SET007 Axioms: SET007+115.ax
%------------------------------------------------------------------------------
% File : SET007+115 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Definable Functions
% 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 : zfmodel2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 25 ( 0 unt; 0 def)
% Number of atoms : 298 ( 38 equ)
% Maximal formula atoms : 25 ( 11 avg)
% Number of connectives : 330 ( 57 ~; 11 |; 113 &)
% ( 8 <=>; 141 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 14 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 19 ( 18 usr; 0 prp; 1-3 aty)
% Number of functors : 31 ( 31 usr; 8 con; 0-4 aty)
% Number of variables : 120 ( 118 !; 2 ?)
% 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(t1_zfmodel2,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_zf_lang)
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( ( v1_zf_lang(C)
& m2_finseq_1(C,k5_numbers) )
=> r1_tarski(k2_zf_model(k6_zf_lang1(C,A,B)),k2_xboole_0(k4_xboole_0(k2_zf_model(C),k1_tarski(A)),k1_tarski(B))) ) ) ) ).
fof(t2_zfmodel2,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_zf_lang)
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( ( v1_zf_lang(C)
& m2_finseq_1(C,k5_numbers) )
=> ( ~ r2_hidden(A,k4_zf_lang1(C))
=> ( ( r2_hidden(B,k2_zf_model(C))
=> k2_zf_model(k6_zf_lang1(C,B,A)) = k2_xboole_0(k4_xboole_0(k2_zf_model(C),k1_tarski(B)),k1_tarski(A)) )
& ( ~ r2_hidden(B,k2_zf_model(C))
=> k2_zf_model(k6_zf_lang1(C,B,A)) = k2_zf_model(C) ) ) ) ) ) ) ).
fof(t3_zfmodel2,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> v1_finset_1(k4_zf_lang1(A)) ) ).
fof(t4_zfmodel2,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ( ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(k2_zf_lang(C),k4_zf_lang1(A))
& r1_xreal_0(B,C) ) ) )
& ~ ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> r2_hidden(B,k4_zf_lang1(A)) ) ) ) ).
fof(t5_zfmodel2,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_zf_lang)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_zf_lang(C)
& m2_finseq_1(C,k5_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_zf_lang,B)
& m2_relset_1(D,k1_zf_lang,B) )
=> ( ~ r2_hidden(A,k4_zf_lang1(C))
=> ( r1_zf_model(B,D,C)
<=> r1_zf_model(B,D,k8_zf_lang(A,C)) ) ) ) ) ) ) ).
fof(t6_zfmodel2,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_zf_lang)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,B)
=> ! [D] :
( ( v1_zf_lang(D)
& m2_finseq_1(D,k5_numbers) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k1_zf_lang,B)
& m2_relset_1(E,k1_zf_lang,B) )
=> ( ~ r2_hidden(A,k4_zf_lang1(D))
=> ( r1_zf_model(B,E,D)
<=> r1_zf_model(B,k1_zf_lang1(B,E,A,C),D) ) ) ) ) ) ) ) ).
fof(t7_zfmodel2,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_zf_lang)
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( m1_subset_1(E,D)
=> ! [F] :
( m1_subset_1(F,D)
=> ! [G] :
( m1_subset_1(G,D)
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,k1_zf_lang,D)
& m2_relset_1(H,k1_zf_lang,D) )
=> ~ ( A != B
& B != C
& C != A
& ~ ( k1_zf_lang1(D,k1_zf_lang1(D,k1_zf_lang1(D,H,A,E),B,F),C,G) = k1_zf_lang1(D,k1_zf_lang1(D,k1_zf_lang1(D,H,C,G),B,F),A,E)
& k1_zf_lang1(D,k1_zf_lang1(D,k1_zf_lang1(D,H,A,E),B,F),C,G) = k1_zf_lang1(D,k1_zf_lang1(D,k1_zf_lang1(D,H,B,F),C,G),A,E) ) ) ) ) ) ) ) ) ) ) ).
