TPTP Problem File: GRP618+2.p
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%------------------------------------------------------------------------------
% File : GRP618+2 : TPTP v8.2.0. Released v3.4.0.
% Domain : Group Theory
% Problem : On the Group of Inner Automorphisms T01
% Version : [Urb08] axioms : Especial.
% English :
% Refs : [Kor96] Kornilowicz (1996), On the Group of Inner Automorphism
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : t1_autgroup [Urb08]
% Status : Theorem
% Rating : 0.67 v8.2.0, 0.69 v8.1.0, 0.78 v7.5.0, 0.81 v7.4.0, 0.73 v7.3.0, 0.76 v7.2.0, 0.72 v7.1.0, 0.65 v7.0.0, 0.77 v6.4.0, 0.73 v6.3.0, 0.71 v6.2.0, 0.84 v6.1.0, 0.87 v6.0.0, 0.83 v5.5.0, 0.85 v5.4.0, 0.86 v5.3.0, 0.89 v5.2.0, 0.80 v5.1.0, 0.81 v5.0.0, 0.79 v4.1.0, 0.83 v3.7.0, 0.90 v3.5.0, 0.95 v3.4.0
% Syntax : Number of formulae : 3809 ( 965 unt; 0 def)
% Number of atoms : 19251 (2727 equ)
% Maximal formula atoms : 49 ( 5 avg)
% Number of connectives : 17575 (2133 ~; 132 |;8478 &)
% ( 623 <=>;6209 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 246 ( 244 usr; 1 prp; 0-4 aty)
% Number of functors : 625 ( 625 usr; 245 con; 0-8 aty)
% Number of variables : 8407 (7953 !; 454 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : Bushy version: includes all articles that contribute axioms to the
% Normal version.
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : The problem encoding is based on set theory.
%------------------------------------------------------------------------------
include('Axioms/SET007/SET007+0.ax').
include('Axioms/SET007/SET007+1.ax').
include('Axioms/SET007/SET007+2.ax').
include('Axioms/SET007/SET007+3.ax').
include('Axioms/SET007/SET007+6.ax').
include('Axioms/SET007/SET007+7.ax').
include('Axioms/SET007/SET007+9.ax').
include('Axioms/SET007/SET007+10.ax').
include('Axioms/SET007/SET007+11.ax').
include('Axioms/SET007/SET007+13.ax').
include('Axioms/SET007/SET007+14.ax').
include('Axioms/SET007/SET007+16.ax').
include('Axioms/SET007/SET007+17.ax').
include('Axioms/SET007/SET007+20.ax').
include('Axioms/SET007/SET007+23.ax').
include('Axioms/SET007/SET007+24.ax').
include('Axioms/SET007/SET007+26.ax').
include('Axioms/SET007/SET007+31.ax').
include('Axioms/SET007/SET007+32.ax').
include('Axioms/SET007/SET007+34.ax').
include('Axioms/SET007/SET007+35.ax').
include('Axioms/SET007/SET007+40.ax').
include('Axioms/SET007/SET007+48.ax').
include('Axioms/SET007/SET007+54.ax').
include('Axioms/SET007/SET007+55.ax').
include('Axioms/SET007/SET007+117.ax').
include('Axioms/SET007/SET007+200.ax').
include('Axioms/SET007/SET007+210.ax').
include('Axioms/SET007/SET007+212.ax').
include('Axioms/SET007/SET007+213.ax').
include('Axioms/SET007/SET007+223.ax').
include('Axioms/SET007/SET007+246.ax').
include('Axioms/SET007/SET007+252.ax').
include('Axioms/SET007/SET007+298.ax').
include('Axioms/SET007/SET007+312.ax').
include('Axioms/SET007/SET007+338.ax').
%------------------------------------------------------------------------------
fof(dt_k1_autgroup,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_group_1(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> m1_fraenkel(k1_autgroup(A),u1_struct_0(A),u1_struct_0(A)) ) ).
fof(dt_k2_autgroup,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_group_1(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ( v1_funct_1(k2_autgroup(A))
& v1_funct_2(k2_autgroup(A),k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A))
& m2_relset_1(k2_autgroup(A),k2_zfmisc_1(k1_autgroup(A),k1_autgroup(A)),k1_autgroup(A)) ) ) ).
fof(dt_k3_autgroup,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_group_1(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ( ~ v3_struct_0(k3_autgroup(A))
& v1_group_1(k3_autgroup(A))
& v3_group_1(k3_autgroup(A))
& v4_group_1(k3_autgroup(A))
& l1_group_1(k3_autgroup(A)) ) ) ).
fof(dt_k4_autgroup,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_group_1(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> m1_fraenkel(k4_autgroup(A),u1_struct_0(A),u1_struct_0(A)) ) ).
fof(dt_k5_autgroup,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_group_1(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ( v1_group_1(k5_autgroup(A))
& v1_group_3(k5_autgroup(A),k3_autgroup(A))
& m1_group_2(k5_autgroup(A),k3_autgroup(A)) ) ) ).
fof(dt_k6_autgroup,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v1_group_1(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m2_fraenkel(k6_autgroup(A,B),u1_struct_0(A),u1_struct_0(A),k4_autgroup(A)) ) ).
fof(l1_autgroup,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_group_1(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( m1_subset_1(D,u1_struct_0(B))
=> r1_rlvect_1(B,k2_group_3(A,D,C)) ) ) )
=> v1_group_3(B,A) ) ) ) ).
fof(l2_autgroup,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_group_1(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ( v1_group_3(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( m1_subset_1(D,u1_struct_0(B))
=> r1_rlvect_1(B,k2_group_3(A,D,C)) ) ) ) ) ) ) ).
fof(t1_autgroup,conjecture,
! [A] :
( ( ~ v3_struct_0(A)
& v1_group_1(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( m1_subset_1(D,u1_struct_0(B))
=> r1_rlvect_1(B,k2_group_3(A,D,C)) ) ) )
<=> v1_group_3(B,A) ) ) ) ).
%------------------------------------------------------------------------------