%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU351+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:48:29 PM UTC 2026
% Result : Theorem 4.69s 1.63s
% Output : Refutation 6.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 26
% Syntax : Number of formulae : 320 ( 19 unt; 13 def)
% Number of atoms : 1594 ( 93 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 2188 ( 914 ~;1067 |; 144 &)
% ( 30 <=>; 31 =>; 0 <=; 2 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 32 ( 30 usr; 14 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 458 ( 0 sgn 428 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( latt_str(X0)
=> ( ( ~ empty_carrier(X0)
& lattice(X0) )
=> ( ~ empty_carrier(X0)
& join_commutative(X0)
& join_associative(X0)
& meet_commutative(X0)
& meet_associative(X0)
& meet_absorbing(X0)
& join_absorbing(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattices) ).
fof(f4,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& latt_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( latt_set_smaller(X0,X1,X2)
<=> ! [X3] :
( element(X3,the_carrier(X0))
=> ( in(X3,X2)
=> below(X0,X1,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d16_lattice3) ).
fof(f5,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& latt_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( latt_element_smaller(X0,X1,X2)
<=> ! [X3] :
( element(X3,the_carrier(X0))
=> ( in(X3,X2)
=> below(X0,X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d17_lattice3) ).
fof(f6,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& latt_str(X0) )
=> ( ( ~ empty_carrier(X0)
& lattice(X0)
& complete_latt_str(X0)
& latt_str(X0) )
=> ! [X1,X2] :
( element(X2,the_carrier(X0))
=> ( X2 = join_of_latt_set(X0,X1)
<=> ( latt_element_smaller(X0,X2,X1)
& ! [X3] :
( element(X3,the_carrier(X0))
=> ( latt_element_smaller(X0,X3,X1)
=> below(X0,X2,X3) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d21_lattice3) ).
fof(f7,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& latt_str(X0) )
=> ! [X1] : meet_of_latt_set(X0,X1) = join_of_latt_set(X0,a_2_2_lattice3(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d22_lattice3) ).
fof(f8,axiom,
! [X0,X1] :
( ( ~ empty_carrier(X0)
& latt_str(X0) )
=> element(join_of_latt_set(X0,X1),the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k15_lattice3) ).
fof(f9,axiom,
! [X0,X1] :
( ( ~ empty_carrier(X0)
& latt_str(X0) )
=> element(meet_of_latt_set(X0,X1),the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k16_lattice3) ).
fof(f24,axiom,
! [X0,X1,X2] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> ( in(X0,a_2_2_lattice3(X1,X2))
<=> ? [X3] :
( element(X3,the_carrier(X1))
& X0 = X3
& latt_set_smaller(X1,X3,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_2_lattice3) ).
fof(f29,axiom,
! [X0,X1,X2] :
( ( ~ empty_carrier(X0)
& meet_commutative(X0)
& meet_absorbing(X0)
& join_absorbing(X0)
& latt_str(X0)
& element(X1,the_carrier(X0))
& element(X2,the_carrier(X0)) )
=> ( below_refl(X0,X1,X2)
<=> below(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r3_lattices) ).
fof(f31,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f32,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f34,conjecture,
! [X0] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& complete_latt_str(X0)
& latt_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( X1 = meet_of_latt_set(X0,X2)
<=> ( latt_set_smaller(X0,X1,X2)
& ! [X3] :
( element(X3,the_carrier(X0))
=> ( latt_set_smaller(X0,X3,X2)
=> below_refl(X0,X3,X1) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_lattice3) ).
fof(f35,negated_conjecture,
~ ! [X0] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& complete_latt_str(X0)
& latt_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( X1 = meet_of_latt_set(X0,X2)
<=> ( latt_set_smaller(X0,X1,X2)
& ! [X3] :
( element(X3,the_carrier(X0))
=> ( latt_set_smaller(X0,X3,X2)
=> below_refl(X0,X3,X1) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
fof(f36,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f41,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( X1 = meet_of_latt_set(X0,X2)
<~> ( latt_set_smaller(X0,X1,X2)
& ! [X3] :
( below_refl(X0,X3,X1)
| ~ latt_set_smaller(X0,X3,X2)
| ~ element(X3,the_carrier(X0)) ) ) )
& element(X1,the_carrier(X0)) )
& ~ empty_carrier(X0)
& lattice(X0)
& complete_latt_str(X0)
& latt_str(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f42,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( X1 = meet_of_latt_set(X0,X2)
<~> ( latt_set_smaller(X0,X1,X2)
& ! [X3] :
( below_refl(X0,X3,X1)
| ~ latt_set_smaller(X0,X3,X2)
| ~ element(X3,the_carrier(X0)) ) ) )
& element(X1,the_carrier(X0)) )
& ~ empty_carrier(X0)
& lattice(X0)
& complete_latt_str(X0)
& latt_str(X0) ),
inference(flattening,[],[f41]) ).
fof(f44,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ( in(X0,a_2_2_lattice3(X1,X2))
<=> ? [X3] :
( element(X3,the_carrier(X1))
& X0 = X3
& latt_set_smaller(X1,X3,X2) ) )
| empty_carrier(X1)
| ~ latt_str(X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ( in(X0,a_2_2_lattice3(X1,X2))
<=> ? [X3] :
( element(X3,the_carrier(X1))
& X0 = X3
& latt_set_smaller(X1,X3,X2) ) )
| empty_carrier(X1)
| ~ latt_str(X1) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0] :
( ! [X1] : meet_of_latt_set(X0,X1) = join_of_latt_set(X0,a_2_2_lattice3(X0,X1))
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f51,plain,
! [X0] :
( ! [X1] : meet_of_latt_set(X0,X1) = join_of_latt_set(X0,a_2_2_lattice3(X0,X1))
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = join_of_latt_set(X0,X1)
<=> ( latt_element_smaller(X0,X2,X1)
& ! [X3] :
( below(X0,X2,X3)
| ~ latt_element_smaller(X0,X3,X1)
| ~ element(X3,the_carrier(X0)) ) ) )
| ~ element(X2,the_carrier(X0)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ complete_latt_str(X0)
| ~ latt_str(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f53,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = join_of_latt_set(X0,X1)
<=> ( latt_element_smaller(X0,X2,X1)
& ! [X3] :
( below(X0,X2,X3)
| ~ latt_element_smaller(X0,X3,X1)
| ~ element(X3,the_carrier(X0)) ) ) )
| ~ element(X2,the_carrier(X0)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ complete_latt_str(X0)
| ~ latt_str(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f52]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ( below_refl(X0,X1,X2)
<=> below(X0,X1,X2) )
| empty_carrier(X0)
| ~ meet_commutative(X0)
| ~ meet_absorbing(X0)
| ~ join_absorbing(X0)
| ~ latt_str(X0)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0)) ),
inference(ennf_transformation,[],[f29]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ( below_refl(X0,X1,X2)
<=> below(X0,X1,X2) )
| empty_carrier(X0)
| ~ meet_commutative(X0)
| ~ meet_absorbing(X0)
| ~ join_absorbing(X0)
| ~ latt_str(X0)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0)) ),
inference(flattening,[],[f56]) ).
fof(f60,plain,
! [X0,X1] :
( element(meet_of_latt_set(X0,X1),the_carrier(X0))
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f61,plain,
! [X0,X1] :
( element(meet_of_latt_set(X0,X1),the_carrier(X0))
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f60]) ).
fof(f62,plain,
! [X0,X1] :
( element(join_of_latt_set(X0,X1),the_carrier(X0))
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f63,plain,
! [X0,X1] :
( element(join_of_latt_set(X0,X1),the_carrier(X0))
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( latt_element_smaller(X0,X1,X2)
<=> ! [X3] :
( below(X0,X3,X1)
| ~ in(X3,X2)
| ~ element(X3,the_carrier(X0)) ) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( latt_element_smaller(X0,X1,X2)
<=> ! [X3] :
( below(X0,X3,X1)
| ~ in(X3,X2)
| ~ element(X3,the_carrier(X0)) ) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( latt_set_smaller(X0,X1,X2)
<=> ! [X3] :
( below(X0,X1,X3)
| ~ in(X3,X2)
| ~ element(X3,the_carrier(X0)) ) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f67,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( latt_set_smaller(X0,X1,X2)
<=> ! [X3] :
( below(X0,X1,X3)
| ~ in(X3,X2)
| ~ element(X3,the_carrier(X0)) ) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f66]) ).
fof(f70,plain,
! [X0] :
( ( ~ empty_carrier(X0)
& join_commutative(X0)
& join_associative(X0)
& meet_commutative(X0)
& meet_associative(X0)
& meet_absorbing(X0)
& join_absorbing(X0) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f71,plain,
! [X0] :
( ( ~ empty_carrier(X0)
& join_commutative(X0)
& join_associative(X0)
& meet_commutative(X0)
& meet_associative(X0)
& meet_absorbing(X0)
& join_absorbing(X0) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f70]) ).
fof(f72,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f73,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f75,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ latt_set_smaller(X0,X1,X2)
| ? [X3] :
( ~ below_refl(X0,X3,X1)
& latt_set_smaller(X0,X3,X2)
& element(X3,the_carrier(X0)) )
| meet_of_latt_set(X0,X2) != X1 )
& ( ( latt_set_smaller(X0,X1,X2)
& ! [X3] :
( below_refl(X0,X3,X1)
| ~ latt_set_smaller(X0,X3,X2)
| ~ element(X3,the_carrier(X0)) ) )
| X1 = meet_of_latt_set(X0,X2) ) )
& element(X1,the_carrier(X0)) )
& ~ empty_carrier(X0)
& lattice(X0)
& complete_latt_str(X0)
& latt_str(X0) ),
inference(nnf_transformation,[],[f42]) ).
fof(f76,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ latt_set_smaller(X0,X1,X2)
| ? [X3] :
( ~ below_refl(X0,X3,X1)
& latt_set_smaller(X0,X3,X2)
& element(X3,the_carrier(X0)) )
| meet_of_latt_set(X0,X2) != X1 )
& ( ( latt_set_smaller(X0,X1,X2)
& ! [X3] :
( below_refl(X0,X3,X1)
| ~ latt_set_smaller(X0,X3,X2)
| ~ element(X3,the_carrier(X0)) ) )
| X1 = meet_of_latt_set(X0,X2) ) )
& element(X1,the_carrier(X0)) )
& ~ empty_carrier(X0)
& lattice(X0)
& complete_latt_str(X0)
& latt_str(X0) ),
inference(flattening,[],[f75]) ).
fof(f77,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ latt_set_smaller(X0,X1,X2)
| ? [X3] :
( ~ below_refl(X0,X3,X1)
& latt_set_smaller(X0,X3,X2)
& element(X3,the_carrier(X0)) )
| meet_of_latt_set(X0,X2) != X1 )
& ( ( latt_set_smaller(X0,X1,X2)
& ! [X4] :
( below_refl(X0,X4,X1)
| ~ latt_set_smaller(X0,X4,X2)
| ~ element(X4,the_carrier(X0)) ) )
| X1 = meet_of_latt_set(X0,X2) ) )
& element(X1,the_carrier(X0)) )
& ~ empty_carrier(X0)
& lattice(X0)
& complete_latt_str(X0)
& latt_str(X0) ),
inference(rectify,[],[f76]) ).
