SET007 Axioms: SET007+862.ax
%------------------------------------------------------------------------------
% File : SET007+862 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : A Sequent Calculus for 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 : calcul_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 89 ( 1 unt; 0 def)
% Number of atoms : 621 ( 112 equ)
% Maximal formula atoms : 120 ( 6 avg)
% Number of connectives : 592 ( 60 ~; 12 |; 200 &)
% ( 33 <=>; 287 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 9 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 30 ( 28 usr; 1 prp; 0-4 aty)
% Number of functors : 64 ( 64 usr; 21 con; 0-4 aty)
% Number of variables : 280 ( 233 !; 47 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_calcul_1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ( v1_relat_1(k7_relat_1(A,B))
& v1_funct_1(k7_relat_1(A,B))
& v2_finseq_1(k7_relat_1(A,B)) ) ) ).
fof(d1_calcul_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m2_finseq_1(C,A)
=> ( ( ~ r1_xreal_0(k3_finseq_1(B),np__0)
=> ( C = k1_calcul_1(A,B)
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( k3_finseq_1(B) = k1_nat_1(D,np__1)
=> C = k8_relset_1(k5_numbers,A,B,k2_finseq_1(D)) ) ) ) )
& ( r1_xreal_0(k3_finseq_1(B),np__0)
=> ( C = k1_calcul_1(A,B)
<=> C = k1_xboole_0 ) ) ) ) ) ) ).
fof(d2_calcul_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_finseq_1(B,A)
=> ( ~ r1_xreal_0(k3_finseq_1(B),np__0)
=> k2_calcul_1(A,B) = k1_funct_1(B,k3_finseq_1(B)) ) ) ) ).
fof(d3_calcul_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m2_finseq_1(C,A)
=> ( r1_calcul_1(A,B,C)
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& r2_hidden(D,k4_relset_1(k5_numbers,A,C))
& k1_funct_1(C,D) = B ) ) ) ) ) ).
fof(d4_calcul_1,axiom,
! [A] :
( m2_finseq_1(A,k7_cqc_lang)
=> ! [B] :
( m2_finseq_1(B,k7_cqc_lang)
=> ( r2_calcul_1(A,B)
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(k5_numbers))
& r1_tarski(A,k15_finseq_1(k8_relset_1(k5_numbers,k7_cqc_lang,B,C))) ) ) ) ) ).
fof(t1_calcul_1,axiom,
! [A] :
( m2_finseq_1(A,k7_cqc_lang)
=> ! [B] :
( m2_finseq_1(B,k7_cqc_lang)
=> ( r2_calcul_1(A,B)
=> ( r1_tarski(k5_relset_1(k5_numbers,k7_cqc_lang,A),k5_relset_1(k5_numbers,k7_cqc_lang,B))
& ? [C] :
( m1_subset_1(C,k1_zfmisc_1(k5_numbers))
& r1_tarski(k5_relset_1(k5_numbers,k7_cqc_lang,A),k5_relset_1(k5_numbers,k7_cqc_lang,k8_relset_1(k5_numbers,k7_cqc_lang,B,C))) ) ) ) ) ) ).
fof(t2_calcul_1,axiom,
! [A] :
( m2_finseq_1(A,k7_cqc_lang)
=> ( ~ r1_xreal_0(k3_finseq_1(A),np__0)
=> ( k1_nat_1(k3_finseq_1(k1_calcul_1(k7_cqc_lang,A)),np__1) = k3_finseq_1(A)
& ~ r1_xreal_0(k3_finseq_1(A),k3_finseq_1(k1_calcul_1(k7_cqc_lang,A))) ) ) ) ).
fof(t3_calcul_1,axiom,
! [A] :
( m2_finseq_1(A,k7_cqc_lang)
=> ( ~ r1_xreal_0(k3_finseq_1(A),np__0)
=> ( A = k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,A),k12_finseq_1(k7_cqc_lang,k2_calcul_1(k7_cqc_lang,A)))
& k5_relset_1(k5_numbers,k7_cqc_lang,A) = k4_subset_1(k7_cqc_lang,k5_relset_1(k5_numbers,k7_cqc_lang,k1_calcul_1(k7_cqc_lang,A)),k6_domain_1(k7_cqc_lang,k2_calcul_1(k7_cqc_lang,A))) ) ) ) ).
fof(t4_calcul_1,axiom,
! [A] :
( m2_finseq_1(A,k7_cqc_lang)
=> ~ ( ~ r1_xreal_0(k3_finseq_1(A),np__1)
& r1_xreal_0(k3_finseq_1(k1_calcul_1(k7_cqc_lang,A)),np__0) ) ) ).
fof(t5_calcul_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_finseq_1(B,k7_cqc_lang)
=> ( k2_calcul_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,B,k12_finseq_1(k7_cqc_lang,A))) = A
& k1_calcul_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,B,k12_finseq_1(k7_cqc_lang,A))) = B ) ) ) ).
fof(t6_calcul_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( r1_xreal_0(k3_finseq_1(A),k3_finseq_1(k7_finseq_1(A,B)))
& r1_xreal_0(k3_finseq_1(B),k3_finseq_1(k7_finseq_1(A,B)))
& ( A != k1_xboole_0
=> ( r1_xreal_0(np__1,k3_finseq_1(A))
& ~ r1_xreal_0(k3_finseq_1(k7_finseq_1(B,A)),k3_finseq_1(B)) ) ) ) ) ) ).
fof(t7_calcul_1,axiom,
! [A] :
( m2_finseq_1(A,k7_cqc_lang)
=> ! [B] :
( m2_finseq_1(B,k7_cqc_lang)
=> k15_finseq_1(k8_relset_1(k5_numbers,k7_cqc_lang,k8_finseq_1(k7_cqc_lang,A,B),k4_relset_1(k5_numbers,k7_cqc_lang,A))) = k8_relset_1(k5_numbers,k7_cqc_lang,k8_finseq_1(k7_cqc_lang,A,B),k4_relset_1(k5_numbers,k7_cqc_lang,A)) ) ) ).
