SET007 Axioms: SET007+130.ax
%------------------------------------------------------------------------------
% File : SET007+130 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Intuitionistic Propositional Calculus with Modal Operator. Part I
% 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 : intpro_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 145 ( 18 unt; 0 def)
% Number of atoms : 603 ( 20 equ)
% Maximal formula atoms : 23 ( 4 avg)
% Number of connectives : 462 ( 4 ~; 1 |; 129 &)
% ( 23 <=>; 305 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 1 prp; 0-3 aty)
% Number of functors : 29 ( 29 usr; 14 con; 0-2 aty)
% Number of variables : 281 ( 280 !; 1 ?)
% 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(cc1_intpro_1,axiom,
! [A] :
( v7_intpro_1(A)
=> ( ~ v1_xboole_0(A)
& v1_intpro_1(A)
& v2_intpro_1(A)
& v3_intpro_1(A)
& v4_intpro_1(A)
& v5_intpro_1(A)
& v6_intpro_1(A) ) ) ).
fof(cc2_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k13_finseq_1(k5_numbers)))
=> ( ( v1_intpro_1(A)
& v2_intpro_1(A)
& v3_intpro_1(A)
& v4_intpro_1(A)
& v5_intpro_1(A)
& v6_intpro_1(A) )
=> v7_intpro_1(A) ) ) ).
fof(fc1_intpro_1,axiom,
( ~ v1_xboole_0(k1_intpro_1)
& v1_intpro_1(k1_intpro_1)
& v2_intpro_1(k1_intpro_1)
& v3_intpro_1(k1_intpro_1)
& v4_intpro_1(k1_intpro_1)
& v5_intpro_1(k1_intpro_1)
& v6_intpro_1(k1_intpro_1)
& v7_intpro_1(k1_intpro_1) ) ).
fof(rc1_intpro_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_intpro_1(A)
& v2_intpro_1(A)
& v3_intpro_1(A)
& v4_intpro_1(A)
& v5_intpro_1(A)
& v6_intpro_1(A)
& v7_intpro_1(A) ) ).
fof(fc2_intpro_1,axiom,
( ~ v1_xboole_0(k1_intpro_1)
& v1_fraenkel(k1_intpro_1)
& v1_intpro_1(k1_intpro_1)
& v2_intpro_1(k1_intpro_1)
& v3_intpro_1(k1_intpro_1)
& v4_intpro_1(k1_intpro_1)
& v5_intpro_1(k1_intpro_1)
& v6_intpro_1(k1_intpro_1)
& v7_intpro_1(k1_intpro_1) ) ).
fof(cc3_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finset_1(A)
& v1_finseq_1(A) ) ) ).
fof(fc3_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> v8_intpro_1(k7_intpro_1(A)) ) ).
fof(fc4_intpro_1,axiom,
v8_intpro_1(k8_intpro_1) ).
fof(fc5_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> v9_intpro_1(k11_intpro_1(A)) ) ).
fof(fc6_intpro_1,axiom,
v9_intpro_1(k12_intpro_1) ).
fof(fc7_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> v10_intpro_1(k13_intpro_1(A)) ) ).
fof(fc8_intpro_1,axiom,
v10_intpro_1(k14_intpro_1) ).
fof(d1_intpro_1,axiom,
! [A] :
( v1_intpro_1(A)
<=> r2_hidden(k12_finseq_1(k5_numbers,np__0),A) ) ).
fof(d2_intpro_1,axiom,
! [A] :
( v2_intpro_1(A)
<=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ( ( r2_hidden(B,A)
& r2_hidden(C,A) )
=> r2_hidden(k7_finseq_1(k7_finseq_1(k12_finseq_1(k5_numbers,np__1),B),C),A) ) ) ) ) ).
fof(d3_intpro_1,axiom,
! [A] :
( v3_intpro_1(A)
<=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ( ( r2_hidden(B,A)
& r2_hidden(C,A) )
=> r2_hidden(k7_finseq_1(k7_finseq_1(k12_finseq_1(k5_numbers,np__2),B),C),A) ) ) ) ) ).
