,k12_cqc_lang(k12_cqc_lang(k10_cqc_lang(B),B),B)) ) ) ) ).
fof(t54_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ! [D] :
( m1_valuat_1(D,A)
=> r2_valuat_1(A,D,k12_cqc_lang(B,k12_cqc_lang(k10_cqc_lang(B),C))) ) ) ) ) ).
fof(t55_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [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,k8_qc_lang1,k7_cqc_lang)
=> ! [E] :
( m1_valuat_1(E,A)
=> r2_valuat_1(A,E,k12_cqc_lang(k12_cqc_lang(B,C),k12_cqc_lang(k10_cqc_lang(k11_cqc_lang(C,D)),k10_cqc_lang(k11_cqc_lang(B,D))))) ) ) ) ) ) ).
fof(t56_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ! [D] :
( m1_valuat_1(D,A)
=> ( ( r2_valuat_1(A,D,B)
& r2_valuat_1(A,D,k12_cqc_lang(B,C)) )
=> r2_valuat_1(A,D,C) ) ) ) ) ) ).
fof(t57_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ! [D] :
( m1_valuat_1(D,A)
=> r2_valuat_1(A,D,k12_cqc_lang(k15_cqc_lang(B,C),C)) ) ) ) ) ).
fof(t58_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ! [E] :
( m1_valuat_1(E,A)
=> ( r2_valuat_1(A,E,k12_cqc_lang(C,D))
=> ( r2_hidden(B,k24_qc_lang1(C))
| r2_valuat_1(A,E,k12_cqc_lang(C,k15_cqc_lang(B,D))) ) ) ) ) ) ) ) ).
fof(t59_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ! [E] :
( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
=> ! [F] :
( m1_valuat_1(F,A)
=> ! [G] :
( m1_subset_1(G,k8_qc_lang1)
=> ( ( D = k17_cqc_lang(G,B)
& E = k17_cqc_lang(G,C)
& r2_valuat_1(A,F,D) )
=> ( r2_hidden(B,k24_qc_lang1(G))
| r2_valuat_1(A,F,E) ) ) ) ) ) ) ) ) ) ).
fof(s1_valuat_1,axiom,
? [A] :
( m2_fraenkel(A,k2_qc_lang1,f1_s1_valuat_1,k2_valuat_1(f1_s1_valuat_1))
& ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ( B != f2_s1_valuat_1
=> k8_funct_2(k2_qc_lang1,f1_s1_valuat_1,A,B) = k8_funct_2(k2_qc_lang1,f1_s1_valuat_1,f4_s1_valuat_1,B) ) )
& k8_funct_2(k2_qc_lang1,f1_s1_valuat_1,A,f2_s1_valuat_1) = k8_funct_2(k2_qc_lang1,f1_s1_valuat_1,f5_s1_valuat_1,f3_s1_valuat_1) ) ).
fof(dt_m1_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_valuat_1(B,A)
=> ( v1_funct_1(B)
& v1_funct_2(B,k5_qc_lang1,k3_margrel1(A))
& m2_relset_1(B,k5_qc_lang1,k3_margrel1(A)) ) ) ) ).
fof(existence_m1_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] : m1_valuat_1(B,A) ) ).
fof(dt_k1_valuat_1,axiom,
$true ).
fof(dt_k2_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> m1_fraenkel(k2_valuat_1(A),k2_qc_lang1,A) ) ).
fof(redefinition_k2_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> k2_valuat_1(A) = k1_valuat_1(A) ) ).
fof(dt_k3_valuat_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_valuat_1(A) )
=> ( v1_relat_1(k3_valuat_1(A))
& v1_funct_1(k3_valuat_1(A)) ) ) ).
fof(dt_k4_valuat_1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_valuat_1(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_valuat_1(B) )
=> ( v1_relat_1(k4_valuat_1(A,B))
& v1_funct_1(k4_valuat_1(A,B)) ) ) ).
fof(commutativity_k4_valuat_1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_valuat_1(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_valuat_1(B) )
=> k4_valuat_1(A,B) = k4_valuat_1(B,A) ) ).
fof(dt_k5_valuat_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k1_fraenkel(A,k6_margrel1)) )
=> m2_fraenkel(k5_valuat_1(A,B),A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) ) ).
fof(redefinition_k5_valuat_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k1_fraenkel(A,k6_margrel1)) )
=> k5_valuat_1(A,B) = k3_valuat_1(B) ) ).
fof(dt_k6_valuat_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
& m1_subset_1(C,k1_fraenkel(A,k6_margrel1)) )
=> m2_fraenkel(k6_valuat_1(A,B,C),A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) ) ).
fof(commutativity_k6_valuat_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
& m1_subset_1(C,k1_fraenkel(A,k6_margrel1)) )
=> k6_valuat_1(A,B,C) = k6_valuat_1(A,C,B) ) ).
