SET007 Axioms: SET007+440.ax
%------------------------------------------------------------------------------
% File : SET007+440 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Continuous, Stable, and Linear Maps of Coherence Spaces
% 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 : cohsp_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 194 ( 25 unt; 0 def)
% Number of atoms : 1416 ( 111 equ)
% Maximal formula atoms : 26 ( 7 avg)
% Number of connectives : 1465 ( 243 ~; 6 |; 814 &)
% ( 57 <=>; 345 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 32 ( 30 usr; 1 prp; 0-3 aty)
% Number of functors : 51 ( 51 usr; 5 con; 0-4 aty)
% Number of variables : 557 ( 517 !; 40 ?)
% 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_cohsp_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_finset_1(A)
& v1_coh_sp(A) ) ).
fof(fc1_cohsp_1,axiom,
( ~ v1_xboole_0(k1_tarski(k1_xboole_0))
& v1_classes1(k1_tarski(k1_xboole_0))
& v1_finset_1(k1_tarski(k1_xboole_0))
& v1_coh_sp(k1_tarski(k1_xboole_0)) ) ).
fof(fc2_cohsp_1,axiom,
! [A] :
( ~ v1_xboole_0(k1_zfmisc_1(A))
& v1_finsub_1(k1_zfmisc_1(A))
& v3_finsub_1(k1_zfmisc_1(A))
& v4_finsub_1(k1_zfmisc_1(A))
& v1_classes1(k1_zfmisc_1(A))
& v1_coh_sp(k1_zfmisc_1(A)) ) ).
fof(fc3_cohsp_1,axiom,
! [A] :
( ~ v1_xboole_0(k1_cohsp_1(A))
& v1_classes1(k1_cohsp_1(A))
& v1_coh_sp(k1_cohsp_1(A)) ) ).
fof(fc4_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A) )
=> ( ~ v1_xboole_0(k2_cohsp_1(A))
& v1_classes1(k2_cohsp_1(A)) ) ) ).
fof(rc2_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ? [B] :
( m1_subset_1(B,A)
& v1_finset_1(B) ) ) ).
fof(cc1_cohsp_1,axiom,
! [A] :
( v1_cohsp_1(A)
=> ~ v1_xboole_0(A) ) ).
fof(cc2_cohsp_1,axiom,
! [A] :
( v2_cohsp_1(A)
=> ~ v1_xboole_0(A) ) ).
fof(rc3_cohsp_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_finset_1(A)
& v1_cohsp_1(A)
& v2_cohsp_1(A) ) ).
fof(rc4_cohsp_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(B)
& v1_finset_1(B)
& v1_cohsp_1(B)
& v2_cohsp_1(B) ) ) ).
fof(fc5_cohsp_1,axiom,
! [A] :
( ~ v1_xboole_0(k5_finsub_1(A))
& v1_finsub_1(k5_finsub_1(A))
& v3_finsub_1(k5_finsub_1(A))
& v4_finsub_1(k5_finsub_1(A))
& v1_cohsp_1(k5_finsub_1(A))
& v2_cohsp_1(k5_finsub_1(A)) ) ).
fof(rc5_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(B)
& v1_finsub_1(B)
& v3_finsub_1(B)
& v4_finsub_1(B) ) ) ).
fof(cc3_cohsp_1,axiom,
! [A] :
( v1_classes1(A)
=> v2_finsub_1(A) ) ).
fof(cc4_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ( ~ v1_xboole_0(A)
& v2_finsub_1(A)
& v1_classes1(A)
& v1_coh_sp(A)
& v3_cohsp_1(A) ) ) ).
fof(rc6_cohsp_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v2_finsub_1(A)
& v1_classes1(A)
& v1_coh_sp(A)
& v3_cohsp_1(A) ) ).
fof(cc5_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v5_cohsp_1(A) )
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v6_cohsp_1(A) ) ) ).
fof(cc6_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v4_cohsp_1(A) )
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v5_cohsp_1(A) ) ) ).
fof(rc7_cohsp_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A)
& ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ? [C] :
( m1_relset_1(C,A,B)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& v4_cohsp_1(C)
& v5_cohsp_1(C)
& v6_cohsp_1(C)
& v7_cohsp_1(C) ) ) ).
fof(rc8_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ? [B] :
( m1_pboole(B,A)
& v1_relat_1(B)
& v1_funct_1(B)
& v4_cohsp_1(B)
& v5_cohsp_1(B)
& v6_cohsp_1(B)
& v7_cohsp_1(B) ) ) ).
fof(cc7_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v8_cohsp_1(A) )
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v5_cohsp_1(A)
& v6_cohsp_1(A) ) ) ).
fof(cc8_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v9_cohsp_1(A) )
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v7_cohsp_1(A)
& v8_cohsp_1(A) ) ) ).
fof(cc9_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v10_cohsp_1(A) )
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v4_cohsp_1(A)
& v5_cohsp_1(A)
& v6_cohsp_1(A)
& v9_cohsp_1(A) ) ) ).
fof(cc10_cohsp_1,axiom,
! [A] :
( v3_cohsp_1(A)
=> ! [B] :
( m1_pboole(B,A)
=> ( v5_cohsp_1(B)
=> v8_cohsp_1(B) ) ) ) ).
fof(cc11_cohsp_1,axiom,
! [A] :
( v2_finsub_1(A)
=> ! [B] :
( m1_pboole(B,A)
=> ( ( v7_cohsp_1(B)
& v8_cohsp_1(B) )
=> v9_cohsp_1(B) ) ) ) ).
fof(cc12_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v4_cohsp_1(A)
& v9_cohsp_1(A) )
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v4_cohsp_1(A)
& v5_cohsp_1(A)
& v6_cohsp_1(A)
& v7_cohsp_1(A)
& v8_cohsp_1(A)
& v9_cohsp_1(A)
& v10_cohsp_1(A) ) ) ).
fof(rc9_cohsp_1,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& v4_cohsp_1(A)
& v5_cohsp_1(A)
& v6_cohsp_1(A)
& v7_cohsp_1(A)
& v8_cohsp_1(A)
& v9_cohsp_1(A)
& v10_cohsp_1(A) ) ).
fof(rc10_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ? [B] :
( m1_pboole(B,A)
& v1_relat_1(B)
& v1_funct_1(B)
& v4_cohsp_1(B)
& v5_cohsp_1(B)
& v6_cohsp_1(B)
& v7_cohsp_1(B)
& v8_cohsp_1(B)
& v9_cohsp_1(B)
& v10_cohsp_1(B) ) ) ).
