TPTP Problem File: SEU410+3.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SEU410+3 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Problem : The Operation of Addition of Relational Structures T19
% Version : [Urb08] axioms : Especial.
% English :
% Refs : [RG04] Romanowicz & Grabowski (2004), The Operation of Additi
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : t19_latsum_1 [Urb08]
% Status : Theorem
% Rating : 1.00 v7.5.0, 0.97 v7.4.0, 1.00 v3.4.0
% Syntax : Number of formulae : 19045 (2909 unt; 0 def)
% Number of atoms : 138191 (13097 equ)
% Maximal formula atoms : 123 ( 7 avg)
% Number of connectives : 136462 (17316 ~; 603 |;71900 &)
% (3732 <=>;42911 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 8 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 1228 (1226 usr; 2 prp; 0-6 aty)
% Number of functors : 2902 (2902 usr; 731 con; 0-10 aty)
% Number of variables : 50536 (47909 !;2627 ?)
% 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').
include('Axioms/SET007/SET007+699.ax').
%------------------------------------------------------------------------------
fof(dt_k1_latsum_1,axiom,
! [A,B] :
( ( l1_orders_2(A)
& l1_orders_2(B) )
=> ( v1_orders_2(k1_latsum_1(A,B))
& l1_orders_2(k1_latsum_1(A,B)) ) ) ).
fof(t1_latsum_1,axiom,
! [A,B,C,D] :
~ ( r2_hidden(A,k2_xboole_0(C,D))
& r2_hidden(B,k2_xboole_0(C,D))
& ~ ( r2_hidden(A,k4_xboole_0(C,D))
& r2_hidden(B,k4_xboole_0(C,D)) )
& ~ ( r2_hidden(A,D)
& r2_hidden(B,D) )
& ~ ( r2_hidden(A,k4_xboole_0(C,D))
& r2_hidden(B,D) )
& ~ ( r2_hidden(A,D)
& r2_hidden(B,k4_xboole_0(C,D)) ) ) ).
fof(d1_latsum_1,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ( r1_latsum_1(A,B)
<=> ! [C,D] :
( ( r2_hidden(C,k3_xboole_0(u1_struct_0(A),u1_struct_0(B)))
& r2_hidden(D,k3_xboole_0(u1_struct_0(A),u1_struct_0(B))) )
=> ( r2_hidden(k4_tarski(C,D),u1_orders_2(A))
<=> r2_hidden(k4_tarski(C,D),u1_orders_2(B)) ) ) ) ) ) ).
fof(d2_latsum_1,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( ( v1_orders_2(C)
& l1_orders_2(C) )
=> ( C = k1_latsum_1(A,B)
<=> ( u1_struct_0(C) = k2_xboole_0(u1_struct_0(A),u1_struct_0(B))
& u1_orders_2(C) = k2_xboole_0(k2_xboole_0(u1_orders_2(A),u1_orders_2(B)),k7_relset_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_orders_2(A),u1_orders_2(B))) ) ) ) ) ) ).
fof(fc1_latsum_1,axiom,
! [A,B] :
( ( l1_orders_2(A)
& ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k1_latsum_1(A,B))
& v1_orders_2(k1_latsum_1(A,B)) ) ) ).
fof(fc2_latsum_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k1_latsum_1(A,B))
& v1_orders_2(k1_latsum_1(A,B)) ) ) ).
fof(t2_latsum_1,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ( r1_tarski(u1_orders_2(A),u1_orders_2(k1_latsum_1(A,B)))
& r1_tarski(u1_orders_2(B),u1_orders_2(k1_latsum_1(A,B))) ) ) ) ).
fof(t3_latsum_1,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ( ( v2_orders_2(A)
& v2_orders_2(B) )
=> v2_orders_2(k1_latsum_1(A,B)) ) ) ) ).
fof(t4_latsum_1,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C,D] :
( ( r2_hidden(k4_tarski(C,D),u1_orders_2(k1_latsum_1(A,B)))
& r2_hidden(C,u1_struct_0(A))
& r2_hidden(D,u1_struct_0(A))
& r1_latsum_1(A,B)
& v3_orders_2(A) )
=> r2_hidden(k4_tarski(C,D),u1_orders_2(A)) ) ) ) ).
fof(t5_latsum_1,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C,D] :
( ( r2_hidden(k4_tarski(C,D),u1_orders_2(k1_latsum_1(A,B)))
& r2_hidden(C,u1_struct_0(B))
& r2_hidden(D,u1_struct_0(B))
& r1_latsum_1(A,B)
& v3_orders_2(B) )
=> r2_hidden(k4_tarski(C,D),u1_orders_2(B)) ) ) ) ).
