%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU346+2 : 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 : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:48:27 PM UTC 2026
% Result : Theorem 11.09s 2.72s
% Output : Refutation 13.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 41
% Syntax : Number of formulae : 338 ( 62 unt; 14 def)
% Number of atoms : 1265 ( 149 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1567 ( 640 ~; 718 |; 146 &)
% ( 24 <=>; 37 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 42 ( 40 usr; 11 prp; 0-3 aty)
% Number of functors : 30 ( 30 usr; 7 con; 0-4 aty)
% Number of variables : 338 ( 0 sgn 319 !; 19 ?)
% 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(f64,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(f82,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(f95,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> cast_to_el_of_LattPOSet(X0,X1) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattice3) ).
fof(f118,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(f138,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(f148,axiom,
! [X0] :
( strict_latt_str(boole_lattice(X0))
& latt_str(boole_lattice(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice3) ).
fof(f163,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(f173,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) )
=> ( strict_rel_str(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& transitive_relstr(poset_of_lattice(X0))
& antisymmetric_relstr(poset_of_lattice(X0))
& rel_str(poset_of_lattice(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_lattice3) ).
fof(f179,axiom,
! [X0,X1] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0)
& element(X1,the_carrier(X0)) )
=> element(cast_to_el_of_LattPOSet(X0,X1),the_carrier(poset_of_lattice(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_lattice3) ).
fof(f203,axiom,
! [X0] :
( rel_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
fof(f206,axiom,
! [X0] :
( join_semilatt_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).
fof(f207,axiom,
! [X0] :
( latt_str(X0)
=> ( meet_semilatt_str(X0)
& join_semilatt_str(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(f244,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f254,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)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_lattice3) ).
fof(f285,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) )
=> ( ~ empty_carrier(poset_of_lattice(X0))
& strict_rel_str(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& transitive_relstr(poset_of_lattice(X0))
& antisymmetric_relstr(poset_of_lattice(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_lattice3) ).
fof(f302,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(f330,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
=> element(X0,powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l71_subset_1) ).
fof(f367,axiom,
! [X0,X1,X2,X3] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0)
& ~ empty_carrier(X1)
& lattice(X1)
& latt_str(X1)
& element(X2,the_carrier(X0))
& element(X3,the_carrier(X1)) )
=> k10_filter_1(X0,X1,X2,X3) = ordered_pair(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k10_filter_1) ).
fof(f368,axiom,
! [X0,X1,X2,X3] :
( ( ~ empty(X0)
& ~ empty(X1)
& element(X2,X0)
& element(X3,X1) )
=> ordered_pair_as_product_element(X0,X1,X2,X3) = ordered_pair(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_domain_1) ).
fof(f370,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) )
=> k2_lattice3(X0) = relation_of_lattice(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_lattice3) ).
fof(f380,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(f384,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(f447,axiom,
! [X0] :
( one_sorted_str(X0)
=> cast_as_carrier_subset(X0) = the_carrier(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_pre_topc) ).
fof(f528,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0))
<=> below_refl(X0,X1,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_filter_1) ).
fof(f600,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f610,conjecture,
! [X0] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( below_refl(X0,X1,X2)
<=> related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_lattice3) ).
fof(f611,negated_conjecture,
~ ! [X0] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( below_refl(X0,X1,X2)
<=> related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f610]) ).
fof(f692,plain,
! [X0] :
( X0 = rel_str_of(the_carrier(X0),the_InternalRel(X0))
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f693,plain,
! [X0] :
( X0 = rel_str_of(the_carrier(X0),the_InternalRel(X0))
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f692]) ).
fof(f768,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,[],[f64]) ).
fof(f769,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,[],[f768]) ).
fof(f786,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,[],[f82]) ).
fof(f787,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,[],[f786]) ).
fof(f800,plain,
! [X0] :
( ! [X1] :
( cast_to_el_of_LattPOSet(X0,X1) = X1
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f95]) ).
fof(f801,plain,
! [X0] :
( ! [X1] :
( cast_to_el_of_LattPOSet(X0,X1) = X1
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f800]) ).
fof(f847,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,[],[f138]) ).
fof(f865,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,[],[f163]) ).
fof(f866,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,[],[f865]) ).
fof(f871,plain,
! [X0] :
( ( strict_rel_str(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& transitive_relstr(poset_of_lattice(X0))
& antisymmetric_relstr(poset_of_lattice(X0))
& rel_str(poset_of_lattice(X0)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f173]) ).
fof(f872,plain,
! [X0] :
( ( strict_rel_str(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& transitive_relstr(poset_of_lattice(X0))
& antisymmetric_relstr(poset_of_lattice(X0))
& rel_str(poset_of_lattice(X0)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f871]) ).
fof(f876,plain,
! [X0,X1] :
( element(cast_to_el_of_LattPOSet(X0,X1),the_carrier(poset_of_lattice(X0)))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0)
| ~ element(X1,the_carrier(X0)) ),
inference(ennf_transformation,[],[f179]) ).
fof(f877,plain,
! [X0,X1] :
( element(cast_to_el_of_LattPOSet(X0,X1),the_carrier(poset_of_lattice(X0)))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0)
| ~ element(X1,the_carrier(X0)) ),
inference(flattening,[],[f876]) ).
fof(f905,plain,
! [X0] :
( one_sorted_str(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f203]) ).
fof(f907,plain,
! [X0] :
( one_sorted_str(X0)
| ~ join_semilatt_str(X0) ),
inference(ennf_transformation,[],[f206]) ).
fof(f908,plain,
! [X0] :
( ( meet_semilatt_str(X0)
& join_semilatt_str(X0) )
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f207]) ).
fof(f935,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f244]) ).
fof(f936,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f935]) ).
fof(f983,plain,
! [X0] :
( ( ~ empty_carrier(poset_of_lattice(X0))
& strict_rel_str(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& transitive_relstr(poset_of_lattice(X0))
& antisymmetric_relstr(poset_of_lattice(X0)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f285]) ).
fof(f984,plain,
! [X0] :
( ( ~ empty_carrier(poset_of_lattice(X0))
& strict_rel_str(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& transitive_relstr(poset_of_lattice(X0))
& antisymmetric_relstr(poset_of_lattice(X0)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f983]) ).
fof(f1010,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,[],[f302]) ).
fof(f1038,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) ),
inference(ennf_transformation,[],[f330]) ).
fof(f1054,plain,
! [X0,X1,X2,X3] :
( k10_filter_1(X0,X1,X2,X3) = ordered_pair(X2,X3)
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X0))
| ~ element(X3,the_carrier(X1)) ),
inference(ennf_transformation,[],[f367]) ).
fof(f1055,plain,
! [X0,X1,X2,X3] :
( k10_filter_1(X0,X1,X2,X3) = ordered_pair(X2,X3)
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X0))
| ~ element(X3,the_carrier(X1)) ),
inference(flattening,[],[f1054]) ).
fof(f1056,plain,
! [X0,X1,X2,X3] :
( ordered_pair_as_product_element(X0,X1,X2,X3) = ordered_pair(X2,X3)
| empty(X0)
| empty(X1)
| ~ element(X2,X0)
| ~ element(X3,X1) ),
inference(ennf_transformation,[],[f368]) ).
fof(f1057,plain,
! [X0,X1,X2,X3] :
( ordered_pair_as_product_element(X0,X1,X2,X3) = ordered_pair(X2,X3)
| empty(X0)
| empty(X1)
| ~ element(X2,X0)
| ~ element(X3,X1) ),
inference(flattening,[],[f1056]) ).
fof(f1060,plain,
! [X0] :
( k2_lattice3(X0) = relation_of_lattice(X0)
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f370]) ).
fof(f1061,plain,
! [X0] :
( k2_lattice3(X0) = relation_of_lattice(X0)
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f1060]) ).
fof(f1080,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,[],[f384]) ).
