%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU347+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 : n005.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 12:48:27 PM UTC 2026
% Result : Theorem 4.12s 1.59s
% Output : Refutation 5.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 32
% Syntax : Number of formulae : 314 ( 28 unt; 19 def)
% Number of atoms : 1403 ( 11 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 1866 ( 777 ~; 892 |; 128 &)
% ( 36 <=>; 31 =>; 0 <=; 2 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 43 ( 41 usr; 20 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 280 ( 0 sgn 264 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,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(f6,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(f8,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> cast_to_el_of_LattPOSet(X0,X1) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattice3) ).
fof(f9,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(poset_of_lattice(X0)))
=> cast_to_el_of_lattice(X0,X1) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_lattice3) ).
fof(f10,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1,X2] :
( element(X2,the_carrier(X0))
=> ( relstr_element_smaller(X0,X1,X2)
<=> ! [X3] :
( element(X3,the_carrier(X0))
=> ( in(X3,X1)
=> related(X0,X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_lattice3) ).
fof(f16,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) )
=> ( strict_rel_str(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& transitive_relstr(poset_of_lattice(X0))
& antisymmetric_relstr(poset_of_lattice(X0))
& rel_str(poset_of_lattice(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lattice3) ).
fof(f17,axiom,
! [X0,X1] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0)
& element(X1,the_carrier(X0)) )
=> element(cast_to_el_of_LattPOSet(X0,X1),the_carrier(poset_of_lattice(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_lattice3) ).
fof(f18,axiom,
! [X0,X1] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0)
& element(X1,the_carrier(poset_of_lattice(X0))) )
=> element(cast_to_el_of_lattice(X0,X1),the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_lattice3) ).
fof(f44,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) )
=> ( ~ empty_carrier(poset_of_lattice(X0))
& strict_rel_str(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& transitive_relstr(poset_of_lattice(X0))
& antisymmetric_relstr(poset_of_lattice(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_lattice3) ).
fof(f57,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(f58,axiom,
! [X0,X1,X2] :
( ( ~ empty_carrier(X0)
& reflexive_relstr(X0)
& rel_str(X0)
& element(X1,the_carrier(X0))
& element(X2,the_carrier(X0)) )
=> ( related_reflexive(X0,X1,X2)
<=> related(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r3_orders_2) ).
fof(f63,conjecture,
! [X0,X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ( latt_set_smaller(X1,X2,X0)
<=> relstr_element_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_lattice3) ).
fof(f64,negated_conjecture,
~ ! [X0,X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ( latt_set_smaller(X1,X2,X0)
<=> relstr_element_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2)) ) ) ),
inference(negated_conjecture,[status(cth)],[f63]) ).
fof(f71,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( below_refl(X0,X1,X2)
<=> related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_lattice3) ).
fof(f87,plain,
! [X0] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) )
=> ( strict_rel_str(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& antisymmetric_relstr(poset_of_lattice(X0))
& rel_str(poset_of_lattice(X0)) ) ),
inference(pure_predicate_removal,[],[f16]) ).
fof(f89,plain,
! [X0] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) )
=> ( ~ empty_carrier(poset_of_lattice(X0))
& strict_rel_str(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& antisymmetric_relstr(poset_of_lattice(X0)) ) ),
inference(pure_predicate_removal,[],[f44]) ).
fof(f91,plain,
! [X0] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) )
=> ( strict_rel_str(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& rel_str(poset_of_lattice(X0)) ) ),
inference(pure_predicate_removal,[],[f87]) ).
fof(f92,plain,
! [X0] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) )
=> ( ~ empty_carrier(poset_of_lattice(X0))
& strict_rel_str(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0)) ) ),
inference(pure_predicate_removal,[],[f89]) ).
fof(f93,plain,
? [X0,X1] :
( ? [X2] :
( ( latt_set_smaller(X1,X2,X0)
<~> relstr_element_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2)) )
& element(X2,the_carrier(X1)) )
& ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) ),
inference(ennf_transformation,[],[f64]) ).
fof(f94,plain,
? [X0,X1] :
( ? [X2] :
( ( latt_set_smaller(X1,X2,X0)
<~> relstr_element_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2)) )
& element(X2,the_carrier(X1)) )
& ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) ),
inference(flattening,[],[f93]) ).
fof(f95,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( below_refl(X0,X1,X2)
<=> related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2)) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f71]) ).
fof(f96,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( below_refl(X0,X1,X2)
<=> related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2)) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f95]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ( related_reflexive(X0,X1,X2)
<=> related(X0,X1,X2) )
| empty_carrier(X0)
| ~ reflexive_relstr(X0)
| ~ rel_str(X0)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0)) ),
inference(ennf_transformation,[],[f58]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ( related_reflexive(X0,X1,X2)
<=> related(X0,X1,X2) )
| empty_carrier(X0)
| ~ reflexive_relstr(X0)
| ~ rel_str(X0)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0)) ),
inference(flattening,[],[f101]) ).
fof(f103,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,[],[f57]) ).
fof(f104,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,[],[f103]) ).
fof(f110,plain,
! [X0,X1] :
( element(cast_to_el_of_lattice(X0,X1),the_carrier(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0)
| ~ element(X1,the_carrier(poset_of_lattice(X0))) ),
inference(ennf_transformation,[],[f18]) ).
fof(f111,plain,
! [X0,X1] :
( element(cast_to_el_of_lattice(X0,X1),the_carrier(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0)
| ~ element(X1,the_carrier(poset_of_lattice(X0))) ),
inference(flattening,[],[f110]) ).
fof(f112,plain,
! [X0,X1] :
( element(cast_to_el_of_LattPOSet(X0,X1),the_carrier(poset_of_lattice(X0)))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0)
| ~ element(X1,the_carrier(X0)) ),
inference(ennf_transformation,[],[f17]) ).
fof(f113,plain,
! [X0,X1] :
( element(cast_to_el_of_LattPOSet(X0,X1),the_carrier(poset_of_lattice(X0)))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0)
| ~ element(X1,the_carrier(X0)) ),
inference(flattening,[],[f112]) ).
fof(f116,plain,
! [X0] :
( ! [X1,X2] :
( ( relstr_element_smaller(X0,X1,X2)
<=> ! [X3] :
( related(X0,X2,X3)
| ~ in(X3,X1)
| ~ element(X3,the_carrier(X0)) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f117,plain,
! [X0] :
( ! [X1,X2] :
( ( relstr_element_smaller(X0,X1,X2)
<=> ! [X3] :
( related(X0,X2,X3)
| ~ in(X3,X1)
| ~ element(X3,the_carrier(X0)) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(flattening,[],[f116]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( cast_to_el_of_lattice(X0,X1) = X1
| ~ element(X1,the_carrier(poset_of_lattice(X0))) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( cast_to_el_of_lattice(X0,X1) = X1
| ~ element(X1,the_carrier(poset_of_lattice(X0))) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f118]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( cast_to_el_of_LattPOSet(X0,X1) = X1
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f121,plain,
! [X0] :
( ! [X1] :
( cast_to_el_of_LattPOSet(X0,X1) = X1
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f120]) ).
fof(f124,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,[],[f6]) ).
fof(f125,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,[],[f124]) ).
fof(f130,plain,
! [X0] :
( ( ~ empty_carrier(poset_of_lattice(X0))
& strict_rel_str(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f92]) ).
fof(f131,plain,
! [X0] :
( ( ~ empty_carrier(poset_of_lattice(X0))
& strict_rel_str(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f130]) ).
fof(f132,plain,
! [X0] :
( ( strict_rel_str(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& rel_str(poset_of_lattice(X0)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f91]) ).
fof(f133,plain,
! [X0] :
( ( strict_rel_str(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& rel_str(poset_of_lattice(X0)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f132]) ).
fof(f136,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,[],[f3]) ).
fof(f137,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,[],[f136]) ).
fof(f146,plain,
? [X0,X1] :
( ? [X2] :
( ( ~ relstr_element_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
| ~ latt_set_smaller(X1,X2,X0) )
& ( relstr_element_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
| latt_set_smaller(X1,X2,X0) )
& element(X2,the_carrier(X1)) )
& ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) ),
inference(nnf_transformation,[],[f94]) ).
fof(f147,plain,
? [X0,X1] :
( ? [X2] :
( ( ~ relstr_element_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
| ~ latt_set_smaller(X1,X2,X0) )
& ( relstr_element_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
| latt_set_smaller(X1,X2,X0) )
& element(X2,the_carrier(X1)) )
& ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) ),
inference(flattening,[],[f146]) ).
fof(f148,plain,
( ( ~ relstr_element_smaller(poset_of_lattice(sK1),sK0,cast_to_el_of_LattPOSet(sK1,sK2))
| ~ latt_set_smaller(sK1,sK2,sK0) )
& ( relstr_element_smaller(poset_of_lattice(sK1),sK0,cast_to_el_of_LattPOSet(sK1,sK2))
| latt_set_smaller(sK1,sK2,sK0) )
& element(sK2,the_carrier(sK1))
& ~ empty_carrier(sK1)
& lattice(sK1)
& latt_str(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f147]) ).
fof(f149,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( below_refl(X0,X1,X2)
| ~ related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2)) )
& ( related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2))
| ~ below_refl(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(nnf_transformation,[],[f96]) ).
fof(f150,plain,
! [X0,X1,X2] :
( ( ( related_reflexive(X0,X1,X2)
| ~ related(X0,X1,X2) )
& ( related(X0,X1,X2)
| ~ related_reflexive(X0,X1,X2) ) )
| empty_carrier(X0)
| ~ reflexive_relstr(X0)
| ~ rel_str(X0)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0)) ),
inference(nnf_transformation,[],[f102]) ).
fof(f151,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,[],[f104]) ).
fof(f153,plain,
! [X0] :
( ! [X1,X2] :
( ( ( relstr_element_smaller(X0,X1,X2)
| ? [X3] :
( ~ related(X0,X2,X3)
& in(X3,X1)
& element(X3,the_carrier(X0)) ) )
& ( ! [X3] :
( related(X0,X2,X3)
| ~ in(X3,X1)
| ~ element(X3,the_carrier(X0)) )
| ~ relstr_element_smaller(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(nnf_transformation,[],[f117]) ).
