SET007 Axioms: SET007+73.ax
%------------------------------------------------------------------------------
% File : SET007+73 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Replacing of Variables in Formulas of ZF Theory
% 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 : zf_lang1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 215 ( 9 unt; 0 def)
% Number of atoms : 1575 ( 234 equ)
% Maximal formula atoms : 23 ( 7 avg)
% Number of connectives : 1505 ( 145 ~; 5 |; 588 &)
% ( 41 <=>; 726 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 33 ( 31 usr; 1 prp; 0-3 aty)
% Number of functors : 60 ( 60 usr; 9 con; 0-7 aty)
% Number of variables : 669 ( 661 !; 8 ?)
% 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_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m1_finseq_1(A,k5_numbers) )
=> v1_finset_1(k1_zf_model(A)) ) ).
fof(t1_zf_lang1,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_zf_lang)
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ( k18_zf_lang(k4_zf_lang(A,B)) = A
& k19_zf_lang(k4_zf_lang(A,B)) = B ) ) ) ).
fof(t2_zf_lang1,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_zf_lang)
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ( k18_zf_lang(k5_zf_lang(A,B)) = A
& k19_zf_lang(k5_zf_lang(A,B)) = B ) ) ) ).
fof(t3_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> k20_zf_lang(k6_zf_lang(A)) = A ) ).
fof(t4_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ( k21_zf_lang(k7_zf_lang(A,B)) = A
& k22_zf_lang(k7_zf_lang(A,B)) = B ) ) ) ).
fof(t5_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ( k21_zf_lang(k10_zf_lang(A,B)) = A
& k22_zf_lang(k10_zf_lang(A,B)) = B ) ) ) ).
fof(t6_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ( k25_zf_lang(k11_zf_lang(A,B)) = A
& k26_zf_lang(k11_zf_lang(A,B)) = B ) ) ) ).
fof(t7_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ( k27_zf_lang(k12_zf_lang(A,B)) = A
& k28_zf_lang(k12_zf_lang(A,B)) = B ) ) ) ).
fof(t8_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ( k23_zf_lang(k8_zf_lang(B,A)) = B
& k24_zf_lang(k8_zf_lang(B,A)) = A ) ) ) ).
fof(t9_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ( k23_zf_lang(k13_zf_lang(B,A)) = B
& k24_zf_lang(k13_zf_lang(B,A)) = A ) ) ) ).
fof(t10_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> k10_zf_lang(A,B) = k11_zf_lang(k6_zf_lang(A),B) ) ) ).
fof(t11_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k1_zf_lang)
=> ! [E] :
( m2_subset_1(E,k5_numbers,k1_zf_lang)
=> ( k14_zf_lang(C,D,A) = k8_zf_lang(E,B)
=> ( C = E
& k8_zf_lang(D,A) = B ) ) ) ) ) ) ) ).
fof(t12_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k1_zf_lang)
=> ! [E] :
( m2_subset_1(E,k5_numbers,k1_zf_lang)
=> ( k15_zf_lang(C,D,A) = k13_zf_lang(E,B)
=> ( C = E
& k13_zf_lang(D,A) = B ) ) ) ) ) ) ) ).
fof(t13_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ( v6_zf_lang(k14_zf_lang(B,C,A))
& k23_zf_lang(k14_zf_lang(B,C,A)) = B
& k24_zf_lang(k14_zf_lang(B,C,A)) = k8_zf_lang(C,A) ) ) ) ) ).
fof(t14_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ( v11_zf_lang(k15_zf_lang(B,C,A))
& k23_zf_lang(k15_zf_lang(B,C,A)) = B
& k24_zf_lang(k15_zf_lang(B,C,A)) = k13_zf_lang(C,A) ) ) ) ) ).
fof(t15_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [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)
=> ( k16_zf_lang(B,C,D,A) = k8_zf_lang(B,k8_zf_lang(C,k8_zf_lang(D,A)))
& k16_zf_lang(B,C,D,A) = k14_zf_lang(B,C,k8_zf_lang(D,A)) ) ) ) ) ) ).
fof(t16_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k1_zf_lang)
=> ! [E] :
( m2_subset_1(E,k5_numbers,k1_zf_lang)
=> ! [F] :
( m2_subset_1(F,k5_numbers,k1_zf_lang)
=> ( k14_zf_lang(C,D,A) = k14_zf_lang(E,F,B)
=> ( C = E
& D = F
& A = B ) ) ) ) ) ) ) ) ).
fof(t17_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k1_zf_lang)
=> ! [E] :
( m2_subset_1(E,k5_numbers,k1_zf_lang)
=> ! [F] :
( m2_subset_1(F,k5_numbers,k1_zf_lang)
=> ! [G] :
( m2_subset_1(G,k5_numbers,k1_zf_lang)
=> ! [H] :
( m2_subset_1(H,k5_numbers,k1_zf_lang)
=> ( k16_zf_lang(C,D,E,A) = k16_zf_lang(F,G,H,B)
=> ( C = F
& D = G
& E = H
& A = B ) ) ) ) ) ) ) ) ) ) ).
fof(t18_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k1_zf_lang)
=> ! [E] :
( m2_subset_1(E,k5_numbers,k1_zf_lang)
=> ! [F] :
( m2_subset_1(F,k5_numbers,k1_zf_lang)
=> ( k16_zf_lang(C,D,E,A) = k8_zf_lang(F,B)
=> ( C = F
& k14_zf_lang(D,E,A) = B ) ) ) ) ) ) ) ) ).
fof(t19_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k1_zf_lang)
=> ! [E] :
( m2_subset_1(E,k5_numbers,k1_zf_lang)
=> ! [F] :
( m2_subset_1(F,k5_numbers,k1_zf_lang)
=> ! [G] :
( m2_subset_1(G,k5_numbers,k1_zf_lang)
=> ( k16_zf_lang(C,D,E,A) = k14_zf_lang(F,G,B)
=> ( C = F
& D = G
& k8_zf_lang(E,A) = B ) ) ) ) ) ) ) ) ) ).
fof(t20_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k1_zf_lang)
=> ! [E] :
( m2_subset_1(E,k5_numbers,k1_zf_lang)
=> ! [F] :
( m2_subset_1(F,k5_numbers,k1_zf_lang)
=> ( k15_zf_lang(C,D,A) = k15_zf_lang(E,F,B)
=> ( C = E
& D = F
& A = B ) ) ) ) ) ) ) ) ).
fof(t21_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [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)
=> ( k17_zf_lang(B,C,D,A) = k13_zf_lang(B,k13_zf_lang(C,k13_zf_lang(D,A)))
& k17_zf_lang(B,C,D,A) = k15_zf_lang(B,C,k13_zf_lang(D,A)) ) ) ) ) ) ).
fof(t22_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k1_zf_lang)
=> ! [E] :
( m2_subset_1(E,k5_numbers,k1_zf_lang)
=> ! [F] :
( m2_subset_1(F,k5_numbers,k1_zf_lang)
=> ! [G] :
( m2_subset_1(G,k5_numbers,k1_zf_lang)
=> ! [H] :
( m2_subset_1(H,k5_numbers,k1_zf_lang)
=> ( k17_zf_lang(C,D,E,A) = k17_zf_lang(F,G,H,B)
=> ( C = F
& D = G
& E = H
& A = B ) ) ) ) ) ) ) ) ) ) ).
fof(t23_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k1_zf_lang)
=> ! [E] :
( m2_subset_1(E,k5_numbers,k1_zf_lang)
=> ! [F] :
( m2_subset_1(F,k5_numbers,k1_zf_lang)
=> ( k17_zf_lang(C,D,E,A) = k13_zf_lang(F,B)
=> ( C = F
& k15_zf_lang(D,E,A) = B ) ) ) ) ) ) ) ) ).