fof(f1081,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,[],[f1080]) ).
fof(f1182,plain,
! [X0] :
( cast_as_carrier_subset(X0) = the_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f447]) ).
fof(f1295,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0))
<=> below_refl(X0,X1,X2) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f528]) ).
fof(f1296,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0))
<=> below_refl(X0,X1,X2) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f1295]) ).
fof(f1396,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( below_refl(X0,X1,X2)
<~> related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2)) )
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) )
& ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) ),
inference(ennf_transformation,[],[f611]) ).
fof(f1397,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( below_refl(X0,X1,X2)
<~> related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2)) )
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) )
& ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) ),
inference(flattening,[],[f1396]) ).
fof(f1558,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,[],[f769]) ).
fof(f1559,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,[],[f1558]) ).
fof(f1560,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,[],[f1559]) ).
fof(f1561,plain,
! [X0,X1] :
( ( ( X1 = boole_lattice(X0)
| powerset(X0) != the_carrier(X1)
| ( ( apply_binary(the_L_join(X1),sK82(X0,X1),sK83(X0,X1)) != subset_union2(X0,sK82(X0,X1),sK83(X0,X1))
| apply_binary(the_L_meet(X1),sK82(X0,X1),sK83(X0,X1)) != subset_intersection2(X0,sK82(X0,X1),sK83(X0,X1)) )
& element(sK83(X0,X1),powerset(X0))
& element(sK82(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,[sK82,sK83]),skolemize(X2,sK82(X0,X1)),skolemize(X3,sK83(X0,X1))],[f1560]) ).
fof(f1722,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,[],[f847]) ).
fof(f1757,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ( ~ in(sK185(X0,X1),X1)
& in(sK185(X0,X1),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK185]),skolemize(X2,sK185(X0,X1))],[f1038]) ).
fof(f1795,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,[],[f380]) ).
fof(f1799,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,[],[f1081]) ).
fof(f2084,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0))
| ~ below_refl(X0,X1,X2) )
& ( below_refl(X0,X1,X2)
| ~ in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0)) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(nnf_transformation,[],[f1296]) ).
fof(f2131,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2))
| ~ below_refl(X0,X1,X2) )
& ( related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2))
| below_refl(X0,X1,X2) )
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) )
& ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) ),
inference(nnf_transformation,[],[f1397]) ).
fof(f2132,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2))
| ~ below_refl(X0,X1,X2) )
& ( related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2))
| below_refl(X0,X1,X2) )
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) )
& ~ empty_carrier(X0)
& lattice(X0)
& latt_str(X0) ),
inference(flattening,[],[f2131]) ).
fof(f2133,plain,
( ( ~ related_reflexive(poset_of_lattice(sK491),cast_to_el_of_LattPOSet(sK491,sK492),cast_to_el_of_LattPOSet(sK491,sK493))
| ~ below_refl(sK491,sK492,sK493) )
& ( related_reflexive(poset_of_lattice(sK491),cast_to_el_of_LattPOSet(sK491,sK492),cast_to_el_of_LattPOSet(sK491,sK493))
| below_refl(sK491,sK492,sK493) )
& element(sK493,the_carrier(sK491))
& element(sK492,the_carrier(sK491))
& ~ empty_carrier(sK491)
& lattice(sK491)
& latt_str(sK491) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK491,sK492,sK493]),skolemize(X0,sK491),skolemize(X1,sK492),skolemize(X2,sK493)],[f2132]) ).
fof(f2142,plain,
! [X0] :
( ~ strict_rel_str(X0)
| rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f693]) ).
fof(f2320,plain,
! [X0,X1] :
( powerset(X0) = the_carrier(X1)
| boole_lattice(X0) != X1
| ~ strict_latt_str(X1)
| ~ latt_str(X1) ),
inference(cnf_transformation,[],[f1561]) ).
fof(f2393,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,[],[f787]) ).
fof(f2447,plain,
! [X0,X1] :
( ~ element(X1,the_carrier(X0))
| cast_to_el_of_LattPOSet(X0,X1) = X1
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f801]) ).
fof(f2539,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f118]) ).
fof(f2612,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,[],[f1722]) ).
fof(f2613,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,[],[f1722]) ).
fof(f2622,plain,
! [X0] : latt_str(boole_lattice(X0)),
inference(cnf_transformation,[],[f148]) ).
fof(f2631,plain,
! [X0] :
( relation_of2_as_subset(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f866]) ).
fof(f2640,plain,
! [X0] :
( rel_str(poset_of_lattice(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f872]) ).
fof(f2647,plain,
! [X0,X1] :
( element(cast_to_el_of_LattPOSet(X0,X1),the_carrier(poset_of_lattice(X0)))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0)
| ~ element(X1,the_carrier(X0)) ),
inference(cnf_transformation,[],[f877]) ).
fof(f2668,plain,
! [X0] :
( ~ rel_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f905]) ).
fof(f2670,plain,
! [X0] :
( ~ join_semilatt_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f907]) ).
fof(f2671,plain,
! [X0] :
( ~ latt_str(X0)
| join_semilatt_str(X0) ),
inference(cnf_transformation,[],[f908]) ).
fof(f2730,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f936]) ).
fof(f2749,plain,
! [X0] : lattice(boole_lattice(X0)),
inference(cnf_transformation,[],[f254]) ).
fof(f2756,plain,
! [X0] : strict_latt_str(boole_lattice(X0)),
inference(cnf_transformation,[],[f254]) ).
fof(f2757,plain,
! [X0] : ~ empty_carrier(boole_lattice(X0)),
inference(cnf_transformation,[],[f254]) ).
fof(f2845,plain,
! [X0] :
( reflexive_relstr(poset_of_lattice(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f984]) ).
fof(f2846,plain,
! [X0] :
( strict_rel_str(poset_of_lattice(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f984]) ).
fof(f2847,plain,
! [X0] :
( ~ empty_carrier(poset_of_lattice(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f984]) ).
fof(f2883,plain,
! [X2,X3,X0,X1] :
( rel_str_of(X0,X1) != rel_str_of(X2,X3)
| X1 = X3
| ~ relation_of2(X1,X0,X0) ),
inference(cnf_transformation,[],[f1010]) ).
fof(f2935,plain,
! [X0,X1] :
( in(sK185(X0,X1),X0)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f1757]) ).
fof(f2936,plain,
! [X0,X1] :
( ~ in(sK185(X0,X1),X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f1757]) ).
fof(f3058,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X2,X3) = k10_filter_1(X0,X1,X2,X3)
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X0))
| ~ element(X3,the_carrier(X1)) ),
inference(cnf_transformation,[],[f1055]) ).
fof(f3059,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X2,X3) = ordered_pair_as_product_element(X0,X1,X2,X3)
| empty(X0)
| empty(X1)
| ~ element(X2,X0)
| ~ element(X3,X1) ),
inference(cnf_transformation,[],[f1057]) ).
fof(f3061,plain,
! [X0] :
( ~ lattice(X0)
| empty_carrier(X0)
| k2_lattice3(X0) = relation_of_lattice(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f1061]) ).
fof(f3071,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f1795]) ).
fof(f3079,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,[],[f1799]) ).
fof(f3080,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,[],[f1799]) ).
fof(f3586,plain,
! [X0] :
( ~ one_sorted_str(X0)
| the_carrier(X0) = cast_as_carrier_subset(X0) ),
inference(cnf_transformation,[],[f1182]) ).
fof(f3713,plain,
! [X2,X0,X1] :
( ~ in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0))
| below_refl(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f2084]) ).
fof(f3714,plain,
! [X2,X0,X1] :
( in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),relation_of_lattice(X0))
| ~ below_refl(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f2084]) ).
fof(f3850,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f600]) ).
fof(f3863,plain,
latt_str(sK491),
inference(cnf_transformation,[],[f2133]) ).
fof(f3864,plain,
lattice(sK491),
inference(cnf_transformation,[],[f2133]) ).
