SET007 Axioms: SET007+373.ax
%------------------------------------------------------------------------------
% File : SET007+373 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Subalgebras of the Universal Algebra. Lattices of Subalgebras
% 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 : unialg_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 74 ( 1 unt; 0 def)
% Number of atoms : 708 ( 58 equ)
% Maximal formula atoms : 18 ( 9 avg)
% Number of connectives : 751 ( 117 ~; 1 |; 439 &)
% ( 16 <=>; 178 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 9 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 32 ( 30 usr; 1 prp; 0-3 aty)
% Number of functors : 39 ( 39 usr; 4 con; 0-6 aty)
% Number of variables : 179 ( 171 !; 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(rc1_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ? [B] :
( m3_unialg_2(B,A)
& ~ v3_struct_0(B)
& v3_unialg_1(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B) ) ) ).
fof(rc2_unialg_2,axiom,
? [A] :
( l1_unialg_1(A)
& ~ v3_struct_0(A)
& v3_unialg_1(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A) ) ).
fof(fc1_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> ~ v1_xboole_0(k6_unialg_2(A)) ) ).
fof(fc2_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ~ v1_xboole_0(k9_unialg_2(A)) ) ).
fof(t1_unialg_2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(B)) )
=> k3_xboole_0(k4_finseq_2(A,B),k4_finseq_2(A,C)) = k4_finseq_2(A,C) ) ) ) ).
fof(t2_unialg_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_funct_1(B)
& v1_unialg_1(B,A)
& v2_unialg_1(B,A)
& m2_relset_1(B,k3_finseq_2(A),A) )
=> k1_relat_1(B) = k4_finseq_2(k2_unialg_1(A,B),A) ) ) ).
fof(d1_unialg_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ( m1_unialg_2(B,A)
<=> ! [C] :
( m1_subset_1(C,B)
=> ( ~ v1_xboole_0(C)
& v1_funct_1(C)
& v1_unialg_1(C,A)
& v2_unialg_1(C,A)
& m2_relset_1(C,k3_finseq_2(A),A) ) ) ) ) ) ).
fof(d2_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ( r1_unialg_2(A,B)
<=> k3_unialg_1(A) = k3_unialg_1(B) ) ) ) ).
fof(t3_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ( r1_unialg_2(A,B)
=> k3_finseq_1(u1_unialg_1(A)) = k3_finseq_1(u1_unialg_1(B)) ) ) ) ).
fof(t4_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_unialg_1(C)
& v7_unialg_1(C)
& v8_unialg_1(C)
& l1_unialg_1(C) )
=> ( ( r1_unialg_2(A,B)
& r1_unialg_2(B,C) )
=> r1_unialg_2(A,C) ) ) ) ) ).
fof(t5_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ( ~ v1_xboole_0(k2_relat_1(u1_unialg_1(A)))
& m1_subset_1(k2_relat_1(u1_unialg_1(A)),k1_zfmisc_1(k4_partfun1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)))) ) ) ).
fof(d3_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> k1_unialg_2(A) = k2_relat_1(u1_unialg_1(A)) ) ).
fof(t6_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( r2_hidden(B,k4_finseq_1(u1_unialg_1(A)))
=> m2_unialg_2(k1_funct_1(u1_unialg_1(A),B),u1_struct_0(A),k1_unialg_2(A)) ) ) ).
fof(d4_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m2_unialg_2(C,u1_struct_0(A),k1_unialg_2(A))
=> ( r2_unialg_2(A,B,C)
<=> ! [D] :
( m2_finseq_1(D,B)
=> ( k3_finseq_1(D) = k2_unialg_1(u1_struct_0(A),C)
=> r2_hidden(k1_funct_1(C,D),B) ) ) ) ) ) ) ).
fof(d5_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_unialg_2(B,A)
<=> ! [C] :
( m2_unialg_2(C,u1_struct_0(A),k1_unialg_2(A))
=> r2_unialg_2(A,B,C) ) ) ) ) ).
fof(d6_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m2_unialg_2(C,u1_struct_0(A),k1_unialg_2(A))
=> ( r2_unialg_2(A,B,C)
=> k2_unialg_2(A,B,C) = k2_partfun1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A),C,k4_finseq_2(k2_unialg_1(u1_struct_0(A),C),B)) ) ) ) ) ).
