%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU349+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 12:52:58 PM UTC 2026
% Result : Theorem 6.87s 1.57s
% Output : Refutation 6.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 64
% Number of leaves : 29
% Syntax : Number of formulae : 322 ( 42 unt; 7 def)
% Number of atoms : 1340 ( 48 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 1668 ( 650 ~; 823 |; 135 &)
% ( 22 <=>; 36 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 38 ( 36 usr; 5 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 295 ( 0 sgn 279 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( rel_str(X0)
=> ( strict_rel_str(X0)
=> X0 = rel_str_of(the_carrier(X0),the_InternalRel(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
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_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(f7,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) )
=> poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_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(f10,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1,X2] :
( element(X2,the_carrier(X0))
=> ( relstr_set_smaller(X0,X1,X2)
<=> ! [X3] :
( element(X3,the_carrier(X0))
=> ( in(X3,X1)
=> related(X0,X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_lattice3) ).
fof(f14,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) )
=> ( reflexive(k2_lattice3(X0))
& antisymmetric(k2_lattice3(X0))
& transitive(k2_lattice3(X0))
& v1_partfun1(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
& relation_of2_as_subset(k2_lattice3(X0),the_carrier(X0),the_carrier(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_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(f21,axiom,
! [X0] :
( rel_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
fof(f23,axiom,
! [X0] :
( join_semilatt_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).
fof(f24,axiom,
! [X0] :
( latt_str(X0)
=> ( meet_semilatt_str(X0)
& join_semilatt_str(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(f39,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
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(f46,axiom,
! [X0,X1] :
( relation_of2(X1,X0,X0)
=> ! [X2,X3] :
( rel_str_of(X0,X1) = rel_str_of(X2,X3)
=> ( X0 = X2
& X1 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_orders_2) ).
fof(f56,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
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(f62,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f63,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f64,conjecture,
! [X0,X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ( latt_element_smaller(X1,X2,X0)
<=> relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_lattice3) ).
fof(f65,negated_conjecture,
~ ! [X0,X1] :
( ( ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ( latt_element_smaller(X1,X2,X0)
<=> relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2)) ) ) ),
inference(negated_conjecture,[status(cth)],[f64]) ).
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(f78,plain,
! [X0] :
( X0 = rel_str_of(the_carrier(X0),the_InternalRel(X0))
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f79,plain,
! [X0] :
( X0 = rel_str_of(the_carrier(X0),the_InternalRel(X0))
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f78]) ).
fof(f81,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(f82,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,[],[f81]) ).
fof(f85,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,[],[f6]) ).
fof(f86,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,[],[f85]) ).
fof(f87,plain,
! [X0] :
( poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f88,plain,
! [X0] :
( poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f87]) ).
fof(f89,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(f90,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,[],[f89]) ).
fof(f93,plain,
! [X0] :
( ! [X1,X2] :
( ( relstr_set_smaller(X0,X1,X2)
<=> ! [X3] :
( related(X0,X3,X2)
| ~ in(X3,X1)
| ~ element(X3,the_carrier(X0)) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f94,plain,
! [X0] :
( ! [X1,X2] :
( ( relstr_set_smaller(X0,X1,X2)
<=> ! [X3] :
( related(X0,X3,X2)
| ~ in(X3,X1)
| ~ element(X3,the_carrier(X0)) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(flattening,[],[f93]) ).
fof(f96,plain,
! [X0] :
( ( reflexive(k2_lattice3(X0))
& antisymmetric(k2_lattice3(X0))
& transitive(k2_lattice3(X0))
& v1_partfun1(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
& relation_of2_as_subset(k2_lattice3(X0),the_carrier(X0),the_carrier(X0)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f97,plain,
! [X0] :
( ( reflexive(k2_lattice3(X0))
& antisymmetric(k2_lattice3(X0))
& transitive(k2_lattice3(X0))
& v1_partfun1(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
& relation_of2_as_subset(k2_lattice3(X0),the_carrier(X0),the_carrier(X0)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f96]) ).
fof(f98,plain,
! [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)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f99,plain,
! [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)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f98]) ).
fof(f100,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(f101,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,[],[f100]) ).
fof(f105,plain,
! [X0] :
( one_sorted_str(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f106,plain,
! [X0] :
( one_sorted_str(X0)
| ~ join_semilatt_str(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f107,plain,
! [X0] :
( ( meet_semilatt_str(X0)
& join_semilatt_str(X0) )
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f112,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f113,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f112]) ).
fof(f118,plain,
! [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)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f119,plain,
! [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)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f118]) ).
fof(f122,plain,
! [X0,X1] :
( ! [X2,X3] :
( ( X0 = X2
& X1 = X3 )
| rel_str_of(X0,X1) != rel_str_of(X2,X3) )
| ~ relation_of2(X1,X0,X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f128,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(f129,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,[],[f128]) ).
fof(f130,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(f131,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,[],[f130]) ).
fof(f136,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f62]) ).
fof(f137,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f63]) ).
fof(f138,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f137]) ).
fof(f139,plain,
? [X0,X1] :
( ? [X2] :
( ( latt_element_smaller(X1,X2,X0)
<~> relstr_set_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,[],[f65]) ).
fof(f140,plain,
? [X0,X1] :
( ? [X2] :
( ( latt_element_smaller(X1,X2,X0)
<~> relstr_set_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,[],[f139]) ).
fof(f147,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(f148,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,[],[f147]) ).
fof(f150,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,[],[f86]) ).
fof(f151,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,[],[f150]) ).
fof(f152,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( latt_element_smaller(X0,X1,X2)
| ( ~ below(X0,sK0(X0,X1,X2),X1)
& in(sK0(X0,X1,X2),X2)
& element(sK0(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,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f151]) ).
fof(f153,plain,
! [X0] :
( ! [X1,X2] :
( ( ( relstr_set_smaller(X0,X1,X2)
| ? [X3] :
( ~ related(X0,X3,X2)
& in(X3,X1)
& element(X3,the_carrier(X0)) ) )
& ( ! [X3] :
( related(X0,X3,X2)
| ~ in(X3,X1)
| ~ element(X3,the_carrier(X0)) )
| ~ relstr_set_smaller(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(nnf_transformation,[],[f94]) ).
fof(f154,plain,
! [X0] :
( ! [X1,X2] :
( ( ( relstr_set_smaller(X0,X1,X2)
| ? [X3] :
( ~ related(X0,X3,X2)
& in(X3,X1)
& element(X3,the_carrier(X0)) ) )
& ( ! [X4] :
( related(X0,X4,X2)
| ~ in(X4,X1)
| ~ element(X4,the_carrier(X0)) )
| ~ relstr_set_smaller(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(rectify,[],[f153]) ).
fof(f155,plain,
! [X0] :
( ! [X1,X2] :
( ( ( relstr_set_smaller(X0,X1,X2)
| ( ~ related(X0,sK1(X0,X1,X2),X2)
& in(sK1(X0,X1,X2),X1)
& element(sK1(X0,X1,X2),the_carrier(X0)) ) )
& ( ! [X4] :
( related(X0,X4,X2)
| ~ in(X4,X1)
| ~ element(X4,the_carrier(X0)) )
| ~ relstr_set_smaller(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f154]) ).
fof(f172,plain,
! [X0,X1,X2] :
( ( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) )
& ( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f173,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,[],[f129]) ).
fof(f174,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,[],[f131]) ).
fof(f175,plain,
? [X0,X1] :
( ? [X2] :
( ( ~ relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
| ~ latt_element_smaller(X1,X2,X0) )
& ( relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
| latt_element_smaller(X1,X2,X0) )
& element(X2,the_carrier(X1)) )
& ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) ),
inference(nnf_transformation,[],[f140]) ).
fof(f176,plain,
? [X0,X1] :
( ? [X2] :
( ( ~ relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
| ~ latt_element_smaller(X1,X2,X0) )
& ( relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
| latt_element_smaller(X1,X2,X0) )
& element(X2,the_carrier(X1)) )
& ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1) ),
inference(flattening,[],[f175]) ).
fof(f177,plain,
( ( ~ relstr_set_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
| ~ latt_element_smaller(sK19,sK20,sK18) )
& ( relstr_set_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
| latt_element_smaller(sK19,sK20,sK18) )
& element(sK20,the_carrier(sK19))
& ~ empty_carrier(sK19)
& lattice(sK19)
& latt_str(sK19) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18,sK19,sK20]),skolemize(X0,sK18),skolemize(X1,sK19),skolemize(X2,sK20)],[f176]) ).
fof(f178,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,[],[f148]) ).
fof(f179,plain,
! [X0] :
( ~ strict_rel_str(X0)
| rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f181,plain,
! [X0] :
( ~ lattice(X0)
| empty_carrier(X0)
| join_absorbing(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f182,plain,
! [X0] :
( ~ lattice(X0)
| empty_carrier(X0)
| meet_absorbing(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f184,plain,
! [X0] :
( ~ lattice(X0)
| empty_carrier(X0)
| meet_commutative(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f190,plain,
! [X2,X0,X1,X4] :
( ~ latt_element_smaller(X0,X1,X2)
| ~ in(X4,X2)
| ~ element(X4,the_carrier(X0))
| below(X0,X4,X1)
| ~ element(X1,the_carrier(X0))
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f152]) ).