fof(f154,plain,
! [X0] :
( ! [X1,X2] :
( ( ( relstr_element_smaller(X0,X1,X2)
| ? [X3] :
( ~ related(X0,X2,X3)
& in(X3,X1)
& element(X3,the_carrier(X0)) ) )
& ( ! [X4] :
( related(X0,X2,X4)
| ~ in(X4,X1)
| ~ element(X4,the_carrier(X0)) )
| ~ relstr_element_smaller(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(rectify,[],[f153]) ).
fof(f155,plain,
! [X0] :
( ! [X1,X2] :
( ( ( relstr_element_smaller(X0,X1,X2)
| ( ~ related(X0,X2,sK4(X0,X1,X2))
& in(sK4(X0,X1,X2),X1)
& element(sK4(X0,X1,X2),the_carrier(X0)) ) )
& ( ! [X4] :
( related(X0,X2,X4)
| ~ in(X4,X1)
| ~ element(X4,the_carrier(X0)) )
| ~ relstr_element_smaller(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f154]) ).
fof(f156,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,[],[f125]) ).
fof(f157,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,[],[f156]) ).
fof(f158,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( latt_set_smaller(X0,X1,X2)
| ( ~ below(X0,X1,sK5(X0,X1,X2))
& in(sK5(X0,X1,X2),X2)
& element(sK5(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,[sK5]),skolemize(X3,sK5(X0,X1,X2))],[f157]) ).
fof(f165,plain,
latt_str(sK1),
inference(cnf_transformation,[],[f148]) ).
fof(f166,plain,
lattice(sK1),
inference(cnf_transformation,[],[f148]) ).
fof(f167,plain,
~ empty_carrier(sK1),
inference(cnf_transformation,[],[f148]) ).
fof(f168,plain,
element(sK2,the_carrier(sK1)),
inference(cnf_transformation,[],[f148]) ).
fof(f169,plain,
( relstr_element_smaller(poset_of_lattice(sK1),sK0,cast_to_el_of_LattPOSet(sK1,sK2))
| latt_set_smaller(sK1,sK2,sK0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f170,plain,
( ~ relstr_element_smaller(poset_of_lattice(sK1),sK0,cast_to_el_of_LattPOSet(sK1,sK2))
| ~ latt_set_smaller(sK1,sK2,sK0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f171,plain,
! [X2,X0,X1] :
( ~ lattice(X0)
| ~ below_refl(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| empty_carrier(X0)
| related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2))
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f172,plain,
! [X2,X0,X1] :
( ~ lattice(X0)
| ~ related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| empty_carrier(X0)
| below_refl(X0,X1,X2)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f175,plain,
! [X2,X0,X1] :
( ~ related_reflexive(X0,X1,X2)
| related(X0,X1,X2)
| empty_carrier(X0)
| ~ reflexive_relstr(X0)
| ~ rel_str(X0)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0)) ),
inference(cnf_transformation,[],[f150]) ).
fof(f176,plain,
! [X2,X0,X1] :
( related_reflexive(X0,X1,X2)
| ~ related(X0,X1,X2)
| empty_carrier(X0)
| ~ reflexive_relstr(X0)
| ~ rel_str(X0)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0)) ),
inference(cnf_transformation,[],[f150]) ).
fof(f177,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,[],[f151]) ).
fof(f178,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,[],[f151]) ).
fof(f183,plain,
! [X0,X1] :
( element(cast_to_el_of_lattice(X0,X1),the_carrier(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0)
| ~ element(X1,the_carrier(poset_of_lattice(X0))) ),
inference(cnf_transformation,[],[f111]) ).
fof(f184,plain,
! [X0,X1] :
( element(cast_to_el_of_LattPOSet(X0,X1),the_carrier(poset_of_lattice(X0)))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0)
| ~ element(X1,the_carrier(X0)) ),
inference(cnf_transformation,[],[f113]) ).
fof(f186,plain,
! [X2,X0,X1,X4] :
( related(X0,X2,X4)
| ~ in(X4,X1)
| ~ element(X4,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f155]) ).
fof(f187,plain,
! [X2,X0,X1] :
( element(sK4(X0,X1,X2),the_carrier(X0))
| relstr_element_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f155]) ).
fof(f188,plain,
! [X2,X0,X1] :
( relstr_element_smaller(X0,X1,X2)
| in(sK4(X0,X1,X2),X1)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f155]) ).
fof(f189,plain,
! [X2,X0,X1] :
( ~ related(X0,X2,sK4(X0,X1,X2))
| relstr_element_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f155]) ).
fof(f190,plain,
! [X0,X1] :
( cast_to_el_of_lattice(X0,X1) = X1
| ~ element(X1,the_carrier(poset_of_lattice(X0)))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f191,plain,
! [X0,X1] :
( ~ lattice(X0)
| ~ element(X1,the_carrier(X0))
| empty_carrier(X0)
| cast_to_el_of_LattPOSet(X0,X1) = X1
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f193,plain,
! [X2,X0,X1,X4] :
( ~ latt_set_smaller(X0,X1,X2)
| ~ in(X4,X2)
| ~ element(X4,the_carrier(X0))
| below(X0,X1,X4)
| ~ element(X1,the_carrier(X0))
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f194,plain,
! [X2,X0,X1] :
( element(sK5(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,[],[f158]) ).
fof(f195,plain,
! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X2)
| latt_set_smaller(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f196,plain,
! [X2,X0,X1] :
( ~ below(X0,X1,sK5(X0,X1,X2))
| latt_set_smaller(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f201,plain,
! [X0] :
( ~ empty_carrier(poset_of_lattice(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f203,plain,
! [X0] :
( rel_str(poset_of_lattice(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f204,plain,
! [X0] :
( reflexive_relstr(poset_of_lattice(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f208,plain,
! [X0] :
( join_absorbing(X0)
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f209,plain,
! [X0] :
( meet_absorbing(X0)
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f211,plain,
! [X0] :
( meet_commutative(X0)
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f232,definition,
( spl12_1
<=> latt_set_smaller(sK1,sK2,sK0) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f233,plain,
( ~ latt_set_smaller(sK1,sK2,sK0)
| spl12_1 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f234,plain,
( latt_set_smaller(sK1,sK2,sK0)
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f236,definition,
( spl12_2
<=> relstr_element_smaller(poset_of_lattice(sK1),sK0,cast_to_el_of_LattPOSet(sK1,sK2)) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f237,plain,
( ~ relstr_element_smaller(poset_of_lattice(sK1),sK0,cast_to_el_of_LattPOSet(sK1,sK2))
| spl12_2 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f238,plain,
( relstr_element_smaller(poset_of_lattice(sK1),sK0,cast_to_el_of_LattPOSet(sK1,sK2))
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f239,plain,
( spl12_1
| spl12_2 ),
inference(avatar_split_clause,[],[f169,f236,f232]) ).
fof(f240,plain,
( ~ spl12_1
| ~ spl12_2 ),
inference(avatar_split_clause,[],[f170,f236,f232]) ).
fof(f252,plain,
! [X0] :
( ~ element(X0,the_carrier(sK1))
| empty_carrier(sK1)
| cast_to_el_of_LattPOSet(sK1,X0) = X0
| ~ latt_str(sK1) ),
inference(resolution,[],[f191,f166]) ).
fof(f253,plain,
! [X0] :
( ~ element(X0,the_carrier(sK1))
| cast_to_el_of_LattPOSet(sK1,X0) = X0
| ~ latt_str(sK1) ),
inference(forward_subsumption_resolution,[],[f252,f167]) ).
fof(f254,plain,
! [X0] :
( cast_to_el_of_LattPOSet(sK1,X0) = X0
| ~ element(X0,the_carrier(sK1)) ),
inference(forward_subsumption_resolution,[],[f253,f165]) ).
fof(f255,plain,
( relstr_element_smaller(poset_of_lattice(sK1),sK0,sK2)
| ~ element(sK2,the_carrier(sK1))
| ~ spl12_2 ),
inference(superposition,[],[f238,f254]) ).
fof(f256,plain,
( relstr_element_smaller(poset_of_lattice(sK1),sK0,sK2)
| ~ spl12_2 ),
inference(forward_subsumption_resolution,[],[f255,f168]) ).
fof(f266,plain,
! [X0,X1] :
( element(X0,the_carrier(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X0,the_carrier(poset_of_lattice(X1)))
| ~ element(X0,the_carrier(poset_of_lattice(X1)))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1) ),
inference(superposition,[],[f183,f190]) ).
fof(f267,plain,
! [X0,X1] :
( element(X0,the_carrier(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X0,the_carrier(poset_of_lattice(X1))) ),
inference(duplicate_literal_removal,[],[f266]) ).
fof(f270,plain,
! [X0] :
( element(X0,the_carrier(poset_of_lattice(sK1)))
| empty_carrier(sK1)
| ~ lattice(sK1)
| ~ latt_str(sK1)
| ~ element(X0,the_carrier(sK1))
| ~ element(X0,the_carrier(sK1)) ),
inference(superposition,[],[f184,f254]) ).
fof(f271,plain,
! [X0] :
( element(X0,the_carrier(poset_of_lattice(sK1)))
| empty_carrier(sK1)
| ~ lattice(sK1)
| ~ latt_str(sK1)
| ~ element(X0,the_carrier(sK1)) ),
inference(duplicate_literal_removal,[],[f270]) ).
fof(f272,plain,
! [X0] :
( element(X0,the_carrier(poset_of_lattice(sK1)))
| ~ lattice(sK1)
| ~ latt_str(sK1)
| ~ element(X0,the_carrier(sK1)) ),
inference(forward_subsumption_resolution,[],[f271,f167]) ).
fof(f273,plain,
! [X0] :
( element(X0,the_carrier(poset_of_lattice(sK1)))
| ~ latt_str(sK1)
| ~ element(X0,the_carrier(sK1)) ),
inference(forward_subsumption_resolution,[],[f272,f166]) ).
