%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU370+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 : n002.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 12:48:34 PM UTC 2026
% Result : Theorem 20.44s 3.85s
% Output : Refutation 21.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 36
% Syntax : Number of formulae : 281 ( 71 unt; 0 def)
% Number of atoms : 953 ( 240 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 1109 ( 437 ~; 502 |; 122 &)
% ( 19 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 42 ( 40 usr; 1 prp; 0-3 aty)
% Number of functors : 33 ( 33 usr; 1 con; 0-3 aty)
% Number of variables : 566 ( 548 !; 18 ?)
% 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(f7,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f20,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f21,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f25,axiom,
! [X0,X1] :
( ( strict_latt_str(X1)
& latt_str(X1) )
=> ( X1 = boole_lattice(X0)
<=> ( the_carrier(X1) = powerset(X0)
& ! [X2] :
( element(X2,powerset(X0))
=> ! [X3] :
( element(X3,powerset(X0))
=> ( apply_binary(the_L_join(X1),X2,X3) = subset_union2(X0,X2,X3)
& apply_binary(the_L_meet(X1),X2,X3) = subset_intersection2(X0,X2,X3) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_lattice3) ).
fof(f26,axiom,
! [X0,X1] :
( relation(X1)
=> ( X1 = inclusion_relation(X0)
<=> ( relation_field(X1) = X0
& ! [X2,X3] :
( ( in(X2,X0)
& in(X3,X0) )
=> ( in(ordered_pair(X2,X3),X1)
<=> subset(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_wellord2) ).
fof(f27,axiom,
! [X0] : incl_POSet(X0) = rel_str_of(X0,inclusion_order(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_yellow_1) ).
fof(f28,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(f29,axiom,
! [X0] : boole_POSet(X0) = poset_of_lattice(boole_lattice(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_yellow_1) ).
fof(f30,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(f31,axiom,
! [X0] :
( relation(X0)
=> relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_1) ).
fof(f32,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(f36,axiom,
! [X0] :
( strict_latt_str(boole_lattice(X0))
& latt_str(boole_lattice(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice3) ).
fof(f39,axiom,
! [X0] : relation(inclusion_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_wellord2) ).
fof(f41,axiom,
! [X0] :
( reflexive(inclusion_order(X0))
& antisymmetric(inclusion_order(X0))
& transitive(inclusion_order(X0))
& v1_partfun1(inclusion_order(X0),X0,X0)
& relation_of2_as_subset(inclusion_order(X0),X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_yellow_1) ).
fof(f43,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(f52,axiom,
! [X0] :
( strict_rel_str(boole_POSet(X0))
& rel_str(boole_POSet(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_yellow_1) ).
fof(f53,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> element(relation_dom_as_subset(X0,X1,X2),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relset_1) ).
fof(f54,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X0))
& element(X2,powerset(X0)) )
=> element(subset_union2(X0,X1,X2),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_subset_1) ).
fof(f56,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> element(relation_rng_as_subset(X0,X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relset_1) ).
fof(f66,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f92,axiom,
! [X0] :
( ~ empty_carrier(boole_lattice(X0))
& strict_latt_str(boole_lattice(X0))
& join_commutative(boole_lattice(X0))
& join_associative(boole_lattice(X0))
& meet_commutative(boole_lattice(X0))
& meet_associative(boole_lattice(X0))
& meet_absorbing(boole_lattice(X0))
& join_absorbing(boole_lattice(X0))
& lattice(boole_lattice(X0))
& distributive_lattstr(boole_lattice(X0))
& modular_lattstr(boole_lattice(X0))
& lower_bounded_semilattstr(boole_lattice(X0))
& upper_bounded_semilattstr(boole_lattice(X0))
& bounded_lattstr(boole_lattice(X0))
& complemented_lattstr(boole_lattice(X0))
& boolean_lattstr(boole_lattice(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_lattice3) ).
fof(f104,axiom,
! [X0] :
( ~ empty_carrier(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& complete_relstr(boole_POSet(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_yellow_1) ).
fof(f105,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(f131,axiom,
! [X0] : inclusion_order(X0) = inclusion_relation(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_yellow_1) ).
fof(f133,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
fof(f134,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X0))
& element(X2,powerset(X0)) )
=> subset_union2(X0,X1,X2) = set_union2(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_subset_1) ).
fof(f135,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
=> relation_rng_as_subset(X0,X1,X2) = relation_rng(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_relset_1) ).
fof(f137,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(f138,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(f139,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f142,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f143,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X1,X0)
=> ( ! [X3] :
~ ( in(X3,X1)
& ! [X4] : ~ in(ordered_pair(X3,X4),X2) )
<=> relation_dom_as_subset(X1,X0,X2) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_relset_1) ).
fof(f147,axiom,
! [X0,X1] :
( element(X1,the_carrier(boole_POSet(X0)))
=> ! [X2] :
( element(X2,the_carrier(boole_POSet(X0)))
=> ( related_reflexive(boole_POSet(X0),X1,X2)
<=> subset(X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_yellow_1) ).
fof(f149,axiom,
! [X0,X1,X2] :
( ( in(X0,X1)
& element(X1,powerset(X2)) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f150,conjecture,
! [X0] : boole_POSet(X0) = incl_POSet(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_yellow_1) ).
fof(f151,negated_conjecture,
~ ! [X0] : boole_POSet(X0) = incl_POSet(powerset(X0)),
inference(negated_conjecture,[status(cth)],[f150]) ).
fof(f158,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f139]) ).
fof(f159,plain,
! [X0] :
( X0 = rel_str_of(the_carrier(X0),the_InternalRel(X0))
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f160,plain,
! [X0] :
( X0 = rel_str_of(the_carrier(X0),the_InternalRel(X0))
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f159]) ).
fof(f170,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f7]) ).
fof(f199,plain,
! [X0,X1] :
( ( X1 = boole_lattice(X0)
<=> ( the_carrier(X1) = powerset(X0)
& ! [X2] :
( ! [X3] :
( ( apply_binary(the_L_join(X1),X2,X3) = subset_union2(X0,X2,X3)
& apply_binary(the_L_meet(X1),X2,X3) = subset_intersection2(X0,X2,X3) )
| ~ element(X3,powerset(X0)) )
| ~ element(X2,powerset(X0)) ) ) )
| ~ strict_latt_str(X1)
| ~ latt_str(X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f200,plain,
! [X0,X1] :
( ( X1 = boole_lattice(X0)
<=> ( the_carrier(X1) = powerset(X0)
& ! [X2] :
( ! [X3] :
( ( apply_binary(the_L_join(X1),X2,X3) = subset_union2(X0,X2,X3)
& apply_binary(the_L_meet(X1),X2,X3) = subset_intersection2(X0,X2,X3) )
| ~ element(X3,powerset(X0)) )
| ~ element(X2,powerset(X0)) ) ) )
| ~ strict_latt_str(X1)
| ~ latt_str(X1) ),
inference(flattening,[],[f199]) ).
fof(f201,plain,
! [X0,X1] :
( ( X1 = inclusion_relation(X0)
<=> ( relation_field(X1) = X0
& ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
<=> subset(X2,X3) )
| ~ in(X2,X0)
| ~ in(X3,X0) ) ) )
| ~ relation(X1) ),
inference(ennf_transformation,[],[f26]) ).
fof(f202,plain,
! [X0,X1] :
( ( X1 = inclusion_relation(X0)
<=> ( relation_field(X1) = X0
& ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
<=> subset(X2,X3) )
| ~ in(X2,X0)
| ~ in(X3,X0) ) ) )
| ~ relation(X1) ),
inference(flattening,[],[f201]) ).
fof(f203,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,[],[f28]) ).
fof(f204,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,[],[f203]) ).
fof(f205,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f206,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,[],[f32]) ).
fof(f210,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,[],[f43]) ).
fof(f211,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,[],[f210]) ).
fof(f214,plain,
! [X0,X1,X2] :
( element(relation_dom_as_subset(X0,X1,X2),powerset(X0))
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f53]) ).
fof(f215,plain,
! [X0,X1,X2] :
( element(subset_union2(X0,X1,X2),powerset(X0))
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f54]) ).
fof(f216,plain,
! [X0,X1,X2] :
( element(subset_union2(X0,X1,X2),powerset(X0))
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(flattening,[],[f215]) ).
fof(f217,plain,
! [X0,X1,X2] :
( element(relation_rng_as_subset(X0,X1,X2),powerset(X1))
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f56]) ).
fof(f226,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f66]) ).
fof(f256,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,[],[f105]) ).
fof(f268,plain,
! [X0,X1,X2] :
( relation_dom_as_subset(X0,X1,X2) = relation_dom(X2)
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f133]) ).
fof(f269,plain,
! [X0,X1,X2] :
( subset_union2(X0,X1,X2) = set_union2(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f134]) ).
fof(f270,plain,
! [X0,X1,X2] :
( subset_union2(X0,X1,X2) = set_union2(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(flattening,[],[f269]) ).
fof(f271,plain,
! [X0,X1,X2] :
( relation_rng_as_subset(X0,X1,X2) = relation_rng(X2)
| ~ relation_of2(X2,X0,X1) ),
inference(ennf_transformation,[],[f135]) ).
fof(f274,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,[],[f138]) ).
fof(f275,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,[],[f274]) ).
fof(f278,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f142]) ).
fof(f279,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ~ in(X3,X1)
| ? [X4] : in(ordered_pair(X3,X4),X2) )
<=> relation_dom_as_subset(X1,X0,X2) = X1 )
| ~ relation_of2_as_subset(X2,X1,X0) ),
inference(ennf_transformation,[],[f143]) ).
fof(f283,plain,
! [X0,X1] :
( ! [X2] :
( ( related_reflexive(boole_POSet(X0),X1,X2)
<=> subset(X1,X2) )
| ~ element(X2,the_carrier(boole_POSet(X0))) )
| ~ element(X1,the_carrier(boole_POSet(X0))) ),
inference(ennf_transformation,[],[f147]) ).
fof(f284,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(ennf_transformation,[],[f149]) ).
fof(f285,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(flattening,[],[f284]) ).
fof(f286,plain,
? [X0] : boole_POSet(X0) != incl_POSet(powerset(X0)),
inference(ennf_transformation,[],[f151]) ).
fof(f291,plain,
! [X0,X1] :
( ( ( X1 = boole_lattice(X0)
| powerset(X0) != the_carrier(X1)
| ? [X2] :
( ? [X3] :
( ( apply_binary(the_L_join(X1),X2,X3) != subset_union2(X0,X2,X3)
| apply_binary(the_L_meet(X1),X2,X3) != subset_intersection2(X0,X2,X3) )
& element(X3,powerset(X0)) )
& element(X2,powerset(X0)) ) )
& ( ( the_carrier(X1) = powerset(X0)
& ! [X2] :
( ! [X3] :
( ( apply_binary(the_L_join(X1),X2,X3) = subset_union2(X0,X2,X3)
& apply_binary(the_L_meet(X1),X2,X3) = subset_intersection2(X0,X2,X3) )
| ~ element(X3,powerset(X0)) )
| ~ element(X2,powerset(X0)) ) )
| boole_lattice(X0) != X1 ) )
| ~ strict_latt_str(X1)
| ~ latt_str(X1) ),
inference(nnf_transformation,[],[f200]) ).
