SET007 Axioms: SET007+282.ax
%------------------------------------------------------------------------------
% File : SET007+282 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : A Construction of Analytical Ordered Trapezium 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 : geomtrap [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 94 ( 5 unt; 0 def)
% Number of atoms : 1230 ( 114 equ)
% Maximal formula atoms : 55 ( 13 avg)
% Number of connectives : 1257 ( 121 ~; 16 |; 613 &)
% ( 22 <=>; 485 =>; 0 <=; 0 <~>)
% Maximal formula depth : 42 ( 14 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 34 ( 32 usr; 1 prp; 0-7 aty)
% Number of functors : 31 ( 31 usr; 3 con; 0-6 aty)
% Number of variables : 479 ( 463 !; 16 ?)
% 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_geomtrap,axiom,
? [A] :
( l1_geomtrap(A)
& v1_geomtrap(A) ) ).
fof(rc2_geomtrap,axiom,
? [A] :
( l1_geomtrap(A)
& ~ v3_struct_0(A)
& v1_geomtrap(A) ) ).
fof(fc1_geomtrap,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( ~ v3_struct_0(k7_geomtrap(A,B,C))
& v1_geomtrap(k7_geomtrap(A,B,C)) ) ) ).
fof(fc2_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_geomtrap(A) )
=> ( ~ v3_struct_0(k8_geomtrap(A))
& v1_analoaf(k8_geomtrap(A)) ) ) ).
fof(rc3_geomtrap,axiom,
? [A] :
( l1_geomtrap(A)
& ~ v3_struct_0(A)
& v1_geomtrap(A)
& v2_geomtrap(A) ) ).
fof(rc4_geomtrap,axiom,
? [A] :
( l1_analoaf(A)
& ~ v3_struct_0(A)
& v1_analoaf(A)
& v3_geomtrap(A) ) ).
fof(fc3_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_geomtrap(A)
& l1_geomtrap(A) )
=> ( ~ v3_struct_0(k8_geomtrap(A))
& v1_analoaf(k8_geomtrap(A))
& v3_geomtrap(k8_geomtrap(A)) ) ) ).
fof(rc5_geomtrap,axiom,
? [A] :
( l1_analoaf(A)
& ~ v3_struct_0(A)
& v1_analoaf(A)
& v4_geomtrap(A) ) ).
fof(fc4_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_geomtrap(A)
& l1_analoaf(A) )
=> ( ~ v3_struct_0(k2_diraf(A))
& v1_analoaf(k2_diraf(A))
& v4_geomtrap(k2_diraf(A)) ) ) ).
fof(rc6_geomtrap,axiom,
? [A] :
( l1_analoaf(A)
& ~ v3_struct_0(A)
& v1_analoaf(A)
& v3_geomtrap(A)
& v5_geomtrap(A) ) ).
fof(fc5_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_geomtrap(A)
& l1_geomtrap(A) )
=> ( ~ v3_struct_0(k8_geomtrap(A))
& v1_analoaf(k8_geomtrap(A))
& v3_geomtrap(k8_geomtrap(A))
& v5_geomtrap(k8_geomtrap(A)) ) ) ).
fof(d1_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> ( r1_geomtrap(A,B,C,D,E)
<=> ( r1_analoaf(A,B,C,D,E)
| r1_analoaf(A,B,C,E,D) ) ) ) ) ) ) ) ).
fof(t1_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_analmetr(A,B,C)
=> ( ~ v3_struct_0(k2_analoaf(A))
& ~ v3_realset2(k2_analoaf(A))
& v2_analoaf(k2_analoaf(A))
& l1_analoaf(k2_analoaf(A)) ) ) ) ) ) ).