fof(t8_zfmodel2,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_zf_lang)
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k1_zf_lang)
=> ! [E] :
( ~ v1_xboole_0(E)
=> ! [F] :
( m1_subset_1(F,E)
=> ! [G] :
( m1_subset_1(G,E)
=> ! [H] :
( m1_subset_1(H,E)
=> ! [I] :
( m1_subset_1(I,E)
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,k1_zf_lang,E)
& m2_relset_1(J,k1_zf_lang,E) )
=> ~ ( A != B
& A != C
& A != D
& B != C
& B != D
& C != D
& ~ ( k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,J,A,F),B,G),C,H),D,I) = k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,J,B,G),C,H),D,I),A,F)
& k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,J,A,F),B,G),C,H),D,I) = k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,J,C,H),D,I),A,F),B,G)
& k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,J,A,F),B,G),C,H),D,I) = k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,J,D,I),B,G),C,H),A,F) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t9_zfmodel2,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_zf_lang)
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k1_zf_lang)
=> ! [E] :
( ~ v1_xboole_0(E)
=> ! [F] :
( m1_subset_1(F,E)
=> ! [G] :
( m1_subset_1(G,E)
=> ! [H] :
( m1_subset_1(H,E)
=> ! [I] :
( m1_subset_1(I,E)
=> ! [J] :
( m1_subset_1(J,E)
=> ! [K] :
( ( v1_funct_1(K)
& v1_funct_2(K,k1_zf_lang,E)
& m2_relset_1(K,k1_zf_lang,E) )
=> ( k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,K,A,F),B,G),A,H) = k1_zf_lang1(E,k1_zf_lang1(E,K,B,G),A,H)
& k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,K,A,F),B,G),C,I),A,H) = k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,K,B,G),C,I),A,H)
& k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,K,A,F),B,G),C,I),D,J),A,H) = k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,k1_zf_lang1(E,K,B,G),C,I),D,J),A,H) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t10_zfmodel2,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_zf_lang)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,B)
=> ! [D] :
( ( v1_zf_lang(D)
& m2_finseq_1(D,k5_numbers) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k1_zf_lang,B)
& m2_relset_1(E,k1_zf_lang,B) )
=> ( ~ r2_hidden(A,k2_zf_model(D))
=> ( r1_zf_model(B,E,D)
<=> r1_zf_model(B,k1_zf_lang1(B,E,A,C),D) ) ) ) ) ) ) ) ).
fof(t11_zfmodel2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_zf_lang,A)
& m2_relset_1(C,k1_zf_lang,A) )
=> ( r1_zf_model(A,C,k8_zf_lang(k2_zf_lang(np__3),k13_zf_lang(k2_zf_lang(np__0),k8_zf_lang(k2_zf_lang(np__4),k12_zf_lang(B,k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0)))))))
=> ( r2_hidden(k2_zf_lang(np__0),k2_zf_model(B))
| ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> ( k8_funct_2(A,A,k1_zfmodel1(B,A,C),D) = E
<=> r1_zf_model(A,k1_zf_lang1(A,k1_zf_lang1(A,C,k2_zf_lang(np__3),D),k2_zf_lang(np__4),E),B) ) ) ) ) ) ) ) ) ).
fof(t12_zfmodel2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_zf_lang,A)
& m2_relset_1(C,k1_zf_lang,A) )
=> ( ( r1_tarski(k2_zf_model(B),k2_tarski(k2_zf_lang(np__3),k2_zf_lang(np__4)))
& r2_zf_model(A,k8_zf_lang(k2_zf_lang(np__3),k13_zf_lang(k2_zf_lang(np__0),k8_zf_lang(k2_zf_lang(np__4),k12_zf_lang(B,k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0))))))) )
=> k1_zfmodel1(B,A,C) = k2_zfmodel1(B,A) ) ) ) ) ).
fof(t13_zfmodel2,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_zf_lang)
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_zf_lang(D)
& m2_finseq_1(D,k5_numbers) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k1_zf_lang,C)
& m2_relset_1(E,k1_zf_lang,C) )
=> ( ~ r2_hidden(A,k4_zf_lang1(D))
=> ( r1_zf_model(C,E,k6_zf_lang1(D,B,A))
<=> r1_zf_model(C,k1_zf_lang1(C,E,B,k8_funct_2(k1_zf_lang,C,E,A)),D) ) ) ) ) ) ) ) ).
fof(t14_zfmodel2,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_zf_lang)
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_zf_lang(D)
& m2_finseq_1(D,k5_numbers) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k1_zf_lang,C)
& m2_relset_1(E,k1_zf_lang,C) )
=> ( r1_zf_model(C,E,D)
=> ( r2_hidden(A,k4_zf_lang1(D))
| r1_zf_model(C,k1_zf_lang1(C,E,A,k8_funct_2(k1_zf_lang,C,E,B)),k6_zf_lang1(D,B,A)) ) ) ) ) ) ) ) ).