fof(f3865,plain,
~ empty_carrier(sK491),
inference(cnf_transformation,[],[f2133]) ).
fof(f3866,plain,
element(sK492,the_carrier(sK491)),
inference(cnf_transformation,[],[f2133]) ).
fof(f3867,plain,
element(sK493,the_carrier(sK491)),
inference(cnf_transformation,[],[f2133]) ).
fof(f3868,plain,
( related_reflexive(poset_of_lattice(sK491),cast_to_el_of_LattPOSet(sK491,sK492),cast_to_el_of_LattPOSet(sK491,sK493))
| below_refl(sK491,sK492,sK493) ),
inference(cnf_transformation,[],[f2133]) ).
fof(f3869,plain,
( ~ related_reflexive(poset_of_lattice(sK491),cast_to_el_of_LattPOSet(sK491,sK492),cast_to_el_of_LattPOSet(sK491,sK493))
| ~ below_refl(sK491,sK492,sK493) ),
inference(cnf_transformation,[],[f2133]) ).
fof(f3908,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f2539,f3850]) ).
fof(f4020,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),the_InternalRel(X0))
| related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(definition_unfolding,[],[f2613,f3908]) ).
fof(f4021,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),the_InternalRel(X0))
| ~ related(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0) ),
inference(definition_unfolding,[],[f2612,f3908]) ).
fof(f4095,plain,
! [X2,X3,X0,X1] :
( ~ element(X3,the_carrier(X1))
| empty_carrier(X0)
| ~ lattice(X0)
| ~ latt_str(X0)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X2,the_carrier(X0))
| k10_filter_1(X0,X1,X2,X3) = unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ),
inference(definition_unfolding,[],[f3058,f3908]) ).
fof(f4096,plain,
! [X2,X3,X0,X1] :
( ~ element(X3,X1)
| empty(X0)
| empty(X1)
| ~ element(X2,X0)
| ordered_pair_as_product_element(X0,X1,X2,X3) = unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ),
inference(definition_unfolding,[],[f3059,f3908]) ).
fof(f4334,plain,
! [X0] :
( powerset(X0) = the_carrier(boole_lattice(X0))
| ~ strict_latt_str(boole_lattice(X0))
| ~ latt_str(boole_lattice(X0)) ),
inference(equality_resolution,[],[f2320]) ).
fof(f4550,definition,
sF497 = poset_of_lattice(sK491),
introduced(definition,[new_symbols(definition,[sF497])],[function_definition]) ).
fof(f4551,plain,
poset_of_lattice(sK491) = sF497,
inference(reorient_equations,[],[f4550]) ).
fof(f4552,definition,
sF498 = cast_to_el_of_LattPOSet(sK491,sK492),
introduced(definition,[new_symbols(definition,[sF498])],[function_definition]) ).
fof(f4553,plain,
cast_to_el_of_LattPOSet(sK491,sK492) = sF498,
inference(reorient_equations,[],[f4552]) ).
fof(f4554,definition,
sF499 = cast_to_el_of_LattPOSet(sK491,sK493),
introduced(definition,[new_symbols(definition,[sF499])],[function_definition]) ).
fof(f4555,plain,
cast_to_el_of_LattPOSet(sK491,sK493) = sF499,
inference(reorient_equations,[],[f4554]) ).
fof(f4556,plain,
( ~ related_reflexive(sF497,sF498,sF499)
| ~ below_refl(sK491,sK492,sK493) ),
inference(definition_folding,[],[f3869,f4555,f4553,f4551]) ).
fof(f4557,plain,
( related_reflexive(sF497,sF498,sF499)
| below_refl(sK491,sK492,sK493) ),
inference(definition_folding,[],[f3868,f4555,f4553,f4551]) ).
fof(f4558,definition,
sF500 = the_carrier(sK491),
introduced(definition,[new_symbols(definition,[sF500])],[function_definition]) ).
fof(f4559,plain,
the_carrier(sK491) = sF500,
inference(reorient_equations,[],[f4558]) ).
fof(f4560,plain,
element(sK493,sF500),
inference(definition_folding,[],[f3867,f4559]) ).
fof(f4561,plain,
element(sK492,sF500),
inference(definition_folding,[],[f3866,f4559]) ).
fof(f4584,definition,
( spl501_1
<=> below_refl(sK491,sK492,sK493) ),
introduced(definition,[new_symbols(definition,[spl501_1])],[avatar_definition]) ).
fof(f4585,plain,
( ~ below_refl(sK491,sK492,sK493)
| spl501_1 ),
inference(avatar_component_clause,[],[f4584]) ).
fof(f4586,plain,
( below_refl(sK491,sK492,sK493)
| ~ spl501_1 ),
inference(avatar_component_clause,[],[f4584]) ).
fof(f4588,definition,
( spl501_2
<=> related_reflexive(sF497,sF498,sF499) ),
introduced(definition,[new_symbols(definition,[spl501_2])],[avatar_definition]) ).
fof(f4589,plain,
( ~ related_reflexive(sF497,sF498,sF499)
| spl501_2 ),
inference(avatar_component_clause,[],[f4588]) ).
fof(f4590,plain,
( related_reflexive(sF497,sF498,sF499)
| ~ spl501_2 ),
inference(avatar_component_clause,[],[f4588]) ).
fof(f4591,plain,
( spl501_1
| spl501_2 ),
inference(avatar_split_clause,[],[f4557,f4588,f4584]) ).
fof(f4592,plain,
( ~ spl501_1
| ~ spl501_2 ),
inference(avatar_split_clause,[],[f4556,f4588,f4584]) ).
fof(f4893,plain,
! [X0] :
( powerset(X0) = the_carrier(boole_lattice(X0))
| ~ latt_str(boole_lattice(X0)) ),
inference(forward_subsumption_resolution,[],[f4334,f2756]) ).
fof(f4911,plain,
! [X0] : powerset(X0) = the_carrier(boole_lattice(X0)),
inference(forward_subsumption_resolution,[],[f4893,f2622]) ).
fof(f4912,plain,
( element(sF499,the_carrier(poset_of_lattice(sK491)))
| empty_carrier(sK491)
| ~ lattice(sK491)
| ~ latt_str(sK491)
| ~ element(sK493,the_carrier(sK491)) ),
inference(superposition,[],[f2647,f4555]) ).
fof(f4913,plain,
( element(sF498,the_carrier(poset_of_lattice(sK491)))
| empty_carrier(sK491)
| ~ lattice(sK491)
| ~ latt_str(sK491)
| ~ element(sK492,the_carrier(sK491)) ),
inference(superposition,[],[f2647,f4553]) ).
fof(f4916,plain,
( element(sF498,the_carrier(poset_of_lattice(sK491)))
| ~ lattice(sK491)
| ~ latt_str(sK491)
| ~ element(sK492,the_carrier(sK491)) ),
inference(forward_subsumption_resolution,[],[f4913,f3865]) ).
fof(f4917,plain,
( element(sF499,the_carrier(poset_of_lattice(sK491)))
| ~ lattice(sK491)
| ~ latt_str(sK491)
| ~ element(sK493,the_carrier(sK491)) ),
inference(forward_subsumption_resolution,[],[f4912,f3865]) ).
fof(f4919,plain,
( element(sF498,the_carrier(poset_of_lattice(sK491)))
| ~ latt_str(sK491)
| ~ element(sK492,the_carrier(sK491)) ),
inference(forward_subsumption_resolution,[],[f4916,f3864]) ).
fof(f4920,plain,
( element(sF499,the_carrier(poset_of_lattice(sK491)))
| ~ latt_str(sK491)
| ~ element(sK493,the_carrier(sK491)) ),
inference(forward_subsumption_resolution,[],[f4917,f3864]) ).
