%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT295+3 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 18:32:47 EDT 2022
% Result : Theorem 2.79s 2.96s
% Output : Proof 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 14
% Syntax : Number of formulae : 18 ( 2 unt; 10 typ; 0 def)
% Number of atoms : 931 ( 316 equ)
% Maximal formula atoms : 34 ( 116 avg)
% Number of connectives : 1162 ( 317 ~; 277 |; 330 &)
% ( 39 <=>; 199 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 16 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 78 ( 78 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 10 >; 9 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 0 con; 1-3 aty)
% Number of variables : 198 ( 192 !; 0 ?; 198 :)
% Comments :
%------------------------------------------------------------------------------
tff(g3_lattices_type,type,
g3_lattices: ( $i * $i * $i ) > $i ).
tff(u1_lattices_type,type,
u1_lattices: $i > $i ).
tff(u2_lattices_type,type,
u2_lattices: $i > $i ).
tff(u1_struct_0_type,type,
u1_struct_0: $i > $i ).
tff(r1_lattices_type,type,
r1_lattices: ( $i * $i * $i ) > $o ).
tff(k2_lattices_type,type,
k2_lattices: ( $i * $i * $i ) > $i ).
tff(k1_lattices_type,type,
k1_lattices: ( $i * $i * $i ) > $i ).
tff(m1_subset_1_type,type,
m1_subset_1: ( $i * $i ) > $o ).
tff(l3_lattices_type,type,
l3_lattices: $i > $o ).
tff(v3_struct_0_type,type,
v3_struct_0: $i > $o ).
tff(1,plain,
( ~ ! [A: $i] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ! [B: $i] :
( ( ~ v3_struct_0(B)
& l3_lattices(B) )
=> ( ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) )
=> ! [C: $i] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D: $i] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E: $i] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F: $i] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) )
& ( r1_lattices(B,E,F)
=> r1_lattices(A,C,D) ) ) ) ) ) ) ) ) ) )
<=> ~ ! [A: $i] :
( ~ ( ~ v3_struct_0(A)
& l3_lattices(A) )
| ! [B: $i] :
( ~ ( ~ v3_struct_0(B)
& l3_lattices(B) )
| ! [C: $i] :
( ~ m1_subset_1(C,u1_struct_0(A))
| ! [D: $i] :
( ~ m1_subset_1(D,u1_struct_0(A))
| ! [E: $i] :
( ~ m1_subset_1(E,u1_struct_0(B))
| ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) ) )
| ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) != g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ ! [A: $i] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ! [B: $i] :
( ( ~ v3_struct_0(B)
& l3_lattices(B) )
=> ( ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) )
=> ! [C: $i] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D: $i] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E: $i] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F: $i] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) )
& ( r1_lattices(B,E,F)
=> r1_lattices(A,C,D) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_filter_2) ).
tff(3,plain,
~ ! [A: $i] :
( ~ ( ~ v3_struct_0(A)
& l3_lattices(A) )
| ! [B: $i] :
( ~ ( ~ v3_struct_0(B)
& l3_lattices(B) )
| ! [C: $i] :
( ~ m1_subset_1(C,u1_struct_0(A))
| ! [D: $i] :
( ~ m1_subset_1(D,u1_struct_0(A))
| ! [E: $i] :
( ~ m1_subset_1(E,u1_struct_0(B))
| ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) ) )
| ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) != g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) ) ) ),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [A: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [B: $i] :
trans(
monotonicity(
trans(
monotonicity(
quant_intro(
proof_bind(
^ [C: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [D: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [E: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [F: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) )
<=> ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) ) )),
( ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) ) )
<=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) ) ) )),
rewrite(
( ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) ) )
<=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) ) ) )),
( ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) ) )
<=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) ) ) )),
rewrite(
( ( r1_lattices(B,E,F)