fof(t2_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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(k2_analoaf(A)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k2_analoaf(A)))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k2_analoaf(A)))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k2_analoaf(A)))
=> ( ( F = B
& G = C
& H = D
& I = E )
=> ( r2_analoaf(k2_analoaf(A),F,G,H,I)
<=> r1_analoaf(A,B,C,D,E) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t3_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> ( r1_analmetr(A,B,C)
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k2_diraf(k2_analoaf(A))))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k2_diraf(k2_analoaf(A))))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(k2_diraf(k2_analoaf(A))))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(k2_diraf(k2_analoaf(A))))
=> ( ( H = D
& I = E
& J = F
& K = G )
=> ( r2_analoaf(k2_diraf(k2_analoaf(A)),H,I,J,K)
<=> r1_geomtrap(A,D,E,F,G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t4_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k2_analmetr(A,B,C)))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k2_analmetr(A,B,C)))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(k2_analmetr(A,B,C)))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(k2_analmetr(A,B,C)))
=> ( ( H = D
& I = E
& J = F
& K = G )
=> ( r4_analmetr(k2_analmetr(A,B,C),H,I,J,K)
<=> r1_geomtrap(A,D,E,F,G) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d2_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> ( D = k1_geomtrap(A,B,C)
<=> k4_rlvect_1(A,D,D) = k4_rlvect_1(A,B,C) ) ) ) ) ) ).
fof(t5_geomtrap,axiom,
$true ).
fof(t6_geomtrap,axiom,
$true ).
fof(t7_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
& k1_geomtrap(A,B,D) = C ) ) ) ) ).
fof(t8_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> k1_geomtrap(A,k1_geomtrap(A,B,C),k1_geomtrap(A,D,E)) = k1_geomtrap(A,k1_geomtrap(A,B,D),k1_geomtrap(A,C,E)) ) ) ) ) ) ).
fof(t9_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> ( k1_geomtrap(A,B,C) = k1_geomtrap(A,B,D)
=> C = D ) ) ) ) ) ).
fof(t10_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> r1_analoaf(A,B,C,k1_geomtrap(A,D,B),k1_geomtrap(A,D,C)) ) ) ) ) ).
fof(t11_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> r1_geomtrap(A,B,C,k1_geomtrap(A,D,B),k1_geomtrap(A,D,C)) ) ) ) ) ).
fof(t12_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k3_rlvect_1(A,k6_rlvect_1(A,k1_geomtrap(A,B,C),B),np__2) = k6_rlvect_1(A,C,B)
& k3_rlvect_1(A,k6_rlvect_1(A,C,k1_geomtrap(A,B,C)),np__2) = k6_rlvect_1(A,C,B) ) ) ) ) ).
fof(t13_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_analoaf(A,B,k1_geomtrap(A,B,C),k1_geomtrap(A,B,C),C) ) ) ) ).
fof(t14_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_analoaf(A,B,C,B,k1_geomtrap(A,B,C))
& r1_analoaf(A,B,C,k1_geomtrap(A,B,C),C) ) ) ) ) ).
fof(t15_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> ( r1_analoaf(A,B,C,C,D)
=> r1_analoaf(A,k1_geomtrap(A,B,C),C,C,k1_geomtrap(A,C,D)) ) ) ) ) ) ).
fof(t16_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> ( r1_analoaf(A,B,C,D,E)
=> r1_analoaf(A,B,C,k1_geomtrap(A,B,D),k1_geomtrap(A,C,E)) ) ) ) ) ) ) ).
fof(d3_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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_geomtrap(A,B,C,D,E,F,G)
<=> ( r1_analoaf(A,D,E,F,G)
& r3_analmetr(A,D,E,k1_geomtrap(A,D,E),k1_geomtrap(A,F,G),B,C)
& r3_analmetr(A,F,G,k1_geomtrap(A,D,E),k1_geomtrap(A,F,G),B,C) ) ) ) ) ) ) ) ) ) ).
fof(t17_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> ( r1_analmetr(A,B,C)
=> r2_geomtrap(A,B,C,D,D,E,E) ) ) ) ) ) ) ).
fof(t18_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> ( r1_analmetr(A,B,C)
=> r2_geomtrap(A,B,C,D,E,D,E) ) ) ) ) ) ) ).
fof(t19_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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_geomtrap(A,D,E,B,C,C,B)
=> B = C ) ) ) ) ) ) ).
fof(t20_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> ( ( r1_analmetr(A,B,C)
& r2_geomtrap(A,B,C,D,E,E,F) )
=> ( D = E
& E = F ) ) ) ) ) ) ) ) ).