fof(d4_intpro_1,axiom,
! [A] :
( v4_intpro_1(A)
<=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ( ( r2_hidden(B,A)
& r2_hidden(C,A) )
=> r2_hidden(k7_finseq_1(k7_finseq_1(k12_finseq_1(k5_numbers,np__3),B),C),A) ) ) ) ) ).
fof(d5_intpro_1,axiom,
! [A] :
( v5_intpro_1(A)
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r2_hidden(k12_finseq_1(k5_numbers,k1_nat_1(np__5,k2_nat_1(np__2,B))),A) ) ) ).
fof(d6_intpro_1,axiom,
! [A] :
( v6_intpro_1(A)
<=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( r2_hidden(B,A)
=> r2_hidden(k7_finseq_1(k12_finseq_1(k5_numbers,np__6),B),A) ) ) ) ).
fof(d7_intpro_1,axiom,
! [A] :
( v7_intpro_1(A)
<=> ( r1_tarski(A,k13_finseq_1(k5_numbers))
& v1_intpro_1(A)
& v2_intpro_1(A)
& v3_intpro_1(A)
& v4_intpro_1(A)
& v5_intpro_1(A)
& v6_intpro_1(A) ) ) ).
fof(d8_intpro_1,axiom,
! [A] :
( A = k1_intpro_1
<=> ( v7_intpro_1(A)
& ! [B] :
( v7_intpro_1(B)
=> r1_tarski(A,B) ) ) ) ).
fof(d9_intpro_1,axiom,
k2_intpro_1 = k12_finseq_1(k5_numbers,np__0) ).
fof(d10_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> k3_intpro_1(A,B) = k7_finseq_1(k7_finseq_1(k12_finseq_1(k5_numbers,np__1),A),B) ) ) ).
fof(d11_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> k4_intpro_1(A,B) = k7_finseq_1(k7_finseq_1(k12_finseq_1(k5_numbers,np__2),A),B) ) ) ).
fof(d12_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> k5_intpro_1(A,B) = k7_finseq_1(k7_finseq_1(k12_finseq_1(k5_numbers,np__3),A),B) ) ) ).
fof(d13_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> k6_intpro_1(A) = k7_finseq_1(k12_finseq_1(k5_numbers,np__6),A) ) ).
fof(d14_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ( v8_intpro_1(A)
<=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> ! [D] :
( m1_subset_1(D,k1_intpro_1)
=> ( r2_hidden(k3_intpro_1(B,k3_intpro_1(C,B)),A)
& r2_hidden(k3_intpro_1(k3_intpro_1(B,k3_intpro_1(C,D)),k3_intpro_1(k3_intpro_1(B,C),k3_intpro_1(B,D))),A)
& r2_hidden(k3_intpro_1(k4_intpro_1(B,C),B),A)
& r2_hidden(k3_intpro_1(k4_intpro_1(B,C),C),A)
& r2_hidden(k3_intpro_1(B,k3_intpro_1(C,k4_intpro_1(B,C))),A)
& r2_hidden(k3_intpro_1(B,k5_intpro_1(B,C)),A)
& r2_hidden(k3_intpro_1(C,k5_intpro_1(B,C)),A)
& r2_hidden(k3_intpro_1(k3_intpro_1(B,D),k3_intpro_1(k3_intpro_1(C,D),k3_intpro_1(k5_intpro_1(B,C),D))),A)
& r2_hidden(k3_intpro_1(k2_intpro_1,B),A)
& ( ( r2_hidden(B,A)
& r2_hidden(k3_intpro_1(B,C),A) )
=> r2_hidden(C,A) ) ) ) ) ) ) ) ).
fof(d15_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_intpro_1))
=> ( B = k7_intpro_1(A)
<=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> ( r2_hidden(C,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_intpro_1))
=> ( ( v8_intpro_1(D)
& r1_tarski(A,D) )
=> r2_hidden(C,D) ) ) ) ) ) ) ) ).
fof(d16_intpro_1,axiom,
k8_intpro_1 = k7_intpro_1(k1_subset_1(k1_intpro_1)) ).
fof(d17_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> k9_intpro_1(A) = k3_intpro_1(A,k2_intpro_1) ) ).
fof(d18_intpro_1,axiom,
k10_intpro_1 = k3_intpro_1(k2_intpro_1,k2_intpro_1) ).