fof(f274,plain,
! [X0] :
( element(X0,the_carrier(poset_of_lattice(sK1)))
| ~ element(X0,the_carrier(sK1)) ),
inference(forward_subsumption_resolution,[],[f273,f165]) ).
fof(f314,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,[],[f177,f208]) ).
fof(f315,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,[],[f314]) ).
fof(f316,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,[],[f315,f211]) ).
fof(f317,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,[],[f316,f209]) ).
fof(f329,plain,
! [X0,X1] :
( ~ below_refl(sK1,X0,X1)
| ~ element(X1,the_carrier(sK1))
| ~ element(X0,the_carrier(sK1))
| empty_carrier(sK1)
| related_reflexive(poset_of_lattice(sK1),cast_to_el_of_LattPOSet(sK1,X0),cast_to_el_of_LattPOSet(sK1,X1))
| ~ latt_str(sK1) ),
inference(resolution,[],[f171,f166]) ).
fof(f330,plain,
! [X0,X1] :
( ~ below_refl(sK1,X0,X1)
| ~ element(X1,the_carrier(sK1))
| ~ element(X0,the_carrier(sK1))
| related_reflexive(poset_of_lattice(sK1),cast_to_el_of_LattPOSet(sK1,X0),cast_to_el_of_LattPOSet(sK1,X1))
| ~ latt_str(sK1) ),
inference(forward_subsumption_resolution,[],[f329,f167]) ).
fof(f331,plain,
! [X0,X1] :
( ~ below_refl(sK1,X0,X1)
| ~ element(X1,the_carrier(sK1))
| ~ element(X0,the_carrier(sK1))
| related_reflexive(poset_of_lattice(sK1),cast_to_el_of_LattPOSet(sK1,X0),cast_to_el_of_LattPOSet(sK1,X1)) ),
inference(forward_subsumption_resolution,[],[f330,f165]) ).
fof(f333,plain,
! [X0,X1] :
( ~ element(X0,the_carrier(sK1))
| ~ element(X1,the_carrier(sK1))
| related_reflexive(poset_of_lattice(sK1),cast_to_el_of_LattPOSet(sK1,X1),cast_to_el_of_LattPOSet(sK1,X0))
| ~ below(sK1,X1,X0)
| empty_carrier(sK1)
| ~ meet_commutative(sK1)
| ~ meet_absorbing(sK1)
| ~ join_absorbing(sK1)
| ~ latt_str(sK1)
| ~ element(X1,the_carrier(sK1))
| ~ element(X0,the_carrier(sK1)) ),
inference(resolution,[],[f331,f178]) ).
fof(f334,plain,
! [X0,X1] :
( ~ element(X0,the_carrier(sK1))
| ~ element(X1,the_carrier(sK1))
| related_reflexive(poset_of_lattice(sK1),cast_to_el_of_LattPOSet(sK1,X1),cast_to_el_of_LattPOSet(sK1,X0))
| ~ below(sK1,X1,X0)
| empty_carrier(sK1)
| ~ meet_commutative(sK1)
| ~ meet_absorbing(sK1)
| ~ join_absorbing(sK1)
| ~ latt_str(sK1) ),
inference(duplicate_literal_removal,[],[f333]) ).
fof(f336,plain,
! [X0,X1] :
( ~ element(X0,the_carrier(sK1))
| ~ element(X1,the_carrier(sK1))
| related_reflexive(poset_of_lattice(sK1),cast_to_el_of_LattPOSet(sK1,X1),cast_to_el_of_LattPOSet(sK1,X0))
| ~ below(sK1,X1,X0)
| ~ meet_commutative(sK1)
| ~ meet_absorbing(sK1)
| ~ join_absorbing(sK1)
| ~ latt_str(sK1) ),
inference(forward_subsumption_resolution,[],[f334,f167]) ).
fof(f338,plain,
! [X0,X1] :
( ~ element(X0,the_carrier(sK1))
| ~ element(X1,the_carrier(sK1))
| related_reflexive(poset_of_lattice(sK1),cast_to_el_of_LattPOSet(sK1,X1),cast_to_el_of_LattPOSet(sK1,X0))
| ~ below(sK1,X1,X0)
| ~ meet_commutative(sK1)
| ~ meet_absorbing(sK1)
| ~ join_absorbing(sK1) ),
inference(forward_subsumption_resolution,[],[f336,f165]) ).
fof(f341,definition,
( spl12_9
<=> join_absorbing(sK1) ),
introduced(definition,[new_symbols(definition,[spl12_9])],[avatar_definition]) ).
fof(f343,plain,
( ~ join_absorbing(sK1)
| spl12_9 ),
inference(avatar_component_clause,[],[f341]) ).
fof(f345,definition,
( spl12_10
<=> meet_absorbing(sK1) ),
introduced(definition,[new_symbols(definition,[spl12_10])],[avatar_definition]) ).
fof(f347,plain,
( ~ meet_absorbing(sK1)
| spl12_10 ),
inference(avatar_component_clause,[],[f345]) ).
fof(f349,definition,
( spl12_11
<=> meet_commutative(sK1) ),
introduced(definition,[new_symbols(definition,[spl12_11])],[avatar_definition]) ).
fof(f351,plain,
( ~ meet_commutative(sK1)
| spl12_11 ),
inference(avatar_component_clause,[],[f349]) ).
fof(f353,definition,
( spl12_12
<=> ! [X0,X1] :
( ~ element(X0,the_carrier(sK1))
| ~ below(sK1,X1,X0)
| ~ element(X1,the_carrier(sK1))
| related_reflexive(poset_of_lattice(sK1),cast_to_el_of_LattPOSet(sK1,X1),cast_to_el_of_LattPOSet(sK1,X0)) ) ),
introduced(definition,[new_symbols(definition,[spl12_12])],[avatar_definition]) ).
fof(f354,plain,
( ! [X0,X1] :
( ~ below(sK1,X1,X0)
| ~ element(X0,the_carrier(sK1))
| ~ element(X1,the_carrier(sK1))
| related_reflexive(poset_of_lattice(sK1),cast_to_el_of_LattPOSet(sK1,X1),cast_to_el_of_LattPOSet(sK1,X0)) )
| ~ spl12_12 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f355,plain,
( ~ spl12_9
| ~ spl12_10
| ~ spl12_11
| spl12_12 ),
inference(avatar_split_clause,[],[f338,f353,f349,f345,f341]) ).
fof(f363,plain,
! [X0,X1] :
( ~ related_reflexive(poset_of_lattice(sK1),cast_to_el_of_LattPOSet(sK1,X0),cast_to_el_of_LattPOSet(sK1,X1))
| ~ element(X1,the_carrier(sK1))
| ~ element(X0,the_carrier(sK1))
| empty_carrier(sK1)
| below_refl(sK1,X0,X1)
| ~ latt_str(sK1) ),
inference(resolution,[],[f172,f166]) ).
fof(f364,plain,
! [X0,X1] :
( ~ related_reflexive(poset_of_lattice(sK1),cast_to_el_of_LattPOSet(sK1,X0),cast_to_el_of_LattPOSet(sK1,X1))
| ~ element(X1,the_carrier(sK1))
| ~ element(X0,the_carrier(sK1))
| below_refl(sK1,X0,X1)
| ~ latt_str(sK1) ),
inference(forward_subsumption_resolution,[],[f363,f167]) ).
fof(f365,plain,
! [X0,X1] :
( below_refl(sK1,X0,X1)
| ~ element(X1,the_carrier(sK1))
| ~ element(X0,the_carrier(sK1))
| ~ related_reflexive(poset_of_lattice(sK1),cast_to_el_of_LattPOSet(sK1,X0),cast_to_el_of_LattPOSet(sK1,X1)) ),
inference(forward_subsumption_resolution,[],[f364,f165]) ).
fof(f366,plain,
( empty_carrier(sK1)
| ~ lattice(sK1)
| ~ latt_str(sK1)
| spl12_9 ),
inference(resolution,[],[f343,f208]) ).
fof(f367,plain,
( ~ lattice(sK1)
| ~ latt_str(sK1)
| spl12_9 ),
inference(forward_subsumption_resolution,[],[f366,f167]) ).
fof(f368,plain,
( ~ latt_str(sK1)
| spl12_9 ),
inference(forward_subsumption_resolution,[],[f367,f166]) ).
fof(f369,plain,
( $false
| spl12_9 ),
inference(forward_subsumption_resolution,[],[f368,f165]) ).
fof(f370,plain,
spl12_9,
inference(avatar_contradiction_clause,[],[f369]) ).
fof(f375,plain,
( empty_carrier(sK1)
| ~ lattice(sK1)
| ~ latt_str(sK1)
| spl12_10 ),
inference(resolution,[],[f347,f209]) ).
fof(f376,plain,
( ~ lattice(sK1)
| ~ latt_str(sK1)
| spl12_10 ),
inference(forward_subsumption_resolution,[],[f375,f167]) ).
fof(f377,plain,
( ~ latt_str(sK1)
| spl12_10 ),
inference(forward_subsumption_resolution,[],[f376,f166]) ).
fof(f378,plain,
( $false
| spl12_10 ),
inference(forward_subsumption_resolution,[],[f377,f165]) ).
fof(f379,plain,
spl12_10,
inference(avatar_contradiction_clause,[],[f378]) ).
fof(f380,plain,
! [X0,X1] :
( empty_carrier(sK1)
| below(sK1,X0,X1)
| ~ latt_str(sK1)
| ~ element(X0,the_carrier(sK1))
| ~ element(X1,the_carrier(sK1))
| ~ below_refl(sK1,X0,X1) ),
inference(resolution,[],[f317,f166]) ).
fof(f381,plain,
! [X0,X1] :
( below(sK1,X0,X1)
| ~ latt_str(sK1)
| ~ element(X0,the_carrier(sK1))
| ~ element(X1,the_carrier(sK1))
| ~ below_refl(sK1,X0,X1) ),
inference(forward_subsumption_resolution,[],[f380,f167]) ).