fof(f191,plain,
! [X2,X0,X1] :
( element(sK0(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,[],[f152]) ).
fof(f192,plain,
! [X2,X0,X1] :
( ~ element(X1,the_carrier(X0))
| in(sK0(X0,X1,X2),X2)
| latt_element_smaller(X0,X1,X2)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f152]) ).
fof(f193,plain,
! [X2,X0,X1] :
( ~ below(X0,sK0(X0,X1,X2),X1)
| latt_element_smaller(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f152]) ).
fof(f194,plain,
! [X0] :
( ~ lattice(X0)
| empty_carrier(X0)
| poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0))
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f195,plain,
! [X0,X1] :
( ~ element(X1,the_carrier(X0))
| cast_to_el_of_LattPOSet(X0,X1) = X1
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f197,plain,
! [X2,X0,X1,X4] :
( ~ relstr_set_smaller(X0,X1,X2)
| ~ in(X4,X1)
| ~ element(X4,the_carrier(X0))
| related(X0,X4,X2)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f155]) ).
fof(f198,plain,
! [X2,X0,X1] :
( element(sK1(X0,X1,X2),the_carrier(X0))
| relstr_set_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f155]) ).
fof(f199,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(X0))
| in(sK1(X0,X1,X2),X1)
| relstr_set_smaller(X0,X1,X2)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f155]) ).
fof(f200,plain,
! [X2,X0,X1] :
( ~ related(X0,sK1(X0,X1,X2),X2)
| relstr_set_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f155]) ).
fof(f203,plain,
! [X0] :
( ~ lattice(X0)
| empty_carrier(X0)
| relation_of2_as_subset(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f208,plain,
! [X0] :
( ~ lattice(X0)
| empty_carrier(X0)
| rel_str(poset_of_lattice(X0))
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f213,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,[],[f101]) ).
fof(f216,plain,
! [X0] :
( ~ rel_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f217,plain,
! [X0] :
( ~ join_semilatt_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f218,plain,
! [X0] :
( ~ latt_str(X0)
| join_semilatt_str(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f232,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f245,plain,
! [X0] :
( ~ lattice(X0)
| empty_carrier(X0)
| reflexive_relstr(poset_of_lattice(X0))
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f246,plain,
! [X0] :
( ~ lattice(X0)
| empty_carrier(X0)
| strict_rel_str(poset_of_lattice(X0))
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f247,plain,
! [X0] :
( ~ empty_carrier(poset_of_lattice(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f250,plain,
! [X2,X3,X0,X1] :
( rel_str_of(X0,X1) != rel_str_of(X2,X3)
| X0 = X2
| ~ relation_of2(X1,X0,X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f270,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f172]) ).
fof(f272,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,[],[f173]) ).
fof(f273,plain,
! [X2,X0,X1] :
( ~ 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(cnf_transformation,[],[f173]) ).
fof(f274,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,[],[f174]) ).
fof(f275,plain,
! [X2,X0,X1] :
( ~ 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(cnf_transformation,[],[f174]) ).
fof(f279,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f136]) ).
fof(f280,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f138]) ).
fof(f281,plain,
latt_str(sK19),
inference(cnf_transformation,[],[f177]) ).
fof(f282,plain,
lattice(sK19),
inference(cnf_transformation,[],[f177]) ).
fof(f283,plain,
~ empty_carrier(sK19),
inference(cnf_transformation,[],[f177]) ).
fof(f284,plain,
element(sK20,the_carrier(sK19)),
inference(cnf_transformation,[],[f177]) ).
fof(f285,plain,
( relstr_set_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
| latt_element_smaller(sK19,sK20,sK18) ),
inference(cnf_transformation,[],[f177]) ).
fof(f286,plain,
( ~ relstr_set_smaller(poset_of_lattice(sK19),sK18,cast_to_el_of_LattPOSet(sK19,sK20))
| ~ latt_element_smaller(sK19,sK20,sK18) ),
inference(cnf_transformation,[],[f177]) ).
fof(f292,plain,
! [X2,X0,X1] :
( ~ 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(cnf_transformation,[],[f178]) ).
fof(f293,plain,
! [X2,X0,X1] :
( ~ 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(cnf_transformation,[],[f178]) ).
fof(f295,definition,
sF21 = poset_of_lattice(sK19),
introduced(definition,[new_symbols(definition,[sF21])],[function_definition]) ).
fof(f296,plain,
poset_of_lattice(sK19) = sF21,
inference(reorient_equations,[],[f295]) ).
fof(f297,definition,
sF22 = cast_to_el_of_LattPOSet(sK19,sK20),
introduced(definition,[new_symbols(definition,[sF22])],[function_definition]) ).
fof(f298,plain,
cast_to_el_of_LattPOSet(sK19,sK20) = sF22,
inference(reorient_equations,[],[f297]) ).
fof(f299,plain,
( ~ relstr_set_smaller(sF21,sK18,sF22)
| ~ latt_element_smaller(sK19,sK20,sK18) ),
inference(definition_folding,[],[f286,f298,f296]) ).
fof(f300,plain,
( relstr_set_smaller(sF21,sK18,sF22)
| latt_element_smaller(sK19,sK20,sK18) ),
inference(definition_folding,[],[f285,f298,f296]) ).
fof(f301,definition,
sF23 = the_carrier(sK19),
introduced(definition,[new_symbols(definition,[sF23])],[function_definition]) ).
fof(f302,plain,
the_carrier(sK19) = sF23,
inference(reorient_equations,[],[f301]) ).
fof(f303,plain,
element(sK20,sF23),
inference(definition_folding,[],[f284,f302]) ).
fof(f305,definition,
( spl24_1
<=> latt_element_smaller(sK19,sK20,sK18) ),
introduced(definition,[new_symbols(definition,[spl24_1])],[avatar_definition]) ).
fof(f306,plain,
( ~ latt_element_smaller(sK19,sK20,sK18)
| spl24_1 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f307,plain,
( latt_element_smaller(sK19,sK20,sK18)
| ~ spl24_1 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f309,definition,
( spl24_2
<=> relstr_set_smaller(sF21,sK18,sF22) ),
introduced(definition,[new_symbols(definition,[spl24_2])],[avatar_definition]) ).
fof(f310,plain,
( ~ relstr_set_smaller(sF21,sK18,sF22)
| spl24_2 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f311,plain,
( relstr_set_smaller(sF21,sK18,sF22)
| ~ spl24_2 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f312,plain,
( spl24_1
| spl24_2 ),
inference(avatar_split_clause,[],[f300,f309,f305]) ).
fof(f313,plain,
( ~ spl24_1
| ~ spl24_2 ),
inference(avatar_split_clause,[],[f299,f309,f305]) ).
fof(f319,plain,
join_semilatt_str(sK19),
inference(resolution,[],[f218,f281]) ).
fof(f321,plain,
one_sorted_str(sK19),
inference(resolution,[],[f319,f217]) ).
fof(f333,plain,
( ~ empty(sF23)
| empty_carrier(sK19)
| ~ one_sorted_str(sK19) ),
inference(superposition,[],[f232,f302]) ).
fof(f334,plain,
( ~ empty(sF23)
| ~ one_sorted_str(sK19) ),
inference(forward_subsumption_resolution,[],[f333,f283]) ).
fof(f335,plain,
~ empty(sF23),
inference(forward_subsumption_resolution,[],[f334,f321]) ).
fof(f341,plain,
( empty_carrier(sK19)
| join_absorbing(sK19)
| ~ latt_str(sK19) ),
inference(resolution,[],[f181,f282]) ).
fof(f342,plain,
( join_absorbing(sK19)
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f341,f283]) ).
fof(f343,plain,
join_absorbing(sK19),
inference(forward_subsumption_resolution,[],[f342,f281]) ).
fof(f344,plain,
( empty_carrier(sK19)
| meet_absorbing(sK19)
| ~ latt_str(sK19) ),
inference(resolution,[],[f182,f282]) ).
fof(f345,plain,
( meet_absorbing(sK19)
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f344,f283]) ).
fof(f346,plain,
meet_absorbing(sK19),
inference(forward_subsumption_resolution,[],[f345,f281]) ).
fof(f350,plain,
( empty_carrier(sK19)
| meet_commutative(sK19)
| ~ latt_str(sK19) ),
inference(resolution,[],[f184,f282]) ).
fof(f351,plain,
( meet_commutative(sK19)
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f350,f283]) ).
fof(f352,plain,
meet_commutative(sK19),
inference(forward_subsumption_resolution,[],[f351,f281]) ).
fof(f392,plain,
( empty_carrier(sK19)
| rel_str(poset_of_lattice(sK19))
| ~ latt_str(sK19) ),
inference(resolution,[],[f208,f282]) ).