fof(d7_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m2_finseq_1(C,k4_partfun1(k13_finseq_1(B),B))
=> ( C = k3_unialg_2(A,B)
<=> ( k4_finseq_1(C) = k4_finseq_1(u1_unialg_1(A))
& ! [D,E] :
( m2_unialg_2(E,u1_struct_0(A),k1_unialg_2(A))
=> ( ( r2_hidden(D,k4_finseq_1(C))
& E = k1_funct_1(u1_unialg_1(A),D) )
=> k1_funct_1(C,D) = k2_unialg_2(A,B,E) ) ) ) ) ) ) ) ).
fof(t7_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( B = u1_struct_0(A)
=> ( v1_unialg_2(B,A)
& ! [C] :
( m2_unialg_2(C,u1_struct_0(A),k1_unialg_2(A))
=> k2_unialg_2(A,B,C) = C ) ) ) ) ) ).
fof(t8_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m2_unialg_2(C,u1_struct_0(A),k1_unialg_2(A))
=> ( r2_unialg_2(A,B,C)
=> k2_unialg_1(B,k2_unialg_2(A,B,C)) = k2_unialg_1(u1_struct_0(A),C) ) ) ) ) ).
fof(d8_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ( m3_unialg_2(B,A)
<=> ( m1_subset_1(u1_struct_0(B),k1_zfmisc_1(u1_struct_0(A)))
& ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( C = u1_struct_0(B)
=> ( u1_unialg_1(B) = k3_unialg_2(A,C)
& v1_unialg_2(C,A) ) ) ) ) ) ) ) ).
fof(t9_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ! [C] :
( m2_unialg_2(C,u1_struct_0(A),k1_unialg_2(A))
=> ! [D] :
( m2_unialg_2(D,u1_struct_0(B),k1_unialg_2(B))
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( m3_unialg_2(A,B)
& r2_hidden(E,k4_finseq_1(u1_unialg_1(A)))
& C = k1_funct_1(u1_unialg_1(A),E)
& D = k1_funct_1(u1_unialg_1(B),E) )
=> k2_unialg_1(u1_struct_0(A),C) = k2_unialg_1(u1_struct_0(B),D) ) ) ) ) ) ) ).
fof(t10_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ( m3_unialg_2(A,B)
=> k4_finseq_1(u1_unialg_1(A)) = k4_finseq_1(u1_unialg_1(B)) ) ) ) ).
fof(t11_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> m3_unialg_2(A,A) ) ).
fof(t12_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v6_unialg_1(C)
& v7_unialg_1(C)
& v8_unialg_1(C)
& l1_unialg_1(C) )
=> ( ( m3_unialg_2(A,B)
& m3_unialg_2(B,C) )
=> m3_unialg_2(A,C) ) ) ) ) ).
fof(t13_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ( ( v3_unialg_1(A)
& m3_unialg_2(A,B)
& v3_unialg_1(B)
& m3_unialg_2(B,A) )
=> A = B ) ) ) ).
fof(t14_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m3_unialg_2(B,A)
=> ! [C] :
( m3_unialg_2(C,A)
=> ( r1_tarski(u1_struct_0(B),u1_struct_0(C))
=> m3_unialg_2(B,C) ) ) ) ) ).
fof(t15_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( v3_unialg_1(B)
& m3_unialg_2(B,A) )
=> ! [C] :
( ( v3_unialg_1(C)
& m3_unialg_2(C,A) )
=> ( u1_struct_0(B) = u1_struct_0(C)
=> B = C ) ) ) ) ).
fof(t16_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ( m3_unialg_2(A,B)
=> r1_unialg_2(A,B) ) ) ) ).
fof(t17_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v3_struct_0(g1_unialg_1(B,k3_unialg_2(A,B)))
& v3_unialg_1(g1_unialg_1(B,k3_unialg_2(A,B)))
& v6_unialg_1(g1_unialg_1(B,k3_unialg_2(A,B)))
& v7_unialg_1(g1_unialg_1(B,k3_unialg_2(A,B)))
& v8_unialg_1(g1_unialg_1(B,k3_unialg_2(A,B)))
& l1_unialg_1(g1_unialg_1(B,k3_unialg_2(A,B))) ) ) ) ).