fof(f292,plain,
! [X0,X1] :
( ( ( X1 = boole_lattice(X0)
| powerset(X0) != the_carrier(X1)
| ? [X2] :
( ? [X3] :
( ( apply_binary(the_L_join(X1),X2,X3) != subset_union2(X0,X2,X3)
| apply_binary(the_L_meet(X1),X2,X3) != subset_intersection2(X0,X2,X3) )
& element(X3,powerset(X0)) )
& element(X2,powerset(X0)) ) )
& ( ( the_carrier(X1) = powerset(X0)
& ! [X2] :
( ! [X3] :
( ( apply_binary(the_L_join(X1),X2,X3) = subset_union2(X0,X2,X3)
& apply_binary(the_L_meet(X1),X2,X3) = subset_intersection2(X0,X2,X3) )
| ~ element(X3,powerset(X0)) )
| ~ element(X2,powerset(X0)) ) )
| boole_lattice(X0) != X1 ) )
| ~ strict_latt_str(X1)
| ~ latt_str(X1) ),
inference(flattening,[],[f291]) ).
fof(f293,plain,
! [X0,X1] :
( ( ( X1 = boole_lattice(X0)
| powerset(X0) != the_carrier(X1)
| ? [X2] :
( ? [X3] :
( ( apply_binary(the_L_join(X1),X2,X3) != subset_union2(X0,X2,X3)
| apply_binary(the_L_meet(X1),X2,X3) != subset_intersection2(X0,X2,X3) )
& element(X3,powerset(X0)) )
& element(X2,powerset(X0)) ) )
& ( ( the_carrier(X1) = powerset(X0)
& ! [X4] :
( ! [X5] :
( ( apply_binary(the_L_join(X1),X4,X5) = subset_union2(X0,X4,X5)
& apply_binary(the_L_meet(X1),X4,X5) = subset_intersection2(X0,X4,X5) )
| ~ element(X5,powerset(X0)) )
| ~ element(X4,powerset(X0)) ) )
| boole_lattice(X0) != X1 ) )
| ~ strict_latt_str(X1)
| ~ latt_str(X1) ),
inference(rectify,[],[f292]) ).
fof(f294,plain,
! [X0,X1] :
( ( ( X1 = boole_lattice(X0)
| powerset(X0) != the_carrier(X1)
| ( ( apply_binary(the_L_join(X1),sK0(X0,X1),sK1(X0,X1)) != subset_union2(X0,sK0(X0,X1),sK1(X0,X1))
| apply_binary(the_L_meet(X1),sK0(X0,X1),sK1(X0,X1)) != subset_intersection2(X0,sK0(X0,X1),sK1(X0,X1)) )
& element(sK1(X0,X1),powerset(X0))
& element(sK0(X0,X1),powerset(X0)) ) )
& ( ( the_carrier(X1) = powerset(X0)
& ! [X4] :
( ! [X5] :
( ( apply_binary(the_L_join(X1),X4,X5) = subset_union2(X0,X4,X5)
& apply_binary(the_L_meet(X1),X4,X5) = subset_intersection2(X0,X4,X5) )
| ~ element(X5,powerset(X0)) )
| ~ element(X4,powerset(X0)) ) )
| boole_lattice(X0) != X1 ) )
| ~ strict_latt_str(X1)
| ~ latt_str(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1))],[f293]) ).
fof(f295,plain,
! [X0,X1] :
( ( ( X1 = inclusion_relation(X0)
| relation_field(X1) != X0
| ? [X2,X3] :
( ( ~ subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X1) )
& ( subset(X2,X3)
| in(ordered_pair(X2,X3),X1) )
& in(X2,X0)
& in(X3,X0) ) )
& ( ( relation_field(X1) = X0
& ! [X2,X3] :
( ( ( in(ordered_pair(X2,X3),X1)
| ~ subset(X2,X3) )
& ( subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X1) ) )
| ~ in(X2,X0)
| ~ in(X3,X0) ) )
| inclusion_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(nnf_transformation,[],[f202]) ).
fof(f296,plain,
! [X0,X1] :
( ( ( X1 = inclusion_relation(X0)
| relation_field(X1) != X0
| ? [X2,X3] :
( ( ~ subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X1) )
& ( subset(X2,X3)
| in(ordered_pair(X2,X3),X1) )
& in(X2,X0)
& in(X3,X0) ) )
& ( ( relation_field(X1) = X0
& ! [X2,X3] :
( ( ( in(ordered_pair(X2,X3),X1)
| ~ subset(X2,X3) )
& ( subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X1) ) )
| ~ in(X2,X0)
| ~ in(X3,X0) ) )
| inclusion_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(flattening,[],[f295]) ).
fof(f297,plain,
! [X0,X1] :
( ( ( X1 = inclusion_relation(X0)
| relation_field(X1) != X0
| ? [X2,X3] :
( ( ~ subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X1) )
& ( subset(X2,X3)
| in(ordered_pair(X2,X3),X1) )
& in(X2,X0)
& in(X3,X0) ) )
& ( ( relation_field(X1) = X0
& ! [X4,X5] :
( ( ( in(ordered_pair(X4,X5),X1)
| ~ subset(X4,X5) )
& ( subset(X4,X5)
| ~ in(ordered_pair(X4,X5),X1) ) )
| ~ in(X4,X0)
| ~ in(X5,X0) ) )
| inclusion_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(rectify,[],[f296]) ).
fof(f298,plain,
! [X0,X1] :
( ( ( X1 = inclusion_relation(X0)
| relation_field(X1) != X0
| ( ( ~ subset(sK2(X0,X1),sK3(X0,X1))
| ~ in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X1) )
& ( subset(sK2(X0,X1),sK3(X0,X1))
| in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X1) )
& in(sK2(X0,X1),X0)
& in(sK3(X0,X1),X0) ) )
& ( ( relation_field(X1) = X0
& ! [X4,X5] :
( ( ( in(ordered_pair(X4,X5),X1)
| ~ subset(X4,X5) )
& ( subset(X4,X5)
| ~ in(ordered_pair(X4,X5),X1) ) )
| ~ in(X4,X0)
| ~ in(X5,X0) ) )
| inclusion_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X2,sK2(X0,X1)),skolemize(X3,sK3(X0,X1))],[f297]) ).
fof(f299,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,[],[f206]) ).
fof(f328,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,[],[f137]) ).
fof(f329,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,[],[f275]) ).
fof(f330,plain,
! [X0,X1,X2] :
( ( ( ! [X3] :
( ~ in(X3,X1)
| ? [X4] : in(ordered_pair(X3,X4),X2) )
| relation_dom_as_subset(X1,X0,X2) != X1 )
& ( relation_dom_as_subset(X1,X0,X2) = X1
| ? [X3] :
( in(X3,X1)
& ! [X4] : ~ in(ordered_pair(X3,X4),X2) ) ) )
| ~ relation_of2_as_subset(X2,X1,X0) ),
inference(nnf_transformation,[],[f279]) ).
fof(f331,plain,
! [X0,X1,X2] :
( ( ( ! [X3] :
( ~ in(X3,X1)
| ? [X4] : in(ordered_pair(X3,X4),X2) )
| relation_dom_as_subset(X1,X0,X2) != X1 )
& ( relation_dom_as_subset(X1,X0,X2) = X1
| ? [X5] :
( in(X5,X1)
& ! [X6] : ~ in(ordered_pair(X5,X6),X2) ) ) )
| ~ relation_of2_as_subset(X2,X1,X0) ),
inference(rectify,[],[f330]) ).
fof(f332,plain,
! [X0,X1,X2] :
( ( ( ! [X3] :
( ~ in(X3,X1)
| in(ordered_pair(X3,sK32(X2,X3)),X2) )
| relation_dom_as_subset(X1,X0,X2) != X1 )
& ( relation_dom_as_subset(X1,X0,X2) = X1
| ( in(sK33(X1,X2),X1)
& ! [X6] : ~ in(ordered_pair(sK33(X1,X2),X6),X2) ) ) )
| ~ relation_of2_as_subset(X2,X1,X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32,sK33]),skolemize(X4,sK32(X2,X3)),skolemize(X5,sK33(X1,X2))],[f331]) ).
fof(f336,plain,
! [X0,X1] :
( ! [X2] :
( ( ( related_reflexive(boole_POSet(X0),X1,X2)
| ~ subset(X1,X2) )
& ( subset(X1,X2)
| ~ related_reflexive(boole_POSet(X0),X1,X2) ) )
| ~ element(X2,the_carrier(boole_POSet(X0))) )
| ~ element(X1,the_carrier(boole_POSet(X0))) ),
inference(nnf_transformation,[],[f283]) ).
fof(f338,plain,
boole_POSet(sK36) != incl_POSet(powerset(sK36)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(X0,sK36)],[f286]) ).
fof(f339,plain,
! [X0] :
( ~ strict_rel_str(X0)
| rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f160]) ).
fof(f361,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(cnf_transformation,[],[f170]) ).
fof(f400,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f20]) ).
fof(f401,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f21]) ).
fof(f407,plain,
! [X0,X1] :
( powerset(X0) = the_carrier(X1)
| boole_lattice(X0) != X1
| ~ strict_latt_str(X1)
| ~ latt_str(X1) ),
inference(cnf_transformation,[],[f294]) ).
fof(f412,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X4,X5),X1)
| ~ subset(X4,X5)
| ~ in(X4,X0)
| ~ in(X5,X0)
| inclusion_relation(X0) != X1
| ~ relation(X1) ),
inference(cnf_transformation,[],[f298]) ).
fof(f414,plain,
! [X0,X1] :
( inclusion_relation(X0) = X1
| relation_field(X1) != X0
| in(sK3(X0,X1),X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f298]) ).
fof(f415,plain,
! [X0,X1] :
( inclusion_relation(X0) = X1
| relation_field(X1) != X0
| in(sK2(X0,X1),X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f298]) ).
fof(f416,plain,
! [X0,X1] :
( inclusion_relation(X0) = X1
| relation_field(X1) != X0
| subset(sK2(X0,X1),sK3(X0,X1))
| in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f298]) ).
fof(f417,plain,
! [X0,X1] :
( inclusion_relation(X0) = X1
| relation_field(X1) != X0
| ~ subset(sK2(X0,X1),sK3(X0,X1))
| ~ in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f298]) ).
fof(f418,plain,
! [X0] : incl_POSet(X0) = rel_str_of(X0,inclusion_order(X0)),
inference(cnf_transformation,[],[f27]) ).
fof(f419,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,[],[f204]) ).
fof(f420,plain,
! [X0] : boole_POSet(X0) = poset_of_lattice(boole_lattice(X0)),
inference(cnf_transformation,[],[f29]) ).
fof(f421,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f30]) ).
fof(f422,plain,
! [X0] :
( ~ relation(X0)
| relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
inference(cnf_transformation,[],[f205]) ).
fof(f423,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,[],[f299]) ).
fof(f424,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,[],[f299]) ).
fof(f429,plain,
! [X0] : latt_str(boole_lattice(X0)),
inference(cnf_transformation,[],[f36]) ).