fof(t24_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k1_zf_lang)
=> ! [E] :
( m2_subset_1(E,k5_numbers,k1_zf_lang)
=> ! [F] :
( m2_subset_1(F,k5_numbers,k1_zf_lang)
=> ! [G] :
( m2_subset_1(G,k5_numbers,k1_zf_lang)
=> ( k17_zf_lang(C,D,E,A) = k15_zf_lang(F,G,B)
=> ( C = F
& D = G
& k13_zf_lang(E,A) = B ) ) ) ) ) ) ) ) ) ).
fof(t25_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [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)
=> ( v6_zf_lang(k16_zf_lang(B,C,D,A))
& k23_zf_lang(k16_zf_lang(B,C,D,A)) = B
& k24_zf_lang(k16_zf_lang(B,C,D,A)) = k14_zf_lang(C,D,A) ) ) ) ) ) ).
fof(t26_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [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)
=> ( v11_zf_lang(k17_zf_lang(B,C,D,A))
& k23_zf_lang(k17_zf_lang(B,C,D,A)) = B
& k24_zf_lang(k17_zf_lang(B,C,D,A)) = k15_zf_lang(C,D,A) ) ) ) ) ) ).
fof(t27_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ( v8_zf_lang(A)
=> k21_zf_lang(A) = k20_zf_lang(k21_zf_lang(k20_zf_lang(A))) ) ) ).
fof(t28_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ( v8_zf_lang(A)
=> k22_zf_lang(A) = k20_zf_lang(k22_zf_lang(k20_zf_lang(A))) ) ) ).
fof(t29_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ( v9_zf_lang(A)
=> k25_zf_lang(A) = k21_zf_lang(k20_zf_lang(A)) ) ) ).
fof(t30_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ( v9_zf_lang(A)
=> k26_zf_lang(A) = k20_zf_lang(k22_zf_lang(k20_zf_lang(A))) ) ) ).
fof(t31_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ( v10_zf_lang(A)
=> ( k27_zf_lang(A) = k25_zf_lang(k21_zf_lang(A))
& k27_zf_lang(A) = k26_zf_lang(k22_zf_lang(A)) ) ) ) ).
fof(t32_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ( v10_zf_lang(A)
=> ( k28_zf_lang(A) = k26_zf_lang(k21_zf_lang(A))
& k28_zf_lang(A) = k25_zf_lang(k22_zf_lang(A)) ) ) ) ).
fof(t33_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ( v11_zf_lang(A)
=> ( k23_zf_lang(A) = k23_zf_lang(k20_zf_lang(A))
& k24_zf_lang(A) = k20_zf_lang(k24_zf_lang(k20_zf_lang(A))) ) ) ) ).
fof(t34_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ( k20_zf_lang(k10_zf_lang(A,B)) = k7_zf_lang(k6_zf_lang(A),k6_zf_lang(B))
& k25_zf_lang(k10_zf_lang(A,B)) = k6_zf_lang(A)
& k26_zf_lang(k10_zf_lang(A,B)) = B ) ) ) ).
fof(t35_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> k20_zf_lang(k11_zf_lang(A,B)) = k7_zf_lang(A,k6_zf_lang(B)) ) ) ).
fof(t36_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ( k21_zf_lang(k12_zf_lang(A,B)) = k11_zf_lang(A,B)
& k22_zf_lang(k12_zf_lang(A,B)) = k11_zf_lang(B,A) ) ) ) ).
fof(t37_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> k20_zf_lang(k13_zf_lang(B,A)) = k8_zf_lang(B,k6_zf_lang(A)) ) ) ).
fof(t38_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ( v8_zf_lang(A)
=> ( v9_zf_lang(A)
& v4_zf_lang(A)
& v5_zf_lang(k20_zf_lang(A))
& v4_zf_lang(k21_zf_lang(k20_zf_lang(A)))
& v4_zf_lang(k22_zf_lang(k20_zf_lang(A))) ) ) ) ).
fof(t39_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ( v9_zf_lang(A)
=> ( v4_zf_lang(A)
& v5_zf_lang(k20_zf_lang(A))
& v4_zf_lang(k22_zf_lang(k20_zf_lang(A))) ) ) ) ).
fof(t40_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ( v10_zf_lang(A)
=> ( v5_zf_lang(A)
& v9_zf_lang(k21_zf_lang(A))
& v9_zf_lang(k22_zf_lang(A)) ) ) ) ).
fof(t41_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ( v11_zf_lang(A)
=> ( v4_zf_lang(A)
& v6_zf_lang(k20_zf_lang(A))
& v4_zf_lang(k24_zf_lang(k20_zf_lang(A))) ) ) ) ).
fof(t42_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ( ~ ( v2_zf_lang(A)
& ~ ( ~ v3_zf_lang(A)
& ~ v4_zf_lang(A)
& ~ v5_zf_lang(A)
& ~ v6_zf_lang(A) ) )
& ~ ( v3_zf_lang(A)
& ~ ( ~ v4_zf_lang(A)
& ~ v5_zf_lang(A)
& ~ v6_zf_lang(A) ) )
& ~ ( v4_zf_lang(A)
& ( v5_zf_lang(A)
| v6_zf_lang(A) ) )
& ~ ( v5_zf_lang(A)
& v6_zf_lang(A) ) ) ) ).
fof(t43_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ( r2_zf_lang(A,B)
=> r1_xreal_0(k3_finseq_1(A),k3_finseq_1(B)) ) ) ) ).
fof(t44_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ( v1_zf_lang(C)
& m2_finseq_1(C,k5_numbers) )
=> ( ~ ( ~ ( r3_zf_lang(A,B)
& r2_zf_lang(B,C) )
& ~ ( r2_zf_lang(A,B)
& r3_zf_lang(B,C) )
& ~ ( r2_zf_lang(A,B)
& r1_zf_lang(B,C) )
& ~ ( r1_zf_lang(A,B)
& r2_zf_lang(B,C) )
& ~ ( r3_zf_lang(A,B)
& r1_zf_lang(B,C) )
& ~ ( r1_zf_lang(A,B)
& r3_zf_lang(B,C) ) )
=> r3_zf_lang(A,C) ) ) ) ) ).
fof(t45_zf_lang1,axiom,
$true ).
fof(t46_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ~ r1_zf_lang(A,A) ) ).
fof(t47_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ~ ( r3_zf_lang(A,B)
& r2_zf_lang(B,A) ) ) ) ).
fof(t48_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ~ ( r3_zf_lang(A,B)
& r3_zf_lang(B,A) ) ) ) ).
fof(t49_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ~ ( r2_zf_lang(A,B)
& r1_zf_lang(B,A) ) ) ) ).
fof(t50_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ~ ( r3_zf_lang(A,B)
& r1_zf_lang(B,A) ) ) ) ).
fof(t51_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ( r2_zf_lang(k6_zf_lang(A),B)
=> r3_zf_lang(A,B) ) ) ) ).
fof(t52_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ( v1_zf_lang(C)
& m2_finseq_1(C,k5_numbers) )
=> ( r2_zf_lang(k7_zf_lang(A,B),C)
=> ( r3_zf_lang(A,C)
& r3_zf_lang(B,C) ) ) ) ) ) ).
fof(t53_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ( r2_zf_lang(k8_zf_lang(C,A),B)
=> r3_zf_lang(A,B) ) ) ) ) ).
fof(t54_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ( r3_zf_lang(k7_zf_lang(A,k6_zf_lang(B)),k11_zf_lang(A,B))
& r3_zf_lang(A,k11_zf_lang(A,B))
& r3_zf_lang(k6_zf_lang(B),k11_zf_lang(A,B))
& r3_zf_lang(B,k11_zf_lang(A,B)) ) ) ) ).