fof(t21_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ( ( r1_analmetr(A,B,C)
& r2_geomtrap(A,B,C,D,E,F,G)
& r2_geomtrap(A,B,C,D,E,H,I) )
=> ( D = E
| r2_geomtrap(A,B,C,F,G,H,I) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t22_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> ~ ( r1_analmetr(A,B,C)
& ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( ~ r2_geomtrap(A,B,C,D,E,F,G)
& ~ r2_geomtrap(A,B,C,D,E,G,F) ) ) ) ) ) ) ) ) ) ).
fof(t23_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> ( ( r1_analmetr(A,B,C)
& r2_geomtrap(A,B,C,D,E,F,G) )
=> r2_geomtrap(A,B,C,F,G,D,E) ) ) ) ) ) ) ) ) ).
fof(t24_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> ( ( r1_analmetr(A,B,C)
& r2_geomtrap(A,B,C,D,E,F,G) )
=> r2_geomtrap(A,B,C,E,D,G,F) ) ) ) ) ) ) ) ) ).
fof(t25_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> ( ( r1_analmetr(A,B,C)
& r2_geomtrap(A,B,C,D,E,D,F) )
=> E = F ) ) ) ) ) ) ) ).
fof(t26_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ~ ( r1_analmetr(A,B,C)
& r2_geomtrap(A,B,C,D,E,F,G)
& r2_geomtrap(A,B,C,D,E,F,H)
& D != E
& G != H ) ) ) ) ) ) ) ) ) ).
fof(t27_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ( ( r1_analmetr(A,B,C)
& r2_geomtrap(A,B,C,D,E,F,G) )
=> ( D = E
| ( ~ r2_geomtrap(A,B,C,D,E,F,H)
& ~ r2_geomtrap(A,B,C,D,E,H,F) )
| G = H ) ) ) ) ) ) ) ) ) ) ).
fof(t28_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> ( ( r1_analmetr(A,B,C)
& r2_geomtrap(A,B,C,D,E,F,G) )
=> r2_geomtrap(A,B,C,D,E,k1_geomtrap(A,D,F),k1_geomtrap(A,E,G)) ) ) ) ) ) ) ) ) ).
fof(t29_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> ~ ( r1_analmetr(A,B,C)
& r2_geomtrap(A,B,C,D,E,F,G)
& ~ r2_geomtrap(A,B,C,D,E,k1_geomtrap(A,D,G),k1_geomtrap(A,E,F))
& ~ r2_geomtrap(A,B,C,D,E,k1_geomtrap(A,E,F),k1_geomtrap(A,D,G)) ) ) ) ) ) ) ) ) ).
fof(t30_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(A))
=> ! [L] :
( m1_subset_1(L,u1_struct_0(A))
=> ( ( r1_analmetr(A,B,C)
& D = k1_geomtrap(A,E,I)
& D = k1_geomtrap(A,F,J)
& D = k1_geomtrap(A,G,K)
& D = k1_geomtrap(A,H,L)
& r2_geomtrap(A,B,C,E,F,G,H) )
=> r2_geomtrap(A,B,C,I,J,K,L) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d4_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> ( r1_analmetr(A,B,C)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( E = k2_geomtrap(A,B,C,D)
<=> ? [F] :
( m1_subset_1(F,k1_numbers)
& D = k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)) ) ) ) ) ) ) ) ) ).
fof(d5_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> ( r1_analmetr(A,B,C)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( E = k3_geomtrap(A,B,C,D)
<=> ? [F] :
( m1_subset_1(F,k1_numbers)
& D = k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,E)) ) ) ) ) ) ) ) ) ).
fof(d6_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> k4_geomtrap(A,B,C,D,E) = k3_real_1(k4_real_1(k2_geomtrap(A,B,C,D),k2_geomtrap(A,B,C,E)),k4_real_1(k3_geomtrap(A,B,C,D),k3_geomtrap(A,B,C,E))) ) ) ) ) ) ).
fof(t31_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> k4_geomtrap(A,B,C,D,E) = k4_geomtrap(A,B,C,E,D) ) ) ) ) ) ).