fof(f393,plain,
( rel_str(poset_of_lattice(sK19))
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f392,f283]) ).
fof(f394,plain,
rel_str(poset_of_lattice(sK19)),
inference(forward_subsumption_resolution,[],[f393,f281]) ).
fof(f395,plain,
rel_str(sF21),
inference(forward_demodulation,[],[f394,f296]) ).
fof(f396,plain,
one_sorted_str(sF21),
inference(resolution,[],[f395,f216]) ).
fof(f416,plain,
( empty_carrier(sK19)
| reflexive_relstr(poset_of_lattice(sK19))
| ~ latt_str(sK19) ),
inference(resolution,[],[f245,f282]) ).
fof(f417,plain,
( reflexive_relstr(poset_of_lattice(sK19))
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f416,f283]) ).
fof(f418,plain,
reflexive_relstr(poset_of_lattice(sK19)),
inference(forward_subsumption_resolution,[],[f417,f281]) ).
fof(f419,plain,
reflexive_relstr(sF21),
inference(forward_demodulation,[],[f418,f296]) ).
fof(f420,plain,
( empty_carrier(sK19)
| strict_rel_str(poset_of_lattice(sK19))
| ~ latt_str(sK19) ),
inference(resolution,[],[f246,f282]) ).
fof(f421,plain,
( strict_rel_str(poset_of_lattice(sK19))
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f420,f283]) ).
fof(f422,plain,
strict_rel_str(poset_of_lattice(sK19)),
inference(forward_subsumption_resolution,[],[f421,f281]) ).
fof(f423,plain,
strict_rel_str(sF21),
inference(forward_demodulation,[],[f422,f296]) ).
fof(f424,plain,
( ~ empty_carrier(sF21)
| empty_carrier(sK19)
| ~ lattice(sK19)
| ~ latt_str(sK19) ),
inference(superposition,[],[f247,f296]) ).
fof(f425,plain,
( ~ empty_carrier(sF21)
| ~ lattice(sK19)
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f424,f283]) ).
fof(f426,plain,
( ~ empty_carrier(sF21)
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f425,f282]) ).
fof(f427,plain,
~ empty_carrier(sF21),
inference(forward_subsumption_resolution,[],[f426,f281]) ).
fof(f480,plain,
( sF21 = rel_str_of(the_carrier(sF21),the_InternalRel(sF21))
| ~ rel_str(sF21) ),
inference(resolution,[],[f179,f423]) ).
fof(f481,plain,
sF21 = rel_str_of(the_carrier(sF21),the_InternalRel(sF21)),
inference(forward_subsumption_resolution,[],[f480,f395]) ).
fof(f512,plain,
( empty_carrier(sK19)
| relation_of2_as_subset(k2_lattice3(sK19),the_carrier(sK19),the_carrier(sK19))
| ~ latt_str(sK19) ),
inference(resolution,[],[f203,f282]) ).
fof(f513,plain,
( relation_of2_as_subset(k2_lattice3(sK19),the_carrier(sK19),the_carrier(sK19))
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f512,f283]) ).
fof(f514,plain,
relation_of2_as_subset(k2_lattice3(sK19),the_carrier(sK19),the_carrier(sK19)),
inference(forward_subsumption_resolution,[],[f513,f281]) ).
fof(f515,plain,
relation_of2_as_subset(k2_lattice3(sK19),sF23,sF23),
inference(forward_demodulation,[],[f514,f302]) ).
fof(f516,plain,
relation_of2(k2_lattice3(sK19),sF23,sF23),
inference(resolution,[],[f515,f270]) ).
fof(f521,plain,
( empty_carrier(sK19)
| poset_of_lattice(sK19) = rel_str_of(the_carrier(sK19),k2_lattice3(sK19))
| ~ latt_str(sK19) ),
inference(resolution,[],[f194,f282]) ).
fof(f522,plain,
( poset_of_lattice(sK19) = rel_str_of(the_carrier(sK19),k2_lattice3(sK19))
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f521,f283]) ).
fof(f523,plain,
poset_of_lattice(sK19) = rel_str_of(the_carrier(sK19),k2_lattice3(sK19)),
inference(forward_subsumption_resolution,[],[f522,f281]) ).
fof(f524,plain,
poset_of_lattice(sK19) = rel_str_of(sF23,k2_lattice3(sK19)),
inference(forward_demodulation,[],[f523,f302]) ).
fof(f525,plain,
sF21 = rel_str_of(sF23,k2_lattice3(sK19)),
inference(forward_demodulation,[],[f524,f296]) ).
fof(f541,plain,
! [X0,X1] :
( rel_str_of(X0,X1) != sF21
| sF23 = X0
| ~ relation_of2(k2_lattice3(sK19),sF23,sF23) ),
inference(superposition,[],[f250,f525]) ).
fof(f544,plain,
! [X0,X1] :
( rel_str_of(X0,X1) != sF21
| sF23 = X0 ),
inference(forward_subsumption_resolution,[],[f541,f516]) ).
fof(f546,plain,
! [X0] :
( ~ element(X0,sF23)
| cast_to_el_of_LattPOSet(sK19,X0) = X0
| empty_carrier(sK19)
| ~ lattice(sK19)
| ~ latt_str(sK19) ),
inference(superposition,[],[f195,f302]) ).
fof(f547,plain,
! [X0] :
( ~ element(X0,sF23)
| cast_to_el_of_LattPOSet(sK19,X0) = X0
| ~ lattice(sK19)
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f546,f283]) ).
fof(f548,plain,
! [X0] :
( ~ element(X0,sF23)
| cast_to_el_of_LattPOSet(sK19,X0) = X0
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f547,f282]) ).
fof(f549,plain,
! [X0] :
( ~ element(X0,sF23)
| cast_to_el_of_LattPOSet(sK19,X0) = X0 ),
inference(forward_subsumption_resolution,[],[f548,f281]) ).
fof(f582,plain,
sK20 = cast_to_el_of_LattPOSet(sK19,sK20),
inference(resolution,[],[f549,f303]) ).
fof(f586,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(X0))
| relstr_set_smaller(X0,X1,X2)
| ~ rel_str(X0)
| in(sK1(X0,X1,X2),the_carrier(X0))
| empty(the_carrier(X0)) ),
inference(resolution,[],[f198,f280]) ).
fof(f591,plain,
sK20 = sF22,
inference(superposition,[],[f298,f582]) ).
fof(f592,plain,
( relstr_set_smaller(sF21,sK18,sK20)
| ~ spl24_2 ),
inference(superposition,[],[f311,f591]) ).
fof(f597,plain,
( element(sK20,the_carrier(poset_of_lattice(sK19)))
| empty_carrier(sK19)
| ~ lattice(sK19)
| ~ latt_str(sK19)
| ~ element(sK20,the_carrier(sK19)) ),
inference(superposition,[],[f213,f582]) ).
fof(f603,plain,
( element(sK20,the_carrier(poset_of_lattice(sK19)))
| ~ lattice(sK19)
| ~ latt_str(sK19)
| ~ element(sK20,the_carrier(sK19)) ),
inference(forward_subsumption_resolution,[],[f597,f283]) ).
fof(f608,plain,
( element(sK20,the_carrier(poset_of_lattice(sK19)))
| ~ latt_str(sK19)
| ~ element(sK20,the_carrier(sK19)) ),
inference(forward_subsumption_resolution,[],[f603,f282]) ).
fof(f611,plain,
( element(sK20,the_carrier(poset_of_lattice(sK19)))
| ~ element(sK20,the_carrier(sK19)) ),
inference(forward_subsumption_resolution,[],[f608,f281]) ).
fof(f614,plain,
( element(sK20,the_carrier(sF21))
| ~ element(sK20,the_carrier(sK19)) ),
inference(forward_demodulation,[],[f611,f296]) ).
fof(f616,plain,
( ~ element(sK20,sF23)
| element(sK20,the_carrier(sF21)) ),
inference(forward_demodulation,[],[f614,f302]) ).
fof(f618,plain,
element(sK20,the_carrier(sF21)),
inference(forward_subsumption_resolution,[],[f616,f303]) ).
fof(f620,plain,
! [X0] :
( in(sK1(sF21,X0,sK20),X0)
| relstr_set_smaller(sF21,X0,sK20)
| ~ rel_str(sF21) ),
inference(resolution,[],[f618,f199]) ).
fof(f624,definition,
( spl24_10
<=> empty(the_carrier(sF21)) ),
introduced(definition,[new_symbols(definition,[spl24_10])],[avatar_definition]) ).
fof(f625,plain,
( ~ empty(the_carrier(sF21))
| spl24_10 ),
inference(avatar_component_clause,[],[f624]) ).
fof(f626,plain,
( empty(the_carrier(sF21))
| ~ spl24_10 ),
inference(avatar_component_clause,[],[f624]) ).
fof(f633,plain,
! [X0] :
( relstr_set_smaller(sF21,X0,sK20)
| in(sK1(sF21,X0,sK20),X0) ),
inference(forward_subsumption_resolution,[],[f620,f395]) ).