fof(f78,plain,
( ( ~ latt_set_smaller(sK0,sK1,sK2)
| ( ~ below_refl(sK0,sK3,sK1)
& latt_set_smaller(sK0,sK3,sK2)
& element(sK3,the_carrier(sK0)) )
| sK1 != meet_of_latt_set(sK0,sK2) )
& ( ( latt_set_smaller(sK0,sK1,sK2)
& ! [X4] :
( below_refl(sK0,X4,sK1)
| ~ latt_set_smaller(sK0,X4,sK2)
| ~ element(X4,the_carrier(sK0)) ) )
| sK1 = meet_of_latt_set(sK0,sK2) )
& element(sK1,the_carrier(sK0))
& ~ empty_carrier(sK0)
& lattice(sK0)
& complete_latt_str(sK0)
& latt_str(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f77]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ( ( in(X0,a_2_2_lattice3(X1,X2))
| ! [X3] :
( ~ element(X3,the_carrier(X1))
| X0 != X3
| ~ latt_set_smaller(X1,X3,X2) ) )
& ( ? [X3] :
( element(X3,the_carrier(X1))
& X0 = X3
& latt_set_smaller(X1,X3,X2) )
| ~ in(X0,a_2_2_lattice3(X1,X2)) ) )
| empty_carrier(X1)
| ~ latt_str(X1) ),
inference(nnf_transformation,[],[f49]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ( ( in(X0,a_2_2_lattice3(X1,X2))
| ! [X3] :
( ~ element(X3,the_carrier(X1))
| X0 != X3
| ~ latt_set_smaller(X1,X3,X2) ) )
& ( ? [X4] :
( element(X4,the_carrier(X1))
& X0 = X4
& latt_set_smaller(X1,X4,X2) )
| ~ in(X0,a_2_2_lattice3(X1,X2)) ) )
| empty_carrier(X1)
| ~ latt_str(X1) ),
inference(rectify,[],[f84]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ( ( in(X0,a_2_2_lattice3(X1,X2))
| ! [X3] :
( ~ element(X3,the_carrier(X1))
| X0 != X3
| ~ latt_set_smaller(X1,X3,X2) ) )
& ( ( element(sK6(X0,X1,X2),the_carrier(X1))
& sK6(X0,X1,X2) = X0
& latt_set_smaller(X1,sK6(X0,X1,X2),X2) )
| ~ in(X0,a_2_2_lattice3(X1,X2)) ) )
| empty_carrier(X1)
| ~ latt_str(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X4,sK6(X0,X1,X2))],[f85]) ).
fof(f87,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = join_of_latt_set(X0,X1)
| ~ latt_element_smaller(X0,X2,X1)
| ? [X3] :
( ~ below(X0,X2,X3)
& latt_element_smaller(X0,X3,X1)
& element(X3,the_carrier(X0)) ) )
& ( ( latt_element_smaller(X0,X2,X1)
& ! [X3] :
( below(X0,X2,X3)
| ~ latt_element_smaller(X0,X3,X1)
| ~ element(X3,the_carrier(X0)) ) )
| join_of_latt_set(X0,X1) != X2 ) )
| ~ element(X2,the_carrier(X0)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ complete_latt_str(X0)
| ~ latt_str(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(nnf_transformation,[],[f53]) ).
fof(f88,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = join_of_latt_set(X0,X1)
| ~ latt_element_smaller(X0,X2,X1)
| ? [X3] :
( ~ below(X0,X2,X3)
& latt_element_smaller(X0,X3,X1)
& element(X3,the_carrier(X0)) ) )
& ( ( latt_element_smaller(X0,X2,X1)
& ! [X3] :
( below(X0,X2,X3)
| ~ latt_element_smaller(X0,X3,X1)
| ~ element(X3,the_carrier(X0)) ) )
| join_of_latt_set(X0,X1) != X2 ) )
| ~ element(X2,the_carrier(X0)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ complete_latt_str(X0)
| ~ latt_str(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f87]) ).
fof(f89,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = join_of_latt_set(X0,X1)
| ~ latt_element_smaller(X0,X2,X1)
| ? [X3] :
( ~ below(X0,X2,X3)
& latt_element_smaller(X0,X3,X1)
& element(X3,the_carrier(X0)) ) )
& ( ( latt_element_smaller(X0,X2,X1)
& ! [X4] :
( below(X0,X2,X4)
| ~ latt_element_smaller(X0,X4,X1)
| ~ element(X4,the_carrier(X0)) ) )
| join_of_latt_set(X0,X1) != X2 ) )
| ~ element(X2,the_carrier(X0)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ complete_latt_str(X0)
| ~ latt_str(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(rectify,[],[f88]) ).
fof(f90,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = join_of_latt_set(X0,X1)
| ~ latt_element_smaller(X0,X2,X1)
| ( ~ below(X0,X2,sK7(X0,X1,X2))
& latt_element_smaller(X0,sK7(X0,X1,X2),X1)
& element(sK7(X0,X1,X2),the_carrier(X0)) ) )
& ( ( latt_element_smaller(X0,X2,X1)
& ! [X4] :
( below(X0,X2,X4)
| ~ latt_element_smaller(X0,X4,X1)
| ~ element(X4,the_carrier(X0)) ) )
| join_of_latt_set(X0,X1) != X2 ) )
| ~ element(X2,the_carrier(X0)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ complete_latt_str(X0)
| ~ latt_str(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f89]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ( ( below_refl(X0,X1,X2)
| ~ below(X0,X1,X2) )
& ( below(X0,X1,X2)
| ~ below_refl(X0,X1,X2) ) )
| empty_carrier(X0)
| ~ meet_commutative(X0)
| ~ meet_absorbing(X0)
| ~ join_absorbing(X0)
| ~ latt_str(X0)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0)) ),
inference(nnf_transformation,[],[f57]) ).
fof(f92,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( latt_element_smaller(X0,X1,X2)
| ? [X3] :
( ~ below(X0,X3,X1)
& in(X3,X2)
& element(X3,the_carrier(X0)) ) )
& ( ! [X3] :
( below(X0,X3,X1)
| ~ in(X3,X2)
| ~ element(X3,the_carrier(X0)) )
| ~ latt_element_smaller(X0,X1,X2) ) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(nnf_transformation,[],[f65]) ).
fof(f93,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( latt_element_smaller(X0,X1,X2)
| ? [X3] :
( ~ below(X0,X3,X1)
& in(X3,X2)
& element(X3,the_carrier(X0)) ) )
& ( ! [X4] :
( below(X0,X4,X1)
| ~ in(X4,X2)
| ~ element(X4,the_carrier(X0)) )
| ~ latt_element_smaller(X0,X1,X2) ) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(rectify,[],[f92]) ).
fof(f94,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( latt_element_smaller(X0,X1,X2)
| ( ~ below(X0,sK8(X0,X1,X2),X1)
& in(sK8(X0,X1,X2),X2)
& element(sK8(X0,X1,X2),the_carrier(X0)) ) )
& ( ! [X4] :
( below(X0,X4,X1)
| ~ in(X4,X2)
| ~ element(X4,the_carrier(X0)) )
| ~ latt_element_smaller(X0,X1,X2) ) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X3,sK8(X0,X1,X2))],[f93]) ).
fof(f95,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( latt_set_smaller(X0,X1,X2)
| ? [X3] :
( ~ below(X0,X1,X3)
& in(X3,X2)
& element(X3,the_carrier(X0)) ) )
& ( ! [X3] :
( below(X0,X1,X3)
| ~ in(X3,X2)
| ~ element(X3,the_carrier(X0)) )
| ~ latt_set_smaller(X0,X1,X2) ) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(nnf_transformation,[],[f67]) ).
fof(f96,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( latt_set_smaller(X0,X1,X2)
| ? [X3] :
( ~ below(X0,X1,X3)
& in(X3,X2)
& element(X3,the_carrier(X0)) ) )
& ( ! [X4] :
( below(X0,X1,X4)
| ~ in(X4,X2)
| ~ element(X4,the_carrier(X0)) )
| ~ latt_set_smaller(X0,X1,X2) ) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(rectify,[],[f95]) ).
fof(f97,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( latt_set_smaller(X0,X1,X2)
| ( ~ below(X0,X1,sK9(X0,X1,X2))
& in(sK9(X0,X1,X2),X2)
& element(sK9(X0,X1,X2),the_carrier(X0)) ) )
& ( ! [X4] :
( below(X0,X1,X4)
| ~ in(X4,X2)
| ~ element(X4,the_carrier(X0)) )
| ~ latt_set_smaller(X0,X1,X2) ) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X3,sK9(X0,X1,X2))],[f96]) ).
fof(f101,plain,
latt_str(sK0),
inference(cnf_transformation,[],[f78]) ).
fof(f102,plain,
complete_latt_str(sK0),
inference(cnf_transformation,[],[f78]) ).
fof(f103,plain,
lattice(sK0),
inference(cnf_transformation,[],[f78]) ).
fof(f104,plain,
~ empty_carrier(sK0),
inference(cnf_transformation,[],[f78]) ).
fof(f105,plain,
element(sK1,the_carrier(sK0)),
inference(cnf_transformation,[],[f78]) ).
fof(f106,plain,
! [X4] :
( below_refl(sK0,X4,sK1)
| ~ latt_set_smaller(sK0,X4,sK2)
| ~ element(X4,the_carrier(sK0))
| sK1 = meet_of_latt_set(sK0,sK2) ),
inference(cnf_transformation,[],[f78]) ).
fof(f107,plain,
( latt_set_smaller(sK0,sK1,sK2)
| sK1 = meet_of_latt_set(sK0,sK2) ),
inference(cnf_transformation,[],[f78]) ).
fof(f108,plain,
( ~ latt_set_smaller(sK0,sK1,sK2)
| element(sK3,the_carrier(sK0))
| sK1 != meet_of_latt_set(sK0,sK2) ),
inference(cnf_transformation,[],[f78]) ).
fof(f109,plain,
( ~ latt_set_smaller(sK0,sK1,sK2)
| latt_set_smaller(sK0,sK3,sK2)
| sK1 != meet_of_latt_set(sK0,sK2) ),
inference(cnf_transformation,[],[f78]) ).
fof(f110,plain,
( ~ latt_set_smaller(sK0,sK1,sK2)
| ~ below_refl(sK0,sK3,sK1)
| sK1 != meet_of_latt_set(sK0,sK2) ),
inference(cnf_transformation,[],[f78]) ).
fof(f112,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f44]) ).