fof(t32_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_analmetr(A,B,C)
=> ! [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))
=> ( k4_geomtrap(A,B,C,D,k4_rlvect_1(A,E,F)) = k3_real_1(k4_geomtrap(A,B,C,D,E),k4_geomtrap(A,B,C,D,F))
& k4_geomtrap(A,B,C,D,k6_rlvect_1(A,E,F)) = k5_real_1(k4_geomtrap(A,B,C,D,E),k4_geomtrap(A,B,C,D,F))
& k4_geomtrap(A,B,C,k6_rlvect_1(A,E,F),D) = k5_real_1(k4_geomtrap(A,B,C,E,D),k4_geomtrap(A,B,C,F,D))
& k4_geomtrap(A,B,C,k4_rlvect_1(A,E,F),D) = k3_real_1(k4_geomtrap(A,B,C,E,D),k4_geomtrap(A,B,C,F,D)) ) ) ) ) ) ) ) ) ).
fof(t33_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_analmetr(A,B,C)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ( k4_geomtrap(A,B,C,k3_rlvect_1(A,D,F),E) = k4_real_1(F,k4_geomtrap(A,B,C,D,E))
& k4_geomtrap(A,B,C,D,k3_rlvect_1(A,E,F)) = k4_real_1(F,k4_geomtrap(A,B,C,D,E))
& k4_geomtrap(A,B,C,k3_rlvect_1(A,D,F),E) = k4_real_1(k4_geomtrap(A,B,C,D,E),F)
& k4_geomtrap(A,B,C,D,k3_rlvect_1(A,E,F)) = k4_real_1(k4_geomtrap(A,B,C,D,E),F) ) ) ) ) ) ) ) ) ).
fof(t34_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_analmetr(A,B,C)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r2_analmetr(A,D,E,B,C)
<=> k4_geomtrap(A,B,C,D,E) = np__0 ) ) ) ) ) ) ) ).
fof(t35_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_analmetr(A,B,C)
=> ! [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))
=> ( r3_analmetr(A,D,E,F,G,B,C)
<=> k4_geomtrap(A,B,C,k6_rlvect_1(A,E,D),k6_rlvect_1(A,G,F)) = np__0 ) ) ) ) ) ) ) ) ) ).
fof(t36_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_analmetr(A,B,C)
=> ! [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))
=> k4_real_1(np__2,k4_geomtrap(A,B,C,D,k1_geomtrap(A,E,F))) = k3_real_1(k4_geomtrap(A,B,C,D,E),k4_geomtrap(A,B,C,D,F)) ) ) ) ) ) ) ) ).
fof(t37_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_analmetr(A,B,C)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( D != E
& k4_geomtrap(A,B,C,k6_rlvect_1(A,D,E),k6_rlvect_1(A,D,E)) = np__0 ) ) ) ) ) ) ) ).
fof(t38_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_analmetr(A,B,C)
=> ! [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))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,k1_numbers)
=> ( ( r2_geomtrap(A,B,C,D,E,F,G)
& I = k4_real_1(k5_real_1(k4_geomtrap(A,B,C,k6_rlvect_1(A,D,E),k4_rlvect_1(A,D,E)),k4_real_1(np__2,k4_geomtrap(A,B,C,k6_rlvect_1(A,D,E),F))),k2_real_1(k4_geomtrap(A,B,C,k6_rlvect_1(A,D,E),k6_rlvect_1(A,D,E))))
& H = k4_rlvect_1(A,F,k3_rlvect_1(A,k6_rlvect_1(A,D,E),I)) )
=> ( D = E
| G = H ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t39_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_analmetr(A,B,C)
=> ! [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))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(A))
=> ! [L] :
( m1_subset_1(L,u1_struct_0(A))
=> ! [M] :
( m1_subset_1(M,u1_struct_0(A))
=> ( ( r2_geomtrap(A,B,C,D,E,F,J)
& r2_geomtrap(A,B,C,D,E,G,K)
& r2_geomtrap(A,B,C,D,E,H,L)
& r2_geomtrap(A,B,C,D,E,I,M)
& r1_analoaf(A,F,G,H,I) )
=> ( D = E
| r1_analoaf(A,J,K,L,M) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t40_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_analmetr(A,B,C)
=> ! [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))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(A))
=> ( ( r2_geomtrap(A,B,C,D,E,F,I)
& r2_geomtrap(A,B,C,D,E,G,J)
& r2_geomtrap(A,B,C,D,E,H,K)
& H = k1_geomtrap(A,F,G) )
=> ( D = E
| K = k1_geomtrap(A,I,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t41_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_analmetr(A,B,C)
=> ! [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))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ( ( r2_geomtrap(A,B,C,D,E,F,H)
