TPTP Problem File: SEU383+1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SEU383+1 : TPTP v8.2.0. Released v3.3.0.
% Domain : Set theory
% Problem : MPTP bushy problem t8_waybel_7
% Version : [Urb07] axioms : Especial.
% English :
% Refs : [Ban01] Bancerek et al. (2001), On the Characterizations of Co
% : [Urb07] Urban (2006), Email to G. Sutcliffe
% Source : [Urb07]
% Names : bushy-t8_waybel_7 [Urb07]
% Status : Theorem
% Rating : 0.53 v8.2.0, 0.56 v8.1.0, 0.58 v7.5.0, 0.59 v7.4.0, 0.47 v7.3.0, 0.52 v7.2.0, 0.48 v7.1.0, 0.52 v7.0.0, 0.47 v6.4.0, 0.50 v6.3.0, 0.58 v6.2.0, 0.60 v6.1.0, 0.70 v6.0.0, 0.65 v5.5.0, 0.67 v5.4.0, 0.68 v5.3.0, 0.70 v5.2.0, 0.55 v5.1.0, 0.57 v5.0.0, 0.62 v4.1.0, 0.57 v4.0.0, 0.58 v3.7.0, 0.55 v3.5.0, 0.58 v3.4.0, 0.53 v3.3.0
% Syntax : Number of formulae : 45 ( 13 unt; 0 def)
% Number of atoms : 123 ( 5 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 109 ( 31 ~; 1 |; 37 &)
% ( 5 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 67 ( 54 !; 13 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% library, www.mizar.org
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ) ).
fof(cc1_finset_1,axiom,
! [A] :
( empty(A)
=> finite(A) ) ).
fof(cc1_yellow_3,axiom,
! [A] :
( rel_str(A)
=> ( empty_carrier(A)
=> v1_yellow_3(A) ) ) ).
fof(cc2_finset_1,axiom,
! [A] :
( finite(A)
=> ! [B] :
( element(B,powerset(A))
=> finite(B) ) ) ).
fof(cc2_yellow_3,axiom,
! [A] :
( rel_str(A)
=> ( ~ v1_yellow_3(A)
=> ~ empty_carrier(A) ) ) ).
fof(cc3_yellow_3,axiom,
! [A] :
( rel_str(A)
=> ( ( ~ empty_carrier(A)
& reflexive_relstr(A) )
=> ( ~ empty_carrier(A)
& ~ v1_yellow_3(A) ) ) ) ).
fof(d11_yellow_0,axiom,
! [A] :
( rel_str(A)
=> bottom_of_relstr(A) = join_on_relstr(A,empty_set) ) ).
fof(d20_waybel_0,axiom,
! [A] :
( rel_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( upper_relstr_subset(B,A)
<=> ! [C] :
( element(C,the_carrier(A))
=> ! [D] :
( element(D,the_carrier(A))
=> ( ( in(C,B)
& related(A,C,D) )
=> in(D,B) ) ) ) ) ) ) ).
fof(dt_k1_xboole_0,axiom,
$true ).
fof(dt_k1_yellow_0,axiom,
! [A,B] :
( rel_str(A)
=> element(join_on_relstr(A,B),the_carrier(A)) ) ).
fof(dt_k1_zfmisc_1,axiom,
$true ).
fof(dt_k3_yellow_0,axiom,
! [A] :
( rel_str(A)
=> element(bottom_of_relstr(A),the_carrier(A)) ) ).
fof(dt_l1_orders_2,axiom,
! [A] :
( rel_str(A)
=> one_sorted_str(A) ) ).
fof(dt_l1_struct_0,axiom,
$true ).
fof(dt_m1_subset_1,axiom,
$true ).
fof(dt_u1_struct_0,axiom,
$true ).
fof(existence_l1_orders_2,axiom,
? [A] : rel_str(A) ).
fof(existence_l1_struct_0,axiom,
? [A] : one_sorted_str(A) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A) ).
fof(fc1_struct_0,axiom,
! [A] :
( ( ~ empty_carrier(A)
& one_sorted_str(A) )
=> ~ empty(the_carrier(A)) ) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)) ).
fof(fc1_xboole_0,axiom,
empty(empty_set) ).
fof(rc10_waybel_0,axiom,
! [A] :
( ( ~ empty_carrier(A)
& reflexive_relstr(A)
& transitive_relstr(A)
& rel_str(A) )
=> ? [B] :
( element(B,powerset(the_carrier(A)))
& ~ empty(B)
& filtered_subset(B,A)
& upper_relstr_subset(B,A) ) ) ).
fof(rc1_finset_1,axiom,
? [A] :
( ~ empty(A)
& finite(A) ) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( element(B,powerset(A))
& ~ empty(B) ) ) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( element(B,powerset(A))
& empty(B) ) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A) ).
fof(rc3_finset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( element(B,powerset(A))
& ~ empty(B)
& finite(B) ) ) ).
fof(rc3_struct_0,axiom,
? [A] :
( one_sorted_str(A)
& ~ empty_carrier(A) ) ).
fof(rc4_finset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( element(B,powerset(A))
& ~ empty(B)
& finite(B) ) ) ).
fof(rc5_struct_0,axiom,
! [A] :
( ( ~ empty_carrier(A)
& one_sorted_str(A) )
=> ? [B] :
( element(B,powerset(the_carrier(A)))
& ~ empty(B) ) ) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ) ).
fof(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ) ).
fof(t44_yellow_0,axiom,
! [A] :
( ( ~ empty_carrier(A)
& antisymmetric_relstr(A)
& lower_bounded_relstr(A)
& rel_str(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> related(A,bottom_of_relstr(A),B) ) ) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( in(A,B)
& element(B,powerset(C)) )
=> element(A,C) ) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( in(A,B)
& element(B,powerset(C))
& empty(C) ) ).
fof(t5_tex_2,axiom,
! [A,B] :
( element(B,powerset(A))
=> ( proper_element(B,powerset(A))
<=> B != A ) ) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( in(A,B)
& empty(B) ) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(A)
& A != B
& empty(B) ) ).
fof(t8_waybel_7,conjecture,
! [A] :
( ( ~ empty_carrier(A)
& reflexive_relstr(A)
& transitive_relstr(A)
& antisymmetric_relstr(A)
& lower_bounded_relstr(A)
& rel_str(A) )
=> ! [B] :
( ( ~ empty(B)
& filtered_subset(B,A)
& upper_relstr_subset(B,A)
& element(B,powerset(the_carrier(A))) )
=> ( proper_element(B,powerset(the_carrier(A)))
<=> ~ in(bottom_of_relstr(A),B) ) ) ) ).
%------------------------------------------------------------------------------