%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU346+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:48:27 PM UTC 2026
% Result : Theorem 6.69s 2.02s
% Output : Refutation 8.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 33
% Syntax : Number of formulae : 287 ( 53 unt; 13 def)
% Number of atoms : 1138 ( 84 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1464 ( 613 ~; 691 |; 108 &)
% ( 20 <=>; 30 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 34 ( 32 usr; 10 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 7 con; 0-4 aty)
% Number of variables : 253 ( 0 sgn 241 !; 12 ?)
% 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(f8,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(f9,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,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f11,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( related(X0,X1,X2)
<=> in(ordered_pair(X1,X2),the_InternalRel(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_orders_2) ).
fof(f19,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(f22,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(f23,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(f30,axiom,
! [X0] :
( join_semilatt_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).
fof(f31,axiom,
! [X0] :
( latt_str(X0)
=> ( meet_semilatt_str(X0)
& join_semilatt_str(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(f48,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f59,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(f62,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(f75,axiom,
! [X0,X1,X2,X3] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0)
& ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1)
& element(X2,the_carrier(X0))
& element(X3,the_carrier(X1)) )
=> k10_filter_1(X0,X1,X2,X3) = ordered_pair(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k10_filter_1) ).
fof(f76,axiom,
! [X0,X1,X2,X3] :
( ( ~ empty(X0)
& ~ empty(X1)
& element(X2,X0)
& element(X3,X1) )
=> ordered_pair_as_product_element(X0,X1,X2,X3) = ordered_pair(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_domain_1) ).
fof(f77,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) )
=> k2_lattice3(X0) = relation_of_lattice(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_lattice3) ).
fof(f78,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(f80,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(f86,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0))
<=> below_refl(X0,X1,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_filter_1) ).
fof(f92,conjecture,
! [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(f93,negated_conjecture,
~ ! [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)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f92]) ).
fof(f108,plain,
! [X0] :
( X0 = rel_str_of(the_carrier(X0),the_InternalRel(X0))
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f109,plain,
! [X0] :
( X0 = rel_str_of(the_carrier(X0),the_InternalRel(X0))
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f108]) ).
fof(f117,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,[],[f8]) ).
fof(f118,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,[],[f117]) ).
fof(f119,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,[],[f9]) ).
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(flattening,[],[f119]) ).
fof(f121,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( related(X0,X1,X2)
<=> in(ordered_pair(X1,X2),the_InternalRel(X0)) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f129,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,[],[f19]) ).
fof(f130,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,[],[f129]) ).
fof(f131,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,[],[f22]) ).
fof(f132,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,[],[f131]) ).
fof(f133,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,[],[f23]) ).
fof(f134,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,[],[f133]) ).
fof(f139,plain,
! [X0] :
( one_sorted_str(X0)
| ~ join_semilatt_str(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f140,plain,
! [X0] :
( ( meet_semilatt_str(X0)
& join_semilatt_str(X0) )
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f147,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f48]) ).
fof(f148,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f147]) ).
fof(f161,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,[],[f59]) ).
fof(f162,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,[],[f161]) ).
fof(f167,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,[],[f62]) ).
fof(f173,plain,
! [X0,X1,X2,X3] :
( k10_filter_1(X0,X1,X2,X3) = ordered_pair(X2,X3)
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X0))
| ~ element(X3,the_carrier(X1)) ),
inference(ennf_transformation,[],[f75]) ).
fof(f174,plain,
! [X0,X1,X2,X3] :
( k10_filter_1(X0,X1,X2,X3) = ordered_pair(X2,X3)
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X0))
| ~ element(X3,the_carrier(X1)) ),
inference(flattening,[],[f173]) ).
fof(f175,plain,
! [X0,X1,X2,X3] :
( ordered_pair_as_product_element(X0,X1,X2,X3) = ordered_pair(X2,X3)
| empty(X0)
| empty(X1)
| ~ element(X2,X0)
| ~ element(X3,X1) ),
inference(ennf_transformation,[],[f76]) ).
fof(f176,plain,
! [X0,X1,X2,X3] :
( ordered_pair_as_product_element(X0,X1,X2,X3) = ordered_pair(X2,X3)
| empty(X0)
| empty(X1)
| ~ element(X2,X0)
| ~ element(X3,X1) ),
inference(flattening,[],[f175]) ).
fof(f177,plain,
! [X0] :
( k2_lattice3(X0) = relation_of_lattice(X0)
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f77]) ).
fof(f178,plain,
! [X0] :
( k2_lattice3(X0) = relation_of_lattice(X0)
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f177]) ).
fof(f181,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,[],[f80]) ).
fof(f182,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,[],[f181]) ).
fof(f190,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0))
<=> below_refl(X0,X1,X2) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f86]) ).
fof(f191,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0))
<=> below_refl(X0,X1,X2) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f190]) ).
fof(f198,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,[],[f93]) ).
fof(f199,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,[],[f198]) ).
fof(f201,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( related(X0,X1,X2)
| ~ in(ordered_pair(X1,X2),the_InternalRel(X0)) )
& ( in(ordered_pair(X1,X2),the_InternalRel(X0))
| ~ related(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(nnf_transformation,[],[f121]) ).
fof(f221,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,[],[f78]) ).
fof(f223,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,[],[f182]) ).
fof(f224,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0))
| ~ below_refl(X0,X1,X2) )
& ( below_refl(X0,X1,X2)
| ~ in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0)) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(nnf_transformation,[],[f191]) ).
fof(f225,plain,
? [X0] :
( ? [X1] :
( ? [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) )
& ( 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,[],[f199]) ).
fof(f226,plain,
? [X0] :
( ? [X1] :
( ? [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) )
& ( 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(flattening,[],[f225]) ).
fof(f227,plain,
( ( ~ related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK20),cast_to_el_of_LattPOSet(sK19,sK21))
| ~ below_refl(sK19,sK20,sK21) )
& ( related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK20),cast_to_el_of_LattPOSet(sK19,sK21))
| below_refl(sK19,sK20,sK21) )
& element(sK21,the_carrier(sK19))
& element(sK20,the_carrier(sK19))
& ~ empty_carrier(sK19)
& lattice(sK19)
& latt_str(sK19) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19,sK20,sK21]),skolemize(X0,sK19),skolemize(X1,sK20),skolemize(X2,sK21)],[f226]) ).
fof(f228,plain,
! [X0] :
( ~ strict_rel_str(X0)
| rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f241,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,[],[f118]) ).
fof(f242,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,[],[f120]) ).
fof(f243,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f244,plain,
! [X2,X0,X1] :
( in(ordered_pair(X1,X2),the_InternalRel(X0))
| ~ related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f201]) ).
fof(f245,plain,
! [X2,X0,X1] :
( related(X0,X1,X2)
| ~ in(ordered_pair(X1,X2),the_InternalRel(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f201]) ).
fof(f252,plain,
! [X0] :
( relation_of2_as_subset(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f257,plain,
! [X0] :
( rel_str(poset_of_lattice(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f262,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,[],[f134]) ).
fof(f267,plain,
! [X0] :
( ~ join_semilatt_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f268,plain,
! [X0] :
( ~ latt_str(X0)
| join_semilatt_str(X0) ),
inference(cnf_transformation,[],[f140]) ).
fof(f288,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f314,plain,
! [X0] :
( reflexive_relstr(poset_of_lattice(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f162]) ).
fof(f315,plain,
! [X0] :
( strict_rel_str(poset_of_lattice(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f162]) ).
fof(f316,plain,
! [X0] :
( ~ empty_carrier(poset_of_lattice(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f162]) ).
fof(f321,plain,
! [X2,X3,X0,X1] :
( rel_str_of(X0,X1) != rel_str_of(X2,X3)
| X1 = X3
| ~ relation_of2(X1,X0,X0) ),
inference(cnf_transformation,[],[f167]) ).
fof(f359,plain,
! [X2,X3,X0,X1] :
( k10_filter_1(X0,X1,X2,X3) = ordered_pair(X2,X3)
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X0))
| ~ element(X3,the_carrier(X1)) ),
inference(cnf_transformation,[],[f174]) ).