fof(t55_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ( r3_zf_lang(k7_zf_lang(k6_zf_lang(A),k6_zf_lang(B)),k10_zf_lang(A,B))
& r3_zf_lang(k6_zf_lang(A),k10_zf_lang(A,B))
& r3_zf_lang(k6_zf_lang(B),k10_zf_lang(A,B))
& r3_zf_lang(A,k10_zf_lang(A,B))
& r3_zf_lang(B,k10_zf_lang(A,B)) ) ) ) ).
fof(t56_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ( r3_zf_lang(k8_zf_lang(B,k6_zf_lang(A)),k13_zf_lang(B,A))
& r3_zf_lang(k6_zf_lang(A),k13_zf_lang(B,A)) ) ) ) ).
fof(t57_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ( r2_zf_lang(A,B)
<=> r2_hidden(A,k29_zf_lang(B)) ) ) ) ).
fof(t58_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ( r2_hidden(A,k29_zf_lang(B))
=> r1_tarski(k29_zf_lang(A),k29_zf_lang(B)) ) ) ) ).
fof(t59_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> r2_hidden(A,k29_zf_lang(A)) ) ).
fof(t60_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> k29_zf_lang(k11_zf_lang(A,B)) = k2_xboole_0(k2_xboole_0(k29_zf_lang(A),k29_zf_lang(B)),k1_enumset1(k6_zf_lang(B),k7_zf_lang(A,k6_zf_lang(B)),k11_zf_lang(A,B))) ) ) ).
fof(t61_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> k29_zf_lang(k10_zf_lang(A,B)) = k2_xboole_0(k2_xboole_0(k29_zf_lang(A),k29_zf_lang(B)),k2_enumset1(k6_zf_lang(B),k6_zf_lang(A),k7_zf_lang(k6_zf_lang(A),k6_zf_lang(B)),k10_zf_lang(A,B))) ) ) ).
fof(t62_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> k29_zf_lang(k12_zf_lang(A,B)) = k2_xboole_0(k2_xboole_0(k29_zf_lang(A),k29_zf_lang(B)),k5_enumset1(k6_zf_lang(B),k7_zf_lang(A,k6_zf_lang(B)),k11_zf_lang(A,B),k6_zf_lang(A),k7_zf_lang(B,k6_zf_lang(A)),k11_zf_lang(B,A),k12_zf_lang(A,B))) ) ) ).
fof(t63_zf_lang1,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_zf_lang)
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> k2_zf_model(k4_zf_lang(A,B)) = k2_tarski(A,B) ) ) ).
fof(t64_zf_lang1,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_zf_lang)
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> k2_zf_model(k5_zf_lang(A,B)) = k2_tarski(A,B) ) ) ).
fof(t65_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> k2_zf_model(k6_zf_lang(A)) = k2_zf_model(A) ) ).
fof(t66_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> k2_zf_model(k7_zf_lang(A,B)) = k4_subset_1(k1_zf_lang,k2_zf_model(A),k2_zf_model(B)) ) ) ).
fof(t67_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> k2_zf_model(k8_zf_lang(B,A)) = k4_xboole_0(k2_zf_model(A),k1_tarski(B)) ) ) ).
fof(t68_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> k2_zf_model(k10_zf_lang(A,B)) = k4_subset_1(k1_zf_lang,k2_zf_model(A),k2_zf_model(B)) ) ) ).
fof(t69_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> k2_zf_model(k11_zf_lang(A,B)) = k4_subset_1(k1_zf_lang,k2_zf_model(A),k2_zf_model(B)) ) ) ).
fof(t70_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> k2_zf_model(k12_zf_lang(A,B)) = k4_subset_1(k1_zf_lang,k2_zf_model(A),k2_zf_model(B)) ) ) ).
fof(t71_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> k2_zf_model(k13_zf_lang(B,A)) = k4_xboole_0(k2_zf_model(A),k1_tarski(B)) ) ) ).
fof(t72_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> k2_zf_model(k14_zf_lang(B,C,A)) = k4_xboole_0(k2_zf_model(A),k2_tarski(B,C)) ) ) ) ).
fof(t73_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [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)
=> k2_zf_model(k16_zf_lang(B,C,D,A)) = k4_xboole_0(k2_zf_model(A),k1_enumset1(B,C,D)) ) ) ) ) ).
fof(t74_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> k2_zf_model(k15_zf_lang(B,C,A)) = k4_xboole_0(k2_zf_model(A),k2_tarski(B,C)) ) ) ) ).
fof(t75_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [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)
=> k2_zf_model(k17_zf_lang(B,C,D,A)) = k4_xboole_0(k2_zf_model(A),k1_enumset1(B,C,D)) ) ) ) ) ).
fof(d1_zf_lang1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k1_zf_lang,A)
& m2_relset_1(B,k1_zf_lang,A) )
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k1_zf_lang,A)
& m2_relset_1(E,k1_zf_lang,A) )
=> ( E = k1_zf_lang1(A,B,C,D)
<=> ( k8_funct_2(k1_zf_lang,A,E,C) = D
& ! [F] :
( m2_subset_1(F,k5_numbers,k1_zf_lang)
=> ( k8_funct_2(k1_zf_lang,A,E,F) != k8_funct_2(k1_zf_lang,A,B,F)
=> C = F ) ) ) ) ) ) ) ) ) ).
fof(d2_zf_lang1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ( r1_tarski(B,C)
=> k2_zf_lang1(A,B,C,D) = D ) ) ) ) ) ).
fof(t76_zf_lang1,axiom,
$true ).
fof(t77_zf_lang1,axiom,
$true ).
fof(t78_zf_lang1,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_zf_lang)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,B)
=> ! [D] :
( m1_subset_1(D,B)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k1_zf_lang,B)
& m2_relset_1(E,k1_zf_lang,B) )
=> ( k1_zf_lang1(B,k1_zf_lang1(B,E,A,C),A,D) = k1_zf_lang1(B,E,A,D)
& k1_zf_lang1(B,E,A,k8_funct_2(k1_zf_lang,B,E,A)) = E ) ) ) ) ) ) ).
fof(t79_zf_lang1,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] :
( m1_subset_1(D,C)
=> ! [E] :
( m1_subset_1(E,C)
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k1_zf_lang,C)
& m2_relset_1(F,k1_zf_lang,C) )
=> ( A != B
=> k1_zf_lang1(C,k1_zf_lang1(C,F,A,D),B,E) = k1_zf_lang1(C,k1_zf_lang1(C,F,B,E),A,D) ) ) ) ) ) ) ) ).
fof(t80_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_zf_lang,C)
& m2_relset_1(D,k1_zf_lang,C) )
=> ( r1_zf_model(C,D,k8_zf_lang(B,A))
<=> ! [E] :
( m1_subset_1(E,C)
=> r1_zf_model(C,k1_zf_lang1(C,D,B,E),A) ) ) ) ) ) ) ).
fof(t81_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,C)
=> ! [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(B,A))
<=> r1_zf_model(C,k1_zf_lang1(C,E,B,D),k8_zf_lang(B,A)) ) ) ) ) ) ) ).
fof(t82_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_zf_lang,C)
& m2_relset_1(D,k1_zf_lang,C) )
=> ( r1_zf_model(C,D,k13_zf_lang(B,A))
<=> ? [E] :
( m1_subset_1(E,C)
& r1_zf_model(C,k1_zf_lang1(C,D,B,E),A) ) ) ) ) ) ) ).
fof(t83_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,C)
=> ! [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,k13_zf_lang(B,A))
<=> r1_zf_model(C,k1_zf_lang1(C,E,B,D),k13_zf_lang(B,A)) ) ) ) ) ) ) ).
