TPTP Problem File: LAT353+3.p
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%------------------------------------------------------------------------------
% File : LAT353+3 : TPTP v8.2.0. Released v3.4.0.
% Domain : Lattice Theory
% Problem : Duality Based on Galois Connection - Part I T03
% Version : [Urb08] axioms : Especial.
% English :
% Refs : [Ban01] Bancerek (2001), Duality Based on the Galois Connectio
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : t3_waybel34 [Urb08]
% Status : Theorem
% Rating : 1.00 v3.4.0
% Syntax : Number of formulae : 18913 (2907 unt; 0 def)
% Number of atoms : 136419 (13023 equ)
% Maximal formula atoms : 123 ( 7 avg)
% Number of connectives : 134670 (17164 ~; 600 |;70757 &)
% (3678 <=>;42471 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 8 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 1220 (1218 usr; 2 prp; 0-6 aty)
% Number of functors : 2901 (2901 usr; 731 con; 0-10 aty)
% Number of variables : 50101 (47482 !;2619 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : Chainy small version: includes all preceding MML articles that
% are included in any Bushy 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+4.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+15.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+21.ax').
include('Axioms/SET007/SET007+22.ax').
include('Axioms/SET007/SET007+23.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+33.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+50.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+61.ax').
include('Axioms/SET007/SET007+64.ax').
include('Axioms/SET007/SET007+66.ax').
include('Axioms/SET007/SET007+67.ax').
include('Axioms/SET007/SET007+68.ax').
include('Axioms/SET007/SET007+71.ax').
include('Axioms/SET007/SET007+75.ax').
include('Axioms/SET007/SET007+76.ax').
include('Axioms/SET007/SET007+77.ax').
include('Axioms/SET007/SET007+79.ax').
include('Axioms/SET007/SET007+80.ax').
include('Axioms/SET007/SET007+86.ax').
include('Axioms/SET007/SET007+91.ax').
include('Axioms/SET007/SET007+117.ax').
include('Axioms/SET007/SET007+125.ax').
include('Axioms/SET007/SET007+126.ax').
include('Axioms/SET007/SET007+148.ax').
include('Axioms/SET007/SET007+159.ax').
include('Axioms/SET007/SET007+165.ax').
include('Axioms/SET007/SET007+170.ax').
include('Axioms/SET007/SET007+182.ax').
include('Axioms/SET007/SET007+186.ax').
include('Axioms/SET007/SET007+188.ax').
include('Axioms/SET007/SET007+190.ax').
include('Axioms/SET007/SET007+200.ax').
include('Axioms/SET007/SET007+202.ax').
include('Axioms/SET007/SET007+205.ax').
include('Axioms/SET007/SET007+206.ax').
include('Axioms/SET007/SET007+207.ax').
include('Axioms/SET007/SET007+209.ax').
include('Axioms/SET007/SET007+210.ax').
include('Axioms/SET007/SET007+211.ax').
include('Axioms/SET007/SET007+212.ax').
include('Axioms/SET007/SET007+213.ax').
include('Axioms/SET007/SET007+217.ax').
include('Axioms/SET007/SET007+218.ax').
include('Axioms/SET007/SET007+223.ax').
include('Axioms/SET007/SET007+224.ax').
include('Axioms/SET007/SET007+225.ax').
include('Axioms/SET007/SET007+227.ax').
include('Axioms/SET007/SET007+237.ax').
include('Axioms/SET007/SET007+241.ax').
include('Axioms/SET007/SET007+242.ax').
include('Axioms/SET007/SET007+246.ax').
include('Axioms/SET007/SET007+247.ax').
include('Axioms/SET007/SET007+248.ax').
include('Axioms/SET007/SET007+252.ax').
include('Axioms/SET007/SET007+253.ax').
include('Axioms/SET007/SET007+255.ax').
include('Axioms/SET007/SET007+256.ax').
include('Axioms/SET007/SET007+276.ax').
include('Axioms/SET007/SET007+278.ax').
include('Axioms/SET007/SET007+279.ax').
include('Axioms/SET007/SET007+280.ax').
include('Axioms/SET007/SET007+281.ax').
include('Axioms/SET007/SET007+293.ax').
include('Axioms/SET007/SET007+295.ax').
include('Axioms/SET007/SET007+297.ax').
include('Axioms/SET007/SET007+298.ax').
include('Axioms/SET007/SET007+299.ax').
include('Axioms/SET007/SET007+301.ax').
include('Axioms/SET007/SET007+308.ax').