fof(f4922,plain,
( element(sF498,the_carrier(poset_of_lattice(sK491)))
| ~ element(sK492,the_carrier(sK491)) ),
inference(forward_subsumption_resolution,[],[f4919,f3863]) ).
fof(f4923,plain,
( element(sF499,the_carrier(poset_of_lattice(sK491)))
| ~ element(sK493,the_carrier(sK491)) ),
inference(forward_subsumption_resolution,[],[f4920,f3863]) ).
fof(f4925,plain,
( element(sF498,the_carrier(sF497))
| ~ element(sK492,the_carrier(sK491)) ),
inference(forward_demodulation,[],[f4922,f4551]) ).
fof(f4926,plain,
( element(sF499,the_carrier(sF497))
| ~ element(sK493,the_carrier(sK491)) ),
inference(forward_demodulation,[],[f4923,f4551]) ).
fof(f4927,plain,
( ~ element(sK492,sF500)
| element(sF498,the_carrier(sF497)) ),
inference(forward_demodulation,[],[f4925,f4559]) ).
fof(f4928,plain,
( ~ element(sK493,sF500)
| element(sF499,the_carrier(sF497)) ),
inference(forward_demodulation,[],[f4926,f4559]) ).
fof(f4929,plain,
element(sF498,the_carrier(sF497)),
inference(forward_subsumption_resolution,[],[f4927,f4561]) ).
fof(f4930,plain,
element(sF499,the_carrier(sF497)),
inference(forward_subsumption_resolution,[],[f4928,f4560]) ).
fof(f4937,plain,
! [X0] :
( ~ element(X0,sF500)
| cast_to_el_of_LattPOSet(sK491,X0) = X0
| empty_carrier(sK491)
| ~ lattice(sK491)
| ~ latt_str(sK491) ),
inference(superposition,[],[f2447,f4559]) ).
fof(f4938,plain,
! [X0] :
( ~ element(X0,sF500)
| cast_to_el_of_LattPOSet(sK491,X0) = X0
| ~ lattice(sK491)
| ~ latt_str(sK491) ),
inference(forward_subsumption_resolution,[],[f4937,f3865]) ).
fof(f4948,definition,
( spl501_63
<=> empty_carrier(sF497) ),
introduced(definition,[new_symbols(definition,[spl501_63])],[avatar_definition]) ).
fof(f4949,plain,
( ~ empty_carrier(sF497)
| spl501_63 ),
inference(avatar_component_clause,[],[f4948]) ).
fof(f4966,plain,
! [X0] :
( ~ element(X0,sF500)
| cast_to_el_of_LattPOSet(sK491,X0) = X0
| ~ latt_str(sK491) ),
inference(forward_subsumption_resolution,[],[f4938,f3864]) ).
fof(f4967,plain,
! [X0] :
( ~ element(X0,sF500)
| cast_to_el_of_LattPOSet(sK491,X0) = X0 ),
inference(forward_subsumption_resolution,[],[f4966,f3863]) ).
fof(f4968,plain,
sK492 = cast_to_el_of_LattPOSet(sK491,sK492),
inference(resolution,[],[f4967,f4561]) ).
fof(f4969,plain,
sK493 = cast_to_el_of_LattPOSet(sK491,sK493),
inference(resolution,[],[f4967,f4560]) ).
fof(f4970,plain,
sK493 = sF499,
inference(forward_demodulation,[],[f4969,f4555]) ).
fof(f4971,plain,
sK492 = sF498,
inference(forward_demodulation,[],[f4968,f4553]) ).
fof(f4972,plain,
element(sK493,the_carrier(sF497)),
inference(superposition,[],[f4930,f4970]) ).
fof(f4975,plain,
element(sK492,the_carrier(sF497)),
inference(superposition,[],[f4929,f4971]) ).
fof(f4980,plain,
( related(sF497,sF498,sF499)
| empty_carrier(sF497)
| ~ reflexive_relstr(sF497)
| ~ rel_str(sF497)
| ~ element(sF498,the_carrier(sF497))
| ~ element(sF499,the_carrier(sF497))
| ~ spl501_2 ),
inference(resolution,[],[f3079,f4590]) ).
fof(f4983,plain,
( related(sF497,sF498,sF499)
| empty_carrier(sF497)
| ~ reflexive_relstr(sF497)
| ~ rel_str(sF497)
| ~ element(sF499,the_carrier(sF497))
| ~ spl501_2 ),
inference(forward_subsumption_resolution,[],[f4980,f4929]) ).
fof(f4985,plain,
( related(sF497,sF498,sF499)
| empty_carrier(sF497)
| ~ reflexive_relstr(sF497)
| ~ rel_str(sF497)
| ~ spl501_2 ),
inference(forward_subsumption_resolution,[],[f4983,f4930]) ).
fof(f4987,definition,
( spl501_67
<=> rel_str(sF497) ),
introduced(definition,[new_symbols(definition,[spl501_67])],[avatar_definition]) ).
fof(f4988,plain,
( rel_str(sF497)
| ~ spl501_67 ),
inference(avatar_component_clause,[],[f4987]) ).
fof(f4989,plain,
( ~ rel_str(sF497)
| spl501_67 ),
inference(avatar_component_clause,[],[f4987]) ).
fof(f4991,definition,
( spl501_68
<=> reflexive_relstr(sF497) ),
introduced(definition,[new_symbols(definition,[spl501_68])],[avatar_definition]) ).
fof(f4992,plain,
( reflexive_relstr(sF497)
| ~ spl501_68 ),
inference(avatar_component_clause,[],[f4991]) ).
fof(f4995,definition,
( spl501_69
<=> related(sF497,sK492,sK493) ),
introduced(definition,[new_symbols(definition,[spl501_69])],[avatar_definition]) ).
fof(f4996,plain,
( ~ related(sF497,sK492,sK493)
| spl501_69 ),
inference(avatar_component_clause,[],[f4995]) ).
fof(f4997,plain,
( related(sF497,sK492,sK493)
| ~ spl501_69 ),
inference(avatar_component_clause,[],[f4995]) ).
fof(f4999,plain,
( related(sF497,sF498,sK493)
| empty_carrier(sF497)
| ~ reflexive_relstr(sF497)
| ~ rel_str(sF497)
| ~ spl501_2 ),
inference(forward_demodulation,[],[f4985,f4970]) ).
fof(f5000,plain,
( related(sF497,sK492,sK493)
| empty_carrier(sF497)
| ~ reflexive_relstr(sF497)
| ~ rel_str(sF497)
| ~ spl501_2 ),
inference(forward_demodulation,[],[f4999,f4971]) ).
fof(f5001,plain,
( ~ spl501_67
| ~ spl501_68
| spl501_63
| spl501_69
| ~ spl501_2 ),
inference(avatar_split_clause,[],[f5000,f4588,f4995,f4948,f4991,f4987]) ).
fof(f5002,plain,
( ~ empty_carrier(sF497)
| empty_carrier(sK491)
| ~ lattice(sK491)
| ~ latt_str(sK491) ),
inference(superposition,[],[f2847,f4551]) ).
fof(f5003,plain,
( ~ empty_carrier(sF497)
| ~ lattice(sK491)
| ~ latt_str(sK491) ),
inference(forward_subsumption_resolution,[],[f5002,f3865]) ).
fof(f5004,plain,
( ~ empty_carrier(sF497)
| ~ latt_str(sK491) ),
inference(forward_subsumption_resolution,[],[f5003,f3864]) ).
fof(f5005,plain,
~ empty_carrier(sF497),
inference(forward_subsumption_resolution,[],[f5004,f3863]) ).
fof(f5006,plain,
~ spl501_63,
inference(avatar_split_clause,[],[f5005,f4948]) ).
fof(f5007,plain,
join_semilatt_str(sK491),
inference(resolution,[],[f2671,f3863]) ).