fof(t15_zfmodel2,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_zf_lang)
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_zf_lang(D)
& m2_finseq_1(D,k5_numbers) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k1_zf_lang,C)
& m2_relset_1(E,k1_zf_lang,C) )
=> ( r1_zf_model(C,E,k8_zf_lang(k2_zf_lang(np__3),k13_zf_lang(k2_zf_lang(np__0),k8_zf_lang(k2_zf_lang(np__4),k12_zf_lang(D,k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0)))))))
=> ( r2_hidden(k2_zf_lang(np__0),k2_zf_model(D))
| r2_hidden(A,k4_zf_lang1(D))
| B = k2_zf_lang(np__3)
| B = k2_zf_lang(np__4)
| r2_hidden(B,k2_zf_model(D))
| A = k2_zf_lang(np__0)
| A = k2_zf_lang(np__3)
| A = k2_zf_lang(np__4)
| ( ~ r2_hidden(k2_zf_lang(np__0),k2_zf_model(k6_zf_lang1(D,B,A)))
& r1_zf_model(C,k1_zf_lang1(C,E,A,k8_funct_2(k1_zf_lang,C,E,B)),k8_zf_lang(k2_zf_lang(np__3),k13_zf_lang(k2_zf_lang(np__0),k8_zf_lang(k2_zf_lang(np__4),k12_zf_lang(k6_zf_lang1(D,B,A),k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0)))))))
& k1_zfmodel1(D,C,E) = k1_zfmodel1(k6_zf_lang1(D,B,A),C,k1_zf_lang1(C,E,A,k8_funct_2(k1_zf_lang,C,E,B))) ) ) ) ) ) ) ) ) ).
fof(t16_zfmodel2,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_zf_lang)
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_zf_lang(D)
& m2_finseq_1(D,k5_numbers) )
=> ( ~ r2_hidden(A,k4_zf_lang1(D))
=> ( r2_zf_model(C,k6_zf_lang1(D,B,A))
<=> r2_zf_model(C,D) ) ) ) ) ) ) ).
fof(t17_zfmodel2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_zf_lang(C)
& m2_finseq_1(C,k5_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_zf_lang,A)
& m2_relset_1(D,k1_zf_lang,A) )
=> ~ ( ~ r2_hidden(k2_zf_lang(np__0),k2_zf_model(C))
& r1_zf_model(A,D,k8_zf_lang(k2_zf_lang(np__3),k13_zf_lang(k2_zf_lang(np__0),k8_zf_lang(k2_zf_lang(np__4),k12_zf_lang(C,k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0)))))))
& ! [E] :
( ( v1_zf_lang(E)
& m2_finseq_1(E,k5_numbers) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k1_zf_lang,A)
& m2_relset_1(F,k1_zf_lang,A) )
=> ~ ( ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(B,G)
& r2_hidden(k2_zf_lang(G),k4_zf_lang1(E))
& G != np__3
& G != np__4 ) )
& ~ r2_hidden(k2_zf_lang(np__0),k2_zf_model(E))
& r1_zf_model(A,F,k8_zf_lang(k2_zf_lang(np__3),k13_zf_lang(k2_zf_lang(np__0),k8_zf_lang(k2_zf_lang(np__4),k12_zf_lang(E,k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0)))))))
& k1_zfmodel1(C,A,D) = k1_zfmodel1(E,A,F) ) ) ) ) ) ) ) ) ).
fof(t18_zfmodel2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_zf_lang,A)
& m2_relset_1(C,k1_zf_lang,A) )
=> ~ ( ~ r2_hidden(k2_zf_lang(np__0),k2_zf_model(B))
& r1_zf_model(A,C,k8_zf_lang(k2_zf_lang(np__3),k13_zf_lang(k2_zf_lang(np__0),k8_zf_lang(k2_zf_lang(np__4),k12_zf_lang(B,k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0)))))))
& ! [D] :
( ( v1_zf_lang(D)
& m2_finseq_1(D,k5_numbers) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k1_zf_lang,A)
& m2_relset_1(E,k1_zf_lang,A) )
=> ~ ( r1_tarski(k5_subset_1(k1_zf_lang,k2_zf_model(B),k2_zf_model(D)),k2_tarski(k2_zf_lang(np__3),k2_zf_lang(np__4)))
& ~ r2_hidden(k2_zf_lang(np__0),k2_zf_model(D))
& r1_zf_model(A,E,k8_zf_lang(k2_zf_lang(np__3),k13_zf_lang(k2_zf_lang(np__0),k8_zf_lang(k2_zf_lang(np__4),k12_zf_lang(D,k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0)))))))
& k1_zfmodel1(B,A,C) = k1_zfmodel1(D,A,E) ) ) ) ) ) ) ) ).
fof(t19_zfmodel2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( ( r1_zfmodel1(B,A)
& r1_zfmodel1(C,A) )
=> r1_zfmodel1(k5_relat_1(C,B),A) ) ) ) ) ).