fof(t8_calcul_1,axiom,
! [A] :
( m2_finseq_1(A,k7_cqc_lang)
=> ! [B] :
( m2_finseq_1(B,k7_cqc_lang)
=> r2_calcul_1(A,k8_finseq_1(k7_cqc_lang,A,B)) ) ) ).
fof(t9_calcul_1,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ~ r1_xreal_0(k3_finseq_1(k7_finseq_1(k7_finseq_1(C,k9_finseq_1(A)),k9_finseq_1(B))),np__1) ) ).
fof(t10_calcul_1,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( r1_xreal_0(np__1,k3_finseq_1(k7_finseq_1(B,k9_finseq_1(A))))
& r2_hidden(k3_finseq_1(k7_finseq_1(B,k9_finseq_1(A))),k1_relat_1(k7_finseq_1(B,k9_finseq_1(A)))) ) ) ).
fof(t11_calcul_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(A,np__0)
=> k3_finseq_1(k14_finseq_1(k4_subset_1(k5_numbers,k2_finseq_1(B),k6_domain_1(k5_numbers,k1_nat_1(B,A))))) = k1_nat_1(B,np__1) ) ) ) ).
fof(t12_calcul_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(A,np__0)
=> k4_relset_1(k5_numbers,k5_numbers,k14_finseq_1(k4_subset_1(k5_numbers,k2_finseq_1(B),k6_domain_1(k5_numbers,k1_nat_1(B,A))))) = k2_finseq_1(k1_nat_1(B,np__1)) ) ) ) ).
fof(t13_calcul_1,axiom,
! [A] :
( m2_finseq_1(A,k7_cqc_lang)
=> ! [B] :
( m2_finseq_1(B,k7_cqc_lang)
=> ( ~ r1_xreal_0(k3_finseq_1(A),np__0)
=> r2_calcul_1(A,k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,A),B),k12_finseq_1(k7_cqc_lang,k2_calcul_1(k7_cqc_lang,A)))) ) ) ) ).
fof(t14_calcul_1,axiom,
! [A,B,C] :
( m2_finseq_1(C,k7_cqc_lang)
=> ( r2_hidden(np__1,k1_relat_1(k10_finseq_1(A,B)))
& r2_hidden(np__2,k1_relat_1(k10_finseq_1(A,B)))
& k1_funct_1(k7_finseq_1(C,k10_finseq_1(A,B)),k1_nat_1(k3_finseq_1(C),np__1)) = A
& k1_funct_1(k7_finseq_1(C,k10_finseq_1(A,B)),k1_nat_1(k3_finseq_1(C),np__2)) = B ) ) ).
fof(d5_calcul_1,axiom,
! [A] :
( m2_finseq_1(A,k7_cqc_lang)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k2_qc_lang1))
=> ( B = k3_calcul_1(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& ? [E] :
( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
& r2_hidden(D,k4_relset_1(k5_numbers,k7_cqc_lang,A))
& E = k1_funct_1(A,D)
& r2_hidden(C,k24_qc_lang1(E)) ) ) ) ) ) ) ).
fof(d6_calcul_1,axiom,
! [A] :
( A = k4_calcul_1
<=> ! [B] :
( r2_hidden(B,A)
<=> m2_finseq_1(B,k7_cqc_lang) ) ) ).
fof(d7_calcul_1,axiom,
! [A] :
( m2_finseq_1(A,k2_zfmisc_1(k4_calcul_1,k2_cqc_the1))
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( k2_mcart_1(k1_funct_1(A,B)) = np__0
=> ( r3_calcul_1(A,B)
<=> ? [C] :
( m2_finseq_1(C,k7_cqc_lang)
& r1_calcul_1(k7_cqc_lang,k2_calcul_1(k7_cqc_lang,C),k1_calcul_1(k7_cqc_lang,C))
& k1_mcart_1(k1_funct_1(A,B)) = C ) ) )
& ( k2_mcart_1(k1_funct_1(A,B)) = np__1
=> ( r3_calcul_1(A,B)
<=> ? [C] :
( m2_finseq_1(C,k7_cqc_lang)
& k1_mcart_1(k1_funct_1(A,B)) = k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,k9_cqc_lang)) ) ) )
& ( k2_mcart_1(k1_funct_1(A,B)) = np__2
=> ( r3_calcul_1(A,B)
<=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& ? [D] :
( m2_finseq_1(D,k7_cqc_lang)
& ? [E] :
( m2_finseq_1(E,k7_cqc_lang)
& r1_xreal_0(np__1,C)
& ~ r1_xreal_0(B,C)
& r2_calcul_1(k1_calcul_1(k7_cqc_lang,D),k1_calcul_1(k7_cqc_lang,E))
& k2_calcul_1(k7_cqc_lang,D) = k2_calcul_1(k7_cqc_lang,E)
& k1_mcart_1(k1_funct_1(A,C)) = D
& k1_mcart_1(k1_funct_1(A,B)) = E ) ) ) ) )
& ( k2_mcart_1(k1_funct_1(A,B)) = np__3
=> ( r3_calcul_1(A,B)
<=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& ? [E] :
( m2_finseq_1(E,k7_cqc_lang)
& ? [F] :
( m2_finseq_1(F,k7_cqc_lang)
& r1_xreal_0(np__1,C)
& ~ r1_xreal_0(B,C)
& r1_xreal_0(np__1,D)
& ~ r1_xreal_0(C,D)
& ~ r1_xreal_0(k3_finseq_1(E),np__1)
& ~ r1_xreal_0(k3_finseq_1(F),np__1)
& k1_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,E)) = k1_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,F))
& k10_cqc_lang(k2_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,E))) = k2_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,F))
