%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT295+3 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 Jun 21 05:14:13 AM UTC 2025
% Result : Theorem 2.72s 2.88s
% Output : Proof 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 8 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 1085 ( 326 equ)
% Maximal formula atoms : 32 ( 135 avg)
% Number of connectives : 1356 ( 381 ~; 341 |; 375 &)
% ( 51 <=>; 208 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 15 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 102 ( 102 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 0 con; 1-3 aty)
% Number of variables : 152 ( 146 !; 0 ?; 152 :)
% 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(B))
| ~ m1_subset_1(D,u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| 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(B))
| ~ m1_subset_1(D,u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| 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(trans(quant_intro(proof_bind(^ [E: $i] :
trans(monotonicity(trans(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) ) ) ) )),
trans(trans(der(( ! [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) ) ) )
<=> ! [F: $i] :
( ( ( k1_lattices(A,C,D) = k1_lattices(B,E,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,D) )
& ( ~ r1_lattices(B,E,D)
| r1_lattices(A,C,D) ) )
| ~ m1_subset_1(D,u1_struct_0(B))
| ( C != E ) ) )),
elim_unused(( ! [F: $i] :
( ( ( k1_lattices(A,C,D) = k1_lattices(B,E,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,D) )
& ( ~ r1_lattices(B,E,D)
| r1_lattices(A,C,D) ) )
| ~ m1_subset_1(D,u1_struct_0(B))
| ( C != E ) )
<=> ( ( ( k1_lattices(A,C,D) = k1_lattices(B,E,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,D) )
& ( ~ r1_lattices(B,E,D)
| r1_lattices(A,C,D) ) )
| ~ m1_subset_1(D,u1_struct_0(B))
| ( C != E ) ) )),
( ! [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) ) ) )
<=> ( ( ( k1_lattices(A,C,D) = k1_lattices(B,E,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,D) )
& ( ~ r1_lattices(B,E,D)
| r1_lattices(A,C,D) ) )
| ~ m1_subset_1(D,u1_struct_0(B))
| ( C != E ) ) )),
rewrite(( ( ( ( k1_lattices(A,C,D) = k1_lattices(B,E,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,D) )
& ( ~ r1_lattices(B,E,D)
| r1_lattices(A,C,D) ) )
| ~ m1_subset_1(D,u1_struct_0(B))
| ( C != E ) )
<=> ( ( C != E )
| ~ m1_subset_1(D,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,D) )
& ( ~ r1_lattices(B,E,D)
| 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) ) ) )
<=> ( ( C != E )
| ~ m1_subset_1(D,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,D) )
& ( ~ r1_lattices(B,E,D)
| 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) ) ) ) )
<=> ( ( C != E )
| ~ m1_subset_1(D,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,D) )
& ( ~ r1_lattices(B,E,D)
| 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))
=> ( ( C != E )
| ~ m1_subset_1(D,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,D) )
& ( ~ r1_lattices(B,E,D)
| r1_lattices(A,C,D) ) ) ) ) )),
rewrite(( ( m1_subset_1(E,u1_struct_0(B))
=> ( ( C != E )
| ~ m1_subset_1(D,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,D) )
& ( ~ r1_lattices(B,E,D)
| r1_lattices(A,C,D) ) ) ) )
<=> ( ( C != E )
| ~ m1_subset_1(E,u1_struct_0(B))
| ~ m1_subset_1(D,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,D) )
& ( ~ r1_lattices(B,E,D)
| 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) ) ) ) ) )
<=> ( ( C != E )
| ~ m1_subset_1(E,u1_struct_0(B))
| ~ m1_subset_1(D,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,D) )
& ( ~ r1_lattices(B,E,D)
| 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] :
( ( C != E )
| ~ m1_subset_1(E,u1_struct_0(B))
| ~ m1_subset_1(D,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,D) )
& ( ~ r1_lattices(B,E,D)
| r1_lattices(A,C,D) ) ) ) )),
trans(trans(der(( ! [E: $i] :
( ( C != E )
| ~ m1_subset_1(E,u1_struct_0(B))
| ~ m1_subset_1(D,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,D) )
& ( ~ r1_lattices(B,E,D)
| r1_lattices(A,C,D) ) ) )
<=> ! [E: $i] :
( ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| r1_lattices(A,C,D) ) )
| ~ m1_subset_1(C,u1_struct_0(B))
| ~ m1_subset_1(D,u1_struct_0(B)) ) )),
elim_unused(( ! [E: $i] :
( ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| r1_lattices(A,C,D) ) )
| ~ m1_subset_1(C,u1_struct_0(B))
| ~ m1_subset_1(D,u1_struct_0(B)) )
<=> ( ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| r1_lattices(A,C,D) ) )
| ~ m1_subset_1(C,u1_struct_0(B))
| ~ m1_subset_1(D,u1_struct_0(B)) ) )),
( ! [E: $i] :
( ( C != E )
| ~ m1_subset_1(E,u1_struct_0(B))
| ~ m1_subset_1(D,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,D) )
& ( ~ r1_lattices(B,E,D)
| r1_lattices(A,C,D) ) ) )
<=> ( ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| r1_lattices(A,C,D) ) )
| ~ m1_subset_1(C,u1_struct_0(B))
| ~ m1_subset_1(D,u1_struct_0(B)) ) )),
rewrite(( ( ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| r1_lattices(A,C,D) ) )
