SET007 Axioms: SET007+236.ax
%------------------------------------------------------------------------------
% File : SET007+236 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Transformations in Affine 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 : transgeo [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 134 ( 24 unt; 0 def)
% Number of atoms : 1406 ( 82 equ)
% Maximal formula atoms : 27 ( 10 avg)
% Number of connectives : 1479 ( 207 ~; 23 |; 738 &)
% ( 30 <=>; 481 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 39 ( 37 usr; 1 prp; 0-5 aty)
% Number of functors : 16 ( 16 usr; 1 con; 0-4 aty)
% Number of variables : 423 ( 417 !; 6 ?)
% 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_transgeo,axiom,
? [A] :
( l1_analoaf(A)
& ~ v3_struct_0(A)
& v1_analoaf(A)
& v1_transgeo(A) ) ).
fof(t1_transgeo,axiom,
$true ).
fof(t2_transgeo,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,A)
& v3_funct_2(C,A,A)
& m2_relset_1(C,A,A) )
=> ? [D] :
( m1_subset_1(D,A)
& k8_funct_2(A,A,C,D) = B ) ) ) ) ).
fof(t3_transgeo,axiom,
$true ).
fof(t4_transgeo,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,A)
& v3_funct_2(D,A,A)
& m2_relset_1(D,A,A) )
=> ( k8_funct_2(A,A,D,B) = C
<=> k8_funct_2(A,A,k6_funct_2(A,D),C) = B ) ) ) ) ) ).
fof(d1_transgeo,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& v3_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,A)
& v3_funct_2(C,A,A)
& m2_relset_1(C,A,A) )
=> k2_transgeo(A,B,C) = k1_transgeo(A,k6_funct_2(A,C),k1_transgeo(A,B,C)) ) ) ) ).
fof(t5_transgeo,axiom,
$true ).
fof(t6_transgeo,axiom,
$true ).
fof(t7_transgeo,axiom,
$true ).
fof(t8_transgeo,axiom,
$true ).
fof(t9_transgeo,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,A)
& v3_funct_2(C,A,A)
& m2_relset_1(C,A,A) )
=> ( k8_funct_2(A,A,C,k8_funct_2(A,A,k6_funct_2(A,C),B)) = B
& k8_funct_2(A,A,k6_funct_2(A,C),k8_funct_2(A,A,C,B)) = B ) ) ) ) ).
fof(t10_transgeo,axiom,
$true ).
fof(t11_transgeo,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& v3_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> k1_transgeo(A,k6_partfun1(A),B) = k1_transgeo(A,B,k6_partfun1(A)) ) ) ).
fof(t12_transgeo,axiom,
$true ).
fof(t13_transgeo,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& v3_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,A)
& v3_funct_2(C,A,A)
& m2_relset_1(C,A,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,A)
& v3_funct_2(D,A,A)
& m2_relset_1(D,A,A) )
=> ( ( k1_transgeo(A,C,B) = k1_transgeo(A,C,D)
| k1_transgeo(A,B,C) = k1_transgeo(A,D,C) )
=> B = D ) ) ) ) ) ).
fof(t14_transgeo,axiom,
$true ).
fof(t15_transgeo,axiom,
$true ).
fof(t16_transgeo,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& v3_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,A)
& v3_funct_2(C,A,A)
& m2_relset_1(C,A,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,A)
& v3_funct_2(D,A,A)
& m2_relset_1(D,A,A) )
=> k2_transgeo(A,k1_transgeo(A,C,B),D) = k1_transgeo(A,k2_transgeo(A,C,D),k2_transgeo(A,B,D)) ) ) ) ) ).
fof(t17_transgeo,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& v3_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,A)
& v3_funct_2(C,A,A)
& m2_relset_1(C,A,A) )
=> k2_transgeo(A,k6_funct_2(A,B),C) = k6_funct_2(A,k2_transgeo(A,B,C)) ) ) ) ).