fof(f360,plain,
! [X2,X3,X0,X1] :
( ordered_pair_as_product_element(X0,X1,X2,X3) = ordered_pair(X2,X3)
| empty(X0)
| empty(X1)
| ~ element(X2,X0)
| ~ element(X3,X1) ),
inference(cnf_transformation,[],[f176]) ).
fof(f361,plain,
! [X0] :
( ~ lattice(X0)
| empty_carrier(X0)
| k2_lattice3(X0) = relation_of_lattice(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f178]) ).
fof(f362,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f221]) ).
fof(f366,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,[],[f223]) ).
fof(f367,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,[],[f223]) ).
fof(f373,plain,
! [X2,X0,X1] :
( ~ in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0))
| 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,[],[f224]) ).
fof(f374,plain,
! [X2,X0,X1] :
( in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0))
| ~ 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,[],[f224]) ).
fof(f380,plain,
latt_str(sK19),
inference(cnf_transformation,[],[f227]) ).
fof(f381,plain,
lattice(sK19),
inference(cnf_transformation,[],[f227]) ).
fof(f382,plain,
~ empty_carrier(sK19),
inference(cnf_transformation,[],[f227]) ).
fof(f383,plain,
element(sK20,the_carrier(sK19)),
inference(cnf_transformation,[],[f227]) ).
fof(f384,plain,
element(sK21,the_carrier(sK19)),
inference(cnf_transformation,[],[f227]) ).
fof(f385,plain,
( related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK20),cast_to_el_of_LattPOSet(sK19,sK21))
| below_refl(sK19,sK20,sK21) ),
inference(cnf_transformation,[],[f227]) ).
fof(f386,plain,
( ~ related_reflexive(poset_of_lattice(sK19),cast_to_el_of_LattPOSet(sK19,sK20),cast_to_el_of_LattPOSet(sK19,sK21))
| ~ below_refl(sK19,sK20,sK21) ),
inference(cnf_transformation,[],[f227]) ).
fof(f388,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),the_InternalRel(X0))
| related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(definition_unfolding,[],[f245,f243]) ).
fof(f389,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),the_InternalRel(X0))
| ~ related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(definition_unfolding,[],[f244,f243]) ).
fof(f390,plain,
! [X2,X3,X0,X1] :
( ~ element(X3,the_carrier(X1))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X0))
| k10_filter_1(X0,X1,X2,X3) = unordered_pair(unordered_pair(X2,X3),singleton(X2)) ),
inference(definition_unfolding,[],[f359,f243]) ).
fof(f391,plain,
! [X2,X3,X0,X1] :
( ~ element(X3,X1)
| empty(X0)
| empty(X1)
| ~ element(X2,X0)
| ordered_pair_as_product_element(X0,X1,X2,X3) = unordered_pair(unordered_pair(X2,X3),singleton(X2)) ),
inference(definition_unfolding,[],[f360,f243]) ).
fof(f392,definition,
sF22 = poset_of_lattice(sK19),
introduced(definition,[new_symbols(definition,[sF22])],[function_definition]) ).
fof(f393,plain,
poset_of_lattice(sK19) = sF22,
inference(reorient_equations,[],[f392]) ).
fof(f394,definition,
sF23 = cast_to_el_of_LattPOSet(sK19,sK20),
introduced(definition,[new_symbols(definition,[sF23])],[function_definition]) ).
fof(f395,plain,
cast_to_el_of_LattPOSet(sK19,sK20) = sF23,
inference(reorient_equations,[],[f394]) ).
fof(f396,definition,
sF24 = cast_to_el_of_LattPOSet(sK19,sK21),
introduced(definition,[new_symbols(definition,[sF24])],[function_definition]) ).
fof(f397,plain,
cast_to_el_of_LattPOSet(sK19,sK21) = sF24,
inference(reorient_equations,[],[f396]) ).
fof(f398,plain,
( ~ related_reflexive(sF22,sF23,sF24)
| ~ below_refl(sK19,sK20,sK21) ),
inference(definition_folding,[],[f386,f397,f395,f393]) ).
fof(f399,plain,
( related_reflexive(sF22,sF23,sF24)
| below_refl(sK19,sK20,sK21) ),
inference(definition_folding,[],[f385,f397,f395,f393]) ).
fof(f400,definition,
sF25 = the_carrier(sK19),
introduced(definition,[new_symbols(definition,[sF25])],[function_definition]) ).
fof(f401,plain,
the_carrier(sK19) = sF25,
inference(reorient_equations,[],[f400]) ).
fof(f402,plain,
element(sK21,sF25),
inference(definition_folding,[],[f384,f401]) ).
fof(f403,plain,
element(sK20,sF25),
inference(definition_folding,[],[f383,f401]) ).
fof(f405,definition,
( spl26_1
<=> below_refl(sK19,sK20,sK21) ),
introduced(definition,[new_symbols(definition,[spl26_1])],[avatar_definition]) ).
fof(f406,plain,
( ~ below_refl(sK19,sK20,sK21)
| spl26_1 ),
inference(avatar_component_clause,[],[f405]) ).
fof(f407,plain,
( below_refl(sK19,sK20,sK21)
| ~ spl26_1 ),
inference(avatar_component_clause,[],[f405]) ).
fof(f409,definition,
( spl26_2
<=> related_reflexive(sF22,sF23,sF24) ),
introduced(definition,[new_symbols(definition,[spl26_2])],[avatar_definition]) ).
fof(f410,plain,
( ~ related_reflexive(sF22,sF23,sF24)
| spl26_2 ),
inference(avatar_component_clause,[],[f409]) ).
fof(f411,plain,
( related_reflexive(sF22,sF23,sF24)
| ~ spl26_2 ),
inference(avatar_component_clause,[],[f409]) ).
fof(f412,plain,
( spl26_1
| spl26_2 ),
inference(avatar_split_clause,[],[f399,f409,f405]) ).
fof(f413,plain,
( ~ spl26_1
| ~ spl26_2 ),
inference(avatar_split_clause,[],[f398,f409,f405]) ).
fof(f414,plain,
( element(sF23,the_carrier(poset_of_lattice(sK19)))
| empty_carrier(sK19)
| ~ lattice(sK19)
| ~ latt_str(sK19)
| ~ element(sK20,the_carrier(sK19)) ),
inference(superposition,[],[f262,f395]) ).
fof(f415,plain,
( element(sF24,the_carrier(poset_of_lattice(sK19)))
| empty_carrier(sK19)
| ~ lattice(sK19)
| ~ latt_str(sK19)
| ~ element(sK21,the_carrier(sK19)) ),
inference(superposition,[],[f262,f397]) ).
fof(f416,plain,
( element(sF24,the_carrier(poset_of_lattice(sK19)))
| ~ lattice(sK19)
| ~ latt_str(sK19)
| ~ element(sK21,the_carrier(sK19)) ),
inference(forward_subsumption_resolution,[],[f415,f382]) ).
fof(f417,plain,
( element(sF23,the_carrier(poset_of_lattice(sK19)))
| ~ lattice(sK19)
| ~ latt_str(sK19)
| ~ element(sK20,the_carrier(sK19)) ),
inference(forward_subsumption_resolution,[],[f414,f382]) ).
fof(f418,plain,
( element(sF24,the_carrier(poset_of_lattice(sK19)))
| ~ latt_str(sK19)
| ~ element(sK21,the_carrier(sK19)) ),
inference(forward_subsumption_resolution,[],[f416,f381]) ).
fof(f419,plain,
( element(sF23,the_carrier(poset_of_lattice(sK19)))
| ~ latt_str(sK19)
| ~ element(sK20,the_carrier(sK19)) ),
inference(forward_subsumption_resolution,[],[f417,f381]) ).
fof(f420,plain,
( element(sF24,the_carrier(poset_of_lattice(sK19)))
| ~ element(sK21,the_carrier(sK19)) ),
inference(forward_subsumption_resolution,[],[f418,f380]) ).
fof(f421,plain,
( element(sF23,the_carrier(poset_of_lattice(sK19)))
| ~ element(sK20,the_carrier(sK19)) ),
inference(forward_subsumption_resolution,[],[f419,f380]) ).