fof(f119,plain,
! [X2,X0,X1] :
( latt_set_smaller(X1,sK6(X0,X1,X2),X2)
| ~ in(X0,a_2_2_lattice3(X1,X2))
| empty_carrier(X1)
| ~ latt_str(X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f120,plain,
! [X2,X0,X1] :
( sK6(X0,X1,X2) = X0
| ~ in(X0,a_2_2_lattice3(X1,X2))
| empty_carrier(X1)
| ~ latt_str(X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f121,plain,
! [X2,X0,X1] :
( element(sK6(X0,X1,X2),the_carrier(X1))
| ~ in(X0,a_2_2_lattice3(X1,X2))
| empty_carrier(X1)
| ~ latt_str(X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f122,plain,
! [X2,X3,X0,X1] :
( in(X0,a_2_2_lattice3(X1,X2))
| ~ element(X3,the_carrier(X1))
| X0 != X3
| ~ latt_set_smaller(X1,X3,X2)
| empty_carrier(X1)
| ~ latt_str(X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f123,plain,
! [X0,X1] :
( meet_of_latt_set(X0,X1) = join_of_latt_set(X0,a_2_2_lattice3(X0,X1))
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f124,plain,
! [X2,X0,X1,X4] :
( below(X0,X2,X4)
| ~ latt_element_smaller(X0,X4,X1)
| ~ element(X4,the_carrier(X0))
| join_of_latt_set(X0,X1) != X2
| ~ element(X2,the_carrier(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ complete_latt_str(X0)
| ~ latt_str(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f125,plain,
! [X2,X0,X1] :
( latt_element_smaller(X0,X2,X1)
| join_of_latt_set(X0,X1) != X2
| ~ element(X2,the_carrier(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ complete_latt_str(X0)
| ~ latt_str(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f126,plain,
! [X2,X0,X1] :
( join_of_latt_set(X0,X1) = X2
| ~ latt_element_smaller(X0,X2,X1)
| element(sK7(X0,X1,X2),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ complete_latt_str(X0)
| ~ latt_str(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f127,plain,
! [X2,X0,X1] :
( join_of_latt_set(X0,X1) = X2
| ~ latt_element_smaller(X0,X2,X1)
| latt_element_smaller(X0,sK7(X0,X1,X2),X1)
| ~ element(X2,the_carrier(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ complete_latt_str(X0)
| ~ latt_str(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f128,plain,
! [X2,X0,X1] :
( join_of_latt_set(X0,X1) = X2
| ~ latt_element_smaller(X0,X2,X1)
| ~ below(X0,X2,sK7(X0,X1,X2))
| ~ element(X2,the_carrier(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ complete_latt_str(X0)
| ~ latt_str(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f130,plain,
! [X2,X0,X1] :
( ~ join_absorbing(X0)
| ~ below_refl(X0,X1,X2)
| empty_carrier(X0)
| ~ meet_commutative(X0)
| ~ meet_absorbing(X0)
| below(X0,X1,X2)
| ~ latt_str(X0)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f131,plain,
! [X2,X0,X1] :
( below_refl(X0,X1,X2)
| ~ below(X0,X1,X2)
| empty_carrier(X0)
| ~ meet_commutative(X0)
| ~ meet_absorbing(X0)
| ~ join_absorbing(X0)
| ~ latt_str(X0)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f133,plain,
! [X0,X1] :
( element(meet_of_latt_set(X0,X1),the_carrier(X0))
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f134,plain,
! [X0,X1] :
( element(join_of_latt_set(X0,X1),the_carrier(X0))
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f135,plain,
! [X2,X0,X1,X4] :
( empty_carrier(X0)
| ~ in(X4,X2)
| ~ element(X4,the_carrier(X0))
| ~ latt_element_smaller(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| below(X0,X4,X1)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f136,plain,
! [X2,X0,X1] :
( element(sK8(X0,X1,X2),the_carrier(X0))
| latt_element_smaller(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f137,plain,
! [X2,X0,X1] :
( in(sK8(X0,X1,X2),X2)
| latt_element_smaller(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f138,plain,
! [X2,X0,X1] :
( ~ below(X0,sK8(X0,X1,X2),X1)
| latt_element_smaller(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f139,plain,
! [X2,X0,X1,X4] :
( empty_carrier(X0)
| ~ in(X4,X2)
| ~ element(X4,the_carrier(X0))
| ~ latt_set_smaller(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| below(X0,X1,X4)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f140,plain,
! [X2,X0,X1] :
( element(sK9(X0,X1,X2),the_carrier(X0))
| latt_set_smaller(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f141,plain,
! [X2,X0,X1] :
( in(sK9(X0,X1,X2),X2)
| latt_set_smaller(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f142,plain,
! [X2,X0,X1] :
( ~ below(X0,X1,sK9(X0,X1,X2))
| latt_set_smaller(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f146,plain,
! [X0] :
( join_absorbing(X0)
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f147,plain,
! [X0] :
( meet_absorbing(X0)
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f149,plain,
! [X0] :
( meet_commutative(X0)
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f155,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f156,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f159,plain,
! [X2,X3,X1] :
( in(X3,a_2_2_lattice3(X1,X2))
| ~ element(X3,the_carrier(X1))
| ~ latt_set_smaller(X1,X3,X2)
| empty_carrier(X1)
| ~ latt_str(X1) ),
inference(equality_resolution,[],[f122]) ).
fof(f160,plain,
! [X0,X1] :
( latt_element_smaller(X0,join_of_latt_set(X0,X1),X1)
| ~ element(join_of_latt_set(X0,X1),the_carrier(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ complete_latt_str(X0)
| ~ latt_str(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(equality_resolution,[],[f125]) ).
fof(f161,plain,
! [X0,X1,X4] :
( below(X0,join_of_latt_set(X0,X1),X4)
| ~ latt_element_smaller(X0,X4,X1)
| ~ element(X4,the_carrier(X0))
| ~ element(join_of_latt_set(X0,X1),the_carrier(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ complete_latt_str(X0)
| ~ latt_str(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(equality_resolution,[],[f124]) ).
fof(f162,plain,
! [X0,X1,X4] :
( below(X0,join_of_latt_set(X0,X1),X4)
| ~ latt_element_smaller(X0,X4,X1)
| ~ element(X4,the_carrier(X0))
| ~ element(join_of_latt_set(X0,X1),the_carrier(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ complete_latt_str(X0)
| ~ latt_str(X0) ),
inference(duplicate_literal_removal,[],[f161]) ).
fof(f163,plain,
! [X0,X1] :
( latt_element_smaller(X0,join_of_latt_set(X0,X1),X1)
| ~ element(join_of_latt_set(X0,X1),the_carrier(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ complete_latt_str(X0)
| ~ latt_str(X0) ),
inference(duplicate_literal_removal,[],[f160]) ).
fof(f164,plain,
! [X2,X0,X1] :
( element(sK7(X0,X1,X2),the_carrier(X0))
| ~ latt_element_smaller(X0,X2,X1)
| join_of_latt_set(X0,X1) = X2
| ~ element(X2,the_carrier(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ complete_latt_str(X0)
| ~ latt_str(X0) ),
inference(duplicate_literal_removal,[],[f126]) ).
fof(f165,plain,
! [X2,X0,X1] :
( ~ complete_latt_str(X0)
| ~ latt_element_smaller(X0,X2,X1)
| latt_element_smaller(X0,sK7(X0,X1,X2),X1)
| ~ element(X2,the_carrier(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| join_of_latt_set(X0,X1) = X2
| ~ latt_str(X0) ),
inference(duplicate_literal_removal,[],[f127]) ).
fof(f166,plain,
! [X2,X0,X1] :
( ~ complete_latt_str(X0)
| ~ latt_element_smaller(X0,X2,X1)
| ~ below(X0,X2,sK7(X0,X1,X2))
| ~ element(X2,the_carrier(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| join_of_latt_set(X0,X1) = X2
| ~ latt_str(X0) ),
inference(duplicate_literal_removal,[],[f128]) ).
fof(f167,plain,
! [X0,X1,X4] :
( ~ complete_latt_str(X0)
| ~ latt_element_smaller(X0,X4,X1)
| ~ element(X4,the_carrier(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| below(X0,join_of_latt_set(X0,X1),X4)
| ~ latt_str(X0) ),
inference(forward_subsumption_resolution,[],[f162,f134]) ).
fof(f168,plain,
! [X0,X1] :
( ~ complete_latt_str(X0)
| empty_carrier(X0)
| ~ lattice(X0)
| latt_element_smaller(X0,join_of_latt_set(X0,X1),X1)
| ~ latt_str(X0) ),
inference(forward_subsumption_resolution,[],[f163,f134]) ).
fof(f170,definition,
( spl13_1
<=> sK1 = meet_of_latt_set(sK0,sK2) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f171,plain,
( sK1 != meet_of_latt_set(sK0,sK2)
| spl13_1 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f172,plain,
( sK1 = meet_of_latt_set(sK0,sK2)
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f174,definition,
( spl13_2
<=> ! [X4] :
( below_refl(sK0,X4,sK1)
| ~ element(X4,the_carrier(sK0))
| ~ latt_set_smaller(sK0,X4,sK2) ) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f175,plain,
( ! [X4] :
( below_refl(sK0,X4,sK1)
| ~ element(X4,the_carrier(sK0))
| ~ latt_set_smaller(sK0,X4,sK2) )
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f176,plain,
( spl13_1
| spl13_2 ),
inference(avatar_split_clause,[],[f106,f174,f170]) ).
fof(f178,definition,
( spl13_3
<=> latt_set_smaller(sK0,sK1,sK2) ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
fof(f179,plain,
( ~ latt_set_smaller(sK0,sK1,sK2)
| spl13_3 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f180,plain,
( latt_set_smaller(sK0,sK1,sK2)
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f181,plain,
( spl13_1
| spl13_3 ),
inference(avatar_split_clause,[],[f107,f178,f170]) ).
fof(f183,definition,
( spl13_4
<=> element(sK3,the_carrier(sK0)) ),
introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition]) ).
fof(f185,plain,
( element(sK3,the_carrier(sK0))
| ~ spl13_4 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f186,plain,
( ~ spl13_1
| spl13_4
| ~ spl13_3 ),
inference(avatar_split_clause,[],[f108,f178,f183,f170]) ).
fof(f188,definition,
( spl13_5
<=> latt_set_smaller(sK0,sK3,sK2) ),
introduced(definition,[new_symbols(definition,[spl13_5])],[avatar_definition]) ).
fof(f190,plain,
( latt_set_smaller(sK0,sK3,sK2)
| ~ spl13_5 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f191,plain,
( ~ spl13_1
| spl13_5
| ~ spl13_3 ),
inference(avatar_split_clause,[],[f109,f178,f188,f170]) ).
fof(f193,definition,
( spl13_6
<=> below_refl(sK0,sK3,sK1) ),
introduced(definition,[new_symbols(definition,[spl13_6])],[avatar_definition]) ).
fof(f195,plain,
( ~ below_refl(sK0,sK3,sK1)
| spl13_6 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f196,plain,
( ~ spl13_1
| ~ spl13_6
| ~ spl13_3 ),
inference(avatar_split_clause,[],[f110,f178,f193,f170]) ).
fof(f203,plain,
! [X0] :
( empty_carrier(sK0)
| ~ lattice(sK0)
| latt_element_smaller(sK0,join_of_latt_set(sK0,X0),X0)
| ~ latt_str(sK0) ),
inference(resolution,[],[f168,f102]) ).
fof(f204,plain,
! [X0] :
( ~ lattice(sK0)
| latt_element_smaller(sK0,join_of_latt_set(sK0,X0),X0)
| ~ latt_str(sK0) ),
inference(forward_subsumption_resolution,[],[f203,f104]) ).
fof(f205,plain,
! [X0] :
( latt_element_smaller(sK0,join_of_latt_set(sK0,X0),X0)
| ~ latt_str(sK0) ),
inference(forward_subsumption_resolution,[],[f204,f103]) ).
fof(f206,plain,
! [X0] : latt_element_smaller(sK0,join_of_latt_set(sK0,X0),X0),
inference(forward_subsumption_resolution,[],[f205,f101]) ).
fof(f210,plain,
! [X2,X0,X1] :
( latt_set_smaller(X1,X0,X2)
| ~ in(X0,a_2_2_lattice3(X1,X2))
| empty_carrier(X1)
| ~ latt_str(X1)
| ~ in(X0,a_2_2_lattice3(X1,X2))
| empty_carrier(X1)
| ~ latt_str(X1) ),
inference(superposition,[],[f119,f120]) ).
fof(f211,plain,
! [X2,X0,X1] :
( latt_set_smaller(X1,X0,X2)
| ~ in(X0,a_2_2_lattice3(X1,X2))
| empty_carrier(X1)
| ~ latt_str(X1) ),
inference(duplicate_literal_removal,[],[f210]) ).
fof(f212,plain,
! [X2,X0,X1] :
( element(X0,the_carrier(X1))
| ~ in(X0,a_2_2_lattice3(X1,X2))
| empty_carrier(X1)
| ~ latt_str(X1)
| ~ in(X0,a_2_2_lattice3(X1,X2))
| empty_carrier(X1)
| ~ latt_str(X1) ),
inference(superposition,[],[f121,f120]) ).
fof(f213,plain,
! [X2,X0,X1] :
( element(X0,the_carrier(X1))
| ~ in(X0,a_2_2_lattice3(X1,X2))
| empty_carrier(X1)
| ~ latt_str(X1) ),
inference(duplicate_literal_removal,[],[f212]) ).