| ~ m1_subset_1(C,u1_struct_0(B))
| ~ m1_subset_1(D,u1_struct_0(B)) )
<=> ( ~ m1_subset_1(D,u1_struct_0(B))
| ~ m1_subset_1(C,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| r1_lattices(A,C,D) ) ) ) )),
( ! [E: $i] :
( ( C != E )
| ~ m1_subset_1(E,u1_struct_0(B))
| ~ m1_subset_1(D,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,E,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,E,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,E,D) )
& ( ~ r1_lattices(B,E,D)
| r1_lattices(A,C,D) ) ) )
<=> ( ~ m1_subset_1(D,u1_struct_0(B))
| ~ m1_subset_1(C,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| 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) ) ) ) ) )
<=> ( ~ m1_subset_1(D,u1_struct_0(B))
| ~ m1_subset_1(C,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| 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))
=> ( ~ m1_subset_1(D,u1_struct_0(B))
| ~ m1_subset_1(C,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| r1_lattices(A,C,D) ) ) ) ) )),
rewrite(( ( m1_subset_1(D,u1_struct_0(A))
=> ( ~ m1_subset_1(D,u1_struct_0(B))
| ~ m1_subset_1(C,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| r1_lattices(A,C,D) ) ) ) )
<=> ( ~ m1_subset_1(D,u1_struct_0(B))
| ~ m1_subset_1(D,u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| 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(B))
| ~ m1_subset_1(D,u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| 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(B))
| ~ m1_subset_1(D,u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| 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(B))
| ~ m1_subset_1(D,u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| r1_lattices(A,C,D) ) ) ) ) )),
rewrite(( ( m1_subset_1(C,u1_struct_0(A))
=> ! [D: $i] :
( ~ m1_subset_1(D,u1_struct_0(B))
| ~ m1_subset_1(D,u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| r1_lattices(A,C,D) ) ) ) )
<=> ( ~ m1_subset_1(C,u1_struct_0(A))
| ! [D: $i] :
( ~ m1_subset_1(D,u1_struct_0(B))
| ~ m1_subset_1(D,u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| 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(B))
| ~ m1_subset_1(D,u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| 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(B))
| ~ m1_subset_1(D,u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| 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(B))
| ~ m1_subset_1(D,u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| 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(B))
| ~ m1_subset_1(D,u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| 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(B))
| ~ m1_subset_1(D,u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| 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(B))
| ~ m1_subset_1(D,u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| 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(B))
| ~ m1_subset_1(D,u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| 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(B))
| ~ m1_subset_1(D,u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| 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(B))
| ~ m1_subset_1(D,u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| 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(B))
| ~ m1_subset_1(D,u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| 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(B))
| ~ m1_subset_1(D,u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| 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(B))
| ~ m1_subset_1(D,u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| 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(B))
| ~ m1_subset_1(D,u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| 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(B))
| ~ m1_subset_1(D,u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| 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(B))
| ~ m1_subset_1(D,u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| 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(B))
| ~ m1_subset_1(D,u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| 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(B))
| ~ m1_subset_1(D,u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(B))
| ( ( k1_lattices(A,C,D) = k1_lattices(B,C,D) )
& ( k2_lattices(A,C,D) = k2_lattices(B,C,D) )
& ( ~ r1_lattices(A,C,D)
| r1_lattices(B,C,D) )
& ( ~ r1_lattices(B,C,D)
| 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
% 0.08/0.12 % Problem : LAT295+3 : TPTP v9.0.0. Released v3.4.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.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 Jun 19 20:05:21 EDT 2025
% 0.12/0.33 % CPUTime :
% 2.72/2.88 % SZS status Theorem
% 2.72/2.88 % SZS output start Proof
% See solution above
% 3.62/3.77 % E exiting
%------------------------------------------------------------------------------