fof(t84_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_zf_lang,B)
& m2_relset_1(C,k1_zf_lang,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_zf_lang,B)
& m2_relset_1(D,k1_zf_lang,B) )
=> ( ( ! [E] :
( m2_subset_1(E,k5_numbers,k1_zf_lang)
=> ( r2_hidden(E,k2_zf_model(A))
=> k8_funct_2(k1_zf_lang,B,D,E) = k8_funct_2(k1_zf_lang,B,C,E) ) )
& r1_zf_model(B,C,A) )
=> r1_zf_model(B,D,A) ) ) ) ) ) ).
fof(t85_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> v1_finset_1(k2_zf_model(A)) ) ).
fof(t86_zf_lang1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( k2_zf_lang(A) = k2_zf_lang(B)
=> A = B ) ) ) ).
fof(t87_zf_lang1,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_zf_lang)
=> ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& A = k2_zf_lang(B) ) ) ).
fof(t88_zf_lang1,axiom,
$true ).
fof(t89_zf_lang1,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_zf_lang)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_zf_lang,B)
& m2_relset_1(C,k1_zf_lang,B) )
=> r1_zf_model(B,C,k4_zf_lang(A,A)) ) ) ) ).
fof(t90_zf_lang1,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_zf_lang)
=> ! [B] :
( ~ v1_xboole_0(B)
=> r2_zf_model(B,k4_zf_lang(A,A)) ) ) ).
fof(t91_zf_lang1,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_zf_lang)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_zf_lang,B)
& m2_relset_1(C,k1_zf_lang,B) )
=> ~ r1_zf_model(B,C,k5_zf_lang(A,A)) ) ) ) ).
fof(t92_zf_lang1,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_zf_lang)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ( ~ r2_zf_model(B,k5_zf_lang(A,A))
& r2_zf_model(B,k6_zf_lang(k5_zf_lang(A,A))) ) ) ) ).
fof(t93_zf_lang1,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)
=> ( r2_zf_model(C,k4_zf_lang(A,B))
<=> ~ ( A != B
& ! [D] : k1_tarski(D) != C ) ) ) ) ) ).
fof(t94_zf_lang1,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)
=> ( r2_zf_model(C,k6_zf_lang(k5_zf_lang(A,B)))
<=> ( A = B
| ! [D] :
( r2_hidden(D,C)
=> r1_xboole_0(D,C) ) ) ) ) ) ) ).
fof(t95_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_zf_lang,B)
& m2_relset_1(C,k1_zf_lang,B) )
=> ( v2_zf_lang(A)
=> ( r1_zf_model(B,C,A)
<=> k8_funct_2(k1_zf_lang,B,C,k18_zf_lang(A)) = k8_funct_2(k1_zf_lang,B,C,k19_zf_lang(A)) ) ) ) ) ) ).
fof(t96_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_zf_lang,B)
& m2_relset_1(C,k1_zf_lang,B) )
=> ( v3_zf_lang(A)
=> ( r1_zf_model(B,C,A)
<=> r2_hidden(k8_funct_2(k1_zf_lang,B,C,k18_zf_lang(A)),k8_funct_2(k1_zf_lang,B,C,k19_zf_lang(A))) ) ) ) ) ) ).
fof(t97_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_zf_lang,B)
& m2_relset_1(C,k1_zf_lang,B) )
=> ( v4_zf_lang(A)
=> ( r1_zf_model(B,C,A)
<=> ~ r1_zf_model(B,C,k20_zf_lang(A)) ) ) ) ) ) ).
fof(t98_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_zf_lang,B)
& m2_relset_1(C,k1_zf_lang,B) )
=> ( v5_zf_lang(A)
=> ( r1_zf_model(B,C,A)
<=> ( r1_zf_model(B,C,k21_zf_lang(A))
& r1_zf_model(B,C,k22_zf_lang(A)) ) ) ) ) ) ) ).
fof(t99_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_zf_lang,B)
& m2_relset_1(C,k1_zf_lang,B) )
=> ( v6_zf_lang(A)
=> ( r1_zf_model(B,C,A)
<=> ! [D] :
( m1_subset_1(D,B)
=> r1_zf_model(B,k1_zf_lang1(B,C,k23_zf_lang(A),D),k24_zf_lang(A)) ) ) ) ) ) ) ).
fof(t100_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_zf_lang,B)
& m2_relset_1(C,k1_zf_lang,B) )
=> ( v8_zf_lang(A)
=> ( r1_zf_model(B,C,A)
<=> ( r1_zf_model(B,C,k21_zf_lang(A))
| r1_zf_model(B,C,k22_zf_lang(A)) ) ) ) ) ) ) ).
fof(t101_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_zf_lang,B)
& m2_relset_1(C,k1_zf_lang,B) )
=> ( v9_zf_lang(A)
=> ( r1_zf_model(B,C,A)
<=> ( r1_zf_model(B,C,k25_zf_lang(A))
=> r1_zf_model(B,C,k26_zf_lang(A)) ) ) ) ) ) ) ).
fof(t102_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_zf_lang,B)
& m2_relset_1(C,k1_zf_lang,B) )
=> ( v10_zf_lang(A)
=> ( r1_zf_model(B,C,A)
<=> ( r1_zf_model(B,C,k27_zf_lang(A))
<=> r1_zf_model(B,C,k28_zf_lang(A)) ) ) ) ) ) ) ).
fof(t103_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_zf_lang,B)
& m2_relset_1(C,k1_zf_lang,B) )
=> ( v11_zf_lang(A)
=> ( r1_zf_model(B,C,A)
<=> ? [D] :
( m1_subset_1(D,B)
& r1_zf_model(B,k1_zf_lang1(B,C,k23_zf_lang(A),D),k24_zf_lang(A)) ) ) ) ) ) ) ).
fof(t104_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ( r2_zf_model(C,k13_zf_lang(B,A))
<=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_zf_lang,C)
& m2_relset_1(D,k1_zf_lang,C) )
=> ? [E] :
( m1_subset_1(E,C)
& r1_zf_model(C,k1_zf_lang1(C,D,B,E),A) ) ) ) ) ) ) ).
fof(t105_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ( r2_zf_model(C,A)
=> r2_zf_model(C,k13_zf_lang(B,A)) ) ) ) ) ).
fof(t106_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [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)
=> ( r2_zf_model(D,A)
<=> r2_zf_model(D,k14_zf_lang(B,C,A)) ) ) ) ) ) ).
fof(t107_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [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)
=> ( r2_zf_model(D,A)
=> r2_zf_model(D,k15_zf_lang(B,C,A)) ) ) ) ) ) ).
fof(t108_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [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)
=> ( r2_zf_model(E,A)
<=> r2_zf_model(E,k16_zf_lang(B,C,D,A)) ) ) ) ) ) ) ).
fof(t109_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [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)
=> ( r2_zf_model(E,A)
=> r2_zf_model(E,k17_zf_lang(B,C,D,A)) ) ) ) ) ) ) ).
fof(t110_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_zf_lang,C)
& m2_relset_1(D,k1_zf_lang,C) )
=> ( r1_zf_model(C,D,k11_zf_lang(k12_zf_lang(A,B),k11_zf_lang(A,B)))
& r2_zf_model(C,k11_zf_lang(k12_zf_lang(A,B),k11_zf_lang(A,B))) ) ) ) ) ) ).
fof(t111_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_zf_lang,C)
& m2_relset_1(D,k1_zf_lang,C) )
=> ( r1_zf_model(C,D,k11_zf_lang(k12_zf_lang(A,B),k11_zf_lang(B,A)))
& r2_zf_model(C,k11_zf_lang(k12_zf_lang(A,B),k11_zf_lang(B,A))) ) ) ) ) ) ).