fof(t1_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(B,k3_intpro_1(C,B)),k7_intpro_1(A)) ) ) ) ).
fof(t2_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> ! [D] :
( m1_subset_1(D,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k3_intpro_1(B,k3_intpro_1(C,D)),k3_intpro_1(k3_intpro_1(B,C),k3_intpro_1(B,D))),k7_intpro_1(A)) ) ) ) ) ).
fof(t3_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k4_intpro_1(B,C),B),k7_intpro_1(A)) ) ) ) ).
fof(t4_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k4_intpro_1(B,C),C),k7_intpro_1(A)) ) ) ) ).
fof(t5_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(B,k3_intpro_1(C,k4_intpro_1(B,C))),k7_intpro_1(A)) ) ) ) ).
fof(t6_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(B,k5_intpro_1(B,C)),k7_intpro_1(A)) ) ) ) ).
fof(t7_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(B,k5_intpro_1(C,B)),k7_intpro_1(A)) ) ) ) ).
fof(t8_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> ! [D] :
( m1_subset_1(D,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k3_intpro_1(B,C),k3_intpro_1(k3_intpro_1(D,C),k3_intpro_1(k5_intpro_1(B,D),C))),k7_intpro_1(A)) ) ) ) ) ).
fof(t9_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k2_intpro_1,B),k7_intpro_1(A)) ) ) ).
fof(t10_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> ( ( r2_hidden(B,k7_intpro_1(A))
& r2_hidden(k3_intpro_1(B,C),k7_intpro_1(A)) )
=> r2_hidden(C,k7_intpro_1(A)) ) ) ) ) ).
fof(t11_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_intpro_1))
=> ( ( v8_intpro_1(A)
& r1_tarski(B,A) )
=> r1_tarski(k7_intpro_1(B),A) ) ) ) ).
fof(t12_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> r1_tarski(A,k7_intpro_1(A)) ) ).
fof(t13_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_intpro_1))
=> ( r1_tarski(A,B)
=> r1_tarski(k7_intpro_1(A),k7_intpro_1(B)) ) ) ) ).
fof(t14_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> k7_intpro_1(k7_intpro_1(A)) = k7_intpro_1(A) ) ).
fof(t15_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ( v8_intpro_1(A)
<=> k7_intpro_1(A) = A ) ) ).
fof(t16_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ( v8_intpro_1(A)
=> r1_tarski(k8_intpro_1,A) ) ) ).
fof(t17_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> r2_hidden(k3_intpro_1(A,A),k8_intpro_1) ) ).
fof(t18_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ( r2_hidden(A,k8_intpro_1)
=> r2_hidden(k3_intpro_1(B,A),k8_intpro_1) ) ) ) ).
fof(t19_intpro_1,axiom,
r2_hidden(k10_intpro_1,k8_intpro_1) ).
fof(t20_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k3_intpro_1(A,B),k3_intpro_1(A,A)),k8_intpro_1) ) ) ).
fof(t21_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k3_intpro_1(A,B),k3_intpro_1(B,B)),k8_intpro_1) ) ) ).
fof(t22_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k3_intpro_1(A,B),k3_intpro_1(k3_intpro_1(C,A),k3_intpro_1(C,B))),k8_intpro_1) ) ) ) ).
fof(t23_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> ( r2_hidden(k3_intpro_1(A,k3_intpro_1(B,C)),k8_intpro_1)
=> r2_hidden(k3_intpro_1(B,k3_intpro_1(A,C)),k8_intpro_1) ) ) ) ) ).
fof(t24_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k3_intpro_1(A,B),k3_intpro_1(k3_intpro_1(B,C),k3_intpro_1(A,C))),k8_intpro_1) ) ) ) ).
fof(t25_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> ( r2_hidden(k3_intpro_1(A,B),k8_intpro_1)
=> r2_hidden(k3_intpro_1(k3_intpro_1(B,C),k3_intpro_1(A,C)),k8_intpro_1) ) ) ) ) ).
fof(t26_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> ( ( r2_hidden(k3_intpro_1(A,B),k8_intpro_1)
& r2_hidden(k3_intpro_1(B,C),k8_intpro_1) )
=> r2_hidden(k3_intpro_1(A,C),k8_intpro_1) ) ) ) ) ).