=> r1_lattices(A,C,D) )
<=> ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) )),
( ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) )
& ( r1_lattices(B,E,F)
=> r1_lattices(A,C,D) ) )
<=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) )),
rewrite(
( ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) )
<=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) )),
( ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) )
& ( r1_lattices(B,E,F)
=> r1_lattices(A,C,D) ) )
<=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) )),
( ( ( ( C = E )
& ( D = F ) )
=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) )
& ( r1_lattices(B,E,F)
=> r1_lattices(A,C,D) ) ) )
<=> ( ( ( C = E )
& ( D = F ) )
=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) )),
rewrite(
( ( ( ( C = E )
& ( D = F ) )
=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) )
<=> ( ~ ( ( C = E )
& ( D = F ) )
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) )),
( ( ( ( C = E )
& ( D = F ) )
=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) )
& ( r1_lattices(B,E,F)
=> r1_lattices(A,C,D) ) ) )
<=> ( ~ ( ( C = E )
& ( D = F ) )
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) )),
( ( m1_subset_1(F,u1_struct_0(B))
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) )
& ( r1_lattices(B,E,F)
=> r1_lattices(A,C,D) ) ) ) )
<=> ( m1_subset_1(F,u1_struct_0(B))
=> ( ~ ( ( C = E )
& ( D = F ) )
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) )),
rewrite(
( ( m1_subset_1(F,u1_struct_0(B))
=> ( ~ ( ( C = E )
& ( D = F ) )
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) )
<=> ( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) )),
( ( m1_subset_1(F,u1_struct_0(B))
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) )
& ( r1_lattices(B,E,F)
=> r1_lattices(A,C,D) ) ) ) )
<=> ( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ))),
( ! [F: $i] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) )
& ( r1_lattices(B,E,F)
=> r1_lattices(A,C,D) ) ) ) )
<=> ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) )),
( ( m1_subset_1(E,u1_struct_0(B))
=> ! [F: $i] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) )
& ( r1_lattices(B,E,F)
=> r1_lattices(A,C,D) ) ) ) ) )
<=> ( m1_subset_1(E,u1_struct_0(B))
=> ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) )),
rewrite(
( ( m1_subset_1(E,u1_struct_0(B))
=> ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) )
<=> ( ~ m1_subset_1(E,u1_struct_0(B))
| ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) )),
( ( m1_subset_1(E,u1_struct_0(B))
=> ! [F: $i] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) )
& ( r1_lattices(B,E,F)
=> r1_lattices(A,C,D) ) ) ) ) )
<=> ( ~ m1_subset_1(E,u1_struct_0(B))
| ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) ))),
( ! [E: $i] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F: $i] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) )
& ( r1_lattices(B,E,F)
=> r1_lattices(A,C,D) ) ) ) ) )
<=> ! [E: $i] :
( ~ m1_subset_1(E,u1_struct_0(B))
| ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) )),
( ( m1_subset_1(D,u1_struct_0(A))
=> ! [E: $i] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F: $i] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) )
& ( r1_lattices(B,E,F)
=> r1_lattices(A,C,D) ) ) ) ) ) )
<=> ( m1_subset_1(D,u1_struct_0(A))
=> ! [E: $i] :
( ~ m1_subset_1(E,u1_struct_0(B))
| ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) ) )),
rewrite(
( ( m1_subset_1(D,u1_struct_0(A))
=> ! [E: $i] :
( ~ m1_subset_1(E,u1_struct_0(B))
| ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) )
<=> ( ~ m1_subset_1(D,u1_struct_0(A))
| ! [E: $i] :
( ~ m1_subset_1(E,u1_struct_0(B))
| ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) ) )),
( ( m1_subset_1(D,u1_struct_0(A))
=> ! [E: $i] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F: $i] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) )
& ( r1_lattices(B,E,F)
=> r1_lattices(A,C,D) ) ) ) ) ) )
<=> ( ~ m1_subset_1(D,u1_struct_0(A))
| ! [E: $i] :
( ~ m1_subset_1(E,u1_struct_0(B))
| ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) ) ))),
( ! [D: $i] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E: $i] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F: $i] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) )