fof(t18_transgeo,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& v3_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,A)
& v3_funct_2(C,A,A)
& m2_relset_1(C,A,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,A)
& v3_funct_2(D,A,A)
& m2_relset_1(D,A,A) )
=> k2_transgeo(A,B,k1_transgeo(A,D,C)) = k2_transgeo(A,k2_transgeo(A,B,D),C) ) ) ) ) ).
fof(t19_transgeo,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& v3_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> k2_transgeo(A,k6_partfun1(A),B) = k6_partfun1(A) ) ) ).
fof(t20_transgeo,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& v3_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> k2_transgeo(A,B,k6_partfun1(A)) = B ) ) ).
fof(t21_transgeo,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,A)
& v3_funct_2(C,A,A)
& m2_relset_1(C,A,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,A)
& v3_funct_2(D,A,A)
& m2_relset_1(D,A,A) )
=> ( k8_funct_2(A,A,C,B) = B
=> k8_funct_2(A,A,k2_transgeo(A,C,D),k8_funct_2(A,A,D,B)) = k8_funct_2(A,A,D,B) ) ) ) ) ) ).
fof(d2_transgeo,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& v3_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> ! [C] :
( m2_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
=> ( r1_transgeo(A,B,C)
<=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> r2_hidden(k4_tarski(k4_tarski(D,E),k4_tarski(k8_funct_2(A,A,B,D),k8_funct_2(A,A,B,E))),C) ) ) ) ) ) ) ).
fof(t22_transgeo,axiom,
$true ).
fof(t23_transgeo,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_relset_1(B,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
=> ( r1_relat_2(B,k2_zfmisc_1(A,A))
=> r1_transgeo(A,k6_partfun1(A),B) ) ) ) ).
fof(t24_transgeo,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& v3_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> ! [C] :
( m2_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
=> ( ( r3_relat_2(C,k2_zfmisc_1(A,A))
& r1_transgeo(A,B,C) )
=> r1_transgeo(A,k6_funct_2(A,B),C) ) ) ) ) ).
fof(t25_transgeo,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& v3_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,A)
& v3_funct_2(C,A,A)
& m2_relset_1(C,A,A) )
=> ! [D] :
( m2_relset_1(D,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
=> ( ( r8_relat_2(D,k2_zfmisc_1(A,A))
& r1_transgeo(A,B,D)
& r1_transgeo(A,C,D) )
=> r1_transgeo(A,k1_transgeo(A,C,B),D) ) ) ) ) ) ).
fof(t26_transgeo,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& v3_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,A)
& v3_funct_2(C,A,A)
& m2_relset_1(C,A,A) )
=> ! [D] :
( m2_relset_1(D,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
=> ( ( ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m1_subset_1(F,A)
=> ! [G] :
( m1_subset_1(G,A)
=> ! [H] :
( m1_subset_1(H,A)
=> ! [I] :
( m1_subset_1(I,A)
=> ! [J] :
( m1_subset_1(J,A)
=> ( ( r2_hidden(k4_tarski(k4_tarski(G,H),k4_tarski(E,F)),D)
& r2_hidden(k4_tarski(k4_tarski(E,F),k4_tarski(I,J)),D) )
=> ( E = F
| r2_hidden(k4_tarski(k4_tarski(G,H),k4_tarski(I,J)),D) ) ) ) ) ) ) ) )
& ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m1_subset_1(F,A)
=> ! [G] :
( m1_subset_1(G,A)
=> r2_hidden(k4_tarski(k4_tarski(E,E),k4_tarski(F,G)),D) ) ) )
& r1_transgeo(A,B,D)
& r1_transgeo(A,C,D) )
=> r1_transgeo(A,k1_transgeo(A,C,B),D) ) ) ) ) ) ).
fof(d3_transgeo,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& v3_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> ! [C] :
( m2_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
=> ( r2_transgeo(A,B,C)
<=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m1_subset_1(F,A)
=> ! [G] :
( m1_subset_1(G,A)
=> ( r2_hidden(k4_tarski(k4_tarski(D,E),k4_tarski(F,G)),C)
<=> r2_hidden(k4_tarski(k4_tarski(k8_funct_2(A,A,B,D),k8_funct_2(A,A,B,E)),k4_tarski(k8_funct_2(A,A,B,F),k8_funct_2(A,A,B,G))),C) ) ) ) ) ) ) ) ) ) ).