fof(t27_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> ! [D] :
( m1_subset_1(D,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k3_intpro_1(A,k3_intpro_1(B,C)),k3_intpro_1(k3_intpro_1(D,B),k3_intpro_1(A,k3_intpro_1(D,C)))),k8_intpro_1) ) ) ) ) ).
fof(t28_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k3_intpro_1(k3_intpro_1(A,B),C),k3_intpro_1(B,C)),k8_intpro_1) ) ) ) ).
fof(t29_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k3_intpro_1(A,k3_intpro_1(B,C)),k3_intpro_1(B,k3_intpro_1(A,C))),k8_intpro_1) ) ) ) ).
fof(t30_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k3_intpro_1(A,k3_intpro_1(A,B)),k3_intpro_1(A,B)),k8_intpro_1) ) ) ).
fof(t31_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> r2_hidden(k3_intpro_1(A,k3_intpro_1(k3_intpro_1(A,B),B)),k8_intpro_1) ) ) ).
fof(t32_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> ( ( r2_hidden(k3_intpro_1(A,k3_intpro_1(B,C)),k8_intpro_1)
& r2_hidden(B,k8_intpro_1) )
=> r2_hidden(k3_intpro_1(A,C),k8_intpro_1) ) ) ) ) ).
fof(t33_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> r2_hidden(k3_intpro_1(A,k4_intpro_1(A,A)),k8_intpro_1) ) ).
fof(t34_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ( r2_hidden(k4_intpro_1(A,B),k8_intpro_1)
<=> ( r2_hidden(A,k8_intpro_1)
& r2_hidden(B,k8_intpro_1) ) ) ) ) ).
fof(t35_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ( r2_hidden(k4_intpro_1(A,B),k8_intpro_1)
<=> r2_hidden(k4_intpro_1(B,A),k8_intpro_1) ) ) ) ).
fof(t36_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k3_intpro_1(k4_intpro_1(A,B),C),k3_intpro_1(A,k3_intpro_1(B,C))),k8_intpro_1) ) ) ) ).
fof(t37_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k3_intpro_1(A,k3_intpro_1(B,C)),k3_intpro_1(k4_intpro_1(A,B),C)),k8_intpro_1) ) ) ) ).
fof(t38_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k3_intpro_1(A,B),k3_intpro_1(k3_intpro_1(A,C),k3_intpro_1(A,k4_intpro_1(B,C)))),k8_intpro_1) ) ) ) ).
fof(t39_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k4_intpro_1(k3_intpro_1(A,B),A),B),k8_intpro_1) ) ) ).
fof(t40_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k4_intpro_1(k4_intpro_1(k3_intpro_1(A,B),A),C),B),k8_intpro_1) ) ) ) ).
fof(t41_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k3_intpro_1(A,B),k3_intpro_1(k4_intpro_1(C,A),B)),k8_intpro_1) ) ) ) ).
fof(t42_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k3_intpro_1(A,B),k3_intpro_1(k4_intpro_1(A,C),B)),k8_intpro_1) ) ) ) ).
fof(t43_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k3_intpro_1(k4_intpro_1(A,B),C),k3_intpro_1(k4_intpro_1(A,B),k4_intpro_1(C,B))),k8_intpro_1) ) ) ) ).
fof(t44_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k3_intpro_1(A,B),k3_intpro_1(k4_intpro_1(A,C),k4_intpro_1(B,C))),k8_intpro_1) ) ) ) ).
fof(t45_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k4_intpro_1(k3_intpro_1(A,B),k4_intpro_1(A,C)),k4_intpro_1(B,C)),k8_intpro_1) ) ) ) ).
fof(t46_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k4_intpro_1(A,B),k4_intpro_1(B,A)),k8_intpro_1) ) ) ).
fof(t47_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k4_intpro_1(k3_intpro_1(A,B),k4_intpro_1(A,C)),k4_intpro_1(C,B)),k8_intpro_1) ) ) ) ).
fof(t48_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k3_intpro_1(A,B),k3_intpro_1(k4_intpro_1(A,C),k4_intpro_1(C,B))),k8_intpro_1) ) ) ) ).
