SET007 Axioms: SET007+368.ax
%------------------------------------------------------------------------------
% File : SET007+368 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Subspaces of Real Linear Space Generated by Vectors
% 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 : rlvect_4 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 43 ( 2 unt; 0 def)
% Number of atoms : 535 ( 94 equ)
% Maximal formula atoms : 21 ( 12 avg)
% Number of connectives : 566 ( 74 ~; 34 |; 283 &)
% ( 7 <=>; 168 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 12 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 1 prp; 0-3 aty)
% Number of functors : 41 ( 41 usr; 26 con; 0-4 aty)
% Number of variables : 169 ( 153 !; 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(t1_rlvect_4,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))
=> ( k6_rlvect_1(A,k4_rlvect_1(A,B,C),B) = C
& k6_rlvect_1(A,k4_rlvect_1(A,C,B),B) = C
& k4_rlvect_1(A,k6_rlvect_1(A,B,B),C) = C
& k4_rlvect_1(A,k6_rlvect_1(A,C,B),B) = C
& k4_rlvect_1(A,B,k6_rlvect_1(A,C,B)) = C
& k4_rlvect_1(A,C,k6_rlvect_1(A,B,B)) = C
& k6_rlvect_1(A,B,k6_rlvect_1(A,B,C)) = C ) ) ) ) ).
fof(t2_rlvect_4,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))
=> k6_rlvect_1(A,k4_rlvect_1(A,B,C),D) = k4_rlvect_1(A,k6_rlvect_1(A,B,D),C) ) ) ) ) ).
fof(t3_rlvect_4,axiom,
$true ).
fof(t4_rlvect_4,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))
=> ( k6_rlvect_1(A,B,C) = k6_rlvect_1(A,D,C)
=> B = D ) ) ) ) ) ).
fof(t5_rlvect_4,axiom,
$true ).
fof(t6_rlvect_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& l2_rlvect_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> k5_rlvect_1(B,k3_rlvect_1(B,C,A)) = k3_rlvect_1(B,C,k1_real_1(A)) ) ) ) ).
fof(t7_rlvect_4,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_rlsub_1(C,A)
=> ! [D] :
( m1_rlsub_1(D,A)
=> ( m1_rlsub_1(C,D)
=> r1_tarski(k3_rlsub_1(A,B,C),k3_rlsub_1(A,B,D)) ) ) ) ) ) ).
fof(t8_rlvect_4,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_rlsub_1(D,A)
=> ( r2_hidden(B,k3_rlsub_1(A,C,D))
=> k3_rlsub_1(A,C,D) = k3_rlsub_1(A,B,D) ) ) ) ) ) ).
fof(t9_rlvect_4,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] :
( m2_rlvect_2(E,A,k9_rlvect_2(A,B,C,D))
=> ~ ( B != C
& B != D
& C != D
& k13_rlvect_2(A,E) != k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,k8_funct_2(u1_struct_0(A),k1_numbers,E,B)),k3_rlvect_1(A,C,k8_funct_2(u1_struct_0(A),k1_numbers,E,C))),k3_rlvect_1(A,D,k8_funct_2(u1_struct_0(A),k1_numbers,E,D))) ) ) ) ) ) ) ).
fof(t10_rlvect_4,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))
=> ( ( B != C
& B != D
& C != D
& v1_rlvect_3(k9_rlvect_2(A,B,C,D),A) )
<=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ( k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)),k3_rlvect_1(A,D,G)) = k1_rlvect_1(A)
=> ( E = np__0
& F = np__0
& G = np__0 ) ) ) ) ) ) ) ) ) ) ).
fof(t11_rlvect_4,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& l2_rlvect_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ( r1_rlvect_1(k1_rlvect_3(B,k7_rlvect_2(B,C)),A)
<=> ? [D] :
( m1_subset_1(D,k1_numbers)
& A = k3_rlvect_1(B,C,D) ) ) ) ) ).
fof(t12_rlvect_4,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))
=> r1_rlvect_1(k1_rlvect_3(A,k7_rlvect_2(A,B)),B) ) ) ).
fof(t13_rlvect_4,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& l2_rlvect_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( r2_hidden(A,k3_rlsub_1(B,C,k1_rlvect_3(B,k7_rlvect_2(B,D))))
<=> ? [E] :
( m1_subset_1(E,k1_numbers)
& A = k4_rlvect_1(B,C,k3_rlvect_1(B,D,E)) ) ) ) ) ) ).