& r2_geomtrap(A,B,C,D,E,G,I) )
=> ( D = E
| r2_geomtrap(A,B,C,D,E,k1_geomtrap(A,F,G),k1_geomtrap(A,H,I)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t42_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_analmetr(A,B,C)
=> ! [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))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(A))
=> ! [L] :
( m1_subset_1(L,u1_struct_0(A))
=> ! [M] :
( m1_subset_1(M,u1_struct_0(A))
=> ( ( r2_geomtrap(A,B,C,D,E,F,J)
& r2_geomtrap(A,B,C,D,E,G,K)
& r2_geomtrap(A,B,C,D,E,H,L)
& r2_geomtrap(A,B,C,D,E,I,M)
& r3_analmetr(A,F,G,H,I,B,C) )
=> ( D = E
| r3_analmetr(A,J,K,L,M,B,C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t43_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(A))
=> ! [L] :
( m1_subset_1(L,u1_struct_0(A))
=> ! [M] :
( m1_subset_1(M,u1_struct_0(A))
=> ( ( r1_analmetr(A,B,C)
& r2_geomtrap(A,B,C,D,E,F,J)
& r2_geomtrap(A,B,C,D,E,G,K)
& r2_geomtrap(A,B,C,D,E,H,L)
& r2_geomtrap(A,B,C,D,E,I,M)
& r2_geomtrap(A,B,C,F,G,H,I) )
=> ( D = E
| r2_geomtrap(A,B,C,J,K,L,M) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d7_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m2_relset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
=> ( D = k5_geomtrap(A,B,C)
<=> ! [E,F] :
( r2_hidden(k4_tarski(E,F),D)
<=> ? [G] :
( m1_subset_1(G,u1_struct_0(A))
& ? [H] :
( m1_subset_1(H,u1_struct_0(A))
& ? [I] :
( m1_subset_1(I,u1_struct_0(A))
& ? [J] :
( m1_subset_1(J,u1_struct_0(A))
& E = k1_domain_1(u1_struct_0(A),u1_struct_0(A),G,H)
& F = k1_domain_1(u1_struct_0(A),u1_struct_0(A),I,J)
& r2_geomtrap(A,B,C,G,H,I,J) ) ) ) ) ) ) ) ) ) ) ).
fof(t44_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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_hidden(k1_domain_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C),k1_domain_1(u1_struct_0(A),u1_struct_0(A),D,E)),k5_geomtrap(A,F,G))
<=> r2_geomtrap(A,F,G,B,C,D,E) ) ) ) ) ) ) ) ) ).
fof(d8_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) )
=> ( B = k6_geomtrap(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B,C,D) = k1_geomtrap(A,C,D) ) ) ) ) ) ).
fof(d9_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k7_geomtrap(A,B,C) = g1_geomtrap(u1_struct_0(A),k6_geomtrap(A),k5_geomtrap(A,B,C)) ) ) ) ).
fof(d10_geomtrap,axiom,
! [A] :
( l1_geomtrap(A)
=> k8_geomtrap(A) = g1_analoaf(u1_struct_0(A),u1_analoaf(A)) ) ).
fof(d11_geomtrap,axiom,
$true ).
fof(d12_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_geomtrap(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k9_geomtrap(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_midsp_1(A),B,C) ) ) ) ).
fof(t45_geomtrap,axiom,
$true ).
fof(t46_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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(k7_geomtrap(A,B,C)))
<=> m1_subset_1(D,u1_struct_0(A)) ) ) ) ) ).
fof(t47_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k7_geomtrap(A,B,C)))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k7_geomtrap(A,B,C)))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(k7_geomtrap(A,B,C)))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(k7_geomtrap(A,B,C)))
=> ( ( r1_analmetr(A,B,C)
& D = H
& E = I
& F = J
& G = K )
=> ( r2_analoaf(k7_geomtrap(A,B,C),H,I,J,K)
<=> r2_geomtrap(A,B,C,D,E,F,G) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t48_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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(k7_geomtrap(A,B,C)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k7_geomtrap(A,B,C)))
=> ( ( r1_analmetr(A,B,C)
& D = F
& E = G )
=> k1_geomtrap(A,D,E) = k9_geomtrap(k7_geomtrap(A,B,C),F,G) ) ) ) ) ) ) ) ) ).