fof(t49_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k3_intpro_1(A,B),k3_intpro_1(k4_intpro_1(C,A),k4_intpro_1(C,B))),k8_intpro_1) ) ) ) ).
fof(t50_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k4_intpro_1(A,k4_intpro_1(B,C)),k4_intpro_1(A,k4_intpro_1(C,B))),k8_intpro_1) ) ) ) ).
fof(t51_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k4_intpro_1(k3_intpro_1(A,B),k3_intpro_1(A,C)),k3_intpro_1(A,k4_intpro_1(B,C))),k8_intpro_1) ) ) ) ).
fof(t52_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k4_intpro_1(k4_intpro_1(A,B),C),k4_intpro_1(A,k4_intpro_1(B,C))),k8_intpro_1) ) ) ) ).
fof(t53_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k4_intpro_1(A,k4_intpro_1(B,C)),k4_intpro_1(k4_intpro_1(A,B),C)),k8_intpro_1) ) ) ) ).
fof(t54_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k5_intpro_1(A,A),A),k8_intpro_1) ) ).
fof(t55_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ( ( r2_hidden(A,k8_intpro_1)
| r2_hidden(B,k8_intpro_1) )
=> r2_hidden(k5_intpro_1(A,B),k8_intpro_1) ) ) ) ).
fof(t56_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k5_intpro_1(A,B),k5_intpro_1(B,A)),k8_intpro_1) ) ) ).
fof(t57_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ( r2_hidden(k5_intpro_1(A,B),k8_intpro_1)
<=> r2_hidden(k5_intpro_1(B,A),k8_intpro_1) ) ) ) ).
fof(t58_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k3_intpro_1(A,B),k3_intpro_1(A,k5_intpro_1(B,C))),k8_intpro_1) ) ) ) ).
fof(t59_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k3_intpro_1(A,B),k3_intpro_1(A,k5_intpro_1(C,B))),k8_intpro_1) ) ) ) ).
fof(t60_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k3_intpro_1(A,B),k3_intpro_1(k5_intpro_1(A,C),k5_intpro_1(B,C))),k8_intpro_1) ) ) ) ).
fof(t61_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> ( r2_hidden(k3_intpro_1(A,B),k8_intpro_1)
=> r2_hidden(k3_intpro_1(k5_intpro_1(A,C),k5_intpro_1(B,C)),k8_intpro_1) ) ) ) ) ).
fof(t62_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k3_intpro_1(A,B),k3_intpro_1(k5_intpro_1(C,A),k5_intpro_1(C,B))),k8_intpro_1) ) ) ) ).
fof(t63_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> ( r2_hidden(k3_intpro_1(A,B),k8_intpro_1)
=> r2_hidden(k3_intpro_1(k5_intpro_1(C,A),k5_intpro_1(C,B)),k8_intpro_1) ) ) ) ) ).
fof(t64_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k5_intpro_1(A,k5_intpro_1(B,C)),k5_intpro_1(B,k5_intpro_1(A,C))),k8_intpro_1) ) ) ) ).
fof(t65_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k5_intpro_1(A,k5_intpro_1(B,C)),k5_intpro_1(k5_intpro_1(A,B),C)),k8_intpro_1) ) ) ) ).
fof(t66_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k5_intpro_1(k5_intpro_1(A,B),C),k5_intpro_1(A,k5_intpro_1(B,C))),k8_intpro_1) ) ) ) ).
fof(d19_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ( v9_intpro_1(A)
<=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> ! [D] :
( m1_subset_1(D,k1_intpro_1)
=> ( r2_hidden(k3_intpro_1(B,k3_intpro_1(C,B)),A)
& r2_hidden(k3_intpro_1(k3_intpro_1(B,k3_intpro_1(C,D)),k3_intpro_1(k3_intpro_1(B,C),k3_intpro_1(B,D))),A)
& r2_hidden(k3_intpro_1(k4_intpro_1(B,C),B),A)
& r2_hidden(k3_intpro_1(k4_intpro_1(B,C),C),A)
& r2_hidden(k3_intpro_1(B,k3_intpro_1(C,k4_intpro_1(B,C))),A)
& r2_hidden(k3_intpro_1(B,k5_intpro_1(B,C)),A)
& r2_hidden(k3_intpro_1(C,k5_intpro_1(B,C)),A)
& r2_hidden(k3_intpro_1(k3_intpro_1(B,D),k3_intpro_1(k3_intpro_1(C,D),k3_intpro_1(k5_intpro_1(B,C),D))),A)
& r2_hidden(k3_intpro_1(k2_intpro_1,B),A)
& r2_hidden(k5_intpro_1(B,k3_intpro_1(B,k2_intpro_1)),A)
& ( ( r2_hidden(B,A)
& r2_hidden(k3_intpro_1(B,C),A) )
=> r2_hidden(C,A) ) ) ) ) ) ) ) ).