fof(f5061,plain,
! [X0,X1] :
( ~ in(ordered_pair_as_product_element(sF500,sF500,X0,X1),relation_of_lattice(sK491))
| below_refl(sK491,X0,X1)
| ~ element(X1,sF500)
| ~ element(X0,sF500)
| empty_carrier(sK491)
| ~ lattice(sK491)
| ~ latt_str(sK491) ),
inference(superposition,[],[f3713,f4559]) ).
fof(f5062,plain,
! [X0,X1] :
( ~ in(ordered_pair_as_product_element(sF500,sF500,X0,X1),relation_of_lattice(sK491))
| below_refl(sK491,X0,X1)
| ~ element(X1,sF500)
| ~ element(X0,sF500)
| ~ lattice(sK491)
| ~ latt_str(sK491) ),
inference(forward_subsumption_resolution,[],[f5061,f3865]) ).
fof(f5063,plain,
! [X0,X1] :
( ~ in(ordered_pair_as_product_element(sF500,sF500,X0,X1),relation_of_lattice(sK491))
| below_refl(sK491,X0,X1)
| ~ element(X1,sF500)
| ~ element(X0,sF500)
| ~ latt_str(sK491) ),
inference(forward_subsumption_resolution,[],[f5062,f3864]) ).
fof(f5064,plain,
! [X0,X1] :
( ~ in(ordered_pair_as_product_element(sF500,sF500,X0,X1),relation_of_lattice(sK491))
| below_refl(sK491,X0,X1)
| ~ element(X1,sF500)
| ~ element(X0,sF500) ),
inference(forward_subsumption_resolution,[],[f5063,f3863]) ).
fof(f5065,plain,
( strict_rel_str(sF497)
| empty_carrier(sK491)
| ~ lattice(sK491)
| ~ latt_str(sK491) ),
inference(superposition,[],[f2846,f4551]) ).
fof(f5066,plain,
( strict_rel_str(sF497)
| ~ lattice(sK491)
| ~ latt_str(sK491) ),
inference(forward_subsumption_resolution,[],[f5065,f3865]) ).
fof(f5067,plain,
( strict_rel_str(sF497)
| ~ latt_str(sK491) ),
inference(forward_subsumption_resolution,[],[f5066,f3864]) ).
fof(f5068,plain,
strict_rel_str(sF497),
inference(forward_subsumption_resolution,[],[f5067,f3863]) ).
fof(f5069,plain,
( reflexive_relstr(sF497)
| empty_carrier(sK491)
| ~ lattice(sK491)
| ~ latt_str(sK491) ),
inference(superposition,[],[f2845,f4551]) ).
fof(f5070,plain,
( reflexive_relstr(sF497)
| ~ lattice(sK491)
| ~ latt_str(sK491) ),
inference(forward_subsumption_resolution,[],[f5069,f3865]) ).
fof(f5071,plain,
( reflexive_relstr(sF497)
| ~ latt_str(sK491) ),
inference(forward_subsumption_resolution,[],[f5070,f3864]) ).
fof(f5072,plain,
reflexive_relstr(sF497),
inference(forward_subsumption_resolution,[],[f5071,f3863]) ).
fof(f5073,plain,
spl501_68,
inference(avatar_split_clause,[],[f5072,f4991]) ).
fof(f5100,plain,
( rel_str(sF497)
| empty_carrier(sK491)
| ~ lattice(sK491)
| ~ latt_str(sK491) ),
inference(superposition,[],[f2640,f4551]) ).
fof(f5101,plain,
( empty_carrier(sK491)
| ~ lattice(sK491)
| ~ latt_str(sK491)
| spl501_67 ),
inference(forward_subsumption_resolution,[],[f5100,f4989]) ).
fof(f5102,plain,
( ~ lattice(sK491)
| ~ latt_str(sK491)
| spl501_67 ),
inference(forward_subsumption_resolution,[],[f5101,f3865]) ).
fof(f5103,plain,
( ~ latt_str(sK491)
| spl501_67 ),
inference(forward_subsumption_resolution,[],[f5102,f3864]) ).
fof(f5104,plain,
( $false
| spl501_67 ),
inference(forward_subsumption_resolution,[],[f5103,f3863]) ).
fof(f5105,plain,
spl501_67,
inference(avatar_contradiction_clause,[],[f5104]) ).
fof(f5131,plain,
( ~ empty(sF500)
| empty_carrier(sK491)
| ~ one_sorted_str(sK491) ),
inference(superposition,[],[f2730,f4559]) ).
fof(f5132,plain,
( ~ empty(sF500)
| ~ one_sorted_str(sK491) ),
inference(forward_subsumption_resolution,[],[f5131,f3865]) ).
fof(f5134,definition,
( spl501_79
<=> one_sorted_str(sK491) ),
introduced(definition,[new_symbols(definition,[spl501_79])],[avatar_definition]) ).
fof(f5136,plain,
( ~ one_sorted_str(sK491)
| spl501_79 ),
inference(avatar_component_clause,[],[f5134]) ).
fof(f5138,definition,
( spl501_80
<=> empty(sF500) ),
introduced(definition,[new_symbols(definition,[spl501_80])],[avatar_definition]) ).
fof(f5140,plain,
( ~ empty(sF500)
| spl501_80 ),
inference(avatar_component_clause,[],[f5138]) ).
fof(f5141,plain,
( ~ spl501_79
| ~ spl501_80 ),
inference(avatar_split_clause,[],[f5132,f5138,f5134]) ).
fof(f5143,plain,
! [X0,X1] :
( in(ordered_pair_as_product_element(sF500,sF500,X0,X1),relation_of_lattice(sK491))
| ~ below_refl(sK491,X0,X1)
| ~ element(X1,sF500)
| ~ element(X0,sF500)
| empty_carrier(sK491)
| ~ lattice(sK491)
| ~ latt_str(sK491) ),
inference(superposition,[],[f3714,f4559]) ).
fof(f5145,plain,
! [X0,X1] :
( in(ordered_pair_as_product_element(sF500,sF500,X0,X1),relation_of_lattice(sK491))
| ~ below_refl(sK491,X0,X1)
| ~ element(X1,sF500)
| ~ element(X0,sF500)
| ~ lattice(sK491)
| ~ latt_str(sK491) ),
inference(forward_subsumption_resolution,[],[f5143,f3865]) ).
fof(f5146,plain,
! [X0,X1] :
( in(ordered_pair_as_product_element(sF500,sF500,X0,X1),relation_of_lattice(sK491))
| ~ below_refl(sK491,X0,X1)
| ~ element(X1,sF500)
| ~ element(X0,sF500)
| ~ latt_str(sK491) ),
inference(forward_subsumption_resolution,[],[f5145,f3864]) ).
fof(f5147,plain,
! [X0,X1] :
( in(ordered_pair_as_product_element(sF500,sF500,X0,X1),relation_of_lattice(sK491))
| ~ below_refl(sK491,X0,X1)
| ~ element(X1,sF500)
| ~ element(X0,sF500) ),
inference(forward_subsumption_resolution,[],[f5146,f3863]) ).
fof(f5158,plain,
( empty_carrier(sK491)
| poset_of_lattice(sK491) = rel_str_of(the_carrier(sK491),k2_lattice3(sK491))
| ~ latt_str(sK491) ),
inference(resolution,[],[f2393,f3864]) ).
fof(f5159,plain,
( poset_of_lattice(sK491) = rel_str_of(the_carrier(sK491),k2_lattice3(sK491))
| ~ latt_str(sK491) ),
inference(forward_subsumption_resolution,[],[f5158,f3865]) ).
fof(f5160,plain,
poset_of_lattice(sK491) = rel_str_of(the_carrier(sK491),k2_lattice3(sK491)),
inference(forward_subsumption_resolution,[],[f5159,f3863]) ).
fof(f5161,plain,
poset_of_lattice(sK491) = rel_str_of(sF500,k2_lattice3(sK491)),
inference(forward_demodulation,[],[f5160,f4559]) ).