fof(f234,plain,
! [X0,X1] :
( ~ latt_element_smaller(sK0,X0,X1)
| ~ element(X0,the_carrier(sK0))
| empty_carrier(sK0)
| ~ lattice(sK0)
| below(sK0,join_of_latt_set(sK0,X1),X0)
| ~ latt_str(sK0) ),
inference(resolution,[],[f167,f102]) ).
fof(f235,plain,
! [X0,X1] :
( ~ latt_element_smaller(sK0,X0,X1)
| ~ element(X0,the_carrier(sK0))
| ~ lattice(sK0)
| below(sK0,join_of_latt_set(sK0,X1),X0)
| ~ latt_str(sK0) ),
inference(forward_subsumption_resolution,[],[f234,f104]) ).
fof(f236,plain,
! [X0,X1] :
( ~ latt_element_smaller(sK0,X0,X1)
| ~ element(X0,the_carrier(sK0))
| below(sK0,join_of_latt_set(sK0,X1),X0)
| ~ latt_str(sK0) ),
inference(forward_subsumption_resolution,[],[f235,f103]) ).
fof(f237,plain,
! [X0,X1] :
( below(sK0,join_of_latt_set(sK0,X1),X0)
| ~ element(X0,the_carrier(sK0))
| ~ latt_element_smaller(sK0,X0,X1) ),
inference(forward_subsumption_resolution,[],[f236,f101]) ).
fof(f238,plain,
! [X0,X1] :
( ~ element(sK9(sK0,join_of_latt_set(sK0,X0),X1),the_carrier(sK0))
| ~ latt_element_smaller(sK0,sK9(sK0,join_of_latt_set(sK0,X0),X1),X0)
| latt_set_smaller(sK0,join_of_latt_set(sK0,X0),X1)
| ~ element(join_of_latt_set(sK0,X0),the_carrier(sK0))
| empty_carrier(sK0)
| ~ latt_str(sK0) ),
inference(resolution,[],[f237,f142]) ).
fof(f241,plain,
! [X0,X1] :
( ~ latt_element_smaller(sK0,sK9(sK0,join_of_latt_set(sK0,X0),X1),X0)
| latt_set_smaller(sK0,join_of_latt_set(sK0,X0),X1)
| ~ element(join_of_latt_set(sK0,X0),the_carrier(sK0))
| empty_carrier(sK0)
| ~ latt_str(sK0) ),
inference(forward_subsumption_resolution,[],[f238,f140]) ).
fof(f243,plain,
! [X0,X1] :
( ~ latt_element_smaller(sK0,sK9(sK0,join_of_latt_set(sK0,X0),X1),X0)
| latt_set_smaller(sK0,join_of_latt_set(sK0,X0),X1)
| empty_carrier(sK0)
| ~ latt_str(sK0) ),
inference(forward_subsumption_resolution,[],[f241,f134]) ).
fof(f244,plain,
! [X0,X1] :
( ~ latt_element_smaller(sK0,sK9(sK0,join_of_latt_set(sK0,X0),X1),X0)
| latt_set_smaller(sK0,join_of_latt_set(sK0,X0),X1)
| ~ latt_str(sK0) ),
inference(forward_subsumption_resolution,[],[f243,f104]) ).
fof(f245,plain,
! [X0,X1] :
( ~ latt_element_smaller(sK0,sK9(sK0,join_of_latt_set(sK0,X0),X1),X0)
| latt_set_smaller(sK0,join_of_latt_set(sK0,X0),X1) ),
inference(forward_subsumption_resolution,[],[f244,f101]) ).
fof(f246,plain,
! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ element(X0,the_carrier(sK0))
| ~ latt_element_smaller(sK0,X2,X1)
| ~ element(X2,the_carrier(sK0))
| below(sK0,X0,X2)
| ~ latt_str(sK0) ),
inference(resolution,[],[f135,f104]) ).
fof(f256,plain,
! [X2,X0,X1] :
( ~ latt_element_smaller(sK0,X2,X1)
| ~ element(X0,the_carrier(sK0))
| ~ in(X0,X1)
| ~ element(X2,the_carrier(sK0))
| below(sK0,X0,X2) ),
inference(forward_subsumption_resolution,[],[f246,f101]) ).
fof(f257,plain,
! [X0,X1] :
( ~ latt_element_smaller(sK0,sK9(sK0,meet_of_latt_set(sK0,X0),X1),a_2_2_lattice3(sK0,X0))
| latt_set_smaller(sK0,meet_of_latt_set(sK0,X0),X1)
| empty_carrier(sK0)
| ~ latt_str(sK0) ),
inference(superposition,[],[f245,f123]) ).
fof(f258,plain,
! [X0,X1] :
( ~ latt_element_smaller(sK0,sK9(sK0,meet_of_latt_set(sK0,X0),X1),a_2_2_lattice3(sK0,X0))
| latt_set_smaller(sK0,meet_of_latt_set(sK0,X0),X1)
| ~ latt_str(sK0) ),
inference(forward_subsumption_resolution,[],[f257,f104]) ).
fof(f259,plain,
! [X0,X1] :
( ~ latt_element_smaller(sK0,sK9(sK0,meet_of_latt_set(sK0,X0),X1),a_2_2_lattice3(sK0,X0))
| latt_set_smaller(sK0,meet_of_latt_set(sK0,X0),X1) ),
inference(forward_subsumption_resolution,[],[f258,f101]) ).
fof(f260,plain,
! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ element(X0,the_carrier(sK0))
| ~ latt_set_smaller(sK0,X2,X1)
| ~ element(X2,the_carrier(sK0))
| below(sK0,X2,X0)
| ~ latt_str(sK0) ),
inference(resolution,[],[f139,f104]) ).
fof(f262,plain,
! [X2,X0,X1] :
( below(sK0,X2,X0)
| ~ element(X0,the_carrier(sK0))
| ~ latt_set_smaller(sK0,X2,X1)
| ~ element(X2,the_carrier(sK0))
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[],[f260,f101]) ).
fof(f266,plain,
! [X2,X0,X1] :
( ~ below_refl(X0,X1,X2)
| empty_carrier(X0)
| ~ meet_commutative(X0)
| ~ meet_absorbing(X0)
| below(X0,X1,X2)
| ~ latt_str(X0)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(resolution,[],[f130,f146]) ).
fof(f267,plain,
! [X2,X0,X1] :
( ~ below_refl(X0,X1,X2)
| empty_carrier(X0)
| ~ meet_commutative(X0)
| ~ meet_absorbing(X0)
| below(X0,X1,X2)
| ~ latt_str(X0)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ lattice(X0) ),
inference(duplicate_literal_removal,[],[f266]) ).
fof(f268,plain,
! [X2,X0,X1] :
( ~ below_refl(X0,X1,X2)
| empty_carrier(X0)
| ~ meet_absorbing(X0)
| below(X0,X1,X2)
| ~ latt_str(X0)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ lattice(X0) ),
inference(forward_subsumption_resolution,[],[f267,f149]) ).
fof(f269,plain,
! [X2,X0,X1] :
( ~ lattice(X0)
| empty_carrier(X0)
| below(X0,X1,X2)
| ~ latt_str(X0)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ below_refl(X0,X1,X2) ),
inference(forward_subsumption_resolution,[],[f268,f147]) ).
fof(f270,plain,
! [X0,X1] :
( below(sK0,X0,join_of_latt_set(sK0,X1))
| ~ in(X0,X1)
| ~ element(join_of_latt_set(sK0,X1),the_carrier(sK0))
| ~ element(X0,the_carrier(sK0)) ),
inference(resolution,[],[f256,f206]) ).
fof(f272,plain,
! [X2,X0,X1] :
( ~ element(X0,the_carrier(sK0))
| ~ latt_set_smaller(sK0,sK8(sK0,X0,X1),X2)
| ~ element(sK8(sK0,X0,X1),the_carrier(sK0))
| ~ in(X0,X2)
| latt_element_smaller(sK0,X0,X1)
| ~ element(X0,the_carrier(sK0))
| empty_carrier(sK0)
| ~ latt_str(sK0) ),
inference(resolution,[],[f262,f138]) ).
fof(f275,plain,
! [X2,X0,X1] :
( ~ element(X0,the_carrier(sK0))
| ~ latt_set_smaller(sK0,sK8(sK0,X0,X1),X2)
| ~ element(sK8(sK0,X0,X1),the_carrier(sK0))
| ~ in(X0,X2)
| latt_element_smaller(sK0,X0,X1)
| empty_carrier(sK0)
| ~ latt_str(sK0) ),
inference(duplicate_literal_removal,[],[f272]) ).
fof(f277,plain,
! [X2,X0,X1] :
( ~ element(X0,the_carrier(sK0))
| ~ latt_set_smaller(sK0,sK8(sK0,X0,X1),X2)
| ~ in(X0,X2)
| latt_element_smaller(sK0,X0,X1)
| empty_carrier(sK0)
| ~ latt_str(sK0) ),
inference(forward_subsumption_resolution,[],[f275,f136]) ).
fof(f279,plain,
! [X2,X0,X1] :
( ~ element(X0,the_carrier(sK0))
| ~ latt_set_smaller(sK0,sK8(sK0,X0,X1),X2)
| ~ in(X0,X2)
| latt_element_smaller(sK0,X0,X1)
| ~ latt_str(sK0) ),
inference(forward_subsumption_resolution,[],[f277,f104]) ).
fof(f281,plain,
! [X2,X0,X1] :
( ~ latt_set_smaller(sK0,sK8(sK0,X0,X1),X2)
| ~ element(X0,the_carrier(sK0))
| ~ in(X0,X2)
| latt_element_smaller(sK0,X0,X1) ),
inference(forward_subsumption_resolution,[],[f279,f101]) ).
fof(f282,plain,
! [X0,X1] :
( ~ latt_element_smaller(sK0,X0,X1)
| latt_element_smaller(sK0,sK7(sK0,X1,X0),X1)
| ~ element(X0,the_carrier(sK0))
| empty_carrier(sK0)
| ~ lattice(sK0)
| join_of_latt_set(sK0,X1) = X0
| ~ latt_str(sK0) ),
inference(resolution,[],[f165,f102]) ).
fof(f283,plain,
! [X0,X1] :
( ~ latt_element_smaller(sK0,X0,X1)
| latt_element_smaller(sK0,sK7(sK0,X1,X0),X1)
| ~ element(X0,the_carrier(sK0))
| ~ lattice(sK0)
| join_of_latt_set(sK0,X1) = X0
| ~ latt_str(sK0) ),
inference(forward_subsumption_resolution,[],[f282,f104]) ).
fof(f284,plain,
! [X0,X1] :
( ~ latt_element_smaller(sK0,X0,X1)
| latt_element_smaller(sK0,sK7(sK0,X1,X0),X1)
| ~ element(X0,the_carrier(sK0))
| join_of_latt_set(sK0,X1) = X0
| ~ latt_str(sK0) ),
inference(forward_subsumption_resolution,[],[f283,f103]) ).
fof(f285,plain,
! [X0,X1] :
( latt_element_smaller(sK0,sK7(sK0,X1,X0),X1)
| ~ latt_element_smaller(sK0,X0,X1)
| ~ element(X0,the_carrier(sK0))
| join_of_latt_set(sK0,X1) = X0 ),
inference(forward_subsumption_resolution,[],[f284,f101]) ).
fof(f286,plain,
! [X0,X1] :
( ~ latt_element_smaller(sK0,X0,X1)
| ~ below(sK0,X0,sK7(sK0,X1,X0))
| ~ element(X0,the_carrier(sK0))
| empty_carrier(sK0)
| ~ lattice(sK0)
| join_of_latt_set(sK0,X1) = X0
| ~ latt_str(sK0) ),
inference(resolution,[],[f166,f102]) ).