fof(f422,plain,
( element(sF24,the_carrier(sF22))
| ~ element(sK21,the_carrier(sK19)) ),
inference(forward_demodulation,[],[f420,f393]) ).
fof(f423,plain,
( element(sF23,the_carrier(sF22))
| ~ element(sK20,the_carrier(sK19)) ),
inference(forward_demodulation,[],[f421,f393]) ).
fof(f424,plain,
( ~ element(sK21,sF25)
| element(sF24,the_carrier(sF22)) ),
inference(forward_demodulation,[],[f422,f401]) ).
fof(f425,plain,
( ~ element(sK20,sF25)
| element(sF23,the_carrier(sF22)) ),
inference(forward_demodulation,[],[f423,f401]) ).
fof(f426,plain,
element(sF24,the_carrier(sF22)),
inference(forward_subsumption_resolution,[],[f424,f402]) ).
fof(f427,plain,
element(sF23,the_carrier(sF22)),
inference(forward_subsumption_resolution,[],[f425,f403]) ).
fof(f436,plain,
! [X0] :
( ~ element(X0,sF25)
| cast_to_el_of_LattPOSet(sK19,X0) = X0
| empty_carrier(sK19)
| ~ lattice(sK19)
| ~ latt_str(sK19) ),
inference(superposition,[],[f242,f401]) ).
fof(f437,plain,
! [X0] :
( ~ element(X0,sF25)
| cast_to_el_of_LattPOSet(sK19,X0) = X0
| ~ lattice(sK19)
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f436,f382]) ).
fof(f447,definition,
( spl26_5
<=> empty_carrier(sF22) ),
introduced(definition,[new_symbols(definition,[spl26_5])],[avatar_definition]) ).
fof(f448,plain,
( ~ empty_carrier(sF22)
| spl26_5 ),
inference(avatar_component_clause,[],[f447]) ).
fof(f461,plain,
! [X0] :
( ~ element(X0,sF25)
| cast_to_el_of_LattPOSet(sK19,X0) = X0
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f437,f381]) ).
fof(f462,plain,
! [X0] :
( ~ element(X0,sF25)
| cast_to_el_of_LattPOSet(sK19,X0) = X0 ),
inference(forward_subsumption_resolution,[],[f461,f380]) ).
fof(f463,plain,
sK20 = cast_to_el_of_LattPOSet(sK19,sK20),
inference(resolution,[],[f462,f403]) ).
fof(f464,plain,
sK21 = cast_to_el_of_LattPOSet(sK19,sK21),
inference(resolution,[],[f462,f402]) ).
fof(f465,plain,
sK21 = sF24,
inference(forward_demodulation,[],[f464,f397]) ).
fof(f466,plain,
sK20 = sF23,
inference(forward_demodulation,[],[f463,f395]) ).
fof(f467,plain,
element(sK21,the_carrier(sF22)),
inference(superposition,[],[f426,f465]) ).
fof(f468,plain,
( related_reflexive(sF22,sF23,sK21)
| ~ spl26_2 ),
inference(superposition,[],[f411,f465]) ).
fof(f469,plain,
( related_reflexive(sF22,sK20,sK21)
| ~ spl26_2 ),
inference(forward_demodulation,[],[f468,f466]) ).
fof(f470,plain,
element(sK20,the_carrier(sF22)),
inference(superposition,[],[f427,f466]) ).
fof(f474,plain,
( related(sF22,sK20,sK21)
| empty_carrier(sF22)
| ~ reflexive_relstr(sF22)
| ~ rel_str(sF22)
| ~ element(sK20,the_carrier(sF22))
| ~ element(sK21,the_carrier(sF22))
| ~ spl26_2 ),
inference(resolution,[],[f366,f469]) ).
fof(f475,plain,
( related(sF22,sK20,sK21)
| empty_carrier(sF22)
| ~ reflexive_relstr(sF22)
| ~ rel_str(sF22)
| ~ element(sK21,the_carrier(sF22))
| ~ spl26_2 ),
inference(forward_subsumption_resolution,[],[f474,f470]) ).
fof(f477,plain,
( related(sF22,sK20,sK21)
| empty_carrier(sF22)
| ~ reflexive_relstr(sF22)
| ~ rel_str(sF22)
| ~ spl26_2 ),
inference(forward_subsumption_resolution,[],[f475,f467]) ).
fof(f480,definition,
( spl26_8
<=> rel_str(sF22) ),
introduced(definition,[new_symbols(definition,[spl26_8])],[avatar_definition]) ).
fof(f481,plain,
( rel_str(sF22)
| ~ spl26_8 ),
inference(avatar_component_clause,[],[f480]) ).
fof(f482,plain,
( ~ rel_str(sF22)
| spl26_8 ),
inference(avatar_component_clause,[],[f480]) ).
fof(f484,definition,
( spl26_9
<=> reflexive_relstr(sF22) ),
introduced(definition,[new_symbols(definition,[spl26_9])],[avatar_definition]) ).
fof(f485,plain,
( reflexive_relstr(sF22)
| ~ spl26_9 ),
inference(avatar_component_clause,[],[f484]) ).
fof(f488,definition,
( spl26_10
<=> related(sF22,sK20,sK21) ),
introduced(definition,[new_symbols(definition,[spl26_10])],[avatar_definition]) ).
fof(f490,plain,
( related(sF22,sK20,sK21)
| ~ spl26_10 ),
inference(avatar_component_clause,[],[f488]) ).
fof(f491,plain,
( ~ spl26_8
| ~ spl26_9
| spl26_5
| spl26_10
| ~ spl26_2 ),
inference(avatar_split_clause,[],[f477,f409,f488,f447,f484,f480]) ).
fof(f526,plain,
! [X0,X1] :
( ~ in(ordered_pair_as_product_element(sF25,sF25,X0,X1),relation_of_lattice(sK19))
| below_refl(sK19,X0,X1)
| ~ element(X1,sF25)
| ~ element(X0,sF25)
| empty_carrier(sK19)
| ~ lattice(sK19)
| ~ latt_str(sK19) ),
inference(superposition,[],[f373,f401]) ).
fof(f527,plain,
! [X0,X1] :
( ~ in(ordered_pair_as_product_element(sF25,sF25,X0,X1),relation_of_lattice(sK19))
| below_refl(sK19,X0,X1)
| ~ element(X1,sF25)
| ~ element(X0,sF25)
| ~ lattice(sK19)
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f526,f382]) ).
fof(f528,plain,
! [X0,X1] :
( ~ in(ordered_pair_as_product_element(sF25,sF25,X0,X1),relation_of_lattice(sK19))
| below_refl(sK19,X0,X1)
| ~ element(X1,sF25)
| ~ element(X0,sF25)
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f527,f381]) ).
fof(f529,plain,
! [X0,X1] :
( ~ in(ordered_pair_as_product_element(sF25,sF25,X0,X1),relation_of_lattice(sK19))
| below_refl(sK19,X0,X1)
| ~ element(X1,sF25)
| ~ element(X0,sF25) ),
inference(forward_subsumption_resolution,[],[f528,f380]) ).
fof(f530,plain,
( ~ empty_carrier(sF22)
| empty_carrier(sK19)
| ~ lattice(sK19)
| ~ latt_str(sK19) ),
inference(superposition,[],[f316,f393]) ).
fof(f531,plain,
( ~ empty_carrier(sF22)
| ~ lattice(sK19)
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f530,f382]) ).
fof(f532,plain,
( ~ empty_carrier(sF22)
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f531,f381]) ).
fof(f533,plain,
~ empty_carrier(sF22),
inference(forward_subsumption_resolution,[],[f532,f380]) ).
fof(f534,plain,
~ spl26_5,
inference(avatar_split_clause,[],[f533,f447]) ).
fof(f561,plain,
( empty_carrier(sK19)
| relation_of_lattice(sK19) = k2_lattice3(sK19)
| ~ latt_str(sK19) ),
inference(resolution,[],[f361,f381]) ).