fof(d9_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_unialg_2(B,A)
=> k4_unialg_2(A,B) = g1_unialg_1(B,k3_unialg_2(A,B)) ) ) ) ).
fof(d10_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m3_unialg_2(B,A)
=> ! [C] :
( m3_unialg_2(C,A)
=> ( ~ r2_subset_1(u1_struct_0(B),u1_struct_0(C))
=> ! [D] :
( ( v3_unialg_1(D)
& m3_unialg_2(D,A) )
=> ( D = k5_unialg_2(A,B,C)
<=> ( u1_struct_0(D) = k3_xboole_0(u1_struct_0(B),u1_struct_0(C))
& ! [E] :
( ( ~ v1_xboole_0(E)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) )
=> ( E = u1_struct_0(D)
=> ( u1_unialg_1(D) = k3_unialg_2(A,E)
& v1_unialg_2(E,A) ) ) ) ) ) ) ) ) ) ) ).
fof(d12_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ( v2_unialg_2(A)
<=> ? [B] :
( m2_unialg_2(B,u1_struct_0(A),k1_unialg_2(A))
& k2_unialg_1(u1_struct_0(A),B) = np__0 ) ) ) ).
fof(t18_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m3_unialg_2(B,A)
=> m1_subset_1(k6_unialg_2(A),k1_zfmisc_1(u1_struct_0(B))) ) ) ).
fof(t19_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> ! [B] :
( m3_unialg_2(B,A)
=> ( ~ v1_xboole_0(k6_unialg_2(A))
& m1_subset_1(k6_unialg_2(A),k1_zfmisc_1(u1_struct_0(B))) ) ) ) ).
fof(t20_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> ! [B] :
( m3_unialg_2(B,A)
=> ! [C] :
( m3_unialg_2(C,A)
=> ~ r2_subset_1(u1_struct_0(B),u1_struct_0(C)) ) ) ) ).
fof(d13_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ~ ( k6_unialg_2(A) = k1_xboole_0
& B = k1_xboole_0 )
=> ! [C] :
( ( v3_unialg_1(C)
& m3_unialg_2(C,A) )
=> ( C = k7_unialg_2(A,B)
<=> ( r1_tarski(B,u1_struct_0(C))
& ! [D] :
( m3_unialg_2(D,A)
=> ( r1_tarski(B,u1_struct_0(D))
=> m3_unialg_2(C,D) ) ) ) ) ) ) ) ) ).
fof(t21_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_unialg_1(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> k7_unialg_2(A,k2_subset_1(u1_struct_0(A))) = A ) ).
fof(t22_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( v3_unialg_1(B)
& m3_unialg_2(B,A) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( C = u1_struct_0(B)
=> k7_unialg_2(A,C) = B ) ) ) ) ).
fof(d14_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m3_unialg_2(B,A)
=> ! [C] :
( m3_unialg_2(C,A)
=> ! [D] :
( ( v3_unialg_1(D)
& m3_unialg_2(D,A) )
=> ( D = k8_unialg_2(A,B,C)
<=> ! [E] :
( ( ~ v1_xboole_0(E)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) )
=> ( E = k2_xboole_0(u1_struct_0(B),u1_struct_0(C))
=> D = k7_unialg_2(A,E) ) ) ) ) ) ) ) ).
fof(t23_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m3_unialg_2(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( D = k2_xboole_0(C,u1_struct_0(B))
=> ( ( C = k1_xboole_0
& k6_unialg_2(A) = k1_xboole_0 )
| k8_unialg_2(A,k7_unialg_2(A,C),B) = k7_unialg_2(A,D) ) ) ) ) ) ) ).
fof(t24_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m3_unialg_2(B,A)
=> ! [C] :
( m3_unialg_2(C,A)
=> k8_unialg_2(A,B,C) = k8_unialg_2(A,C,B) ) ) ) ).
