TPTP Problem File: LAT341+2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : LAT341+2 : TPTP v8.2.0. Released v3.4.0.
% Domain : Lattice Theory
% Problem : Dual Concept Lattices T07
% Version : [Urb08] axioms : Especial.
% English :
% Refs : [Sch01] Schwarzweller (2001), A Characterization of Concept La
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : t7_conlat_2 [Urb08]
% Status : Unknown
% Rating : 1.00 v3.4.0
% Syntax : Number of formulae : 5479 (1322 unt; 0 def)
% Number of atoms : 28644 (3442 equ)
% Maximal formula atoms : 49 ( 5 avg)
% Number of connectives : 26750 (3585 ~; 195 |;12610 &)
% ( 986 <=>;9374 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 7 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 398 ( 396 usr; 1 prp; 0-4 aty)
% Number of functors : 732 ( 732 usr; 181 con; 0-9 aty)
% Number of variables : 13167 (12512 !; 655 ?)
% SPC : FOF_UNK_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.
% : Infinox says this has no finite (counter-) models.
%------------------------------------------------------------------------------
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+5.ax').
include('Axioms/SET007/SET007+6.ax').
include('Axioms/SET007/SET007+7.ax').
include('Axioms/SET007/SET007+8.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+18.ax').
include('Axioms/SET007/SET007+19.ax').
include('Axioms/SET007/SET007+20.ax').
include('Axioms/SET007/SET007+22.ax').
include('Axioms/SET007/SET007+24.ax').
include('Axioms/SET007/SET007+25.ax').
include('Axioms/SET007/SET007+26.ax').
include('Axioms/SET007/SET007+31.ax').
include('Axioms/SET007/SET007+32.ax').
include('Axioms/SET007/SET007+35.ax').
include('Axioms/SET007/SET007+51.ax').
include('Axioms/SET007/SET007+54.ax').
include('Axioms/SET007/SET007+55.ax').
include('Axioms/SET007/SET007+59.ax').
include('Axioms/SET007/SET007+60.ax').
include('Axioms/SET007/SET007+64.ax').
include('Axioms/SET007/SET007+80.ax').
include('Axioms/SET007/SET007+200.ax').
include('Axioms/SET007/SET007+205.ax').
include('Axioms/SET007/SET007+206.ax').
include('Axioms/SET007/SET007+218.ax').
include('Axioms/SET007/SET007+242.ax').
include('Axioms/SET007/SET007+253.ax').
include('Axioms/SET007/SET007+295.ax').
include('Axioms/SET007/SET007+335.ax').
include('Axioms/SET007/SET007+375.ax').
include('Axioms/SET007/SET007+432.ax').
include('Axioms/SET007/SET007+480.ax').
include('Axioms/SET007/SET007+481.ax').
include('Axioms/SET007/SET007+483.ax').
include('Axioms/SET007/SET007+484.ax').
include('Axioms/SET007/SET007+485.ax').
include('Axioms/SET007/SET007+567.ax').
include('Axioms/SET007/SET007+603.ax').
%------------------------------------------------------------------------------
fof(fraenkel_a_2_0_conlat_2,axiom,
! [A,B,C] :
( ( ~ v3_conlat_1(B)
& l2_conlat_1(B)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_conlat_1(B)))) )
=> ( r2_hidden(A,a_2_0_conlat_2(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_conlat_1(B)))
& A = k8_funct_2(k1_zfmisc_1(u1_conlat_1(B)),k1_zfmisc_1(u2_conlat_1(B)),k1_conlat_1(B),D)
& r2_hidden(D,C) ) ) ) ).
fof(fraenkel_a_2_10_conlat_2,axiom,
! [A,B,C] :
( ( ~ v3_conlat_1(B)
& l2_conlat_1(B)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k11_conlat_1(B)))) )
=> ( r2_hidden(A,a_2_10_conlat_2(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_conlat_1(B)))
& A = k8_funct_2(k1_zfmisc_1(u1_conlat_1(B)),k1_zfmisc_1(u2_conlat_1(B)),k1_conlat_1(B),D)
& r2_hidden(D,a_2_2_conlat_2(B,C)) ) ) ) ).
