SET007 Axioms: SET007+865.ax
%------------------------------------------------------------------------------
% File : SET007+865 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Godel's Completeness Theorem
% 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 : goedelcp [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 53 ( 3 unt; 0 def)
% Number of atoms : 298 ( 22 equ)
% Maximal formula atoms : 17 ( 5 avg)
% Number of connectives : 263 ( 18 ~; 5 |; 67 &)
% ( 27 <=>; 146 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 25 ( 24 usr; 0 prp; 1-4 aty)
% Number of functors : 43 ( 43 usr; 12 con; 0-4 aty)
% Number of variables : 136 ( 127 !; 9 ?)
% 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(d1_goedelcp,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ( v1_goedelcp(A)
<=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( r1_henmodel(A,B)
| r1_henmodel(A,k10_cqc_lang(B)) ) ) ) ) ).
fof(d2_goedelcp,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ( v2_goedelcp(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,k1_qc_lang1,k2_qc_lang1)
& r1_henmodel(A,k13_cqc_lang(k10_cqc_lang(k16_cqc_lang(B,C)),k4_substut2(C,B,D))) ) ) ) ) ) ).
fof(t1_goedelcp,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( ( v1_henmodel(B)
& m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang)) )
=> ( v1_goedelcp(B)
=> ( r1_henmodel(B,A)
<=> ~ r1_henmodel(B,k10_cqc_lang(A)) ) ) ) ) ).
fof(t2_goedelcp,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,k13_cqc_lang(k10_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(t3_goedelcp,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(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)
=> ( v2_goedelcp(A)
=> ( r1_henmodel(A,k16_cqc_lang(C,B))
<=> ? [D] :
( m2_subset_1(D,k1_qc_lang1,k2_qc_lang1)
& r1_henmodel(A,k4_substut2(B,C,D)) ) ) ) ) ) ) ).
fof(t4_goedelcp,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( ( v1_henmodel(B)
& m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang)) )
=> ! [C] :
( m1_henmodel(C,B)
=> ( ( v1_goedelcp(B)
& v2_goedelcp(B) )
=> ( ( v1_goedelcp(B)
& v2_goedelcp(B)
& ~ ( r1_valuat_1(k2_henmodel,A,C,k4_henmodel)
<=> r1_henmodel(B,A) ) )
| ( r1_valuat_1(k2_henmodel,k10_cqc_lang(A),C,k4_henmodel)
<=> r1_henmodel(B,k10_cqc_lang(A)) ) ) ) ) ) ) ).
fof(t5_goedelcp,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,B))) )
=> r4_calcul_1(k8_finseq_1(k7_cqc_lang,C,k12_finseq_1(k7_cqc_lang,k11_cqc_lang(A,B)))) ) ) ) ) ).
fof(t6_goedelcp,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(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)
=> ( ( r1_henmodel(A,B)
& r1_henmodel(A,C) )
<=> r1_henmodel(A,k11_cqc_lang(B,C)) ) ) ) ) ).
fof(t7_goedelcp,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( ( v1_henmodel(C)
& m1_subset_1(C,k1_zfmisc_1(k7_cqc_lang)) )
=> ! [D] :
( m1_henmodel(D,C)
=> ( ( v1_goedelcp(C)
& v2_goedelcp(C) )
=> ( ( v1_goedelcp(C)
& v2_goedelcp(C)
& ~ ( r1_valuat_1(k2_henmodel,A,D,k4_henmodel)
<=> r1_henmodel(C,A) ) )
| ( v1_goedelcp(C)
& v2_goedelcp(C)
& ~ ( r1_valuat_1(k2_henmodel,B,D,k4_henmodel)
<=> r1_henmodel(C,B) ) )
| ( r1_valuat_1(k2_henmodel,k11_cqc_lang(A,B),D,k4_henmodel)
<=> r1_henmodel(C,k11_cqc_lang(A,B)) ) ) ) ) ) ) ) ).
fof(t8_goedelcp,axiom,
! [A] :
( ( v1_henmodel(A)
& m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang)) )
=> ! [B] :
( m1_henmodel(B,A)
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ( ( r1_xreal_0(k6_cqc_sim1(C),np__0)
& v1_goedelcp(A)
& v2_goedelcp(A) )
=> ( r1_valuat_1(k2_henmodel,C,B,k4_henmodel)
<=> r1_henmodel(A,C) ) ) ) ) ) ).