fof(t20_zfmodel2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_zf_lang,A)
& m2_relset_1(C,k1_zf_lang,A) )
=> ( ~ r2_hidden(k2_zf_lang(np__0),k2_zf_model(B))
=> ( r1_zf_model(A,C,k8_zf_lang(k2_zf_lang(np__3),k13_zf_lang(k2_zf_lang(np__0),k8_zf_lang(k2_zf_lang(np__4),k12_zf_lang(B,k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0)))))))
<=> ! [D] :
( m1_subset_1(D,A)
=> ? [E] :
( m1_subset_1(E,A)
& ! [F] :
( m1_subset_1(F,A)
=> ( r1_zf_model(A,k1_zf_lang1(A,k1_zf_lang1(A,C,k2_zf_lang(np__3),D),k2_zf_lang(np__4),F),B)
<=> F = E ) ) ) ) ) ) ) ) ) ).
fof(t21_zfmodel2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( ( r1_zfmodel1(C,A)
& r1_zfmodel1(D,A)
& r1_tarski(k2_zf_model(B),k1_tarski(k2_zf_lang(np__3))) )
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( ( k1_relat_1(E) = A
& ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k1_zf_lang,A)
& m2_relset_1(F,k1_zf_lang,A) )
=> ( ( r1_zf_model(A,F,B)
=> k1_funct_1(E,k8_funct_2(k1_zf_lang,A,F,k2_zf_lang(np__3))) = k1_funct_1(C,k8_funct_2(k1_zf_lang,A,F,k2_zf_lang(np__3))) )
& ( r1_zf_model(A,F,k6_zf_lang(B))
=> k1_funct_1(E,k8_funct_2(k1_zf_lang,A,F,k2_zf_lang(np__3))) = k1_funct_1(D,k8_funct_2(k1_zf_lang,A,F,k2_zf_lang(np__3))) ) ) ) )
=> r1_zfmodel1(E,A) ) ) ) ) ) ) ) ).
fof(t22_zfmodel2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( ( r2_zfmodel1(B,A)
& r2_zfmodel1(C,A) )
=> r2_zfmodel1(k5_relat_1(B,C),A) ) ) ) ) ).
fof(t23_zfmodel2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ( v1_zf_lang(C)
& m2_finseq_1(C,k5_numbers) )
=> ! [D] :
( ( v1_zf_lang(D)
& m2_finseq_1(D,k5_numbers) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k1_zf_lang,A)
& m2_relset_1(E,k1_zf_lang,A) )
=> ( ( r1_xboole_0(k1_enumset1(k2_zf_lang(np__0),k2_zf_lang(np__1),k2_zf_lang(np__2)),k2_zf_model(B))
& r1_zf_model(A,E,k8_zf_lang(k2_zf_lang(np__3),k13_zf_lang(k2_zf_lang(np__0),k8_zf_lang(k2_zf_lang(np__4),k12_zf_lang(B,k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0)))))))
& r1_xboole_0(k1_enumset1(k2_zf_lang(np__0),k2_zf_lang(np__1),k2_zf_lang(np__2)),k2_zf_model(C))
& r1_zf_model(A,E,k8_zf_lang(k2_zf_lang(np__3),k13_zf_lang(k2_zf_lang(np__0),k8_zf_lang(k2_zf_lang(np__4),k12_zf_lang(C,k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0)))))))
& r1_xboole_0(k1_enumset1(k2_zf_lang(np__0),k2_zf_lang(np__1),k2_zf_lang(np__2)),k2_zf_model(D)) )
=> ( r2_hidden(k2_zf_lang(np__4),k2_zf_model(D))
| ! [F] :
( ( v1_relat_1(F)
& v1_funct_1(F) )
=> ( ( k1_relat_1(F) = A
& ! [G] :
( m1_subset_1(G,A)
=> ( ( r1_zf_model(A,k1_zf_lang1(A,E,k2_zf_lang(np__3),G),D)
=> k1_funct_1(F,G) = k8_funct_2(A,A,k1_zfmodel1(B,A,E),G) )
& ( r1_zf_model(A,k1_zf_lang1(A,E,k2_zf_lang(np__3),G),k6_zf_lang(D))
=> k1_funct_1(F,G) = k8_funct_2(A,A,k1_zfmodel1(C,A,E),G) ) ) ) )
=> r2_zfmodel1(F,A) ) ) ) ) ) ) ) ) ) ).
fof(t24_zfmodel2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> r1_zfmodel1(k6_partfun1(A),A) ) ).
fof(t25_zfmodel2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> r2_zfmodel1(k6_partfun1(A),A) ) ).
%------------------------------------------------------------------------------