fof(fraenkel_a_2_2_conlat_2,axiom,
! [A,B,C] :
( ( ~ v3_conlat_1(B)
& l2_conlat_1(B)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k11_conlat_1(B)))) )
=> ( r2_hidden(A,a_2_2_conlat_2(B,C))
<=> ? [D,E] :
( m1_subset_1(D,k1_zfmisc_1(u1_conlat_1(B)))
& m1_subset_1(E,k1_zfmisc_1(u2_conlat_1(B)))
& A = u4_conlat_1(B,g3_conlat_1(B,D,E))
& r2_hidden(g3_conlat_1(B,D,E),C) ) ) ) ).
fof(fraenkel_a_2_3_conlat_2,axiom,
! [A,B,C] :
( ( ~ v3_conlat_1(B)
& l2_conlat_1(B)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k11_conlat_1(B)))) )
=> ( r2_hidden(A,a_2_3_conlat_2(B,C))
<=> ? [D,E] :
( m1_subset_1(D,k1_zfmisc_1(u1_conlat_1(B)))
& m1_subset_1(E,k1_zfmisc_1(u2_conlat_1(B)))
& A = u5_conlat_1(B,g3_conlat_1(B,D,E))
& r2_hidden(g3_conlat_1(B,D,E),C) ) ) ) ).
fof(dt_k1_conlat_2,axiom,
! [A,B] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A)
& v6_conlat_1(B,A)
& ~ v7_conlat_1(B,A)
& v9_conlat_1(B,A)
& l3_conlat_1(B,A) )
=> m1_subset_1(k1_conlat_2(A,B),u1_struct_0(k11_conlat_1(A))) ) ).
fof(dt_k2_conlat_2,axiom,
! [A,B] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) )
=> ( ~ v7_conlat_1(k2_conlat_2(A,B),A)
& v9_conlat_1(k2_conlat_2(A,B),A)
& l3_conlat_1(k2_conlat_2(A,B),A) ) ) ).
fof(dt_k3_conlat_2,axiom,
! [A,B] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) )
=> ( ~ v7_conlat_1(k3_conlat_2(A,B),A)
& v9_conlat_1(k3_conlat_2(A,B),A)
& l3_conlat_1(k3_conlat_2(A,B),A) ) ) ).
fof(dt_k4_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( v1_funct_1(k4_conlat_2(A))
& v1_funct_2(k4_conlat_2(A),u1_conlat_1(A),u1_struct_0(k11_conlat_1(A)))
& m2_relset_1(k4_conlat_2(A),u1_conlat_1(A),u1_struct_0(k11_conlat_1(A))) ) ) ).
fof(dt_k5_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( v1_funct_1(k5_conlat_2(A))
& v1_funct_2(k5_conlat_2(A),u2_conlat_1(A),u1_struct_0(k11_conlat_1(A)))
& m2_relset_1(k5_conlat_2(A),u2_conlat_1(A),u1_struct_0(k11_conlat_1(A))) ) ) ).
fof(dt_k6_conlat_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ( ~ v3_conlat_1(k6_conlat_2(A))
& v4_conlat_1(k6_conlat_2(A))
& l2_conlat_1(k6_conlat_2(A)) ) ) ).
fof(dt_k7_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( ~ v3_conlat_1(k7_conlat_2(A))
& v4_conlat_1(k7_conlat_2(A))
& l2_conlat_1(k7_conlat_2(A)) ) ) ).
fof(dt_k8_conlat_2,axiom,
! [A,B] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A)
& l3_conlat_1(B,A) )
=> ( v6_conlat_1(k8_conlat_2(A,B),k7_conlat_2(A))
& l3_conlat_1(k8_conlat_2(A,B),k7_conlat_2(A)) ) ) ).
fof(dt_k9_conlat_2,axiom,
! [A,B] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A)
& ~ v7_conlat_1(B,A)
& v9_conlat_1(B,A)
& l3_conlat_1(B,A) )
=> ( v6_conlat_1(k9_conlat_2(A,B),k7_conlat_2(A))
& ~ v7_conlat_1(k9_conlat_2(A,B),k7_conlat_2(A))
& v9_conlat_1(k9_conlat_2(A,B),k7_conlat_2(A))
& l3_conlat_1(k9_conlat_2(A,B),k7_conlat_2(A)) ) ) ).