fof(t9_goedelcp,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_valuat_1(D,C)
=> ! [E] :
( m1_subset_1(E,k2_valuat_1(C))
=> ( r1_valuat_1(C,k16_cqc_lang(B,A),D,E)
<=> ? [F] :
( m1_subset_1(F,C)
& r1_valuat_1(C,A,D,k1_sublemma(C,E,k13_sublemma(C,F,B))) ) ) ) ) ) ) ) ).
fof(t10_goedelcp,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( ( v1_henmodel(C)
& m1_subset_1(C,k1_zfmisc_1(k7_cqc_lang)) )
=> ! [D] :
( m1_henmodel(D,C)
=> ( r1_valuat_1(k2_henmodel,k16_cqc_lang(B,A),D,k4_henmodel)
<=> ? [E] :
( m2_subset_1(E,k1_qc_lang1,k2_qc_lang1)
& r1_valuat_1(k2_henmodel,k4_substut2(A,B,E),D,k4_henmodel) ) ) ) ) ) ) ).
fof(t11_goedelcp,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_valuat_1(D,C)
=> ! [E] :
( m1_subset_1(E,k2_valuat_1(C))
=> ( r1_valuat_1(C,k10_cqc_lang(k16_cqc_lang(B,k10_cqc_lang(A))),D,E)
<=> r1_valuat_1(C,k15_cqc_lang(B,A),D,E) ) ) ) ) ) ) ).
fof(t12_goedelcp,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(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)
=> ( r1_henmodel(A,k10_cqc_lang(k16_cqc_lang(C,k10_cqc_lang(B))))
<=> r1_henmodel(A,k15_cqc_lang(C,B)) ) ) ) ) ).
fof(t13_goedelcp,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(k16_cqc_lang(B,A)) = k1_nat_1(k6_cqc_sim1(A),np__1) ) ) ).
fof(t14_goedelcp,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)
=> k6_cqc_sim1(A) = k6_cqc_sim1(k4_substut2(A,B,C)) ) ) ) ).
fof(t15_goedelcp,axiom,
! [A] :
( ( v1_henmodel(A)
& m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang)) )
=> ! [B] :
( m1_henmodel(B,A)
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ( ( k6_cqc_sim1(C) = np__1
& v1_goedelcp(A)
& v2_goedelcp(A) )
=> ( r1_valuat_1(k2_henmodel,C,B,k4_henmodel)
<=> r1_henmodel(A,C) ) ) ) ) ) ).
fof(t16_goedelcp,axiom,
! [A] :
( ( v1_henmodel(A)
& m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang)) )
=> ! [B] :
( m1_henmodel(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ( ( r1_xreal_0(k6_cqc_sim1(D),C)
& v1_goedelcp(A)
& v2_goedelcp(A) )
=> ( r1_valuat_1(k2_henmodel,D,B,k4_henmodel)
<=> r1_henmodel(A,D) ) ) )
=> ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ( ( r1_xreal_0(k6_cqc_sim1(D),k1_nat_1(C,np__1))
& v1_goedelcp(A)
& v2_goedelcp(A) )
=> ( r1_valuat_1(k2_henmodel,D,B,k4_henmodel)
<=> r1_henmodel(A,D) ) ) ) ) ) ) ) ).
fof(t17_goedelcp,axiom,
! [A] :
( ( v1_henmodel(A)
& m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang)) )
=> ! [B] :
( m1_henmodel(B,A)
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ( ( v1_goedelcp(A)
& v2_goedelcp(A) )
=> ( r1_valuat_1(k2_henmodel,C,B,k4_henmodel)
<=> r1_henmodel(A,C) ) ) ) ) ) ).
fof(t18_goedelcp,axiom,
v1_card_4(k8_qc_lang1) ).
fof(d3_goedelcp,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ( A = k1_goedelcp
<=> ! [B] :
( r2_hidden(B,A)
<=> ? [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
& ? [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
& B = k16_cqc_lang(C,D) ) ) ) ) ) ).