fof(t67_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ( v9_intpro_1(A)
=> v8_intpro_1(A) ) ) ).
fof(d20_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_intpro_1))
=> ( B = k11_intpro_1(A)
<=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> ( r2_hidden(C,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_intpro_1))
=> ( ( v9_intpro_1(D)
& r1_tarski(A,D) )
=> r2_hidden(C,D) ) ) ) ) ) ) ) ).
fof(d21_intpro_1,axiom,
k12_intpro_1 = k11_intpro_1(k1_subset_1(k1_intpro_1)) ).
fof(t68_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> r1_tarski(k7_intpro_1(A),k11_intpro_1(A)) ) ).
fof(t69_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> ! [D] :
( m1_subset_1(D,k1_intpro_1)
=> ( r2_hidden(k3_intpro_1(B,k3_intpro_1(C,B)),k11_intpro_1(A))
& r2_hidden(k3_intpro_1(k3_intpro_1(B,k3_intpro_1(C,D)),k3_intpro_1(k3_intpro_1(B,C),k3_intpro_1(B,D))),k11_intpro_1(A))
& r2_hidden(k3_intpro_1(k4_intpro_1(B,C),B),k11_intpro_1(A))
& r2_hidden(k3_intpro_1(k4_intpro_1(B,C),C),k11_intpro_1(A))
& r2_hidden(k3_intpro_1(B,k3_intpro_1(C,k4_intpro_1(B,C))),k11_intpro_1(A))
& r2_hidden(k3_intpro_1(B,k5_intpro_1(B,C)),k11_intpro_1(A))
& r2_hidden(k3_intpro_1(C,k5_intpro_1(B,C)),k11_intpro_1(A))
& r2_hidden(k3_intpro_1(k3_intpro_1(B,D),k3_intpro_1(k3_intpro_1(C,D),k3_intpro_1(k5_intpro_1(B,C),D))),k11_intpro_1(A))
& r2_hidden(k3_intpro_1(k2_intpro_1,B),k11_intpro_1(A))
& r2_hidden(k5_intpro_1(B,k3_intpro_1(B,k2_intpro_1)),k11_intpro_1(A)) ) ) ) ) ) ).
fof(t70_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> ( ( r2_hidden(B,k11_intpro_1(A))
& r2_hidden(k3_intpro_1(B,C),k11_intpro_1(A)) )
=> r2_hidden(C,k11_intpro_1(A)) ) ) ) ) ).
fof(t71_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_intpro_1))
=> ( ( v9_intpro_1(A)
& r1_tarski(B,A) )
=> r1_tarski(k11_intpro_1(B),A) ) ) ) ).
fof(t72_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> r1_tarski(A,k11_intpro_1(A)) ) ).
fof(t73_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_intpro_1))
=> ( r1_tarski(A,B)
=> r1_tarski(k11_intpro_1(A),k11_intpro_1(B)) ) ) ) ).
fof(t74_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> k11_intpro_1(k11_intpro_1(A)) = k11_intpro_1(A) ) ).
fof(t75_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ( v9_intpro_1(A)
<=> k11_intpro_1(A) = A ) ) ).
fof(t76_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ( v9_intpro_1(A)
=> r1_tarski(k12_intpro_1,A) ) ) ).
fof(t77_intpro_1,axiom,
r1_tarski(k8_intpro_1,k12_intpro_1) ).