include('Axioms/SET007/SET007+309.ax').
include('Axioms/SET007/SET007+311.ax').
include('Axioms/SET007/SET007+312.ax').
include('Axioms/SET007/SET007+317.ax').
include('Axioms/SET007/SET007+321.ax').
include('Axioms/SET007/SET007+322.ax').
include('Axioms/SET007/SET007+327.ax').
include('Axioms/SET007/SET007+335.ax').
include('Axioms/SET007/SET007+338.ax').
include('Axioms/SET007/SET007+339.ax').
include('Axioms/SET007/SET007+354.ax').
include('Axioms/SET007/SET007+363.ax').
include('Axioms/SET007/SET007+365.ax').
include('Axioms/SET007/SET007+370.ax').
include('Axioms/SET007/SET007+375.ax').
include('Axioms/SET007/SET007+377.ax').
include('Axioms/SET007/SET007+384.ax').
include('Axioms/SET007/SET007+387.ax').
include('Axioms/SET007/SET007+388.ax').
include('Axioms/SET007/SET007+393.ax').
include('Axioms/SET007/SET007+394.ax').
include('Axioms/SET007/SET007+395.ax').
include('Axioms/SET007/SET007+396.ax').
include('Axioms/SET007/SET007+399.ax').
include('Axioms/SET007/SET007+401.ax').
include('Axioms/SET007/SET007+405.ax').
include('Axioms/SET007/SET007+406.ax').
include('Axioms/SET007/SET007+407.ax').
include('Axioms/SET007/SET007+411.ax').
include('Axioms/SET007/SET007+412.ax').
include('Axioms/SET007/SET007+426.ax').
include('Axioms/SET007/SET007+427.ax').
include('Axioms/SET007/SET007+432.ax').
include('Axioms/SET007/SET007+433.ax').
include('Axioms/SET007/SET007+438.ax').
include('Axioms/SET007/SET007+441.ax').
include('Axioms/SET007/SET007+445.ax').
include('Axioms/SET007/SET007+448.ax').
include('Axioms/SET007/SET007+449.ax').
include('Axioms/SET007/SET007+455.ax').
include('Axioms/SET007/SET007+463.ax').
include('Axioms/SET007/SET007+464.ax').
include('Axioms/SET007/SET007+466.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+486.ax').
include('Axioms/SET007/SET007+487.ax').
include('Axioms/SET007/SET007+488.ax').
include('Axioms/SET007/SET007+489.ax').
include('Axioms/SET007/SET007+490.ax').
include('Axioms/SET007/SET007+492.ax').
include('Axioms/SET007/SET007+493.ax').
include('Axioms/SET007/SET007+494.ax').
include('Axioms/SET007/SET007+495.ax').
include('Axioms/SET007/SET007+496.ax').
include('Axioms/SET007/SET007+497.ax').
include('Axioms/SET007/SET007+498.ax').
include('Axioms/SET007/SET007+500.ax').
include('Axioms/SET007/SET007+503.ax').
include('Axioms/SET007/SET007+505.ax').
include('Axioms/SET007/SET007+506.ax').
include('Axioms/SET007/SET007+509.ax').
include('Axioms/SET007/SET007+513.ax').
include('Axioms/SET007/SET007+514.ax').
include('Axioms/SET007/SET007+517.ax').
include('Axioms/SET007/SET007+520.ax').
include('Axioms/SET007/SET007+525.ax').
include('Axioms/SET007/SET007+527.ax').
include('Axioms/SET007/SET007+530.ax').
include('Axioms/SET007/SET007+537.ax').
include('Axioms/SET007/SET007+538.ax').
include('Axioms/SET007/SET007+542.ax').
include('Axioms/SET007/SET007+544.ax').
include('Axioms/SET007/SET007+545.ax').
include('Axioms/SET007/SET007+558.ax').
include('Axioms/SET007/SET007+559.ax').
include('Axioms/SET007/SET007+560.ax').
include('Axioms/SET007/SET007+561.ax').
include('Axioms/SET007/SET007+567.ax').
include('Axioms/SET007/SET007+572.ax').
include('Axioms/SET007/SET007+573.ax').
include('Axioms/SET007/SET007+586.ax').
include('Axioms/SET007/SET007+603.ax').
include('Axioms/SET007/SET007+620.ax').
include('Axioms/SET007/SET007+636.ax').
include('Axioms/SET007/SET007+637.ax').
include('Axioms/SET007/SET007+654.ax').
include('Axioms/SET007/SET007+655.ax').
include('Axioms/SET007/SET007+682.ax').
include('Axioms/SET007/SET007+695.ax').
include('Axioms/SET007/SET007+696.ax').
include('Axioms/SET007/SET007+697.ax').
include('Axioms/SET007/SET007+698.ax').