fof(t14_rlvect_4,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& l2_rlvect_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( r1_rlvect_1(k1_rlvect_3(B,k8_rlvect_2(B,C,D)),A)
<=> ? [E] :
( m1_subset_1(E,k1_numbers)
& ? [F] :
( m1_subset_1(F,k1_numbers)
& A = k4_rlvect_1(B,k3_rlvect_1(B,C,E),k3_rlvect_1(B,D,F)) ) ) ) ) ) ) ).
fof(t15_rlvect_4,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_rlvect_1(k1_rlvect_3(A,k8_rlvect_2(A,B,C)),B)
& r1_rlvect_1(k1_rlvect_3(A,k8_rlvect_2(A,B,C)),C) ) ) ) ) ).
fof(t16_rlvect_4,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& l2_rlvect_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( r2_hidden(A,k3_rlsub_1(B,C,k1_rlvect_3(B,k8_rlvect_2(B,D,E))))
<=> ? [F] :
( m1_subset_1(F,k1_numbers)
& ? [G] :
( m1_subset_1(G,k1_numbers)
& A = k4_rlvect_1(B,k4_rlvect_1(B,C,k3_rlvect_1(B,D,F)),k3_rlvect_1(B,E,G)) ) ) ) ) ) ) ) ).
fof(t17_rlvect_4,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& l2_rlvect_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( r1_rlvect_1(k1_rlvect_3(B,k9_rlvect_2(B,C,D,E)),A)
<=> ? [F] :
( m1_subset_1(F,k1_numbers)
& ? [G] :
( m1_subset_1(G,k1_numbers)
& ? [H] :
( m1_subset_1(H,k1_numbers)
& A = k4_rlvect_1(B,k4_rlvect_1(B,k3_rlvect_1(B,C,F),k3_rlvect_1(B,D,G)),k3_rlvect_1(B,E,H)) ) ) ) ) ) ) ) ) ).
fof(t18_rlvect_4,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_rlvect_1(k1_rlvect_3(A,k9_rlvect_2(A,B,C,D)),B)
& r1_rlvect_1(k1_rlvect_3(A,k9_rlvect_2(A,B,C,D)),C)
& r1_rlvect_1(k1_rlvect_3(A,k9_rlvect_2(A,B,C,D)),D) ) ) ) ) ) ).
fof(t19_rlvect_4,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& l2_rlvect_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( r2_hidden(A,k3_rlsub_1(B,C,k1_rlvect_3(B,k9_rlvect_2(B,D,E,F))))
<=> ? [G] :
( m1_subset_1(G,k1_numbers)
& ? [H] :
( m1_subset_1(H,k1_numbers)
& ? [I] :
( m1_subset_1(I,k1_numbers)
& A = k4_rlvect_1(B,k4_rlvect_1(B,k4_rlvect_1(B,C,k3_rlvect_1(B,D,G)),k3_rlvect_1(B,E,H)),k3_rlvect_1(B,F,I)) ) ) ) ) ) ) ) ) ) ).
fof(t20_rlvect_4,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))
=> ( v1_rlvect_3(k8_rlvect_2(A,B,C),A)
=> ( B = C
| v1_rlvect_3(k8_rlvect_2(A,B,k6_rlvect_1(A,C,B)),A) ) ) ) ) ) ).
fof(t21_rlvect_4,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))
=> ( v1_rlvect_3(k8_rlvect_2(A,B,C),A)
=> ( B = C
| v1_rlvect_3(k8_rlvect_2(A,B,k4_rlvect_1(A,C,B)),A) ) ) ) ) ) ).
fof(t22_rlvect_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& l2_rlvect_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( v1_rlvect_3(k8_rlvect_2(B,C,D),B)
=> ( C = D
| A = np__0
| v1_rlvect_3(k8_rlvect_2(B,C,k3_rlvect_1(B,D,A)),B) ) ) ) ) ) ) ).
fof(t23_rlvect_4,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))
=> ( v1_rlvect_3(k8_rlvect_2(A,B,C),A)
=> ( B = C
| v1_rlvect_3(k8_rlvect_2(A,B,k5_rlvect_1(A,C)),A) ) ) ) ) ) ).