fof(f431,plain,
! [X0] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[],[f39]) ).
fof(f432,plain,
! [X0] : relation_of2_as_subset(inclusion_order(X0),X0,X0),
inference(cnf_transformation,[],[f41]) ).
fof(f437,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,[],[f211]) ).
fof(f449,plain,
! [X0] : rel_str(boole_POSet(X0)),
inference(cnf_transformation,[],[f52]) ).
fof(f451,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| element(relation_dom_as_subset(X0,X1,X2),powerset(X0)) ),
inference(cnf_transformation,[],[f214]) ).
fof(f452,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| element(subset_union2(X0,X1,X2),powerset(X0)) ),
inference(cnf_transformation,[],[f216]) ).
fof(f453,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| element(relation_rng_as_subset(X0,X1,X2),powerset(X1)) ),
inference(cnf_transformation,[],[f217]) ).
fof(f461,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f226]) ).
fof(f542,plain,
! [X0] : lattice(boole_lattice(X0)),
inference(cnf_transformation,[],[f92]) ).
fof(f549,plain,
! [X0] : strict_latt_str(boole_lattice(X0)),
inference(cnf_transformation,[],[f92]) ).
fof(f550,plain,
! [X0] : ~ empty_carrier(boole_lattice(X0)),
inference(cnf_transformation,[],[f92]) ).
fof(f606,plain,
! [X0] : reflexive_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f104]) ).
fof(f607,plain,
! [X0] : strict_rel_str(boole_POSet(X0)),
inference(cnf_transformation,[],[f104]) ).
fof(f608,plain,
! [X0] : ~ empty_carrier(boole_POSet(X0)),
inference(cnf_transformation,[],[f104]) ).
fof(f609,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2(X1,X0,X0)
| rel_str_of(X0,X1) != rel_str_of(X2,X3)
| X1 = X3 ),
inference(cnf_transformation,[],[f256]) ).
fof(f610,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2(X1,X0,X0)
| rel_str_of(X0,X1) != rel_str_of(X2,X3)
| X0 = X2 ),
inference(cnf_transformation,[],[f256]) ).
fof(f748,plain,
! [X0] : inclusion_relation(X0) = inclusion_order(X0),
inference(cnf_transformation,[],[f131]) ).
fof(f750,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_dom_as_subset(X0,X1,X2) = relation_dom(X2) ),
inference(cnf_transformation,[],[f268]) ).
fof(f751,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_union2(X0,X1,X2) = set_union2(X1,X2) ),
inference(cnf_transformation,[],[f270]) ).
fof(f752,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_rng_as_subset(X0,X1,X2) = relation_rng(X2) ),
inference(cnf_transformation,[],[f271]) ).
fof(f754,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f328]) ).
fof(f756,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,[],[f329]) ).
fof(f757,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,[],[f329]) ).
fof(f758,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f158]) ).
fof(f761,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f278]) ).
fof(f762,plain,
! [X2,X0,X1,X6] :
( relation_dom_as_subset(X1,X0,X2) = X1
| ~ in(ordered_pair(sK33(X1,X2),X6),X2)
| ~ relation_of2_as_subset(X2,X1,X0) ),
inference(cnf_transformation,[],[f332]) ).
fof(f763,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X1,X0)
| in(sK33(X1,X2),X1)
| relation_dom_as_subset(X1,X0,X2) = X1 ),
inference(cnf_transformation,[],[f332]) ).
fof(f770,plain,
! [X2,X0,X1] :
( subset(X1,X2)
| ~ related_reflexive(boole_POSet(X0),X1,X2)
| ~ element(X2,the_carrier(boole_POSet(X0)))
| ~ element(X1,the_carrier(boole_POSet(X0))) ),
inference(cnf_transformation,[],[f336]) ).
fof(f771,plain,
! [X2,X0,X1] :
( related_reflexive(boole_POSet(X0),X1,X2)
| ~ subset(X1,X2)
| ~ element(X2,the_carrier(boole_POSet(X0)))
| ~ element(X1,the_carrier(boole_POSet(X0))) ),
inference(cnf_transformation,[],[f336]) ).
fof(f774,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f285]) ).
fof(f775,plain,
boole_POSet(sK36) != incl_POSet(powerset(sK36)),
inference(cnf_transformation,[],[f338]) ).
fof(f780,plain,
! [X0,X1] :
( inclusion_order(X0) = X1
| relation_field(X1) != X0
| ~ subset(sK2(X0,X1),sK3(X0,X1))
| ~ in(unordered_pair(unordered_pair(sK2(X0,X1),sK3(X0,X1)),singleton(sK2(X0,X1))),X1)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f417,f748,f421]) ).
fof(f781,plain,
! [X0,X1] :
( inclusion_order(X0) = X1
| relation_field(X1) != X0
| subset(sK2(X0,X1),sK3(X0,X1))
| in(unordered_pair(unordered_pair(sK2(X0,X1),sK3(X0,X1)),singleton(sK2(X0,X1))),X1)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f416,f748,f421]) ).
fof(f782,plain,
! [X0,X1] :
( inclusion_order(X0) = X1
| relation_field(X1) != X0
| in(sK2(X0,X1),X0)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f415,f748]) ).
fof(f783,plain,
! [X0,X1] :
( inclusion_order(X0) = X1
| relation_field(X1) != X0
| in(sK3(X0,X1),X0)
| ~ relation(X1) ),
inference(definition_unfolding,[],[f414,f748]) ).
fof(f785,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X1)
| ~ subset(X4,X5)
| ~ in(X4,X0)
| ~ in(X5,X0)
| inclusion_order(X0) != X1
| ~ relation(X1) ),
inference(definition_unfolding,[],[f412,f421,f748]) ).
fof(f787,plain,
! [X2,X0,X1] :
( ~ element(X1,the_carrier(X0))
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),the_InternalRel(X0))
| ~ element(X2,the_carrier(X0))
| related(X0,X1,X2)
| ~ rel_str(X0) ),
inference(definition_unfolding,[],[f424,f421]) ).
fof(f788,plain,
! [X2,X0,X1] :
( ~ rel_str(X0)
| ~ related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),the_InternalRel(X0)) ),
inference(definition_unfolding,[],[f423,f421]) ).
fof(f789,plain,
! [X0] : relation(inclusion_order(X0)),
inference(definition_unfolding,[],[f431,f748]) ).
fof(f793,plain,
! [X0] : rel_str(poset_of_lattice(boole_lattice(X0))),
inference(definition_unfolding,[],[f449,f420]) ).
fof(f808,plain,
! [X0] : ~ empty_carrier(poset_of_lattice(boole_lattice(X0))),
inference(definition_unfolding,[],[f608,f420]) ).
fof(f809,plain,
! [X0] : strict_rel_str(poset_of_lattice(boole_lattice(X0))),
inference(definition_unfolding,[],[f607,f420]) ).
fof(f810,plain,
! [X0] : reflexive_relstr(poset_of_lattice(boole_lattice(X0))),
inference(definition_unfolding,[],[f606,f420]) ).
fof(f820,plain,
! [X2,X0,X1,X6] :
( ~ relation_of2_as_subset(X2,X1,X0)
| ~ in(unordered_pair(unordered_pair(sK33(X1,X2),X6),singleton(sK33(X1,X2))),X2)
| relation_dom_as_subset(X1,X0,X2) = X1 ),
inference(definition_unfolding,[],[f762,f421]) ).
fof(f823,plain,
! [X2,X0,X1] :
( ~ element(X1,the_carrier(poset_of_lattice(boole_lattice(X0))))
| ~ subset(X1,X2)
| ~ element(X2,the_carrier(poset_of_lattice(boole_lattice(X0))))
| related_reflexive(poset_of_lattice(boole_lattice(X0)),X1,X2) ),
inference(definition_unfolding,[],[f771,f420,f420,f420]) ).
fof(f824,plain,
! [X2,X0,X1] :
( ~ element(X1,the_carrier(poset_of_lattice(boole_lattice(X0))))
| ~ related_reflexive(poset_of_lattice(boole_lattice(X0)),X1,X2)
| ~ element(X2,the_carrier(poset_of_lattice(boole_lattice(X0))))
| subset(X1,X2) ),
inference(definition_unfolding,[],[f770,f420,f420,f420]) ).
fof(f825,plain,
poset_of_lattice(boole_lattice(sK36)) != rel_str_of(powerset(sK36),inclusion_order(powerset(sK36))),
inference(definition_unfolding,[],[f775,f420,f418]) ).
fof(f826,plain,
! [X0] :
( powerset(X0) = the_carrier(boole_lattice(X0))
| ~ strict_latt_str(boole_lattice(X0))
| ~ latt_str(boole_lattice(X0)) ),
inference(equality_resolution,[],[f407]) ).
fof(f829,plain,
! [X1] :
( ~ relation(X1)
| ~ subset(sK2(relation_field(X1),X1),sK3(relation_field(X1),X1))
| ~ in(unordered_pair(unordered_pair(sK2(relation_field(X1),X1),sK3(relation_field(X1),X1)),singleton(sK2(relation_field(X1),X1))),X1)
| inclusion_order(relation_field(X1)) = X1 ),
inference(equality_resolution,[],[f780]) ).
fof(f830,plain,
! [X1] :
( ~ relation(X1)
| subset(sK2(relation_field(X1),X1),sK3(relation_field(X1),X1))
| in(unordered_pair(unordered_pair(sK2(relation_field(X1),X1),sK3(relation_field(X1),X1)),singleton(sK2(relation_field(X1),X1))),X1)
| inclusion_order(relation_field(X1)) = X1 ),
inference(equality_resolution,[],[f781]) ).
fof(f831,plain,
! [X1] :
( in(sK2(relation_field(X1),X1),relation_field(X1))
| inclusion_order(relation_field(X1)) = X1
| ~ relation(X1) ),
inference(equality_resolution,[],[f782]) ).
fof(f832,plain,
! [X1] :
( in(sK3(relation_field(X1),X1),relation_field(X1))
| inclusion_order(relation_field(X1)) = X1
| ~ relation(X1) ),
inference(equality_resolution,[],[f783]) ).
fof(f834,plain,
! [X0,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),inclusion_order(X0))
| ~ subset(X4,X5)
| ~ in(X4,X0)
| ~ in(X5,X0)
| ~ relation(inclusion_order(X0)) ),
inference(equality_resolution,[],[f785]) ).
fof(f837,plain,
! [X0,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),inclusion_order(X0))
| ~ subset(X4,X5)
| ~ in(X4,X0)
| ~ in(X5,X0) ),
inference(forward_subsumption_resolution,[],[f834,f789]) ).
fof(f841,plain,
! [X0] :
( powerset(X0) = the_carrier(boole_lattice(X0))
| ~ latt_str(boole_lattice(X0)) ),
inference(forward_subsumption_resolution,[],[f826,f549]) ).
fof(f843,plain,
! [X0,X4,X5] :
( ~ subset(X4,X5)
| in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),inclusion_order(X0))
| ~ in(X4,X0)
| ~ in(X5,X0) ),
inference(forward_demodulation,[],[f837,f400]) ).
fof(f846,plain,
! [X0] : powerset(X0) = the_carrier(boole_lattice(X0)),
inference(forward_subsumption_resolution,[],[f841,f429]) ).