%------------------------------------------------------------------------------
fof(dt_k1_waybel34,axiom,
! [A,B,C] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_funct_1(k1_waybel34(A,B,C))
& v1_funct_2(k1_waybel34(A,B,C),u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(k1_waybel34(A,B,C),u1_struct_0(B),u1_struct_0(A)) ) ) ).
fof(dt_k2_waybel34,axiom,
! [A,B,C] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m1_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( v1_funct_1(k2_waybel34(A,B,C))
& v1_funct_2(k2_waybel34(A,B,C),u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(k2_waybel34(A,B,C),u1_struct_0(A),u1_struct_0(B)) ) ) ).
fof(dt_k3_waybel34,axiom,
! [A,B,C] :
( ( l1_orders_2(A)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_funct_1(k3_waybel34(A,B,C))
& v1_funct_2(k3_waybel34(A,B,C),u1_struct_0(k7_lattice3(A)),u1_struct_0(k7_lattice3(B)))
& m2_relset_1(k3_waybel34(A,B,C),u1_struct_0(k7_lattice3(A)),u1_struct_0(k7_lattice3(B))) ) ) ).
fof(dt_k4_waybel34,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( ~ v3_struct_0(k4_waybel34(A))
& v2_altcat_1(k4_waybel34(A))
& v6_altcat_1(k4_waybel34(A))
& v11_altcat_1(k4_waybel34(A))
& v12_altcat_1(k4_waybel34(A))
& v2_yellow21(k4_waybel34(A))
& l2_altcat_1(k4_waybel34(A)) ) ) ).
fof(dt_k5_waybel34,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( ~ v3_struct_0(k5_waybel34(A))
& v2_altcat_1(k5_waybel34(A))
& v6_altcat_1(k5_waybel34(A))
& v11_altcat_1(k5_waybel34(A))
& v12_altcat_1(k5_waybel34(A))
& v2_yellow21(k5_waybel34(A))
& l2_altcat_1(k5_waybel34(A)) ) ) ).
fof(dt_k6_waybel34,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ( v9_functor0(k6_waybel34(A),k4_waybel34(A),k5_waybel34(A))
& v16_functor0(k6_waybel34(A),k4_waybel34(A),k5_waybel34(A))
& m2_functor0(k6_waybel34(A),k4_waybel34(A),k5_waybel34(A)) ) ) ).
fof(dt_k7_waybel34,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ( v9_functor0(k7_waybel34(A),k5_waybel34(A),k4_waybel34(A))
& v16_functor0(k7_waybel34(A),k5_waybel34(A),k4_waybel34(A))
& m2_functor0(k7_waybel34(A),k5_waybel34(A),k4_waybel34(A)) ) ) ).
fof(dt_k8_waybel34,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( ~ v3_struct_0(k8_waybel34(A))
& v2_altcat_1(k8_waybel34(A))
& v6_altcat_1(k8_waybel34(A))
& v3_altcat_2(k8_waybel34(A),k4_waybel34(A))
& m1_altcat_2(k8_waybel34(A),k4_waybel34(A)) ) ) ).
fof(dt_k9_waybel34,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ( ~ v3_struct_0(k9_waybel34(A))
& v2_altcat_1(k9_waybel34(A))
& v6_altcat_1(k9_waybel34(A))
& v3_altcat_2(k9_waybel34(A),k5_waybel34(A))
& m1_altcat_2(k9_waybel34(A),k5_waybel34(A)) ) ) ).
fof(dt_k10_waybel34,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ( ~ v3_struct_0(k10_waybel34(A))
& v2_altcat_1(k10_waybel34(A))
& v6_altcat_1(k10_waybel34(A))
& v2_altcat_2(k10_waybel34(A),k8_waybel34(A))
& v3_altcat_2(k10_waybel34(A),k8_waybel34(A))
& m1_altcat_2(k10_waybel34(A),k8_waybel34(A)) ) ) ).
fof(dt_k11_waybel34,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ( ~ v3_struct_0(k11_waybel34(A))
& v2_altcat_1(k11_waybel34(A))
& v6_altcat_1(k11_waybel34(A))
& v2_altcat_2(k11_waybel34(A),k9_waybel34(A))
& v3_altcat_2(k11_waybel34(A),k9_waybel34(A))
& m1_altcat_2(k11_waybel34(A),k9_waybel34(A)) ) ) ).