fof(redefinition_k9_conlat_2,axiom,
! [A,B] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A)
& ~ v7_conlat_1(B,A)
& v9_conlat_1(B,A)
& l3_conlat_1(B,A) )
=> k9_conlat_2(A,B) = k8_conlat_2(A,B) ) ).
fof(dt_k10_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> m1_lattice4(k10_conlat_2(A),k1_lattice2(k11_conlat_1(A)),k11_conlat_1(k7_conlat_2(A))) ) ).
fof(d1_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( ( v6_conlat_1(B,A)
& ~ v7_conlat_1(B,A)
& v9_conlat_1(B,A)
& l3_conlat_1(B,A) )
=> k1_conlat_2(A,B) = B ) ) ).
fof(fc1_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( ~ v3_struct_0(k11_conlat_1(A))
& v3_lattices(k11_conlat_1(A))
& v4_lattices(k11_conlat_1(A))
& v5_lattices(k11_conlat_1(A))
& v6_lattices(k11_conlat_1(A))
& v7_lattices(k11_conlat_1(A))
& v8_lattices(k11_conlat_1(A))
& v9_lattices(k11_conlat_1(A))
& v10_lattices(k11_conlat_1(A))
& v13_lattices(k11_conlat_1(A))
& v14_lattices(k11_conlat_1(A))
& v15_lattices(k11_conlat_1(A))
& v4_lattice3(k11_conlat_1(A)) ) ) ).
fof(t1_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( k5_lattices(k11_conlat_1(A)) = k6_conlat_1(A)
& k6_lattices(k11_conlat_1(A)) = k5_conlat_1(A) ) ) ).
fof(t2_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_conlat_1(A)))) )
=> k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k5_setfam_1(u1_conlat_1(A),B)) = k1_setfam_1(a_2_0_conlat_2(A,B)) ) ) ).
fof(t3_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u2_conlat_1(A)))) )
=> k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k5_setfam_1(u2_conlat_1(A),B)) = k1_setfam_1(a_2_1_conlat_2(A,B)) ) ) ).
fof(t4_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A))))
=> ( ~ v7_conlat_1(k16_lattice3(k11_conlat_1(A),B),A)
& v9_conlat_1(k16_lattice3(k11_conlat_1(A),B),A)
& l3_conlat_1(k16_lattice3(k11_conlat_1(A),B),A)
& ~ v7_conlat_1(k15_lattice3(k11_conlat_1(A),B),A)
& v9_conlat_1(k15_lattice3(k11_conlat_1(A),B),A)
& l3_conlat_1(k15_lattice3(k11_conlat_1(A),B),A) ) ) ) ).
fof(d2_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A))))
=> k2_conlat_2(A,B) = k16_lattice3(k11_conlat_1(A),B) ) ) ).
fof(d3_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A))))
=> k3_conlat_2(A,B) = k15_lattice3(k11_conlat_1(A),B) ) ) ).
fof(t5_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( k3_conlat_2(A,k1_pre_topc(k11_conlat_1(A))) = k6_conlat_1(A)
& k2_conlat_2(A,k1_pre_topc(k11_conlat_1(A))) = k5_conlat_1(A) ) ) ).
fof(t6_conlat_2,axiom,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ( k3_conlat_2(A,k2_subset_1(u1_struct_0(k11_conlat_1(A)))) = k5_conlat_1(A)
& k2_conlat_2(A,k2_subset_1(u1_struct_0(k11_conlat_1(A)))) = k6_conlat_1(A) ) ) ).
fof(t7_conlat_2,conjecture,
! [A] :
( ( ~ v3_conlat_1(A)
& l2_conlat_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) )
=> ( u4_conlat_1(A,k3_conlat_2(A,B)) = k1_funct_1(k2_conlat_1(A),k1_funct_1(k1_conlat_1(A),k3_tarski(a_2_2_conlat_2(A,B))))
& u5_conlat_1(A,k3_conlat_2(A,B)) = k1_setfam_1(a_2_3_conlat_2(A,B)) ) ) ) ).
%------------------------------------------------------------------------------