fof(t112_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ( v1_zf_lang(C)
& m2_finseq_1(C,k5_numbers) )
=> ! [D] :
( ~ v1_xboole_0(D)
=> r2_zf_model(D,k11_zf_lang(k11_zf_lang(A,B),k11_zf_lang(k11_zf_lang(B,C),k11_zf_lang(A,C)))) ) ) ) ) ).
fof(t113_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ( v1_zf_lang(C)
& m2_finseq_1(C,k5_numbers) )
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k1_zf_lang,D)
& m2_relset_1(E,k1_zf_lang,D) )
=> ( ( r1_zf_model(D,E,k11_zf_lang(A,B))
& r1_zf_model(D,E,k11_zf_lang(B,C)) )
=> r1_zf_model(D,E,k11_zf_lang(A,C)) ) ) ) ) ) ) ).
fof(t114_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ( v1_zf_lang(C)
& m2_finseq_1(C,k5_numbers) )
=> ! [D] :
( ~ v1_xboole_0(D)
=> ( ( r2_zf_model(D,k11_zf_lang(A,B))
& r2_zf_model(D,k11_zf_lang(B,C)) )
=> r2_zf_model(D,k11_zf_lang(A,C)) ) ) ) ) ) ).
fof(t115_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ( v1_zf_lang(C)
& m2_finseq_1(C,k5_numbers) )
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k1_zf_lang,D)
& m2_relset_1(E,k1_zf_lang,D) )
=> ( r1_zf_model(D,E,k11_zf_lang(k7_zf_lang(k11_zf_lang(A,B),k11_zf_lang(B,C)),k11_zf_lang(A,C)))
& r2_zf_model(D,k11_zf_lang(k7_zf_lang(k11_zf_lang(A,B),k11_zf_lang(B,C)),k11_zf_lang(A,C))) ) ) ) ) ) ) ).
fof(t116_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_zf_lang,C)
& m2_relset_1(D,k1_zf_lang,C) )
=> ( r1_zf_model(C,D,k11_zf_lang(A,k11_zf_lang(B,A)))
& r2_zf_model(C,k11_zf_lang(A,k11_zf_lang(B,A))) ) ) ) ) ) ).
fof(t117_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ( v1_zf_lang(C)
& m2_finseq_1(C,k5_numbers) )
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k1_zf_lang,D)
& m2_relset_1(E,k1_zf_lang,D) )
=> ( r1_zf_model(D,E,k11_zf_lang(k11_zf_lang(A,k11_zf_lang(B,C)),k11_zf_lang(k11_zf_lang(A,B),k11_zf_lang(A,C))))
& r2_zf_model(D,k11_zf_lang(k11_zf_lang(A,k11_zf_lang(B,C)),k11_zf_lang(k11_zf_lang(A,B),k11_zf_lang(A,C)))) ) ) ) ) ) ) ).
fof(t118_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_zf_lang,C)
& m2_relset_1(D,k1_zf_lang,C) )
=> ( r1_zf_model(C,D,k11_zf_lang(k7_zf_lang(A,B),A))
& r2_zf_model(C,k11_zf_lang(k7_zf_lang(A,B),A)) ) ) ) ) ) ).
fof(t119_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_zf_lang,C)
& m2_relset_1(D,k1_zf_lang,C) )
=> ( r1_zf_model(C,D,k11_zf_lang(k7_zf_lang(A,B),B))
& r2_zf_model(C,k11_zf_lang(k7_zf_lang(A,B),B)) ) ) ) ) ) ).
fof(t120_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_zf_lang,C)
& m2_relset_1(D,k1_zf_lang,C) )
=> ( r1_zf_model(C,D,k11_zf_lang(k7_zf_lang(A,B),k7_zf_lang(B,A)))
& r2_zf_model(C,k11_zf_lang(k7_zf_lang(A,B),k7_zf_lang(B,A))) ) ) ) ) ) ).
fof(t121_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_zf_lang,B)
& m2_relset_1(C,k1_zf_lang,B) )
=> ( r1_zf_model(B,C,k11_zf_lang(A,k7_zf_lang(A,A)))
& r2_zf_model(B,k11_zf_lang(A,k7_zf_lang(A,A))) ) ) ) ) ).
fof(t122_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ( v1_zf_lang(C)
& m2_finseq_1(C,k5_numbers) )
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k1_zf_lang,D)
& m2_relset_1(E,k1_zf_lang,D) )
=> ( r1_zf_model(D,E,k11_zf_lang(k11_zf_lang(A,B),k11_zf_lang(k11_zf_lang(A,C),k11_zf_lang(A,k7_zf_lang(B,C)))))
& r2_zf_model(D,k11_zf_lang(k11_zf_lang(A,B),k11_zf_lang(k11_zf_lang(A,C),k11_zf_lang(A,k7_zf_lang(B,C))))) ) ) ) ) ) ) ).
fof(t123_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_zf_lang,C)
& m2_relset_1(D,k1_zf_lang,C) )
=> ( r1_zf_model(C,D,k11_zf_lang(A,k10_zf_lang(A,B)))
& r2_zf_model(C,k11_zf_lang(A,k10_zf_lang(A,B))) ) ) ) ) ) ).
fof(t124_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_zf_lang,C)
& m2_relset_1(D,k1_zf_lang,C) )
=> ( r1_zf_model(C,D,k11_zf_lang(A,k10_zf_lang(B,A)))
& r2_zf_model(C,k11_zf_lang(A,k10_zf_lang(B,A))) ) ) ) ) ) ).
fof(t125_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_zf_lang,C)
& m2_relset_1(D,k1_zf_lang,C) )
=> ( r1_zf_model(C,D,k11_zf_lang(k10_zf_lang(A,B),k10_zf_lang(B,A)))
& r2_zf_model(C,k11_zf_lang(k10_zf_lang(A,B),k10_zf_lang(B,A))) ) ) ) ) ) ).
fof(t126_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_zf_lang,B)
& m2_relset_1(C,k1_zf_lang,B) )
=> ( r1_zf_model(B,C,k11_zf_lang(A,k10_zf_lang(A,A)))
& r2_zf_model(B,k11_zf_lang(A,k10_zf_lang(A,A))) ) ) ) ) ).
fof(t127_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ( v1_zf_lang(C)
& m2_finseq_1(C,k5_numbers) )
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k1_zf_lang,D)
& m2_relset_1(E,k1_zf_lang,D) )
=> ( r1_zf_model(D,E,k11_zf_lang(k11_zf_lang(A,B),k11_zf_lang(k11_zf_lang(C,B),k11_zf_lang(k10_zf_lang(A,C),B))))
& r2_zf_model(D,k11_zf_lang(k11_zf_lang(A,B),k11_zf_lang(k11_zf_lang(C,B),k11_zf_lang(k10_zf_lang(A,C),B)))) ) ) ) ) ) ) ).
fof(t128_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ( v1_zf_lang(C)
& m2_finseq_1(C,k5_numbers) )
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k1_zf_lang,D)
& m2_relset_1(E,k1_zf_lang,D) )
=> ( r1_zf_model(D,E,k11_zf_lang(k7_zf_lang(k11_zf_lang(A,B),k11_zf_lang(C,B)),k11_zf_lang(k10_zf_lang(A,C),B)))
& r2_zf_model(D,k11_zf_lang(k7_zf_lang(k11_zf_lang(A,B),k11_zf_lang(C,B)),k11_zf_lang(k10_zf_lang(A,C),B))) ) ) ) ) ) ) ).