fof(t19_goedelcp,axiom,
v1_card_4(k7_cqc_lang) ).
fof(t20_goedelcp,axiom,
( ~ v1_xboole_0(k1_goedelcp)
& v1_card_4(k1_goedelcp) ) ).
fof(d4_goedelcp,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> ( v4_qc_lang2(A)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ( B = k2_goedelcp(A)
<=> ? [C] :
( m1_subset_1(C,k8_qc_lang1)
& A = k5_qc_lang2(B,C) ) ) ) ) ) ).
fof(d5_goedelcp,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ( v4_qc_lang2(A)
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( B = k3_goedelcp(A)
<=> ? [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
& A = k16_cqc_lang(C,B) ) ) ) ) ) ).
fof(d6_goedelcp,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k7_cqc_lang)
& m2_relset_1(A,k5_numbers,k7_cqc_lang) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_qc_lang1,k2_qc_lang1)
=> ( C = k4_goedelcp(A,B)
<=> ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ( D = k8_funct_2(k5_numbers,k7_cqc_lang,A,B)
=> C = k2_goedelcp(D) ) ) ) ) ) ) ).
fof(d7_goedelcp,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k7_cqc_lang)
& m2_relset_1(A,k5_numbers,k7_cqc_lang) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ( C = k5_goedelcp(A,B)
<=> ! [D] :
( m2_subset_1(D,k8_qc_lang1,k7_cqc_lang)
=> ( D = k8_funct_2(k5_numbers,k7_cqc_lang,A,B)
=> C = k3_goedelcp(D) ) ) ) ) ) ) ).
fof(t21_goedelcp,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( r2_hidden(B,A)
=> r1_henmodel(A,B) ) ) ) ).
fof(t22_goedelcp,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> ( k2_goedelcp(k16_cqc_lang(B,A)) = B
& k3_goedelcp(k16_cqc_lang(B,A)) = A ) ) ) ).
fof(t23_goedelcp,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> r1_henmodel(A,k9_cqc_lang) ) ).
fof(t24_goedelcp,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ( r1_henmodel(A,k10_cqc_lang(k9_cqc_lang))
<=> ~ v1_henmodel(A) ) ) ).
fof(t25_goedelcp,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)
=> ( r4_calcul_1(k8_finseq_1(k7_cqc_lang,B,k12_finseq_1(k7_cqc_lang,A)))
=> ( r1_xreal_0(k3_finseq_1(B),np__0)
| r4_calcul_1(k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,k8_finseq_1(k7_cqc_lang,k1_calcul_1(k7_cqc_lang,B),C),k12_finseq_1(k7_cqc_lang,k2_calcul_1(k7_cqc_lang,B))),k12_finseq_1(k7_cqc_lang,A))) ) ) ) ) ) ).
fof(t26_goedelcp,axiom,
! [A] :
( m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)
=> k6_goedelcp(k6_domain_1(k7_cqc_lang,A)) = k24_qc_lang1(A) ) ).
fof(t27_goedelcp,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
=> k6_goedelcp(k4_subset_1(k7_cqc_lang,A,B)) = k4_subset_1(k2_qc_lang1,k6_goedelcp(A),k6_goedelcp(B)) ) ) ).
fof(t28_goedelcp,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k2_qc_lang1))
=> ~ ( v1_finset_1(A)
& ! [B] :
( m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)
=> r2_hidden(B,A) ) ) ) ).
fof(t29_goedelcp,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
=> ( r1_tarski(A,B)
=> r1_tarski(k6_goedelcp(A),k6_goedelcp(B)) ) ) ) ).
fof(t30_goedelcp,axiom,
! [A] :
( m2_finseq_1(A,k7_cqc_lang)
=> k6_goedelcp(k5_relset_1(k5_numbers,k7_cqc_lang,A)) = k3_calcul_1(A) ) ).
fof(t31_goedelcp,axiom,
! [A] :
( ( v1_henmodel(A)
& m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang)) )
=> ~ ( v1_finset_1(k6_goedelcp(A))
& ! [B] :
( ( v1_henmodel(B)
& m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang)) )
=> ~ ( r1_tarski(A,B)
& v2_goedelcp(B) ) ) ) ) ).