fof(d13_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_geomtrap(A) )
=> ( v2_geomtrap(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))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(A))
=> ( k9_geomtrap(A,B,C) = k9_geomtrap(A,C,B)
& k9_geomtrap(A,B,B) = B
& k9_geomtrap(A,k9_geomtrap(A,B,C),k9_geomtrap(A,D,E)) = k9_geomtrap(A,k9_geomtrap(A,B,D),k9_geomtrap(A,C,E))
& ? [L] :
( m1_subset_1(L,u1_struct_0(A))
& k9_geomtrap(A,L,B) = C )
& ( k9_geomtrap(A,B,C) = k9_geomtrap(A,B,D)
=> C = D )
& ( r2_analoaf(A,B,C,D,E)
=> r2_analoaf(A,B,C,k9_geomtrap(A,B,D),k9_geomtrap(A,C,E)) )
& ~ ( r2_analoaf(A,B,C,D,E)
& ~ r2_analoaf(A,B,C,k9_geomtrap(A,B,E),k9_geomtrap(A,C,D))
& ~ r2_analoaf(A,B,C,k9_geomtrap(A,C,D),k9_geomtrap(A,B,E)) )
& ( ( r2_analoaf(A,B,C,D,E)
& k9_geomtrap(A,B,F) = J
& k9_geomtrap(A,C,G) = J
& k9_geomtrap(A,D,H) = J
& k9_geomtrap(A,E,I) = J )
=> r2_analoaf(A,F,G,H,I) )
& ( ( r2_analoaf(A,J,K,B,F)
& r2_analoaf(A,J,K,C,G)
& r2_analoaf(A,J,K,D,H)
& r2_analoaf(A,J,K,E,I)
& r2_analoaf(A,B,C,D,E) )
=> ( J = K
| r2_analoaf(A,F,G,H,I) ) )
& ( r2_analoaf(A,B,C,C,D)
=> ( B = C
& C = D ) )
& ( ( r2_analoaf(A,B,C,F,G)
& r2_analoaf(A,B,C,H,I) )
=> ( B = C
| r2_analoaf(A,F,G,H,I) ) )
& ( r2_analoaf(A,B,C,D,E)
=> ( r2_analoaf(A,D,E,B,C)
& r2_analoaf(A,C,B,E,D) ) )
& ~ ! [L] :
( m1_subset_1(L,u1_struct_0(A))
=> ( ~ r2_analoaf(A,B,C,D,L)
& ~ r2_analoaf(A,B,C,L,D) ) )
& ~ ( r2_analoaf(A,B,C,D,J)
& r2_analoaf(A,B,C,D,K)
& B != C
& J != K ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t49_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_analmetr(A,B,C)
=> ( ~ v3_struct_0(k7_geomtrap(A,B,C))
& v2_geomtrap(k7_geomtrap(A,B,C))
& l1_geomtrap(k7_geomtrap(A,B,C)) ) ) ) ) ) ).
fof(d14_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analoaf(A) )
=> ( v3_geomtrap(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))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(A))
=> ( ( r2_analoaf(A,B,C,C,D)
=> ( B = C
& C = D ) )
& ( ( r2_analoaf(A,B,C,F,G)
& r2_analoaf(A,B,C,H,I) )
=> ( B = C
| r2_analoaf(A,F,G,H,I) ) )
& ( r2_analoaf(A,B,C,D,E)
=> ( r2_analoaf(A,D,E,B,C)
& r2_analoaf(A,C,B,E,D) ) )
& ~ ! [L] :
( m1_subset_1(L,u1_struct_0(A))
=> ( ~ r2_analoaf(A,B,C,D,L)
& ~ r2_analoaf(A,B,C,L,D) ) )
& ~ ( r2_analoaf(A,B,C,D,J)
& r2_analoaf(A,B,C,D,K)
& B != C
& J != K ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t50_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_geomtrap(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
<=> m1_subset_1(B,u1_struct_0(k2_diraf(A))) ) ) ).