fof(f5162,plain,
sF497 = rel_str_of(sF500,k2_lattice3(sK491)),
inference(forward_demodulation,[],[f5161,f4551]) ).
fof(f5163,plain,
one_sorted_str(sK491),
inference(resolution,[],[f2670,f5007]) ).
fof(f5164,plain,
( $false
| spl501_79 ),
inference(forward_subsumption_resolution,[],[f5163,f5136]) ).
fof(f5165,plain,
spl501_79,
inference(avatar_contradiction_clause,[],[f5164]) ).
fof(f5181,plain,
! [X2,X0,X1] :
( ~ element(X0,sF500)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| empty_carrier(sK491)
| ~ lattice(sK491)
| ~ latt_str(sK491)
| ~ element(X2,the_carrier(X1))
| k10_filter_1(X1,sK491,X2,X0) = unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)) ),
inference(superposition,[],[f4095,f4559]) ).
fof(f5182,plain,
! [X2,X0,X1] :
( ~ element(X0,sF500)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ lattice(sK491)
| ~ latt_str(sK491)
| ~ element(X2,the_carrier(X1))
| k10_filter_1(X1,sK491,X2,X0) = unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)) ),
inference(forward_subsumption_resolution,[],[f5181,f3865]) ).
fof(f5184,plain,
! [X2,X0,X1] :
( ~ element(X0,sF500)
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ latt_str(sK491)
| ~ element(X2,the_carrier(X1))
| k10_filter_1(X1,sK491,X2,X0) = unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)) ),
inference(forward_subsumption_resolution,[],[f5182,f3864]) ).
fof(f5185,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(X1))
| empty_carrier(X1)
| ~ lattice(X1)
| ~ latt_str(X1)
| ~ element(X0,sF500)
| k10_filter_1(X1,sK491,X2,X0) = unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)) ),
inference(forward_subsumption_resolution,[],[f5184,f3863]) ).
fof(f5192,plain,
! [X0,X1] :
( ~ element(X0,sF500)
| empty_carrier(sK491)
| ~ lattice(sK491)
| ~ latt_str(sK491)
| ~ element(X1,sF500)
| unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) = k10_filter_1(sK491,sK491,X0,X1) ),
inference(superposition,[],[f5185,f4559]) ).
fof(f5193,plain,
! [X0,X1] :
( ~ element(X0,sF500)
| ~ lattice(sK491)
| ~ latt_str(sK491)
| ~ element(X1,sF500)
| unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) = k10_filter_1(sK491,sK491,X0,X1) ),
inference(forward_subsumption_resolution,[],[f5192,f3865]) ).
fof(f5195,plain,
! [X0,X1] :
( ~ element(X0,sF500)
| ~ latt_str(sK491)
| ~ element(X1,sF500)
| unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) = k10_filter_1(sK491,sK491,X0,X1) ),
inference(forward_subsumption_resolution,[],[f5193,f3864]) ).
fof(f5196,plain,
! [X0,X1] :
( ~ element(X1,sF500)
| ~ element(X0,sF500)
| unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) = k10_filter_1(sK491,sK491,X0,X1) ),
inference(forward_subsumption_resolution,[],[f5195,f3863]) ).
fof(f5198,plain,
! [X0] :
( ~ element(X0,sF500)
| unordered_pair(unordered_pair(X0,sK493),unordered_pair(X0,X0)) = k10_filter_1(sK491,sK491,X0,sK493) ),
inference(resolution,[],[f5196,f4560]) ).
fof(f5199,plain,
unordered_pair(unordered_pair(sK492,sK493),unordered_pair(sK492,sK492)) = k10_filter_1(sK491,sK491,sK492,sK493),
inference(resolution,[],[f5198,f4561]) ).
fof(f5210,plain,
( relation_of2_as_subset(k2_lattice3(sK491),sF500,sF500)
| empty_carrier(sK491)
| ~ lattice(sK491)
| ~ latt_str(sK491) ),
inference(superposition,[],[f2631,f4559]) ).
fof(f5211,plain,
( relation_of2_as_subset(k2_lattice3(sK491),sF500,sF500)
| ~ lattice(sK491)
| ~ latt_str(sK491) ),
inference(forward_subsumption_resolution,[],[f5210,f3865]) ).
fof(f5212,plain,
( relation_of2_as_subset(k2_lattice3(sK491),sF500,sF500)
| ~ latt_str(sK491) ),
inference(forward_subsumption_resolution,[],[f5211,f3864]) ).
fof(f5213,plain,
relation_of2_as_subset(k2_lattice3(sK491),sF500,sF500),
inference(forward_subsumption_resolution,[],[f5212,f3863]) ).
fof(f5214,plain,
relation_of2(k2_lattice3(sK491),sF500,sF500),
inference(resolution,[],[f5213,f3071]) ).
fof(f5224,plain,
( empty_carrier(sK491)
| relation_of_lattice(sK491) = k2_lattice3(sK491)
| ~ latt_str(sK491) ),
inference(resolution,[],[f3061,f3864]) ).
fof(f5225,plain,
( relation_of_lattice(sK491) = k2_lattice3(sK491)
| ~ latt_str(sK491) ),
inference(forward_subsumption_resolution,[],[f5224,f3865]) ).
fof(f5226,plain,
relation_of_lattice(sK491) = k2_lattice3(sK491),
inference(forward_subsumption_resolution,[],[f5225,f3863]) ).
fof(f5227,plain,
! [X0,X1] :
( in(ordered_pair_as_product_element(sF500,sF500,X0,X1),k2_lattice3(sK491))
| ~ below_refl(sK491,X0,X1)
| ~ element(X1,sF500)
| ~ element(X0,sF500) ),
inference(superposition,[],[f5147,f5226]) ).
fof(f5228,plain,
! [X0,X1] :
( ~ in(ordered_pair_as_product_element(sF500,sF500,X0,X1),k2_lattice3(sK491))
| below_refl(sK491,X0,X1)
| ~ element(X1,sF500)
| ~ element(X0,sF500) ),
inference(superposition,[],[f5064,f5226]) ).
fof(f5256,plain,
( one_sorted_str(sF497)
| ~ spl501_67 ),
inference(resolution,[],[f2668,f4988]) ).
fof(f5257,plain,
( the_carrier(sF497) = cast_as_carrier_subset(sF497)
| ~ spl501_67 ),
inference(resolution,[],[f5256,f3586]) ).
fof(f5397,plain,
! [X0] :
( ~ in(k10_filter_1(sK491,sK491,sK492,sK493),the_InternalRel(X0))
| related(X0,sK492,sK493)
| ~ element(sK493,the_carrier(X0))
| ~ element(sK492,the_carrier(X0))
| ~ rel_str(X0) ),
inference(superposition,[],[f4020,f5199]) ).
fof(f5552,plain,
( sF497 = rel_str_of(the_carrier(sF497),the_InternalRel(sF497))
| ~ rel_str(sF497) ),
inference(resolution,[],[f2142,f5068]) ).
fof(f5553,plain,
( sF497 = rel_str_of(the_carrier(sF497),the_InternalRel(sF497))
| ~ spl501_67 ),
inference(forward_subsumption_resolution,[],[f5552,f4988]) ).
fof(f5555,plain,
( sF497 = rel_str_of(cast_as_carrier_subset(sF497),the_InternalRel(sF497))
| ~ spl501_67 ),
inference(forward_demodulation,[],[f5553,f5257]) ).
fof(f5576,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X0))
| empty_carrier(boole_lattice(X0))
| ~ lattice(boole_lattice(X0))
| ~ latt_str(boole_lattice(X0))
| ~ element(X2,sF500)
| unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)) = k10_filter_1(boole_lattice(X0),sK491,X1,X2) ),
inference(superposition,[],[f5185,f4911]) ).