fof(rc11_cohsp_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A)
& ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ? [C] :
( m1_relset_1(C,B,A)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,B,A)
& v4_cohsp_1(C)
& v5_cohsp_1(C)
& v6_cohsp_1(C)
& v7_cohsp_1(C)
& v8_cohsp_1(C)
& v9_cohsp_1(C)
& v10_cohsp_1(C) ) ) ).
fof(fc6_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v8_cohsp_1(A) )
=> v3_cohsp_1(k1_relat_1(A)) ) ).
fof(fc7_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v9_cohsp_1(A) )
=> ( v2_finsub_1(k1_relat_1(A))
& v3_cohsp_1(k1_relat_1(A)) ) ) ).
fof(fc8_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> v1_relat_1(k5_cohsp_1(A)) ) ).
fof(fc9_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> v1_relat_1(k7_cohsp_1(A)) ) ).
fof(fc10_cohsp_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A)
& ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ( ~ v1_xboole_0(k9_cohsp_1(A,B))
& v2_finsub_1(k9_cohsp_1(A,B))
& v1_classes1(k9_cohsp_1(A,B))
& v1_coh_sp(k9_cohsp_1(A,B))
& v3_cohsp_1(k9_cohsp_1(A,B)) ) ) ).
fof(fc11_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> v1_relat_1(k10_cohsp_1(A)) ) ).
fof(fc12_cohsp_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A)
& ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ( ~ v1_xboole_0(k12_cohsp_1(A,B))
& v2_finsub_1(k12_cohsp_1(A,B))
& v1_classes1(k12_cohsp_1(A,B))
& v1_coh_sp(k12_cohsp_1(A,B))
& v3_cohsp_1(k12_cohsp_1(A,B)) ) ) ).
fof(fc13_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ( ~ v1_xboole_0(k13_cohsp_1(A))
& v2_finsub_1(k13_cohsp_1(A))
& v1_classes1(k13_cohsp_1(A))
& v1_coh_sp(k13_cohsp_1(A))
& v3_cohsp_1(k13_cohsp_1(A)) ) ) ).
fof(fc14_cohsp_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A)
& ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ( ~ v1_xboole_0(k15_cohsp_1(A,B))
& v2_finsub_1(k15_cohsp_1(A,B))
& v1_classes1(k15_cohsp_1(A,B))
& v1_coh_sp(k15_cohsp_1(A,B))
& v3_cohsp_1(k15_cohsp_1(A,B)) ) ) ).
fof(fc15_cohsp_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A)
& ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ( ~ v1_xboole_0(k16_cohsp_1(A,B))
& v2_finsub_1(k16_cohsp_1(A,B))
& v1_classes1(k16_cohsp_1(A,B))
& v1_coh_sp(k16_cohsp_1(A,B))
& v3_cohsp_1(k16_cohsp_1(A,B)) ) ) ).
fof(fc16_cohsp_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A)
& ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ~ v1_xboole_0(k17_cohsp_1(A,B)) ) ).
fof(fc17_cohsp_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A)
& ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ( ~ v1_xboole_0(k17_cohsp_1(A,B))
& v2_finsub_1(k17_cohsp_1(A,B))
& v1_classes1(k17_cohsp_1(A,B))
& v1_coh_sp(k17_cohsp_1(A,B))
& v3_cohsp_1(k17_cohsp_1(A,B)) ) ) ).
fof(d1_cohsp_1,axiom,
! [A] :
( v1_coh_sp(A)
<=> ! [B] :
( ! [C,D] :
( ( r2_hidden(C,B)
& r2_hidden(D,B) )
=> r2_hidden(k2_xboole_0(C,D),A) )
=> r2_hidden(k3_tarski(B),A) ) ) ).
fof(d2_cohsp_1,axiom,
! [A] : k1_cohsp_1(A) = k2_coh_sp(A,k6_partfun1(A)) ).
fof(d3_cohsp_1,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ( B = k2_cohsp_1(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ( r2_hidden(C,A)
& v1_finset_1(C) ) ) ) ) ).
fof(t1_cohsp_1,axiom,
! [A,B] :
( r2_hidden(B,k1_cohsp_1(A))
<=> ~ ( B != k1_xboole_0
& ! [C] :
~ ( B = k1_tarski(C)
& r2_hidden(C,A) ) ) ) ).
fof(t2_cohsp_1,axiom,
! [A] : k3_tarski(k1_cohsp_1(A)) = A ).
fof(t3_cohsp_1,axiom,
! [A] :
( ( v1_classes1(A)
& v1_finset_1(A) )
=> k2_cohsp_1(A) = A ) ).
fof(t4_cohsp_1,axiom,
k1_coh_sp(k1_tarski(k1_xboole_0)) = k1_xboole_0 ).
fof(d4_cohsp_1,axiom,
! [A] :
( v1_cohsp_1(A)
<=> ! [B] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> ? [C] :
( r1_tarski(k3_tarski(B),C)
& r2_hidden(C,A) ) ) ) ).
fof(d5_cohsp_1,axiom,
! [A] :
( v2_cohsp_1(A)
<=> ! [B] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> ? [C] :
( ! [D] :
( r2_hidden(D,B)
=> r1_tarski(C,D) )
& r2_hidden(C,A) ) ) ) ).
fof(t5_cohsp_1,axiom,
! [A] :
( v1_cohsp_1(A)
=> ! [B,C] :
~ ( r2_hidden(B,A)
& r2_hidden(C,A)
& ! [D] :
~ ( r1_tarski(k2_xboole_0(B,C),D)
& r2_hidden(D,A) ) ) ) ).
fof(t6_cohsp_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( ! [B,C] :
~ ( r2_hidden(B,A)
& r2_hidden(C,A)
& ! [D] :
~ ( r1_tarski(k2_xboole_0(B,C),D)
& r2_hidden(D,A) ) )
=> v1_cohsp_1(A) ) ) ).
fof(t7_cohsp_1,axiom,
! [A] :
( v2_cohsp_1(A)
=> ! [B,C] :
~ ( r2_hidden(B,A)
& r2_hidden(C,A)
& ! [D] :
~ ( r1_tarski(D,k3_xboole_0(B,C))
& r2_hidden(D,A) ) ) ) ).
fof(t8_cohsp_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( ! [B,C] :
~ ( r2_hidden(B,A)
& r2_hidden(C,A)
& ! [D] :
~ ( r1_tarski(D,k3_xboole_0(B,C))
& r2_hidden(D,A) ) )
=> v2_cohsp_1(A) ) ) ).
fof(t9_cohsp_1,axiom,
! [A] :
( v1_cohsp_1(k1_tarski(A))
& v2_cohsp_1(k1_tarski(A)) ) ).
fof(t10_cohsp_1,axiom,
! [A,B] : v1_cohsp_1(k1_enumset1(A,B,k2_xboole_0(A,B))) ).