& ( r1_lattices(B,E,F)
=> r1_lattices(A,C,D) ) ) ) ) ) )
<=> ! [D: $i] :
( ~ m1_subset_1(D,u1_struct_0(A))
| ! [E: $i] :
( ~ m1_subset_1(E,u1_struct_0(B))
| ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) ) )),
( ( m1_subset_1(C,u1_struct_0(A))
=> ! [D: $i] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E: $i] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F: $i] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) )
& ( r1_lattices(B,E,F)
=> r1_lattices(A,C,D) ) ) ) ) ) ) )
<=> ( m1_subset_1(C,u1_struct_0(A))
=> ! [D: $i] :
( ~ m1_subset_1(D,u1_struct_0(A))
| ! [E: $i] :
( ~ m1_subset_1(E,u1_struct_0(B))
| ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) ) ) )),
rewrite(
( ( m1_subset_1(C,u1_struct_0(A))
=> ! [D: $i] :
( ~ m1_subset_1(D,u1_struct_0(A))
| ! [E: $i] :
( ~ m1_subset_1(E,u1_struct_0(B))
| ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) ) )
<=> ( ~ m1_subset_1(C,u1_struct_0(A))
| ! [D: $i] :
( ~ m1_subset_1(D,u1_struct_0(A))
| ! [E: $i] :
( ~ m1_subset_1(E,u1_struct_0(B))
| ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) ) ) )),
( ( m1_subset_1(C,u1_struct_0(A))
=> ! [D: $i] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E: $i] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F: $i] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) )
& ( r1_lattices(B,E,F)
=> r1_lattices(A,C,D) ) ) ) ) ) ) )
<=> ( ~ m1_subset_1(C,u1_struct_0(A))
| ! [D: $i] :
( ~ m1_subset_1(D,u1_struct_0(A))
| ! [E: $i] :
( ~ m1_subset_1(E,u1_struct_0(B))
| ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) ) ) ))),
( ! [C: $i] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D: $i] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E: $i] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F: $i] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) )
& ( r1_lattices(B,E,F)
=> r1_lattices(A,C,D) ) ) ) ) ) ) )
<=> ! [C: $i] :
( ~ m1_subset_1(C,u1_struct_0(A))
| ! [D: $i] :
( ~ m1_subset_1(D,u1_struct_0(A))
| ! [E: $i] :
( ~ m1_subset_1(E,u1_struct_0(B))
| ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) ) ) )),
( ( ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) )
=> ! [C: $i] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D: $i] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E: $i] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F: $i] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) )
& ( r1_lattices(B,E,F)
=> r1_lattices(A,C,D) ) ) ) ) ) ) ) )
<=> ( ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) )
=> ! [C: $i] :
( ~ m1_subset_1(C,u1_struct_0(A))
| ! [D: $i] :
( ~ m1_subset_1(D,u1_struct_0(A))
| ! [E: $i] :
( ~ m1_subset_1(E,u1_struct_0(B))
| ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) ) ) ) )),
rewrite(
( ( ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) )
=> ! [C: $i] :
( ~ m1_subset_1(C,u1_struct_0(A))
| ! [D: $i] :
( ~ m1_subset_1(D,u1_struct_0(A))
| ! [E: $i] :
( ~ m1_subset_1(E,u1_struct_0(B))
| ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) ) ) )
<=> ( ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) != g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) )
| ! [C: $i] :
( ~ m1_subset_1(C,u1_struct_0(A))
| ! [D: $i] :
( ~ m1_subset_1(D,u1_struct_0(A))
| ! [E: $i] :
( ~ m1_subset_1(E,u1_struct_0(B))
| ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) ) ) ) )),
( ( ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) )
=> ! [C: $i] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D: $i] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E: $i] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F: $i] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) )
& ( r1_lattices(B,E,F)
=> r1_lattices(A,C,D) ) ) ) ) ) ) ) )
<=> ( ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) != g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) )
| ! [C: $i] :
( ~ m1_subset_1(C,u1_struct_0(A))
| ! [D: $i] :
( ~ m1_subset_1(D,u1_struct_0(A))
| ! [E: $i] :
( ~ m1_subset_1(E,u1_struct_0(B))
| ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) ) ) ) )),
( ( ( ~ v3_struct_0(B)
& l3_lattices(B) )
=> ( ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) )