& k2_calcul_1(k7_cqc_lang,E) = k2_calcul_1(k7_cqc_lang,F)
& E = k1_mcart_1(k1_funct_1(A,D))
& F = k1_mcart_1(k1_funct_1(A,C))
& k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,E)),k12_finseq_1(k7_cqc_lang,k2_calcul_1(k7_cqc_lang,E))) = k1_mcart_1(k1_funct_1(A,B)) ) ) ) ) ) )
& ( k2_mcart_1(k1_funct_1(A,B)) = np__4
=> ( r3_calcul_1(A,B)
<=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& ? [E] :
( m2_finseq_1(E,k7_cqc_lang)
& ? [F] :
( m2_finseq_1(F,k7_cqc_lang)
& ? [G] :
( m2_subset_1(G,k8_qc_lang1,k7_cqc_lang)
& r1_xreal_0(np__1,C)
& ~ r1_xreal_0(B,C)
& r1_xreal_0(np__1,D)
& ~ r1_xreal_0(C,D)
& ~ r1_xreal_0(k3_finseq_1(E),np__1)
& k1_calcul_1(k7_cqc_lang,E) = k1_calcul_1(k7_cqc_lang,F)
& k2_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,E)) = k10_cqc_lang(G)
& k10_cqc_lang(k2_calcul_1(k7_cqc_lang,E)) = k2_calcul_1(k7_cqc_lang,F)
& E = k1_mcart_1(k1_funct_1(A,D))
& F = k1_mcart_1(k1_funct_1(A,C))
& k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,E)),k12_finseq_1(k7_cqc_lang,G)) = k1_mcart_1(k1_funct_1(A,B)) ) ) ) ) ) ) )
& ( k2_mcart_1(k1_funct_1(A,B)) = np__5
=> ( r3_calcul_1(A,B)
<=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& ? [E] :
( m2_finseq_1(E,k7_cqc_lang)
& ? [F] :
( m2_finseq_1(F,k7_cqc_lang)
& r1_xreal_0(np__1,C)
& ~ r1_xreal_0(B,C)
& r1_xreal_0(np__1,D)
& ~ r1_xreal_0(C,D)
& k1_calcul_1(k7_cqc_lang,E) = k1_calcul_1(k7_cqc_lang,F)
& E = k1_mcart_1(k1_funct_1(A,D))
& F = k1_mcart_1(k1_funct_1(A,C))
& k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,E),k12_finseq_1(k7_cqc_lang,k11_cqc_lang(k2_calcul_1(k7_cqc_lang,E),k2_calcul_1(k7_cqc_lang,F)))) = k1_mcart_1(k1_funct_1(A,B)) ) ) ) ) ) )
& ( k2_mcart_1(k1_funct_1(A,B)) = np__6
=> ( r3_calcul_1(A,B)
<=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& ? [D] :
( m2_finseq_1(D,k7_cqc_lang)
& ? [E] :
( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
& ? [F] :
( m2_subset_1(F,k8_qc_lang1,k7_cqc_lang)
& r1_xreal_0(np__1,C)
& ~ r1_xreal_0(B,C)
& k11_cqc_lang(E,F) = k2_calcul_1(k7_cqc_lang,D)
& D = k1_mcart_1(k1_funct_1(A,C))
& k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,D),k12_finseq_1(k7_cqc_lang,E)) = k1_mcart_1(k1_funct_1(A,B)) ) ) ) ) ) )
& ( k2_mcart_1(k1_funct_1(A,B)) = np__7
=> ( r3_calcul_1(A,B)
<=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& ? [D] :
( m2_finseq_1(D,k7_cqc_lang)
& ? [E] :
( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
& ? [F] :
( m2_subset_1(F,k8_qc_lang1,k7_cqc_lang)
& r1_xreal_0(np__1,C)
& ~ r1_xreal_0(B,C)
& k11_cqc_lang(E,F) = k2_calcul_1(k7_cqc_lang,D)
& D = k1_mcart_1(k1_funct_1(A,C))
& k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,D),k12_finseq_1(k7_cqc_lang,F)) = k1_mcart_1(k1_funct_1(A,B)) ) ) ) ) ) )
& ( k2_mcart_1(k1_funct_1(A,B)) = np__8
=> ( r3_calcul_1(A,B)
<=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& ? [D] :
( m2_finseq_1(D,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_qc_lang1,k2_qc_lang1)
& r1_xreal_0(np__1,C)
& ~ r1_xreal_0(B,C)
& k2_calcul_1(k7_cqc_lang,D) = k15_cqc_lang(F,E)
& D = k1_mcart_1(k1_funct_1(A,C))
& k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,D),k12_finseq_1(k7_cqc_lang,k4_substut2(E,F,G))) = k1_mcart_1(k1_funct_1(A,B)) ) ) ) ) ) ) )
& ( k2_mcart_1(k1_funct_1(A,B)) = np__9
=> ( r3_calcul_1(A,B)
<=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& ? [D] :
( m2_finseq_1(D,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_qc_lang1,k2_qc_lang1)
& r1_xreal_0(np__1,C)
& ~ r1_xreal_0(B,C)
& k2_calcul_1(k7_cqc_lang,D) = k4_substut2(E,F,G)
& ~ r2_hidden(G,k3_calcul_1(k1_calcul_1(k7_cqc_lang,D)))
& ~ r2_hidden(G,k24_qc_lang1(k15_cqc_lang(F,E)))
& D = k1_mcart_1(k1_funct_1(A,C))
& k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,D),k12_finseq_1(k7_cqc_lang,k15_cqc_lang(F,E))) = k1_mcart_1(k1_funct_1(A,B)) ) ) ) ) ) ) ) ) ) ) ).