fof(t11_cohsp_1,axiom,
! [A,B] : v2_cohsp_1(k1_enumset1(A,B,k3_xboole_0(A,B))) ).
fof(t12_cohsp_1,axiom,
! [A] :
( v1_cohsp_1(k5_finsub_1(A))
& v2_cohsp_1(k5_finsub_1(A)) ) ).
fof(t13_cohsp_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
~ ( v1_cohsp_1(A)
& r1_tarski(B,k3_tarski(A))
& v1_finset_1(B)
& ! [C] :
~ ( r2_hidden(C,A)
& r1_tarski(B,C) ) ) ) ).
fof(d6_cohsp_1,axiom,
$true ).
fof(d7_cohsp_1,axiom,
! [A] :
( v3_cohsp_1(A)
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ( v1_cohsp_1(B)
=> r2_hidden(k3_tarski(B),A) ) ) ) ).
fof(t14_cohsp_1,axiom,
$true ).
fof(t15_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( v1_cohsp_1(B)
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> r2_hidden(k3_tarski(B),A) ) ) ).
fof(d8_cohsp_1,axiom,
! [A,B] :
( r1_cohsp_1(A,B)
<=> ! [C,D] :
( ( r2_hidden(C,B)
& r2_hidden(D,B) )
=> ( r2_hidden(k3_xboole_0(C,D),A)
& r2_hidden(k2_xboole_0(C,D),A) ) ) ) ).
fof(t16_cohsp_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( r1_cohsp_1(A,A)
=> ( v1_cohsp_1(A)
& v2_cohsp_1(A) ) ) ) ).
fof(d9_cohsp_1,axiom,
! [A,B,C] :
( r2_cohsp_1(A,B,C)
<=> r1_cohsp_1(A,k2_tarski(B,C)) ) ).
fof(t17_cohsp_1,axiom,
! [A,B,C] :
( r2_cohsp_1(A,B,C)
<=> ( r2_hidden(B,A)
& r2_hidden(C,A)
& r2_hidden(k3_xboole_0(B,C),A)
& r2_hidden(k2_xboole_0(B,C),A) ) ) ).
fof(d10_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v4_cohsp_1(A)
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_relat_1(A)))
=> ( r2_hidden(k3_tarski(B),k1_relat_1(A))
=> k1_funct_1(A,k3_tarski(B)) = k3_tarski(k9_relat_1(A,B)) ) ) ) ) ).
fof(d11_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v5_cohsp_1(A)
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_relat_1(A)))
=> ( ( v1_cohsp_1(B)
& r2_hidden(k3_tarski(B),k1_relat_1(A)) )
=> k1_funct_1(A,k3_tarski(B)) = k3_tarski(k9_relat_1(A,B)) ) ) ) ) ).
fof(d12_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v6_cohsp_1(A)
<=> ! [B,C] :
( ( r2_hidden(B,k1_relat_1(A))
& r2_hidden(C,k1_relat_1(A))
& r1_tarski(B,C) )
=> r1_tarski(k1_funct_1(A,B),k1_funct_1(A,C)) ) ) ) ).
fof(d13_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v7_cohsp_1(A)
<=> ! [B,C] :
( r2_cohsp_1(k1_relat_1(A),B,C)
=> k1_funct_1(A,k3_xboole_0(B,C)) = k3_xboole_0(k1_funct_1(A,B),k1_funct_1(A,C)) ) ) ) ).
fof(t18_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v4_cohsp_1(A)
=> ! [B,C] :
( ( r2_hidden(B,k1_relat_1(A))
& r2_hidden(C,k1_relat_1(A))
& r2_hidden(k2_xboole_0(B,C),k1_relat_1(A)) )
=> k1_funct_1(A,k2_xboole_0(B,C)) = k2_xboole_0(k1_funct_1(A,B),k1_funct_1(A,C)) ) ) ) ).
fof(t19_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v4_cohsp_1(A)
=> k1_funct_1(A,k1_xboole_0) = k1_xboole_0 ) ) ).
fof(d14_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v8_cohsp_1(A)
<=> ( v3_cohsp_1(k1_relat_1(A))
& v5_cohsp_1(A) ) ) ) ).
fof(d15_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v9_cohsp_1(A)
<=> ( v2_finsub_1(k1_relat_1(A))
& v8_cohsp_1(A)
& v7_cohsp_1(A) ) ) ) ).
fof(d16_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v10_cohsp_1(A)
<=> ( v9_cohsp_1(A)
& v4_cohsp_1(A) ) ) ) ).
fof(t20_cohsp_1,axiom,
! [A] : k3_tarski(k5_finsub_1(A)) = A ).
fof(t21_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v8_cohsp_1(A) )
=> ( v1_classes1(k1_relat_1(A))
=> ! [B] :
( r2_hidden(B,k1_relat_1(A))
=> k1_funct_1(A,B) = k3_tarski(k9_relat_1(A,k5_finsub_1(B))) ) ) ) ).
fof(t22_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v1_classes1(k1_relat_1(A))
=> ( v8_cohsp_1(A)
<=> ( v3_cohsp_1(k1_relat_1(A))
& v6_cohsp_1(A)
& ! [B,C] :
~ ( r2_hidden(B,k1_relat_1(A))
& r2_hidden(C,k1_funct_1(A,B))
& ! [D] :
~ ( v1_finset_1(D)
& r1_tarski(D,B)
& r2_hidden(C,k1_funct_1(A,D)) ) ) ) ) ) ) ).
fof(t23_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( ( v1_classes1(k1_relat_1(A))
& v3_cohsp_1(k1_relat_1(A)) )
=> ( v9_cohsp_1(A)
<=> ( v6_cohsp_1(A)
& ! [B,C] :
~ ( r2_hidden(B,k1_relat_1(A))
& r2_hidden(C,k1_funct_1(A,B))
& ! [D] :
~ ( v1_finset_1(D)
& r1_tarski(D,B)
& r2_hidden(C,k1_funct_1(A,D))
& ! [E] :
( ( r1_tarski(E,B)
& r2_hidden(C,k1_funct_1(A,E)) )
=> r1_tarski(D,E) ) ) ) ) ) ) ) ).
fof(t24_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( ( v1_classes1(k1_relat_1(A))
& v3_cohsp_1(k1_relat_1(A)) )
=> ( v10_cohsp_1(A)
<=> ( v6_cohsp_1(A)
& ! [B,C] :
~ ( r2_hidden(B,k1_relat_1(A))
& r2_hidden(C,k1_funct_1(A,B))
& ! [D] :
~ ( r2_hidden(D,B)
& r2_hidden(C,k1_funct_1(A,k1_tarski(D)))
& ! [E] :
( ( r1_tarski(E,B)
& r2_hidden(C,k1_funct_1(A,E)) )
=> r2_hidden(D,E) ) ) ) ) ) ) ) ).