fof(f562,plain,
( relation_of_lattice(sK19) = k2_lattice3(sK19)
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f561,f382]) ).
fof(f563,plain,
relation_of_lattice(sK19) = k2_lattice3(sK19),
inference(forward_subsumption_resolution,[],[f562,f380]) ).
fof(f564,plain,
! [X0,X1] :
( ~ in(ordered_pair_as_product_element(sF25,sF25,X0,X1),k2_lattice3(sK19))
| below_refl(sK19,X0,X1)
| ~ element(X1,sF25)
| ~ element(X0,sF25) ),
inference(superposition,[],[f529,f563]) ).
fof(f578,plain,
! [X2,X0,X1] :
( ~ element(X0,sF25)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| empty_carrier(sK19)
| ~ lattice(sK19)
| ~ latt_str(sK19)
| ~ element(X2,the_carrier(X1))
| k10_filter_1(X1,sK19,X2,X0) = unordered_pair(unordered_pair(X2,X0),singleton(X2)) ),
inference(superposition,[],[f390,f401]) ).
fof(f579,plain,
! [X2,X0,X1] :
( ~ element(X0,sF25)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ lattice(sK19)
| ~ latt_str(sK19)
| ~ element(X2,the_carrier(X1))
| k10_filter_1(X1,sK19,X2,X0) = unordered_pair(unordered_pair(X2,X0),singleton(X2)) ),
inference(forward_subsumption_resolution,[],[f578,f382]) ).
fof(f581,plain,
! [X2,X0,X1] :
( ~ element(X0,sF25)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ latt_str(sK19)
| ~ element(X2,the_carrier(X1))
| k10_filter_1(X1,sK19,X2,X0) = unordered_pair(unordered_pair(X2,X0),singleton(X2)) ),
inference(forward_subsumption_resolution,[],[f579,f381]) ).
fof(f582,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X0,sF25)
| k10_filter_1(X1,sK19,X2,X0) = unordered_pair(unordered_pair(X2,X0),singleton(X2)) ),
inference(forward_subsumption_resolution,[],[f581,f380]) ).
fof(f589,plain,
! [X0,X1] :
( ~ element(X0,sF25)
| empty_carrier(sK19)
| ~ lattice(sK19)
| ~ latt_str(sK19)
| ~ element(X1,sF25)
| unordered_pair(unordered_pair(X0,X1),singleton(X0)) = k10_filter_1(sK19,sK19,X0,X1) ),
inference(superposition,[],[f582,f401]) ).
fof(f590,plain,
! [X0,X1] :
( ~ element(X0,sF25)
| ~ lattice(sK19)
| ~ latt_str(sK19)
| ~ element(X1,sF25)
| unordered_pair(unordered_pair(X0,X1),singleton(X0)) = k10_filter_1(sK19,sK19,X0,X1) ),
inference(forward_subsumption_resolution,[],[f589,f382]) ).
fof(f592,plain,
! [X0,X1] :
( ~ element(X0,sF25)
| ~ latt_str(sK19)
| ~ element(X1,sF25)
| unordered_pair(unordered_pair(X0,X1),singleton(X0)) = k10_filter_1(sK19,sK19,X0,X1) ),
inference(forward_subsumption_resolution,[],[f590,f381]) ).
fof(f593,plain,
! [X0,X1] :
( ~ element(X1,sF25)
| ~ element(X0,sF25)
| unordered_pair(unordered_pair(X0,X1),singleton(X0)) = k10_filter_1(sK19,sK19,X0,X1) ),
inference(forward_subsumption_resolution,[],[f592,f380]) ).
fof(f595,plain,
! [X0] :
( ~ element(X0,sF25)
| unordered_pair(unordered_pair(X0,sK21),singleton(X0)) = k10_filter_1(sK19,sK19,X0,sK21) ),
inference(resolution,[],[f593,f402]) ).
fof(f598,plain,
unordered_pair(unordered_pair(sK20,sK21),singleton(sK20)) = k10_filter_1(sK19,sK19,sK20,sK21),
inference(resolution,[],[f595,f403]) ).
fof(f601,plain,
! [X0,X1] :
( in(ordered_pair_as_product_element(sF25,sF25,X0,X1),relation_of_lattice(sK19))
| ~ below_refl(sK19,X0,X1)
| ~ element(X1,sF25)
| ~ element(X0,sF25)
| empty_carrier(sK19)
| ~ lattice(sK19)
| ~ latt_str(sK19) ),
inference(superposition,[],[f374,f401]) ).
fof(f605,plain,
! [X0,X1] :
( in(ordered_pair_as_product_element(sF25,sF25,X0,X1),relation_of_lattice(sK19))
| ~ below_refl(sK19,X0,X1)
| ~ element(X1,sF25)
| ~ element(X0,sF25)
| ~ lattice(sK19)
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f601,f382]) ).
fof(f607,plain,
! [X0,X1] :
( in(ordered_pair_as_product_element(sF25,sF25,X0,X1),relation_of_lattice(sK19))
| ~ below_refl(sK19,X0,X1)
| ~ element(X1,sF25)
| ~ element(X0,sF25)
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f605,f381]) ).
fof(f609,plain,
! [X0,X1] :
( in(ordered_pair_as_product_element(sF25,sF25,X0,X1),relation_of_lattice(sK19))
| ~ below_refl(sK19,X0,X1)
| ~ element(X1,sF25)
| ~ element(X0,sF25) ),
inference(forward_subsumption_resolution,[],[f607,f380]) ).
fof(f611,plain,
! [X0,X1] :
( in(ordered_pair_as_product_element(sF25,sF25,X0,X1),k2_lattice3(sK19))
| ~ below_refl(sK19,X0,X1)
| ~ element(X1,sF25)
| ~ element(X0,sF25) ),
inference(forward_demodulation,[],[f609,f563]) ).
fof(f616,plain,
join_semilatt_str(sK19),
inference(resolution,[],[f268,f380]) ).
fof(f618,plain,
( empty_carrier(sK19)
| poset_of_lattice(sK19) = rel_str_of(the_carrier(sK19),k2_lattice3(sK19))
| ~ latt_str(sK19) ),
inference(resolution,[],[f241,f381]) ).
fof(f619,plain,
( poset_of_lattice(sK19) = rel_str_of(the_carrier(sK19),k2_lattice3(sK19))
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f618,f382]) ).
fof(f620,plain,
poset_of_lattice(sK19) = rel_str_of(the_carrier(sK19),k2_lattice3(sK19)),
inference(forward_subsumption_resolution,[],[f619,f380]) ).
fof(f621,plain,
poset_of_lattice(sK19) = rel_str_of(sF25,k2_lattice3(sK19)),
inference(forward_demodulation,[],[f620,f401]) ).
fof(f622,plain,
sF22 = rel_str_of(sF25,k2_lattice3(sK19)),
inference(forward_demodulation,[],[f621,f393]) ).
fof(f624,plain,
! [X0,X1] :
( empty(X0)
| empty(sF25)
| ~ element(X1,X0)
| unordered_pair(unordered_pair(X1,sK21),singleton(X1)) = ordered_pair_as_product_element(X0,sF25,X1,sK21) ),
inference(resolution,[],[f391,f402]) ).
fof(f650,definition,
( spl26_23
<=> empty(sF25) ),
introduced(definition,[new_symbols(definition,[spl26_23])],[avatar_definition]) ).
fof(f651,plain,
( ~ empty(sF25)
| spl26_23 ),
inference(avatar_component_clause,[],[f650]) ).
fof(f652,plain,
( empty(sF25)
| ~ spl26_23 ),
inference(avatar_component_clause,[],[f650]) ).
fof(f654,definition,
( spl26_24
<=> ! [X0,X1] :
( empty(X0)
| unordered_pair(unordered_pair(X1,sK21),singleton(X1)) = ordered_pair_as_product_element(X0,sF25,X1,sK21)
| ~ element(X1,X0) ) ),
introduced(definition,[new_symbols(definition,[spl26_24])],[avatar_definition]) ).
