SET007 Axioms: SET007+276.ax
%------------------------------------------------------------------------------
% File : SET007+276 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Groups, Rings, Left- and Right-Modules
% 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 : mod_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 43 ( 33 unt; 0 def)
% Number of atoms : 222 ( 19 equ)
% Maximal formula atoms : 23 ( 5 avg)
% Number of connectives : 203 ( 24 ~; 2 |; 135 &)
% ( 2 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 0 con; 1-4 aty)
% Number of variables : 38 ( 38 !; 0 ?)
% 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_mod_1,axiom,
$true ).
fof(t2_mod_1,axiom,
$true ).
fof(t3_mod_1,axiom,
$true ).
fof(t4_mod_1,axiom,
$true ).
fof(t5_mod_1,axiom,
$true ).
fof(t6_mod_1,axiom,
$true ).
fof(t7_mod_1,axiom,
$true ).
fof(t8_mod_1,axiom,
$true ).
fof(t9_mod_1,axiom,
$true ).
fof(t10_mod_1,axiom,
$true ).
fof(t11_mod_1,axiom,
$true ).
fof(t12_mod_1,axiom,
$true ).
fof(t13_mod_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& v6_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k1_group_1(A,B,k5_rlvect_1(A,k2_group_1(A))) = k5_rlvect_1(A,B) ) ) ).
fof(t14_mod_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v5_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k1_group_1(A,k5_rlvect_1(A,k2_group_1(A)),B) = k5_rlvect_1(A,B) ) ) ).
fof(t15_mod_1,axiom,
$true ).
fof(t16_mod_1,axiom,
$true ).
fof(t17_mod_1,axiom,
$true ).
fof(t18_mod_1,axiom,
$true ).
fof(t19_mod_1,axiom,
$true ).
fof(t20_mod_1,axiom,
$true ).
fof(t21_mod_1,axiom,
$true ).
fof(t22_mod_1,axiom,
$true ).
fof(t23_mod_1,axiom,
$true ).
fof(t24_mod_1,axiom,
$true ).
fof(t25_mod_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ( k6_vectsp_1(A,C,B,D) = k1_rlvect_1(C)
<=> ( B = k1_rlvect_1(A)
| D = k1_rlvect_1(C) ) ) ) ) ) ) ).
fof(t26_mod_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ( B != k1_rlvect_1(A)
=> k6_vectsp_1(A,C,k1_vectsp_2(A,B),k6_vectsp_1(A,C,B,D)) = D ) ) ) ) ) ).
fof(t27_mod_1,axiom,
$true ).
fof(t28_mod_1,axiom,
$true ).
fof(t29_mod_1,axiom,
$true ).
fof(t30_mod_1,axiom,
$true ).
fof(t31_mod_1,axiom,
$true ).
fof(t32_mod_1,axiom,
$true ).
fof(t33_mod_1,axiom,
$true ).
fof(t34_mod_1,axiom,
$true ).
fof(t35_mod_1,axiom,
$true ).
fof(t36_mod_1,axiom,
$true ).
fof(t37_mod_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v5_vectsp_2(B,A)
& l1_vectsp_2(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( k6_vectsp_2(A,B,k1_rlvect_1(A),D) = k1_rlvect_1(B)
& k6_vectsp_2(A,B,k5_rlvect_1(A,k2_group_1(A)),D) = k5_rlvect_1(B,D)
& k6_vectsp_2(A,B,C,k1_rlvect_1(B)) = k1_rlvect_1(B) ) ) ) ) ) ).
fof(t38_mod_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v5_vectsp_2(B,A)
& l1_vectsp_2(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( k5_rlvect_1(B,k6_vectsp_2(A,B,C,D)) = k6_vectsp_2(A,B,k5_rlvect_1(A,C),D)
& k6_rlvect_1(B,E,k6_vectsp_2(A,B,C,D)) = k2_rlvect_1(B,E,k6_vectsp_2(A,B,k5_rlvect_1(A,C),D)) ) ) ) ) ) ) ).
fof(t39_mod_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v5_vectsp_2(B,A)
& l1_vectsp_2(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> k6_vectsp_2(A,B,C,k5_rlvect_1(B,D)) = k5_rlvect_1(B,k6_vectsp_2(A,B,C,D)) ) ) ) ) ).
fof(t40_mod_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v5_vectsp_2(B,A)
& l1_vectsp_2(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> k6_vectsp_2(A,B,C,k6_rlvect_1(B,D,E)) = k6_rlvect_1(B,k6_vectsp_2(A,B,C,D),k6_vectsp_2(A,B,C,E)) ) ) ) ) ) ).
fof(t41_mod_1,axiom,
$true ).
fof(t42_mod_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v5_vectsp_2(C,A)
& l1_vectsp_2(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ( k6_vectsp_2(A,C,B,D) = k1_rlvect_1(C)
<=> ( B = k1_rlvect_1(A)
| D = k1_rlvect_1(C) ) ) ) ) ) ) ).
fof(t43_mod_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v5_vectsp_2(C,A)
& l1_vectsp_2(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ( B != k1_rlvect_1(A)
=> k6_vectsp_2(A,C,k1_vectsp_2(A,B),k6_vectsp_2(A,C,B,D)) = D ) ) ) ) ) ).
%------------------------------------------------------------------------------