fof(f287,plain,
! [X0,X1] :
( ~ latt_element_smaller(sK0,X0,X1)
| ~ below(sK0,X0,sK7(sK0,X1,X0))
| ~ element(X0,the_carrier(sK0))
| ~ lattice(sK0)
| join_of_latt_set(sK0,X1) = X0
| ~ latt_str(sK0) ),
inference(forward_subsumption_resolution,[],[f286,f104]) ).
fof(f288,plain,
! [X0,X1] :
( ~ latt_element_smaller(sK0,X0,X1)
| ~ below(sK0,X0,sK7(sK0,X1,X0))
| ~ element(X0,the_carrier(sK0))
| join_of_latt_set(sK0,X1) = X0
| ~ latt_str(sK0) ),
inference(forward_subsumption_resolution,[],[f287,f103]) ).
fof(f289,plain,
! [X0,X1] :
( ~ below(sK0,X0,sK7(sK0,X1,X0))
| ~ latt_element_smaller(sK0,X0,X1)
| ~ element(X0,the_carrier(sK0))
| join_of_latt_set(sK0,X1) = X0 ),
inference(forward_subsumption_resolution,[],[f288,f101]) ).
fof(f292,plain,
! [X2,X0,X1] :
( ~ element(X0,the_carrier(sK0))
| ~ in(X0,X1)
| latt_element_smaller(sK0,X0,X2)
| ~ in(sK8(sK0,X0,X2),a_2_2_lattice3(sK0,X1))
| empty_carrier(sK0)
| ~ latt_str(sK0) ),
inference(resolution,[],[f281,f211]) ).
fof(f293,plain,
! [X2,X0,X1] :
( ~ element(X0,the_carrier(sK0))
| ~ in(X0,X1)
| latt_element_smaller(sK0,X0,X2)
| ~ in(sK8(sK0,X0,X2),a_2_2_lattice3(sK0,X1))
| ~ latt_str(sK0) ),
inference(forward_subsumption_resolution,[],[f292,f104]) ).
fof(f294,plain,
! [X2,X0,X1] :
( ~ in(sK8(sK0,X0,X2),a_2_2_lattice3(sK0,X1))
| ~ in(X0,X1)
| latt_element_smaller(sK0,X0,X2)
| ~ element(X0,the_carrier(sK0)) ),
inference(forward_subsumption_resolution,[],[f293,f101]) ).
fof(f295,plain,
! [X2,X0,X1] :
( below(sK0,X2,sK7(sK0,X1,X0))
| ~ element(X0,the_carrier(sK0))
| join_of_latt_set(sK0,X1) = X0
| ~ element(X2,the_carrier(sK0))
| ~ in(X2,X1)
| ~ element(sK7(sK0,X1,X0),the_carrier(sK0))
| ~ latt_element_smaller(sK0,X0,X1) ),
inference(resolution,[],[f285,f256]) ).
fof(f297,plain,
! [X0,X1] :
( below(sK0,X1,meet_of_latt_set(sK0,X0))
| ~ in(X1,a_2_2_lattice3(sK0,X0))
| ~ element(meet_of_latt_set(sK0,X0),the_carrier(sK0))
| ~ element(X1,the_carrier(sK0))
| empty_carrier(sK0)
| ~ latt_str(sK0) ),
inference(superposition,[],[f270,f123]) ).
fof(f299,plain,
! [X0,X1] :
( below(sK0,X1,meet_of_latt_set(sK0,X0))
| ~ in(X1,a_2_2_lattice3(sK0,X0))
| ~ element(X1,the_carrier(sK0))
| empty_carrier(sK0)
| ~ latt_str(sK0) ),
inference(forward_subsumption_resolution,[],[f297,f133]) ).
fof(f301,plain,
! [X0,X1] :
( below(sK0,X1,meet_of_latt_set(sK0,X0))
| ~ in(X1,a_2_2_lattice3(sK0,X0))
| empty_carrier(sK0)
| ~ latt_str(sK0) ),
inference(forward_subsumption_resolution,[],[f299,f213]) ).
fof(f303,plain,
! [X0,X1] :
( below(sK0,X1,meet_of_latt_set(sK0,X0))
| ~ in(X1,a_2_2_lattice3(sK0,X0))
| ~ latt_str(sK0) ),
inference(forward_subsumption_resolution,[],[f301,f104]) ).
fof(f305,plain,
! [X0,X1] :
( below(sK0,X1,meet_of_latt_set(sK0,X0))
| ~ in(X1,a_2_2_lattice3(sK0,X0)) ),
inference(forward_subsumption_resolution,[],[f303,f101]) ).
fof(f330,plain,
! [X0,X1] :
( empty_carrier(sK0)
| below(sK0,X0,X1)
| ~ latt_str(sK0)
| ~ element(X0,the_carrier(sK0))
| ~ element(X1,the_carrier(sK0))
| ~ below_refl(sK0,X0,X1) ),
inference(resolution,[],[f269,f103]) ).
fof(f333,plain,
! [X0,X1] :
( below(sK0,X0,X1)
| ~ latt_str(sK0)
| ~ element(X0,the_carrier(sK0))
| ~ element(X1,the_carrier(sK0))
| ~ below_refl(sK0,X0,X1) ),
inference(forward_subsumption_resolution,[],[f330,f104]) ).
fof(f334,plain,
! [X0,X1] :
( ~ below_refl(sK0,X0,X1)
| ~ element(X0,the_carrier(sK0))
| ~ element(X1,the_carrier(sK0))
| below(sK0,X0,X1) ),
inference(forward_subsumption_resolution,[],[f333,f101]) ).
fof(f344,plain,
( ! [X0] :
( ~ element(X0,the_carrier(sK0))
| ~ element(sK1,the_carrier(sK0))
| below(sK0,X0,sK1)
| ~ element(X0,the_carrier(sK0))
| ~ latt_set_smaller(sK0,X0,sK2) )
| ~ spl13_2 ),
inference(resolution,[],[f334,f175]) ).
fof(f349,plain,
( ! [X0] :
( ~ element(X0,the_carrier(sK0))
| ~ element(sK1,the_carrier(sK0))
| below(sK0,X0,sK1)
| ~ latt_set_smaller(sK0,X0,sK2) )
| ~ spl13_2 ),
inference(duplicate_literal_removal,[],[f344]) ).
fof(f351,plain,
( ! [X0] :
( below(sK0,X0,sK1)
| ~ element(X0,the_carrier(sK0))
| ~ latt_set_smaller(sK0,X0,sK2) )
| ~ spl13_2 ),
inference(forward_subsumption_resolution,[],[f349,f105]) ).
fof(f357,definition,
( spl13_11
<=> join_absorbing(sK0) ),
introduced(definition,[new_symbols(definition,[spl13_11])],[avatar_definition]) ).
fof(f358,plain,
( join_absorbing(sK0)
| ~ spl13_11 ),
inference(avatar_component_clause,[],[f357]) ).
fof(f359,plain,
( ~ join_absorbing(sK0)
| spl13_11 ),
inference(avatar_component_clause,[],[f357]) ).
fof(f361,definition,
( spl13_12
<=> meet_absorbing(sK0) ),
introduced(definition,[new_symbols(definition,[spl13_12])],[avatar_definition]) ).
fof(f362,plain,
( meet_absorbing(sK0)
| ~ spl13_12 ),
inference(avatar_component_clause,[],[f361]) ).
fof(f363,plain,
( ~ meet_absorbing(sK0)
| spl13_12 ),
inference(avatar_component_clause,[],[f361]) ).
fof(f365,definition,
( spl13_13
<=> meet_commutative(sK0) ),
introduced(definition,[new_symbols(definition,[spl13_13])],[avatar_definition]) ).
fof(f366,plain,
( meet_commutative(sK0)
| ~ spl13_13 ),
inference(avatar_component_clause,[],[f365]) ).
fof(f367,plain,
( ~ meet_commutative(sK0)
| spl13_13 ),
inference(avatar_component_clause,[],[f365]) ).
fof(f375,plain,
( empty_carrier(sK0)
| ~ lattice(sK0)
| ~ latt_str(sK0)
| spl13_11 ),
inference(resolution,[],[f359,f146]) ).
fof(f376,plain,
( ~ lattice(sK0)
| ~ latt_str(sK0)
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f375,f104]) ).
fof(f377,plain,
( ~ latt_str(sK0)
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f376,f103]) ).
fof(f378,plain,
( $false
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f377,f101]) ).
fof(f379,plain,
spl13_11,
inference(avatar_contradiction_clause,[],[f378]) ).
fof(f388,plain,
( empty_carrier(sK0)
| ~ lattice(sK0)
| ~ latt_str(sK0)
| spl13_12 ),
inference(resolution,[],[f363,f147]) ).
fof(f389,plain,
( ~ lattice(sK0)
| ~ latt_str(sK0)
| spl13_12 ),
inference(forward_subsumption_resolution,[],[f388,f104]) ).
fof(f390,plain,
( ~ latt_str(sK0)
| spl13_12 ),
inference(forward_subsumption_resolution,[],[f389,f103]) ).
fof(f391,plain,
( $false
| spl13_12 ),
inference(forward_subsumption_resolution,[],[f390,f101]) ).
fof(f392,plain,
spl13_12,
inference(avatar_contradiction_clause,[],[f391]) ).
fof(f403,plain,
! [X0,X1] :
( ~ element(X0,the_carrier(sK0))
| join_of_latt_set(sK0,X1) = X0
| ~ element(X0,the_carrier(sK0))
| ~ in(X0,X1)
| ~ element(sK7(sK0,X1,X0),the_carrier(sK0))
| ~ latt_element_smaller(sK0,X0,X1)
| ~ latt_element_smaller(sK0,X0,X1)
| ~ element(X0,the_carrier(sK0))
| join_of_latt_set(sK0,X1) = X0 ),
inference(resolution,[],[f295,f289]) ).
fof(f406,plain,
! [X0,X1] :
( ~ element(sK7(sK0,X1,X0),the_carrier(sK0))
| join_of_latt_set(sK0,X1) = X0
| ~ in(X0,X1)
| ~ element(X0,the_carrier(sK0))
| ~ latt_element_smaller(sK0,X0,X1) ),
inference(duplicate_literal_removal,[],[f403]) ).
fof(f414,plain,
( empty_carrier(sK0)
| ~ lattice(sK0)
| ~ latt_str(sK0)
| spl13_13 ),
inference(resolution,[],[f367,f149]) ).
fof(f415,plain,
( ~ lattice(sK0)
| ~ latt_str(sK0)
| spl13_13 ),
inference(forward_subsumption_resolution,[],[f414,f104]) ).
fof(f416,plain,
( ~ latt_str(sK0)
| spl13_13 ),
inference(forward_subsumption_resolution,[],[f415,f103]) ).
fof(f417,plain,
( $false
| spl13_13 ),
inference(forward_subsumption_resolution,[],[f416,f101]) ).
fof(f418,plain,
spl13_13,
inference(avatar_contradiction_clause,[],[f417]) ).
fof(f468,plain,
( ! [X0] :
( ~ element(sK8(sK0,sK1,X0),the_carrier(sK0))
| ~ latt_set_smaller(sK0,sK8(sK0,sK1,X0),sK2)
| latt_element_smaller(sK0,sK1,X0)
| ~ element(sK1,the_carrier(sK0))
| empty_carrier(sK0)
| ~ latt_str(sK0) )
| ~ spl13_2 ),
inference(resolution,[],[f351,f138]) ).