fof(f847,plain,
! [X0] :
( poset_of_lattice(boole_lattice(X0)) = rel_str_of(the_carrier(poset_of_lattice(boole_lattice(X0))),the_InternalRel(poset_of_lattice(boole_lattice(X0))))
| ~ rel_str(poset_of_lattice(boole_lattice(X0))) ),
inference(resolution,[],[f809,f339]) ).
fof(f848,plain,
! [X0] : poset_of_lattice(boole_lattice(X0)) = rel_str_of(the_carrier(poset_of_lattice(boole_lattice(X0))),the_InternalRel(poset_of_lattice(boole_lattice(X0)))),
inference(forward_subsumption_resolution,[],[f847,f793]) ).
fof(f853,plain,
! [X0] :
( empty_carrier(boole_lattice(X0))
| poset_of_lattice(boole_lattice(X0)) = rel_str_of(the_carrier(boole_lattice(X0)),k2_lattice3(boole_lattice(X0)))
| ~ latt_str(boole_lattice(X0)) ),
inference(resolution,[],[f542,f419]) ).
fof(f854,plain,
! [X0] :
( poset_of_lattice(boole_lattice(X0)) = rel_str_of(the_carrier(boole_lattice(X0)),k2_lattice3(boole_lattice(X0)))
| ~ latt_str(boole_lattice(X0)) ),
inference(forward_subsumption_resolution,[],[f853,f550]) ).
fof(f855,plain,
! [X0] : poset_of_lattice(boole_lattice(X0)) = rel_str_of(the_carrier(boole_lattice(X0)),k2_lattice3(boole_lattice(X0))),
inference(forward_subsumption_resolution,[],[f854,f429]) ).
fof(f856,plain,
! [X0] : poset_of_lattice(boole_lattice(X0)) = rel_str_of(powerset(X0),k2_lattice3(boole_lattice(X0))),
inference(forward_demodulation,[],[f855,f846]) ).
fof(f867,plain,
! [X0] : relation_of2(inclusion_order(X0),X0,X0),
inference(resolution,[],[f754,f432]) ).
fof(f868,plain,
! [X0] : relation_dom(inclusion_order(X0)) = relation_dom_as_subset(X0,X0,inclusion_order(X0)),
inference(resolution,[],[f867,f750]) ).
fof(f900,plain,
! [X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),inclusion_order(X1))
| ~ in(X0,X1)
| ~ in(X0,X1) ),
inference(resolution,[],[f758,f843]) ).
fof(f901,plain,
! [X0,X1] :
( ~ in(X0,X1)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),inclusion_order(X1)) ),
inference(duplicate_literal_removal,[],[f900]) ).
fof(f918,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK33(X0,inclusion_order(X0)),X1),singleton(sK33(X0,inclusion_order(X0)))),inclusion_order(X0))
| relation_dom_as_subset(X0,X0,inclusion_order(X0)) = X0 ),
inference(resolution,[],[f820,f432]) ).
fof(f919,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(sK33(X0,inclusion_order(X0))),unordered_pair(sK33(X0,inclusion_order(X0)),X1)),inclusion_order(X0))
| relation_dom_as_subset(X0,X0,inclusion_order(X0)) = X0 ),
inference(forward_demodulation,[],[f918,f400]) ).
fof(f921,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(sK33(X0,inclusion_order(X0))),unordered_pair(sK33(X0,inclusion_order(X0)),X1)),inclusion_order(X0))
| relation_dom(inclusion_order(X0)) = X0 ),
inference(forward_demodulation,[],[f919,f868]) ).
fof(f937,plain,
! [X0] :
( empty_carrier(boole_lattice(X0))
| relation_of2_as_subset(k2_lattice3(boole_lattice(X0)),the_carrier(boole_lattice(X0)),the_carrier(boole_lattice(X0)))
| ~ latt_str(boole_lattice(X0)) ),
inference(resolution,[],[f437,f542]) ).
fof(f938,plain,
! [X0] :
( relation_of2_as_subset(k2_lattice3(boole_lattice(X0)),the_carrier(boole_lattice(X0)),the_carrier(boole_lattice(X0)))
| ~ latt_str(boole_lattice(X0)) ),
inference(forward_subsumption_resolution,[],[f937,f550]) ).
fof(f939,plain,
! [X0] : relation_of2_as_subset(k2_lattice3(boole_lattice(X0)),the_carrier(boole_lattice(X0)),the_carrier(boole_lattice(X0))),
inference(forward_subsumption_resolution,[],[f938,f429]) ).
fof(f940,plain,
! [X0] : relation_of2_as_subset(k2_lattice3(boole_lattice(X0)),powerset(X0),powerset(X0)),
inference(forward_demodulation,[],[f939,f846]) ).
fof(f941,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK33(powerset(X0),k2_lattice3(boole_lattice(X0))),X1),singleton(sK33(powerset(X0),k2_lattice3(boole_lattice(X0))))),k2_lattice3(boole_lattice(X0)))
| powerset(X0) = relation_dom_as_subset(powerset(X0),powerset(X0),k2_lattice3(boole_lattice(X0))) ),
inference(resolution,[],[f940,f820]) ).
fof(f942,plain,
! [X0] : element(k2_lattice3(boole_lattice(X0)),powerset(cartesian_product2(powerset(X0),powerset(X0)))),
inference(resolution,[],[f940,f461]) ).
fof(f943,plain,
! [X0] : relation_of2(k2_lattice3(boole_lattice(X0)),powerset(X0),powerset(X0)),
inference(resolution,[],[f940,f754]) ).
fof(f944,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(sK33(powerset(X0),k2_lattice3(boole_lattice(X0)))),unordered_pair(sK33(powerset(X0),k2_lattice3(boole_lattice(X0))),X1)),k2_lattice3(boole_lattice(X0)))
| powerset(X0) = relation_dom_as_subset(powerset(X0),powerset(X0),k2_lattice3(boole_lattice(X0))) ),
inference(forward_demodulation,[],[f941,f400]) ).
fof(f947,plain,
! [X0] : relation_dom_as_subset(powerset(X0),powerset(X0),k2_lattice3(boole_lattice(X0))) = relation_dom(k2_lattice3(boole_lattice(X0))),
inference(resolution,[],[f943,f750]) ).
fof(f948,plain,
! [X0] : relation_rng_as_subset(powerset(X0),powerset(X0),k2_lattice3(boole_lattice(X0))) = relation_rng(k2_lattice3(boole_lattice(X0))),
inference(resolution,[],[f943,f752]) ).
fof(f949,plain,
! [X2,X0,X1] :
( rel_str_of(X1,X2) != rel_str_of(powerset(X0),k2_lattice3(boole_lattice(X0)))
| k2_lattice3(boole_lattice(X0)) = X2 ),
inference(resolution,[],[f943,f609]) ).
fof(f950,plain,
! [X2,X0,X1] :
( rel_str_of(X1,X2) != rel_str_of(powerset(X0),k2_lattice3(boole_lattice(X0)))
| powerset(X0) = X1 ),
inference(resolution,[],[f943,f610]) ).
fof(f951,plain,
! [X2,X0,X1] :
( poset_of_lattice(boole_lattice(X0)) != rel_str_of(X1,X2)
| powerset(X0) = X1 ),
inference(forward_demodulation,[],[f950,f856]) ).
fof(f952,plain,
! [X2,X0,X1] :
( poset_of_lattice(boole_lattice(X0)) != rel_str_of(X1,X2)
| k2_lattice3(boole_lattice(X0)) = X2 ),
inference(forward_demodulation,[],[f949,f856]) ).
fof(f953,plain,
! [X0,X1] :
( poset_of_lattice(boole_lattice(X0)) != poset_of_lattice(boole_lattice(X1))
| the_InternalRel(poset_of_lattice(boole_lattice(X0))) = k2_lattice3(boole_lattice(X1)) ),
inference(superposition,[],[f952,f848]) ).
fof(f959,plain,
! [X0] : the_InternalRel(poset_of_lattice(boole_lattice(X0))) = k2_lattice3(boole_lattice(X0)),
inference(equality_resolution,[],[f953]) ).
fof(f960,plain,
! [X0] : poset_of_lattice(boole_lattice(X0)) = rel_str_of(the_carrier(poset_of_lattice(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),
inference(superposition,[],[f848,f959]) ).
fof(f966,plain,
! [X0,X1] :
( poset_of_lattice(boole_lattice(X0)) != poset_of_lattice(boole_lattice(X1))
| powerset(X1) = the_carrier(poset_of_lattice(boole_lattice(X0))) ),
inference(superposition,[],[f951,f960]) ).
fof(f969,plain,
! [X0] : powerset(X0) = the_carrier(poset_of_lattice(boole_lattice(X0))),
inference(equality_resolution,[],[f966]) ).
fof(f972,plain,
! [X2,X0,X1] :
( ~ related_reflexive(poset_of_lattice(boole_lattice(X0)),X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0))
| subset(X1,X2) ),
inference(superposition,[],[f824,f969]) ).
fof(f973,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0))
| related_reflexive(poset_of_lattice(boole_lattice(X0)),X1,X2) ),
inference(superposition,[],[f823,f969]) ).
fof(f974,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X0))
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),the_InternalRel(poset_of_lattice(boole_lattice(X0))))
| ~ element(X2,powerset(X0))
| related(poset_of_lattice(boole_lattice(X0)),X1,X2)
| ~ rel_str(poset_of_lattice(boole_lattice(X0))) ),
inference(superposition,[],[f787,f969]) ).
fof(f975,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X0))
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),the_InternalRel(poset_of_lattice(boole_lattice(X0))))
| ~ element(X2,powerset(X0))
| related(poset_of_lattice(boole_lattice(X0)),X1,X2) ),
inference(forward_subsumption_resolution,[],[f974,f793]) ).
fof(f977,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),k2_lattice3(boole_lattice(X0)))
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0))
| related(poset_of_lattice(boole_lattice(X0)),X1,X2) ),
inference(forward_demodulation,[],[f975,f959]) ).
fof(f978,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),k2_lattice3(boole_lattice(X0)))
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0))
| related(poset_of_lattice(boole_lattice(X0)),X1,X2) ),
inference(forward_demodulation,[],[f977,f400]) ).
fof(f979,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| ~ element(X0,powerset(X1))
| related_reflexive(poset_of_lattice(boole_lattice(X1)),X0,X0) ),
inference(resolution,[],[f973,f758]) ).
fof(f980,plain,
! [X0,X1] :
( related_reflexive(poset_of_lattice(boole_lattice(X1)),X0,X0)
| ~ element(X0,powerset(X1)) ),
inference(duplicate_literal_removal,[],[f979]) ).
fof(f981,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| related(poset_of_lattice(boole_lattice(X1)),X0,X0)
| empty_carrier(poset_of_lattice(boole_lattice(X1)))
| ~ reflexive_relstr(poset_of_lattice(boole_lattice(X1)))
| ~ rel_str(poset_of_lattice(boole_lattice(X1)))
| ~ element(X0,the_carrier(poset_of_lattice(boole_lattice(X1))))
| ~ element(X0,the_carrier(poset_of_lattice(boole_lattice(X1)))) ),
inference(resolution,[],[f980,f756]) ).