fof(d8_calcul_1,axiom,
! [A] :
( m2_finseq_1(A,k2_zfmisc_1(k4_calcul_1,k2_cqc_the1))
=> ( v1_calcul_1(A)
<=> ( A != k1_xboole_0
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(B,k3_finseq_1(A)) )
=> r3_calcul_1(A,B) ) ) ) ) ) ).
fof(d9_calcul_1,axiom,
! [A] :
( m2_finseq_1(A,k7_cqc_lang)
=> ( r4_calcul_1(A)
<=> ? [B] :
( m2_finseq_1(B,k2_zfmisc_1(k4_calcul_1,k2_cqc_the1))
& v1_calcul_1(B)
& A = k1_mcart_1(k1_funct_1(B,k3_finseq_1(B))) ) ) ) ).
fof(d10_calcul_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
=> ( r5_calcul_1(A,B)
<=> ? [C] :
( m2_finseq_1(C,k7_cqc_lang)
& r1_tarski(k5_relset_1(k5_numbers,k7_cqc_lang,k1_calcul_1(k7_cqc_lang,C)),B)
& k2_calcul_1(k7_cqc_lang,C) = A
& r4_calcul_1(C) ) ) ) ) ).
fof(d11_calcul_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_valuat_1(C,B)
=> ! [D] :
( m2_fraenkel(D,k2_qc_lang1,B,k2_valuat_1(B))
=> ( r6_calcul_1(A,B,C,D)
<=> ! [E] :
( m2_subset_1(E,k8_qc_lang1,k7_cqc_lang)
=> ( r2_hidden(E,A)
=> r1_valuat_1(B,E,C,D) ) ) ) ) ) ) ) ).
fof(d12_calcul_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( r7_calcul_1(A,B)
<=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_valuat_1(D,C)
=> ! [E] :
( m2_fraenkel(E,k2_qc_lang1,C,k2_valuat_1(C))
=> ( r6_calcul_1(A,C,D,E)
=> r1_valuat_1(C,B,D,E) ) ) ) ) ) ) ) ).
fof(d13_calcul_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ( r8_calcul_1(A)
<=> r7_calcul_1(k1_subset_1(k7_cqc_lang),A) ) ) ).
fof(d14_calcul_1,axiom,
! [A] :
( m2_finseq_1(A,k7_cqc_lang)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_valuat_1(C,B)
=> ! [D] :
( m2_fraenkel(D,k2_qc_lang1,B,k2_valuat_1(B))
=> ( r9_calcul_1(A,B,C,D)
<=> r6_calcul_1(k5_relset_1(k5_numbers,k7_cqc_lang,A),B,C,D) ) ) ) ) ) ).
fof(d15_calcul_1,axiom,
! [A] :
( m2_finseq_1(A,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( r10_calcul_1(A,B)
<=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_valuat_1(D,C)
=> ! [E] :
( m2_fraenkel(E,k2_qc_lang1,C,k2_valuat_1(C))
=> ( r9_calcul_1(A,C,D,E)
=> r1_valuat_1(C,B,D,E) ) ) ) ) ) ) ) ).
fof(t15_calcul_1,axiom,
! [A] :
( m2_finseq_1(A,k7_cqc_lang)
=> ( r1_calcul_1(k7_cqc_lang,k2_calcul_1(k7_cqc_lang,A),k1_calcul_1(k7_cqc_lang,A))
=> r10_calcul_1(k1_calcul_1(k7_cqc_lang,A),k2_calcul_1(k7_cqc_lang,A)) ) ) ).
fof(t16_calcul_1,axiom,
! [A] :
( m2_finseq_1(A,k7_cqc_lang)
=> ! [B] :
( m2_finseq_1(B,k7_cqc_lang)
=> ( ( r2_calcul_1(k1_calcul_1(k7_cqc_lang,A),k1_calcul_1(k7_cqc_lang,B))
& k2_calcul_1(k7_cqc_lang,A) = k2_calcul_1(k7_cqc_lang,B)
& r10_calcul_1(k1_calcul_1(k7_cqc_lang,A),k2_calcul_1(k7_cqc_lang,A)) )
=> r10_calcul_1(k1_calcul_1(k7_cqc_lang,B),k2_calcul_1(k7_cqc_lang,B)) ) ) ) ).
fof(t17_calcul_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_valuat_1(B,A)
=> ! [C] :
( m2_fraenkel(C,k2_qc_lang1,A,k2_valuat_1(A))
=> ! [D] :
( m2_finseq_1(D,k7_cqc_lang)
=> ( ~ r1_xreal_0(k3_finseq_1(D),np__0)
=> ( ( r9_calcul_1(k1_calcul_1(k7_cqc_lang,D),A,B,C)
& r1_valuat_1(A,k2_calcul_1(k7_cqc_lang,D),B,C) )
<=> r9_calcul_1(D,A,B,C) ) ) ) ) ) ) ).
fof(t18_calcul_1,axiom,
! [A] :
( m2_finseq_1(A,k7_cqc_lang)
=> ! [B] :
( m2_finseq_1(B,k7_cqc_lang)
=> ( ( k1_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,A)) = k1_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,B))
& k10_cqc_lang(k2_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,A))) = k2_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,B))
& k2_calcul_1(k7_cqc_lang,A) = k2_calcul_1(k7_cqc_lang,B)
& r10_calcul_1(k1_calcul_1(k7_cqc_lang,A),k2_calcul_1(k7_cqc_lang,A))
& r10_calcul_1(k1_calcul_1(k7_cqc_lang,B),k2_calcul_1(k7_cqc_lang,B)) )
=> ( r1_xreal_0(k3_finseq_1(A),np__1)
| r1_xreal_0(k3_finseq_1(B),np__1)
| r10_calcul_1(k1_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,A)),k2_calcul_1(k7_cqc_lang,A)) ) ) ) ) ).