fof(f469,plain,
( ! [X0] :
( ~ latt_set_smaller(sK0,sK8(sK0,sK1,X0),sK2)
| latt_element_smaller(sK0,sK1,X0)
| ~ element(sK1,the_carrier(sK0))
| empty_carrier(sK0)
| ~ latt_str(sK0) )
| ~ spl13_2 ),
inference(forward_subsumption_resolution,[],[f468,f136]) ).
fof(f470,plain,
( ! [X0] :
( ~ latt_set_smaller(sK0,sK8(sK0,sK1,X0),sK2)
| latt_element_smaller(sK0,sK1,X0)
| empty_carrier(sK0)
| ~ latt_str(sK0) )
| ~ spl13_2 ),
inference(forward_subsumption_resolution,[],[f469,f105]) ).
fof(f471,plain,
( ! [X0] :
( ~ latt_set_smaller(sK0,sK8(sK0,sK1,X0),sK2)
| latt_element_smaller(sK0,sK1,X0)
| ~ latt_str(sK0) )
| ~ spl13_2 ),
inference(forward_subsumption_resolution,[],[f470,f104]) ).
fof(f472,plain,
( ! [X0] :
( latt_element_smaller(sK0,sK1,X0)
| ~ latt_set_smaller(sK0,sK8(sK0,sK1,X0),sK2) )
| ~ spl13_2 ),
inference(forward_subsumption_resolution,[],[f471,f101]) ).
fof(f491,plain,
! [X0,X1] :
( ~ in(X0,X1)
| latt_element_smaller(sK0,X0,a_2_2_lattice3(sK0,X1))
| ~ element(X0,the_carrier(sK0))
| latt_element_smaller(sK0,X0,a_2_2_lattice3(sK0,X1))
| ~ element(X0,the_carrier(sK0))
| empty_carrier(sK0)
| ~ latt_str(sK0) ),
inference(resolution,[],[f294,f137]) ).
fof(f492,plain,
! [X0,X1] :
( ~ in(X0,X1)
| latt_element_smaller(sK0,X0,a_2_2_lattice3(sK0,X1))
| ~ element(X0,the_carrier(sK0))
| empty_carrier(sK0)
| ~ latt_str(sK0) ),
inference(duplicate_literal_removal,[],[f491]) ).
fof(f493,plain,
! [X0,X1] :
( ~ in(X0,X1)
| latt_element_smaller(sK0,X0,a_2_2_lattice3(sK0,X1))
| ~ element(X0,the_carrier(sK0))
| ~ latt_str(sK0) ),
inference(forward_subsumption_resolution,[],[f492,f104]) ).
fof(f495,plain,
! [X0,X1] :
( latt_element_smaller(sK0,X0,a_2_2_lattice3(sK0,X1))
| ~ in(X0,X1)
| ~ element(X0,the_carrier(sK0)) ),
inference(forward_subsumption_resolution,[],[f493,f101]) ).
fof(f507,plain,
! [X0,X1] :
( join_of_latt_set(sK0,X0) = X1
| ~ in(X1,X0)
| ~ element(X1,the_carrier(sK0))
| ~ latt_element_smaller(sK0,X1,X0)
| ~ latt_element_smaller(sK0,X1,X0)
| join_of_latt_set(sK0,X0) = X1
| ~ element(X1,the_carrier(sK0))
| empty_carrier(sK0)
| ~ lattice(sK0)
| ~ complete_latt_str(sK0)
| ~ latt_str(sK0) ),
inference(resolution,[],[f406,f164]) ).
fof(f511,plain,
! [X0,X1] :
( join_of_latt_set(sK0,X0) = X1
| ~ in(X1,X0)
| ~ element(X1,the_carrier(sK0))
| ~ latt_element_smaller(sK0,X1,X0)
| empty_carrier(sK0)
| ~ lattice(sK0)
| ~ complete_latt_str(sK0)
| ~ latt_str(sK0) ),
inference(duplicate_literal_removal,[],[f507]) ).
fof(f513,plain,
! [X0,X1] :
( join_of_latt_set(sK0,X0) = X1
| ~ in(X1,X0)
| ~ element(X1,the_carrier(sK0))
| ~ latt_element_smaller(sK0,X1,X0)
| ~ lattice(sK0)
| ~ complete_latt_str(sK0)
| ~ latt_str(sK0) ),
inference(forward_subsumption_resolution,[],[f511,f104]) ).
fof(f515,plain,
! [X0,X1] :
( join_of_latt_set(sK0,X0) = X1
| ~ in(X1,X0)
| ~ element(X1,the_carrier(sK0))
| ~ latt_element_smaller(sK0,X1,X0)
| ~ complete_latt_str(sK0)
| ~ latt_str(sK0) ),
inference(forward_subsumption_resolution,[],[f513,f103]) ).
fof(f516,plain,
! [X0,X1] :
( join_of_latt_set(sK0,X0) = X1
| ~ in(X1,X0)
| ~ element(X1,the_carrier(sK0))
| ~ latt_element_smaller(sK0,X1,X0)
| ~ latt_str(sK0) ),
inference(forward_subsumption_resolution,[],[f515,f102]) ).
fof(f517,plain,
! [X0,X1] :
( ~ in(X1,X0)
| join_of_latt_set(sK0,X0) = X1
| ~ element(X1,the_carrier(sK0))
| ~ latt_element_smaller(sK0,X1,X0) ),
inference(forward_subsumption_resolution,[],[f516,f101]) ).
fof(f518,plain,
! [X0,X1] :
( empty(X0)
| ~ element(X1,the_carrier(sK0))
| ~ latt_element_smaller(sK0,X1,X0)
| join_of_latt_set(sK0,X0) = X1
| ~ element(X1,X0) ),
inference(resolution,[],[f517,f155]) ).
fof(f553,plain,
! [X0,X1] :
( ~ latt_element_smaller(sK0,X0,X1)
| ~ element(X0,the_carrier(sK0))
| join_of_latt_set(sK0,X1) = X0
| ~ element(X0,X1)
| empty_set = X1 ),
inference(resolution,[],[f518,f112]) ).
fof(f885,definition,
( spl13_26
<=> element(sK1,a_2_2_lattice3(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl13_26])],[avatar_definition]) ).
fof(f886,plain,
( element(sK1,a_2_2_lattice3(sK0,sK2))
| ~ spl13_26 ),
inference(avatar_component_clause,[],[f885]) ).
fof(f887,plain,
( ~ element(sK1,a_2_2_lattice3(sK0,sK2))
| spl13_26 ),
inference(avatar_component_clause,[],[f885]) ).
fof(f896,plain,
( ~ in(sK1,a_2_2_lattice3(sK0,sK2))
| spl13_26 ),
inference(resolution,[],[f887,f156]) ).
fof(f987,definition,
( spl13_31
<=> sK1 = join_of_latt_set(sK0,a_2_2_lattice3(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl13_31])],[avatar_definition]) ).
fof(f988,plain,
( sK1 != join_of_latt_set(sK0,a_2_2_lattice3(sK0,sK2))
| spl13_31 ),
inference(avatar_component_clause,[],[f987]) ).
fof(f989,plain,
( sK1 = join_of_latt_set(sK0,a_2_2_lattice3(sK0,sK2))
| ~ spl13_31 ),
inference(avatar_component_clause,[],[f987]) ).
fof(f1010,definition,
( spl13_32
<=> latt_element_smaller(sK0,sK1,a_2_2_lattice3(sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl13_32])],[avatar_definition]) ).
fof(f1011,plain,
( latt_element_smaller(sK0,sK1,a_2_2_lattice3(sK0,sK2))
| ~ spl13_32 ),
inference(avatar_component_clause,[],[f1010]) ).
fof(f1012,plain,
( ~ latt_element_smaller(sK0,sK1,a_2_2_lattice3(sK0,sK2))
| spl13_32 ),
inference(avatar_component_clause,[],[f1010]) ).
fof(f1022,plain,
( ~ element(sK1,the_carrier(sK0))
| ~ latt_set_smaller(sK0,sK1,sK2)
| empty_carrier(sK0)
| ~ latt_str(sK0)
| spl13_26 ),
inference(resolution,[],[f896,f159]) ).
fof(f1024,plain,
( ~ latt_set_smaller(sK0,sK1,sK2)
| empty_carrier(sK0)
| ~ latt_str(sK0)
| spl13_26 ),
inference(forward_subsumption_resolution,[],[f1022,f105]) ).
fof(f1025,plain,
( empty_carrier(sK0)
| ~ latt_str(sK0)
| ~ spl13_3
| spl13_26 ),
inference(forward_subsumption_resolution,[],[f1024,f180]) ).
fof(f1026,plain,
( ~ latt_str(sK0)
| ~ spl13_3
| spl13_26 ),
inference(forward_subsumption_resolution,[],[f1025,f104]) ).
fof(f1027,plain,
( $false
| ~ spl13_3
| spl13_26 ),
inference(forward_subsumption_resolution,[],[f1026,f101]) ).
fof(f1028,plain,
( ~ spl13_3
| spl13_26 ),
inference(avatar_contradiction_clause,[],[f1027]) ).
fof(f1040,plain,
( ~ latt_set_smaller(sK0,sK8(sK0,sK1,a_2_2_lattice3(sK0,sK2)),sK2)
| ~ spl13_2
| spl13_32 ),
inference(resolution,[],[f1012,f472]) ).
fof(f1125,plain,
( ~ in(sK8(sK0,sK1,a_2_2_lattice3(sK0,sK2)),a_2_2_lattice3(sK0,sK2))
| empty_carrier(sK0)
| ~ latt_str(sK0)
| ~ spl13_2
| spl13_32 ),
inference(resolution,[],[f1040,f211]) ).
fof(f1126,plain,
( ~ in(sK8(sK0,sK1,a_2_2_lattice3(sK0,sK2)),a_2_2_lattice3(sK0,sK2))
| ~ latt_str(sK0)
| ~ spl13_2
| spl13_32 ),
inference(forward_subsumption_resolution,[],[f1125,f104]) ).
fof(f1135,plain,
( ~ in(sK8(sK0,sK1,a_2_2_lattice3(sK0,sK2)),a_2_2_lattice3(sK0,sK2))
| ~ spl13_2
| spl13_32 ),
inference(forward_subsumption_resolution,[],[f1126,f101]) ).
fof(f1181,plain,
( ~ element(sK1,the_carrier(sK0))
| sK1 = join_of_latt_set(sK0,a_2_2_lattice3(sK0,sK2))
| ~ element(sK1,a_2_2_lattice3(sK0,sK2))
| empty_set = a_2_2_lattice3(sK0,sK2)
| ~ spl13_32 ),
inference(resolution,[],[f1011,f553]) ).
fof(f1184,plain,
( sK1 = join_of_latt_set(sK0,a_2_2_lattice3(sK0,sK2))
| ~ element(sK1,a_2_2_lattice3(sK0,sK2))
| empty_set = a_2_2_lattice3(sK0,sK2)
| ~ spl13_32 ),
inference(forward_subsumption_resolution,[],[f1181,f105]) ).
fof(f1185,plain,
( sK1 = join_of_latt_set(sK0,a_2_2_lattice3(sK0,sK2))
| empty_set = a_2_2_lattice3(sK0,sK2)
| ~ spl13_26
| ~ spl13_32 ),
inference(forward_subsumption_resolution,[],[f1184,f886]) ).
fof(f1187,definition,
( spl13_36
<=> empty_set = a_2_2_lattice3(sK0,sK2) ),
introduced(definition,[new_symbols(definition,[spl13_36])],[avatar_definition]) ).
fof(f1189,plain,
( empty_set = a_2_2_lattice3(sK0,sK2)
| ~ spl13_36 ),
inference(avatar_component_clause,[],[f1187]) ).
fof(f1190,plain,
( spl13_36
| spl13_31
| ~ spl13_26
| ~ spl13_32 ),
inference(avatar_split_clause,[],[f1185,f1010,f885,f987,f1187]) ).