fof(t129_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_zf_lang,C)
& m2_relset_1(D,k1_zf_lang,C) )
=> ( r1_zf_model(C,D,k11_zf_lang(k11_zf_lang(A,k6_zf_lang(B)),k11_zf_lang(B,k6_zf_lang(A))))
& r2_zf_model(C,k11_zf_lang(k11_zf_lang(A,k6_zf_lang(B)),k11_zf_lang(B,k6_zf_lang(A)))) ) ) ) ) ) ).
fof(t130_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_zf_lang,C)
& m2_relset_1(D,k1_zf_lang,C) )
=> ( r1_zf_model(C,D,k11_zf_lang(k6_zf_lang(A),k11_zf_lang(A,B)))
& r2_zf_model(C,k11_zf_lang(k6_zf_lang(A),k11_zf_lang(A,B))) ) ) ) ) ) ).
fof(t131_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_zf_lang,C)
& m2_relset_1(D,k1_zf_lang,C) )
=> ( r1_zf_model(C,D,k11_zf_lang(k7_zf_lang(k11_zf_lang(A,B),k11_zf_lang(A,k6_zf_lang(B))),k6_zf_lang(A)))
& r2_zf_model(C,k11_zf_lang(k7_zf_lang(k11_zf_lang(A,B),k11_zf_lang(A,k6_zf_lang(B))),k6_zf_lang(A))) ) ) ) ) ) ).
fof(t132_zf_lang1,axiom,
$true ).
fof(t133_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ~ v1_xboole_0(C)
=> ( ( r2_zf_model(C,k11_zf_lang(A,B))
& r2_zf_model(C,A) )
=> r2_zf_model(C,B) ) ) ) ) ).
fof(t134_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_zf_lang,C)
& m2_relset_1(D,k1_zf_lang,C) )
=> ( r1_zf_model(C,D,k11_zf_lang(k6_zf_lang(k7_zf_lang(A,B)),k10_zf_lang(k6_zf_lang(A),k6_zf_lang(B))))
& r2_zf_model(C,k11_zf_lang(k6_zf_lang(k7_zf_lang(A,B)),k10_zf_lang(k6_zf_lang(A),k6_zf_lang(B)))) ) ) ) ) ) ).
fof(t135_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_zf_lang,C)
& m2_relset_1(D,k1_zf_lang,C) )
=> ( r1_zf_model(C,D,k11_zf_lang(k10_zf_lang(k6_zf_lang(A),k6_zf_lang(B)),k6_zf_lang(k7_zf_lang(A,B))))
& r2_zf_model(C,k11_zf_lang(k10_zf_lang(k6_zf_lang(A),k6_zf_lang(B)),k6_zf_lang(k7_zf_lang(A,B)))) ) ) ) ) ) ).
fof(t136_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_zf_lang,C)
& m2_relset_1(D,k1_zf_lang,C) )
=> ( r1_zf_model(C,D,k11_zf_lang(k6_zf_lang(k10_zf_lang(A,B)),k7_zf_lang(k6_zf_lang(A),k6_zf_lang(B))))
& r2_zf_model(C,k11_zf_lang(k6_zf_lang(k10_zf_lang(A,B)),k7_zf_lang(k6_zf_lang(A),k6_zf_lang(B)))) ) ) ) ) ) ).
fof(t137_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k1_zf_lang,C)
& m2_relset_1(D,k1_zf_lang,C) )
=> ( r1_zf_model(C,D,k11_zf_lang(k7_zf_lang(k6_zf_lang(A),k6_zf_lang(B)),k6_zf_lang(k10_zf_lang(A,B))))
& r2_zf_model(C,k11_zf_lang(k7_zf_lang(k6_zf_lang(A),k6_zf_lang(B)),k6_zf_lang(k10_zf_lang(A,B)))) ) ) ) ) ) ).
fof(t138_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( ~ v1_xboole_0(C)
=> r2_zf_model(C,k11_zf_lang(k8_zf_lang(B,A),A)) ) ) ) ).
fof(t139_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( ~ v1_xboole_0(C)
=> r2_zf_model(C,k11_zf_lang(A,k13_zf_lang(B,A))) ) ) ) ).
fof(t140_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ( ~ r2_hidden(C,k2_zf_model(A))
=> r2_zf_model(D,k11_zf_lang(k8_zf_lang(C,k11_zf_lang(A,B)),k11_zf_lang(A,k8_zf_lang(C,B)))) ) ) ) ) ) ).
fof(t141_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ( r2_zf_model(D,k11_zf_lang(A,B))
=> ( r2_hidden(C,k2_zf_model(A))
| r2_zf_model(D,k11_zf_lang(A,k8_zf_lang(C,B))) ) ) ) ) ) ) ).
fof(t142_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ( ~ r2_hidden(C,k2_zf_model(A))
=> r2_zf_model(D,k11_zf_lang(k8_zf_lang(C,k11_zf_lang(B,A)),k11_zf_lang(k13_zf_lang(C,B),A))) ) ) ) ) ) ).
fof(t143_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ( r2_zf_model(D,k11_zf_lang(B,A))
=> ( r2_hidden(C,k2_zf_model(A))
| r2_zf_model(D,k11_zf_lang(k13_zf_lang(C,B),A)) ) ) ) ) ) ) ).
fof(t144_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ( r2_zf_model(D,k11_zf_lang(A,k8_zf_lang(C,B)))
=> r2_zf_model(D,k11_zf_lang(A,B)) ) ) ) ) ) ).
fof(t145_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ( r2_zf_model(D,k11_zf_lang(k13_zf_lang(C,A),B))
=> r2_zf_model(D,k11_zf_lang(A,B)) ) ) ) ) ) ).
fof(t146_zf_lang1,axiom,
r1_tarski(k9_zf_lang,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers))) ).
fof(d3_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> k3_zf_lang1(A) = k4_xboole_0(k2_relat_1(A),k3_enumset1(np__0,np__1,np__2,np__3,np__4)) ) ).
fof(t147_zf_lang1,axiom,
$true ).
fof(t148_zf_lang1,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_zf_lang)
=> ( A != np__0
& A != np__1
& A != np__2
& A != np__3
& A != np__4 ) ) ).
fof(t149_zf_lang1,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_zf_lang)
=> ~ r2_hidden(A,k3_enumset1(np__0,np__1,np__2,np__3,np__4)) ) ).
fof(t150_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( r2_hidden(B,k3_zf_lang1(A))
=> ( B != np__0
& B != np__1
& B != np__2
& B != np__3
& B != np__4 ) ) ) ).
fof(t151_zf_lang1,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_zf_lang)
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> k3_zf_lang1(k4_zf_lang(A,B)) = k2_tarski(A,B) ) ) ).
fof(t152_zf_lang1,axiom,
! [A] :
( m2_subset_1(A,k5_numbers,k1_zf_lang)
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> k3_zf_lang1(k5_zf_lang(A,B)) = k2_tarski(A,B) ) ) ).
fof(t153_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> k3_zf_lang1(k6_zf_lang(A)) = k3_zf_lang1(A) ) ).
fof(t154_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> k3_zf_lang1(k7_zf_lang(A,B)) = k2_xboole_0(k3_zf_lang1(A),k3_zf_lang1(B)) ) ) ).
fof(t155_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> k3_zf_lang1(k8_zf_lang(B,A)) = k2_xboole_0(k3_zf_lang1(A),k1_tarski(B)) ) ) ).
fof(t156_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> k3_zf_lang1(k10_zf_lang(A,B)) = k2_xboole_0(k3_zf_lang1(A),k3_zf_lang1(B)) ) ) ).
fof(t157_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> k3_zf_lang1(k11_zf_lang(A,B)) = k2_xboole_0(k3_zf_lang1(A),k3_zf_lang1(B)) ) ) ).