fof(t6_latsum_1,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C,D] :
( ( r2_hidden(k4_tarski(C,D),u1_orders_2(A))
=> r2_hidden(k4_tarski(C,D),u1_orders_2(k1_latsum_1(A,B))) )
& ( r2_hidden(k4_tarski(C,D),u1_orders_2(B))
=> r2_hidden(k4_tarski(C,D),u1_orders_2(k1_latsum_1(A,B))) ) ) ) ) ).
fof(t7_latsum_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B)))
=> ( r2_hidden(C,u1_struct_0(A))
| r2_hidden(C,k4_xboole_0(u1_struct_0(B),u1_struct_0(A))) ) ) ) ) ).
fof(t8_latsum_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k1_latsum_1(A,B)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k1_latsum_1(A,B)))
=> ( ( C = E
& D = F
& r1_latsum_1(A,B)
& v3_orders_2(A) )
=> ( r1_orders_2(A,C,D)
<=> r1_orders_2(k1_latsum_1(A,B),E,F) ) ) ) ) ) ) ) ) ).
fof(t9_latsum_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k1_latsum_1(A,B)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( C = E
& D = F
& r1_latsum_1(A,B)
& v3_orders_2(B) )
=> ( r1_orders_2(k1_latsum_1(A,B),C,D)
<=> r1_orders_2(B,E,F) ) ) ) ) ) ) ) ) ).
fof(t10_latsum_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( r2_hidden(C,u1_struct_0(A))
=> m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B))) ) ) ) ).
fof(t11_latsum_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( r2_hidden(C,u1_struct_0(B))
=> m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B))) ) ) ) ).
fof(t12_latsum_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( r2_hidden(C,k3_xboole_0(u1_struct_0(A),u1_struct_0(B)))
=> m1_subset_1(C,u1_struct_0(A)) ) ) ) ).
fof(t13_latsum_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( r2_hidden(C,k3_xboole_0(u1_struct_0(A),u1_struct_0(B)))
=> m1_subset_1(C,u1_struct_0(B)) ) ) ) ).
fof(t14_latsum_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k1_latsum_1(A,B)))
=> ( ( r2_hidden(C,u1_struct_0(A))
& r2_hidden(D,u1_struct_0(B))
& r1_latsum_1(A,B) )
=> ( r1_orders_2(k1_latsum_1(A,B),C,D)
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(k1_latsum_1(A,B)))
& r2_hidden(E,k3_xboole_0(u1_struct_0(A),u1_struct_0(B)))
& r1_orders_2(k1_latsum_1(A,B),C,E)
& r1_orders_2(k1_latsum_1(A,B),E,D) ) ) ) ) ) ) ) ).
fof(t15_latsum_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( C = E
& D = F
& r1_latsum_1(A,B)
& v3_orders_2(A)
& v3_orders_2(B) )
=> ( r1_orders_2(A,C,D)
<=> r1_orders_2(B,E,F) ) ) ) ) ) ) ) ) ).
fof(t16_latsum_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_waybel_0(B,A)
& v12_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(C,B)
& r2_hidden(D,B) )
=> r2_hidden(k13_lattice3(A,C,D),B) ) ) ) ) ) ).
fof(t17_latsum_1,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C,D] :
( ( v13_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),A)
& m1_subset_1(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(A)))
& r2_hidden(k4_tarski(C,D),u1_orders_2(k1_latsum_1(A,B)))
& r2_hidden(C,u1_struct_0(B)) )
=> r2_hidden(D,u1_struct_0(B)) ) ) ) ).
fof(t18_latsum_1,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k1_latsum_1(A,B)))
=> ( ( v13_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),A)
& m1_subset_1(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(A)))
& r1_orders_2(k1_latsum_1(A,B),C,D)
& r2_hidden(C,u1_struct_0(B)) )
=> r2_hidden(D,u1_struct_0(B)) ) ) ) ) ) ).
fof(t19_latsum_1,conjecture,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( v1_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),B)
& v12_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),B)
& m1_subset_1(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B)))
& v13_waybel_0(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),A)
& m1_subset_1(k3_xboole_0(u1_struct_0(A),u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(A)))
& r1_latsum_1(A,B)
& C = E
& D = F )
=> k13_lattice3(A,C,D) = k13_lattice3(B,E,F) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------