fof(t32_goedelcp,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
=> ! [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
=> ( ( r1_henmodel(A,C)
& r1_tarski(A,B) )
=> r1_henmodel(B,C) ) ) ) ) ).
fof(t33_goedelcp,axiom,
! [A] :
( ( v1_henmodel(A)
& m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang)) )
=> ~ ( v2_goedelcp(A)
& ! [B] :
( ( v1_henmodel(B)
& m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang)) )
=> ~ ( r1_tarski(A,B)
& v1_goedelcp(B)
& v2_goedelcp(B) ) ) ) ) ).
fof(t34_goedelcp,axiom,
! [A] :
( ( v1_henmodel(A)
& m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang)) )
=> ~ ( v1_finset_1(k6_goedelcp(A))
& ! [B] :
( ( v1_henmodel(B)
& m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang)) )
=> ! [C] :
( m1_henmodel(C,B)
=> ~ r6_calcul_1(A,k2_henmodel,C,k4_henmodel) ) ) ) ) ).
fof(t35_goedelcp,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_valuat_1(D,C)
=> ! [E] :
( m1_subset_1(E,k2_valuat_1(C))
=> ( ( r6_calcul_1(A,C,D,E)
& r1_tarski(B,A) )
=> r6_calcul_1(B,C,D,E) ) ) ) ) ) ) ).
fof(t36_goedelcp,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( v1_finset_1(k6_goedelcp(A))
=> v1_finset_1(k6_goedelcp(k4_subset_1(k7_cqc_lang,A,k6_domain_1(k7_cqc_lang,B)))) ) ) ) ).
fof(t37_goedelcp,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_valuat_1(D,C)
=> ! [E] :
( m1_subset_1(E,k2_valuat_1(C))
=> ~ ( r7_calcul_1(A,B)
& r6_calcul_1(k4_subset_1(k7_cqc_lang,A,k6_domain_1(k7_cqc_lang,k10_cqc_lang(B))),C,D,E) ) ) ) ) ) ) ).
fof(t38_goedelcp,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> ! [B] :
( m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)
=> ( ( v1_finset_1(k6_goedelcp(A))
& r7_calcul_1(A,B) )
=> r1_henmodel(A,B) ) ) ) ).
fof(dt_k1_goedelcp,axiom,
m1_subset_1(k1_goedelcp,k1_zfmisc_1(k7_cqc_lang)) ).
fof(dt_k2_goedelcp,axiom,
! [A] :
( m1_subset_1(A,k8_qc_lang1)
=> m2_subset_1(k2_goedelcp(A),k1_qc_lang1,k2_qc_lang1) ) ).
fof(dt_k3_goedelcp,axiom,
! [A] :
( m1_subset_1(A,k7_cqc_lang)
=> m2_subset_1(k3_goedelcp(A),k8_qc_lang1,k7_cqc_lang) ) ).
fof(dt_k4_goedelcp,axiom,
! [A,B] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k7_cqc_lang)
& m1_relset_1(A,k5_numbers,k7_cqc_lang)
& m1_subset_1(B,k5_numbers) )
=> m2_subset_1(k4_goedelcp(A,B),k1_qc_lang1,k2_qc_lang1) ) ).
fof(dt_k5_goedelcp,axiom,
! [A,B] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k7_cqc_lang)
& m1_relset_1(A,k5_numbers,k7_cqc_lang)
& m1_subset_1(B,k5_numbers) )
=> m2_subset_1(k5_goedelcp(A,B),k8_qc_lang1,k7_cqc_lang) ) ).
fof(dt_k6_goedelcp,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> m1_subset_1(k6_goedelcp(A),k1_zfmisc_1(k2_qc_lang1)) ) ).
fof(d8_goedelcp,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k7_cqc_lang))
=> k6_goedelcp(A) = k3_tarski(a_1_0_goedelcp(A)) ) ).
fof(fraenkel_a_1_0_goedelcp,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k7_cqc_lang))
=> ( r2_hidden(A,a_1_0_goedelcp(B))
<=> ? [C] :
( m2_subset_1(C,k8_qc_lang1,k7_cqc_lang)
& A = k24_qc_lang1(C)
& r2_hidden(C,B) ) ) ) ).
%------------------------------------------------------------------------------