fof(f655,plain,
( ! [X0,X1] :
( ~ element(X1,X0)
| unordered_pair(unordered_pair(X1,sK21),singleton(X1)) = ordered_pair_as_product_element(X0,sF25,X1,sK21)
| empty(X0) )
| ~ spl26_24 ),
inference(avatar_component_clause,[],[f654]) ).
fof(f656,plain,
( spl26_23
| spl26_24 ),
inference(avatar_split_clause,[],[f624,f654,f650]) ).
fof(f663,plain,
( reflexive_relstr(sF22)
| empty_carrier(sK19)
| ~ lattice(sK19)
| ~ latt_str(sK19) ),
inference(superposition,[],[f314,f393]) ).
fof(f664,plain,
( reflexive_relstr(sF22)
| ~ lattice(sK19)
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f663,f382]) ).
fof(f665,plain,
( reflexive_relstr(sF22)
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f664,f381]) ).
fof(f666,plain,
reflexive_relstr(sF22),
inference(forward_subsumption_resolution,[],[f665,f380]) ).
fof(f667,plain,
spl26_9,
inference(avatar_split_clause,[],[f666,f484]) ).
fof(f700,plain,
! [X0] :
( ~ in(k10_filter_1(sK19,sK19,sK20,sK21),the_InternalRel(X0))
| related(X0,sK20,sK21)
| ~ element(sK21,the_carrier(X0))
| ~ element(sK20,the_carrier(X0))
| ~ rel_str(X0) ),
inference(superposition,[],[f388,f598]) ).
fof(f713,plain,
( ~ empty(sF25)
| empty_carrier(sK19)
| ~ one_sorted_str(sK19) ),
inference(superposition,[],[f288,f401]) ).
fof(f714,plain,
( empty_carrier(sK19)
| ~ one_sorted_str(sK19)
| ~ spl26_23 ),
inference(forward_subsumption_resolution,[],[f713,f652]) ).
fof(f716,plain,
( ~ one_sorted_str(sK19)
| ~ spl26_23 ),
inference(forward_subsumption_resolution,[],[f714,f382]) ).
fof(f717,plain,
( rel_str(sF22)
| empty_carrier(sK19)
| ~ lattice(sK19)
| ~ latt_str(sK19) ),
inference(superposition,[],[f257,f393]) ).
fof(f718,plain,
( empty_carrier(sK19)
| ~ lattice(sK19)
| ~ latt_str(sK19)
| spl26_8 ),
inference(forward_subsumption_resolution,[],[f717,f482]) ).
fof(f719,plain,
( ~ lattice(sK19)
| ~ latt_str(sK19)
| spl26_8 ),
inference(forward_subsumption_resolution,[],[f718,f382]) ).
fof(f720,plain,
( ~ latt_str(sK19)
| spl26_8 ),
inference(forward_subsumption_resolution,[],[f719,f381]) ).
fof(f721,plain,
( $false
| spl26_8 ),
inference(forward_subsumption_resolution,[],[f720,f380]) ).
fof(f722,plain,
spl26_8,
inference(avatar_contradiction_clause,[],[f721]) ).
fof(f759,plain,
( strict_rel_str(sF22)
| empty_carrier(sK19)
| ~ lattice(sK19)
| ~ latt_str(sK19) ),
inference(superposition,[],[f315,f393]) ).
fof(f760,plain,
( strict_rel_str(sF22)
| ~ lattice(sK19)
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f759,f382]) ).
fof(f762,plain,
( strict_rel_str(sF22)
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f760,f381]) ).
fof(f763,plain,
strict_rel_str(sF22),
inference(forward_subsumption_resolution,[],[f762,f380]) ).
fof(f764,plain,
( sF22 = rel_str_of(the_carrier(sF22),the_InternalRel(sF22))
| ~ rel_str(sF22) ),
inference(resolution,[],[f763,f228]) ).
fof(f765,plain,
( sF22 = rel_str_of(the_carrier(sF22),the_InternalRel(sF22))
| ~ spl26_8 ),
inference(forward_subsumption_resolution,[],[f764,f481]) ).
fof(f769,plain,
( ! [X0,X1] :
( rel_str_of(X0,X1) != sF22
| the_InternalRel(sF22) = X1
| ~ relation_of2(X1,X0,X0) )
| ~ spl26_8 ),
inference(superposition,[],[f321,f765]) ).
fof(f780,definition,
( spl26_29
<=> relation_of2(k2_lattice3(sK19),sF25,sF25) ),
introduced(definition,[new_symbols(definition,[spl26_29])],[avatar_definition]) ).
fof(f781,plain,
( relation_of2(k2_lattice3(sK19),sF25,sF25)
| ~ spl26_29 ),
inference(avatar_component_clause,[],[f780]) ).
fof(f782,plain,
( ~ relation_of2(k2_lattice3(sK19),sF25,sF25)
| spl26_29 ),
inference(avatar_component_clause,[],[f780]) ).
fof(f805,plain,
! [X0] :
( in(k10_filter_1(sK19,sK19,sK20,sK21),the_InternalRel(X0))
| ~ related(X0,sK20,sK21)
| ~ element(sK21,the_carrier(X0))
| ~ element(sK20,the_carrier(X0))
| ~ rel_str(X0) ),
inference(superposition,[],[f389,f598]) ).
fof(f812,plain,
one_sorted_str(sK19),
inference(resolution,[],[f267,f616]) ).
fof(f813,plain,
( $false
| ~ spl26_23 ),
inference(forward_subsumption_resolution,[],[f812,f716]) ).
fof(f814,plain,
~ spl26_23,
inference(avatar_contradiction_clause,[],[f813]) ).
fof(f828,plain,
( unordered_pair(unordered_pair(sK20,sK21),singleton(sK20)) = ordered_pair_as_product_element(sF25,sF25,sK20,sK21)
| empty(sF25)
| ~ spl26_24 ),
inference(resolution,[],[f655,f403]) ).
fof(f837,plain,
( unordered_pair(unordered_pair(sK20,sK21),singleton(sK20)) = ordered_pair_as_product_element(sF25,sF25,sK20,sK21)
| spl26_23
| ~ spl26_24 ),
inference(forward_subsumption_resolution,[],[f828,f651]) ).
fof(f839,plain,
( k10_filter_1(sK19,sK19,sK20,sK21) = ordered_pair_as_product_element(sF25,sF25,sK20,sK21)
| spl26_23
| ~ spl26_24 ),
inference(forward_demodulation,[],[f837,f598]) ).
fof(f840,plain,
( ! [X0] :
( ~ in(ordered_pair_as_product_element(sF25,sF25,sK20,sK21),the_InternalRel(X0))
| related(X0,sK20,sK21)
| ~ element(sK21,the_carrier(X0))
| ~ element(sK20,the_carrier(X0))
| ~ rel_str(X0) )
| spl26_23
| ~ spl26_24 ),
inference(superposition,[],[f700,f839]) ).
fof(f846,plain,
( ! [X0] :
( in(ordered_pair_as_product_element(sF25,sF25,sK20,sK21),the_InternalRel(X0))
| ~ related(X0,sK20,sK21)
| ~ element(sK21,the_carrier(X0))
| ~ element(sK20,the_carrier(X0))
| ~ rel_str(X0) )
| spl26_23
| ~ spl26_24 ),
inference(superposition,[],[f805,f839]) ).
fof(f850,plain,
( sF22 != sF22
| k2_lattice3(sK19) = the_InternalRel(sF22)
| ~ relation_of2(k2_lattice3(sK19),sF25,sF25)
| ~ spl26_8 ),
inference(superposition,[],[f769,f622]) ).
fof(f851,plain,
( k2_lattice3(sK19) = the_InternalRel(sF22)
| ~ relation_of2(k2_lattice3(sK19),sF25,sF25)
| ~ spl26_8 ),
inference(trivial_inequality_removal,[],[f850]) ).
fof(f1015,plain,
( relation_of2_as_subset(k2_lattice3(sK19),sF25,sF25)
| empty_carrier(sK19)
| ~ lattice(sK19)
| ~ latt_str(sK19) ),
inference(superposition,[],[f252,f401]) ).