fof(d17_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( B = k5_cohsp_1(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ? [D] :
( v1_finset_1(D)
& ? [E] :
( C = k4_tarski(D,E)
& r2_hidden(D,k1_relat_1(A))
& r2_hidden(E,k1_funct_1(A,D)) ) ) ) ) ) ).
fof(t25_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C] :
( r2_hidden(k4_tarski(B,C),k5_cohsp_1(A))
<=> ( v1_finset_1(B)
& r2_hidden(B,k1_relat_1(A))
& r2_hidden(C,k1_funct_1(A,B)) ) ) ) ).
fof(t26_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v6_cohsp_1(A) )
=> ! [B,C] :
( ( r2_hidden(C,k1_relat_1(A))
& r1_tarski(B,C)
& v1_finset_1(C) )
=> ! [D] :
( r2_hidden(k4_tarski(B,D),k5_cohsp_1(A))
=> r2_hidden(k4_tarski(C,D),k5_cohsp_1(A)) ) ) ) ).
fof(t27_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m2_relset_1(C,A,B) )
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E,F] :
( ( r2_hidden(k4_tarski(D,E),k6_cohsp_1(A,B,C))
& r2_hidden(k4_tarski(D,F),k6_cohsp_1(A,B,C)) )
=> r2_hidden(k2_tarski(E,F),B) ) ) ) ) ) ).
fof(t28_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& v6_cohsp_1(C)
& m2_relset_1(C,A,B) )
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> ( r2_hidden(k2_xboole_0(D,E),A)
=> ! [F,G] :
( ( r2_hidden(k4_tarski(D,F),k6_cohsp_1(A,B,C))
& r2_hidden(k4_tarski(E,G),k6_cohsp_1(A,B,C)) )
=> r2_hidden(k2_tarski(F,G),B) ) ) ) ) ) ) ) ).
fof(t29_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& v8_cohsp_1(C)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& v8_cohsp_1(D)
& m2_relset_1(D,A,B) )
=> ( k6_cohsp_1(A,B,C) = k6_cohsp_1(A,B,D)
=> C = D ) ) ) ) ) ).
fof(t30_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k3_tarski(B))))
=> ~ ( ! [D] :
( r2_hidden(D,C)
=> v1_finset_1(k1_mcart_1(D)) )
& ! [D] :
( ( v1_finset_1(D)
& m1_subset_1(D,A) )
=> ! [E] :
( ( v1_finset_1(E)
& m1_subset_1(E,A) )
=> ( r1_tarski(D,E)
=> ! [F] :
( r2_hidden(k4_tarski(D,F),C)
=> r2_hidden(k4_tarski(E,F),C) ) ) ) )
& ! [D] :
( ( v1_finset_1(D)
& m1_subset_1(D,A) )
=> ! [E,F] :
( ( r2_hidden(k4_tarski(D,E),C)
& r2_hidden(k4_tarski(D,F),C) )
=> r2_hidden(k2_tarski(E,F),B) ) )
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& v8_cohsp_1(D)
& m2_relset_1(D,A,B) )
=> C != k6_cohsp_1(A,B,D) ) ) ) ) ) ).
fof(t31_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& v8_cohsp_1(C)
& m2_relset_1(C,A,B) )
=> ! [D] :
( m1_subset_1(D,A)
=> k8_funct_2(A,B,C,D) = k9_relat_1(k6_cohsp_1(A,B,C),k3_cohsp_1(A,D)) ) ) ) ) ).
fof(d18_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( B = k7_cohsp_1(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ? [D,E] :
( C = k4_tarski(D,E)
& r2_hidden(D,k1_relat_1(A))
& r2_hidden(E,k1_funct_1(A,D))
& ! [F] :
( ( r2_hidden(F,k1_relat_1(A))
& r1_tarski(F,D)
& r2_hidden(E,k1_funct_1(A,F)) )
=> D = F ) ) ) ) ) ).
fof(t32_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C] :
( r2_hidden(k4_tarski(B,C),k7_cohsp_1(A))
<=> ( r2_hidden(B,k1_relat_1(A))
& r2_hidden(C,k1_funct_1(A,B))
& ! [D] :
( ( r2_hidden(D,k1_relat_1(A))
& r1_tarski(D,B)
& r2_hidden(C,k1_funct_1(A,D)) )
=> B = D ) ) ) ) ).
fof(t33_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v8_cohsp_1(A) )
=> ( v1_classes1(k1_relat_1(A))
=> r1_tarski(k7_cohsp_1(A),k5_cohsp_1(A)) ) ) ).
fof(t34_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v8_cohsp_1(A) )
=> ( v1_classes1(k1_relat_1(A))
=> ! [B,C] :
( r2_hidden(k4_tarski(B,C),k7_cohsp_1(A))
=> v1_finset_1(B) ) ) ) ).
fof(t35_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& v6_cohsp_1(C)
& m2_relset_1(C,A,B) )
=> ! [D,E] :
( r2_hidden(k2_xboole_0(D,E),A)
=> ! [F,G] :
( ( r2_hidden(k4_tarski(D,F),k8_cohsp_1(A,B,C))
& r2_hidden(k4_tarski(E,G),k8_cohsp_1(A,B,C)) )
=> r2_hidden(k2_tarski(F,G),B) ) ) ) ) ) ).
fof(t36_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& v7_cohsp_1(C)
& m2_relset_1(C,A,B) )
=> ! [D,E] :
( r2_hidden(k2_xboole_0(D,E),A)
=> ! [F] :
( ( r2_hidden(k4_tarski(D,F),k8_cohsp_1(A,B,C))
& r2_hidden(k4_tarski(E,F),k8_cohsp_1(A,B,C)) )
=> D = E ) ) ) ) ) ).
fof(t37_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& v9_cohsp_1(C)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& v9_cohsp_1(D)
& m2_relset_1(D,A,B) )
=> ( r1_tarski(k8_cohsp_1(A,B,C),k8_cohsp_1(A,B,D))
=> ! [E] :
( m1_subset_1(E,A)
=> r1_tarski(k8_funct_2(A,B,C,E),k8_funct_2(A,B,D,E)) ) ) ) ) ) ) ).
fof(t38_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& v9_cohsp_1(C)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& v9_cohsp_1(D)
& m2_relset_1(D,A,B) )
=> ( k8_cohsp_1(A,B,C) = k8_cohsp_1(A,B,D)
=> C = D ) ) ) ) ) ).