fof(f659,plain,
( empty_carrier(sF21)
| ~ one_sorted_str(sF21)
| ~ spl24_10 ),
inference(resolution,[],[f626,f232]) ).
fof(f663,plain,
( ~ one_sorted_str(sF21)
| ~ spl24_10 ),
inference(forward_subsumption_resolution,[],[f659,f427]) ).
fof(f664,plain,
( $false
| ~ spl24_10 ),
inference(forward_subsumption_resolution,[],[f663,f396]) ).
fof(f665,plain,
~ spl24_10,
inference(avatar_contradiction_clause,[],[f664]) ).
fof(f671,plain,
! [X0,X1] :
( ~ element(X0,sF23)
| in(sK0(sK19,X0,X1),X1)
| latt_element_smaller(sK19,X0,X1)
| empty_carrier(sK19)
| ~ latt_str(sK19) ),
inference(superposition,[],[f192,f302]) ).
fof(f673,plain,
! [X0,X1] :
( ~ element(X0,sF23)
| in(sK0(sK19,X0,X1),X1)
| latt_element_smaller(sK19,X0,X1)
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f671,f283]) ).
fof(f676,plain,
! [X0,X1] :
( ~ element(X0,sF23)
| in(sK0(sK19,X0,X1),X1)
| latt_element_smaller(sK19,X0,X1) ),
inference(forward_subsumption_resolution,[],[f673,f281]) ).
fof(f731,plain,
! [X0,X1] :
( element(sK0(sK19,X0,X1),sF23)
| latt_element_smaller(sK19,X0,X1)
| ~ element(X0,sF23)
| empty_carrier(sK19)
| ~ latt_str(sK19) ),
inference(superposition,[],[f191,f302]) ).
fof(f735,plain,
! [X0,X1] :
( element(sK0(sK19,X0,X1),sF23)
| latt_element_smaller(sK19,X0,X1)
| ~ element(X0,sF23)
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f731,f283]) ).
fof(f737,plain,
! [X0,X1] :
( element(sK0(sK19,X0,X1),sF23)
| latt_element_smaller(sK19,X0,X1)
| ~ element(X0,sF23) ),
inference(forward_subsumption_resolution,[],[f735,f281]) ).
fof(f754,plain,
( sF21 != sF21
| sF23 = the_carrier(sF21) ),
inference(superposition,[],[f544,f481]) ).
fof(f755,plain,
sF23 = the_carrier(sF21),
inference(trivial_inequality_removal,[],[f754]) ).
fof(f829,plain,
! [X0] :
( ~ related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,X0),sK20)
| below_refl(sK19,X0,sK20)
| ~ element(sK20,the_carrier(sK19))
| ~ element(X0,the_carrier(sK19))
| empty_carrier(sK19)
| ~ lattice(sK19)
| ~ latt_str(sK19) ),
inference(superposition,[],[f293,f582]) ).
fof(f834,plain,
! [X0] :
( ~ related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,X0),sK20)
| below_refl(sK19,X0,sK20)
| ~ element(sK20,the_carrier(sK19))
| ~ element(X0,the_carrier(sK19))
| ~ lattice(sK19)
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f829,f283]) ).
fof(f841,plain,
! [X0] :
( ~ related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,X0),sK20)
| below_refl(sK19,X0,sK20)
| ~ element(sK20,the_carrier(sK19))
| ~ element(X0,the_carrier(sK19))
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f834,f282]) ).
fof(f848,plain,
! [X0] :
( ~ related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,X0),sK20)
| below_refl(sK19,X0,sK20)
| ~ element(sK20,the_carrier(sK19))
| ~ element(X0,the_carrier(sK19)) ),
inference(forward_subsumption_resolution,[],[f841,f281]) ).
fof(f855,plain,
! [X0] :
( ~ related_reflexive(sF21,cast_to_el_of_LattPOSet(sK19,X0),sK20)
| below_refl(sK19,X0,sK20)
| ~ element(sK20,the_carrier(sK19))
| ~ element(X0,the_carrier(sK19)) ),
inference(forward_demodulation,[],[f848,f296]) ).
fof(f862,plain,
! [X0] :
( ~ element(sK20,sF23)
| ~ related_reflexive(sF21,cast_to_el_of_LattPOSet(sK19,X0),sK20)
| below_refl(sK19,X0,sK20)
| ~ element(X0,the_carrier(sK19)) ),
inference(forward_demodulation,[],[f855,f302]) ).
fof(f869,plain,
! [X0] :
( ~ related_reflexive(sF21,cast_to_el_of_LattPOSet(sK19,X0),sK20)
| below_refl(sK19,X0,sK20)
| ~ element(X0,the_carrier(sK19)) ),
inference(forward_subsumption_resolution,[],[f862,f303]) ).
fof(f875,plain,
! [X0] :
( ~ related_reflexive(sF21,cast_to_el_of_LattPOSet(sK19,X0),sK20)
| ~ element(X0,sF23)
| below_refl(sK19,X0,sK20) ),
inference(forward_demodulation,[],[f869,f302]) ).
fof(f981,plain,
! [X0] :
( latt_element_smaller(sK19,sK20,X0)
| in(sK0(sK19,sK20,X0),X0) ),
inference(resolution,[],[f676,f303]) ).
fof(f997,plain,
! [X0,X1] :
( latt_element_smaller(sK19,X0,X1)
| ~ element(X0,sF23)
| in(sK0(sK19,X0,X1),sF23)
| empty(sF23) ),
inference(resolution,[],[f737,f280]) ).
fof(f998,plain,
! [X0,X1] :
( ~ element(X0,sF23)
| latt_element_smaller(sK19,X0,X1)
| in(sK0(sK19,X0,X1),sF23) ),
inference(forward_subsumption_resolution,[],[f997,f335]) ).
fof(f1394,plain,
! [X0] :
( relstr_set_smaller(sF21,X0,sK20)
| ~ rel_str(sF21)
| in(sK1(sF21,X0,sK20),the_carrier(sF21))
| empty(the_carrier(sF21)) ),
inference(resolution,[],[f586,f618]) ).
fof(f1399,plain,
! [X0] :
( relstr_set_smaller(sF21,X0,sK20)
| in(sK1(sF21,X0,sK20),the_carrier(sF21))
| empty(the_carrier(sF21)) ),
inference(forward_subsumption_resolution,[],[f1394,f395]) ).
fof(f1404,plain,
( ! [X0] :
( relstr_set_smaller(sF21,X0,sK20)
| in(sK1(sF21,X0,sK20),the_carrier(sF21)) )
| spl24_10 ),
inference(forward_subsumption_resolution,[],[f1399,f625]) ).
fof(f1407,plain,
( ! [X0] :
( relstr_set_smaller(sF21,X0,sK20)
| in(sK1(sF21,X0,sK20),sF23) )
| spl24_10 ),
inference(forward_demodulation,[],[f1404,f755]) ).
fof(f1816,plain,
! [X0] :
( latt_element_smaller(sK19,sK20,X0)
| in(sK0(sK19,sK20,X0),sF23) ),
inference(resolution,[],[f998,f303]) ).
fof(f2180,plain,
( ~ relstr_set_smaller(sF21,sK18,sK20)
| spl24_2 ),
inference(forward_demodulation,[],[f310,f591]) ).
fof(f2181,plain,
( ! [X0] :
( ~ in(X0,sK18)
| ~ element(X0,the_carrier(sK19))
| below(sK19,X0,sK20)
| ~ element(sK20,the_carrier(sK19))
| empty_carrier(sK19)
| ~ latt_str(sK19) )
| ~ spl24_1 ),
inference(resolution,[],[f307,f190]) ).
fof(f2182,plain,
( ! [X0] :
( ~ in(X0,sK18)
| ~ element(X0,the_carrier(sK19))
| below(sK19,X0,sK20)
| ~ element(sK20,the_carrier(sK19))
| ~ latt_str(sK19) )
| ~ spl24_1 ),
inference(forward_subsumption_resolution,[],[f2181,f283]) ).
fof(f2183,plain,
( ! [X0] :
( ~ in(X0,sK18)
| ~ element(X0,the_carrier(sK19))
| below(sK19,X0,sK20)
| ~ element(sK20,the_carrier(sK19)) )
| ~ spl24_1 ),
inference(forward_subsumption_resolution,[],[f2182,f281]) ).
fof(f2184,plain,
( ! [X0] :
( ~ element(X0,sF23)
| ~ in(X0,sK18)
| below(sK19,X0,sK20)
| ~ element(sK20,the_carrier(sK19)) )
| ~ spl24_1 ),
inference(forward_demodulation,[],[f2183,f302]) ).
fof(f2185,plain,
( ! [X0] :
( ~ element(sK20,sF23)
| ~ element(X0,sF23)
| ~ in(X0,sK18)
| below(sK19,X0,sK20) )
| ~ spl24_1 ),
inference(forward_demodulation,[],[f2184,f302]) ).