fof(t25_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( v3_unialg_1(B)
& m3_unialg_2(B,A) )
=> ! [C] :
( ( v3_unialg_1(C)
& m3_unialg_2(C,A) )
=> k5_unialg_2(A,B,k8_unialg_2(A,B,C)) = B ) ) ) ).
fof(t26_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( v3_unialg_1(B)
& m3_unialg_2(B,A) )
=> ! [C] :
( ( v3_unialg_1(C)
& m3_unialg_2(C,A) )
=> k8_unialg_2(A,k5_unialg_2(A,B,C),C) = C ) ) ) ).
fof(d15_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( B = k9_unialg_2(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ( v3_unialg_1(C)
& m3_unialg_2(C,A) ) ) ) ) ).
fof(d16_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(k9_unialg_2(A),k9_unialg_2(A)),k9_unialg_2(A))
& m2_relset_1(B,k2_zfmisc_1(k9_unialg_2(A),k9_unialg_2(A)),k9_unialg_2(A)) )
=> ( B = k10_unialg_2(A)
<=> ! [C] :
( m1_subset_1(C,k9_unialg_2(A))
=> ! [D] :
( m1_subset_1(D,k9_unialg_2(A))
=> ! [E] :
( ( v3_unialg_1(E)
& m3_unialg_2(E,A) )
=> ! [F] :
( ( v3_unialg_1(F)
& m3_unialg_2(F,A) )
=> ( ( C = E
& D = F )
=> k2_binop_1(k9_unialg_2(A),k9_unialg_2(A),k9_unialg_2(A),B,C,D) = k8_unialg_2(A,E,F) ) ) ) ) ) ) ) ) ).
fof(d17_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(k9_unialg_2(A),k9_unialg_2(A)),k9_unialg_2(A))
& m2_relset_1(B,k2_zfmisc_1(k9_unialg_2(A),k9_unialg_2(A)),k9_unialg_2(A)) )
=> ( B = k11_unialg_2(A)
<=> ! [C] :
( m1_subset_1(C,k9_unialg_2(A))
=> ! [D] :
( m1_subset_1(D,k9_unialg_2(A))
=> ! [E] :
( ( v3_unialg_1(E)
& m3_unialg_2(E,A) )
=> ! [F] :
( ( v3_unialg_1(F)
& m3_unialg_2(F,A) )
=> ( ( C = E
& D = F )
=> k2_binop_1(k9_unialg_2(A),k9_unialg_2(A),k9_unialg_2(A),B,C,D) = k5_unialg_2(A,E,F) ) ) ) ) ) ) ) ) ).
fof(t27_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> v1_binop_1(k10_unialg_2(A),k9_unialg_2(A)) ) ).
fof(t28_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> v2_binop_1(k10_unialg_2(A),k9_unialg_2(A)) ) ).
fof(t29_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> v1_binop_1(k11_unialg_2(A),k9_unialg_2(A)) ) ).
fof(t30_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> v2_binop_1(k11_unialg_2(A),k9_unialg_2(A)) ) ).
fof(d18_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> k12_unialg_2(A) = g3_lattices(k9_unialg_2(A),k10_unialg_2(A),k11_unialg_2(A)) ) ).
fof(dt_m1_unialg_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_unialg_2(B,A)
=> ~ v1_xboole_0(B) ) ) ).
fof(existence_m1_unialg_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] : m1_unialg_2(B,A) ) ).
fof(dt_m2_unialg_2,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_unialg_2(B,A) )
=> ! [C] :
( m2_unialg_2(C,A,B)
=> ( ~ v1_xboole_0(C)
& v1_funct_1(C)
& v1_unialg_1(C,A)
& v2_unialg_1(C,A)
& m2_relset_1(C,k3_finseq_2(A),A) ) ) ) ).
fof(existence_m2_unialg_2,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_unialg_2(B,A) )
=> ? [C] : m2_unialg_2(C,A,B) ) ).
fof(redefinition_m2_unialg_2,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_unialg_2(B,A) )
=> ! [C] :
( m2_unialg_2(C,A,B)
<=> m1_subset_1(C,B) ) ) ).
fof(dt_m3_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ! [B] :
( m3_unialg_2(B,A)
=> ( ~ v3_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) ) ) ) ).