fof(t39_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k3_tarski(B))))
=> ~ ( ! [D] :
( r2_hidden(D,C)
=> v1_finset_1(k1_mcart_1(D)) )
& ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> ( r2_hidden(k2_xboole_0(D,E),A)
=> ! [F,G] :
( ( r2_hidden(k4_tarski(D,F),C)
& r2_hidden(k4_tarski(E,G),C) )
=> r2_hidden(k2_tarski(F,G),B) ) ) ) )
& ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> ( r2_hidden(k2_xboole_0(D,E),A)
=> ! [F] :
( ( r2_hidden(k4_tarski(D,F),C)
& r2_hidden(k4_tarski(E,F),C) )
=> D = E ) ) ) )
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& v9_cohsp_1(D)
& m2_relset_1(D,A,B) )
=> C != k8_cohsp_1(A,B,D) ) ) ) ) ) ).
fof(t40_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& v9_cohsp_1(C)
& m2_relset_1(C,A,B) )
=> ! [D] :
( m1_subset_1(D,A)
=> k8_funct_2(A,B,C,D) = k9_relat_1(k8_cohsp_1(A,B,C),k3_cohsp_1(A,D)) ) ) ) ) ).
fof(t41_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& v9_cohsp_1(C)
& m2_relset_1(C,A,B) )
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( r2_hidden(E,k8_funct_2(A,B,C,D))
<=> ? [F] :
( m1_subset_1(F,A)
& r2_hidden(k4_tarski(F,E),k8_cohsp_1(A,B,C))
& r1_tarski(F,D) ) ) ) ) ) ) ).
fof(t42_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,A,B)
& v9_cohsp_1(C)
& m2_relset_1(C,A,B)
& k8_cohsp_1(A,B,C) = k1_xboole_0 ) ) ) ).
fof(t43_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
( ( v1_finset_1(C)
& m1_subset_1(C,A) )
=> ! [D] :
~ ( r2_hidden(D,k3_tarski(B))
& ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& v9_cohsp_1(E)
& m2_relset_1(E,A,B) )
=> k8_cohsp_1(A,B,E) != k1_tarski(k4_tarski(C,D)) ) ) ) ) ) ).
fof(t44_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D,E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& v9_cohsp_1(E)
& m2_relset_1(E,A,B) )
=> ( k8_cohsp_1(A,B,E) = k1_tarski(k4_tarski(C,D))
=> ! [F] :
( m1_subset_1(F,A)
=> ( ( r1_tarski(C,F)
=> k8_funct_2(A,B,E,F) = k1_tarski(D) )
& ( ~ r1_tarski(C,F)
=> k8_funct_2(A,B,E,F) = k1_xboole_0 ) ) ) ) ) ) ) ) ).
fof(t45_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& v9_cohsp_1(C)
& m2_relset_1(C,A,B) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k8_cohsp_1(A,B,C)))
=> ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,A,B)
& v9_cohsp_1(E)
& m2_relset_1(E,A,B)
& k8_cohsp_1(A,B,E) = D ) ) ) ) ) ).
fof(t46_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
~ ( ! [D,E] :
~ ( r2_hidden(D,C)
& r2_hidden(E,C)
& ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,A,B)
& v9_cohsp_1(F)
& m2_relset_1(F,A,B) )
=> k2_xboole_0(D,E) != k8_cohsp_1(A,B,F) ) )
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& v9_cohsp_1(D)
& m2_relset_1(D,A,B) )
=> k3_tarski(C) != k8_cohsp_1(A,B,D) ) ) ) ) ).
fof(d19_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
( C = k9_cohsp_1(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,A,B)
& v9_cohsp_1(E)
& m2_relset_1(E,A,B)
& D = k8_cohsp_1(A,B,E) ) ) ) ) ) ).
fof(t47_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& v9_cohsp_1(C)
& m2_relset_1(C,A,B) )
=> r1_tarski(k8_cohsp_1(A,B,C),k2_zfmisc_1(k2_cohsp_1(A),k3_tarski(B))) ) ) ) ).
fof(t48_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> k3_tarski(k9_cohsp_1(A,B)) = k2_zfmisc_1(k2_cohsp_1(A),k3_tarski(B)) ) ) ).
fof(t49_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
( ( v1_finset_1(C)
& m1_subset_1(C,A) )
=> ! [D] :
( ( v1_finset_1(D)
& m1_subset_1(D,A) )
=> ! [E,F] :
( r2_hidden(k4_tarski(k4_tarski(C,E),k4_tarski(D,F)),k1_coh_sp(k9_cohsp_1(A,B)))
<=> ( ( ~ r2_hidden(k2_xboole_0(C,D),A)
& r2_hidden(E,k3_tarski(B))
& r2_hidden(F,k3_tarski(B)) )
| ( r2_hidden(k4_tarski(E,F),k1_coh_sp(B))
& ( E = F
=> C = D ) ) ) ) ) ) ) ) ).
fof(t50_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& v9_cohsp_1(C)
& m2_relset_1(C,A,B) )
=> ( v10_cohsp_1(C)
<=> ! [D,E] :
~ ( r2_hidden(k4_tarski(D,E),k8_cohsp_1(A,B,C))
& ! [F] : D != k1_tarski(F) ) ) ) ) ) ).
fof(d20_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( B = k10_cohsp_1(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ? [D,E] :
( C = k4_tarski(D,E)
& r2_hidden(k4_tarski(k1_tarski(D),E),k7_cohsp_1(A)) ) ) ) ) ).
fof(t51_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C] :
( r2_hidden(k4_tarski(B,C),k10_cohsp_1(A))
<=> r2_hidden(k4_tarski(k1_tarski(B),C),k7_cohsp_1(A)) ) ) ).
fof(t52_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( k1_funct_1(A,k1_xboole_0) = k1_xboole_0
=> ! [B,C] :
( ( r2_hidden(k1_tarski(B),k1_relat_1(A))
& r2_hidden(C,k1_funct_1(A,k1_tarski(B))) )
=> r2_hidden(k4_tarski(B,C),k10_cohsp_1(A)) ) ) ) ).
fof(t53_cohsp_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C] :
( r2_hidden(k4_tarski(B,C),k10_cohsp_1(A))
=> ( r2_hidden(k1_tarski(B),k1_relat_1(A))
& r2_hidden(C,k1_funct_1(A,k1_tarski(B))) ) ) ) ).
fof(d21_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
( C = k12_cohsp_1(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,A,B)
& v10_cohsp_1(E)
& m2_relset_1(E,A,B)
& D = k11_cohsp_1(A,B,E) ) ) ) ) ) ).
fof(t54_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& v6_cohsp_1(C)
& m2_relset_1(C,A,B) )
=> ! [D,E] :
( r2_hidden(k2_tarski(D,E),A)
=> ! [F,G] :
( ( r2_hidden(k4_tarski(D,F),k11_cohsp_1(A,B,C))
& r2_hidden(k4_tarski(E,G),k11_cohsp_1(A,B,C)) )
=> r2_hidden(k2_tarski(F,G),B) ) ) ) ) ) ).