fof(d22_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ( v10_intpro_1(A)
<=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> ! [D] :
( m1_subset_1(D,k1_intpro_1)
=> ( r2_hidden(k3_intpro_1(B,k3_intpro_1(C,B)),A)
& r2_hidden(k3_intpro_1(k3_intpro_1(B,k3_intpro_1(C,D)),k3_intpro_1(k3_intpro_1(B,C),k3_intpro_1(B,D))),A)
& r2_hidden(k3_intpro_1(k4_intpro_1(B,C),B),A)
& r2_hidden(k3_intpro_1(k4_intpro_1(B,C),C),A)
& r2_hidden(k3_intpro_1(B,k3_intpro_1(C,k4_intpro_1(B,C))),A)
& r2_hidden(k3_intpro_1(B,k5_intpro_1(B,C)),A)
& r2_hidden(k3_intpro_1(C,k5_intpro_1(B,C)),A)
& r2_hidden(k3_intpro_1(k3_intpro_1(B,D),k3_intpro_1(k3_intpro_1(C,D),k3_intpro_1(k5_intpro_1(B,C),D))),A)
& r2_hidden(k3_intpro_1(k2_intpro_1,B),A)
& r2_hidden(k5_intpro_1(B,k3_intpro_1(B,k2_intpro_1)),A)
& r2_hidden(k3_intpro_1(k6_intpro_1(k3_intpro_1(B,C)),k3_intpro_1(k6_intpro_1(B),k6_intpro_1(C))),A)
& r2_hidden(k3_intpro_1(k6_intpro_1(B),B),A)
& r2_hidden(k3_intpro_1(k6_intpro_1(B),k6_intpro_1(k6_intpro_1(B))),A)
& ( ( r2_hidden(B,A)
& r2_hidden(k3_intpro_1(B,C),A) )
=> r2_hidden(C,A) )
& ( r2_hidden(B,A)
=> r2_hidden(k6_intpro_1(B),A) ) ) ) ) ) ) ) ).
fof(t78_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ( v10_intpro_1(A)
=> v9_intpro_1(A) ) ) ).
fof(t79_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ( v10_intpro_1(A)
=> v8_intpro_1(A) ) ) ).
fof(d23_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_intpro_1))
=> ( B = k13_intpro_1(A)
<=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> ( r2_hidden(C,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_intpro_1))
=> ( ( v10_intpro_1(D)
& r1_tarski(A,D) )
=> r2_hidden(C,D) ) ) ) ) ) ) ) ).
fof(d24_intpro_1,axiom,
k14_intpro_1 = k13_intpro_1(k1_subset_1(k1_intpro_1)) ).
fof(t80_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> r1_tarski(k11_intpro_1(A),k13_intpro_1(A)) ) ).
fof(t81_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> r1_tarski(k7_intpro_1(A),k13_intpro_1(A)) ) ).
fof(t82_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> ! [D] :
( m1_subset_1(D,k1_intpro_1)
=> ( r2_hidden(k3_intpro_1(B,k3_intpro_1(C,B)),k13_intpro_1(A))
& r2_hidden(k3_intpro_1(k3_intpro_1(B,k3_intpro_1(C,D)),k3_intpro_1(k3_intpro_1(B,C),k3_intpro_1(B,D))),k13_intpro_1(A))
& r2_hidden(k3_intpro_1(k4_intpro_1(B,C),B),k13_intpro_1(A))
& r2_hidden(k3_intpro_1(k4_intpro_1(B,C),C),k13_intpro_1(A))
& r2_hidden(k3_intpro_1(B,k3_intpro_1(C,k4_intpro_1(B,C))),k13_intpro_1(A))
& r2_hidden(k3_intpro_1(B,k5_intpro_1(B,C)),k13_intpro_1(A))
& r2_hidden(k3_intpro_1(C,k5_intpro_1(B,C)),k13_intpro_1(A))
& r2_hidden(k3_intpro_1(k3_intpro_1(B,D),k3_intpro_1(k3_intpro_1(C,D),k3_intpro_1(k5_intpro_1(B,C),D))),k13_intpro_1(A))
& r2_hidden(k3_intpro_1(k2_intpro_1,B),k13_intpro_1(A))
& r2_hidden(k5_intpro_1(B,k3_intpro_1(B,k2_intpro_1)),k13_intpro_1(A)) ) ) ) ) ) ).