fof(t19_calcul_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_finseq_1(B,k7_cqc_lang)
=> ! [C] :
( m2_finseq_1(C,k7_cqc_lang)
=> ( ( k1_calcul_1(k7_cqc_lang,B) = k1_calcul_1(k7_cqc_lang,C)
& k10_cqc_lang(A) = k2_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,B))
& k10_cqc_lang(k2_calcul_1(k7_cqc_lang,B)) = k2_calcul_1(k7_cqc_lang,C)
& r10_calcul_1(k1_calcul_1(k7_cqc_lang,B),k2_calcul_1(k7_cqc_lang,B))
& r10_calcul_1(k1_calcul_1(k7_cqc_lang,C),k2_calcul_1(k7_cqc_lang,C)) )
=> ( r1_xreal_0(k3_finseq_1(B),np__1)
| r10_calcul_1(k1_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,B)),A) ) ) ) ) ) ).
fof(t20_calcul_1,axiom,
! [A] :
( m2_finseq_1(A,k7_cqc_lang)
=> ! [B] :
( m2_finseq_1(B,k7_cqc_lang)
=> ( ( k1_calcul_1(k7_cqc_lang,A) = k1_calcul_1(k7_cqc_lang,B)
& r10_calcul_1(k1_calcul_1(k7_cqc_lang,A),k2_calcul_1(k7_cqc_lang,A))
& r10_calcul_1(k1_calcul_1(k7_cqc_lang,B),k2_calcul_1(k7_cqc_lang,B)) )
=> r10_calcul_1(k1_calcul_1(k7_cqc_lang,A),k11_cqc_lang(k2_calcul_1(k7_cqc_lang,A),k2_calcul_1(k7_cqc_lang,B))) ) ) ) ).
fof(t21_calcul_1,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_finseq_1(C,k7_cqc_lang)
=> ( ( k2_calcul_1(k7_cqc_lang,C) = k11_cqc_lang(A,B)
& r10_calcul_1(k1_calcul_1(k7_cqc_lang,C),k11_cqc_lang(A,B)) )
=> r10_calcul_1(k1_calcul_1(k7_cqc_lang,C),A) ) ) ) ) ).
fof(t22_calcul_1,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_finseq_1(C,k7_cqc_lang)
=> ( ( k2_calcul_1(k7_cqc_lang,C) = k11_cqc_lang(A,B)
& r10_calcul_1(k1_calcul_1(k7_cqc_lang,C),k11_cqc_lang(A,B)) )
=> r10_calcul_1(k1_calcul_1(k7_cqc_lang,C),B) ) ) ) ) ).
fof(t23_calcul_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_valuat_1(C,B)
=> ! [D] :
( m2_fraenkel(D,k2_qc_lang1,B,k2_valuat_1(B))
=> ! [E] :
( m1_subset_1(E,k1_substut1)
=> ( r1_sublemma(k2_substut2(A,E),B,D,C)
<=> r1_valuat_1(B,A,C,D) ) ) ) ) ) ) ).
fof(t24_calcul_1,axiom,
! [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_qc_lang1,k2_qc_lang1)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( m1_valuat_1(E,D)
=> ! [F] :
( m2_fraenkel(F,k2_qc_lang1,D,k2_valuat_1(D))
=> ( r1_valuat_1(D,k4_substut2(A,B,C),E,F)
<=> ? [G] :
( m1_subset_1(G,D)
& k8_funct_2(k2_qc_lang1,D,F,C) = G
& r1_valuat_1(D,A,E,k1_sublemma(D,F,k13_sublemma(D,G,B))) ) ) ) ) ) ) ) ) ).
fof(t25_calcul_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_finseq_1(C,k7_cqc_lang)
=> ( ( k2_calcul_1(k7_cqc_lang,C) = k15_cqc_lang(B,A)
& r10_calcul_1(k1_calcul_1(k7_cqc_lang,C),k2_calcul_1(k7_cqc_lang,C)) )
=> ! [D] :
( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
=> r10_calcul_1(k1_calcul_1(k7_cqc_lang,C),k4_substut2(A,B,D)) ) ) ) ) ) ).
fof(t26_calcul_1,axiom,
! [A] :
( m2_subset_1(A,k1_qc_lang1,k2_qc_lang1)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m2_fraenkel(C,k2_qc_lang1,B,k2_valuat_1(B))
=> ! [D] :
( m1_subset_1(D,B)
=> ! [E] :
( r1_tarski(E,k2_qc_lang1)
=> ( r2_hidden(A,E)
| k8_relset_1(k2_qc_lang1,B,k1_sublemma(B,C,k13_sublemma(B,D,A)),E) = k8_relset_1(k2_qc_lang1,B,C,E) ) ) ) ) ) ) ).
fof(t27_calcul_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_valuat_1(B,A)
=> ! [C] :
( m2_finseq_1(C,k7_cqc_lang)
=> ! [D] :
( m2_fraenkel(D,k2_qc_lang1,A,k2_valuat_1(A))
=> ! [E] :
( m2_fraenkel(E,k2_qc_lang1,A,k2_valuat_1(A))
=> ( k8_relset_1(k2_qc_lang1,A,D,k3_calcul_1(C)) = k8_relset_1(k2_qc_lang1,A,E,k3_calcul_1(C))
=> ( r9_calcul_1(C,A,B,D)
<=> r9_calcul_1(C,A,B,E) ) ) ) ) ) ) ) ).