fof(f382,plain,
! [X0,X1] :
( below(sK1,X0,X1)
| ~ element(X0,the_carrier(sK1))
| ~ element(X1,the_carrier(sK1))
| ~ below_refl(sK1,X0,X1) ),
inference(forward_subsumption_resolution,[],[f381,f165]) ).
fof(f383,plain,
( empty_carrier(sK1)
| ~ lattice(sK1)
| ~ latt_str(sK1)
| spl12_11 ),
inference(resolution,[],[f351,f211]) ).
fof(f384,plain,
( ~ lattice(sK1)
| ~ latt_str(sK1)
| spl12_11 ),
inference(forward_subsumption_resolution,[],[f383,f167]) ).
fof(f385,plain,
( ~ latt_str(sK1)
| spl12_11 ),
inference(forward_subsumption_resolution,[],[f384,f166]) ).
fof(f386,plain,
( $false
| spl12_11 ),
inference(forward_subsumption_resolution,[],[f385,f165]) ).
fof(f387,plain,
spl12_11,
inference(avatar_contradiction_clause,[],[f386]) ).
fof(f409,definition,
( spl12_15
<=> rel_str(poset_of_lattice(sK1)) ),
introduced(definition,[new_symbols(definition,[spl12_15])],[avatar_definition]) ).
fof(f410,plain,
( rel_str(poset_of_lattice(sK1))
| ~ spl12_15 ),
inference(avatar_component_clause,[],[f409]) ).
fof(f411,plain,
( ~ rel_str(poset_of_lattice(sK1))
| spl12_15 ),
inference(avatar_component_clause,[],[f409]) ).
fof(f413,definition,
( spl12_16
<=> reflexive_relstr(poset_of_lattice(sK1)) ),
introduced(definition,[new_symbols(definition,[spl12_16])],[avatar_definition]) ).
fof(f414,plain,
( reflexive_relstr(poset_of_lattice(sK1))
| ~ spl12_16 ),
inference(avatar_component_clause,[],[f413]) ).
fof(f415,plain,
( ~ reflexive_relstr(poset_of_lattice(sK1))
| spl12_16 ),
inference(avatar_component_clause,[],[f413]) ).
fof(f417,definition,
( spl12_17
<=> empty_carrier(poset_of_lattice(sK1)) ),
introduced(definition,[new_symbols(definition,[spl12_17])],[avatar_definition]) ).
fof(f418,plain,
( ~ empty_carrier(poset_of_lattice(sK1))
| spl12_17 ),
inference(avatar_component_clause,[],[f417]) ).
fof(f419,plain,
( empty_carrier(poset_of_lattice(sK1))
| ~ spl12_17 ),
inference(avatar_component_clause,[],[f417]) ).
fof(f424,plain,
( empty_carrier(sK1)
| ~ lattice(sK1)
| ~ latt_str(sK1)
| spl12_15 ),
inference(resolution,[],[f411,f203]) ).
fof(f425,plain,
( ~ lattice(sK1)
| ~ latt_str(sK1)
| spl12_15 ),
inference(forward_subsumption_resolution,[],[f424,f167]) ).
fof(f426,plain,
( ~ latt_str(sK1)
| spl12_15 ),
inference(forward_subsumption_resolution,[],[f425,f166]) ).
fof(f427,plain,
( $false
| spl12_15 ),
inference(forward_subsumption_resolution,[],[f426,f165]) ).
fof(f428,plain,
spl12_15,
inference(avatar_contradiction_clause,[],[f427]) ).
fof(f429,plain,
! [X0,X1] :
( ~ element(X0,the_carrier(sK1))
| ~ element(sK5(sK1,X0,X1),the_carrier(sK1))
| ~ below_refl(sK1,X0,sK5(sK1,X0,X1))
| latt_set_smaller(sK1,X0,X1)
| ~ element(X0,the_carrier(sK1))
| empty_carrier(sK1)
| ~ latt_str(sK1) ),
inference(resolution,[],[f382,f196]) ).
fof(f430,plain,
! [X0,X1] :
( ~ element(X0,the_carrier(sK1))
| ~ element(sK5(sK1,X0,X1),the_carrier(sK1))
| ~ below_refl(sK1,X0,sK5(sK1,X0,X1))
| latt_set_smaller(sK1,X0,X1)
| empty_carrier(sK1)
| ~ latt_str(sK1) ),
inference(duplicate_literal_removal,[],[f429]) ).
fof(f431,plain,
! [X0,X1] :
( ~ element(X0,the_carrier(sK1))
| ~ below_refl(sK1,X0,sK5(sK1,X0,X1))
| latt_set_smaller(sK1,X0,X1)
| empty_carrier(sK1)
| ~ latt_str(sK1) ),
inference(forward_subsumption_resolution,[],[f430,f194]) ).
fof(f432,plain,
! [X0,X1] :
( ~ element(X0,the_carrier(sK1))
| ~ below_refl(sK1,X0,sK5(sK1,X0,X1))
| latt_set_smaller(sK1,X0,X1)
| ~ latt_str(sK1) ),
inference(forward_subsumption_resolution,[],[f431,f167]) ).
fof(f433,plain,
! [X0,X1] :
( ~ below_refl(sK1,X0,sK5(sK1,X0,X1))
| ~ element(X0,the_carrier(sK1))
| latt_set_smaller(sK1,X0,X1) ),
inference(forward_subsumption_resolution,[],[f432,f165]) ).
fof(f436,plain,
( empty_carrier(sK1)
| ~ lattice(sK1)
| ~ latt_str(sK1)
| spl12_16 ),
inference(resolution,[],[f415,f204]) ).
fof(f437,plain,
( ~ lattice(sK1)
| ~ latt_str(sK1)
| spl12_16 ),
inference(forward_subsumption_resolution,[],[f436,f167]) ).
fof(f438,plain,
( ~ latt_str(sK1)
| spl12_16 ),
inference(forward_subsumption_resolution,[],[f437,f166]) ).
fof(f439,plain,
( $false
| spl12_16 ),
inference(forward_subsumption_resolution,[],[f438,f165]) ).
fof(f440,plain,
spl12_16,
inference(avatar_contradiction_clause,[],[f439]) ).
fof(f452,plain,
( empty_carrier(sK1)
| ~ lattice(sK1)
| ~ latt_str(sK1)
| ~ spl12_17 ),
inference(resolution,[],[f419,f201]) ).
fof(f453,plain,
( ~ lattice(sK1)
| ~ latt_str(sK1)
| ~ spl12_17 ),
inference(forward_subsumption_resolution,[],[f452,f167]) ).
fof(f454,plain,
( ~ latt_str(sK1)
| ~ spl12_17 ),
inference(forward_subsumption_resolution,[],[f453,f166]) ).
fof(f455,plain,
( $false
| ~ spl12_17 ),
inference(forward_subsumption_resolution,[],[f454,f165]) ).
fof(f456,plain,
~ spl12_17,
inference(avatar_contradiction_clause,[],[f455]) ).
fof(f469,plain,
! [X0,X1] :
( ~ element(X0,the_carrier(sK1))
| latt_set_smaller(sK1,X0,X1)
| ~ element(sK5(sK1,X0,X1),the_carrier(sK1))
| ~ element(X0,the_carrier(sK1))
| ~ related_reflexive(poset_of_lattice(sK1),cast_to_el_of_LattPOSet(sK1,X0),cast_to_el_of_LattPOSet(sK1,sK5(sK1,X0,X1))) ),
inference(resolution,[],[f433,f365]) ).
fof(f472,plain,
! [X0,X1] :
( latt_set_smaller(sK1,X0,X1)
| ~ element(X0,the_carrier(sK1))
| ~ element(sK5(sK1,X0,X1),the_carrier(sK1))
| ~ related_reflexive(poset_of_lattice(sK1),cast_to_el_of_LattPOSet(sK1,X0),cast_to_el_of_LattPOSet(sK1,sK5(sK1,X0,X1))) ),
inference(duplicate_literal_removal,[],[f469]) ).
fof(f481,plain,
( ~ element(sK2,the_carrier(sK1))
| ~ element(sK5(sK1,sK2,sK0),the_carrier(sK1))
| ~ related_reflexive(poset_of_lattice(sK1),cast_to_el_of_LattPOSet(sK1,sK2),cast_to_el_of_LattPOSet(sK1,sK5(sK1,sK2,sK0)))
| spl12_1 ),
inference(resolution,[],[f472,f233]) ).
fof(f485,plain,
( ~ element(sK5(sK1,sK2,sK0),the_carrier(sK1))
| ~ related_reflexive(poset_of_lattice(sK1),cast_to_el_of_LattPOSet(sK1,sK2),cast_to_el_of_LattPOSet(sK1,sK5(sK1,sK2,sK0)))
| spl12_1 ),
inference(forward_subsumption_resolution,[],[f481,f168]) ).
fof(f488,definition,
( spl12_21
<=> related_reflexive(poset_of_lattice(sK1),cast_to_el_of_LattPOSet(sK1,sK2),cast_to_el_of_LattPOSet(sK1,sK5(sK1,sK2,sK0))) ),
introduced(definition,[new_symbols(definition,[spl12_21])],[avatar_definition]) ).
fof(f490,plain,
( ~ related_reflexive(poset_of_lattice(sK1),cast_to_el_of_LattPOSet(sK1,sK2),cast_to_el_of_LattPOSet(sK1,sK5(sK1,sK2,sK0)))
| spl12_21 ),
inference(avatar_component_clause,[],[f488]) ).
fof(f492,definition,
( spl12_22
<=> element(sK5(sK1,sK2,sK0),the_carrier(sK1)) ),
introduced(definition,[new_symbols(definition,[spl12_22])],[avatar_definition]) ).
fof(f493,plain,
( element(sK5(sK1,sK2,sK0),the_carrier(sK1))
| ~ spl12_22 ),
inference(avatar_component_clause,[],[f492]) ).