fof(f2186,plain,
( ! [X0] :
( ~ element(X0,sF23)
| ~ in(X0,sK18)
| below(sK19,X0,sK20) )
| ~ spl24_1 ),
inference(forward_subsumption_resolution,[],[f2185,f303]) ).
fof(f2187,plain,
( in(sK1(sF21,sK18,sK20),sF23)
| spl24_2
| spl24_10 ),
inference(resolution,[],[f2180,f1407]) ).
fof(f2188,plain,
( in(sK1(sF21,sK18,sK20),sK18)
| spl24_2 ),
inference(resolution,[],[f2180,f633]) ).
fof(f2419,plain,
( element(sK1(sF21,sK18,sK20),sF23)
| spl24_2
| spl24_10 ),
inference(resolution,[],[f2187,f279]) ).
fof(f2527,plain,
( sK1(sF21,sK18,sK20) = cast_to_el_of_LattPOSet(sK19,sK1(sF21,sK18,sK20))
| spl24_2
| spl24_10 ),
inference(resolution,[],[f2419,f549]) ).
fof(f2553,plain,
( ~ in(sK1(sF21,sK18,sK20),sK18)
| below(sK19,sK1(sF21,sK18,sK20),sK20)
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(resolution,[],[f2419,f2186]) ).
fof(f2555,plain,
( below(sK19,sK1(sF21,sK18,sK20),sK20)
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(forward_subsumption_resolution,[],[f2553,f2188]) ).
fof(f2968,plain,
( below_refl(sK19,sK1(sF21,sK18,sK20),sK20)
| empty_carrier(sK19)
| ~ meet_commutative(sK19)
| ~ meet_absorbing(sK19)
| ~ join_absorbing(sK19)
| ~ latt_str(sK19)
| ~ element(sK1(sF21,sK18,sK20),the_carrier(sK19))
| ~ element(sK20,the_carrier(sK19))
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(resolution,[],[f2555,f273]) ).
fof(f2969,plain,
( below_refl(sK19,sK1(sF21,sK18,sK20),sK20)
| ~ meet_commutative(sK19)
| ~ meet_absorbing(sK19)
| ~ join_absorbing(sK19)
| ~ latt_str(sK19)
| ~ element(sK1(sF21,sK18,sK20),the_carrier(sK19))
| ~ element(sK20,the_carrier(sK19))
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(forward_subsumption_resolution,[],[f2968,f283]) ).
fof(f2970,plain,
( below_refl(sK19,sK1(sF21,sK18,sK20),sK20)
| ~ meet_absorbing(sK19)
| ~ join_absorbing(sK19)
| ~ latt_str(sK19)
| ~ element(sK1(sF21,sK18,sK20),the_carrier(sK19))
| ~ element(sK20,the_carrier(sK19))
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(forward_subsumption_resolution,[],[f2969,f352]) ).
fof(f2971,plain,
( below_refl(sK19,sK1(sF21,sK18,sK20),sK20)
| ~ join_absorbing(sK19)
| ~ latt_str(sK19)
| ~ element(sK1(sF21,sK18,sK20),the_carrier(sK19))
| ~ element(sK20,the_carrier(sK19))
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(forward_subsumption_resolution,[],[f2970,f346]) ).
fof(f2972,plain,
( below_refl(sK19,sK1(sF21,sK18,sK20),sK20)
| ~ latt_str(sK19)
| ~ element(sK1(sF21,sK18,sK20),the_carrier(sK19))
| ~ element(sK20,the_carrier(sK19))
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(forward_subsumption_resolution,[],[f2971,f343]) ).
fof(f2973,plain,
( below_refl(sK19,sK1(sF21,sK18,sK20),sK20)
| ~ element(sK1(sF21,sK18,sK20),the_carrier(sK19))
| ~ element(sK20,the_carrier(sK19))
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(forward_subsumption_resolution,[],[f2972,f281]) ).
fof(f2974,plain,
( ~ element(sK1(sF21,sK18,sK20),sF23)
| below_refl(sK19,sK1(sF21,sK18,sK20),sK20)
| ~ element(sK20,the_carrier(sK19))
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(forward_demodulation,[],[f2973,f302]) ).
fof(f2975,plain,
( below_refl(sK19,sK1(sF21,sK18,sK20),sK20)
| ~ element(sK20,the_carrier(sK19))
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(forward_subsumption_resolution,[],[f2974,f2419]) ).
fof(f2976,plain,
( ~ element(sK20,sF23)
| below_refl(sK19,sK1(sF21,sK18,sK20),sK20)
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(forward_demodulation,[],[f2975,f302]) ).
fof(f2977,plain,
( below_refl(sK19,sK1(sF21,sK18,sK20),sK20)
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(forward_subsumption_resolution,[],[f2976,f303]) ).
fof(f3034,plain,
( related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK1(sF21,sK18,sK20)),cast_to_el_of_LattPOSet(sK19,sK20))
| ~ element(sK20,the_carrier(sK19))
| ~ element(sK1(sF21,sK18,sK20),the_carrier(sK19))
| empty_carrier(sK19)
| ~ lattice(sK19)
| ~ latt_str(sK19)
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(resolution,[],[f2977,f292]) ).
fof(f3036,plain,
( related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK1(sF21,sK18,sK20)),cast_to_el_of_LattPOSet(sK19,sK20))
| ~ element(sK20,the_carrier(sK19))
| ~ element(sK1(sF21,sK18,sK20),the_carrier(sK19))
| ~ lattice(sK19)
| ~ latt_str(sK19)
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(forward_subsumption_resolution,[],[f3034,f283]) ).
fof(f3037,plain,
( related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK1(sF21,sK18,sK20)),cast_to_el_of_LattPOSet(sK19,sK20))
| ~ element(sK20,the_carrier(sK19))
| ~ element(sK1(sF21,sK18,sK20),the_carrier(sK19))
| ~ latt_str(sK19)
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(forward_subsumption_resolution,[],[f3036,f282]) ).
fof(f3038,plain,
( related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK1(sF21,sK18,sK20)),cast_to_el_of_LattPOSet(sK19,sK20))
| ~ element(sK20,the_carrier(sK19))
| ~ element(sK1(sF21,sK18,sK20),the_carrier(sK19))
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(forward_subsumption_resolution,[],[f3037,f281]) ).
fof(f3039,plain,
( related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK1(sF21,sK18,sK20)),sF22)
| ~ element(sK20,the_carrier(sK19))
| ~ element(sK1(sF21,sK18,sK20),the_carrier(sK19))
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(forward_demodulation,[],[f3038,f298]) ).
fof(f3040,plain,
( related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK1(sF21,sK18,sK20)),sK20)
| ~ element(sK20,the_carrier(sK19))
| ~ element(sK1(sF21,sK18,sK20),the_carrier(sK19))
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(forward_demodulation,[],[f3039,f591]) ).
fof(f3041,plain,
( related_reflexive(poset_of_lattice(sK19),sK1(sF21,sK18,sK20),sK20)
| ~ element(sK20,the_carrier(sK19))
| ~ element(sK1(sF21,sK18,sK20),the_carrier(sK19))
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(forward_demodulation,[],[f3040,f2527]) ).
fof(f3042,plain,
( related_reflexive(sF21,sK1(sF21,sK18,sK20),sK20)
| ~ element(sK20,the_carrier(sK19))
| ~ element(sK1(sF21,sK18,sK20),the_carrier(sK19))
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(forward_demodulation,[],[f3041,f296]) ).
fof(f3043,plain,
( ~ element(sK20,sF23)
| related_reflexive(sF21,sK1(sF21,sK18,sK20),sK20)
| ~ element(sK1(sF21,sK18,sK20),the_carrier(sK19))
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(forward_demodulation,[],[f3042,f302]) ).
fof(f3044,plain,
( related_reflexive(sF21,sK1(sF21,sK18,sK20),sK20)
| ~ element(sK1(sF21,sK18,sK20),the_carrier(sK19))
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(forward_subsumption_resolution,[],[f3043,f303]) ).
fof(f3045,plain,
( ~ element(sK1(sF21,sK18,sK20),sF23)
| related_reflexive(sF21,sK1(sF21,sK18,sK20),sK20)
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(forward_demodulation,[],[f3044,f302]) ).
fof(f3046,plain,
( related_reflexive(sF21,sK1(sF21,sK18,sK20),sK20)
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(forward_subsumption_resolution,[],[f3045,f2419]) ).
fof(f3088,plain,
( related(sF21,sK1(sF21,sK18,sK20),sK20)
| empty_carrier(sF21)
| ~ reflexive_relstr(sF21)
| ~ rel_str(sF21)
| ~ element(sK1(sF21,sK18,sK20),the_carrier(sF21))
| ~ element(sK20,the_carrier(sF21))
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(resolution,[],[f3046,f274]) ).