fof(f5582,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X0))
| ~ lattice(boole_lattice(X0))
| ~ latt_str(boole_lattice(X0))
| ~ element(X2,sF500)
| unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)) = k10_filter_1(boole_lattice(X0),sK491,X1,X2) ),
inference(forward_subsumption_resolution,[],[f5576,f2757]) ).
fof(f5597,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X0))
| ~ latt_str(boole_lattice(X0))
| ~ element(X2,sF500)
| unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)) = k10_filter_1(boole_lattice(X0),sK491,X1,X2) ),
inference(forward_subsumption_resolution,[],[f5582,f2749]) ).
fof(f5610,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X0))
| ~ element(X2,sF500)
| unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)) = k10_filter_1(boole_lattice(X0),sK491,X1,X2) ),
inference(forward_subsumption_resolution,[],[f5597,f2622]) ).
fof(f6795,plain,
! [X0] :
( in(k10_filter_1(sK491,sK491,sK492,sK493),the_InternalRel(X0))
| ~ related(X0,sK492,sK493)
| ~ element(sK493,the_carrier(X0))
| ~ element(sK492,the_carrier(X0))
| ~ rel_str(X0) ),
inference(superposition,[],[f4021,f5199]) ).
fof(f6841,plain,
! [X0] :
( element(X0,powerset(X0))
| element(X0,powerset(X0)) ),
inference(resolution,[],[f2935,f2936]) ).
fof(f6843,plain,
! [X0] : element(X0,powerset(X0)),
inference(duplicate_literal_removal,[],[f6841]) ).
fof(f6847,plain,
! [X0,X1] :
( ~ element(X0,sF500)
| unordered_pair(unordered_pair(X1,X0),unordered_pair(X1,X1)) = k10_filter_1(boole_lattice(X1),sK491,X1,X0) ),
inference(resolution,[],[f6843,f5610]) ).
fof(f6873,plain,
! [X0] : unordered_pair(unordered_pair(X0,sK493),unordered_pair(X0,X0)) = k10_filter_1(boole_lattice(X0),sK491,X0,sK493),
inference(resolution,[],[f6847,f4560]) ).
fof(f6889,plain,
k10_filter_1(sK491,sK491,sK492,sK493) = k10_filter_1(boole_lattice(sK492),sK491,sK492,sK493),
inference(superposition,[],[f5199,f6873]) ).
fof(f8205,plain,
! [X0,X1] :
( rel_str_of(X0,X1) != sF497
| k2_lattice3(sK491) = X1
| ~ relation_of2(k2_lattice3(sK491),sF500,sF500) ),
inference(superposition,[],[f2883,f5162]) ).
fof(f8211,plain,
! [X0,X1] :
( rel_str_of(X0,X1) != sF497
| k2_lattice3(sK491) = X1 ),
inference(forward_subsumption_resolution,[],[f8205,f5214]) ).
fof(f8212,plain,
( sF497 != sF497
| k2_lattice3(sK491) = the_InternalRel(sF497)
| ~ spl501_67 ),
inference(superposition,[],[f8211,f5555]) ).
fof(f8213,plain,
( k2_lattice3(sK491) = the_InternalRel(sF497)
| ~ spl501_67 ),
inference(trivial_inequality_removal,[],[f8212]) ).
fof(f8218,plain,
( ! [X0,X1] :
( in(ordered_pair_as_product_element(sF500,sF500,X0,X1),the_InternalRel(sF497))
| ~ below_refl(sK491,X0,X1)
| ~ element(X1,sF500)
| ~ element(X0,sF500) )
| ~ spl501_67 ),
inference(superposition,[],[f5227,f8213]) ).
fof(f8219,plain,
( ! [X0,X1] :
( ~ in(ordered_pair_as_product_element(sF500,sF500,X0,X1),the_InternalRel(sF497))
| below_refl(sK491,X0,X1)
| ~ element(X1,sF500)
| ~ element(X0,sF500) )
| ~ spl501_67 ),
inference(superposition,[],[f5228,f8213]) ).
fof(f9461,definition,
( spl501_128
<=> in(k10_filter_1(sK491,sK491,sK492,sK493),the_InternalRel(sF497)) ),
introduced(definition,[new_symbols(definition,[spl501_128])],[avatar_definition]) ).
fof(f9462,plain,
( in(k10_filter_1(sK491,sK491,sK492,sK493),the_InternalRel(sF497))
| ~ spl501_128 ),
inference(avatar_component_clause,[],[f9461]) ).
fof(f9463,plain,
( ~ in(k10_filter_1(sK491,sK491,sK492,sK493),the_InternalRel(sF497))
| spl501_128 ),
inference(avatar_component_clause,[],[f9461]) ).
fof(f9483,plain,
( ~ related(sF497,sK492,sK493)
| ~ element(sK493,the_carrier(sF497))
| ~ element(sK492,the_carrier(sF497))
| ~ rel_str(sF497)
| spl501_128 ),
inference(resolution,[],[f9463,f6795]) ).
fof(f9484,plain,
( ~ element(sK493,the_carrier(sF497))
| ~ element(sK492,the_carrier(sF497))
| ~ rel_str(sF497)
| ~ spl501_69
| spl501_128 ),
inference(forward_subsumption_resolution,[],[f9483,f4997]) ).
fof(f9485,plain,
( ~ element(sK492,the_carrier(sF497))
| ~ rel_str(sF497)
| ~ spl501_69
| spl501_128 ),
inference(forward_subsumption_resolution,[],[f9484,f4972]) ).
fof(f9486,plain,
( ~ rel_str(sF497)
| ~ spl501_69
| spl501_128 ),
inference(forward_subsumption_resolution,[],[f9485,f4975]) ).
fof(f9487,plain,
( $false
| ~ spl501_67
| ~ spl501_69
| spl501_128 ),
inference(forward_subsumption_resolution,[],[f9486,f4988]) ).
fof(f9488,plain,
( ~ spl501_67
| ~ spl501_69
| spl501_128 ),
inference(avatar_contradiction_clause,[],[f9487]) ).
fof(f9489,plain,
( ~ related_reflexive(sF497,sF498,sK493)
| spl501_2 ),
inference(forward_demodulation,[],[f4589,f4970]) ).
fof(f9490,plain,
( ~ related_reflexive(sF497,sK492,sK493)
| spl501_2 ),
inference(forward_demodulation,[],[f9489,f4971]) ).
fof(f9562,definition,
( spl501_132
<=> in(ordered_pair_as_product_element(sF500,sF500,sK492,sK493),the_InternalRel(sF497)) ),
introduced(definition,[new_symbols(definition,[spl501_132])],[avatar_definition]) ).
fof(f9563,plain,
( in(ordered_pair_as_product_element(sF500,sF500,sK492,sK493),the_InternalRel(sF497))
| ~ spl501_132 ),
inference(avatar_component_clause,[],[f9562]) ).
fof(f9564,plain,
( ~ in(ordered_pair_as_product_element(sF500,sF500,sK492,sK493),the_InternalRel(sF497))
| spl501_132 ),
inference(avatar_component_clause,[],[f9562]) ).
fof(f14989,plain,
! [X0,X1] :
( empty(X0)
| empty(sF500)
| ~ element(X1,X0)
| unordered_pair(unordered_pair(X1,sK493),unordered_pair(X1,X1)) = ordered_pair_as_product_element(X0,sF500,X1,sK493) ),
inference(resolution,[],[f4096,f4560]) ).
fof(f14990,plain,
( ! [X0,X1] :
( empty(X0)
| ~ element(X1,X0)
| unordered_pair(unordered_pair(X1,sK493),unordered_pair(X1,X1)) = ordered_pair_as_product_element(X0,sF500,X1,sK493) )
| spl501_80 ),
inference(forward_subsumption_resolution,[],[f14989,f5140]) ).