fof(f494,plain,
( ~ element(sK5(sK1,sK2,sK0),the_carrier(sK1))
| spl12_22 ),
inference(avatar_component_clause,[],[f492]) ).
fof(f495,plain,
( ~ spl12_21
| ~ spl12_22
| spl12_1 ),
inference(avatar_split_clause,[],[f485,f232,f492,f488]) ).
fof(f498,plain,
( ~ related_reflexive(poset_of_lattice(sK1),cast_to_el_of_LattPOSet(sK1,sK2),sK5(sK1,sK2,sK0))
| ~ element(sK5(sK1,sK2,sK0),the_carrier(sK1))
| spl12_21 ),
inference(superposition,[],[f490,f254]) ).
fof(f500,definition,
( spl12_23
<=> related_reflexive(poset_of_lattice(sK1),cast_to_el_of_LattPOSet(sK1,sK2),sK5(sK1,sK2,sK0)) ),
introduced(definition,[new_symbols(definition,[spl12_23])],[avatar_definition]) ).
fof(f502,plain,
( ~ related_reflexive(poset_of_lattice(sK1),cast_to_el_of_LattPOSet(sK1,sK2),sK5(sK1,sK2,sK0))
| spl12_23 ),
inference(avatar_component_clause,[],[f500]) ).
fof(f503,plain,
( ~ spl12_22
| ~ spl12_23
| spl12_21 ),
inference(avatar_split_clause,[],[f498,f488,f500,f492]) ).
fof(f525,plain,
( latt_set_smaller(sK1,sK2,sK0)
| ~ element(sK2,the_carrier(sK1))
| empty_carrier(sK1)
| ~ latt_str(sK1)
| spl12_22 ),
inference(resolution,[],[f494,f194]) ).
fof(f530,plain,
( ~ element(sK2,the_carrier(sK1))
| empty_carrier(sK1)
| ~ latt_str(sK1)
| spl12_1
| spl12_22 ),
inference(forward_subsumption_resolution,[],[f525,f233]) ).
fof(f532,plain,
( empty_carrier(sK1)
| ~ latt_str(sK1)
| spl12_1
| spl12_22 ),
inference(forward_subsumption_resolution,[],[f530,f168]) ).
fof(f534,plain,
( ~ latt_str(sK1)
| spl12_1
| spl12_22 ),
inference(forward_subsumption_resolution,[],[f532,f167]) ).
fof(f535,plain,
( $false
| spl12_1
| spl12_22 ),
inference(forward_subsumption_resolution,[],[f534,f165]) ).
fof(f536,plain,
( spl12_1
| spl12_22 ),
inference(avatar_contradiction_clause,[],[f535]) ).
fof(f537,plain,
( ! [X0] :
( ~ in(X0,sK0)
| ~ element(X0,the_carrier(sK1))
| below(sK1,sK2,X0)
| ~ element(sK2,the_carrier(sK1))
| empty_carrier(sK1)
| ~ latt_str(sK1) )
| ~ spl12_1 ),
inference(resolution,[],[f234,f193]) ).
fof(f538,plain,
( ! [X0] :
( ~ in(X0,sK0)
| ~ element(X0,the_carrier(sK1))
| below(sK1,sK2,X0)
| empty_carrier(sK1)
| ~ latt_str(sK1) )
| ~ spl12_1 ),
inference(forward_subsumption_resolution,[],[f537,f168]) ).
fof(f539,plain,
( ! [X0] :
( ~ in(X0,sK0)
| ~ element(X0,the_carrier(sK1))
| below(sK1,sK2,X0)
| ~ latt_str(sK1) )
| ~ spl12_1 ),
inference(forward_subsumption_resolution,[],[f538,f167]) ).
fof(f540,plain,
( ! [X0] :
( below(sK1,sK2,X0)
| ~ element(X0,the_carrier(sK1))
| ~ in(X0,sK0) )
| ~ spl12_1 ),
inference(forward_subsumption_resolution,[],[f539,f165]) ).
fof(f543,plain,
( ~ relstr_element_smaller(poset_of_lattice(sK1),sK0,sK2)
| ~ element(sK2,the_carrier(sK1))
| spl12_2 ),
inference(superposition,[],[f237,f254]) ).
fof(f544,plain,
( ~ relstr_element_smaller(poset_of_lattice(sK1),sK0,sK2)
| spl12_2 ),
inference(forward_subsumption_resolution,[],[f543,f168]) ).
fof(f556,plain,
( ! [X0] :
( ~ element(X0,the_carrier(sK1))
| ~ in(X0,sK0)
| ~ element(X0,the_carrier(sK1))
| ~ element(sK2,the_carrier(sK1))
| related_reflexive(poset_of_lattice(sK1),cast_to_el_of_LattPOSet(sK1,sK2),cast_to_el_of_LattPOSet(sK1,X0)) )
| ~ spl12_1
| ~ spl12_12 ),
inference(resolution,[],[f540,f354]) ).
fof(f558,plain,
( ! [X0] :
( ~ element(X0,the_carrier(sK1))
| ~ in(X0,sK0)
| ~ element(sK2,the_carrier(sK1))
| related_reflexive(poset_of_lattice(sK1),cast_to_el_of_LattPOSet(sK1,sK2),cast_to_el_of_LattPOSet(sK1,X0)) )
| ~ spl12_1
| ~ spl12_12 ),
inference(duplicate_literal_removal,[],[f556]) ).
fof(f560,plain,
( ! [X0] :
( ~ in(X0,sK0)
| ~ element(X0,the_carrier(sK1))
| related_reflexive(poset_of_lattice(sK1),cast_to_el_of_LattPOSet(sK1,sK2),cast_to_el_of_LattPOSet(sK1,X0)) )
| ~ spl12_1
| ~ spl12_12 ),
inference(forward_subsumption_resolution,[],[f558,f168]) ).
fof(f565,plain,
( in(sK4(poset_of_lattice(sK1),sK0,sK2),sK0)
| ~ element(sK2,the_carrier(poset_of_lattice(sK1)))
| ~ rel_str(poset_of_lattice(sK1))
| spl12_2 ),
inference(resolution,[],[f544,f188]) ).
fof(f566,plain,
( in(sK4(poset_of_lattice(sK1),sK0,sK2),sK0)
| ~ element(sK2,the_carrier(poset_of_lattice(sK1)))
| spl12_2
| ~ spl12_15 ),
inference(forward_subsumption_resolution,[],[f565,f410]) ).
fof(f569,definition,
( spl12_29
<=> element(sK2,the_carrier(poset_of_lattice(sK1))) ),
introduced(definition,[new_symbols(definition,[spl12_29])],[avatar_definition]) ).
fof(f570,plain,
( element(sK2,the_carrier(poset_of_lattice(sK1)))
| ~ spl12_29 ),
inference(avatar_component_clause,[],[f569]) ).
fof(f571,plain,
( ~ element(sK2,the_carrier(poset_of_lattice(sK1)))
| spl12_29 ),
inference(avatar_component_clause,[],[f569]) ).
fof(f573,definition,
( spl12_30
<=> in(sK4(poset_of_lattice(sK1),sK0,sK2),sK0) ),
introduced(definition,[new_symbols(definition,[spl12_30])],[avatar_definition]) ).
fof(f575,plain,
( in(sK4(poset_of_lattice(sK1),sK0,sK2),sK0)
| ~ spl12_30 ),
inference(avatar_component_clause,[],[f573]) ).
fof(f576,plain,
( ~ spl12_29
| spl12_30
| spl12_2
| ~ spl12_15 ),
inference(avatar_split_clause,[],[f566,f409,f236,f573,f569]) ).
fof(f585,plain,
( ~ element(sK2,the_carrier(sK1))
| spl12_29 ),
inference(resolution,[],[f571,f274]) ).
fof(f590,plain,
( $false
| spl12_29 ),
inference(forward_subsumption_resolution,[],[f585,f168]) ).
fof(f591,plain,
spl12_29,
inference(avatar_contradiction_clause,[],[f590]) ).
fof(f617,plain,
( ~ element(sK4(poset_of_lattice(sK1),sK0,sK2),the_carrier(sK1))
| related_reflexive(poset_of_lattice(sK1),cast_to_el_of_LattPOSet(sK1,sK2),cast_to_el_of_LattPOSet(sK1,sK4(poset_of_lattice(sK1),sK0,sK2)))
| ~ spl12_1
| ~ spl12_12
| ~ spl12_30 ),
inference(resolution,[],[f560,f575]) ).
fof(f619,definition,
( spl12_35
<=> related_reflexive(poset_of_lattice(sK1),cast_to_el_of_LattPOSet(sK1,sK2),cast_to_el_of_LattPOSet(sK1,sK4(poset_of_lattice(sK1),sK0,sK2))) ),
introduced(definition,[new_symbols(definition,[spl12_35])],[avatar_definition]) ).
fof(f621,plain,
( related_reflexive(poset_of_lattice(sK1),cast_to_el_of_LattPOSet(sK1,sK2),cast_to_el_of_LattPOSet(sK1,sK4(poset_of_lattice(sK1),sK0,sK2)))
| ~ spl12_35 ),
inference(avatar_component_clause,[],[f619]) ).
fof(f623,definition,
( spl12_36
<=> element(sK4(poset_of_lattice(sK1),sK0,sK2),the_carrier(sK1)) ),
introduced(definition,[new_symbols(definition,[spl12_36])],[avatar_definition]) ).
fof(f624,plain,
( element(sK4(poset_of_lattice(sK1),sK0,sK2),the_carrier(sK1))
| ~ spl12_36 ),
inference(avatar_component_clause,[],[f623]) ).
fof(f625,plain,
( ~ element(sK4(poset_of_lattice(sK1),sK0,sK2),the_carrier(sK1))
| spl12_36 ),
inference(avatar_component_clause,[],[f623]) ).
fof(f672,plain,
( ~ related_reflexive(poset_of_lattice(sK1),sK2,sK5(sK1,sK2,sK0))
| ~ element(sK2,the_carrier(sK1))
| spl12_23 ),
inference(superposition,[],[f502,f254]) ).