fof(t28_calcul_1,axiom,
! [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_qc_lang1,k2_qc_lang1)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( m2_fraenkel(E,k2_qc_lang1,D,k2_valuat_1(D))
=> ! [F] :
( m1_subset_1(F,D)
=> ( ~ r2_hidden(B,k24_qc_lang1(k15_cqc_lang(C,A)))
=> k8_relset_1(k2_qc_lang1,D,k1_sublemma(D,k1_sublemma(D,E,k13_sublemma(D,F,B)),k13_sublemma(D,F,C)),k24_qc_lang1(A)) = k8_relset_1(k2_qc_lang1,D,k1_sublemma(D,E,k13_sublemma(D,F,C)),k24_qc_lang1(A)) ) ) ) ) ) ) ) ).
fof(t29_calcul_1,axiom,
! [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_qc_lang1,k2_qc_lang1)
=> ! [D] :
( m2_finseq_1(D,k7_cqc_lang)
=> ( ( k2_calcul_1(k7_cqc_lang,D) = k4_substut2(A,B,C)
& r10_calcul_1(k1_calcul_1(k7_cqc_lang,D),k2_calcul_1(k7_cqc_lang,D)) )
=> ( r2_hidden(C,k3_calcul_1(k1_calcul_1(k7_cqc_lang,D)))
| r2_hidden(C,k24_qc_lang1(k15_cqc_lang(B,A)))
| r10_calcul_1(k1_calcul_1(k7_cqc_lang,D),k15_cqc_lang(B,A)) ) ) ) ) ) ) ).
fof(t30_calcul_1,axiom,
! [A] :
( m2_finseq_1(A,k7_cqc_lang)
=> r10_calcul_1(k1_calcul_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,A,k12_finseq_1(k7_cqc_lang,k9_cqc_lang))),k2_calcul_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,A,k12_finseq_1(k7_cqc_lang,k9_cqc_lang)))) ) ).
fof(t31_calcul_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_1(B,k2_zfmisc_1(k4_calcul_1,k2_cqc_the1))
=> ~ ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(B))
& k2_mcart_1(k1_funct_1(B,A)) != np__0
& k2_mcart_1(k1_funct_1(B,A)) != np__1
& k2_mcart_1(k1_funct_1(B,A)) != np__2
& k2_mcart_1(k1_funct_1(B,A)) != np__3
& k2_mcart_1(k1_funct_1(B,A)) != np__4
& k2_mcart_1(k1_funct_1(B,A)) != np__5
& k2_mcart_1(k1_funct_1(B,A)) != np__6
& k2_mcart_1(k1_funct_1(B,A)) != np__7
& k2_mcart_1(k1_funct_1(B,A)) != np__8
& k2_mcart_1(k1_funct_1(B,A)) != np__9 ) ) ) ).
fof(t32_calcul_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
=> ( r5_calcul_1(A,B)
=> r7_calcul_1(B,A) ) ) ) ).
fof(t33_calcul_1,axiom,
! [A] :
( m2_finseq_1(A,k7_cqc_lang)
=> ( r1_calcul_1(k7_cqc_lang,k2_calcul_1(k7_cqc_lang,A),k1_calcul_1(k7_cqc_lang,A))
=> r4_calcul_1(A) ) ) ).
fof(t34_calcul_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_1(B,k2_zfmisc_1(k4_calcul_1,k2_cqc_the1))
=> ! [C] :
( m2_finseq_1(C,k2_zfmisc_1(k4_calcul_1,k2_cqc_the1))
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(B)) )
=> ( r3_calcul_1(B,A)
<=> r3_calcul_1(k8_finseq_1(k2_zfmisc_1(k4_calcul_1,k2_cqc_the1),B,C),A) ) ) ) ) ) ).
fof(t35_calcul_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_1(B,k2_zfmisc_1(k4_calcul_1,k2_cqc_the1))
=> ! [C] :
( m2_finseq_1(C,k2_zfmisc_1(k4_calcul_1,k2_cqc_the1))
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(B))
& r3_calcul_1(B,A) )
=> r3_calcul_1(k8_finseq_1(k2_zfmisc_1(k4_calcul_1,k2_cqc_the1),C,B),k1_nat_1(A,k3_finseq_1(C))) ) ) ) ) ).
fof(t36_calcul_1,axiom,
! [A] :
( m2_finseq_1(A,k7_cqc_lang)
=> ! [B] :
( m2_finseq_1(B,k7_cqc_lang)
=> ( ( r2_calcul_1(k1_calcul_1(k7_cqc_lang,A),k1_calcul_1(k7_cqc_lang,B))
& k2_calcul_1(k7_cqc_lang,A) = k2_calcul_1(k7_cqc_lang,B)
& r4_calcul_1(A) )
=> r4_calcul_1(B) ) ) ) ).
fof(t37_calcul_1,axiom,
! [A] :
( m2_finseq_1(A,k7_cqc_lang)
=> ! [B] :
( m2_finseq_1(B,k7_cqc_lang)
=> ( ( k1_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,A)) = k1_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,B))
& k10_cqc_lang(k2_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,A))) = k2_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,B))
& k2_calcul_1(k7_cqc_lang,A) = k2_calcul_1(k7_cqc_lang,B)
& r4_calcul_1(A)
& r4_calcul_1(B) )
=> ( r1_xreal_0(k3_finseq_1(A),np__1)
| r1_xreal_0(k3_finseq_1(B),np__1)
| r4_calcul_1(k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,A)),k12_finseq_1(k7_cqc_lang,k2_calcul_1(k7_cqc_lang,A)))) ) ) ) ) ).
fof(t38_calcul_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_finseq_1(B,k7_cqc_lang)
=> ! [C] :
( m2_finseq_1(C,k7_cqc_lang)
=> ( ( k1_calcul_1(k7_cqc_lang,B) = k1_calcul_1(k7_cqc_lang,C)
& k2_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,B)) = k10_cqc_lang(A)
& k10_cqc_lang(k2_calcul_1(k7_cqc_lang,B)) = k2_calcul_1(k7_cqc_lang,C)
& r4_calcul_1(B)
& r4_calcul_1(C) )
=> ( r1_xreal_0(k3_finseq_1(B),np__1)
| r4_calcul_1(k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,B)),k12_finseq_1(k7_cqc_lang,A))) ) ) ) ) ) ).