fof(t51_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_geomtrap(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(k2_diraf(A)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k2_diraf(A)))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k2_diraf(A)))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k2_diraf(A)))
=> ( ( B = F
& C = G
& D = H
& E = I )
=> ( r2_analoaf(k2_diraf(A),F,G,H,I)
<=> ( r2_analoaf(A,B,C,D,E)
| r2_analoaf(A,B,C,E,D) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d15_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analoaf(A) )
=> ( v4_geomtrap(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,C,B)
& ~ ( r2_analoaf(A,B,C,D,E)
& r2_analoaf(A,B,C,D,G)
& B != C
& E != G )
& ( ( r2_analoaf(A,F,G,B,C)
& r2_analoaf(A,F,G,D,E) )
=> ( F = G
| r2_analoaf(A,B,C,D,E) ) )
& ( r2_analoaf(A,B,C,D,E)
=> r2_analoaf(A,D,E,B,C) )
& ? [H] :
( m1_subset_1(H,u1_struct_0(A))
& r2_analoaf(A,B,C,D,H) ) ) ) ) ) ) ) ) ) ) ).
fof(d16_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analoaf(A) )
=> ( v5_geomtrap(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))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(A))
=> ( ( r2_analoaf(A,B,C,D,E)
& r2_analoaf(A,B,C,F,G)
& r2_analoaf(A,B,C,H,I)
& r2_analoaf(A,B,C,J,K)
& r2_analoaf(A,D,F,H,J) )
=> ( B = C
| r2_analoaf(A,E,G,I,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_l1_geomtrap,axiom,
! [A] :
( l1_geomtrap(A)
=> ( l1_analoaf(A)
& l1_midsp_1(A) ) ) ).
fof(existence_l1_geomtrap,axiom,
? [A] : l1_geomtrap(A) ).
fof(abstractness_v1_geomtrap,axiom,
! [A] :
( l1_geomtrap(A)
=> ( v1_geomtrap(A)
=> A = g1_geomtrap(u1_struct_0(A),u1_midsp_1(A),u1_analoaf(A)) ) ) ).
fof(dt_k1_geomtrap,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k1_geomtrap(A,B,C),u1_struct_0(A)) ) ).
fof(commutativity_k1_geomtrap,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> k1_geomtrap(A,B,C) = k1_geomtrap(A,C,B) ) ).
fof(idempotence_k1_geomtrap,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> k1_geomtrap(A,B,B) = B ) ).
fof(dt_k2_geomtrap,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(A)) )
=> m1_subset_1(k2_geomtrap(A,B,C,D),k1_numbers) ) ).
fof(dt_k3_geomtrap,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(A)) )
=> m1_subset_1(k3_geomtrap(A,B,C,D),k1_numbers) ) ).
fof(dt_k4_geomtrap,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(A)) )
=> m1_subset_1(k4_geomtrap(A,B,C,D,E),k1_numbers) ) ).
fof(dt_k5_geomtrap,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m2_relset_1(k5_geomtrap(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) ) ).
fof(dt_k6_geomtrap,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ( v1_funct_1(k6_geomtrap(A))
& v1_funct_2(k6_geomtrap(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& m2_relset_1(k6_geomtrap(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ).
fof(dt_k7_geomtrap,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( v1_geomtrap(k7_geomtrap(A,B,C))
& l1_geomtrap(k7_geomtrap(A,B,C)) ) ) ).
fof(dt_k8_geomtrap,axiom,
! [A] :
( l1_geomtrap(A)
=> ( v1_analoaf(k8_geomtrap(A))
& l1_analoaf(k8_geomtrap(A)) ) ) ).
fof(dt_k9_geomtrap,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_geomtrap(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k9_geomtrap(A,B,C),u1_struct_0(A)) ) ).
fof(dt_g1_geomtrap,axiom,
! [A,B,C] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A)) )
=> ( v1_geomtrap(g1_geomtrap(A,B,C))
& l1_geomtrap(g1_geomtrap(A,B,C)) ) ) ).
fof(free_g1_geomtrap,axiom,
! [A,B,C] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A)) )
=> ! [D,E,F] :
( g1_geomtrap(A,B,C) = g1_geomtrap(D,E,F)
=> ( A = D
& B = E
& C = F ) ) ) ).
%------------------------------------------------------------------------------