fof(f673,plain,
( ~ related_reflexive(poset_of_lattice(sK1),sK2,sK5(sK1,sK2,sK0))
| spl12_23 ),
inference(forward_subsumption_resolution,[],[f672,f168]) ).
fof(f679,definition,
( spl12_40
<=> element(sK5(sK1,sK2,sK0),the_carrier(poset_of_lattice(sK1))) ),
introduced(definition,[new_symbols(definition,[spl12_40])],[avatar_definition]) ).
fof(f680,plain,
( element(sK5(sK1,sK2,sK0),the_carrier(poset_of_lattice(sK1)))
| ~ spl12_40 ),
inference(avatar_component_clause,[],[f679]) ).
fof(f681,plain,
( ~ element(sK5(sK1,sK2,sK0),the_carrier(poset_of_lattice(sK1)))
| spl12_40 ),
inference(avatar_component_clause,[],[f679]) ).
fof(f688,plain,
( ~ related(poset_of_lattice(sK1),sK2,sK5(sK1,sK2,sK0))
| empty_carrier(poset_of_lattice(sK1))
| ~ reflexive_relstr(poset_of_lattice(sK1))
| ~ rel_str(poset_of_lattice(sK1))
| ~ element(sK2,the_carrier(poset_of_lattice(sK1)))
| ~ element(sK5(sK1,sK2,sK0),the_carrier(poset_of_lattice(sK1)))
| spl12_23 ),
inference(resolution,[],[f673,f176]) ).
fof(f692,plain,
( ~ element(sK5(sK1,sK2,sK0),the_carrier(sK1))
| spl12_40 ),
inference(resolution,[],[f681,f274]) ).
fof(f697,plain,
( $false
| ~ spl12_22
| spl12_40 ),
inference(forward_subsumption_resolution,[],[f692,f493]) ).
fof(f698,plain,
( ~ spl12_22
| spl12_40 ),
inference(avatar_contradiction_clause,[],[f697]) ).
fof(f704,plain,
( spl12_35
| ~ spl12_36
| ~ spl12_1
| ~ spl12_12
| ~ spl12_30 ),
inference(avatar_split_clause,[],[f617,f573,f353,f232,f623,f619]) ).
fof(f770,plain,
( empty_carrier(sK1)
| ~ lattice(sK1)
| ~ latt_str(sK1)
| ~ element(sK4(poset_of_lattice(sK1),sK0,sK2),the_carrier(poset_of_lattice(sK1)))
| spl12_36 ),
inference(resolution,[],[f625,f267]) ).
fof(f773,plain,
( ~ lattice(sK1)
| ~ latt_str(sK1)
| ~ element(sK4(poset_of_lattice(sK1),sK0,sK2),the_carrier(poset_of_lattice(sK1)))
| spl12_36 ),
inference(forward_subsumption_resolution,[],[f770,f167]) ).
fof(f774,plain,
( ~ latt_str(sK1)
| ~ element(sK4(poset_of_lattice(sK1),sK0,sK2),the_carrier(poset_of_lattice(sK1)))
| spl12_36 ),
inference(forward_subsumption_resolution,[],[f773,f166]) ).
fof(f775,plain,
( ~ element(sK4(poset_of_lattice(sK1),sK0,sK2),the_carrier(poset_of_lattice(sK1)))
| spl12_36 ),
inference(forward_subsumption_resolution,[],[f774,f165]) ).
fof(f798,plain,
( relstr_element_smaller(poset_of_lattice(sK1),sK0,sK2)
| ~ element(sK2,the_carrier(poset_of_lattice(sK1)))
| ~ rel_str(poset_of_lattice(sK1))
| spl12_36 ),
inference(resolution,[],[f775,f187]) ).
fof(f803,plain,
( ~ element(sK2,the_carrier(poset_of_lattice(sK1)))
| ~ rel_str(poset_of_lattice(sK1))
| spl12_2
| spl12_36 ),
inference(forward_subsumption_resolution,[],[f798,f544]) ).
fof(f804,plain,
( ~ rel_str(poset_of_lattice(sK1))
| spl12_2
| ~ spl12_29
| spl12_36 ),
inference(forward_subsumption_resolution,[],[f803,f570]) ).
fof(f805,plain,
( $false
| spl12_2
| ~ spl12_15
| ~ spl12_29
| spl12_36 ),
inference(forward_subsumption_resolution,[],[f804,f410]) ).
fof(f806,plain,
( spl12_2
| ~ spl12_15
| ~ spl12_29
| spl12_36 ),
inference(avatar_contradiction_clause,[],[f805]) ).
fof(f810,plain,
( ~ related(poset_of_lattice(sK1),sK2,sK5(sK1,sK2,sK0))
| ~ reflexive_relstr(poset_of_lattice(sK1))
| ~ rel_str(poset_of_lattice(sK1))
| ~ element(sK2,the_carrier(poset_of_lattice(sK1)))
| ~ element(sK5(sK1,sK2,sK0),the_carrier(poset_of_lattice(sK1)))
| spl12_17
| spl12_23 ),
inference(forward_subsumption_resolution,[],[f688,f418]) ).
fof(f814,plain,
( ~ related(poset_of_lattice(sK1),sK2,sK5(sK1,sK2,sK0))
| ~ rel_str(poset_of_lattice(sK1))
| ~ element(sK2,the_carrier(poset_of_lattice(sK1)))
| ~ element(sK5(sK1,sK2,sK0),the_carrier(poset_of_lattice(sK1)))
| ~ spl12_16
| spl12_17
| spl12_23 ),
inference(forward_subsumption_resolution,[],[f810,f414]) ).
fof(f816,plain,
( ~ related(poset_of_lattice(sK1),sK2,sK5(sK1,sK2,sK0))
| ~ element(sK2,the_carrier(poset_of_lattice(sK1)))
| ~ element(sK5(sK1,sK2,sK0),the_carrier(poset_of_lattice(sK1)))
| ~ spl12_15
| ~ spl12_16
| spl12_17
| spl12_23 ),
inference(forward_subsumption_resolution,[],[f814,f410]) ).
fof(f817,plain,
( ~ related(poset_of_lattice(sK1),sK2,sK5(sK1,sK2,sK0))
| ~ element(sK5(sK1,sK2,sK0),the_carrier(poset_of_lattice(sK1)))
| ~ spl12_15
| ~ spl12_16
| spl12_17
| spl12_23
| ~ spl12_29 ),
inference(forward_subsumption_resolution,[],[f816,f570]) ).
fof(f818,plain,
( ~ related(poset_of_lattice(sK1),sK2,sK5(sK1,sK2,sK0))
| ~ spl12_15
| ~ spl12_16
| spl12_17
| spl12_23
| ~ spl12_29
| ~ spl12_40 ),
inference(forward_subsumption_resolution,[],[f817,f680]) ).
fof(f831,plain,
( related_reflexive(poset_of_lattice(sK1),sK2,cast_to_el_of_LattPOSet(sK1,sK4(poset_of_lattice(sK1),sK0,sK2)))
| ~ element(sK2,the_carrier(sK1))
| ~ spl12_35 ),
inference(superposition,[],[f621,f254]) ).
fof(f833,plain,
( related_reflexive(poset_of_lattice(sK1),sK2,cast_to_el_of_LattPOSet(sK1,sK4(poset_of_lattice(sK1),sK0,sK2)))
| ~ spl12_35 ),
inference(forward_subsumption_resolution,[],[f831,f168]) ).
fof(f870,plain,
( related_reflexive(poset_of_lattice(sK1),sK2,sK4(poset_of_lattice(sK1),sK0,sK2))
| ~ element(sK4(poset_of_lattice(sK1),sK0,sK2),the_carrier(sK1))
| ~ spl12_35 ),
inference(superposition,[],[f833,f254]) ).
fof(f903,plain,
( related_reflexive(poset_of_lattice(sK1),sK2,sK4(poset_of_lattice(sK1),sK0,sK2))
| ~ spl12_35
| ~ spl12_36 ),
inference(forward_subsumption_resolution,[],[f870,f624]) ).
fof(f967,plain,
( related(poset_of_lattice(sK1),sK2,sK4(poset_of_lattice(sK1),sK0,sK2))
| empty_carrier(poset_of_lattice(sK1))
| ~ reflexive_relstr(poset_of_lattice(sK1))
| ~ rel_str(poset_of_lattice(sK1))
| ~ element(sK2,the_carrier(poset_of_lattice(sK1)))
| ~ element(sK4(poset_of_lattice(sK1),sK0,sK2),the_carrier(poset_of_lattice(sK1)))
| ~ spl12_35
| ~ spl12_36 ),
inference(resolution,[],[f903,f175]) ).
fof(f968,plain,
( related(poset_of_lattice(sK1),sK2,sK4(poset_of_lattice(sK1),sK0,sK2))
| ~ reflexive_relstr(poset_of_lattice(sK1))
| ~ rel_str(poset_of_lattice(sK1))
| ~ element(sK2,the_carrier(poset_of_lattice(sK1)))
| ~ element(sK4(poset_of_lattice(sK1),sK0,sK2),the_carrier(poset_of_lattice(sK1)))
| spl12_17
| ~ spl12_35
| ~ spl12_36 ),
inference(forward_subsumption_resolution,[],[f967,f418]) ).
fof(f969,plain,
( related(poset_of_lattice(sK1),sK2,sK4(poset_of_lattice(sK1),sK0,sK2))
| ~ rel_str(poset_of_lattice(sK1))
| ~ element(sK2,the_carrier(poset_of_lattice(sK1)))
| ~ element(sK4(poset_of_lattice(sK1),sK0,sK2),the_carrier(poset_of_lattice(sK1)))
| ~ spl12_16
| spl12_17
| ~ spl12_35
| ~ spl12_36 ),
inference(forward_subsumption_resolution,[],[f968,f414]) ).