fof(t27_transgeo,axiom,
$true ).
fof(t28_transgeo,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_relset_1(B,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
=> r2_transgeo(A,k6_partfun1(A),B) ) ) ).
fof(t29_transgeo,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& v3_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> ! [C] :
( m2_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
=> ( r2_transgeo(A,B,C)
=> r2_transgeo(A,k6_funct_2(A,B),C) ) ) ) ) ).
fof(t30_transgeo,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& v3_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,A)
& v3_funct_2(C,A,A)
& m2_relset_1(C,A,A) )
=> ! [D] :
( m2_relset_1(D,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
=> ( ( r2_transgeo(A,B,D)
& r2_transgeo(A,C,D) )
=> r2_transgeo(A,k1_transgeo(A,B,C),D) ) ) ) ) ) ).
fof(t31_transgeo,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& v3_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> ! [C] :
( m2_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
=> ( ( r3_relat_2(C,k2_zfmisc_1(A,A))
& r8_relat_2(C,k2_zfmisc_1(A,A))
& r1_transgeo(A,B,C) )
=> r2_transgeo(A,B,C) ) ) ) ) ).
fof(t32_transgeo,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& v3_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> ! [C] :
( m2_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
=> ( ( ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m1_subset_1(F,A)
=> ! [G] :
( m1_subset_1(G,A)
=> ! [H] :
( m1_subset_1(H,A)
=> ! [I] :
( m1_subset_1(I,A)
=> ( ( r2_hidden(k4_tarski(k4_tarski(F,G),k4_tarski(D,E)),C)
& r2_hidden(k4_tarski(k4_tarski(D,E),k4_tarski(H,I)),C) )
=> ( D = E
| r2_hidden(k4_tarski(k4_tarski(F,G),k4_tarski(H,I)),C) ) ) ) ) ) ) ) )
& ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,A)
=> ! [F] :
( m1_subset_1(F,A)
=> r2_hidden(k4_tarski(k4_tarski(D,D),k4_tarski(E,F)),C) ) ) )
& r3_relat_2(C,k2_zfmisc_1(A,A))
& r1_transgeo(A,B,C) )
=> r2_transgeo(A,B,C) ) ) ) ) ).
fof(t33_transgeo,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& v3_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,A)
& v3_funct_2(C,A,A)
& m2_relset_1(C,A,A) )
=> ! [D] :
( m2_relset_1(D,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
=> ( ( r1_transgeo(A,B,D)
& r2_transgeo(A,C,D) )
=> r1_transgeo(A,k2_transgeo(A,B,C),D) ) ) ) ) ) ).
fof(d4_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( r3_transgeo(A,B)
<=> r1_transgeo(u1_struct_0(A),B,u1_analoaf(A)) ) ) ) ).
fof(t34_transgeo,axiom,
$true ).
fof(t35_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( r3_transgeo(A,B)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r2_analoaf(A,C,D,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D)) ) ) ) ) ) ).
fof(d5_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analoaf(A) )
=> ( v1_transgeo(A)
<=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( ( r2_analoaf(A,B,C,F,G)
& r2_analoaf(A,F,G,D,E) )
=> ( F = G
| r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r2_analoaf(A,B,B,C,D) ) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r2_analoaf(A,B,C,D,E)
=> r2_analoaf(A,D,E,B,C) ) ) ) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r2_analoaf(A,B,C,B,C) ) ) ) ) ) ).
fof(t36_transgeo,axiom,
$true ).
fof(t37_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_transgeo(A)
& l1_analoaf(A) )
=> r3_transgeo(A,k6_partfun1(u1_struct_0(A))) ) ).