fof(existence_m3_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ? [B] : m3_unialg_2(B,A) ) ).
fof(symmetry_r1_unialg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A)
& ~ v3_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ( r1_unialg_2(A,B)
=> r1_unialg_2(B,A) ) ) ).
fof(reflexivity_r1_unialg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A)
& ~ v3_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> r1_unialg_2(A,A) ) ).
fof(dt_k1_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> m1_unialg_2(k1_unialg_2(A),u1_struct_0(A)) ) ).
fof(dt_k2_unialg_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& m1_subset_1(C,k1_unialg_2(A)) )
=> ( ~ v1_xboole_0(k2_unialg_2(A,B,C))
& v1_funct_1(k2_unialg_2(A,B,C))
& v1_unialg_1(k2_unialg_2(A,B,C),B)
& v2_unialg_1(k2_unialg_2(A,B,C),B)
& m2_relset_1(k2_unialg_2(A,B,C),k3_finseq_2(B),B) ) ) ).
fof(dt_k3_unialg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> m2_finseq_1(k3_unialg_2(A,B),k4_partfun1(k13_finseq_1(B),B)) ) ).
fof(dt_k4_unialg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v3_unialg_1(k4_unialg_2(A,B))
& m3_unialg_2(k4_unialg_2(A,B),A) ) ) ).
fof(dt_k5_unialg_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A)
& m3_unialg_2(B,A)
& m3_unialg_2(C,A) )
=> ( v3_unialg_1(k5_unialg_2(A,B,C))
& m3_unialg_2(k5_unialg_2(A,B,C),A) ) ) ).
fof(dt_k6_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> m1_subset_1(k6_unialg_2(A),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k7_unialg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v3_unialg_1(k7_unialg_2(A,B))
& m3_unialg_2(k7_unialg_2(A,B),A) ) ) ).
fof(dt_k8_unialg_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A)
& m3_unialg_2(B,A)
& m3_unialg_2(C,A) )
=> ( v3_unialg_1(k8_unialg_2(A,B,C))
& m3_unialg_2(k8_unialg_2(A,B,C),A) ) ) ).
fof(dt_k9_unialg_2,axiom,
$true ).
fof(dt_k10_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ( v1_funct_1(k10_unialg_2(A))
& v1_funct_2(k10_unialg_2(A),k2_zfmisc_1(k9_unialg_2(A),k9_unialg_2(A)),k9_unialg_2(A))
& m2_relset_1(k10_unialg_2(A),k2_zfmisc_1(k9_unialg_2(A),k9_unialg_2(A)),k9_unialg_2(A)) ) ) ).
fof(dt_k11_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> ( v1_funct_1(k11_unialg_2(A))
& v1_funct_2(k11_unialg_2(A),k2_zfmisc_1(k9_unialg_2(A),k9_unialg_2(A)),k9_unialg_2(A))
& m2_relset_1(k11_unialg_2(A),k2_zfmisc_1(k9_unialg_2(A),k9_unialg_2(A)),k9_unialg_2(A)) ) ) ).
fof(dt_k12_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& v2_unialg_2(A)
& l1_unialg_1(A) )
=> ( ~ v3_struct_0(k12_unialg_2(A))
& v3_lattices(k12_unialg_2(A))
& v10_lattices(k12_unialg_2(A))
& l3_lattices(k12_unialg_2(A)) ) ) ).
fof(d11_unialg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_unialg_1(A)
& v7_unialg_1(A)
& v8_unialg_1(A)
& l1_unialg_1(A) )
=> k6_unialg_2(A) = a_1_0_unialg_2(A) ) ).
fof(fraenkel_a_1_0_unialg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v6_unialg_1(B)
& v7_unialg_1(B)
& v8_unialg_1(B)
& l1_unialg_1(B) )
=> ( r2_hidden(A,a_1_0_unialg_2(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(B))
& A = C
& ? [D] :
( m2_unialg_2(D,u1_struct_0(B),k1_unialg_2(B))
& k2_unialg_1(u1_struct_0(B),D) = np__0
& r2_hidden(C,k2_relat_1(D)) ) ) ) ) ).
%------------------------------------------------------------------------------