fof(f3089,plain,
( related(sF21,sK1(sF21,sK18,sK20),sK20)
| ~ reflexive_relstr(sF21)
| ~ rel_str(sF21)
| ~ element(sK1(sF21,sK18,sK20),the_carrier(sF21))
| ~ element(sK20,the_carrier(sF21))
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(forward_subsumption_resolution,[],[f3088,f427]) ).
fof(f3090,plain,
( related(sF21,sK1(sF21,sK18,sK20),sK20)
| ~ rel_str(sF21)
| ~ element(sK1(sF21,sK18,sK20),the_carrier(sF21))
| ~ element(sK20,the_carrier(sF21))
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(forward_subsumption_resolution,[],[f3089,f419]) ).
fof(f3091,plain,
( related(sF21,sK1(sF21,sK18,sK20),sK20)
| ~ element(sK1(sF21,sK18,sK20),the_carrier(sF21))
| ~ element(sK20,the_carrier(sF21))
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(forward_subsumption_resolution,[],[f3090,f395]) ).
fof(f3092,plain,
( related(sF21,sK1(sF21,sK18,sK20),sK20)
| ~ element(sK1(sF21,sK18,sK20),the_carrier(sF21))
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(forward_subsumption_resolution,[],[f3091,f618]) ).
fof(f3093,plain,
( ~ element(sK1(sF21,sK18,sK20),sF23)
| related(sF21,sK1(sF21,sK18,sK20),sK20)
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(forward_demodulation,[],[f3092,f755]) ).
fof(f3094,plain,
( related(sF21,sK1(sF21,sK18,sK20),sK20)
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(forward_subsumption_resolution,[],[f3093,f2419]) ).
fof(f3111,plain,
( relstr_set_smaller(sF21,sK18,sK20)
| ~ element(sK20,the_carrier(sF21))
| ~ rel_str(sF21)
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(resolution,[],[f3094,f200]) ).
fof(f3113,plain,
( ~ element(sK20,the_carrier(sF21))
| ~ rel_str(sF21)
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(forward_subsumption_resolution,[],[f3111,f2180]) ).
fof(f3114,plain,
( ~ rel_str(sF21)
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(forward_subsumption_resolution,[],[f3113,f618]) ).
fof(f3115,plain,
( $false
| ~ spl24_1
| spl24_2
| spl24_10 ),
inference(forward_subsumption_resolution,[],[f3114,f395]) ).
fof(f3116,plain,
( ~ spl24_1
| spl24_2
| spl24_10 ),
inference(avatar_contradiction_clause,[],[f3115]) ).
fof(f3119,plain,
( in(sK0(sK19,sK20,sK18),sF23)
| spl24_1 ),
inference(resolution,[],[f306,f1816]) ).
fof(f3120,plain,
( in(sK0(sK19,sK20,sK18),sK18)
| spl24_1 ),
inference(resolution,[],[f306,f981]) ).
fof(f3145,plain,
( ! [X0] :
( ~ in(X0,sK18)
| ~ element(X0,the_carrier(sF21))
| related(sF21,X0,sK20)
| ~ element(sK20,the_carrier(sF21))
| ~ rel_str(sF21) )
| ~ spl24_2 ),
inference(resolution,[],[f592,f197]) ).
fof(f3146,plain,
( ! [X0] :
( ~ in(X0,sK18)
| ~ element(X0,the_carrier(sF21))
| related(sF21,X0,sK20)
| ~ rel_str(sF21) )
| ~ spl24_2 ),
inference(forward_subsumption_resolution,[],[f3145,f618]) ).
fof(f3147,plain,
( ! [X0] :
( ~ in(X0,sK18)
| ~ element(X0,the_carrier(sF21))
| related(sF21,X0,sK20) )
| ~ spl24_2 ),
inference(forward_subsumption_resolution,[],[f3146,f395]) ).
fof(f3148,plain,
( ! [X0] :
( ~ element(X0,sF23)
| ~ in(X0,sK18)
| related(sF21,X0,sK20) )
| ~ spl24_2 ),
inference(forward_demodulation,[],[f3147,f755]) ).
fof(f3245,plain,
( element(sK0(sK19,sK20,sK18),sF23)
| spl24_1 ),
inference(resolution,[],[f3119,f279]) ).
fof(f3308,plain,
( sK0(sK19,sK20,sK18) = cast_to_el_of_LattPOSet(sK19,sK0(sK19,sK20,sK18))
| spl24_1 ),
inference(resolution,[],[f3245,f549]) ).
fof(f5296,definition,
( spl24_100
<=> below(sK19,sK0(sK19,sK20,sK18),sK20) ),
introduced(definition,[new_symbols(definition,[spl24_100])],[avatar_definition]) ).
fof(f5297,plain,
( ~ below(sK19,sK0(sK19,sK20,sK18),sK20)
| spl24_100 ),
inference(avatar_component_clause,[],[f5296]) ).
fof(f5298,plain,
( below(sK19,sK0(sK19,sK20,sK18),sK20)
| ~ spl24_100 ),
inference(avatar_component_clause,[],[f5296]) ).
fof(f6841,plain,
( latt_element_smaller(sK19,sK20,sK18)
| ~ element(sK20,the_carrier(sK19))
| empty_carrier(sK19)
| ~ latt_str(sK19)
| ~ spl24_100 ),
inference(resolution,[],[f5298,f193]) ).
fof(f6844,plain,
( ~ element(sK20,the_carrier(sK19))
| empty_carrier(sK19)
| ~ latt_str(sK19)
| spl24_1
| ~ spl24_100 ),
inference(forward_subsumption_resolution,[],[f6841,f306]) ).
fof(f6846,plain,
( ~ element(sK20,the_carrier(sK19))
| ~ latt_str(sK19)
| spl24_1
| ~ spl24_100 ),
inference(forward_subsumption_resolution,[],[f6844,f283]) ).
fof(f6848,plain,
( ~ element(sK20,the_carrier(sK19))
| spl24_1
| ~ spl24_100 ),
inference(forward_subsumption_resolution,[],[f6846,f281]) ).
fof(f6850,plain,
( ~ element(sK20,sF23)
| spl24_1
| ~ spl24_100 ),
inference(forward_demodulation,[],[f6848,f302]) ).
fof(f6852,plain,
( $false
| spl24_1
| ~ spl24_100 ),
inference(forward_subsumption_resolution,[],[f6850,f303]) ).
fof(f6853,plain,
( spl24_1
| ~ spl24_100 ),
inference(avatar_contradiction_clause,[],[f6852]) ).
fof(f11715,plain,
( ~ in(sK0(sK19,sK20,sK18),sK18)
| related(sF21,sK0(sK19,sK20,sK18),sK20)
| spl24_1
| ~ spl24_2 ),
inference(resolution,[],[f3148,f3245]) ).
fof(f11726,plain,
( related(sF21,sK0(sK19,sK20,sK18),sK20)
| spl24_1
| ~ spl24_2 ),
inference(forward_subsumption_resolution,[],[f11715,f3120]) ).
fof(f11734,plain,
( related_reflexive(sF21,sK0(sK19,sK20,sK18),sK20)
| empty_carrier(sF21)
| ~ reflexive_relstr(sF21)
| ~ rel_str(sF21)
| ~ element(sK0(sK19,sK20,sK18),the_carrier(sF21))
| ~ element(sK20,the_carrier(sF21))
| spl24_1
| ~ spl24_2 ),
inference(resolution,[],[f11726,f275]) ).
fof(f11735,plain,
( related_reflexive(sF21,sK0(sK19,sK20,sK18),sK20)
| ~ reflexive_relstr(sF21)
| ~ rel_str(sF21)
| ~ element(sK0(sK19,sK20,sK18),the_carrier(sF21))
| ~ element(sK20,the_carrier(sF21))
| spl24_1
| ~ spl24_2 ),
inference(forward_subsumption_resolution,[],[f11734,f427]) ).
fof(f11736,plain,
( related_reflexive(sF21,sK0(sK19,sK20,sK18),sK20)
| ~ rel_str(sF21)
| ~ element(sK0(sK19,sK20,sK18),the_carrier(sF21))
| ~ element(sK20,the_carrier(sF21))
| spl24_1
| ~ spl24_2 ),
inference(forward_subsumption_resolution,[],[f11735,f419]) ).
fof(f11737,plain,
( related_reflexive(sF21,sK0(sK19,sK20,sK18),sK20)
| ~ element(sK0(sK19,sK20,sK18),the_carrier(sF21))
| ~ element(sK20,the_carrier(sF21))
| spl24_1
| ~ spl24_2 ),
inference(forward_subsumption_resolution,[],[f11736,f395]) ).
fof(f11738,plain,
( related_reflexive(sF21,sK0(sK19,sK20,sK18),sK20)
| ~ element(sK0(sK19,sK20,sK18),the_carrier(sF21))
| spl24_1
| ~ spl24_2 ),
inference(forward_subsumption_resolution,[],[f11737,f618]) ).
fof(f11739,plain,
( ~ element(sK0(sK19,sK20,sK18),sF23)
| related_reflexive(sF21,sK0(sK19,sK20,sK18),sK20)
| spl24_1
| ~ spl24_2 ),
inference(forward_demodulation,[],[f11738,f755]) ).