fof(t158_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> k3_zf_lang1(k12_zf_lang(A,B)) = k2_xboole_0(k3_zf_lang1(A),k3_zf_lang1(B)) ) ) ).
fof(t159_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> k3_zf_lang1(k13_zf_lang(B,A)) = k2_xboole_0(k3_zf_lang1(A),k1_tarski(B)) ) ) ).
fof(t160_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> k3_zf_lang1(k14_zf_lang(B,C,A)) = k2_xboole_0(k3_zf_lang1(A),k2_tarski(B,C)) ) ) ) ).
fof(t161_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> k3_zf_lang1(k15_zf_lang(B,C,A)) = k2_xboole_0(k3_zf_lang1(A),k2_tarski(B,C)) ) ) ) ).
fof(t162_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [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)
=> k3_zf_lang1(k16_zf_lang(B,C,D,A)) = k2_xboole_0(k3_zf_lang1(A),k1_enumset1(B,C,D)) ) ) ) ) ).
fof(t163_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [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)
=> k3_zf_lang1(k17_zf_lang(B,C,D,A)) = k2_xboole_0(k3_zf_lang1(A),k1_enumset1(B,C,D)) ) ) ) ) ).
fof(t164_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> r1_tarski(k2_zf_model(A),k3_zf_lang1(A)) ) ).
fof(d4_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( D = k5_zf_lang1(A,B,C)
<=> ( k1_relat_1(D) = k4_finseq_1(A)
& ! [E] :
( r2_hidden(E,k4_finseq_1(A))
=> ( ( k1_funct_1(A,E) = B
=> k1_funct_1(D,E) = C )
& ( k1_funct_1(A,E) != B
=> k1_funct_1(D,E) = k1_funct_1(A,E) ) ) ) ) ) ) ) ) ) ).
fof(t165_zf_lang1,axiom,
$true ).
fof(t166_zf_lang1,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] :
( m2_subset_1(E,k5_numbers,k1_zf_lang)
=> ! [F] :
( m2_subset_1(F,k5_numbers,k1_zf_lang)
=> ( k5_zf_lang1(k4_zf_lang(A,B),C,D) = k4_zf_lang(E,F)
<=> ~ ( ~ ( A != C
& B != C
& E = A
& F = B )
& ~ ( A = C
& B != C
& E = D
& F = B )
& ~ ( A != C
& B = C
& E = A
& F = D )
& ~ ( A = C
& B = C
& E = D
& F = D ) ) ) ) ) ) ) ) ) ).
fof(t167_zf_lang1,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] :
( m2_subset_1(E,k5_numbers,k1_zf_lang)
& ? [F] :
( m2_subset_1(F,k5_numbers,k1_zf_lang)
& k5_zf_lang1(k4_zf_lang(A,B),C,D) = k4_zf_lang(E,F) ) ) ) ) ) ) ).
fof(t168_zf_lang1,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] :
( m2_subset_1(E,k5_numbers,k1_zf_lang)
=> ! [F] :
( m2_subset_1(F,k5_numbers,k1_zf_lang)
=> ( k5_zf_lang1(k5_zf_lang(A,B),C,D) = k5_zf_lang(E,F)
<=> ~ ( ~ ( A != C
& B != C
& E = A
& F = B )
& ~ ( A = C
& B != C
& E = D
& F = B )
& ~ ( A != C
& B = C
& E = A
& F = D )
& ~ ( A = C
& B = C
& E = D
& F = D ) ) ) ) ) ) ) ) ) ).
fof(t169_zf_lang1,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] :
( m2_subset_1(E,k5_numbers,k1_zf_lang)
& ? [F] :
( m2_subset_1(F,k5_numbers,k1_zf_lang)
& k5_zf_lang1(k5_zf_lang(A,B),C,D) = k5_zf_lang(E,F) ) ) ) ) ) ) ).
fof(t170_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k1_zf_lang)
=> ( k6_zf_lang(A) = k5_zf_lang1(k6_zf_lang(B),C,D)
<=> A = k5_zf_lang1(B,C,D) ) ) ) ) ) ).
fof(t171_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> r2_hidden(k5_zf_lang1(A,B,C),k9_zf_lang) ) ) ) ).
fof(t172_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [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] :
( m2_subset_1(E,k5_numbers,k1_zf_lang)
=> ! [F] :
( m2_subset_1(F,k5_numbers,k1_zf_lang)
=> ( k7_zf_lang(A,B) = k6_zf_lang1(k7_zf_lang(C,D),E,F)
<=> ( A = k6_zf_lang1(C,E,F)
& B = k6_zf_lang1(D,E,F) ) ) ) ) ) ) ) ) ).
fof(t173_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k1_zf_lang)
=> ! [E] :
( m2_subset_1(E,k5_numbers,k1_zf_lang)
=> ( C != D
=> ( k8_zf_lang(C,A) = k6_zf_lang1(k8_zf_lang(C,B),D,E)
<=> A = k6_zf_lang1(B,D,E) ) ) ) ) ) ) ) ).
fof(t174_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k1_zf_lang)
=> ( k8_zf_lang(C,A) = k6_zf_lang1(k8_zf_lang(D,B),D,C)
<=> A = k6_zf_lang1(B,D,C) ) ) ) ) ) ).
fof(t175_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [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] :
( m2_subset_1(E,k5_numbers,k1_zf_lang)
=> ! [F] :
( m2_subset_1(F,k5_numbers,k1_zf_lang)
=> ( k10_zf_lang(A,B) = k6_zf_lang1(k10_zf_lang(C,D),E,F)
<=> ( A = k6_zf_lang1(C,E,F)
& B = k6_zf_lang1(D,E,F) ) ) ) ) ) ) ) ) ).
fof(t176_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [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] :
( m2_subset_1(E,k5_numbers,k1_zf_lang)
=> ! [F] :
( m2_subset_1(F,k5_numbers,k1_zf_lang)
=> ( k11_zf_lang(A,B) = k6_zf_lang1(k11_zf_lang(C,D),E,F)
<=> ( A = k6_zf_lang1(C,E,F)
& B = k6_zf_lang1(D,E,F) ) ) ) ) ) ) ) ) ).
fof(t177_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [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] :
( m2_subset_1(E,k5_numbers,k1_zf_lang)
=> ! [F] :
( m2_subset_1(F,k5_numbers,k1_zf_lang)
=> ( k12_zf_lang(A,B) = k6_zf_lang1(k12_zf_lang(C,D),E,F)
<=> ( A = k6_zf_lang1(C,E,F)
& B = k6_zf_lang1(D,E,F) ) ) ) ) ) ) ) ) ).
fof(t178_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k1_zf_lang)
=> ! [E] :
( m2_subset_1(E,k5_numbers,k1_zf_lang)
=> ( C != D
=> ( k13_zf_lang(C,A) = k6_zf_lang1(k13_zf_lang(C,B),D,E)
<=> A = k6_zf_lang1(B,D,E) ) ) ) ) ) ) ) ).
fof(t179_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ! [D] :
( m2_subset_1(D,k5_numbers,k1_zf_lang)
=> ( k13_zf_lang(C,A) = k6_zf_lang1(k13_zf_lang(D,B),D,C)
<=> A = k6_zf_lang1(B,D,C) ) ) ) ) ) ).
fof(t180_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ( v2_zf_lang(A)
<=> v2_zf_lang(k6_zf_lang1(A,B,C)) ) ) ) ) ).
fof(t181_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ( v3_zf_lang(A)
<=> v3_zf_lang(k6_zf_lang1(A,B,C)) ) ) ) ) ).
fof(t182_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ( v4_zf_lang(A)
<=> v4_zf_lang(k6_zf_lang1(A,B,C)) ) ) ) ) ).