fof(t55_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& v7_cohsp_1(C)
& m2_relset_1(C,A,B) )
=> ! [D,E] :
( r2_hidden(k2_tarski(D,E),A)
=> ! [F] :
( ( r2_hidden(k4_tarski(D,F),k11_cohsp_1(A,B,C))
& r2_hidden(k4_tarski(E,F),k11_cohsp_1(A,B,C)) )
=> D = E ) ) ) ) ) ).
fof(t56_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& v10_cohsp_1(C)
& m2_relset_1(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& v10_cohsp_1(D)
& m2_relset_1(D,A,B) )
=> ( k11_cohsp_1(A,B,C) = k11_cohsp_1(A,B,D)
=> C = D ) ) ) ) ) ).
fof(t57_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k3_tarski(A),k3_tarski(B))))
=> ~ ( ! [D,E] :
( r2_hidden(k2_tarski(D,E),A)
=> ! [F,G] :
( ( r2_hidden(k4_tarski(D,F),C)
& r2_hidden(k4_tarski(E,G),C) )
=> r2_hidden(k2_tarski(F,G),B) ) )
& ! [D,E] :
( r2_hidden(k2_tarski(D,E),A)
=> ! [F] :
( ( r2_hidden(k4_tarski(D,F),C)
& r2_hidden(k4_tarski(E,F),C) )
=> D = E ) )
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& v10_cohsp_1(D)
& m2_relset_1(D,A,B) )
=> C != k11_cohsp_1(A,B,D) ) ) ) ) ) ).
fof(t58_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& v10_cohsp_1(C)
& m2_relset_1(C,A,B) )
=> ! [D] :
( m1_subset_1(D,A)
=> k8_funct_2(A,B,C,D) = k9_relat_1(k11_cohsp_1(A,B,C),D) ) ) ) ) ).
fof(t59_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,A,B)
& v10_cohsp_1(C)
& m2_relset_1(C,A,B)
& k11_cohsp_1(A,B,C) = k1_xboole_0 ) ) ) ).
fof(t60_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C,D] :
~ ( r2_hidden(C,k3_tarski(A))
& r2_hidden(D,k3_tarski(B))
& ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& v10_cohsp_1(E)
& m2_relset_1(E,A,B) )
=> k11_cohsp_1(A,B,E) != k1_tarski(k4_tarski(C,D)) ) ) ) ) ).
fof(t61_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C,D] :
( ( r2_hidden(C,k3_tarski(A))
& r2_hidden(D,k3_tarski(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,B)
& v10_cohsp_1(E)
& m2_relset_1(E,A,B) )
=> ( k11_cohsp_1(A,B,E) = k1_tarski(k4_tarski(C,D))
=> ! [F] :
( m1_subset_1(F,A)
=> ( ( r2_hidden(C,F)
=> k8_funct_2(A,B,E,F) = k1_tarski(D) )
& ( ~ r2_hidden(C,F)
=> k8_funct_2(A,B,E,F) = k1_xboole_0 ) ) ) ) ) ) ) ) ).
fof(t62_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& v10_cohsp_1(C)
& m2_relset_1(C,A,B) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k11_cohsp_1(A,B,C)))
=> ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,A,B)
& v10_cohsp_1(E)
& m2_relset_1(E,A,B)
& k11_cohsp_1(A,B,E) = D ) ) ) ) ) ).
fof(t63_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
~ ( ! [D,E] :
~ ( r2_hidden(D,C)
& r2_hidden(E,C)
& ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,A,B)
& v10_cohsp_1(F)
& m2_relset_1(F,A,B) )
=> k2_xboole_0(D,E) != k11_cohsp_1(A,B,F) ) )
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& v10_cohsp_1(D)
& m2_relset_1(D,A,B) )
=> k3_tarski(C) != k11_cohsp_1(A,B,D) ) ) ) ) ).
fof(t64_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> k3_tarski(k12_cohsp_1(A,B)) = k2_zfmisc_1(k3_tarski(A),k3_tarski(B)) ) ) ).
fof(t65_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C,D,E,F] :
( r2_hidden(k4_tarski(k4_tarski(C,E),k4_tarski(D,F)),k1_coh_sp(k12_cohsp_1(A,B)))
<=> ( r2_hidden(C,k3_tarski(A))
& r2_hidden(D,k3_tarski(A))
& ( ( ~ r2_hidden(k4_tarski(C,D),k1_coh_sp(A))
& r2_hidden(E,k3_tarski(B))
& r2_hidden(F,k3_tarski(B)) )
| ( r2_hidden(k4_tarski(E,F),k1_coh_sp(B))
& ( E = F
=> C = D ) ) ) ) ) ) ) ).
fof(t66_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( r2_hidden(B,k13_cohsp_1(A))
<=> ( r1_tarski(B,k3_tarski(A))
& ! [C] :
( m1_subset_1(C,A)
=> ? [D] : r1_tarski(k3_xboole_0(B,C),k1_tarski(D)) ) ) ) ) ).
fof(t67_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> k3_tarski(k13_cohsp_1(A)) = k3_tarski(A) ) ).
fof(t68_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B,C] :
~ ( B != C
& r2_hidden(k2_tarski(B,C),A)
& r2_hidden(k2_tarski(B,C),k13_cohsp_1(A)) ) ) ).
fof(t69_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B,C] :
( r1_tarski(k2_tarski(B,C),k3_tarski(A))
=> ( r2_hidden(k2_tarski(B,C),A)
| r2_hidden(k2_tarski(B,C),k13_cohsp_1(A)) ) ) ) ).
fof(t70_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B,C] :
( r2_hidden(k4_tarski(B,C),k1_coh_sp(k13_cohsp_1(A)))
<=> ( r2_hidden(B,k3_tarski(A))
& r2_hidden(C,k3_tarski(A))
& ~ ( B != C
& r2_hidden(k4_tarski(B,C),k1_coh_sp(A)) ) ) ) ) ).
fof(t71_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> k13_cohsp_1(k13_cohsp_1(A)) = A ) ).
fof(t72_cohsp_1,axiom,
k13_cohsp_1(k1_tarski(k1_xboole_0)) = k1_tarski(k1_xboole_0) ).
fof(t73_cohsp_1,axiom,
! [A] :
( k13_cohsp_1(k1_cohsp_1(A)) = k1_zfmisc_1(A)
& k13_cohsp_1(k1_zfmisc_1(A)) = k1_cohsp_1(A) ) ).