fof(t83_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> ( ( r2_hidden(B,k13_intpro_1(A))
& r2_hidden(k3_intpro_1(B,C),k13_intpro_1(A)) )
=> r2_hidden(C,k13_intpro_1(A)) ) ) ) ) ).
fof(t84_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ! [C] :
( m1_subset_1(C,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k6_intpro_1(k3_intpro_1(B,C)),k3_intpro_1(k6_intpro_1(B),k6_intpro_1(C))),k13_intpro_1(A)) ) ) ) ).
fof(t85_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k6_intpro_1(B),B),k13_intpro_1(A)) ) ) ).
fof(t86_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> r2_hidden(k3_intpro_1(k6_intpro_1(B),k6_intpro_1(k6_intpro_1(B))),k13_intpro_1(A)) ) ) ).
fof(t87_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ! [B] :
( m1_subset_1(B,k1_intpro_1)
=> ( r2_hidden(B,k13_intpro_1(A))
=> r2_hidden(k6_intpro_1(B),k13_intpro_1(A)) ) ) ) ).
fof(t88_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_intpro_1))
=> ( ( v10_intpro_1(A)
& r1_tarski(B,A) )
=> r1_tarski(k13_intpro_1(B),A) ) ) ) ).
fof(t89_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> r1_tarski(A,k13_intpro_1(A)) ) ).
fof(t90_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_intpro_1))
=> ( r1_tarski(A,B)
=> r1_tarski(k13_intpro_1(A),k13_intpro_1(B)) ) ) ) ).
fof(t91_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> k13_intpro_1(k13_intpro_1(A)) = k13_intpro_1(A) ) ).
fof(t92_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ( v10_intpro_1(A)
<=> k13_intpro_1(A) = A ) ) ).
fof(t93_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> ( v10_intpro_1(A)
=> r1_tarski(k14_intpro_1,A) ) ) ).
fof(t94_intpro_1,axiom,
r1_tarski(k12_intpro_1,k14_intpro_1) ).
fof(t95_intpro_1,axiom,
r1_tarski(k8_intpro_1,k14_intpro_1) ).
fof(dt_k1_intpro_1,axiom,
$true ).
fof(dt_k2_intpro_1,axiom,
m1_subset_1(k2_intpro_1,k1_intpro_1) ).
fof(dt_k3_intpro_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k1_intpro_1)
& m1_subset_1(B,k1_intpro_1) )
=> m1_subset_1(k3_intpro_1(A,B),k1_intpro_1) ) ).
fof(dt_k4_intpro_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k1_intpro_1)
& m1_subset_1(B,k1_intpro_1) )
=> m1_subset_1(k4_intpro_1(A,B),k1_intpro_1) ) ).
fof(dt_k5_intpro_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k1_intpro_1)
& m1_subset_1(B,k1_intpro_1) )
=> m1_subset_1(k5_intpro_1(A,B),k1_intpro_1) ) ).
fof(dt_k6_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> m1_subset_1(k6_intpro_1(A),k1_intpro_1) ) ).
fof(dt_k7_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> m1_subset_1(k7_intpro_1(A),k1_zfmisc_1(k1_intpro_1)) ) ).
fof(dt_k8_intpro_1,axiom,
m1_subset_1(k8_intpro_1,k1_zfmisc_1(k1_intpro_1)) ).
fof(dt_k9_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_intpro_1)
=> m1_subset_1(k9_intpro_1(A),k1_intpro_1) ) ).
fof(dt_k10_intpro_1,axiom,
m1_subset_1(k10_intpro_1,k1_intpro_1) ).
fof(dt_k11_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> m1_subset_1(k11_intpro_1(A),k1_zfmisc_1(k1_intpro_1)) ) ).
fof(dt_k12_intpro_1,axiom,
m1_subset_1(k12_intpro_1,k1_zfmisc_1(k1_intpro_1)) ).
fof(dt_k13_intpro_1,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1))
=> m1_subset_1(k13_intpro_1(A),k1_zfmisc_1(k1_intpro_1)) ) ).
fof(dt_k14_intpro_1,axiom,
m1_subset_1(k14_intpro_1,k1_zfmisc_1(k1_intpro_1)) ).
%------------------------------------------------------------------------------