fof(f970,plain,
( related(poset_of_lattice(sK1),sK2,sK4(poset_of_lattice(sK1),sK0,sK2))
| ~ element(sK2,the_carrier(poset_of_lattice(sK1)))
| ~ element(sK4(poset_of_lattice(sK1),sK0,sK2),the_carrier(poset_of_lattice(sK1)))
| ~ spl12_15
| ~ spl12_16
| spl12_17
| ~ spl12_35
| ~ spl12_36 ),
inference(forward_subsumption_resolution,[],[f969,f410]) ).
fof(f971,plain,
( related(poset_of_lattice(sK1),sK2,sK4(poset_of_lattice(sK1),sK0,sK2))
| ~ element(sK4(poset_of_lattice(sK1),sK0,sK2),the_carrier(poset_of_lattice(sK1)))
| ~ spl12_15
| ~ spl12_16
| spl12_17
| ~ spl12_29
| ~ spl12_35
| ~ spl12_36 ),
inference(forward_subsumption_resolution,[],[f970,f570]) ).
fof(f973,definition,
( spl12_48
<=> element(sK4(poset_of_lattice(sK1),sK0,sK2),the_carrier(poset_of_lattice(sK1))) ),
introduced(definition,[new_symbols(definition,[spl12_48])],[avatar_definition]) ).
fof(f975,plain,
( ~ element(sK4(poset_of_lattice(sK1),sK0,sK2),the_carrier(poset_of_lattice(sK1)))
| spl12_48 ),
inference(avatar_component_clause,[],[f973]) ).
fof(f977,definition,
( spl12_49
<=> related(poset_of_lattice(sK1),sK2,sK4(poset_of_lattice(sK1),sK0,sK2)) ),
introduced(definition,[new_symbols(definition,[spl12_49])],[avatar_definition]) ).
fof(f979,plain,
( related(poset_of_lattice(sK1),sK2,sK4(poset_of_lattice(sK1),sK0,sK2))
| ~ spl12_49 ),
inference(avatar_component_clause,[],[f977]) ).
fof(f980,plain,
( ~ spl12_48
| spl12_49
| ~ spl12_15
| ~ spl12_16
| spl12_17
| ~ spl12_29
| ~ spl12_35
| ~ spl12_36 ),
inference(avatar_split_clause,[],[f971,f623,f619,f569,f417,f413,f409,f977,f973]) ).
fof(f991,plain,
( relstr_element_smaller(poset_of_lattice(sK1),sK0,sK2)
| ~ element(sK2,the_carrier(poset_of_lattice(sK1)))
| ~ rel_str(poset_of_lattice(sK1))
| spl12_48 ),
inference(resolution,[],[f975,f187]) ).
fof(f998,plain,
( ~ element(sK2,the_carrier(poset_of_lattice(sK1)))
| ~ rel_str(poset_of_lattice(sK1))
| spl12_2
| spl12_48 ),
inference(forward_subsumption_resolution,[],[f991,f544]) ).
fof(f999,plain,
( ~ rel_str(poset_of_lattice(sK1))
| spl12_2
| ~ spl12_29
| spl12_48 ),
inference(forward_subsumption_resolution,[],[f998,f570]) ).
fof(f1000,plain,
( $false
| spl12_2
| ~ spl12_15
| ~ spl12_29
| spl12_48 ),
inference(forward_subsumption_resolution,[],[f999,f410]) ).
fof(f1001,plain,
( spl12_2
| ~ spl12_15
| ~ spl12_29
| spl12_48 ),
inference(avatar_contradiction_clause,[],[f1000]) ).
fof(f1021,plain,
( ! [X0] :
( ~ in(sK5(sK1,sK2,sK0),X0)
| ~ element(sK5(sK1,sK2,sK0),the_carrier(poset_of_lattice(sK1)))
| ~ relstr_element_smaller(poset_of_lattice(sK1),X0,sK2)
| ~ element(sK2,the_carrier(poset_of_lattice(sK1)))
| ~ rel_str(poset_of_lattice(sK1)) )
| ~ spl12_15
| ~ spl12_16
| spl12_17
| spl12_23
| ~ spl12_29
| ~ spl12_40 ),
inference(resolution,[],[f818,f186]) ).
fof(f1022,plain,
( ! [X0] :
( ~ in(sK5(sK1,sK2,sK0),X0)
| ~ relstr_element_smaller(poset_of_lattice(sK1),X0,sK2)
| ~ element(sK2,the_carrier(poset_of_lattice(sK1)))
| ~ rel_str(poset_of_lattice(sK1)) )
| ~ spl12_15
| ~ spl12_16
| spl12_17
| spl12_23
| ~ spl12_29
| ~ spl12_40 ),
inference(forward_subsumption_resolution,[],[f1021,f680]) ).
fof(f1023,plain,
( ! [X0] :
( ~ in(sK5(sK1,sK2,sK0),X0)
| ~ relstr_element_smaller(poset_of_lattice(sK1),X0,sK2)
| ~ rel_str(poset_of_lattice(sK1)) )
| ~ spl12_15
| ~ spl12_16
| spl12_17
| spl12_23
| ~ spl12_29
| ~ spl12_40 ),
inference(forward_subsumption_resolution,[],[f1022,f570]) ).
fof(f1024,plain,
( ! [X0] :
( ~ in(sK5(sK1,sK2,sK0),X0)
| ~ relstr_element_smaller(poset_of_lattice(sK1),X0,sK2) )
| ~ spl12_15
| ~ spl12_16
| spl12_17
| spl12_23
| ~ spl12_29
| ~ spl12_40 ),
inference(forward_subsumption_resolution,[],[f1023,f410]) ).
fof(f1181,plain,
( ~ relstr_element_smaller(poset_of_lattice(sK1),sK0,sK2)
| latt_set_smaller(sK1,sK2,sK0)
| ~ element(sK2,the_carrier(sK1))
| empty_carrier(sK1)
| ~ latt_str(sK1)
| ~ spl12_15
| ~ spl12_16
| spl12_17
| spl12_23
| ~ spl12_29
| ~ spl12_40 ),
inference(resolution,[],[f1024,f195]) ).
fof(f1183,plain,
( latt_set_smaller(sK1,sK2,sK0)
| ~ element(sK2,the_carrier(sK1))
| empty_carrier(sK1)
| ~ latt_str(sK1)
| ~ spl12_2
| ~ spl12_15
| ~ spl12_16
| spl12_17
| spl12_23
| ~ spl12_29
| ~ spl12_40 ),
inference(forward_subsumption_resolution,[],[f1181,f256]) ).
fof(f1184,plain,
( ~ element(sK2,the_carrier(sK1))
| empty_carrier(sK1)
| ~ latt_str(sK1)
| spl12_1
| ~ spl12_2
| ~ spl12_15
| ~ spl12_16
| spl12_17
| spl12_23
| ~ spl12_29
| ~ spl12_40 ),
inference(forward_subsumption_resolution,[],[f1183,f233]) ).
fof(f1185,plain,
( empty_carrier(sK1)
| ~ latt_str(sK1)
| spl12_1
| ~ spl12_2
| ~ spl12_15
| ~ spl12_16
| spl12_17
| spl12_23
| ~ spl12_29
| ~ spl12_40 ),
inference(forward_subsumption_resolution,[],[f1184,f168]) ).
fof(f1186,plain,
( ~ latt_str(sK1)
| spl12_1
| ~ spl12_2
| ~ spl12_15
| ~ spl12_16
| spl12_17
| spl12_23
| ~ spl12_29
| ~ spl12_40 ),
inference(forward_subsumption_resolution,[],[f1185,f167]) ).
fof(f1187,plain,
( $false
| spl12_1
| ~ spl12_2
| ~ spl12_15
| ~ spl12_16
| spl12_17
| spl12_23
| ~ spl12_29
| ~ spl12_40 ),
inference(forward_subsumption_resolution,[],[f1186,f165]) ).
fof(f1188,plain,
( spl12_1
| ~ spl12_2
| ~ spl12_15
| ~ spl12_16
| spl12_17
| spl12_23
| ~ spl12_29
| ~ spl12_40 ),
inference(avatar_contradiction_clause,[],[f1187]) ).
fof(f1220,plain,
( relstr_element_smaller(poset_of_lattice(sK1),sK0,sK2)
| ~ element(sK2,the_carrier(poset_of_lattice(sK1)))
| ~ rel_str(poset_of_lattice(sK1))
| ~ spl12_49 ),
inference(resolution,[],[f979,f189]) ).
fof(f1221,plain,
( ~ element(sK2,the_carrier(poset_of_lattice(sK1)))
| ~ rel_str(poset_of_lattice(sK1))
| spl12_2
| ~ spl12_49 ),
inference(forward_subsumption_resolution,[],[f1220,f544]) ).
fof(f1222,plain,
( ~ rel_str(poset_of_lattice(sK1))
| spl12_2
| ~ spl12_29
| ~ spl12_49 ),
inference(forward_subsumption_resolution,[],[f1221,f570]) ).
fof(f1223,plain,
( $false
| spl12_2
| ~ spl12_15
| ~ spl12_29
| ~ spl12_49 ),
inference(forward_subsumption_resolution,[],[f1222,f410]) ).
fof(f1224,plain,
( spl12_2
| ~ spl12_15
| ~ spl12_29
| ~ spl12_49 ),
inference(avatar_contradiction_clause,[],[f1223]) ).
cnf(s1,plain,
( spl12_1
| spl12_2 ),
inference(sat_conversion,[],[f239]) ).
cnf(s2,plain,
( ~ spl12_1
| ~ spl12_2 ),
inference(sat_conversion,[],[f240]) ).
cnf(s6,plain,
( ~ spl12_9
| ~ spl12_10
| ~ spl12_11
| spl12_12 ),
inference(sat_conversion,[],[f355]) ).
cnf(s8,plain,
spl12_9,
inference(sat_conversion,[],[f370]) ).
cnf(s9,plain,
spl12_10,
inference(sat_conversion,[],[f379]) ).
cnf(s10,plain,
spl12_11,
inference(sat_conversion,[],[f387]) ).