fof(f982,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| related(poset_of_lattice(boole_lattice(X1)),X0,X0)
| empty_carrier(poset_of_lattice(boole_lattice(X1)))
| ~ reflexive_relstr(poset_of_lattice(boole_lattice(X1)))
| ~ rel_str(poset_of_lattice(boole_lattice(X1)))
| ~ element(X0,the_carrier(poset_of_lattice(boole_lattice(X1)))) ),
inference(duplicate_literal_removal,[],[f981]) ).
fof(f983,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| related(poset_of_lattice(boole_lattice(X1)),X0,X0)
| ~ reflexive_relstr(poset_of_lattice(boole_lattice(X1)))
| ~ rel_str(poset_of_lattice(boole_lattice(X1)))
| ~ element(X0,the_carrier(poset_of_lattice(boole_lattice(X1)))) ),
inference(forward_subsumption_resolution,[],[f982,f808]) ).
fof(f984,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| related(poset_of_lattice(boole_lattice(X1)),X0,X0)
| ~ rel_str(poset_of_lattice(boole_lattice(X1)))
| ~ element(X0,the_carrier(poset_of_lattice(boole_lattice(X1)))) ),
inference(forward_subsumption_resolution,[],[f983,f810]) ).
fof(f985,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| related(poset_of_lattice(boole_lattice(X1)),X0,X0)
| ~ element(X0,the_carrier(poset_of_lattice(boole_lattice(X1)))) ),
inference(forward_subsumption_resolution,[],[f984,f793]) ).
fof(f986,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| ~ element(X0,powerset(X1))
| related(poset_of_lattice(boole_lattice(X1)),X0,X0) ),
inference(forward_demodulation,[],[f985,f969]) ).
fof(f987,plain,
! [X0,X1] :
( related(poset_of_lattice(boole_lattice(X1)),X0,X0)
| ~ element(X0,powerset(X1)) ),
inference(duplicate_literal_removal,[],[f986]) ).
fof(f1025,plain,
! [X0] : relation(k2_lattice3(boole_lattice(X0))),
inference(resolution,[],[f942,f361]) ).
fof(f1047,plain,
! [X0] : relation_field(k2_lattice3(boole_lattice(X0))) = set_union2(relation_dom(k2_lattice3(boole_lattice(X0))),relation_rng(k2_lattice3(boole_lattice(X0)))),
inference(resolution,[],[f1025,f422]) ).
fof(f1048,plain,
! [X0] :
( subset(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))
| in(unordered_pair(unordered_pair(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0)))),singleton(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))),k2_lattice3(boole_lattice(X0)))
| k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0)))) ),
inference(resolution,[],[f1025,f830]) ).
fof(f1049,plain,
! [X0] :
( ~ subset(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))
| ~ in(unordered_pair(unordered_pair(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0)))),singleton(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))),k2_lattice3(boole_lattice(X0)))
| k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0)))) ),
inference(resolution,[],[f1025,f829]) ).
fof(f1050,plain,
! [X0] :
( ~ subset(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))
| ~ in(unordered_pair(singleton(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0)))),unordered_pair(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))),k2_lattice3(boole_lattice(X0)))
| k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0)))) ),
inference(forward_demodulation,[],[f1049,f400]) ).
fof(f1051,plain,
! [X0] :
( in(unordered_pair(singleton(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0)))),unordered_pair(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))),k2_lattice3(boole_lattice(X0)))
| subset(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))
| k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0)))) ),
inference(forward_demodulation,[],[f1048,f400]) ).
fof(f1063,plain,
! [X0] : element(relation_rng_as_subset(powerset(X0),powerset(X0),k2_lattice3(boole_lattice(X0))),powerset(powerset(X0))),
inference(resolution,[],[f453,f943]) ).
fof(f1064,plain,
! [X0] : element(relation_rng(k2_lattice3(boole_lattice(X0))),powerset(powerset(X0))),
inference(forward_demodulation,[],[f1063,f948]) ).
fof(f1111,plain,
! [X0] : element(relation_dom_as_subset(powerset(X0),powerset(X0),k2_lattice3(boole_lattice(X0))),powerset(powerset(X0))),
inference(resolution,[],[f451,f943]) ).
fof(f1112,plain,
! [X0] : element(relation_dom(k2_lattice3(boole_lattice(X0))),powerset(powerset(X0))),
inference(forward_demodulation,[],[f1111,f947]) ).
fof(f1179,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(sK33(powerset(X1),k2_lattice3(boole_lattice(X1)))),unordered_pair(X0,sK33(powerset(X1),k2_lattice3(boole_lattice(X1))))),k2_lattice3(boole_lattice(X1)))
| powerset(X1) = relation_dom_as_subset(powerset(X1),powerset(X1),k2_lattice3(boole_lattice(X1))) ),
inference(superposition,[],[f944,f400]) ).
fof(f1180,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(sK33(powerset(X1),k2_lattice3(boole_lattice(X1)))),unordered_pair(X0,sK33(powerset(X1),k2_lattice3(boole_lattice(X1))))),k2_lattice3(boole_lattice(X1)))
| powerset(X1) = relation_dom(k2_lattice3(boole_lattice(X1))) ),
inference(forward_demodulation,[],[f1179,f947]) ).
fof(f1233,plain,
! [X0] :
( in(sK33(X0,inclusion_order(X0)),X0)
| relation_dom_as_subset(X0,X0,inclusion_order(X0)) = X0 ),
inference(resolution,[],[f763,f432]) ).
fof(f1234,plain,
! [X0] :
( in(sK33(powerset(X0),k2_lattice3(boole_lattice(X0))),powerset(X0))
| powerset(X0) = relation_dom_as_subset(powerset(X0),powerset(X0),k2_lattice3(boole_lattice(X0))) ),
inference(resolution,[],[f763,f940]) ).
fof(f1235,plain,
! [X0] :
( in(sK33(powerset(X0),k2_lattice3(boole_lattice(X0))),powerset(X0))
| powerset(X0) = relation_dom(k2_lattice3(boole_lattice(X0))) ),
inference(forward_demodulation,[],[f1234,f947]) ).
fof(f1236,plain,
! [X0] :
( in(sK33(X0,inclusion_order(X0)),X0)
| relation_dom(inclusion_order(X0)) = X0 ),
inference(forward_demodulation,[],[f1233,f868]) ).
fof(f1242,plain,
! [X0] :
( relation_dom(inclusion_order(X0)) = X0
| in(unordered_pair(singleton(sK33(X0,inclusion_order(X0))),unordered_pair(sK33(X0,inclusion_order(X0)),sK33(X0,inclusion_order(X0)))),inclusion_order(X0)) ),
inference(resolution,[],[f1236,f901]) ).
fof(f1244,plain,
! [X0] : relation_dom(inclusion_order(X0)) = X0,
inference(forward_subsumption_resolution,[],[f1242,f921]) ).
fof(f1265,plain,
! [X2,X0,X1] :
( ~ related(poset_of_lattice(boole_lattice(X0)),X1,X2)
| ~ element(X2,the_carrier(poset_of_lattice(boole_lattice(X0))))
| ~ element(X1,the_carrier(poset_of_lattice(boole_lattice(X0))))
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),the_InternalRel(poset_of_lattice(boole_lattice(X0)))) ),
inference(resolution,[],[f788,f793]) ).
fof(f1268,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ related(poset_of_lattice(boole_lattice(X0)),X1,X2)
| ~ element(X1,the_carrier(poset_of_lattice(boole_lattice(X0))))
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),the_InternalRel(poset_of_lattice(boole_lattice(X0)))) ),
inference(forward_demodulation,[],[f1265,f969]) ).
fof(f1270,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0))
| ~ related(poset_of_lattice(boole_lattice(X0)),X1,X2)
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),the_InternalRel(poset_of_lattice(boole_lattice(X0)))) ),
inference(forward_demodulation,[],[f1268,f969]) ).
fof(f1272,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),k2_lattice3(boole_lattice(X0)))
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0))
| ~ related(poset_of_lattice(boole_lattice(X0)),X1,X2) ),
inference(forward_demodulation,[],[f1270,f959]) ).
fof(f1274,plain,
! [X2,X0,X1] :
( ~ related(poset_of_lattice(boole_lattice(X0)),X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0))
| in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),k2_lattice3(boole_lattice(X0))) ),
inference(forward_demodulation,[],[f1272,f400]) ).
fof(f1275,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| ~ element(X0,powerset(X1))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),k2_lattice3(boole_lattice(X1)))
| ~ element(X0,powerset(X1)) ),
inference(resolution,[],[f1274,f987]) ).
fof(f1280,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),k2_lattice3(boole_lattice(X1))) ),
inference(duplicate_literal_removal,[],[f1275]) ).
fof(f1884,plain,
! [X0,X1] :
( ~ element(X0,powerset(powerset(X1)))
| element(subset_union2(powerset(X1),X0,relation_dom(k2_lattice3(boole_lattice(X1)))),powerset(powerset(X1))) ),
inference(resolution,[],[f1112,f452]) ).
fof(f1888,plain,
! [X0,X1] :
( ~ element(X0,powerset(powerset(X1)))
| subset_union2(powerset(X1),X0,relation_dom(k2_lattice3(boole_lattice(X1)))) = set_union2(X0,relation_dom(k2_lattice3(boole_lattice(X1)))) ),
inference(resolution,[],[f1112,f751]) ).
fof(f1975,plain,
! [X0] :
( element(sK33(powerset(X0),k2_lattice3(boole_lattice(X0))),powerset(X0))
| powerset(X0) = relation_dom(k2_lattice3(boole_lattice(X0))) ),
inference(resolution,[],[f1235,f761]) ).
fof(f2097,plain,
! [X0] : subset_union2(powerset(X0),relation_rng(k2_lattice3(boole_lattice(X0))),relation_dom(k2_lattice3(boole_lattice(X0)))) = set_union2(relation_rng(k2_lattice3(boole_lattice(X0))),relation_dom(k2_lattice3(boole_lattice(X0)))),
inference(resolution,[],[f1888,f1064]) ).
fof(f2100,plain,
! [X0] : set_union2(relation_dom(k2_lattice3(boole_lattice(X0))),relation_rng(k2_lattice3(boole_lattice(X0)))) = subset_union2(powerset(X0),relation_rng(k2_lattice3(boole_lattice(X0))),relation_dom(k2_lattice3(boole_lattice(X0)))),
inference(forward_demodulation,[],[f2097,f401]) ).
fof(f2106,plain,
! [X0] : relation_field(k2_lattice3(boole_lattice(X0))) = subset_union2(powerset(X0),relation_rng(k2_lattice3(boole_lattice(X0))),relation_dom(k2_lattice3(boole_lattice(X0)))),
inference(forward_demodulation,[],[f2100,f1047]) ).
fof(f3662,plain,
! [X0] :
( powerset(X0) = relation_dom(k2_lattice3(boole_lattice(X0)))
| in(unordered_pair(singleton(sK33(powerset(X0),k2_lattice3(boole_lattice(X0)))),unordered_pair(sK33(powerset(X0),k2_lattice3(boole_lattice(X0))),sK33(powerset(X0),k2_lattice3(boole_lattice(X0))))),k2_lattice3(boole_lattice(X0))) ),
inference(resolution,[],[f1975,f1280]) ).