=> ! [C: $i] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D: $i] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E: $i] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F: $i] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) )
& ( r1_lattices(B,E,F)
=> r1_lattices(A,C,D) ) ) ) ) ) ) ) ) )
<=> ( ( ~ v3_struct_0(B)
& l3_lattices(B) )
=> ( ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) != g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) )
| ! [C: $i] :
( ~ m1_subset_1(C,u1_struct_0(A))
| ! [D: $i] :
( ~ m1_subset_1(D,u1_struct_0(A))
| ! [E: $i] :
( ~ m1_subset_1(E,u1_struct_0(B))
| ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) ) ) ) ) )),
rewrite(
( ( ( ~ v3_struct_0(B)
& l3_lattices(B) )
=> ( ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) != g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) )
| ! [C: $i] :
( ~ m1_subset_1(C,u1_struct_0(A))
| ! [D: $i] :
( ~ m1_subset_1(D,u1_struct_0(A))
| ! [E: $i] :
( ~ m1_subset_1(E,u1_struct_0(B))
| ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) ) ) ) )
<=> ( ~ ( ~ v3_struct_0(B)
& l3_lattices(B) )
| ! [C: $i] :
( ~ m1_subset_1(C,u1_struct_0(A))
| ! [D: $i] :
( ~ m1_subset_1(D,u1_struct_0(A))
| ! [E: $i] :
( ~ m1_subset_1(E,u1_struct_0(B))
| ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) ) )
| ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) != g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) ) ) )),
( ( ( ~ v3_struct_0(B)
& l3_lattices(B) )
=> ( ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) )
=> ! [C: $i] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D: $i] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E: $i] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F: $i] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) )
& ( r1_lattices(B,E,F)
=> r1_lattices(A,C,D) ) ) ) ) ) ) ) ) )
<=> ( ~ ( ~ v3_struct_0(B)
& l3_lattices(B) )
| ! [C: $i] :
( ~ m1_subset_1(C,u1_struct_0(A))
| ! [D: $i] :
( ~ m1_subset_1(D,u1_struct_0(A))
| ! [E: $i] :
( ~ m1_subset_1(E,u1_struct_0(B))
| ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) ) )
| ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) != g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) ) ) ))),
( ! [B: $i] :
( ( ~ v3_struct_0(B)
& l3_lattices(B) )
=> ( ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) )
=> ! [C: $i] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D: $i] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E: $i] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F: $i] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) )
& ( r1_lattices(B,E,F)
=> r1_lattices(A,C,D) ) ) ) ) ) ) ) ) )
<=> ! [B: $i] :
( ~ ( ~ v3_struct_0(B)
& l3_lattices(B) )
| ! [C: $i] :
( ~ m1_subset_1(C,u1_struct_0(A))
| ! [D: $i] :
( ~ m1_subset_1(D,u1_struct_0(A))
| ! [E: $i] :
( ~ m1_subset_1(E,u1_struct_0(B))
| ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) ) )
| ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) != g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) ) ) )),
( ( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ! [B: $i] :
( ( ~ v3_struct_0(B)
& l3_lattices(B) )
=> ( ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) )
=> ! [C: $i] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D: $i] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E: $i] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F: $i] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) )
& ( r1_lattices(B,E,F)
=> r1_lattices(A,C,D) ) ) ) ) ) ) ) ) ) )
<=> ( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ! [B: $i] :
( ~ ( ~ v3_struct_0(B)
& l3_lattices(B) )
| ! [C: $i] :
( ~ m1_subset_1(C,u1_struct_0(A))
| ! [D: $i] :
( ~ m1_subset_1(D,u1_struct_0(A))
| ! [E: $i] :
( ~ m1_subset_1(E,u1_struct_0(B))
| ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) ) )
| ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) != g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) ) ) ) )),
rewrite(
( ( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ! [B: $i] :
( ~ ( ~ v3_struct_0(B)
& l3_lattices(B) )
| ! [C: $i] :
( ~ m1_subset_1(C,u1_struct_0(A))
| ! [D: $i] :
( ~ m1_subset_1(D,u1_struct_0(A))
| ! [E: $i] :
( ~ m1_subset_1(E,u1_struct_0(B))
| ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) ) )
| ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) != g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) ) ) )
<=> ( ~ ( ~ v3_struct_0(A)
& l3_lattices(A) )
| ! [B: $i] :
( ~ ( ~ v3_struct_0(B)
& l3_lattices(B) )
| ! [C: $i] :
( ~ m1_subset_1(C,u1_struct_0(A))
| ! [D: $i] :
( ~ m1_subset_1(D,u1_struct_0(A))
| ! [E: $i] :
( ~ m1_subset_1(E,u1_struct_0(B))
| ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) ) )
| ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) != g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) ) ) ) )),
( ( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ! [B: $i] :
( ( ~ v3_struct_0(B)
& l3_lattices(B) )
=> ( ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) )
=> ! [C: $i] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D: $i] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E: $i] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F: $i] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) )
& ( r1_lattices(B,E,F)
=> r1_lattices(A,C,D) ) ) ) ) ) ) ) ) ) )
<=> ( ~ ( ~ v3_struct_0(A)
& l3_lattices(A) )
| ! [B: $i] :
( ~ ( ~ v3_struct_0(B)
& l3_lattices(B) )
| ! [C: $i] :
( ~ m1_subset_1(C,u1_struct_0(A))
| ! [D: $i] :
( ~ m1_subset_1(D,u1_struct_0(A))
| ! [E: $i] :
( ~ m1_subset_1(E,u1_struct_0(B))
| ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) ) )
| ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) != g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [A: $i] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ! [B: $i] :
( ( ~ v3_struct_0(B)
& l3_lattices(B) )
=> ( ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) )
=> ! [C: $i] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D: $i] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E: $i] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F: $i] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) )
& ( r1_lattices(B,E,F)
=> r1_lattices(A,C,D) ) ) ) ) ) ) ) ) ) )
<=> ! [A: $i] :
( ~ ( ~ v3_struct_0(A)
& l3_lattices(A) )
| ! [B: $i] :
( ~ ( ~ v3_struct_0(B)
& l3_lattices(B) )
| ! [C: $i] :
( ~ m1_subset_1(C,u1_struct_0(A))
| ! [D: $i] :
( ~ m1_subset_1(D,u1_struct_0(A))
| ! [E: $i] :
( ~ m1_subset_1(E,u1_struct_0(B))
| ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) ) )
| ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) != g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) ) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [A: $i] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ! [B: $i] :
( ( ~ v3_struct_0(B)
& l3_lattices(B) )
=> ( ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) )
=> ! [C: $i] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D: $i] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E: $i] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F: $i] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( ( C = E )
& ( D = F ) )
=> ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( r1_lattices(A,C,D)
=> r1_lattices(B,E,F) )
& ( r1_lattices(B,E,F)
=> r1_lattices(A,C,D) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET007/SET007+401.ax',t1_quantal1) ).
tff(7,plain,
! [A: $i] :
( ~ ( ~ v3_struct_0(A)
& l3_lattices(A) )
| ! [B: $i] :
( ~ ( ~ v3_struct_0(B)
& l3_lattices(B) )
| ! [C: $i] :
( ~ m1_subset_1(C,u1_struct_0(A))
| ! [D: $i] :
( ~ m1_subset_1(D,u1_struct_0(A))
| ! [E: $i] :
( ~ m1_subset_1(E,u1_struct_0(B))
| ! [F: $i] :
( ~ ( ( C = E )
& ( D = F ) )
| ~ m1_subset_1(F,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,F) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,F) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,F) )
& ( ~ r1_lattices(B,E,F)
| r1_lattices(A,C,D) ) ) ) ) ) )
| ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) != g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) ) ) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
$false,
inference(unit_resolution,[status(thm)],[7,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LAT295+3 : TPTP v8.1.0. Released v3.4.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 13:49:50 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 2.79/2.96 % SZS status Theorem
% 2.79/2.96 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------