fof(redefinition_k6_valuat_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k1_fraenkel(A,k6_margrel1))
& m1_subset_1(C,k1_fraenkel(A,k6_margrel1)) )
=> k6_valuat_1(A,B,C) = k4_valuat_1(B,C) ) ).
fof(dt_k7_valuat_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k2_qc_lang1)
& m1_subset_1(C,k1_fraenkel(k2_valuat_1(A),k6_margrel1)) )
=> m2_fraenkel(k7_valuat_1(A,B,C),k2_valuat_1(A),k6_margrel1,k1_fraenkel(k2_valuat_1(A),k6_margrel1)) ) ).
fof(dt_k8_valuat_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k5_numbers)
& v1_cqc_lang(C,B)
& m1_qc_lang1(C,B)
& m1_subset_1(D,k2_valuat_1(A)) )
=> m2_finseq_1(k8_valuat_1(A,B,C,D),A) ) ).
fof(redefinition_k8_valuat_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k5_numbers)
& v1_cqc_lang(C,B)
& m1_qc_lang1(C,B)
& m1_subset_1(D,k2_valuat_1(A)) )
=> k8_valuat_1(A,B,C,D) = k5_relat_1(C,D) ) ).
fof(dt_k9_valuat_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k5_numbers)
& v1_cqc_lang(C,B)
& m1_qc_lang1(C,B)
& m1_subset_1(D,k3_margrel1(A)) )
=> m2_fraenkel(k9_valuat_1(A,B,C,D),k2_valuat_1(A),k6_margrel1,k1_fraenkel(k2_valuat_1(A),k6_margrel1)) ) ).
fof(dt_k10_valuat_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& v1_funct_2(B,k7_cqc_lang,k1_fraenkel(k2_valuat_1(A),k6_margrel1))
& m1_relset_1(B,k7_cqc_lang,k1_fraenkel(k2_valuat_1(A),k6_margrel1))
& m1_subset_1(C,k7_cqc_lang) )
=> m2_fraenkel(k10_valuat_1(A,B,C),k2_valuat_1(A),k6_margrel1,k1_fraenkel(k2_valuat_1(A),k6_margrel1)) ) ).
fof(redefinition_k10_valuat_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& v1_funct_2(B,k7_cqc_lang,k1_fraenkel(k2_valuat_1(A),k6_margrel1))
& m1_relset_1(B,k7_cqc_lang,k1_fraenkel(k2_valuat_1(A),k6_margrel1))
& m1_subset_1(C,k7_cqc_lang) )
=> k10_valuat_1(A,B,C) = k1_funct_1(B,C) ) ).
fof(dt_k11_valuat_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k5_numbers)
& m1_valuat_1(C,A)
& m1_subset_1(D,k7_qc_lang1(B)) )
=> m1_subset_1(k11_valuat_1(A,B,C,D),k3_margrel1(A)) ) ).
fof(redefinition_k11_valuat_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k5_numbers)
& m1_valuat_1(C,A)
& m1_subset_1(D,k7_qc_lang1(B)) )
=> k11_valuat_1(A,B,C,D) = k1_funct_1(C,D) ) ).
fof(dt_k12_valuat_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_valuat_1(B,A)
& m1_subset_1(C,k7_cqc_lang) )
=> m2_fraenkel(k12_valuat_1(A,B,C),k2_valuat_1(A),k6_margrel1,k1_fraenkel(k2_valuat_1(A),k6_margrel1)) ) ).
fof(d7_valuat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_fraenkel(C,k2_valuat_1(A),k6_margrel1,k1_fraenkel(k2_valuat_1(A),k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,k2_valuat_1(A),k6_margrel1,k1_fraenkel(k2_valuat_1(A),k6_margrel1))
=> ( D = k7_valuat_1(A,B,C)
<=> ! [E] :
( m2_fraenkel(E,k2_qc_lang1,A,k2_valuat_1(A))
=> k8_funct_2(k2_valuat_1(A),k6_margrel1,D,E) = k14_margrel1(a_4_0_valuat_1(A,B,C,E)) ) ) ) ) ) ) ).
fof(fraenkel_a_4_0_valuat_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(B)
& m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
& m2_fraenkel(D,k2_valuat_1(B),k6_margrel1,k1_fraenkel(k2_valuat_1(B),k6_margrel1))
& m2_fraenkel(E,k2_qc_lang1,B,k2_valuat_1(B)) )
=> ( r2_hidden(A,a_4_0_valuat_1(B,C,D,E))
<=> ? [F] :
( m2_fraenkel(F,k2_qc_lang1,B,k2_valuat_1(B))
& A = k8_funct_2(k2_valuat_1(B),k6_margrel1,D,F)
& ! [G] :
( m2_subset_1(G,k1_qc_lang1,k2_qc_lang1)
=> ( C != G
=> k8_funct_2(k2_qc_lang1,B,F,G) = k8_funct_2(k2_qc_lang1,B,E,G) ) ) ) ) ) ).
%------------------------------------------------------------------------------