fof(f3722,plain,
! [X0] : powerset(X0) = relation_dom(k2_lattice3(boole_lattice(X0))),
inference(forward_subsumption_resolution,[],[f3662,f1180]) ).
fof(f7924,plain,
! [X0] : element(subset_union2(powerset(X0),relation_rng(k2_lattice3(boole_lattice(X0))),relation_dom(k2_lattice3(boole_lattice(X0)))),powerset(powerset(X0))),
inference(resolution,[],[f1884,f1064]) ).
fof(f7940,plain,
! [X0] : element(relation_field(k2_lattice3(boole_lattice(X0))),powerset(powerset(X0))),
inference(forward_demodulation,[],[f7924,f2106]) ).
fof(f8004,plain,
! [X0,X1] :
( ~ in(X0,relation_field(k2_lattice3(boole_lattice(X1))))
| element(X0,powerset(X1)) ),
inference(resolution,[],[f7940,f774]) ).
fof(f8230,plain,
! [X0] :
( element(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),powerset(X0))
| k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0))))
| ~ relation(k2_lattice3(boole_lattice(X0))) ),
inference(resolution,[],[f8004,f831]) ).
fof(f8231,plain,
! [X0] :
( element(sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),powerset(X0))
| k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0))))
| ~ relation(k2_lattice3(boole_lattice(X0))) ),
inference(resolution,[],[f8004,f832]) ).
fof(f8236,plain,
! [X0] :
( element(sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),powerset(X0))
| k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0)))) ),
inference(forward_subsumption_resolution,[],[f8231,f1025]) ).
fof(f8237,plain,
! [X0] :
( element(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),powerset(X0))
| k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0)))) ),
inference(forward_subsumption_resolution,[],[f8230,f1025]) ).
fof(f16021,plain,
! [X0] :
( subset(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))
| k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0))))
| ~ element(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),powerset(X0))
| ~ element(sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),powerset(X0))
| related(poset_of_lattice(boole_lattice(X0)),sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0)))) ),
inference(resolution,[],[f1051,f978]) ).
fof(f16029,plain,
! [X0] :
( subset(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))
| k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0))))
| ~ element(sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),powerset(X0))
| related(poset_of_lattice(boole_lattice(X0)),sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0)))) ),
inference(forward_subsumption_resolution,[],[f16021,f8237]) ).
fof(f16030,plain,
! [X0] :
( related(poset_of_lattice(boole_lattice(X0)),sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))
| k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0))))
| subset(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0)))) ),
inference(forward_subsumption_resolution,[],[f16029,f8236]) ).
fof(f16032,plain,
! [X0] :
( k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0))))
| subset(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))
| related_reflexive(poset_of_lattice(boole_lattice(X0)),sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))
| empty_carrier(poset_of_lattice(boole_lattice(X0)))
| ~ reflexive_relstr(poset_of_lattice(boole_lattice(X0)))
| ~ rel_str(poset_of_lattice(boole_lattice(X0)))
| ~ element(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),the_carrier(poset_of_lattice(boole_lattice(X0))))
| ~ element(sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),the_carrier(poset_of_lattice(boole_lattice(X0)))) ),
inference(resolution,[],[f16030,f757]) ).
fof(f16033,plain,
! [X0] :
( k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0))))
| related_reflexive(poset_of_lattice(boole_lattice(X0)),sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))
| empty_carrier(poset_of_lattice(boole_lattice(X0)))
| ~ reflexive_relstr(poset_of_lattice(boole_lattice(X0)))
| ~ rel_str(poset_of_lattice(boole_lattice(X0)))
| ~ element(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),the_carrier(poset_of_lattice(boole_lattice(X0))))
| ~ element(sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),the_carrier(poset_of_lattice(boole_lattice(X0)))) ),
inference(forward_subsumption_resolution,[],[f16032,f823]) ).
fof(f16034,plain,
! [X0] :
( k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0))))
| related_reflexive(poset_of_lattice(boole_lattice(X0)),sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))
| ~ reflexive_relstr(poset_of_lattice(boole_lattice(X0)))
| ~ rel_str(poset_of_lattice(boole_lattice(X0)))
| ~ element(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),the_carrier(poset_of_lattice(boole_lattice(X0))))
| ~ element(sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),the_carrier(poset_of_lattice(boole_lattice(X0)))) ),
inference(forward_subsumption_resolution,[],[f16033,f808]) ).
fof(f16035,plain,
! [X0] :
( k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0))))
| related_reflexive(poset_of_lattice(boole_lattice(X0)),sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))
| ~ rel_str(poset_of_lattice(boole_lattice(X0)))
| ~ element(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),the_carrier(poset_of_lattice(boole_lattice(X0))))
| ~ element(sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),the_carrier(poset_of_lattice(boole_lattice(X0)))) ),
inference(forward_subsumption_resolution,[],[f16034,f810]) ).
fof(f16036,plain,
! [X0] :
( k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0))))
| related_reflexive(poset_of_lattice(boole_lattice(X0)),sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))
| ~ element(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),the_carrier(poset_of_lattice(boole_lattice(X0))))
| ~ element(sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),the_carrier(poset_of_lattice(boole_lattice(X0)))) ),
inference(forward_subsumption_resolution,[],[f16035,f793]) ).
fof(f16037,plain,
! [X0] :
( ~ element(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),powerset(X0))
| k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0))))
| related_reflexive(poset_of_lattice(boole_lattice(X0)),sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))
| ~ element(sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),the_carrier(poset_of_lattice(boole_lattice(X0)))) ),
inference(forward_demodulation,[],[f16036,f969]) ).
fof(f16038,plain,
! [X0] :
( k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0))))
| related_reflexive(poset_of_lattice(boole_lattice(X0)),sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))
| ~ element(sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),the_carrier(poset_of_lattice(boole_lattice(X0)))) ),
inference(forward_subsumption_resolution,[],[f16037,f8237]) ).
fof(f16039,plain,
! [X0] :
( ~ element(sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),powerset(X0))
| k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0))))
| related_reflexive(poset_of_lattice(boole_lattice(X0)),sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0)))) ),
inference(forward_demodulation,[],[f16038,f969]) ).
fof(f16040,plain,
! [X0] :
( related_reflexive(poset_of_lattice(boole_lattice(X0)),sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))
| k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0)))) ),
inference(forward_subsumption_resolution,[],[f16039,f8236]) ).
fof(f16041,plain,
! [X0] :
( k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0))))
| ~ element(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),powerset(X0))
| ~ element(sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),powerset(X0))
| subset(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0)))) ),
inference(resolution,[],[f16040,f972]) ).
fof(f16042,plain,
! [X0] :
( k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0))))
| related(poset_of_lattice(boole_lattice(X0)),sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))
| empty_carrier(poset_of_lattice(boole_lattice(X0)))
| ~ reflexive_relstr(poset_of_lattice(boole_lattice(X0)))
| ~ rel_str(poset_of_lattice(boole_lattice(X0)))
| ~ element(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),the_carrier(poset_of_lattice(boole_lattice(X0))))
| ~ element(sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),the_carrier(poset_of_lattice(boole_lattice(X0)))) ),
inference(resolution,[],[f16040,f756]) ).
fof(f16043,plain,
! [X0] :
( k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0))))
| related(poset_of_lattice(boole_lattice(X0)),sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))
| ~ reflexive_relstr(poset_of_lattice(boole_lattice(X0)))
| ~ rel_str(poset_of_lattice(boole_lattice(X0)))
| ~ element(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),the_carrier(poset_of_lattice(boole_lattice(X0))))
| ~ element(sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),the_carrier(poset_of_lattice(boole_lattice(X0)))) ),
inference(forward_subsumption_resolution,[],[f16042,f808]) ).
fof(f16044,plain,
! [X0] :
( k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0))))
| ~ element(sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),powerset(X0))
| subset(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0)))) ),
inference(forward_subsumption_resolution,[],[f16041,f8237]) ).
fof(f16045,plain,
! [X0] :
( k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0))))
| related(poset_of_lattice(boole_lattice(X0)),sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))
| ~ rel_str(poset_of_lattice(boole_lattice(X0)))
| ~ element(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),the_carrier(poset_of_lattice(boole_lattice(X0))))
| ~ element(sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),the_carrier(poset_of_lattice(boole_lattice(X0)))) ),
inference(forward_subsumption_resolution,[],[f16043,f810]) ).
fof(f16046,plain,
! [X0] :
( subset(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))
| k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0)))) ),
inference(forward_subsumption_resolution,[],[f16044,f8236]) ).
fof(f16047,plain,
! [X0] :
( k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0))))
| related(poset_of_lattice(boole_lattice(X0)),sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))
| ~ element(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),the_carrier(poset_of_lattice(boole_lattice(X0))))
| ~ element(sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),the_carrier(poset_of_lattice(boole_lattice(X0)))) ),
inference(forward_subsumption_resolution,[],[f16045,f793]) ).
fof(f16048,plain,
! [X0] :
( ~ element(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),powerset(X0))
| k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0))))
| related(poset_of_lattice(boole_lattice(X0)),sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))
| ~ element(sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),the_carrier(poset_of_lattice(boole_lattice(X0)))) ),
inference(forward_demodulation,[],[f16047,f969]) ).
fof(f16049,plain,
! [X0] :
( k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0))))
| related(poset_of_lattice(boole_lattice(X0)),sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))
| ~ element(sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),the_carrier(poset_of_lattice(boole_lattice(X0)))) ),
inference(forward_subsumption_resolution,[],[f16048,f8237]) ).
fof(f16050,plain,
! [X0] :
( ~ element(sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),powerset(X0))
| k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0))))
| related(poset_of_lattice(boole_lattice(X0)),sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0)))) ),
inference(forward_demodulation,[],[f16049,f969]) ).
fof(f16051,plain,
! [X0] :
( related(poset_of_lattice(boole_lattice(X0)),sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))
| k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0)))) ),
inference(forward_subsumption_resolution,[],[f16050,f8236]) ).
fof(f16052,plain,
! [X0] :
( k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0))))
| ~ element(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),powerset(X0))
| ~ element(sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),powerset(X0))
| in(unordered_pair(singleton(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0)))),unordered_pair(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))),k2_lattice3(boole_lattice(X0))) ),
inference(resolution,[],[f16051,f1274]) ).
fof(f16054,plain,
! [X0] :
( k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0))))
| ~ element(sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),powerset(X0))
| in(unordered_pair(singleton(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0)))),unordered_pair(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))),k2_lattice3(boole_lattice(X0))) ),
inference(forward_subsumption_resolution,[],[f16052,f8237]) ).
fof(f16055,plain,
! [X0] :
( k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0))))
| in(unordered_pair(singleton(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0)))),unordered_pair(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))),k2_lattice3(boole_lattice(X0))) ),
inference(forward_subsumption_resolution,[],[f16054,f8236]) ).
fof(f16056,plain,
! [X0] :
( k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0))))
| ~ in(unordered_pair(singleton(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0)))),unordered_pair(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))),k2_lattice3(boole_lattice(X0)))
| k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0)))) ),
inference(resolution,[],[f16046,f1050]) ).