fof(rc1_waybel34,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B) )
=> ? [C] :
( m1_waybel_1(C,A,B)
& v3_waybel_1(C,A,B) ) ) ).
fof(t1_waybel34,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_orders_2(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& l1_orders_2(D) )
=> ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(C),u1_orders_2(C))
& g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D)) )
=> ! [E] :
( m1_waybel_1(E,A,B)
=> ! [F] :
( m1_waybel_1(F,C,D)
=> ( ( E = F
& v3_waybel_1(E,A,B) )
=> v3_waybel_1(F,C,D) ) ) ) ) ) ) ) ) ).
fof(d1_waybel34,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( ( v3_lattice3(A)
& v3_lattice3(B)
& v17_waybel_0(C,A,B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( D = k1_waybel34(A,B,C)
<=> v3_waybel_1(k1_waybel_1(A,B,C,D),A,B) ) ) ) ) ) ) ).
fof(d2_waybel34,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( ( v3_lattice3(A)
& v3_lattice3(B)
& v18_waybel_0(C,B,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ( D = k2_waybel34(A,B,C)
<=> v3_waybel_1(k1_waybel_1(A,B,D,C),A,B) ) ) ) ) ) ) ).
fof(l4_waybel34,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ( ( v3_lattice3(A)
& v3_lattice3(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v17_waybel_0(C,A,B)
=> ( v5_orders_3(k1_waybel34(A,B,C),B,A)
& v5_waybel_1(k1_waybel34(A,B,C),A,B)
& v18_waybel_0(k1_waybel34(A,B,C),B,A) ) ) ) ) ) ) ).
fof(l5_waybel34,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ( ( v3_lattice3(A)
& v3_lattice3(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v18_waybel_0(C,A,B)
=> ( v5_orders_3(k2_waybel34(B,A,C),B,A)
& v4_waybel_1(k2_waybel34(B,A,C),B,A)
& v17_waybel_0(k2_waybel34(B,A,C),B,A) ) ) ) ) ) ) ).
fof(fc1_waybel34,axiom,
! [A,B,C] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v17_waybel_0(C,A,B)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_relat_1(k1_waybel34(A,B,C))
& v1_funct_1(k1_waybel34(A,B,C))
& ~ v1_xboole_0(k1_waybel34(A,B,C))
& v1_funct_2(k1_waybel34(A,B,C),u1_struct_0(B),u1_struct_0(A))
& v1_partfun1(k1_waybel34(A,B,C),u1_struct_0(B),u1_struct_0(A))
& v18_waybel_0(k1_waybel34(A,B,C),B,A)
& v20_waybel_0(k1_waybel34(A,B,C),B,A)
& v22_waybel_0(k1_waybel34(A,B,C),B,A)
& v5_waybel_1(k1_waybel34(A,B,C),A,B)
& v5_orders_3(k1_waybel34(A,B,C),B,A) ) ) ).
fof(fc2_waybel34,axiom,
! [A,B,C] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v18_waybel_0(C,B,A)
& m1_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( v1_relat_1(k2_waybel34(A,B,C))
& v1_funct_1(k2_waybel34(A,B,C))
& ~ v1_xboole_0(k2_waybel34(A,B,C))
& v1_funct_2(k2_waybel34(A,B,C),u1_struct_0(A),u1_struct_0(B))
& v1_partfun1(k2_waybel34(A,B,C),u1_struct_0(A),u1_struct_0(B))
& v17_waybel_0(k2_waybel34(A,B,C),A,B)
& v19_waybel_0(k2_waybel34(A,B,C),A,B)
& v21_waybel_0(k2_waybel34(A,B,C),A,B)
& v4_waybel_1(k2_waybel34(A,B,C),A,B)
& v5_orders_3(k2_waybel34(A,B,C),A,B) ) ) ).
fof(t2_waybel34,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v17_waybel_0(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> k7_yellow_2(u1_struct_0(B),A,k1_waybel34(A,B,C),D) = k2_yellow_0(A,k5_pre_topc(A,B,C,k7_waybel_0(B,D))) ) ) ) ) ).
fof(t3_waybel34,conjecture,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v18_waybel_0(C,B,A)
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k7_yellow_2(u1_struct_0(A),B,k2_waybel34(A,B,C),D) = k1_yellow_0(B,k5_pre_topc(B,A,C,k6_waybel_0(A,D))) ) ) ) ) ).
%------------------------------------------------------------------------------