fof(d23_cohsp_1,axiom,
! [A,B] : k14_cohsp_1(A,B) = k3_card_3(k2_card_3(k10_finseq_1(A,B))) ).
fof(t74_cohsp_1,axiom,
! [A,B] : k14_cohsp_1(A,B) = k2_xboole_0(k2_zfmisc_1(A,k1_tarski(np__1)),k2_zfmisc_1(B,k1_tarski(np__2))) ).
fof(t75_cohsp_1,axiom,
! [A] :
( k14_cohsp_1(A,k1_xboole_0) = k2_zfmisc_1(A,k1_tarski(np__1))
& k14_cohsp_1(k1_xboole_0,A) = k2_zfmisc_1(A,k1_tarski(np__2)) ) ).
fof(t76_cohsp_1,axiom,
! [A,B,C] :
( r2_hidden(C,k14_cohsp_1(A,B))
=> ( C = k4_tarski(k1_mcart_1(C),k2_mcart_1(C))
& ( ( k2_mcart_1(C) = np__1
& r2_hidden(k1_mcart_1(C),A) )
| ( k2_mcart_1(C) = np__2
& r2_hidden(k1_mcart_1(C),B) ) ) ) ) ).
fof(t77_cohsp_1,axiom,
! [A,B,C] :
( r2_hidden(k4_tarski(C,np__1),k14_cohsp_1(A,B))
<=> r2_hidden(C,A) ) ).
fof(t78_cohsp_1,axiom,
! [A,B,C] :
( r2_hidden(k4_tarski(C,np__2),k14_cohsp_1(A,B))
<=> r2_hidden(C,B) ) ).
fof(t79_cohsp_1,axiom,
! [A,B,C,D] :
( r1_tarski(k14_cohsp_1(A,B),k14_cohsp_1(C,D))
<=> ( r1_tarski(A,C)
& r1_tarski(B,D) ) ) ).
fof(t80_cohsp_1,axiom,
! [A,B,C] :
~ ( r1_tarski(C,k14_cohsp_1(A,B))
& ! [D,E] :
~ ( C = k14_cohsp_1(D,E)
& r1_tarski(D,A)
& r1_tarski(E,B) ) ) ).
fof(t81_cohsp_1,axiom,
! [A,B,C,D] :
( k14_cohsp_1(A,B) = k14_cohsp_1(C,D)
<=> ( A = C
& B = D ) ) ).
fof(t82_cohsp_1,axiom,
! [A,B,C,D] : k2_xboole_0(k14_cohsp_1(A,B),k14_cohsp_1(C,D)) = k14_cohsp_1(k2_xboole_0(A,C),k2_xboole_0(B,D)) ).
fof(t83_cohsp_1,axiom,
! [A,B,C,D] : k3_xboole_0(k14_cohsp_1(A,B),k14_cohsp_1(C,D)) = k14_cohsp_1(k3_xboole_0(A,C),k3_xboole_0(B,D)) ).
fof(t84_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
( r2_hidden(C,k15_cohsp_1(A,B))
<=> ? [D] :
( m1_subset_1(D,A)
& ? [E] :
( m1_subset_1(E,B)
& C = k14_cohsp_1(D,E) ) ) ) ) ) ).
fof(t85_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C,D] :
( r2_hidden(k14_cohsp_1(C,D),k15_cohsp_1(A,B))
<=> ( r2_hidden(C,A)
& r2_hidden(D,B) ) ) ) ) ).
fof(t86_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> k3_tarski(k15_cohsp_1(A,B)) = k14_cohsp_1(k3_tarski(A),k3_tarski(B)) ) ) ).
fof(t87_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C,D] :
( r2_hidden(k14_cohsp_1(C,D),k16_cohsp_1(A,B))
<=> ( ( r2_hidden(C,A)
& D = k1_xboole_0 )
| ( C = k1_xboole_0
& r2_hidden(D,B) ) ) ) ) ) ).
fof(t88_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
~ ( r2_hidden(C,k16_cohsp_1(A,B))
& ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,B)
=> ~ ( C = k14_cohsp_1(D,E)
& ( D = k1_xboole_0
| E = k1_xboole_0 ) ) ) ) ) ) ) ).
fof(t89_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> k3_tarski(k16_cohsp_1(A,B)) = k14_cohsp_1(k3_tarski(A),k3_tarski(B)) ) ) ).
fof(t90_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C,D] :
( r2_hidden(k4_tarski(k4_tarski(C,np__1),k4_tarski(D,np__1)),k1_coh_sp(k15_cohsp_1(A,B)))
<=> r2_hidden(k4_tarski(C,D),k1_coh_sp(A)) ) ) ) ).
fof(t91_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C,D] :
( r2_hidden(k4_tarski(k4_tarski(C,np__2),k4_tarski(D,np__2)),k1_coh_sp(k15_cohsp_1(A,B)))
<=> r2_hidden(k4_tarski(C,D),k1_coh_sp(B)) ) ) ) ).
fof(t92_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C,D] :
( ( r2_hidden(C,k3_tarski(A))
& r2_hidden(D,k3_tarski(B)) )
=> ( r2_hidden(k4_tarski(k4_tarski(C,np__1),k4_tarski(D,np__2)),k1_coh_sp(k15_cohsp_1(A,B)))
& r2_hidden(k4_tarski(k4_tarski(D,np__2),k4_tarski(C,np__1)),k1_coh_sp(k15_cohsp_1(A,B))) ) ) ) ) ).
fof(t93_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C,D] :
( r2_hidden(k4_tarski(k4_tarski(C,np__1),k4_tarski(D,np__1)),k1_coh_sp(k16_cohsp_1(A,B)))
<=> r2_hidden(k4_tarski(C,D),k1_coh_sp(A)) ) ) ) ).
fof(t94_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C,D] :
( r2_hidden(k4_tarski(k4_tarski(C,np__2),k4_tarski(D,np__2)),k1_coh_sp(k16_cohsp_1(A,B)))
<=> r2_hidden(k4_tarski(C,D),k1_coh_sp(B)) ) ) ) ).
fof(t95_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C,D] :
( ~ r2_hidden(k4_tarski(k4_tarski(C,np__1),k4_tarski(D,np__2)),k1_coh_sp(k16_cohsp_1(A,B)))
& ~ r2_hidden(k4_tarski(k4_tarski(D,np__2),k4_tarski(C,np__1)),k1_coh_sp(k16_cohsp_1(A,B))) ) ) ) ).
fof(t96_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> k13_cohsp_1(k15_cohsp_1(A,B)) = k16_cohsp_1(k13_cohsp_1(A),k13_cohsp_1(B)) ) ) ).