fof(t39_calcul_1,axiom,
! [A] :
( m2_finseq_1(A,k7_cqc_lang)
=> ! [B] :
( m2_finseq_1(B,k7_cqc_lang)
=> ( ( k1_calcul_1(k7_cqc_lang,A) = k1_calcul_1(k7_cqc_lang,B)
& r4_calcul_1(A)
& r4_calcul_1(B) )
=> r4_calcul_1(k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,A),k12_finseq_1(k7_cqc_lang,k11_cqc_lang(k2_calcul_1(k7_cqc_lang,A),k2_calcul_1(k7_cqc_lang,B))))) ) ) ) ).
fof(t40_calcul_1,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_finseq_1(C,k7_cqc_lang)
=> ( ( k11_cqc_lang(A,B) = k2_calcul_1(k7_cqc_lang,C)
& r4_calcul_1(C) )
=> r4_calcul_1(k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,C),k12_finseq_1(k7_cqc_lang,A))) ) ) ) ) ).
fof(t41_calcul_1,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_finseq_1(C,k7_cqc_lang)
=> ( ( k11_cqc_lang(A,B) = k2_calcul_1(k7_cqc_lang,C)
& r4_calcul_1(C) )
=> r4_calcul_1(k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,C),k12_finseq_1(k7_cqc_lang,B))) ) ) ) ) ).
fof(t42_calcul_1,axiom,
! [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_qc_lang1,k2_qc_lang1)
=> ! [D] :
( m2_finseq_1(D,k7_cqc_lang)
=> ( ( k2_calcul_1(k7_cqc_lang,D) = k15_cqc_lang(B,A)
& r4_calcul_1(D) )
=> r4_calcul_1(k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,D),k12_finseq_1(k7_cqc_lang,k4_substut2(A,B,C)))) ) ) ) ) ) ).
fof(t43_calcul_1,axiom,
! [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_qc_lang1,k2_qc_lang1)
=> ! [D] :
( m2_finseq_1(D,k7_cqc_lang)
=> ( ( k2_calcul_1(k7_cqc_lang,D) = k4_substut2(A,B,C)
& r4_calcul_1(D) )
=> ( r2_hidden(C,k3_calcul_1(k1_calcul_1(k7_cqc_lang,D)))
| r2_hidden(C,k24_qc_lang1(k15_cqc_lang(B,A)))
| r4_calcul_1(k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,D),k12_finseq_1(k7_cqc_lang,k15_cqc_lang(B,A)))) ) ) ) ) ) ) ).
fof(t44_calcul_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_finseq_1(B,k7_cqc_lang)
=> ( ( r4_calcul_1(B)
& r4_calcul_1(k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,B),k12_finseq_1(k7_cqc_lang,k10_cqc_lang(k2_calcul_1(k7_cqc_lang,B))))) )
=> r4_calcul_1(k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,B),k12_finseq_1(k7_cqc_lang,A))) ) ) ) ).
fof(t45_calcul_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_finseq_1(B,k7_cqc_lang)
=> ( ( r1_xreal_0(np__1,k3_finseq_1(B))
& r4_calcul_1(B)
& r4_calcul_1(k8_finseq_1(k7_cqc_lang,B,k12_finseq_1(k7_cqc_lang,A))) )
=> r4_calcul_1(k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,B),k12_finseq_1(k7_cqc_lang,A))) ) ) ) ).
fof(t46_calcul_1,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_finseq_1(C,k7_cqc_lang)
=> ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,A)),k12_finseq_1(k7_cqc_lang,B)))
=> r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,k10_cqc_lang(B))),k12_finseq_1(k7_cqc_lang,k10_cqc_lang(A)))) ) ) ) ) ).
fof(t47_calcul_1,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_finseq_1(C,k7_cqc_lang)
=> ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,k10_cqc_lang(A))),k12_finseq_1(k7_cqc_lang,k10_cqc_lang(B))))
=> r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,B)),k12_finseq_1(k7_cqc_lang,A))) ) ) ) ) ).
fof(t48_calcul_1,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_finseq_1(C,k7_cqc_lang)
=> ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,k10_cqc_lang(A))),k12_finseq_1(k7_cqc_lang,B)))
=> r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,k10_cqc_lang(B))),k12_finseq_1(k7_cqc_lang,A))) ) ) ) ) ).
fof(t49_calcul_1,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_finseq_1(C,k7_cqc_lang)
=> ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,A)),k12_finseq_1(k7_cqc_lang,k10_cqc_lang(B))))
=> r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,B)),k12_finseq_1(k7_cqc_lang,k10_cqc_lang(A)))) ) ) ) ) ).
fof(t50_calcul_1,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_finseq_1(D,k7_cqc_lang)
=> ( ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,D,k12_finseq_1(k7_cqc_lang,A)),k12_finseq_1(k7_cqc_lang,B)))
& r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,D,k12_finseq_1(k7_cqc_lang,C)),k12_finseq_1(k7_cqc_lang,B))) )
=> r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,D,k12_finseq_1(k7_cqc_lang,k13_cqc_lang(A,C))),k12_finseq_1(k7_cqc_lang,B))) ) ) ) ) ) ).
fof(t51_calcul_1,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_finseq_1(C,k7_cqc_lang)
=> ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,A)))
=> r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,k13_cqc_lang(A,B)))) ) ) ) ) ).
fof(t52_calcul_1,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_finseq_1(C,k7_cqc_lang)
=> ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,A)))
=> r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,k13_cqc_lang(B,A)))) ) ) ) ) ).