fof(f16060,plain,
! [X0] :
( k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0))))
| ~ in(unordered_pair(singleton(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0)))),unordered_pair(sK2(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))),sK3(relation_field(k2_lattice3(boole_lattice(X0))),k2_lattice3(boole_lattice(X0))))),k2_lattice3(boole_lattice(X0))) ),
inference(duplicate_literal_removal,[],[f16056]) ).
fof(f16061,plain,
! [X0] : k2_lattice3(boole_lattice(X0)) = inclusion_order(relation_field(k2_lattice3(boole_lattice(X0)))),
inference(forward_subsumption_resolution,[],[f16060,f16055]) ).
fof(f16139,plain,
! [X0] : relation_dom(k2_lattice3(boole_lattice(X0))) = relation_field(k2_lattice3(boole_lattice(X0))),
inference(superposition,[],[f1244,f16061]) ).
fof(f16209,plain,
! [X0] : powerset(X0) = relation_field(k2_lattice3(boole_lattice(X0))),
inference(forward_demodulation,[],[f16139,f3722]) ).
fof(f16568,plain,
! [X0] : k2_lattice3(boole_lattice(X0)) = inclusion_order(powerset(X0)),
inference(superposition,[],[f16061,f16209]) ).
fof(f16652,plain,
poset_of_lattice(boole_lattice(sK36)) != rel_str_of(powerset(sK36),k2_lattice3(boole_lattice(sK36))),
inference(superposition,[],[f825,f16568]) ).
fof(f16836,plain,
$false,
inference(forward_subsumption_resolution,[],[f16652,f856]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU370+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n002.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 05:01:07 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.25/2.27 % (4158438)Detected formulas, will run a generic FOF schedule.
% 9.25/2.27 % (4158445)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=1548275855:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 9.25/2.27 % (4158449)dis-21_1_sil=8000:lcm=predicate:random_seed=3453854163: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)
% 9.25/2.27 % (4158444)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=3268424779:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 9.25/2.27 % (4158443)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=2879947197:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 9.25/2.27 % (4158446)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4271008029:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 9.25/2.27 % (4158447)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1271933117:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 9.25/2.27 % (4158448)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1360615830:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 9.25/2.27 % (4158446)Refutation not found, incomplete strategy
% 9.25/2.27 % (4158446)------------------------------
% 9.25/2.27 % (4158446)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.25/2.27 % (4158446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.25/2.27 % (4158446)CaDiCaL version: 2.1.3
% 9.25/2.27 % (4158446)Termination reason: Refutation not found, incomplete strategy
% 9.25/2.27 % (4158446)Time elapsed: 0.002 s
% 9.25/2.27 % (4158446)Peak memory usage: 88 MB
% 9.25/2.27 % (4158446)Instructions burned: 1 (million)
% 9.25/2.27 % (4158447)Refutation not found, incomplete strategy
% 9.25/2.27 % (4158447)------------------------------
% 9.25/2.27 % (4158447)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.25/2.27 % (4158447)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.25/2.27 % (4158447)CaDiCaL version: 2.1.3
% 9.25/2.27 % (4158447)Termination reason: Refutation not found, incomplete strategy
% 9.25/2.27 % (4158447)Time elapsed: 0.004 s
% 9.25/2.27 % (4158447)Peak memory usage: 88 MB
% 9.25/2.27 % (4158447)Instructions burned: 4 (million)
% 9.25/2.27 % (4158449)Instruction limit reached!
% 9.25/2.27 % (4158449)------------------------------
% 9.25/2.27 % (4158449)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.25/2.27 % (4158449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.25/2.27 % (4158449)CaDiCaL version: 2.1.3
% 9.25/2.27 % (4158449)Termination reason: Instruction limit
% 9.25/2.27 % (4158449)Termination phase: Saturation
% 9.25/2.27 % (4158449)Time elapsed: 0.074 s
% 9.25/2.27 % (4158449)Peak memory usage: 92 MB
% 9.25/2.27 % (4158449)Instructions burned: 130 (million)
% 9.25/2.27 % (4158448)Instruction limit reached!
% 9.25/2.27 % (4158448)------------------------------
% 9.25/2.27 % (4158448)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.25/2.27 % (4158448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.25/2.27 % (4158448)CaDiCaL version: 2.1.3
% 9.25/2.27 % (4158448)Termination reason: Instruction limit
% 9.25/2.27 % (4158448)Termination phase: Saturation
% 9.25/2.27 % (4158448)Time elapsed: 0.097 s
% 9.25/2.27 % (4158448)Peak memory usage: 90 MB
% 9.25/2.27 % (4158448)Instructions burned: 139 (million)
% 9.25/2.27 % (4158457)lrs+10_1_sil=8000:sp=occurrence:random_seed=3754987081:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 9.25/2.27 % (4158447)------------------------------
% 9.25/2.27 % (4158447)------------------------------
% 9.25/2.27 % (4158446)------------------------------
% 9.25/2.27 % (4158446)------------------------------
% 9.25/2.27 % (4158458)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3437631097:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 9.25/2.27 % (4158458)Instruction limit reached!
% 9.25/2.27 % (4158458)------------------------------
% 9.25/2.27 % (4158458)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.25/2.27 % (4158458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.77/3.10 % (4158458)CaDiCaL version: 2.1.3
% 15.77/3.10 % (4158458)Termination reason: Instruction limit
% 15.77/3.10 % (4158458)Termination phase: Saturation
% 15.77/3.10 % (4158458)Time elapsed: 0.060 s
% 15.77/3.10 % (4158458)Peak memory usage: 89 MB
% 15.77/3.10 % (4158458)Instructions burned: 159 (million)
% 15.77/3.10 % (4158445)Refutation not found, incomplete strategy
% 15.77/3.10 % (4158445)------------------------------
% 15.77/3.10 % (4158445)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.77/3.10 % (4158445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.77/3.10 % (4158445)CaDiCaL version: 2.1.3
% 15.77/3.10 % (4158445)Termination reason: Refutation not found, incomplete strategy
% 15.77/3.10 % (4158445)Time elapsed: 0.398 s
% 15.77/3.10 % (4158445)Peak memory usage: 131 MB
% 15.77/3.10 % (4158445)Instructions burned: 937 (million)
% 15.77/3.10 % (4158460)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2726548448:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 15.77/3.10 % (4158457)Instruction limit reached!
% 15.77/3.10 % (4158457)------------------------------
% 15.77/3.10 % (4158457)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.77/3.10 % (4158457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.77/3.10 % (4158457)CaDiCaL version: 2.1.3
% 15.77/3.10 % (4158457)Termination reason: Instruction limit
% 15.77/3.10 % (4158457)Termination phase: Saturation
% 15.77/3.10 % (4158457)Time elapsed: 0.190 s
% 15.77/3.10 % (4158457)Peak memory usage: 92 MB
% 15.77/3.10 % (4158457)Instructions burned: 304 (million)
% 15.77/3.10 % (4158461)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=1952657566:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 15.77/3.10 % (4158460)Instruction limit reached!
% 15.77/3.10 % (4158460)------------------------------
% 15.77/3.10 % (4158460)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.77/3.10 % (4158460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.77/3.10 % (4158460)CaDiCaL version: 2.1.3
% 15.77/3.10 % (4158460)Termination reason: Instruction limit
% 15.77/3.10 % (4158460)Termination phase: Saturation
% 15.77/3.10 % (4158460)Time elapsed: 0.107 s
% 15.77/3.10 % (4158460)Peak memory usage: 92 MB
% 15.77/3.10 % (4158460)Instructions burned: 326 (million)
% 15.77/3.10 % (4158463)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3652484542:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 15.77/3.10 % (4158463)Refutation not found, incomplete strategy
% 15.77/3.10 % (4158463)------------------------------
% 15.77/3.10 % (4158463)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.77/3.10 % (4158463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.77/3.10 % (4158463)CaDiCaL version: 2.1.3
% 15.77/3.10 % (4158463)Termination reason: Refutation not found, incomplete strategy
% 15.77/3.10 % (4158463)Time elapsed: 0.006 s
% 15.77/3.10 % (4158463)Peak memory usage: 89 MB
% 15.77/3.10 % (4158463)Instructions burned: 8 (million)
% 15.77/3.10 % (4158461)Instruction limit reached!
% 15.77/3.10 % (4158461)------------------------------
% 15.77/3.10 % (4158461)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.77/3.10 % (4158461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.77/3.10 % (4158461)CaDiCaL version: 2.1.3
% 15.77/3.10 % (4158461)Termination reason: Instruction limit
% 15.77/3.10 % (4158461)Termination phase: Saturation
% 15.77/3.10 % (4158461)Time elapsed: 0.151 s
% 15.77/3.10 % (4158461)Peak memory usage: 91 MB
% 15.77/3.10 % (4158461)Instructions burned: 248 (million)
% 15.77/3.10 % (4158466)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2530061438:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 15.77/3.10 % (4158445)------------------------------
% 15.77/3.10 % (4158445)------------------------------
% 15.77/3.10 % (4158467)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3858413526:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 15.77/3.10 % (4158467)Instruction limit reached!
% 15.77/3.10 % (4158467)------------------------------
% 15.77/3.10 % (4158467)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.77/3.10 % (4158467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.77/3.10 % (4158467)CaDiCaL version: 2.1.3
% 20.44/3.85 % (4158467)Termination reason: Instruction limit
% 20.44/3.85 % (4158467)Termination phase: Saturation
% 20.44/3.85 % (4158467)Time elapsed: 0.038 s
% 20.44/3.85 % (4158467)Peak memory usage: 89 MB
% 20.44/3.85 % (4158467)Instructions burned: 114 (million)
% 20.44/3.85 % (4158470)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=820308473:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 20.44/3.85 % (4158470)Refutation not found, incomplete strategy
% 20.44/3.85 % (4158470)------------------------------
% 20.44/3.85 % (4158470)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.44/3.85 % (4158470)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.44/3.85 % (4158470)CaDiCaL version: 2.1.3
% 20.44/3.85 % (4158470)Termination reason: Refutation not found, incomplete strategy
% 20.44/3.85 % (4158470)Time elapsed: 0.010 s
% 20.44/3.85 % (4158470)Peak memory usage: 88 MB
% 20.44/3.85 % (4158470)Instructions burned: 17 (million)
% 20.44/3.85 % (4158472)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=234438837:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 20.44/3.85 % (4158463)------------------------------
% 20.44/3.85 % (4158463)------------------------------
% 20.44/3.85 % (4158473)lrs+10_1_sil=8000:sp=occurrence:random_seed=17083329:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 20.44/3.85 % (4158472)Instruction limit reached!