fof(f11740,plain,
( related_reflexive(sF21,sK0(sK19,sK20,sK18),sK20)
| spl24_1
| ~ spl24_2 ),
inference(forward_subsumption_resolution,[],[f11739,f3245]) ).
fof(f19681,plain,
( ~ related_reflexive(sF21,sK0(sK19,sK20,sK18),sK20)
| ~ element(sK0(sK19,sK20,sK18),sF23)
| below_refl(sK19,sK0(sK19,sK20,sK18),sK20)
| spl24_1 ),
inference(superposition,[],[f875,f3308]) ).
fof(f19696,plain,
( ~ element(sK0(sK19,sK20,sK18),sF23)
| below_refl(sK19,sK0(sK19,sK20,sK18),sK20)
| spl24_1
| ~ spl24_2 ),
inference(forward_subsumption_resolution,[],[f19681,f11740]) ).
fof(f19722,plain,
( below_refl(sK19,sK0(sK19,sK20,sK18),sK20)
| spl24_1
| ~ spl24_2 ),
inference(forward_subsumption_resolution,[],[f19696,f3245]) ).
fof(f19785,plain,
( below(sK19,sK0(sK19,sK20,sK18),sK20)
| empty_carrier(sK19)
| ~ meet_commutative(sK19)
| ~ meet_absorbing(sK19)
| ~ join_absorbing(sK19)
| ~ latt_str(sK19)
| ~ element(sK0(sK19,sK20,sK18),the_carrier(sK19))
| ~ element(sK20,the_carrier(sK19))
| spl24_1
| ~ spl24_2 ),
inference(resolution,[],[f19722,f272]) ).
fof(f19786,plain,
( empty_carrier(sK19)
| ~ meet_commutative(sK19)
| ~ meet_absorbing(sK19)
| ~ join_absorbing(sK19)
| ~ latt_str(sK19)
| ~ element(sK0(sK19,sK20,sK18),the_carrier(sK19))
| ~ element(sK20,the_carrier(sK19))
| spl24_1
| ~ spl24_2
| spl24_100 ),
inference(forward_subsumption_resolution,[],[f19785,f5297]) ).
fof(f19788,plain,
( ~ meet_commutative(sK19)
| ~ meet_absorbing(sK19)
| ~ join_absorbing(sK19)
| ~ latt_str(sK19)
| ~ element(sK0(sK19,sK20,sK18),the_carrier(sK19))
| ~ element(sK20,the_carrier(sK19))
| spl24_1
| ~ spl24_2
| spl24_100 ),
inference(forward_subsumption_resolution,[],[f19786,f283]) ).
fof(f19790,plain,
( ~ meet_absorbing(sK19)
| ~ join_absorbing(sK19)
| ~ latt_str(sK19)
| ~ element(sK0(sK19,sK20,sK18),the_carrier(sK19))
| ~ element(sK20,the_carrier(sK19))
| spl24_1
| ~ spl24_2
| spl24_100 ),
inference(forward_subsumption_resolution,[],[f19788,f352]) ).
fof(f19792,plain,
( ~ join_absorbing(sK19)
| ~ latt_str(sK19)
| ~ element(sK0(sK19,sK20,sK18),the_carrier(sK19))
| ~ element(sK20,the_carrier(sK19))
| spl24_1
| ~ spl24_2
| spl24_100 ),
inference(forward_subsumption_resolution,[],[f19790,f346]) ).
fof(f19794,plain,
( ~ latt_str(sK19)
| ~ element(sK0(sK19,sK20,sK18),the_carrier(sK19))
| ~ element(sK20,the_carrier(sK19))
| spl24_1
| ~ spl24_2
| spl24_100 ),
inference(forward_subsumption_resolution,[],[f19792,f343]) ).
fof(f19796,plain,
( ~ element(sK0(sK19,sK20,sK18),the_carrier(sK19))
| ~ element(sK20,the_carrier(sK19))
| spl24_1
| ~ spl24_2
| spl24_100 ),
inference(forward_subsumption_resolution,[],[f19794,f281]) ).
fof(f19798,plain,
( ~ element(sK0(sK19,sK20,sK18),sF23)
| ~ element(sK20,the_carrier(sK19))
| spl24_1
| ~ spl24_2
| spl24_100 ),
inference(forward_demodulation,[],[f19796,f302]) ).
fof(f19800,plain,
( ~ element(sK20,the_carrier(sK19))
| spl24_1
| ~ spl24_2
| spl24_100 ),
inference(forward_subsumption_resolution,[],[f19798,f3245]) ).
fof(f19801,plain,
( ~ element(sK20,sF23)
| spl24_1
| ~ spl24_2
| spl24_100 ),
inference(forward_demodulation,[],[f19800,f302]) ).
fof(f19802,plain,
( $false
| spl24_1
| ~ spl24_2
| spl24_100 ),
inference(forward_subsumption_resolution,[],[f19801,f303]) ).
fof(f19803,plain,
( spl24_1
| ~ spl24_2
| spl24_100 ),
inference(avatar_contradiction_clause,[],[f19802]) ).
cnf(s1,plain,
( spl24_1
| spl24_2 ),
inference(sat_conversion,[],[f312]) ).
cnf(s2,plain,
( ~ spl24_1
| ~ spl24_2 ),
inference(sat_conversion,[],[f313]) ).
cnf(s13,plain,
~ spl24_10,
inference(sat_conversion,[],[f665]) ).
cnf(s53,plain,
( ~ spl24_1
| spl24_2
| spl24_10 ),
inference(sat_conversion,[],[f3116]) ).
cnf(s116,plain,
( spl24_1
| ~ spl24_100 ),
inference(sat_conversion,[],[f6853]) ).
cnf(s225,plain,
( spl24_1
| ~ spl24_2
| spl24_100 ),
inference(sat_conversion,[],[f19803]) ).
cnf(s251,plain,
spl24_1,
inference(rat,[],[s225,s1,s116]) ).
cnf(s252,plain,
spl24_2,
inference(rat,[],[s53,s13,s251]) ).
cnf(s253,plain,
$false,
inference(rat,[],[s2,s252,s251]) ).
fof(f19804,plain,
$false,
inference(avatar_sat_refutation,[],[s253]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU349+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 % Computer : n026.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 28 04:52:57 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.87/1.57 % (3467755)Will run a generic schedule for satisfiability detection.
% 6.87/1.57 % (3467760)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1293503317_2999 on theBenchmark for (2999ds/0Mi)
% 6.87/1.57 % (3467761)% WARNING: option uhcvi not known.
% 6.87/1.57 % TRYING [1]
% 6.87/1.57 % TRYING [2]
% 6.87/1.57 % TRYING [3]
% 6.87/1.57 % (3467761)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=648561047:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 6.87/1.57 % (3467762)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1930900130:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 6.87/1.57 % (3467763)dis+10_1_sil=32000:sp=arity:random_seed=1435543677:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 6.87/1.57 % (3467764)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3899668437:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 6.87/1.57 % (3467766)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2763618863:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 6.87/1.57 % (3467765)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3037053824:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 6.87/1.57 % TRYING [4]
% 6.87/1.57 % TRYING [5]
% 6.87/1.57 % (3467763)Instruction limit reached!
% 6.87/1.57 % (3467763)------------------------------
% 6.87/1.57 % (3467763)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.87/1.57 % (3467763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.57 % (3467763)CaDiCaL version: 2.1.3
% 6.87/1.57 % (3467763)Termination reason: Instruction limit
% 6.87/1.57 % (3467763)Termination phase: Saturation
% 6.87/1.57 % (3467763)Time elapsed: 0.069 s
% 6.87/1.57 % (3467763)Peak memory usage: 13 MB
% 6.87/1.57 % (3467763)Instructions burned: 103 (million)
% 6.87/1.57 % (3467764)Instruction limit reached!
% 6.87/1.57 % (3467764)------------------------------
% 6.87/1.57 % (3467764)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.87/1.57 % (3467764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.57 % (3467764)CaDiCaL version: 2.1.3
% 6.87/1.57 % (3467764)Termination reason: Instruction limit
% 6.87/1.57 % (3467764)Termination phase: Saturation
% 6.87/1.57 % (3467764)Time elapsed: 0.074 s
% 6.87/1.57 % (3467764)Peak memory usage: 13 MB
% 6.87/1.57 % (3467764)Instructions burned: 118 (million)
% 6.87/1.57 % (3467765)Instruction limit reached!
% 6.87/1.57 % (3467765)------------------------------
% 6.87/1.57 % (3467765)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.87/1.57 % (3467765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.57 % (3467765)CaDiCaL version: 2.1.3
% 6.87/1.57 % (3467765)Termination reason: Instruction limit
% 6.87/1.57 % (3467765)Termination phase: Saturation
% 6.87/1.57 % (3467765)Time elapsed: 0.086 s
% 6.87/1.57 % (3467765)Peak memory usage: 13 MB
% 6.87/1.57 % (3467765)Instructions burned: 132 (million)
% 6.87/1.57 % (3467774)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3081927313:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 6.87/1.57 % (3467775)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3433594643:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 6.87/1.57 % TRYING [1]
% 6.87/1.57 % TRYING [2]
% 6.87/1.57 % TRYING [3]
% 6.87/1.57 % (3467766)Instruction limit reached!