fof(t24_rlvect_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& l2_rlvect_1(C) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ~ ( A != B
& v1_rlvect_3(k8_rlvect_2(C,k3_rlvect_1(C,D,A),k3_rlvect_1(C,D,B)),C) ) ) ) ) ) ).
fof(t25_rlvect_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& l2_rlvect_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ~ ( A != np__1
& v1_rlvect_3(k8_rlvect_2(B,C,k3_rlvect_1(B,C,A)),B) ) ) ) ) ).
fof(t26_rlvect_4,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))
=> ( v1_rlvect_3(k9_rlvect_2(A,B,C,D),A)
=> ( B = D
| B = C
| D = C
| v1_rlvect_3(k9_rlvect_2(A,B,C,k6_rlvect_1(A,D,B)),A) ) ) ) ) ) ) ).
fof(t27_rlvect_4,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))
=> ( v1_rlvect_3(k9_rlvect_2(A,B,C,D),A)
=> ( B = D
| B = C
| D = C
| v1_rlvect_3(k9_rlvect_2(A,B,k6_rlvect_1(A,C,B),k6_rlvect_1(A,D,B)),A) ) ) ) ) ) ) ).
fof(t28_rlvect_4,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))
=> ( v1_rlvect_3(k9_rlvect_2(A,B,C,D),A)
=> ( B = D
| B = C
| D = C
| v1_rlvect_3(k9_rlvect_2(A,B,C,k4_rlvect_1(A,D,B)),A) ) ) ) ) ) ) ).
fof(t29_rlvect_4,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))
=> ( v1_rlvect_3(k9_rlvect_2(A,B,C,D),A)
=> ( B = D
| B = C
| D = C
| v1_rlvect_3(k9_rlvect_2(A,B,k4_rlvect_1(A,C,B),k4_rlvect_1(A,D,B)),A) ) ) ) ) ) ) ).
fof(t30_rlvect_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& l2_rlvect_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( v1_rlvect_3(k9_rlvect_2(B,C,D,E),B)
=> ( C = E
| C = D
| E = D
| A = np__0
| v1_rlvect_3(k9_rlvect_2(B,C,D,k3_rlvect_1(B,E,A)),B) ) ) ) ) ) ) ) ).
fof(t31_rlvect_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& l2_rlvect_1(C) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> ( v1_rlvect_3(k9_rlvect_2(C,D,E,F),C)
=> ( D = F
| D = E
| F = E
| A = np__0
| B = np__0
| v1_rlvect_3(k9_rlvect_2(C,D,k3_rlvect_1(C,E,A),k3_rlvect_1(C,F,B)),C) ) ) ) ) ) ) ) ) ).
fof(t32_rlvect_4,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))
=> ( v1_rlvect_3(k9_rlvect_2(A,B,C,D),A)
=> ( B = D
| B = C
| D = C
| v1_rlvect_3(k9_rlvect_2(A,B,C,k5_rlvect_1(A,D)),A) ) ) ) ) ) ) ).
fof(t33_rlvect_4,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))
=> ( v1_rlvect_3(k9_rlvect_2(A,B,C,D),A)
=> ( B = D
| B = C
| D = C
| v1_rlvect_3(k9_rlvect_2(A,B,k5_rlvect_1(A,C),k5_rlvect_1(A,D)),A) ) ) ) ) ) ) ).
fof(t34_rlvect_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& l2_rlvect_1(C) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ~ ( A != B
& v1_rlvect_3(k9_rlvect_2(C,k3_rlvect_1(C,D,A),k3_rlvect_1(C,D,B),E),C) ) ) ) ) ) ) ).
fof(t35_rlvect_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& l2_rlvect_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ~ ( A != np__1
& v1_rlvect_3(k9_rlvect_2(B,C,k3_rlvect_1(B,C,A),D),B) ) ) ) ) ) ).
fof(t36_rlvect_4,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_rlvect_1(k1_rlvect_3(A,k7_rlvect_2(A,C)),B)
=> ( B = k1_rlvect_1(A)
| k1_rlvect_3(A,k7_rlvect_2(A,B)) = k1_rlvect_3(A,k7_rlvect_2(A,C)) ) ) ) ) ) ).