fof(t38_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_transgeo(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( r3_transgeo(A,B)
=> r3_transgeo(A,k6_funct_2(u1_struct_0(A),B)) ) ) ) ).
fof(t39_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_transgeo(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( r3_transgeo(A,B)
& r3_transgeo(A,C) )
=> r3_transgeo(A,k1_transgeo(u1_struct_0(A),C,B)) ) ) ) ) ).
fof(t40_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> v1_transgeo(A) ) ).
fof(d6_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v2_transgeo(B,A)
<=> r3_transgeo(A,B) ) ) ) ).
fof(t41_transgeo,axiom,
$true ).
fof(t42_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v2_transgeo(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r2_analoaf(A,C,D,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D)) ) ) ) ) ) ).
fof(d7_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v3_transgeo(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r2_analoaf(A,C,D,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C)) ) ) ) ) ) ).
fof(t43_transgeo,axiom,
$true ).
fof(t44_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> v2_transgeo(k6_partfun1(u1_struct_0(A)),A) ) ).
fof(t45_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v2_transgeo(B,A)
=> v2_transgeo(k6_funct_2(u1_struct_0(A),B),A) ) ) ) ).
fof(t46_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( v2_transgeo(B,A)
& v2_transgeo(C,A) )
=> v2_transgeo(k1_transgeo(u1_struct_0(A),C,B),A) ) ) ) ) ).
fof(t47_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ~ ( v3_transgeo(B,A)
& v2_transgeo(B,A) ) ) ) ).
fof(t48_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v3_transgeo(B,A)
=> v3_transgeo(k6_funct_2(u1_struct_0(A),B),A) ) ) ) ).
fof(t49_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( v2_transgeo(B,A)
& v3_transgeo(C,A) )
=> ( v3_transgeo(k1_transgeo(u1_struct_0(A),C,B),A)
& v3_transgeo(k1_transgeo(u1_struct_0(A),B,C),A) ) ) ) ) ) ).
fof(d8_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v4_transgeo(B,A)
<=> r1_transgeo(u1_struct_0(A),B,k1_diraf(u1_struct_0(A),u1_analoaf(A))) ) ) ) ).
fof(t50_transgeo,axiom,
$true ).
fof(t51_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v4_transgeo(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r2_diraf(A,C,D,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D)) ) ) ) ) ) ).
fof(t52_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( v2_transgeo(B,A)
| v3_transgeo(B,A) )
=> v4_transgeo(B,A) ) ) ) ).
fof(t53_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ~ ( v4_transgeo(B,A)
& ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k2_diraf(A)),u1_struct_0(k2_diraf(A)))
& v3_funct_2(C,u1_struct_0(k2_diraf(A)),u1_struct_0(k2_diraf(A)))
& m2_relset_1(C,u1_struct_0(k2_diraf(A)),u1_struct_0(k2_diraf(A))) )
=> ~ ( B = C
& r3_transgeo(k2_diraf(A),C) ) ) ) ) ) ).
fof(t54_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k2_diraf(A)),u1_struct_0(k2_diraf(A)))
& v3_funct_2(B,u1_struct_0(k2_diraf(A)),u1_struct_0(k2_diraf(A)))
& m2_relset_1(B,u1_struct_0(k2_diraf(A)),u1_struct_0(k2_diraf(A))) )
=> ~ ( r3_transgeo(k2_diraf(A),B)
& ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ~ ( B = C
& v4_transgeo(C,A) ) ) ) ) ) ).
fof(t55_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> v4_transgeo(k6_partfun1(u1_struct_0(A)),A) ) ).
fof(t56_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v4_transgeo(B,A)
=> v4_transgeo(k6_funct_2(u1_struct_0(A),B),A) ) ) ) ).
fof(t57_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( v4_transgeo(B,A)
& v4_transgeo(C,A) )
=> v4_transgeo(k1_transgeo(u1_struct_0(A),C,B),A) ) ) ) ) ).
fof(t58_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v4_transgeo(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( r2_diraf(A,C,D,E,F)
<=> r2_diraf(A,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,E),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,F)) ) ) ) ) ) ) ) ) ).