fof(f1198,plain,
( ! [X0] :
( ~ latt_element_smaller(sK0,sK9(sK0,sK1,X0),a_2_2_lattice3(sK0,sK2))
| latt_set_smaller(sK0,sK1,X0) )
| ~ spl13_1 ),
inference(superposition,[],[f259,f172]) ).
fof(f1200,plain,
( ! [X0] :
( below(sK0,X0,sK1)
| ~ in(X0,a_2_2_lattice3(sK0,sK2)) )
| ~ spl13_1 ),
inference(superposition,[],[f305,f172]) ).
fof(f1223,plain,
( sK1 = meet_of_latt_set(sK0,sK2)
| empty_carrier(sK0)
| ~ latt_str(sK0)
| ~ spl13_31 ),
inference(superposition,[],[f989,f123]) ).
fof(f1241,plain,
( ! [X0] :
( ~ in(sK9(sK0,sK1,X0),sK2)
| latt_set_smaller(sK0,sK1,X0)
| ~ element(sK9(sK0,sK1,X0),the_carrier(sK0)) )
| ~ spl13_1 ),
inference(resolution,[],[f1198,f495]) ).
fof(f1337,plain,
( latt_set_smaller(sK0,sK1,sK2)
| ~ element(sK9(sK0,sK1,sK2),the_carrier(sK0))
| latt_set_smaller(sK0,sK1,sK2)
| ~ element(sK1,the_carrier(sK0))
| empty_carrier(sK0)
| ~ latt_str(sK0)
| ~ spl13_1 ),
inference(resolution,[],[f1241,f141]) ).
fof(f1338,plain,
( latt_set_smaller(sK0,sK1,sK2)
| ~ element(sK9(sK0,sK1,sK2),the_carrier(sK0))
| ~ element(sK1,the_carrier(sK0))
| empty_carrier(sK0)
| ~ latt_str(sK0)
| ~ spl13_1 ),
inference(duplicate_literal_removal,[],[f1337]) ).
fof(f1339,plain,
( latt_set_smaller(sK0,sK1,sK2)
| ~ element(sK1,the_carrier(sK0))
| empty_carrier(sK0)
| ~ latt_str(sK0)
| ~ spl13_1 ),
inference(forward_subsumption_resolution,[],[f1338,f140]) ).
fof(f1344,plain,
( ~ element(sK1,the_carrier(sK0))
| empty_carrier(sK0)
| ~ latt_str(sK0)
| ~ spl13_1
| spl13_3 ),
inference(forward_subsumption_resolution,[],[f1339,f179]) ).
fof(f1345,plain,
( empty_carrier(sK0)
| ~ latt_str(sK0)
| ~ spl13_1
| spl13_3 ),
inference(forward_subsumption_resolution,[],[f1344,f105]) ).
fof(f1346,plain,
( ~ latt_str(sK0)
| ~ spl13_1
| spl13_3 ),
inference(forward_subsumption_resolution,[],[f1345,f104]) ).
fof(f1347,plain,
( $false
| ~ spl13_1
| spl13_3 ),
inference(forward_subsumption_resolution,[],[f1346,f101]) ).
fof(f1348,plain,
( ~ spl13_1
| spl13_3 ),
inference(avatar_contradiction_clause,[],[f1347]) ).
fof(f1350,plain,
( ~ below(sK0,sK3,sK1)
| empty_carrier(sK0)
| ~ meet_commutative(sK0)
| ~ meet_absorbing(sK0)
| ~ join_absorbing(sK0)
| ~ latt_str(sK0)
| ~ element(sK3,the_carrier(sK0))
| ~ element(sK1,the_carrier(sK0))
| spl13_6 ),
inference(resolution,[],[f195,f131]) ).
fof(f1351,plain,
( ~ below(sK0,sK3,sK1)
| ~ meet_commutative(sK0)
| ~ meet_absorbing(sK0)
| ~ join_absorbing(sK0)
| ~ latt_str(sK0)
| ~ element(sK3,the_carrier(sK0))
| ~ element(sK1,the_carrier(sK0))
| spl13_6 ),
inference(forward_subsumption_resolution,[],[f1350,f104]) ).
fof(f1353,plain,
( ~ below(sK0,sK3,sK1)
| ~ meet_absorbing(sK0)
| ~ join_absorbing(sK0)
| ~ latt_str(sK0)
| ~ element(sK3,the_carrier(sK0))
| ~ element(sK1,the_carrier(sK0))
| spl13_6
| ~ spl13_13 ),
inference(forward_subsumption_resolution,[],[f1351,f366]) ).
fof(f1356,plain,
( ~ below(sK0,sK3,sK1)
| ~ join_absorbing(sK0)
| ~ latt_str(sK0)
| ~ element(sK3,the_carrier(sK0))
| ~ element(sK1,the_carrier(sK0))
| spl13_6
| ~ spl13_12
| ~ spl13_13 ),
inference(forward_subsumption_resolution,[],[f1353,f362]) ).
fof(f1357,plain,
( ~ below(sK0,sK3,sK1)
| ~ latt_str(sK0)
| ~ element(sK3,the_carrier(sK0))
| ~ element(sK1,the_carrier(sK0))
| spl13_6
| ~ spl13_11
| ~ spl13_12
| ~ spl13_13 ),
inference(forward_subsumption_resolution,[],[f1356,f358]) ).
fof(f1358,plain,
( ~ below(sK0,sK3,sK1)
| ~ element(sK3,the_carrier(sK0))
| ~ element(sK1,the_carrier(sK0))
| spl13_6
| ~ spl13_11
| ~ spl13_12
| ~ spl13_13 ),
inference(forward_subsumption_resolution,[],[f1357,f101]) ).
fof(f1359,plain,
( ~ below(sK0,sK3,sK1)
| ~ element(sK1,the_carrier(sK0))
| ~ spl13_4
| spl13_6
| ~ spl13_11
| ~ spl13_12
| ~ spl13_13 ),
inference(forward_subsumption_resolution,[],[f1358,f185]) ).
fof(f1360,plain,
( ~ below(sK0,sK3,sK1)
| ~ spl13_4
| spl13_6
| ~ spl13_11
| ~ spl13_12
| ~ spl13_13 ),
inference(forward_subsumption_resolution,[],[f1359,f105]) ).
fof(f1363,plain,
( ~ in(sK3,a_2_2_lattice3(sK0,sK2))
| ~ spl13_1
| ~ spl13_4
| spl13_6
| ~ spl13_11
| ~ spl13_12
| ~ spl13_13 ),
inference(resolution,[],[f1360,f1200]) ).
fof(f1378,plain,
( ~ element(sK3,the_carrier(sK0))
| ~ latt_set_smaller(sK0,sK3,sK2)
| empty_carrier(sK0)
| ~ latt_str(sK0)
| ~ spl13_1
| ~ spl13_4
| spl13_6
| ~ spl13_11
| ~ spl13_12
| ~ spl13_13 ),
inference(resolution,[],[f1363,f159]) ).
fof(f1385,plain,
( ~ latt_set_smaller(sK0,sK3,sK2)
| empty_carrier(sK0)
| ~ latt_str(sK0)
| ~ spl13_1
| ~ spl13_4
| spl13_6
| ~ spl13_11
| ~ spl13_12
| ~ spl13_13 ),
inference(forward_subsumption_resolution,[],[f1378,f185]) ).
fof(f1386,plain,
( empty_carrier(sK0)
| ~ latt_str(sK0)
| ~ spl13_1
| ~ spl13_4
| ~ spl13_5
| spl13_6
| ~ spl13_11
| ~ spl13_12
| ~ spl13_13 ),
inference(forward_subsumption_resolution,[],[f1385,f190]) ).
fof(f1387,plain,
( ~ latt_str(sK0)
| ~ spl13_1
| ~ spl13_4
| ~ spl13_5
| spl13_6
| ~ spl13_11
| ~ spl13_12
| ~ spl13_13 ),
inference(forward_subsumption_resolution,[],[f1386,f104]) ).
fof(f1388,plain,
( $false
| ~ spl13_1
| ~ spl13_4
| ~ spl13_5
| spl13_6
| ~ spl13_11
| ~ spl13_12
| ~ spl13_13 ),
inference(forward_subsumption_resolution,[],[f1387,f101]) ).
fof(f1389,plain,
( ~ spl13_1
| ~ spl13_4
| ~ spl13_5
| spl13_6
| ~ spl13_11
| ~ spl13_12
| ~ spl13_13 ),
inference(avatar_contradiction_clause,[],[f1388]) ).
fof(f1392,plain,
( empty_carrier(sK0)
| ~ latt_str(sK0)
| spl13_1
| ~ spl13_31 ),
inference(forward_subsumption_resolution,[],[f1223,f171]) ).
fof(f1395,plain,
( ~ latt_str(sK0)
| spl13_1
| ~ spl13_31 ),
inference(forward_subsumption_resolution,[],[f1392,f104]) ).
fof(f1398,plain,
( $false
| spl13_1
| ~ spl13_31 ),
inference(forward_subsumption_resolution,[],[f1395,f101]) ).
fof(f1399,plain,
( spl13_1
| ~ spl13_31 ),
inference(avatar_contradiction_clause,[],[f1398]) ).
fof(f1409,plain,
( latt_element_smaller(sK0,sK1,empty_set)
| ~ spl13_32
| ~ spl13_36 ),
inference(superposition,[],[f1011,f1189]) ).
fof(f1439,plain,
( ! [X0] :
( in(X0,empty_set)
| ~ element(X0,the_carrier(sK0))
| ~ latt_set_smaller(sK0,X0,sK2)
| empty_carrier(sK0)
| ~ latt_str(sK0) )
| ~ spl13_36 ),
inference(superposition,[],[f159,f1189]) ).
fof(f1442,plain,
( ! [X0] :
( in(X0,empty_set)
| ~ element(X0,the_carrier(sK0))
| ~ latt_set_smaller(sK0,X0,sK2)
| ~ latt_str(sK0) )
| ~ spl13_36 ),
inference(forward_subsumption_resolution,[],[f1439,f104]) ).
fof(f1475,plain,
( ! [X0] :
( ~ latt_set_smaller(sK0,X0,sK2)
| ~ element(X0,the_carrier(sK0))
| in(X0,empty_set) )
| ~ spl13_36 ),
inference(forward_subsumption_resolution,[],[f1442,f101]) ).
fof(f1498,plain,
( sK1 != join_of_latt_set(sK0,empty_set)
| spl13_31
| ~ spl13_36 ),
inference(superposition,[],[f988,f1189]) ).
fof(f2037,plain,
( ~ element(sK1,the_carrier(sK0))
| in(sK1,empty_set)
| ~ spl13_3
| ~ spl13_36 ),
inference(resolution,[],[f1475,f180]) ).
fof(f2047,plain,
( in(sK1,empty_set)
| ~ spl13_3
| ~ spl13_36 ),
inference(forward_subsumption_resolution,[],[f2037,f105]) ).
fof(f2093,plain,
( sK1 = join_of_latt_set(sK0,empty_set)
| ~ element(sK1,the_carrier(sK0))
| ~ latt_element_smaller(sK0,sK1,empty_set)
| ~ spl13_3
| ~ spl13_36 ),
inference(resolution,[],[f2047,f517]) ).
fof(f2094,plain,
( ~ element(sK1,the_carrier(sK0))
| ~ latt_element_smaller(sK0,sK1,empty_set)
| ~ spl13_3
| spl13_31
| ~ spl13_36 ),
inference(forward_subsumption_resolution,[],[f2093,f1498]) ).
fof(f2095,plain,
( ~ latt_element_smaller(sK0,sK1,empty_set)
| ~ spl13_3
| spl13_31
| ~ spl13_36 ),
inference(forward_subsumption_resolution,[],[f2094,f105]) ).