fof(f1016,plain,
( relation_of2_as_subset(k2_lattice3(sK19),sF25,sF25)
| ~ lattice(sK19)
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f1015,f382]) ).
fof(f1017,plain,
( relation_of2_as_subset(k2_lattice3(sK19),sF25,sF25)
| ~ latt_str(sK19) ),
inference(forward_subsumption_resolution,[],[f1016,f381]) ).
fof(f1018,plain,
relation_of2_as_subset(k2_lattice3(sK19),sF25,sF25),
inference(forward_subsumption_resolution,[],[f1017,f380]) ).
fof(f1019,plain,
relation_of2(k2_lattice3(sK19),sF25,sF25),
inference(resolution,[],[f1018,f362]) ).
fof(f1020,plain,
( $false
| spl26_29 ),
inference(forward_subsumption_resolution,[],[f1019,f782]) ).
fof(f1021,plain,
spl26_29,
inference(avatar_contradiction_clause,[],[f1020]) ).
fof(f1023,plain,
( k2_lattice3(sK19) = the_InternalRel(sF22)
| ~ spl26_8
| ~ spl26_29 ),
inference(forward_subsumption_resolution,[],[f851,f781]) ).
fof(f1026,plain,
( ! [X0,X1] :
( in(ordered_pair_as_product_element(sF25,sF25,X0,X1),the_InternalRel(sF22))
| ~ below_refl(sK19,X0,X1)
| ~ element(X1,sF25)
| ~ element(X0,sF25) )
| ~ spl26_8
| ~ spl26_29 ),
inference(superposition,[],[f611,f1023]) ).
fof(f1027,plain,
( ! [X0,X1] :
( ~ in(ordered_pair_as_product_element(sF25,sF25,X0,X1),the_InternalRel(sF22))
| below_refl(sK19,X0,X1)
| ~ element(X1,sF25)
| ~ element(X0,sF25) )
| ~ spl26_8
| ~ spl26_29 ),
inference(superposition,[],[f564,f1023]) ).
fof(f1050,plain,
( ~ below_refl(sK19,sK20,sK21)
| ~ element(sK21,sF25)
| ~ element(sK20,sF25)
| related(sF22,sK20,sK21)
| ~ element(sK21,the_carrier(sF22))
| ~ element(sK20,the_carrier(sF22))
| ~ rel_str(sF22)
| ~ spl26_8
| spl26_23
| ~ spl26_24
| ~ spl26_29 ),
inference(resolution,[],[f1026,f840]) ).
fof(f1180,plain,
( ~ related(sF22,sK20,sK21)
| ~ element(sK21,the_carrier(sF22))
| ~ element(sK20,the_carrier(sF22))
| ~ rel_str(sF22)
| below_refl(sK19,sK20,sK21)
| ~ element(sK21,sF25)
| ~ element(sK20,sF25)
| ~ spl26_8
| spl26_23
| ~ spl26_24
| ~ spl26_29 ),
inference(resolution,[],[f846,f1027]) ).
fof(f1182,plain,
( ~ element(sK21,the_carrier(sF22))
| ~ element(sK20,the_carrier(sF22))
| ~ rel_str(sF22)
| below_refl(sK19,sK20,sK21)
| ~ element(sK21,sF25)
| ~ element(sK20,sF25)
| ~ spl26_8
| ~ spl26_10
| spl26_23
| ~ spl26_24
| ~ spl26_29 ),
inference(forward_subsumption_resolution,[],[f1180,f490]) ).
fof(f1183,plain,
( ~ element(sK20,the_carrier(sF22))
| ~ rel_str(sF22)
| below_refl(sK19,sK20,sK21)
| ~ element(sK21,sF25)
| ~ element(sK20,sF25)
| ~ spl26_8
| ~ spl26_10
| spl26_23
| ~ spl26_24
| ~ spl26_29 ),
inference(forward_subsumption_resolution,[],[f1182,f467]) ).
fof(f1184,plain,
( ~ rel_str(sF22)
| below_refl(sK19,sK20,sK21)
| ~ element(sK21,sF25)
| ~ element(sK20,sF25)
| ~ spl26_8
| ~ spl26_10
| spl26_23
| ~ spl26_24
| ~ spl26_29 ),
inference(forward_subsumption_resolution,[],[f1183,f470]) ).
fof(f1185,plain,
( below_refl(sK19,sK20,sK21)
| ~ element(sK21,sF25)
| ~ element(sK20,sF25)
| ~ spl26_8
| ~ spl26_10
| spl26_23
| ~ spl26_24
| ~ spl26_29 ),
inference(forward_subsumption_resolution,[],[f1184,f481]) ).
fof(f1186,plain,
( ~ element(sK21,sF25)
| ~ element(sK20,sF25)
| spl26_1
| ~ spl26_8
| ~ spl26_10
| spl26_23
| ~ spl26_24
| ~ spl26_29 ),
inference(forward_subsumption_resolution,[],[f1185,f406]) ).
fof(f1187,plain,
( ~ element(sK20,sF25)
| spl26_1
| ~ spl26_8
| ~ spl26_10
| spl26_23
| ~ spl26_24
| ~ spl26_29 ),
inference(forward_subsumption_resolution,[],[f1186,f402]) ).
fof(f1188,plain,
( $false
| spl26_1
| ~ spl26_8
| ~ spl26_10
| spl26_23
| ~ spl26_24
| ~ spl26_29 ),
inference(forward_subsumption_resolution,[],[f1187,f403]) ).
fof(f1189,plain,
( spl26_1
| ~ spl26_8
| ~ spl26_10
| spl26_23
| ~ spl26_24
| ~ spl26_29 ),
inference(avatar_contradiction_clause,[],[f1188]) ).
fof(f1190,plain,
( ~ related_reflexive(sF22,sF23,sK21)
| spl26_2 ),
inference(forward_demodulation,[],[f410,f465]) ).
fof(f1191,plain,
( ~ element(sK21,sF25)
| ~ element(sK20,sF25)
| related(sF22,sK20,sK21)
| ~ element(sK21,the_carrier(sF22))
| ~ element(sK20,the_carrier(sF22))
| ~ rel_str(sF22)
| ~ spl26_1
| ~ spl26_8
| spl26_23
| ~ spl26_24
| ~ spl26_29 ),
inference(forward_subsumption_resolution,[],[f1050,f407]) ).
fof(f1192,plain,
( ~ related_reflexive(sF22,sK20,sK21)
| spl26_2 ),
inference(forward_demodulation,[],[f1190,f466]) ).
fof(f1193,plain,
( ~ element(sK20,sF25)
| related(sF22,sK20,sK21)
| ~ element(sK21,the_carrier(sF22))
| ~ element(sK20,the_carrier(sF22))
| ~ rel_str(sF22)
| ~ spl26_1
| ~ spl26_8
| spl26_23
| ~ spl26_24
| ~ spl26_29 ),
inference(forward_subsumption_resolution,[],[f1191,f402]) ).
fof(f1194,plain,
( related(sF22,sK20,sK21)
| ~ element(sK21,the_carrier(sF22))
| ~ element(sK20,the_carrier(sF22))
| ~ rel_str(sF22)
| ~ spl26_1
| ~ spl26_8
| spl26_23
| ~ spl26_24
| ~ spl26_29 ),
inference(forward_subsumption_resolution,[],[f1193,f403]) ).
fof(f1195,plain,
( related(sF22,sK20,sK21)
| ~ element(sK20,the_carrier(sF22))
| ~ rel_str(sF22)
| ~ spl26_1
| ~ spl26_8
| spl26_23
| ~ spl26_24
| ~ spl26_29 ),
inference(forward_subsumption_resolution,[],[f1194,f467]) ).
fof(f1196,plain,
( related(sF22,sK20,sK21)
| ~ rel_str(sF22)
| ~ spl26_1
| ~ spl26_8
| spl26_23
| ~ spl26_24
| ~ spl26_29 ),
inference(forward_subsumption_resolution,[],[f1195,f470]) ).