fof(t59_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v4_transgeo(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r3_diraf(A,C,D,E)
<=> r3_diraf(A,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,E)) ) ) ) ) ) ) ) ).
fof(t60_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( v4_transgeo(D,A)
& r3_diraf(A,B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B),C) )
=> r3_diraf(A,B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B),k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,C)) ) ) ) ) ) ).
fof(t61_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_diraf(A,B,C,D,E)
& ~ r2_diraf(A,B,D,C,E)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( r3_diraf(A,B,D,F)
& r3_diraf(A,C,E,F) ) ) ) ) ) ) ) ) ).
fof(t62_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v4_transgeo(B,A)
=> ( ( B = k6_partfun1(u1_struct_0(A))
| ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C) != C ) )
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r2_diraf(A,C,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),D,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D)) ) ) ) ) ) ) ).
fof(t63_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(E,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( v4_transgeo(E,A)
& k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,B) = B
& k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,C) = C )
=> ( r3_diraf(A,B,C,D)
| k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,D) = D ) ) ) ) ) ) ) ).
fof(t64_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( v4_transgeo(D,A)
& k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B) = B
& k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,C) = C )
=> ( B = C
| D = k6_partfun1(u1_struct_0(A)) ) ) ) ) ) ) ).
fof(t65_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(E,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(A)) )
=> ~ ( v4_transgeo(D,A)
& v4_transgeo(E,A)
& k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,B)
& k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,C) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,C)
& B != C
& D != E ) ) ) ) ) ) ).
fof(d9_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v5_transgeo(B,A)
<=> ( v4_transgeo(B,A)
& ( B = k6_partfun1(u1_struct_0(A))
| ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> C != k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C) ) ) ) ) ) ) ).
fof(t66_transgeo,axiom,
$true ).
fof(t67_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v4_transgeo(B,A)
=> ( v5_transgeo(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r2_diraf(A,C,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),D,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D)) ) ) ) ) ) ) ).
fof(t68_transgeo,axiom,
$true ).
fof(t69_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(E,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( v5_transgeo(D,A)
& v5_transgeo(E,A)
& k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,B) )
=> ( r3_diraf(A,B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B),C)
| k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,C) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,C) ) ) ) ) ) ) ) ).
fof(t70_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( v5_transgeo(C,A)
& v5_transgeo(D,A)
& k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,B) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B) )
=> C = D ) ) ) ) ) ).
fof(t71_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v5_transgeo(B,A)
=> v5_transgeo(k6_funct_2(u1_struct_0(A),B),A) ) ) ) ).
fof(t72_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( v5_transgeo(B,A)
& v5_transgeo(C,A) )
=> v5_transgeo(k1_transgeo(u1_struct_0(A),C,B),A) ) ) ) ) ).
fof(t73_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v5_transgeo(B,A)
=> v2_transgeo(B,A) ) ) ) ).
fof(t74_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(E,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( v4_transgeo(E,A)
& k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,B) = B
& r1_diraf(A,C,B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,C)) )
=> ( r3_diraf(A,B,C,D)
| r1_diraf(A,D,B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,D)) ) ) ) ) ) ) ) ).
fof(t75_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(E,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( v4_transgeo(E,A)
& k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,B) = B
& r1_diraf(A,C,B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,C)) )
=> ( C = B
| r1_diraf(A,D,B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,D)) ) ) ) ) ) ) ) ).
fof(t76_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(F,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(F,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( v4_transgeo(F,A)
& k8_funct_2(u1_struct_0(A),u1_struct_0(A),F,B) = B
& r1_diraf(A,C,B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),F,C)) )
=> ( C = B
| r3_diraf(A,B,D,E)
| r2_analoaf(A,D,E,k8_funct_2(u1_struct_0(A),u1_struct_0(A),F,E),k8_funct_2(u1_struct_0(A),u1_struct_0(A),F,D)) ) ) ) ) ) ) ) ) ).