fof(f2096,plain,
( $false
| ~ spl13_3
| spl13_31
| ~ spl13_32
| ~ spl13_36 ),
inference(forward_subsumption_resolution,[],[f2095,f1409]) ).
fof(f2097,plain,
( ~ spl13_3
| spl13_31
| ~ spl13_32
| ~ spl13_36 ),
inference(avatar_contradiction_clause,[],[f2096]) ).
fof(f2364,plain,
( latt_element_smaller(sK0,sK1,a_2_2_lattice3(sK0,sK2))
| ~ element(sK1,the_carrier(sK0))
| empty_carrier(sK0)
| ~ latt_str(sK0)
| ~ spl13_2
| spl13_32 ),
inference(resolution,[],[f1135,f137]) ).
fof(f2365,plain,
( ~ element(sK1,the_carrier(sK0))
| empty_carrier(sK0)
| ~ latt_str(sK0)
| ~ spl13_2
| spl13_32 ),
inference(forward_subsumption_resolution,[],[f2364,f1012]) ).
fof(f2371,plain,
( empty_carrier(sK0)
| ~ latt_str(sK0)
| ~ spl13_2
| spl13_32 ),
inference(forward_subsumption_resolution,[],[f2365,f105]) ).
fof(f2372,plain,
( ~ latt_str(sK0)
| ~ spl13_2
| spl13_32 ),
inference(forward_subsumption_resolution,[],[f2371,f104]) ).
fof(f2373,plain,
( $false
| ~ spl13_2
| spl13_32 ),
inference(forward_subsumption_resolution,[],[f2372,f101]) ).
fof(f2374,plain,
( ~ spl13_2
| spl13_32 ),
inference(avatar_contradiction_clause,[],[f2373]) ).
cnf(s1,plain,
( spl13_1
| spl13_2 ),
inference(sat_conversion,[],[f176]) ).
cnf(s2,plain,
( spl13_1
| spl13_3 ),
inference(sat_conversion,[],[f181]) ).
cnf(s3,plain,
( ~ spl13_1
| ~ spl13_3
| spl13_4 ),
inference(sat_conversion,[],[f186]) ).
cnf(s4,plain,
( ~ spl13_1
| ~ spl13_3
| spl13_5 ),
inference(sat_conversion,[],[f191]) ).
cnf(s5,plain,
( ~ spl13_1
| ~ spl13_3
| ~ spl13_6 ),
inference(sat_conversion,[],[f196]) ).
cnf(s9,plain,
spl13_11,
inference(sat_conversion,[],[f379]) ).
cnf(s10,plain,
spl13_12,
inference(sat_conversion,[],[f392]) ).
cnf(s11,plain,
spl13_13,
inference(sat_conversion,[],[f418]) ).
cnf(s28,plain,
( ~ spl13_3
| spl13_26 ),
inference(sat_conversion,[],[f1028]) ).
cnf(s33,plain,
( ~ spl13_26
| spl13_31
| ~ spl13_32
| spl13_36 ),
inference(sat_conversion,[],[f1190]) ).
cnf(s35,plain,
( ~ spl13_1
| spl13_3 ),
inference(sat_conversion,[],[f1348]) ).
cnf(s39,plain,
( ~ spl13_1
| ~ spl13_4
| ~ spl13_5
| spl13_6
| ~ spl13_11
| ~ spl13_12
| ~ spl13_13 ),
inference(sat_conversion,[],[f1389]) ).
cnf(s41,plain,
( spl13_1
| ~ spl13_31 ),
inference(sat_conversion,[],[f1399]) ).
cnf(s57,plain,
( ~ spl13_3
| spl13_31
| ~ spl13_32
| ~ spl13_36 ),
inference(sat_conversion,[],[f2097]) ).
cnf(s73,plain,
( ~ spl13_2
| spl13_32 ),
inference(sat_conversion,[],[f2374]) ).
cnf(s77,plain,
spl13_1,
inference(rat,[],[s33,s57,s73,s28,s1,s2,s41]) ).
cnf(s78,plain,
spl13_3,
inference(rat,[],[s35,s77]) ).
cnf(s81,plain,
~ spl13_6,
inference(rat,[],[s5,s77,s78]) ).
cnf(s82,plain,
spl13_5,
inference(rat,[],[s4,s77,s78]) ).
cnf(s83,plain,
spl13_4,
inference(rat,[],[s3,s77,s78]) ).
cnf(s84,plain,
$false,
inference(rat,[],[s39,s11,s10,s9,s81,s77,s82,s83]) ).
fof(f2375,plain,
$false,
inference(avatar_sat_refutation,[],[s84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU351+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n026.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 04:53:20 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.69/1.63 % (3468193)Detected formulas, will run a generic FOF schedule.
% 4.69/1.63 % (3468202)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2287307139:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.69/1.63 % (3468202)Refutation not found, incomplete strategy
% 4.69/1.63 % (3468202)------------------------------
% 4.69/1.63 % (3468202)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.63 % (3468202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.63 % (3468202)CaDiCaL version: 2.1.3
% 4.69/1.63 % (3468202)Termination reason: Refutation not found, incomplete strategy
% 4.69/1.63 % (3468202)Time elapsed: 0.003 s
% 4.69/1.63 % (3468202)Peak memory usage: 88 MB
% 4.69/1.63 % (3468202)Instructions burned: 5 (million)
% 4.69/1.63 % (3468199)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2240071154:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.69/1.63 % (3468200)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=973350602:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.69/1.63 % (3468201)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2856340490:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.69/1.63 % (3468198)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=728325219:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.69/1.63 % (3468201)Refutation not found, incomplete strategy
% 4.69/1.63 % (3468201)------------------------------
% 4.69/1.63 % (3468201)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.63 % (3468201)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.63 % (3468201)CaDiCaL version: 2.1.3
% 4.69/1.63 % (3468201)Termination reason: Refutation not found, incomplete strategy
% 4.69/1.63 % (3468201)Time elapsed: 0.003 s
% 4.69/1.63 % (3468201)Peak memory usage: 88 MB
% 4.69/1.63 % (3468201)Instructions burned: 2 (million)
% 4.69/1.63 % (3468204)dis-21_1_sil=8000:lcm=predicate:random_seed=3689358732:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 4.69/1.63 % (3468203)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3559667298:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.69/1.63 % (3468204)Instruction limit reached!
% 4.69/1.63 % (3468204)------------------------------
% 4.69/1.63 % (3468204)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.63 % (3468204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.63 % (3468204)CaDiCaL version: 2.1.3
% 4.69/1.63 % (3468204)Termination reason: Instruction limit
% 4.69/1.63 % (3468204)Termination phase: Saturation
% 4.69/1.63 % (3468204)Time elapsed: 0.081 s
% 4.69/1.63 % (3468204)Peak memory usage: 90 MB
% 4.69/1.63 % (3468204)Instructions burned: 130 (million)
% 4.69/1.63 % (3468202)------------------------------
% 4.69/1.63 % (3468202)------------------------------
% 4.69/1.63 % (3468203)Instruction limit reached!
% 4.69/1.63 % (3468203)------------------------------
% 4.69/1.63 % (3468203)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.63 % (3468203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.63 % (3468203)CaDiCaL version: 2.1.3
% 4.69/1.63 % (3468203)Termination reason: Instruction limit
% 4.69/1.63 % (3468203)Termination phase: Saturation
% 4.69/1.63 % (3468203)Time elapsed: 0.095 s
% 4.69/1.63 % (3468203)Peak memory usage: 89 MB
% 4.69/1.63 % (3468203)Instructions burned: 140 (million)
% 4.69/1.63 % (3468213)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1938986439:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.69/1.63 % (3468213)Refutation not found, incomplete strategy
% 4.69/1.63 % (3468213)------------------------------
% 4.69/1.63 % (3468213)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.63 % (3468213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.63 % (3468213)CaDiCaL version: 2.1.3
% 4.69/1.63 % (3468213)Termination reason: Refutation not found, incomplete strategy
% 4.69/1.63 % (3468213)Time elapsed: 0.004 s
% 4.69/1.63 % (3468213)Peak memory usage: 89 MB
% 4.69/1.63 % (3468213)Instructions burned: 9 (million)
% 4.69/1.63 % (3468212)lrs+10_1_sil=8000:sp=occurrence:random_seed=3871792746:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.69/1.63 % (3468201)------------------------------
% 4.69/1.63 % (3468201)------------------------------
% 4.69/1.63 % (3468214)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3604267186:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.69/1.63 % (3468213)------------------------------
% 4.69/1.63 % (3468213)------------------------------
% 4.69/1.63 % (3468214)First to succeed.
% 4.69/1.63 % (3468214)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3468193"
% 4.69/1.63 % (3468212)Instruction limit reached!
% 4.69/1.63 % (3468212)------------------------------
% 4.69/1.63 % (3468212)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.63 % (3468212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.63 % (3468212)CaDiCaL version: 2.1.3
% 4.69/1.63 % (3468212)Termination reason: Instruction limit
% 4.69/1.63 % (3468212)Termination phase: Saturation
% 4.69/1.63 % (3468212)Time elapsed: 0.173 s
% 4.69/1.63 % (3468212)Peak memory usage: 91 MB
% 4.69/1.63 % (3468212)Instructions burned: 286 (million)
% 4.69/1.63 % (3468218)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1996399721:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 4.69/1.63 % (3468219)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=231952936:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 4.69/1.63 % (3468219)Refutation not found, incomplete strategy
% 4.69/1.63 % (3468219)------------------------------
% 4.69/1.63 % (3468219)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.63 % (3468219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.63 % (3468219)CaDiCaL version: 2.1.3
% 4.69/1.63 % (3468219)Termination reason: Refutation not found, incomplete strategy
% 4.69/1.63 % (3468219)Time elapsed: 0.002 s
% 4.69/1.63 % (3468219)Peak memory usage: 88 MB
% 4.69/1.63 % (3468219)Instructions burned: 4 (million)
% 4.69/1.63 % (3468220)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3284301484:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 4.69/1.63 % (3468218)Instruction limit reached!
% 4.69/1.63 % (3468218)------------------------------
% 4.69/1.63 % (3468218)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.69/1.63 % (3468218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.69/1.63 % (3468218)CaDiCaL version: 2.1.3
% 4.69/1.63 % (3468218)Termination reason: Instruction limit
% 4.69/1.63 % (3468218)Termination phase: Saturation
% 4.69/1.63 % (3468218)Time elapsed: 0.139 s
% 4.69/1.63 % (3468218)Peak memory usage: 90 MB
% 4.69/1.63 % (3468218)Instructions burned: 249 (million)
% 4.69/1.63 % (3468219)------------------------------
% 4.69/1.63 % (3468219)------------------------------
% 4.69/1.63 % (3468214)Refutation found. Thanks to Tanya!
% 4.69/1.63 % SZS status Theorem for theBenchmark
% 4.69/1.63 % SZS output start Proof for theBenchmark
% See solution above
% 6.03/1.82 % (3468214)------------------------------
% 6.03/1.82 % (3468214)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.03/1.82 % (3468214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.03/1.82 % (3468214)CaDiCaL version: 2.1.3
% 6.03/1.82 % (3468214)Termination reason: Refutation
% 6.03/1.82 % (3468214)Time elapsed: 0.096 s
% 6.03/1.82 % (3468214)Peak memory usage: 90 MB
% 6.03/1.82 % (3468214)Instructions burned: 139 (million)
% 6.03/1.82 % (3468214)------------------------------
% 6.03/1.82 % (3468214)------------------------------
% 6.03/1.82 % (3468193)Success in time 0.765 s
% 6.03/1.82 % Vampire exiting
%------------------------------------------------------------------------------