cnf(s14,plain,
spl12_15,
inference(sat_conversion,[],[f428]) ).
cnf(s15,plain,
spl12_16,
inference(sat_conversion,[],[f440]) ).
cnf(s17,plain,
~ spl12_17,
inference(sat_conversion,[],[f456]) ).
cnf(s18,plain,
( spl12_1
| ~ spl12_21
| ~ spl12_22 ),
inference(sat_conversion,[],[f495]) ).
cnf(s19,plain,
( spl12_21
| ~ spl12_22
| ~ spl12_23 ),
inference(sat_conversion,[],[f503]) ).
cnf(s21,plain,
( spl12_1
| spl12_22 ),
inference(sat_conversion,[],[f536]) ).
cnf(s24,plain,
( spl12_2
| ~ spl12_15
| ~ spl12_29
| spl12_30 ),
inference(sat_conversion,[],[f576]) ).
cnf(s26,plain,
spl12_29,
inference(sat_conversion,[],[f591]) ).
cnf(s35,plain,
( ~ spl12_22
| spl12_40 ),
inference(sat_conversion,[],[f698]) ).
cnf(s37,plain,
( ~ spl12_1
| ~ spl12_12
| ~ spl12_30
| spl12_35
| ~ spl12_36 ),
inference(sat_conversion,[],[f704]) ).
cnf(s40,plain,
( spl12_2
| ~ spl12_15
| ~ spl12_29
| spl12_36 ),
inference(sat_conversion,[],[f806]) ).
cnf(s51,plain,
( ~ spl12_15
| ~ spl12_16
| spl12_17
| ~ spl12_29
| ~ spl12_35
| ~ spl12_36
| ~ spl12_48
| spl12_49 ),
inference(sat_conversion,[],[f980]) ).
cnf(s53,plain,
( spl12_2
| ~ spl12_15
| ~ spl12_29
| spl12_48 ),
inference(sat_conversion,[],[f1001]) ).
cnf(s63,plain,
( spl12_1
| ~ spl12_2
| ~ spl12_15
| ~ spl12_16
| spl12_17
| spl12_23
| ~ spl12_29
| ~ spl12_40 ),
inference(sat_conversion,[],[f1188]) ).
cnf(s65,plain,
( spl12_2
| ~ spl12_15
| ~ spl12_29
| ~ spl12_49 ),
inference(sat_conversion,[],[f1224]) ).
cnf(s69,plain,
( spl12_2
| ~ spl12_15
| spl12_30 ),
inference(rat,[],[s24,s26]) ).
cnf(s76,plain,
spl12_12,
inference(rat,[],[s6,s10,s9,s8]) ).
cnf(s79,plain,
( spl12_1
| ~ spl12_22 ),
inference(rat,[],[s63,s19,s35,s1,s18,s26,s17,s15,s14]) ).
cnf(s80,plain,
spl12_1,
inference(rat,[],[s79,s21]) ).
cnf(s81,plain,
~ spl12_2,
inference(rat,[],[s2,s80]) ).
cnf(s82,plain,
~ spl12_49,
inference(rat,[],[s65,s14,s26,s81]) ).
cnf(s83,plain,
spl12_48,
inference(rat,[],[s53,s14,s26,s81]) ).
cnf(s84,plain,
spl12_36,
inference(rat,[],[s40,s14,s26,s81]) ).
cnf(s86,plain,
spl12_30,
inference(rat,[],[s69,s14,s81]) ).
cnf(s91,plain,
~ spl12_35,
inference(rat,[],[s51,s82,s83,s14,s15,s26,s17,s84]) ).
cnf(s92,plain,
$false,
inference(rat,[],[s37,s84,s80,s76,s91,s86]) ).
fof(f1225,plain,
$false,
inference(avatar_sat_refutation,[],[s92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU347+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n005.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 04:49:32 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 4.12/1.59 % (438421)Detected formulas, will run a generic FOF schedule.
% 4.12/1.59 % (438426)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=1932217030:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.12/1.59 % (438428)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=1963773513:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.12/1.59 % (438430)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1512565671:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.12/1.59 % (438431)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2641282047:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.12/1.59 % (438429)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3489272557:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.12/1.59 % (438432)dis-21_1_sil=8000:lcm=predicate:random_seed=1701537443: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)
% 4.12/1.59 % (438427)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=2440645377:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.12/1.59 % (438429)Refutation not found, incomplete strategy
% 4.12/1.59 % (438429)------------------------------
% 4.12/1.59 % (438429)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.12/1.59 % (438429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/1.59 % (438429)CaDiCaL version: 2.1.3
% 4.12/1.59 % (438429)Termination reason: Refutation not found, incomplete strategy
% 4.12/1.59 % (438429)Time elapsed: 0.002 s
% 4.12/1.59 % (438429)Peak memory usage: 88 MB
% 4.12/1.59 % (438429)Instructions burned: 1 (million)
% 4.12/1.59 % (438430)Instruction limit reached!
% 4.12/1.59 % (438430)------------------------------
% 4.12/1.59 % (438430)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.12/1.59 % (438430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/1.59 % (438430)CaDiCaL version: 2.1.3
% 4.12/1.59 % (438430)Termination reason: Instruction limit
% 4.12/1.59 % (438430)Termination phase: Saturation
% 4.12/1.59 % (438430)Time elapsed: 0.071 s
% 4.12/1.59 % (438430)Peak memory usage: 88 MB
% 4.12/1.59 % (438430)Instructions burned: 119 (million)
% 4.12/1.59 % (438432)Instruction limit reached!
% 4.12/1.59 % (438432)------------------------------
% 4.12/1.59 % (438432)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.12/1.59 % (438432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/1.59 % (438432)CaDiCaL version: 2.1.3
% 4.12/1.59 % (438432)Termination reason: Instruction limit
% 4.12/1.59 % (438432)Termination phase: Saturation
% 4.12/1.59 % (438432)Time elapsed: 0.075 s
% 4.12/1.59 % (438432)Peak memory usage: 90 MB
% 4.12/1.59 % (438432)Instructions burned: 130 (million)
% 4.12/1.59 % (438431)Instruction limit reached!
% 4.12/1.59 % (438431)------------------------------
% 4.12/1.59 % (438431)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.12/1.59 % (438431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/1.59 % (438431)CaDiCaL version: 2.1.3
% 4.12/1.59 % (438431)Termination reason: Instruction limit
% 4.12/1.59 % (438431)Termination phase: Saturation
% 4.12/1.59 % (438431)Time elapsed: 0.102 s
% 4.12/1.59 % (438431)Peak memory usage: 89 MB
% 4.12/1.59 % (438431)Instructions burned: 139 (million)
% 4.12/1.59 % (438441)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3407542815:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.12/1.59 % (438440)lrs+10_1_sil=8000:sp=occurrence:random_seed=2170058877:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.12/1.59 % (438441)Refutation not found, incomplete strategy
% 4.12/1.59 % (438441)------------------------------
% 4.12/1.59 % (438441)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.12/1.59 % (438441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/1.59 % (438441)CaDiCaL version: 2.1.3
% 4.12/1.59 % (438441)Termination reason: Refutation not found, incomplete strategy
% 4.12/1.59 % (438441)Time elapsed: 0.013 s
% 4.12/1.59 % (438441)Peak memory usage: 88 MB
% 4.12/1.59 % (438441)Instructions burned: 18 (million)
% 4.12/1.59 % (438429)------------------------------
% 4.12/1.59 % (438429)------------------------------
% 4.12/1.59 % (438442)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1654092790:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.12/1.59 % (438442)First to succeed.
% 4.12/1.59 % (438442)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-438421"
% 4.12/1.59 % (438445)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=1489491403:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 4.12/1.59 % (438440)Instruction limit reached!
% 4.12/1.59 % (438440)------------------------------
% 4.12/1.59 % (438440)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.12/1.59 % (438440)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/1.59 % (438440)CaDiCaL version: 2.1.3
% 4.12/1.59 % (438440)Termination reason: Instruction limit
% 4.12/1.59 % (438440)Termination phase: Saturation
% 4.12/1.59 % (438440)Time elapsed: 0.186 s
% 4.12/1.59 % (438440)Peak memory usage: 91 MB
% 4.12/1.59 % (438440)Instructions burned: 286 (million)
% 4.12/1.59 % (438445)Instruction limit reached!
% 4.12/1.59 % (438445)------------------------------
% 4.12/1.59 % (438445)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.12/1.59 % (438445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.12/1.59 % (438445)CaDiCaL version: 2.1.3
% 4.12/1.59 % (438445)Termination reason: Instruction limit
% 4.12/1.59 % (438445)Termination phase: Saturation
% 4.12/1.59 % (438445)Time elapsed: 0.080 s
% 4.12/1.59 % (438445)Peak memory usage: 91 MB
% 4.12/1.59 % (438445)Instructions burned: 249 (million)
% 4.12/1.59 % (438441)------------------------------
% 4.12/1.59 % (438441)------------------------------
% 4.12/1.59 % (438426)Also succeeded, but the first one will report.
% 4.12/1.59 % (438442)Refutation found. Thanks to Tanya!
% 4.12/1.59 % SZS status Theorem for theBenchmark
% 4.12/1.59 % SZS output start Proof for theBenchmark
% See solution above
% 5.67/1.78 % (438442)------------------------------
% 5.67/1.78 % (438442)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.67/1.78 % (438442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.67/1.78 % (438442)CaDiCaL version: 2.1.3
% 5.67/1.78 % (438442)Termination reason: Refutation
% 5.67/1.78 % (438442)Time elapsed: 0.037 s
% 5.67/1.78 % (438442)Peak memory usage: 90 MB
% 5.67/1.78 % (438442)Instructions burned: 49 (million)
% 5.67/1.78 % (438442)------------------------------
% 5.67/1.78 % (438442)------------------------------
% 5.67/1.78 % (438421)Success in time 0.729 s
% 5.67/1.78 % Vampire exiting
%------------------------------------------------------------------------------