% 20.44/3.85 % (4158472)------------------------------
% 20.44/3.85 % (4158472)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.44/3.85 % (4158472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.44/3.85 % (4158472)CaDiCaL version: 2.1.3
% 20.44/3.85 % (4158472)Termination reason: Instruction limit
% 20.44/3.85 % (4158472)Termination phase: Saturation
% 20.44/3.85 % (4158472)Time elapsed: 0.068 s
% 20.44/3.85 % (4158472)Peak memory usage: 89 MB
% 20.44/3.85 % (4158472)Instructions burned: 115 (million)
% 20.44/3.85 % (4158477)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1781992894:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 20.44/3.85 % (4158477)Refutation not found, incomplete strategy
% 20.44/3.85 % (4158477)------------------------------
% 20.44/3.85 % (4158477)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.44/3.85 % (4158477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.44/3.85 % (4158477)CaDiCaL version: 2.1.3
% 20.44/3.85 % (4158477)Termination reason: Refutation not found, incomplete strategy
% 20.44/3.85 % (4158477)Time elapsed: 0.009 s
% 20.44/3.85 % (4158477)Peak memory usage: 89 MB
% 20.44/3.85 % (4158477)Instructions burned: 14 (million)
% 20.44/3.85 % (4158478)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2778718944:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 20.44/3.85 % (4158470)------------------------------
% 20.44/3.85 % (4158470)------------------------------
% 20.44/3.85 % (4158473)Instruction limit reached!
% 20.44/3.85 % (4158473)------------------------------
% 20.44/3.85 % (4158473)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.44/3.85 % (4158473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.44/3.85 % (4158473)CaDiCaL version: 2.1.3
% 20.44/3.85 % (4158473)Termination reason: Instruction limit
% 20.44/3.85 % (4158473)Termination phase: Saturation
% 20.44/3.85 % (4158473)Time elapsed: 0.297 s
% 20.44/3.85 % (4158473)Peak memory usage: 101 MB
% 20.44/3.85 % (4158473)Instructions burned: 910 (million)
% 20.44/3.85 % (4158481)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=1646310150:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2988 on theBenchmark for (2988ds/134Mi)
% 20.44/3.85 % (4158477)------------------------------
% 20.44/3.85 % (4158477)------------------------------
% 20.44/3.85 % (4158482)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=3150555028:st=8:i=592:sd=3:ep=RST:ss=axioms_2987 on theBenchmark for (2987ds/592Mi)
% 20.44/3.85 % (4158481)Instruction limit reached!
% 20.44/3.85 % (4158481)------------------------------
% 20.44/3.85 % (4158481)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.44/3.85 % (4158481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.44/3.85 % (4158481)CaDiCaL version: 2.1.3
% 20.44/3.85 % (4158481)Termination reason: Instruction limit
% 20.44/3.85 % (4158481)Termination phase: Saturation
% 20.44/3.85 % (4158481)Time elapsed: 0.079 s
% 20.44/3.85 % (4158481)Peak memory usage: 91 MB
% 20.44/3.85 % (4158481)Instructions burned: 135 (million)
% 20.44/3.85 % (4158485)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=1419067717:st=3:i=13193:sd=3:ss=axioms_2986 on theBenchmark for (2986ds/13193Mi)
% 20.44/3.85 % (4158482)Instruction limit reached!
% 20.44/3.85 % (4158482)------------------------------
% 20.44/3.85 % (4158482)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.44/3.85 % (4158482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.44/3.85 % (4158482)CaDiCaL version: 2.1.3
% 20.44/3.85 % (4158482)Termination reason: Instruction limit
% 20.44/3.85 % (4158482)Termination phase: Saturation
% 20.44/3.85 % (4158482)Time elapsed: 0.203 s
% 20.44/3.85 % (4158482)Peak memory usage: 99 MB
% 20.44/3.85 % (4158482)Instructions burned: 595 (million)
% 20.44/3.85 % (4158486)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=1718663547:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2985 on theBenchmark for (2985ds/125Mi)
% 20.44/3.85 % (4158486)Instruction limit reached!
% 20.44/3.85 % (4158486)------------------------------
% 20.44/3.85 % (4158486)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.44/3.85 % (4158486)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.44/3.85 % (4158486)CaDiCaL version: 2.1.3
% 20.44/3.85 % (4158486)Termination reason: Instruction limit
% 20.44/3.85 % (4158486)Termination phase: Saturation
% 20.44/3.85 % (4158486)Time elapsed: 0.077 s
% 20.44/3.85 % (4158486)Peak memory usage: 91 MB
% 20.44/3.85 % (4158486)Instructions burned: 126 (million)
% 20.44/3.85 % (4158488)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=2483653850:i=134:gtgl=5:slsql=off:gtg=exists_sym_2984 on theBenchmark for (2984ds/134Mi)
% 20.44/3.85 % (4158488)Instruction limit reached!
% 20.44/3.85 % (4158488)------------------------------
% 20.44/3.85 % (4158488)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.44/3.85 % (4158488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.44/3.85 % (4158488)CaDiCaL version: 2.1.3
% 20.44/3.85 % (4158488)Termination reason: Instruction limit
% 20.44/3.85 % (4158488)Termination phase: Saturation
% 20.44/3.85 % (4158488)Time elapsed: 0.048 s
% 20.44/3.85 % (4158488)Peak memory usage: 91 MB
% 20.44/3.85 % (4158488)Instructions burned: 136 (million)
% 20.44/3.85 % (4158490)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=4009694322:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2983 on theBenchmark for (2983ds/141Mi)
% 20.44/3.85 % (4158490)Refutation not found, incomplete strategy
% 20.44/3.85 % (4158490)------------------------------
% 20.44/3.85 % (4158490)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.44/3.85 % (4158490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.44/3.85 % (4158490)CaDiCaL version: 2.1.3
% 20.44/3.85 % (4158490)Termination reason: Refutation not found, incomplete strategy
% 20.44/3.85 % (4158490)Time elapsed: 0.002 s
% 20.44/3.85 % (4158490)Peak memory usage: 88 MB
% 20.44/3.85 % (4158490)Instructions burned: 1 (million)
% 20.44/3.85 % (4158492)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=238374343:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2982 on theBenchmark for (2982ds/431Mi)
% 20.44/3.85 % (4158492)Refutation not found, incomplete strategy
% 20.44/3.85 % (4158492)------------------------------
% 20.44/3.85 % (4158492)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.44/3.85 % (4158492)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.44/3.85 % (4158492)CaDiCaL version: 2.1.3
% 20.44/3.85 % (4158492)Termination reason: Refutation not found, incomplete strategy
% 20.44/3.85 % (4158492)Time elapsed: 0.002 s
% 20.44/3.85 % (4158492)Peak memory usage: 89 MB
% 20.44/3.85 % (4158492)Instructions burned: 3 (million)
% 20.44/3.85 % (4158492)------------------------------
% 20.44/3.85 % (4158492)------------------------------
% 20.44/3.85 % (4158490)------------------------------
% 20.44/3.85 % (4158490)------------------------------
% 20.44/3.85 % (4158495)lrs+1010_1_ncem=casc2026/models/loop6.pt:sil=64000:tgt=full:npcc=on:prc=on:urr=ec_only:bsr=on:fd=preordered:gs=on:sac=on:newcnf=on:random_seed=2179000573:i=6060:aac=none:ins=25_2979 on theBenchmark for (2979ds/6060Mi)
% 20.44/3.85 % (4158496)lrs+10_16_anc=all:slsqr=32,1:sil=8000:avsql=on:sp=unary_frequency:lcm=predicate:urr=full:rp=on:br=off:slsqc=4:flr=on:sac=on:slsq=on:avsqc=1:random_seed=1636180903:avsq=on:s2a=on:i=150:kws=precedence:nicw=on:gsp=on:rawr=on_2979 on theBenchmark for (2979ds/150Mi)
% 20.44/3.85 % (4158496)Instruction limit reached!
% 20.44/3.85 % (4158496)------------------------------
% 20.44/3.85 % (4158496)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.44/3.85 % (4158496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.44/3.85 % (4158496)CaDiCaL version: 2.1.3
% 20.44/3.85 % (4158496)Termination reason: Instruction limit
% 20.44/3.85 % (4158496)Termination phase: Saturation
% 20.44/3.85 % (4158496)Time elapsed: 0.087 s
% 20.44/3.85 % (4158496)Peak memory usage: 91 MB
% 20.44/3.85 % (4158496)Instructions burned: 151 (million)
% 20.44/3.85 % (4158466)Instruction limit reached!
% 20.44/3.85 % (4158466)------------------------------
% 20.44/3.85 % (4158466)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.44/3.85 % (4158466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.44/3.85 % (4158466)CaDiCaL version: 2.1.3
% 20.44/3.85 % (4158466)Termination reason: Instruction limit
% 20.44/3.85 % (4158466)Termination phase: Saturation
% 20.44/3.85 % (4158466)Time elapsed: 1.603 s
% 20.44/3.85 % (4158466)Peak memory usage: 143 MB
% 20.44/3.85 % (4158466)Instructions burned: 2350 (million)
% 20.44/3.85 % (4158499)lrs+1010_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=ground:npcc=on:sp=arity:urr=on:random_seed=3925472197:i=14155:bd=all_2976 on theBenchmark for (2976ds/14155Mi)
% 20.44/3.85 % (4158500)lrs+10_1024_sil=16000:plsq=on:plsqr=32,1:sos=all:fs=off:gs=on:newcnf=on:random_seed=2129595697:i=667:av=off:fsr=off_2976 on theBenchmark for (2976ds/667Mi)
% 20.44/3.85 % (4158500)Refutation not found, incomplete strategy
% 20.44/3.85 % (4158500)------------------------------
% 20.44/3.85 % (4158500)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.44/3.85 % (4158500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.44/3.85 % (4158500)CaDiCaL version: 2.1.3
% 20.44/3.85 % (4158500)Termination reason: Refutation not found, incomplete strategy
% 20.44/3.85 % (4158500)Time elapsed: 0.008 s
% 20.44/3.85 % (4158500)Peak memory usage: 89 MB
% 20.44/3.85 % (4158500)Instructions burned: 13 (million)
% 20.44/3.85 % (4158444)First to succeed.
% 20.44/3.85 % (4158444)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4158438"
% 20.44/3.85 % (4158500)------------------------------
% 20.44/3.85 % (4158500)------------------------------
% 20.44/3.85 % (4158503)ott-1011_3:1_anc=all_dependent:to=lpo:sil=8000:drc=ordering:sas=cadical:fdtod=off:sp=reverse_frequency:spb=goal_then_units:urr=full:lftc=20:newcnf=on:random_seed=90033674:s2a=on:i=185:s2at=1.8:fdi=4_2972 on theBenchmark for (2972ds/185Mi)
% 20.44/3.85 % (4158444)Refutation found. Thanks to Tanya!
% 20.44/3.85 % SZS status Theorem for theBenchmark
% 20.44/3.85 % SZS output start Proof for theBenchmark
% See solution above
% 21.80/4.05 % (4158444)------------------------------
% 21.80/4.05 % (4158444)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.80/4.05 % (4158444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.80/4.05 % (4158444)CaDiCaL version: 2.1.3
% 21.80/4.05 % (4158444)Termination reason: Refutation
% 21.80/4.05 % (4158444)Time elapsed: 2.561 s
% 21.80/4.05 % (4158444)Peak memory usage: 156 MB
% 21.80/4.05 % (4158444)Instructions burned: 3939 (million)
% 21.80/4.05 % (4158444)------------------------------
% 21.80/4.05 % (4158444)------------------------------
% 21.80/4.05 % (4158438)Success in time 3.001 s
% 21.80/4.05 % Vampire exiting
%------------------------------------------------------------------------------