fof(t77_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(F,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(F,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( v4_transgeo(F,A)
& k8_funct_2(u1_struct_0(A),u1_struct_0(A),F,B) = B
& r1_diraf(A,C,B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),F,C))
& r3_diraf(A,B,D,E) )
=> ( C = B
| r2_analoaf(A,D,E,k8_funct_2(u1_struct_0(A),u1_struct_0(A),F,E),k8_funct_2(u1_struct_0(A),u1_struct_0(A),F,D)) ) ) ) ) ) ) ) ) ).
fof(t78_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( v4_transgeo(D,A)
& k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B) = B
& r1_diraf(A,C,B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,C)) )
=> ( C = B
| v3_transgeo(D,A) ) ) ) ) ) ) ).
fof(t79_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( v4_transgeo(C,A)
& k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,B) = B
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r2_analoaf(A,B,D,B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,D)) ) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> r2_analoaf(A,D,E,k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,E)) ) ) ) ) ) ) ).
fof(t80_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ~ ( v4_transgeo(B,A)
& ~ v2_transgeo(B,A)
& ~ v3_transgeo(B,A) ) ) ) ).
fof(t81_transgeo,axiom,
$true ).
fof(t82_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> v1_transgeo(A) ) ).
fof(t83_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ( ~ v3_struct_0(k2_diraf(A))
& v1_transgeo(k2_diraf(A))
& l1_analoaf(k2_diraf(A)) ) ) ).
fof(d10_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v6_transgeo(B,A)
<=> r3_transgeo(A,B) ) ) ) ).
fof(t84_transgeo,axiom,
$true ).
fof(t85_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v6_transgeo(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r2_analoaf(A,C,D,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D)) ) ) ) ) ) ).
fof(t86_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> v6_transgeo(k6_partfun1(u1_struct_0(A)),A) ) ).
fof(t87_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v6_transgeo(B,A)
=> v6_transgeo(k6_funct_2(u1_struct_0(A),B),A) ) ) ) ).
fof(t88_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( v6_transgeo(B,A)
& v6_transgeo(C,A) )
=> v6_transgeo(k1_transgeo(u1_struct_0(A),C,B),A) ) ) ) ) ).
fof(t89_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v6_transgeo(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( r2_analoaf(A,C,D,E,F)
<=> r2_analoaf(A,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,E),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,F)) ) ) ) ) ) ) ) ) ).
fof(t90_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v6_transgeo(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r1_aff_1(A,C,D,E)
<=> r1_aff_1(A,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,E)) ) ) ) ) ) ) ) ).
fof(t91_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( v6_transgeo(D,A)
& r1_aff_1(A,B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B),C) )
=> r1_aff_1(A,B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B),k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,C)) ) ) ) ) ) ).
fof(t92_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_analoaf(A,B,C,D,E)
& ~ r2_analoaf(A,B,D,C,E)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( r1_aff_1(A,B,D,F)
& r1_aff_1(A,C,E,F) ) ) ) ) ) ) ) ) ).
fof(t93_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v6_transgeo(B,A)
=> ( ( B = k6_partfun1(u1_struct_0(A))
| ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C) != C ) )
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r2_analoaf(A,C,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),D,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D)) ) ) ) ) ) ) ).
fof(t94_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(E,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( v6_transgeo(E,A)
& k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,B) = B
& k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,C) = C )
=> ( r1_aff_1(A,B,C,D)
| k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,D) = D ) ) ) ) ) ) ) ).
fof(t95_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( v6_transgeo(D,A)
& k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B) = B
& k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,C) = C )
=> ( B = C
| D = k6_partfun1(u1_struct_0(A)) ) ) ) ) ) ) ).
fof(t96_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(E,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(A)) )
=> ~ ( v6_transgeo(D,A)
& v6_transgeo(E,A)
& k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,B)
& k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,C) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,C)
& B != C
& D != E ) ) ) ) ) ) ).
