TPTP Problem File: SEU375+1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SEU375+1 : TPTP v8.2.0. Released v3.3.0.
% Domain : Set theory
% Problem : MPTP bushy problem t21_yellow_6
% 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-t21_yellow_6 [Urb07]
% Status : Theorem
% Rating : 0.25 v8.2.0, 0.22 v8.1.0, 0.11 v7.5.0, 0.12 v7.4.0, 0.13 v7.3.0, 0.14 v7.2.0, 0.10 v7.1.0, 0.13 v7.0.0, 0.10 v6.4.0, 0.15 v6.3.0, 0.17 v6.2.0, 0.20 v6.1.0, 0.23 v6.0.0, 0.17 v5.5.0, 0.19 v5.4.0, 0.25 v5.3.0, 0.30 v5.2.0, 0.10 v5.1.0, 0.14 v5.0.0, 0.21 v4.1.0, 0.26 v4.0.0, 0.29 v3.7.0, 0.25 v3.5.0, 0.26 v3.3.0
% Syntax : Number of formulae : 40 ( 7 unt; 0 def)
% Number of atoms : 119 ( 6 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 91 ( 12 ~; 1 |; 37 &)
% ( 1 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 61 ( 46 !; 15 ?)
% 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_funct_1,axiom,
! [A] :
( empty(A)
=> function(A) ) ).
fof(cc1_relat_1,axiom,
! [A] :
( empty(A)
=> relation(A) ) ).
fof(cc1_yellow_3,axiom,
! [A] :
( rel_str(A)
=> ( empty_carrier(A)
=> v1_yellow_3(A) ) ) ).
fof(cc2_funct_1,axiom,
! [A] :
( ( relation(A)
& empty(A)
& function(A) )
=> ( relation(A)
& function(A)
& one_to_one(A) ) ) ).
fof(cc2_yellow_3,axiom,
! [A] :
( rel_str(A)
=> ( ~ v1_yellow_3(A)
=> ~ empty_carrier(A) ) ) ).
fof(d9_yellow_6,axiom,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( net_str(B,A)
=> ! [C] :
( subnetstr(C,A,B)
=> ( full_subnetstr(C,A,B)
<=> ( full_subrelstr(C,B)
& subrelstr(C,B) ) ) ) ) ) ).
fof(dt_k1_xboole_0,axiom,
$true ).
fof(dt_l1_orders_2,axiom,
! [A] :
( rel_str(A)
=> one_sorted_str(A) ) ).
fof(dt_l1_struct_0,axiom,
$true ).
fof(dt_l1_waybel_0,axiom,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( net_str(B,A)
=> rel_str(B) ) ) ).
fof(dt_m1_subset_1,axiom,
$true ).
fof(dt_m1_yellow_0,axiom,
! [A] :
( rel_str(A)
=> ! [B] :
( subrelstr(B,A)
=> rel_str(B) ) ) ).
fof(dt_m1_yellow_6,axiom,
! [A,B] :
( ( one_sorted_str(A)
& net_str(B,A) )
=> ! [C] :
( subnetstr(C,A,B)
=> net_str(C,A) ) ) ).
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_l1_waybel_0,axiom,
! [A] :
( one_sorted_str(A)
=> ? [B] : net_str(B,A) ) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A) ).
fof(existence_m1_yellow_0,axiom,
! [A] :
( rel_str(A)
=> ? [B] : subrelstr(B,A) ) ).
fof(existence_m1_yellow_6,axiom,
! [A,B] :
( ( one_sorted_str(A)
& net_str(B,A) )
=> ? [C] : subnetstr(C,A,B) ) ).
fof(fc12_relat_1,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ) ).
fof(fc1_struct_0,axiom,
! [A] :
( ( ~ empty_carrier(A)
& one_sorted_str(A) )
=> ~ empty(the_carrier(A)) ) ).
fof(fc4_relat_1,axiom,
( empty(empty_set)
& relation(empty_set) ) ).
fof(rc1_funct_1,axiom,
? [A] :
( relation(A)
& function(A) ) ).
fof(rc1_pboole,axiom,
? [A] :
( relation(A)
& relation_empty_yielding(A)
& function(A) ) ).
fof(rc1_relat_1,axiom,
? [A] :
( empty(A)
& relation(A) ) ).
fof(rc2_funct_1,axiom,
? [A] :
( relation(A)
& empty(A)
& function(A) ) ).
fof(rc2_relat_1,axiom,
? [A] :
( ~ empty(A)
& relation(A) ) ).
fof(rc3_funct_1,axiom,
? [A] :
( relation(A)
& function(A)
& one_to_one(A) ) ).
fof(rc3_relat_1,axiom,
? [A] :
( relation(A)
& relation_empty_yielding(A) ) ).
fof(rc3_struct_0,axiom,
? [A] :
( one_sorted_str(A)
& ~ empty_carrier(A) ) ).
fof(rc4_funct_1,axiom,
? [A] :
( relation(A)
& relation_empty_yielding(A)
& function(A) ) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ) ).
fof(t21_yellow_6,conjecture,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( ( ~ empty_carrier(B)
& net_str(B,A) )
=> ! [C] :
( ( ~ empty_carrier(C)
& full_subnetstr(C,A,B)
& subnetstr(C,A,B) )
=> ! [D] :
( element(D,the_carrier(B))
=> ! [E] :
( element(E,the_carrier(B))
=> ! [F] :
( element(F,the_carrier(C))
=> ! [G] :
( element(G,the_carrier(C))
=> ( ( D = F
& E = G
& related(B,D,E) )
=> related(C,F,G) ) ) ) ) ) ) ) ) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ) ).
fof(t61_yellow_0,axiom,
! [A] :
( rel_str(A)
=> ! [B] :
( ( full_subrelstr(B,A)
& subrelstr(B,A) )
=> ! [C] :
( element(C,the_carrier(A))
=> ! [D] :
( element(D,the_carrier(A))
=> ! [E] :
( element(E,the_carrier(B))
=> ! [F] :
( element(F,the_carrier(B))
=> ( ( E = C
& F = D
& related(A,C,D)
& in(E,the_carrier(B))
& in(F,the_carrier(B)) )
=> related(B,E,F) ) ) ) ) ) ) ) ).
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) ) ).
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