% 6.87/1.57 % (3467766)------------------------------
% 6.87/1.57 % (3467766)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.87/1.57 % (3467766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.57 % (3467766)CaDiCaL version: 2.1.3
% 6.87/1.57 % (3467766)Termination reason: Instruction limit
% 6.87/1.57 % (3467766)Termination phase: Saturation
% 6.87/1.57 % (3467766)Time elapsed: 0.103 s
% 6.87/1.57 % (3467766)Peak memory usage: 13 MB
% 6.87/1.57 % (3467766)Instructions burned: 160 (million)
% 6.87/1.57 % TRYING [6]
% 6.87/1.57 % (3467776)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=456183477:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 6.87/1.57 % TRYING [4]
% 6.87/1.57 % (3467779)ott-21_1_sil=16000:fs=off:random_seed=1447309641:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 6.87/1.57 % TRYING [5]
% 6.87/1.57 % (3467775)Instruction limit reached!
% 6.87/1.57 % (3467775)------------------------------
% 6.87/1.57 % (3467775)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.87/1.57 % (3467775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.57 % (3467775)CaDiCaL version: 2.1.3
% 6.87/1.57 % (3467775)Termination reason: Instruction limit
% 6.87/1.57 % (3467775)Termination phase: Saturation
% 6.87/1.57 % (3467775)Time elapsed: 0.087 s
% 6.87/1.57 % (3467775)Peak memory usage: 14 MB
% 6.87/1.57 % (3467775)Instructions burned: 132 (million)
% 6.87/1.57 % (3467782)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3281680229:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 6.87/1.57 % (3467779)Instruction limit reached!
% 6.87/1.57 % (3467779)------------------------------
% 6.87/1.57 % (3467779)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.87/1.57 % (3467779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.57 % (3467779)CaDiCaL version: 2.1.3
% 6.87/1.57 % (3467779)Termination reason: Instruction limit
% 6.87/1.57 % (3467779)Termination phase: Saturation
% 6.87/1.57 % (3467779)Time elapsed: 0.098 s
% 6.87/1.57 % (3467779)Peak memory usage: 13 MB
% 6.87/1.57 % (3467779)Instructions burned: 180 (million)
% 6.87/1.57 % (3467784)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=502455496:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 6.87/1.57 % TRYING [1]
% 6.87/1.57 % TRYING [2]
% 6.87/1.57 % TRYING [3]
% 6.87/1.57 % TRYING [4]
% 6.87/1.57 % TRYING [6]
% 6.87/1.57 % TRYING [5]
% 6.87/1.57 % TRYING [7]
% 6.87/1.57 % (3467774)Instruction limit reached!
% 6.87/1.57 % (3467774)------------------------------
% 6.87/1.57 % (3467774)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.87/1.57 % (3467774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.57 % (3467774)CaDiCaL version: 2.1.3
% 6.87/1.57 % (3467774)Termination reason: Instruction limit
% 6.87/1.57 % (3467774)Termination phase: Finite model building constraint generation
% 6.87/1.57 % (3467774)Time elapsed: 0.322 s
% 6.87/1.57 % (3467774)Peak memory usage: 25 MB
% 6.87/1.57 % (3467774)Instructions burned: 715 (million)
% 6.87/1.57 % (3467786)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=26280888:i=1179_2995 on theBenchmark for (2995ds/1179Mi)
% 6.87/1.57 % TRYING [6]
% 6.87/1.57 % (3467782)Instruction limit reached!
% 6.87/1.57 % (3467782)------------------------------
% 6.87/1.57 % (3467782)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.87/1.57 % (3467782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.57 % (3467782)CaDiCaL version: 2.1.3
% 6.87/1.57 % (3467782)Termination reason: Instruction limit
% 6.87/1.57 % (3467782)Termination phase: Saturation
% 6.87/1.57 % (3467782)Time elapsed: 0.334 s
% 6.87/1.57 % (3467782)Peak memory usage: 15 MB
% 6.87/1.57 % (3467782)Instructions burned: 478 (million)
% 6.87/1.57 % (3467776)Instruction limit reached!
% 6.87/1.57 % (3467776)------------------------------
% 6.87/1.57 % (3467776)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.87/1.57 % (3467776)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.57 % (3467776)CaDiCaL version: 2.1.3
% 6.87/1.57 % (3467776)Termination reason: Instruction limit
% 6.87/1.57 % (3467776)Termination phase: Saturation
% 6.87/1.57 % (3467776)Time elapsed: 0.445 s
% 6.87/1.57 % (3467776)Peak memory usage: 21 MB
% 6.87/1.57 % (3467776)Instructions burned: 685 (million)
% 6.87/1.57 % (3467788)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2022924704:i=889:ins=1_2994 on theBenchmark for (2994ds/889Mi)
% 6.87/1.57 % (3467784)Instruction limit reached!
% 6.87/1.57 % (3467784)------------------------------
% 6.87/1.57 % (3467784)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.87/1.57 % (3467784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.57 % (3467784)CaDiCaL version: 2.1.3
% 6.87/1.57 % (3467784)Termination reason: Instruction limit
% 6.87/1.57 % (3467784)Termination phase: Finite model building SAT solving
% 6.87/1.57 % (3467784)Time elapsed: 0.325 s
% 6.87/1.57 % (3467784)Peak memory usage: 20 MB
% 6.87/1.57 % (3467784)Instructions burned: 867 (million)
% 6.87/1.57 % (3467789)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=970681081:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2994 on theBenchmark for (2994ds/692Mi)
% 6.87/1.57 % (3467791)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1383914646:i=879:kws=inv_precedence:fsr=off_2993 on theBenchmark for (2993ds/879Mi)
% 6.87/1.57 % TRYING [14]
% 6.87/1.57 % TRYING [7]
% 6.87/1.57 % (3467788)Instruction limit reached!
% 6.87/1.57 % (3467788)------------------------------
% 6.87/1.57 % (3467788)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.87/1.57 % (3467788)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.57 % (3467788)CaDiCaL version: 2.1.3
% 6.87/1.57 % (3467788)Termination reason: Instruction limit
% 6.87/1.57 % (3467788)Termination phase: Finite model building constraint generation
% 6.87/1.57 % (3467788)Time elapsed: 0.312 s
% 6.87/1.57 % (3467788)Peak memory usage: 69 MB
% 6.87/1.57 % (3467788)Instructions burned: 891 (million)
% 6.87/1.57 % (3467794)fmb+10_1_sil=64000:random_seed=3583754972:i=22061:nm=2:gsp=on_2990 on theBenchmark for (2990ds/22061Mi)
% 6.87/1.57 % TRYING [1]
% 6.87/1.57 % TRYING [2]
% 6.87/1.57 % TRYING [3]
% 6.87/1.57 % TRYING [4]
% 6.87/1.57 % (3467789)Instruction limit reached!
% 6.87/1.57 % (3467789)------------------------------
% 6.87/1.57 % (3467789)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.87/1.57 % (3467789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.57 % (3467789)CaDiCaL version: 2.1.3
% 6.87/1.57 % (3467789)Termination reason: Instruction limit
% 6.87/1.57 % (3467789)Termination phase: Saturation
% 6.87/1.57 % (3467789)Time elapsed: 0.368 s
% 6.87/1.57 % (3467789)Peak memory usage: 19 MB
% 6.87/1.57 % (3467789)Instructions burned: 694 (million)
% 6.87/1.57 % (3467796)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2217640920:i=9515:nm=5_2990 on theBenchmark for (2990ds/9515Mi)
% 6.87/1.57 % TRYING [20]
% 6.87/1.57 % TRYING [5]
% 6.87/1.57 % (3467786) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3467755-3467786"...
% 6.87/1.57 % (3467786)...printing done.
% 6.87/1.57 % (3467786)Refutation found. Thanks to Tanya!
% 6.87/1.57 % SZS status Theorem for theBenchmark
% 6.87/1.57 % SZS output start Proof for theBenchmark
% See solution above
% 6.87/1.58 % (3467786)------------------------------
% 6.87/1.58 % (3467786)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.87/1.58 % (3467786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.87/1.58 % (3467786)CaDiCaL version: 2.1.3
% 6.87/1.58 % (3467786)Termination reason: Refutation
% 6.87/1.58 % (3467786)Time elapsed: 0.658 s
% 6.87/1.58 % (3467786)Peak memory usage: 26 MB
% 6.87/1.58 % (3467786)Instructions burned: 1072 (million)
% 6.87/1.58 % (3467755)Success in time 1.14 s
% 6.87/1.58 % Vampire exiting
%------------------------------------------------------------------------------