fof(t53_calcul_1,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_finseq_1(D,k7_cqc_lang)
=> ( ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,D,k12_finseq_1(k7_cqc_lang,A)),k12_finseq_1(k7_cqc_lang,B)))
& r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,D,k12_finseq_1(k7_cqc_lang,C)),k12_finseq_1(k7_cqc_lang,B))) )
=> r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,D,k12_finseq_1(k7_cqc_lang,k13_cqc_lang(A,C))),k12_finseq_1(k7_cqc_lang,B))) ) ) ) ) ) ).
fof(t54_calcul_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_finseq_1(B,k7_cqc_lang)
=> ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,B,k12_finseq_1(k7_cqc_lang,A)))
=> r4_calcul_1(k8_finseq_1(k7_cqc_lang,B,k12_finseq_1(k7_cqc_lang,k10_cqc_lang(k10_cqc_lang(A))))) ) ) ) ).
fof(t55_calcul_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_finseq_1(B,k7_cqc_lang)
=> ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,B,k12_finseq_1(k7_cqc_lang,k10_cqc_lang(k10_cqc_lang(A)))))
=> r4_calcul_1(k8_finseq_1(k7_cqc_lang,B,k12_finseq_1(k7_cqc_lang,A))) ) ) ) ).
fof(t56_calcul_1,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_finseq_1(C,k7_cqc_lang)
=> ( ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,k12_cqc_lang(A,B))))
& r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,A))) )
=> r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,B))) ) ) ) ) ).
fof(t57_calcul_1,axiom,
! [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_qc_lang1,k2_qc_lang1)
=> k4_substut2(k10_cqc_lang(A),B,C) = k10_cqc_lang(k4_substut2(A,B,C)) ) ) ) ).
fof(t58_calcul_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_finseq_1(C,k7_cqc_lang)
=> ( ? [D] :
( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
& r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,k4_substut2(A,B,D)))) )
=> r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,k16_cqc_lang(B,A)))) ) ) ) ) ).
fof(t59_calcul_1,axiom,
! [A] :
( m2_finseq_1(A,k7_cqc_lang)
=> ! [B] :
( m2_finseq_1(B,k7_cqc_lang)
=> k3_calcul_1(k8_finseq_1(k7_cqc_lang,A,B)) = k4_subset_1(k2_qc_lang1,k3_calcul_1(A),k3_calcul_1(B)) ) ) ).
fof(t60_calcul_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> k3_calcul_1(k12_finseq_1(k7_cqc_lang,A)) = k24_qc_lang1(A) ) ).
fof(t61_calcul_1,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_qc_lang1,k2_qc_lang1)
=> ! [E] :
( m2_finseq_1(E,k7_cqc_lang)
=> ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,E,k12_finseq_1(k7_cqc_lang,k4_substut2(A,C,D))),k12_finseq_1(k7_cqc_lang,B)))
=> ( r2_hidden(D,k3_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,E,k12_finseq_1(k7_cqc_lang,k16_cqc_lang(C,A))),k12_finseq_1(k7_cqc_lang,B))))
| r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,E,k12_finseq_1(k7_cqc_lang,k16_cqc_lang(C,A))),k12_finseq_1(k7_cqc_lang,B))) ) ) ) ) ) ) ) ).
fof(t63_calcul_1,axiom,
! [A] :
( m2_finseq_1(A,k7_cqc_lang)
=> v1_finset_1(k3_calcul_1(A)) ) ).
fof(t64_calcul_1,axiom,
( k1_card_1(k2_qc_lang1) = k3_card_1(np__0)
& ~ v1_finset_1(k2_qc_lang1) ) ).
fof(t65_calcul_1,axiom,
! [A] :
( m2_finseq_1(A,k7_cqc_lang)
=> ~ ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> r2_hidden(B,k3_calcul_1(A)) ) ) ).
fof(t66_calcul_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_finseq_1(C,k7_cqc_lang)
=> ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,k15_cqc_lang(B,A))))
=> r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,k15_cqc_lang(B,k10_cqc_lang(k10_cqc_lang(A)))))) ) ) ) ) ).
fof(t67_calcul_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_finseq_1(C,k7_cqc_lang)
=> ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,k15_cqc_lang(B,k10_cqc_lang(k10_cqc_lang(A))))))
=> r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,k15_cqc_lang(B,A)))) ) ) ) ) ).
fof(t68_calcul_1,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( m2_finseq_1(C,k7_cqc_lang)
=> ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,k15_cqc_lang(B,A))))
<=> r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,k10_cqc_lang(k16_cqc_lang(B,k10_cqc_lang(A)))))) ) ) ) ) ).
fof(dt_k1_calcul_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(B,A) )
=> m2_finseq_1(k1_calcul_1(A,B),A) ) ).
fof(dt_k2_calcul_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(B,A) )
=> m1_subset_1(k2_calcul_1(A,B),A) ) ).
fof(dt_k3_calcul_1,axiom,
! [A] :
( m1_finseq_1(A,k7_cqc_lang)
=> m1_subset_1(k3_calcul_1(A),k1_zfmisc_1(k2_qc_lang1)) ) ).
fof(dt_k4_calcul_1,axiom,
$true ).
fof(t62_calcul_1,axiom,
! [A] :
( m2_finseq_1(A,k7_cqc_lang)
=> k3_calcul_1(A) = k3_tarski(a_1_0_calcul_1(A)) ) ).
fof(fraenkel_a_1_0_calcul_1,axiom,
! [A,B] :
( m2_finseq_1(B,k7_cqc_lang)
=> ( r2_hidden(A,a_1_0_calcul_1(B))
<=> ? [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
& A = k24_qc_lang1(C)
& ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& r2_hidden(D,k4_relset_1(k5_numbers,k7_cqc_lang,B))
& C = k1_funct_1(B,D) ) ) ) ) ).
%------------------------------------------------------------------------------