fof(t97_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
( r2_hidden(C,k17_cohsp_1(A,B))
<=> ? [D] :
( m1_subset_1(D,A)
& ? [E] :
( m1_subset_1(E,B)
& r1_tarski(C,k2_zfmisc_1(D,E)) ) ) ) ) ) ).
fof(t98_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C] :
( m1_subset_1(C,k17_cohsp_1(A,B))
=> ( r2_hidden(k1_funct_5(C),A)
& r2_hidden(k2_funct_5(C),B)
& r1_tarski(C,k2_zfmisc_1(k1_funct_5(C),k2_funct_5(C))) ) ) ) ) ).
fof(t99_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> k3_tarski(k17_cohsp_1(A,B)) = k2_zfmisc_1(k3_tarski(A),k3_tarski(B)) ) ) ).
fof(t100_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ! [C,D,E,F] :
( r2_hidden(k4_tarski(k4_tarski(C,E),k4_tarski(D,F)),k1_coh_sp(k17_cohsp_1(A,B)))
<=> ( r2_hidden(k4_tarski(C,D),k1_coh_sp(A))
& r2_hidden(k4_tarski(E,F),k1_coh_sp(B)) ) ) ) ) ).
fof(s1_cohsp_1,axiom,
( ( r2_hidden(f1_s1_cohsp_1,f2_s1_cohsp_1)
& p1_s1_cohsp_1(f1_s1_cohsp_1)
& v1_finset_1(f1_s1_cohsp_1) )
=> ? [A] :
( r2_hidden(A,f2_s1_cohsp_1)
& p1_s1_cohsp_1(A)
& ! [B] :
( ( r2_hidden(B,f2_s1_cohsp_1)
& p1_s1_cohsp_1(B)
& r1_tarski(B,A) )
=> B = A ) ) ) ).
fof(dt_k1_cohsp_1,axiom,
$true ).
fof(dt_k2_cohsp_1,axiom,
! [A] : m1_subset_1(k2_cohsp_1(A),k1_zfmisc_1(A)) ).
fof(dt_k3_cohsp_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& m1_subset_1(B,A) )
=> ( ~ v1_xboole_0(k3_cohsp_1(A,B))
& v4_finsub_1(k3_cohsp_1(A,B))
& m1_subset_1(k3_cohsp_1(A,B),k1_zfmisc_1(A)) ) ) ).
fof(redefinition_k3_cohsp_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& m1_subset_1(B,A) )
=> k3_cohsp_1(A,B) = k5_finsub_1(B) ) ).
fof(dt_k4_cohsp_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v3_cohsp_1(A)
& v1_cohsp_1(B)
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> m1_subset_1(k4_cohsp_1(A,B),A) ) ).
fof(redefinition_k4_cohsp_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v3_cohsp_1(A)
& v1_cohsp_1(B)
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> k4_cohsp_1(A,B) = k3_tarski(B) ) ).
fof(dt_k5_cohsp_1,axiom,
$true ).
fof(dt_k6_cohsp_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B) )
=> m1_subset_1(k6_cohsp_1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(A,k3_tarski(B)))) ) ).
fof(redefinition_k6_cohsp_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B) )
=> k6_cohsp_1(A,B,C) = k5_cohsp_1(C) ) ).
fof(dt_k7_cohsp_1,axiom,
$true ).
fof(dt_k8_cohsp_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B) )
=> m1_subset_1(k8_cohsp_1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(A,k3_tarski(B)))) ) ).
fof(redefinition_k8_cohsp_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B) )
=> k8_cohsp_1(A,B,C) = k7_cohsp_1(C) ) ).
fof(dt_k9_cohsp_1,axiom,
$true ).
fof(dt_k10_cohsp_1,axiom,
$true ).
fof(dt_k11_cohsp_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B) )
=> m1_subset_1(k11_cohsp_1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k3_tarski(A),k3_tarski(B)))) ) ).
fof(redefinition_k11_cohsp_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B) )
=> k11_cohsp_1(A,B,C) = k10_cohsp_1(C) ) ).
fof(dt_k12_cohsp_1,axiom,
$true ).
fof(dt_k13_cohsp_1,axiom,
$true ).
fof(dt_k14_cohsp_1,axiom,
$true ).
fof(dt_k15_cohsp_1,axiom,
$true ).
fof(dt_k16_cohsp_1,axiom,
$true ).
fof(dt_k17_cohsp_1,axiom,
$true ).
fof(d22_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> k13_cohsp_1(A) = a_1_0_cohsp_1(A) ) ).
fof(d24_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> k15_cohsp_1(A,B) = a_2_0_cohsp_1(A,B) ) ) ).
fof(d25_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> k16_cohsp_1(A,B) = k2_xboole_0(a_1_1_cohsp_1(A),a_1_2_cohsp_1(B)) ) ) ).
fof(d26_cohsp_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes1(A)
& v1_coh_sp(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> k17_cohsp_1(A,B) = k3_tarski(a_2_1_cohsp_1(A,B)) ) ) ).
fof(fraenkel_a_1_0_cohsp_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ( r2_hidden(A,a_1_0_cohsp_1(B))
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(k3_tarski(B)))
& A = C
& ! [D] :
( m1_subset_1(D,B)
=> ? [E] : r1_tarski(k3_xboole_0(C,D),k1_tarski(E)) ) ) ) ) ).
fof(fraenkel_a_2_0_cohsp_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B)
& ~ v1_xboole_0(C)
& v1_classes1(C)
& v1_coh_sp(C) )
=> ( r2_hidden(A,a_2_0_cohsp_1(B,C))
<=> ? [D,E] :
( m1_subset_1(D,B)
& m1_subset_1(E,C)
& A = k14_cohsp_1(D,E) ) ) ) ).
fof(fraenkel_a_1_1_cohsp_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ( r2_hidden(A,a_1_1_cohsp_1(B))
<=> ? [C] :
( m1_subset_1(C,B)
& A = k14_cohsp_1(C,k1_xboole_0) ) ) ) ).
fof(fraenkel_a_1_2_cohsp_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B) )
=> ( r2_hidden(A,a_1_2_cohsp_1(B))
<=> ? [C] :
( m1_subset_1(C,B)
& A = k14_cohsp_1(k1_xboole_0,C) ) ) ) ).
fof(fraenkel_a_2_1_cohsp_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& v1_classes1(B)
& v1_coh_sp(B)
& ~ v1_xboole_0(C)
& v1_classes1(C)
& v1_coh_sp(C) )
=> ( r2_hidden(A,a_2_1_cohsp_1(B,C))
<=> ? [D,E] :
( m1_subset_1(D,B)
& m1_subset_1(E,C)
& A = k1_zfmisc_1(k2_zfmisc_1(D,E)) ) ) ) ).
%------------------------------------------------------------------------------