fof(t97_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( ( r2_analoaf(A,B,C,D,E)
& r2_analoaf(A,B,C,D,F)
& r2_analoaf(A,B,D,C,E)
& r2_analoaf(A,B,D,C,F) )
=> ( r1_aff_1(A,B,C,D)
| E = F ) ) ) ) ) ) ) ) ).
fof(d11_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v7_transgeo(B,A)
<=> ( v6_transgeo(B,A)
& ( B = k6_partfun1(u1_struct_0(A))
| ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> C != k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C) ) ) ) ) ) ) ).
fof(t98_transgeo,axiom,
$true ).
fof(t99_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> v7_transgeo(k6_partfun1(u1_struct_0(A)),A) ) ).
fof(t100_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v6_transgeo(B,A)
=> ( v7_transgeo(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r2_analoaf(A,C,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),D,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D)) ) ) ) ) ) ) ).
fof(t101_transgeo,axiom,
$true ).
fof(t102_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(E,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( v7_transgeo(D,A)
& v7_transgeo(E,A)
& k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,B) )
=> ( r1_aff_1(A,B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B),C)
| k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,C) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,C) ) ) ) ) ) ) ) ).
fof(t103_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( v7_transgeo(C,A)
& v7_transgeo(D,A)
& k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,B) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B) )
=> C = D ) ) ) ) ) ).
fof(t104_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v7_transgeo(B,A)
=> v7_transgeo(k6_funct_2(u1_struct_0(A),B),A) ) ) ) ).
fof(t105_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( v7_transgeo(B,A)
& v7_transgeo(C,A) )
=> v7_transgeo(k1_transgeo(u1_struct_0(A),C,B),A) ) ) ) ) ).
fof(d12_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v8_transgeo(B,A)
<=> r2_transgeo(u1_struct_0(A),B,u1_analoaf(A)) ) ) ) ).
fof(t106_transgeo,axiom,
$true ).
fof(t107_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v8_transgeo(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( r2_analoaf(A,C,D,E,F)
<=> r2_analoaf(A,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,E),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,F)) ) ) ) ) ) ) ) ) ).
fof(t108_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(E,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(A)) )
=> ( v8_transgeo(E,A)
=> ( r1_aff_1(A,B,C,D)
<=> r1_aff_1(A,k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,B),k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,C),k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,D)) ) ) ) ) ) ) ) ).
fof(t109_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( v8_transgeo(B,A)
& v8_transgeo(C,A) )
=> ( v8_transgeo(k6_funct_2(u1_struct_0(A),B),A)
& v8_transgeo(k1_transgeo(u1_struct_0(A),C,B),A)
& v8_transgeo(k6_partfun1(u1_struct_0(A)),A) ) ) ) ) ) ).
fof(t110_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(B,D)
=> r2_hidden(k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,B),k2_funct_2(u1_struct_0(A),u1_struct_0(A),C,D)) ) ) ) ) ) ).
fof(t111_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(B,k2_funct_2(u1_struct_0(A),u1_struct_0(A),C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& r2_hidden(E,D)
& k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,E) = B ) ) ) ) ) ) ).
fof(t112_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(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)))
=> ( k2_funct_2(u1_struct_0(A),u1_struct_0(A),B,C) = k2_funct_2(u1_struct_0(A),u1_struct_0(A),B,D)
=> C = D ) ) ) ) ) ).
fof(t113_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
=> ( v8_transgeo(D,A)
=> k2_funct_2(u1_struct_0(A),u1_struct_0(A),D,k2_aff_1(A,B,C)) = k2_aff_1(A,k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B),k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,C)) ) ) ) ) ) ).
fof(t114_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v8_transgeo(B,A)
& v1_aff_1(C,A) )
=> v1_aff_1(k2_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),A) ) ) ) ) ).
fof(t115_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(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)))
=> ( ( v8_transgeo(B,A)
& r4_aff_1(A,C,D) )
=> r4_aff_1(A,k2_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),k2_funct_2(u1_struct_0(A),u1_struct_0(A),B,D)) ) ) ) ) ) ).