fof(t37_rlvect_4,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))
=> ( ( v1_rlvect_3(k8_rlvect_2(A,B,C),A)
& r1_rlvect_1(k1_rlvect_3(A,k8_rlvect_2(A,D,E)),B)
& r1_rlvect_1(k1_rlvect_3(A,k8_rlvect_2(A,D,E)),C) )
=> ( B = C
| ( k1_rlvect_3(A,k8_rlvect_2(A,D,E)) = k1_rlvect_3(A,k8_rlvect_2(A,B,C))
& v1_rlvect_3(k8_rlvect_2(A,D,E),A)
& D != E ) ) ) ) ) ) ) ) ).
fof(t38_rlvect_4,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))
=> ~ ( B != k1_rlvect_1(A)
& ~ v1_rlvect_3(k8_rlvect_2(A,C,B),A)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> C != k3_rlvect_1(A,B,D) ) ) ) ) ) ).
fof(t39_rlvect_4,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))
=> ~ ( B != C
& v1_rlvect_3(k8_rlvect_2(A,B,C),A)
& ~ v1_rlvect_3(k9_rlvect_2(A,D,B,C),A)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [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(s1_rlvect_4,axiom,
( ( f3_s1_rlvect_4 != f4_s1_rlvect_4
& f3_s1_rlvect_4 != f5_s1_rlvect_4
& f4_s1_rlvect_4 != f5_s1_rlvect_4 )
=> ? [A] :
( v1_funct_1(A)
& v1_funct_2(A,f1_s1_rlvect_4,f2_s1_rlvect_4)
& m2_relset_1(A,f1_s1_rlvect_4,f2_s1_rlvect_4)
& k8_funct_2(f1_s1_rlvect_4,f2_s1_rlvect_4,A,f3_s1_rlvect_4) = f6_s1_rlvect_4
& k8_funct_2(f1_s1_rlvect_4,f2_s1_rlvect_4,A,f4_s1_rlvect_4) = f7_s1_rlvect_4
& k8_funct_2(f1_s1_rlvect_4,f2_s1_rlvect_4,A,f5_s1_rlvect_4) = f8_s1_rlvect_4
& ! [B] :
( m1_subset_1(B,f1_s1_rlvect_4)
=> ~ ( B != f3_s1_rlvect_4
& B != f4_s1_rlvect_4
& B != f5_s1_rlvect_4
& k8_funct_2(f1_s1_rlvect_4,f2_s1_rlvect_4,A,B) != f9_s1_rlvect_4(B) ) ) ) ) ).
fof(s2_rlvect_4,axiom,
? [A] :
( m2_rlvect_2(A,f1_s2_rlvect_4,k7_rlvect_2(f1_s2_rlvect_4,f2_s2_rlvect_4))
& k8_funct_2(u1_struct_0(f1_s2_rlvect_4),k1_numbers,A,f2_s2_rlvect_4) = f3_s2_rlvect_4 ) ).
fof(s3_rlvect_4,axiom,
( f2_s3_rlvect_4 != f3_s3_rlvect_4
=> ? [A] :
( m2_rlvect_2(A,f1_s3_rlvect_4,k8_rlvect_2(f1_s3_rlvect_4,f2_s3_rlvect_4,f3_s3_rlvect_4))
& k8_funct_2(u1_struct_0(f1_s3_rlvect_4),k1_numbers,A,f2_s3_rlvect_4) = f4_s3_rlvect_4
& k8_funct_2(u1_struct_0(f1_s3_rlvect_4),k1_numbers,A,f3_s3_rlvect_4) = f5_s3_rlvect_4 ) ) ).
fof(s4_rlvect_4,axiom,
( ( f2_s4_rlvect_4 != f3_s4_rlvect_4
& f2_s4_rlvect_4 != f4_s4_rlvect_4
& f3_s4_rlvect_4 != f4_s4_rlvect_4 )
=> ? [A] :
( m2_rlvect_2(A,f1_s4_rlvect_4,k9_rlvect_2(f1_s4_rlvect_4,f2_s4_rlvect_4,f3_s4_rlvect_4,f4_s4_rlvect_4))
& k8_funct_2(u1_struct_0(f1_s4_rlvect_4),k1_numbers,A,f2_s4_rlvect_4) = f5_s4_rlvect_4
& k8_funct_2(u1_struct_0(f1_s4_rlvect_4),k1_numbers,A,f3_s4_rlvect_4) = f6_s4_rlvect_4
& k8_funct_2(u1_struct_0(f1_s4_rlvect_4),k1_numbers,A,f4_s4_rlvect_4) = f7_s4_rlvect_4 ) ) ).
%------------------------------------------------------------------------------