fof(f1197,plain,
( related(sF22,sK20,sK21)
| ~ spl26_1
| ~ spl26_8
| spl26_23
| ~ spl26_24
| ~ spl26_29 ),
inference(forward_subsumption_resolution,[],[f1196,f481]) ).
fof(f1198,plain,
( spl26_10
| ~ spl26_1
| ~ spl26_8
| spl26_23
| ~ spl26_24
| ~ spl26_29 ),
inference(avatar_split_clause,[],[f1197,f780,f654,f650,f480,f405,f488]) ).
fof(f1200,plain,
( related_reflexive(sF22,sK20,sK21)
| empty_carrier(sF22)
| ~ reflexive_relstr(sF22)
| ~ rel_str(sF22)
| ~ element(sK20,the_carrier(sF22))
| ~ element(sK21,the_carrier(sF22))
| ~ spl26_10 ),
inference(resolution,[],[f490,f367]) ).
fof(f1201,plain,
( empty_carrier(sF22)
| ~ reflexive_relstr(sF22)
| ~ rel_str(sF22)
| ~ element(sK20,the_carrier(sF22))
| ~ element(sK21,the_carrier(sF22))
| spl26_2
| ~ spl26_10 ),
inference(forward_subsumption_resolution,[],[f1200,f1192]) ).
fof(f1202,plain,
( ~ reflexive_relstr(sF22)
| ~ rel_str(sF22)
| ~ element(sK20,the_carrier(sF22))
| ~ element(sK21,the_carrier(sF22))
| spl26_2
| spl26_5
| ~ spl26_10 ),
inference(forward_subsumption_resolution,[],[f1201,f448]) ).
fof(f1203,plain,
( ~ rel_str(sF22)
| ~ element(sK20,the_carrier(sF22))
| ~ element(sK21,the_carrier(sF22))
| spl26_2
| spl26_5
| ~ spl26_9
| ~ spl26_10 ),
inference(forward_subsumption_resolution,[],[f1202,f485]) ).
fof(f1204,plain,
( ~ element(sK20,the_carrier(sF22))
| ~ element(sK21,the_carrier(sF22))
| spl26_2
| spl26_5
| ~ spl26_8
| ~ spl26_9
| ~ spl26_10 ),
inference(forward_subsumption_resolution,[],[f1203,f481]) ).
fof(f1205,plain,
( ~ element(sK21,the_carrier(sF22))
| spl26_2
| spl26_5
| ~ spl26_8
| ~ spl26_9
| ~ spl26_10 ),
inference(forward_subsumption_resolution,[],[f1204,f470]) ).
fof(f1206,plain,
( $false
| spl26_2
| spl26_5
| ~ spl26_8
| ~ spl26_9
| ~ spl26_10 ),
inference(forward_subsumption_resolution,[],[f1205,f467]) ).
fof(f1207,plain,
( spl26_2
| spl26_5
| ~ spl26_8
| ~ spl26_9
| ~ spl26_10 ),
inference(avatar_contradiction_clause,[],[f1206]) ).
cnf(s1,plain,
( spl26_1
| spl26_2 ),
inference(sat_conversion,[],[f412]) ).
cnf(s2,plain,
( ~ spl26_1
| ~ spl26_2 ),
inference(sat_conversion,[],[f413]) ).
cnf(s5,plain,
( ~ spl26_2
| spl26_5
| ~ spl26_8
| ~ spl26_9
| spl26_10 ),
inference(sat_conversion,[],[f491]) ).
cnf(s8,plain,
~ spl26_5,
inference(sat_conversion,[],[f534]) ).
cnf(s13,plain,
( spl26_23
| spl26_24 ),
inference(sat_conversion,[],[f656]) ).
cnf(s17,plain,
spl26_9,
inference(sat_conversion,[],[f667]) ).
cnf(s21,plain,
spl26_8,
inference(sat_conversion,[],[f722]) ).
cnf(s24,plain,
~ spl26_23,
inference(sat_conversion,[],[f814]) ).
cnf(s35,plain,
spl26_29,
inference(sat_conversion,[],[f1021]) ).
cnf(s39,plain,
( spl26_1
| ~ spl26_8
| ~ spl26_10
| spl26_23
| ~ spl26_24
| ~ spl26_29 ),
inference(sat_conversion,[],[f1189]) ).
cnf(s40,plain,
( ~ spl26_1
| ~ spl26_8
| spl26_10
| spl26_23
| ~ spl26_24
| ~ spl26_29 ),
inference(sat_conversion,[],[f1198]) ).
cnf(s41,plain,
( spl26_2
| spl26_5
| ~ spl26_8
| ~ spl26_9
| ~ spl26_10 ),
inference(sat_conversion,[],[f1207]) ).
cnf(s53,plain,
spl26_24,
inference(rat,[],[s13,s24]) ).
cnf(s58,plain,
( ~ spl26_2
| spl26_10 ),
inference(rat,[],[s5,s17,s21,s8]) ).
cnf(s61,plain,
spl26_1,
inference(rat,[],[s58,s1,s39,s21,s24,s53,s35]) ).
cnf(s62,plain,
spl26_10,
inference(rat,[],[s40,s35,s53,s24,s21,s61]) ).
cnf(s63,plain,
~ spl26_2,
inference(rat,[],[s2,s61]) ).
cnf(s64,plain,
$false,
inference(rat,[],[s41,s8,s17,s21,s62,s63]) ).
fof(f1208,plain,
$false,
inference(avatar_sat_refutation,[],[s64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU346+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n026.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Mon Sep 28 04:52:42 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.44 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
% 6.69/2.02 % (3467318)Detected formulas, will run a generic FOF schedule.
% 6.69/2.02 % (3467329)dis-21_1_sil=8000:lcm=predicate:random_seed=1684818080: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)
% 6.69/2.02 % (3467324)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=2517025205:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.69/2.02 % (3467325)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=1506688039:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.69/2.02 % (3467323)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=1380091809:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.69/2.02 % (3467328)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3540750828:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.69/2.02 % (3467327)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1309205573:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.69/2.02 % (3467326)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1523102874:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.69/2.02 % (3467326)Refutation not found, incomplete strategy
% 6.69/2.02 % (3467326)------------------------------
% 6.69/2.02 % (3467326)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/2.02 % (3467326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/2.02 % (3467326)CaDiCaL version: 2.1.3
% 6.69/2.02 % (3467326)Termination reason: Refutation not found, incomplete strategy
% 6.69/2.02 % (3467326)Time elapsed: 0.002 s
% 6.69/2.02 % (3467326)Peak memory usage: 88 MB
% 6.69/2.02 % (3467326)Instructions burned: 1 (million)
% 6.69/2.02 % (3467327)Refutation not found, incomplete strategy
% 6.69/2.02 % (3467327)------------------------------
% 6.69/2.02 % (3467327)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/2.02 % (3467327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/2.02 % (3467327)CaDiCaL version: 2.1.3
% 6.69/2.02 % (3467327)Termination reason: Refutation not found, incomplete strategy
% 6.69/2.02 % (3467327)Time elapsed: 0.003 s
% 6.69/2.02 % (3467327)Peak memory usage: 88 MB
% 6.69/2.02 % (3467327)Instructions burned: 3 (million)
% 6.69/2.02 % (3467329)Instruction limit reached!
% 6.69/2.02 % (3467329)------------------------------
% 6.69/2.02 % (3467329)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/2.02 % (3467329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/2.02 % (3467329)CaDiCaL version: 2.1.3
% 6.69/2.02 % (3467329)Termination reason: Instruction limit
% 6.69/2.02 % (3467329)Termination phase: Saturation
% 6.69/2.02 % (3467329)Time elapsed: 0.041 s
% 6.69/2.02 % (3467329)Peak memory usage: 93 MB
% 6.69/2.02 % (3467329)Instructions burned: 130 (million)
% 6.69/2.02 % (3467328)Instruction limit reached!