fof(t116_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& v2_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_aff_1(C,A)
=> v1_aff_1(k2_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),A) ) )
=> v8_transgeo(B,A) ) ) ) ).
fof(t117_transgeo,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_diraf(A)
& v2_diraf(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& v3_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
=> ( ( v8_transgeo(D,A)
& v1_aff_1(B,A)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r2_hidden(E,B)
=> k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,E) = E ) )
& k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,C) = C )
=> ( r2_hidden(C,B)
| D = k6_partfun1(u1_struct_0(A)) ) ) ) ) ) ) ).
fof(s1_transgeo,axiom,
( ( ! [A] :
( m1_subset_1(A,f1_s1_transgeo)
=> ? [B] :
( m1_subset_1(B,f1_s1_transgeo)
& p1_s1_transgeo(A,B) ) )
& ! [A] :
( m1_subset_1(A,f1_s1_transgeo)
=> ? [B] :
( m1_subset_1(B,f1_s1_transgeo)
& p1_s1_transgeo(B,A) ) )
& ! [A] :
( m1_subset_1(A,f1_s1_transgeo)
=> ! [B] :
( m1_subset_1(B,f1_s1_transgeo)
=> ! [C] :
( m1_subset_1(C,f1_s1_transgeo)
=> ( ( p1_s1_transgeo(A,B)
& p1_s1_transgeo(C,B) )
=> A = C ) ) ) )
& ! [A] :
( m1_subset_1(A,f1_s1_transgeo)
=> ! [B] :
( m1_subset_1(B,f1_s1_transgeo)
=> ! [C] :
( m1_subset_1(C,f1_s1_transgeo)
=> ( ( p1_s1_transgeo(A,B)
& p1_s1_transgeo(A,C) )
=> B = C ) ) ) ) )
=> ? [A] :
( v1_funct_1(A)
& v1_funct_2(A,f1_s1_transgeo,f1_s1_transgeo)
& v3_funct_2(A,f1_s1_transgeo,f1_s1_transgeo)
& m2_relset_1(A,f1_s1_transgeo,f1_s1_transgeo)
& ! [B] :
( m1_subset_1(B,f1_s1_transgeo)
=> ! [C] :
( m1_subset_1(C,f1_s1_transgeo)
=> ( k8_funct_2(f1_s1_transgeo,f1_s1_transgeo,A,B) = C
<=> p1_s1_transgeo(B,C) ) ) ) ) ) ).
fof(dt_k1_transgeo,axiom,
! [A,B,C] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& v3_funct_2(B,A,A)
& m1_relset_1(B,A,A)
& v1_funct_1(C)
& v1_funct_2(C,A,A)
& v3_funct_2(C,A,A)
& m1_relset_1(C,A,A) )
=> ( v1_funct_1(k1_transgeo(A,B,C))
& v1_funct_2(k1_transgeo(A,B,C),A,A)
& v3_funct_2(k1_transgeo(A,B,C),A,A)
& m2_relset_1(k1_transgeo(A,B,C),A,A) ) ) ).
fof(redefinition_k1_transgeo,axiom,
! [A,B,C] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& v3_funct_2(B,A,A)
& m1_relset_1(B,A,A)
& v1_funct_1(C)
& v1_funct_2(C,A,A)
& v3_funct_2(C,A,A)
& m1_relset_1(C,A,A) )
=> k1_transgeo(A,B,C) = k5_relat_1(B,C) ) ).
fof(dt_k2_transgeo,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& v1_funct_2(B,A,A)
& v3_funct_2(B,A,A)
& m1_relset_1(B,A,A)
& v1_funct_1(C)
& v1_funct_2(C,A,A)
& v3_funct_2(C,A,A)
& m1_relset_1(C,A,A) )
=> ( v1_funct_1(k2_transgeo(A,B,C))
& v1_funct_2(k2_transgeo(A,B,C),A,A)
& v3_funct_2(k2_transgeo(A,B,C),A,A)
& m2_relset_1(k2_transgeo(A,B,C),A,A) ) ) ).
%------------------------------------------------------------------------------