fof(t183_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ( v5_zf_lang(A)
<=> v5_zf_lang(k6_zf_lang1(A,B,C)) ) ) ) ) ).
fof(t184_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ( v6_zf_lang(A)
<=> v6_zf_lang(k6_zf_lang1(A,B,C)) ) ) ) ) ).
fof(t185_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ( v4_zf_lang(A)
=> k20_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k20_zf_lang(A),B,C) ) ) ) ) ).
fof(t186_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ( v5_zf_lang(A)
=> ( k21_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k21_zf_lang(A),B,C)
& k22_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k22_zf_lang(A),B,C) ) ) ) ) ) ).
fof(t187_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ( v6_zf_lang(A)
=> ( k24_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k24_zf_lang(A),B,C)
& ( k23_zf_lang(A) = B
=> k23_zf_lang(k6_zf_lang1(A,B,C)) = C )
& ( k23_zf_lang(A) != B
=> k23_zf_lang(k6_zf_lang1(A,B,C)) = k23_zf_lang(A) ) ) ) ) ) ) ).
fof(t188_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ( v8_zf_lang(A)
<=> v8_zf_lang(k6_zf_lang1(A,B,C)) ) ) ) ) ).
fof(t189_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ( v9_zf_lang(A)
<=> v9_zf_lang(k6_zf_lang1(A,B,C)) ) ) ) ) ).
fof(t190_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ( v10_zf_lang(A)
=> v10_zf_lang(k6_zf_lang1(A,B,C)) ) ) ) ) ).
fof(t191_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ( v11_zf_lang(A)
<=> v11_zf_lang(k6_zf_lang1(A,B,C)) ) ) ) ) ).
fof(t192_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ( v8_zf_lang(A)
=> ( k21_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k21_zf_lang(A),B,C)
& k22_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k22_zf_lang(A),B,C) ) ) ) ) ) ).
fof(t193_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ( v9_zf_lang(A)
=> ( k25_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k25_zf_lang(A),B,C)
& k26_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k26_zf_lang(A),B,C) ) ) ) ) ) ).
fof(t194_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ( v10_zf_lang(A)
=> ( k27_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k27_zf_lang(A),B,C)
& k28_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k28_zf_lang(A),B,C) ) ) ) ) ) ).
fof(t195_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ( v11_zf_lang(A)
=> ( k24_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k24_zf_lang(A),B,C)
& ( k23_zf_lang(A) = B
=> k23_zf_lang(k6_zf_lang1(A,B,C)) = C )
& ( k23_zf_lang(A) != B
=> k23_zf_lang(k6_zf_lang1(A,B,C)) = k23_zf_lang(A) ) ) ) ) ) ) ).
fof(t196_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ( ~ r2_hidden(B,k4_zf_lang1(A))
=> k6_zf_lang1(A,B,C) = A ) ) ) ) ).
fof(t197_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> k6_zf_lang1(A,B,B) = A ) ) ).
fof(t198_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ~ ( B != C
& r2_hidden(B,k4_zf_lang1(k6_zf_lang1(A,B,C))) ) ) ) ) ).
fof(t199_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> ( r2_hidden(B,k4_zf_lang1(A))
=> r2_hidden(C,k4_zf_lang1(k6_zf_lang1(A,B,C))) ) ) ) ) ).
fof(t200_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [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)
=> ( B != C
=> k6_zf_lang1(k6_zf_lang1(A,B,C),B,D) = k6_zf_lang1(A,B,C) ) ) ) ) ) ).
fof(t201_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ! [C] :
( m2_subset_1(C,k5_numbers,k1_zf_lang)
=> r1_tarski(k4_zf_lang1(k6_zf_lang1(A,B,C)),k2_xboole_0(k4_xboole_0(k4_zf_lang1(A),k1_tarski(B)),k1_tarski(C))) ) ) ) ).
fof(s1_zf_lang1,axiom,
( ( ! [A] :
( m2_subset_1(A,k5_numbers,k1_zf_lang)
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ( p1_s1_zf_lang1(k4_zf_lang(A,B))
& p1_s1_zf_lang1(k5_zf_lang(A,B)) ) ) )
& ! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ( p1_s1_zf_lang1(A)
=> p1_s1_zf_lang1(k6_zf_lang(A)) ) )
& ! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( ( v1_zf_lang(B)
& m2_finseq_1(B,k5_numbers) )
=> ( ( p1_s1_zf_lang1(A)
& p1_s1_zf_lang1(B) )
=> p1_s1_zf_lang1(k7_zf_lang(A,B)) ) ) )
& ! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k5_numbers,k1_zf_lang)
=> ( p1_s1_zf_lang1(A)
=> p1_s1_zf_lang1(k8_zf_lang(B,A)) ) ) ) )
=> ! [A] :
( ( v1_zf_lang(A)
& m2_finseq_1(A,k5_numbers) )
=> p1_s1_zf_lang1(A) ) ) ).
fof(dt_k1_zf_lang1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& v1_funct_2(B,k1_zf_lang,A)
& m1_relset_1(B,k1_zf_lang,A)
& m1_subset_1(C,k1_zf_lang)
& m1_subset_1(D,A) )
=> ( v1_funct_1(k1_zf_lang1(A,B,C,D))
& v1_funct_2(k1_zf_lang1(A,B,C,D),k1_zf_lang,A)
& m2_relset_1(k1_zf_lang1(A,B,C,D),k1_zf_lang,A) ) ) ).
fof(dt_k2_zf_lang1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& v1_funct_1(D)
& v1_funct_2(D,A,B)
& m1_relset_1(D,A,B) )
=> ( v1_funct_1(k2_zf_lang1(A,B,C,D))
& v1_funct_2(k2_zf_lang1(A,B,C,D),A,C)
& m2_relset_1(k2_zf_lang1(A,B,C,D),A,C) ) ) ).
fof(dt_k3_zf_lang1,axiom,
$true ).
fof(dt_k4_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m1_finseq_1(A,k5_numbers) )
=> ( ~ v1_xboole_0(k4_zf_lang1(A))
& m1_subset_1(k4_zf_lang1(A),k1_zfmisc_1(k1_zf_lang)) ) ) ).
fof(redefinition_k4_zf_lang1,axiom,
! [A] :
( ( v1_zf_lang(A)
& m1_finseq_1(A,k5_numbers) )
=> k4_zf_lang1(A) = k3_zf_lang1(A) ) ).
fof(dt_k5_zf_lang1,axiom,
! [A,B,C] :
( ( v1_zf_lang(A)
& m1_finseq_1(A,k5_numbers)
& m1_subset_1(B,k1_zf_lang)
& m1_subset_1(C,k1_zf_lang) )
=> ( v1_relat_1(k5_zf_lang1(A,B,C))
& v1_funct_1(k5_zf_lang1(A,B,C)) ) ) ).
fof(dt_k6_zf_lang1,axiom,
! [A,B,C] :
( ( v1_zf_lang(A)
& m1_finseq_1(A,k5_numbers)
& m1_subset_1(B,k1_zf_lang)
& m1_subset_1(C,k1_zf_lang) )
=> ( v1_zf_lang(k6_zf_lang1(A,B,C))
& m2_finseq_1(k6_zf_lang1(A,B,C),k5_numbers) ) ) ).
fof(redefinition_k6_zf_lang1,axiom,
! [A,B,C] :
( ( v1_zf_lang(A)
& m1_finseq_1(A,k5_numbers)
& m1_subset_1(B,k1_zf_lang)
& m1_subset_1(C,k1_zf_lang) )
=> k6_zf_lang1(A,B,C) = k5_zf_lang1(A,B,C) ) ).
%------------------------------------------------------------------------------