% 6.69/2.02 % (3467328)------------------------------
% 6.69/2.02 % (3467328)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/2.02 % (3467328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/2.02 % (3467328)CaDiCaL version: 2.1.3
% 6.69/2.02 % (3467328)Termination reason: Instruction limit
% 6.69/2.02 % (3467328)Termination phase: Saturation
% 6.69/2.02 % (3467328)Time elapsed: 0.098 s
% 6.69/2.02 % (3467328)Peak memory usage: 90 MB
% 6.69/2.02 % (3467328)Instructions burned: 139 (million)
% 6.69/2.02 % (3467337)lrs+10_1_sil=8000:sp=occurrence:random_seed=3343276047:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 6.69/2.02 % (3467337)Instruction limit reached!
% 6.69/2.02 % (3467337)------------------------------
% 6.69/2.02 % (3467337)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/2.02 % (3467337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/2.02 % (3467337)CaDiCaL version: 2.1.3
% 6.69/2.02 % (3467337)Termination reason: Instruction limit
% 6.69/2.02 % (3467337)Termination phase: Saturation
% 6.69/2.02 % (3467337)Time elapsed: 0.097 s
% 6.69/2.02 % (3467337)Peak memory usage: 92 MB
% 6.69/2.02 % (3467337)Instructions burned: 285 (million)
% 6.69/2.02 % (3467338)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1091994771:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.69/2.02 % (3467338)Refutation not found, incomplete strategy
% 6.69/2.02 % (3467338)------------------------------
% 6.69/2.02 % (3467338)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/2.02 % (3467338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/2.02 % (3467338)CaDiCaL version: 2.1.3
% 6.69/2.02 % (3467338)Termination reason: Refutation not found, incomplete strategy
% 6.69/2.02 % (3467338)Time elapsed: 0.005 s
% 6.69/2.02 % (3467338)Peak memory usage: 89 MB
% 6.69/2.02 % (3467338)Instructions burned: 6 (million)
% 6.69/2.02 % (3467326)------------------------------
% 6.69/2.02 % (3467326)------------------------------
% 6.69/2.02 % (3467327)------------------------------
% 6.69/2.02 % (3467327)------------------------------
% 6.69/2.02 % (3467340)lrs+1011_1_sil=32000:sp=occurrence:random_seed=856913209:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 6.69/2.02 % (3467343)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=4291960909:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.69/2.02 % (3467342)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=1353640940:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 6.69/2.02 % (3467343)Refutation not found, incomplete strategy
% 6.69/2.02 % (3467343)------------------------------
% 6.69/2.02 % (3467343)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/2.02 % (3467343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/2.02 % (3467343)CaDiCaL version: 2.1.3
% 6.69/2.02 % (3467343)Termination reason: Refutation not found, incomplete strategy
% 6.69/2.02 % (3467343)Time elapsed: 0.007 s
% 6.69/2.02 % (3467343)Peak memory usage: 88 MB
% 6.69/2.02 % (3467343)Instructions burned: 9 (million)
% 6.69/2.02 % (3467340)Instruction limit reached!
% 6.69/2.02 % (3467340)------------------------------
% 6.69/2.02 % (3467340)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/2.02 % (3467340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/2.02 % (3467340)CaDiCaL version: 2.1.3
% 6.69/2.02 % (3467340)Termination reason: Instruction limit
% 6.69/2.02 % (3467340)Termination phase: Saturation
% 6.69/2.02 % (3467340)Time elapsed: 0.129 s
% 6.69/2.02 % (3467340)Peak memory usage: 92 MB
% 6.69/2.02 % (3467340)Instructions burned: 326 (million)
% 6.69/2.02 % (3467338)------------------------------
% 6.69/2.02 % (3467338)------------------------------
% 6.69/2.02 % (3467347)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1814487296:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.69/2.02 % (3467342)Instruction limit reached!
% 6.69/2.02 % (3467342)------------------------------
% 6.69/2.02 % (3467342)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/2.02 % (3467342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/2.02 % (3467342)CaDiCaL version: 2.1.3
% 6.69/2.02 % (3467342)Termination reason: Instruction limit
% 6.69/2.02 % (3467342)Termination phase: Saturation
% 6.69/2.02 % (3467342)Time elapsed: 0.149 s
% 6.69/2.02 % (3467342)Peak memory usage: 92 MB
% 6.69/2.02 % (3467342)Instructions burned: 248 (million)
% 6.69/2.02 % (3467348)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1778946686:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 6.69/2.02 % (3467343)------------------------------
% 6.69/2.02 % (3467343)------------------------------
% 6.69/2.02 % (3467350)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2943177040:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 6.69/2.02 % (3467348)Instruction limit reached!
% 6.69/2.02 % (3467348)------------------------------
% 6.69/2.02 % (3467348)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/2.02 % (3467348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/2.02 % (3467348)CaDiCaL version: 2.1.3
% 6.69/2.02 % (3467348)Termination reason: Instruction limit
% 6.69/2.02 % (3467348)Termination phase: Saturation
% 6.69/2.02 % (3467348)Time elapsed: 0.075 s
% 6.69/2.02 % (3467348)Peak memory usage: 91 MB
% 6.69/2.02 % (3467348)Instructions burned: 113 (million)
% 6.69/2.02 % (3467323)First to succeed.
% 6.69/2.02 % (3467323)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3467318"
% 6.69/2.02 % (3467350)Instruction limit reached!
% 6.69/2.02 % (3467350)------------------------------
% 6.69/2.02 % (3467350)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/2.02 % (3467350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/2.02 % (3467350)CaDiCaL version: 2.1.3
% 6.69/2.02 % (3467350)Termination reason: Instruction limit
% 6.69/2.02 % (3467350)Termination phase: Saturation
% 6.69/2.02 % (3467350)Time elapsed: 0.066 s
% 6.69/2.02 % (3467350)Peak memory usage: 89 MB
% 6.69/2.02 % (3467350)Instructions burned: 128 (million)
% 6.69/2.02 % (3467352)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=176264229:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 6.69/2.02 % (3467352)Refutation not found, incomplete strategy
% 6.69/2.02 % (3467352)------------------------------
% 6.69/2.02 % (3467352)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/2.02 % (3467352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/2.02 % (3467352)CaDiCaL version: 2.1.3
% 6.69/2.02 % (3467352)Termination reason: Refutation not found, incomplete strategy
% 6.69/2.02 % (3467352)Time elapsed: 0.005 s
% 6.69/2.02 % (3467352)Peak memory usage: 89 MB
% 6.69/2.02 % (3467352)Instructions burned: 6 (million)
% 6.69/2.02 % (3467324)Also succeeded, but the first one will report.
% 6.69/2.02 % (3467354)lrs+10_1_sil=8000:sp=occurrence:random_seed=2719773872:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 6.69/2.02 % (3467355)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=4201948246:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 6.69/2.02 % (3467355)Refutation not found, incomplete strategy
% 6.69/2.02 % (3467355)------------------------------
% 6.69/2.02 % (3467355)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/2.02 % (3467355)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/2.02 % (3467355)CaDiCaL version: 2.1.3
% 6.69/2.02 % (3467355)Termination reason: Refutation not found, incomplete strategy
% 6.69/2.02 % (3467355)Time elapsed: 0.005 s
% 6.69/2.02 % (3467355)Peak memory usage: 88 MB
% 6.69/2.02 % (3467355)Instructions burned: 8 (million)
% 6.69/2.02 % (3467323)Refutation found. Thanks to Tanya!
% 6.69/2.02 % SZS status Theorem for theBenchmark
% 6.69/2.02 % SZS output start Proof for theBenchmark
% See solution above
% 8.64/2.22 % (3467323)------------------------------
% 8.64/2.22 % (3467323)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.64/2.22 % (3467323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.64/2.22 % (3467323)CaDiCaL version: 2.1.3
% 8.64/2.22 % (3467323)Termination reason: Refutation
% 8.64/2.22 % (3467323)Time elapsed: 0.729 s
% 8.64/2.22 % (3467323)Peak memory usage: 130 MB
% 8.64/2.22 % (3467323)Instructions burned: 1078 (million)
% 8.64/2.22 % (3467323)------------------------------
% 8.64/2.22 % (3467323)------------------------------
% 8.64/2.22 % (3467318)Success in time 1.139 s
% 8.64/2.22 % Vampire exiting
%------------------------------------------------------------------------------