fof(f15029,plain,
( ! [X0,X1] :
( ~ element(X1,X0)
| empty(X0)
| ordered_pair_as_product_element(X0,sF500,X1,sK493) = k10_filter_1(boole_lattice(X1),sK491,X1,sK493) )
| spl501_80 ),
inference(forward_demodulation,[],[f14990,f6873]) ).
fof(f15132,plain,
( empty(sF500)
| k10_filter_1(boole_lattice(sK492),sK491,sK492,sK493) = ordered_pair_as_product_element(sF500,sF500,sK492,sK493)
| spl501_80 ),
inference(resolution,[],[f15029,f4561]) ).
fof(f15135,plain,
( k10_filter_1(boole_lattice(sK492),sK491,sK492,sK493) = ordered_pair_as_product_element(sF500,sF500,sK492,sK493)
| spl501_80 ),
inference(forward_subsumption_resolution,[],[f15132,f5140]) ).
fof(f15174,plain,
( k10_filter_1(sK491,sK491,sK492,sK493) = ordered_pair_as_product_element(sF500,sF500,sK492,sK493)
| spl501_80 ),
inference(forward_demodulation,[],[f15135,f6889]) ).
fof(f15230,plain,
( ! [X0] :
( ~ in(ordered_pair_as_product_element(sF500,sF500,sK492,sK493),the_InternalRel(X0))
| related(X0,sK492,sK493)
| ~ element(sK493,the_carrier(X0))
| ~ element(sK492,the_carrier(X0))
| ~ rel_str(X0) )
| spl501_80 ),
inference(superposition,[],[f5397,f15174]) ).
fof(f15233,plain,
( in(ordered_pair_as_product_element(sF500,sF500,sK492,sK493),the_InternalRel(sF497))
| spl501_80
| ~ spl501_128 ),
inference(superposition,[],[f9462,f15174]) ).
fof(f15236,plain,
( $false
| spl501_80
| ~ spl501_128
| spl501_132 ),
inference(forward_subsumption_resolution,[],[f15233,f9564]) ).
fof(f15237,plain,
( spl501_80
| ~ spl501_128
| spl501_132 ),
inference(avatar_contradiction_clause,[],[f15236]) ).
fof(f15394,plain,
( below_refl(sK491,sK492,sK493)
| ~ element(sK493,sF500)
| ~ element(sK492,sF500)
| ~ spl501_67
| ~ spl501_132 ),
inference(resolution,[],[f9563,f8219]) ).
fof(f15401,plain,
( ~ element(sK493,sF500)
| ~ element(sK492,sF500)
| spl501_1
| ~ spl501_67
| ~ spl501_132 ),
inference(forward_subsumption_resolution,[],[f15394,f4585]) ).
fof(f15402,plain,
( ~ element(sK492,sF500)
| spl501_1
| ~ spl501_67
| ~ spl501_132 ),
inference(forward_subsumption_resolution,[],[f15401,f4560]) ).
fof(f15403,plain,
( $false
| spl501_1
| ~ spl501_67
| ~ spl501_132 ),
inference(forward_subsumption_resolution,[],[f15402,f4561]) ).
fof(f15404,plain,
( spl501_1
| ~ spl501_67
| ~ spl501_132 ),
inference(avatar_contradiction_clause,[],[f15403]) ).
fof(f15662,plain,
( related(sF497,sK492,sK493)
| ~ element(sK493,the_carrier(sF497))
| ~ element(sK492,the_carrier(sF497))
| ~ rel_str(sF497)
| ~ below_refl(sK491,sK492,sK493)
| ~ element(sK493,sF500)
| ~ element(sK492,sF500)
| ~ spl501_67
| spl501_80 ),
inference(resolution,[],[f15230,f8218]) ).
fof(f15663,plain,
( ~ element(sK493,the_carrier(sF497))
| ~ element(sK492,the_carrier(sF497))
| ~ rel_str(sF497)
| ~ below_refl(sK491,sK492,sK493)
| ~ element(sK493,sF500)
| ~ element(sK492,sF500)
| ~ spl501_67
| spl501_69
| spl501_80 ),
inference(forward_subsumption_resolution,[],[f15662,f4996]) ).
fof(f15665,plain,
( ~ element(sK492,the_carrier(sF497))
| ~ rel_str(sF497)
| ~ below_refl(sK491,sK492,sK493)
| ~ element(sK493,sF500)
| ~ element(sK492,sF500)
| ~ spl501_67
| spl501_69
| spl501_80 ),
inference(forward_subsumption_resolution,[],[f15663,f4972]) ).
fof(f15667,plain,
( ~ rel_str(sF497)
| ~ below_refl(sK491,sK492,sK493)
| ~ element(sK493,sF500)
| ~ element(sK492,sF500)
| ~ spl501_67
| spl501_69
| spl501_80 ),
inference(forward_subsumption_resolution,[],[f15665,f4975]) ).
fof(f15669,plain,
( ~ below_refl(sK491,sK492,sK493)
| ~ element(sK493,sF500)
| ~ element(sK492,sF500)
| ~ spl501_67
| spl501_69
| spl501_80 ),
inference(forward_subsumption_resolution,[],[f15667,f4988]) ).
fof(f15672,plain,
( ~ element(sK493,sF500)
| ~ element(sK492,sF500)
| ~ spl501_1
| ~ spl501_67
| spl501_69
| spl501_80 ),
inference(forward_subsumption_resolution,[],[f15669,f4586]) ).
fof(f15673,plain,
( ~ element(sK492,sF500)
| ~ spl501_1
| ~ spl501_67
| spl501_69
| spl501_80 ),
inference(forward_subsumption_resolution,[],[f15672,f4560]) ).
fof(f15674,plain,
( $false
| ~ spl501_1
| ~ spl501_67
| spl501_69
| spl501_80 ),
inference(forward_subsumption_resolution,[],[f15673,f4561]) ).
fof(f15675,plain,
( ~ spl501_1
| ~ spl501_67
| spl501_69
| spl501_80 ),
inference(avatar_contradiction_clause,[],[f15674]) ).
fof(f15695,plain,
( related_reflexive(sF497,sK492,sK493)
| empty_carrier(sF497)
| ~ reflexive_relstr(sF497)
| ~ rel_str(sF497)
| ~ element(sK492,the_carrier(sF497))
| ~ element(sK493,the_carrier(sF497))
| ~ spl501_69 ),
inference(resolution,[],[f4997,f3080]) ).
fof(f15696,plain,
( empty_carrier(sF497)
| ~ reflexive_relstr(sF497)
| ~ rel_str(sF497)
| ~ element(sK492,the_carrier(sF497))
| ~ element(sK493,the_carrier(sF497))
| spl501_2
| ~ spl501_69 ),
inference(forward_subsumption_resolution,[],[f15695,f9490]) ).
fof(f15698,plain,
( ~ reflexive_relstr(sF497)
| ~ rel_str(sF497)
| ~ element(sK492,the_carrier(sF497))
| ~ element(sK493,the_carrier(sF497))
| spl501_2
| spl501_63
| ~ spl501_69 ),
inference(forward_subsumption_resolution,[],[f15696,f4949]) ).
fof(f15700,plain,
( ~ rel_str(sF497)
| ~ element(sK492,the_carrier(sF497))
| ~ element(sK493,the_carrier(sF497))
| spl501_2
| spl501_63
| ~ spl501_68
| ~ spl501_69 ),
inference(forward_subsumption_resolution,[],[f15698,f4992]) ).
fof(f15702,plain,
( ~ element(sK492,the_carrier(sF497))
| ~ element(sK493,the_carrier(sF497))
| spl501_2
| spl501_63
| ~ spl501_67
| ~ spl501_68
| ~ spl501_69 ),
inference(forward_subsumption_resolution,[],[f15700,f4988]) ).
fof(f15704,plain,
( ~ element(sK493,the_carrier(sF497))
| spl501_2
| spl501_63
| ~ spl501_67
| ~ spl501_68
| ~ spl501_69 ),
inference(forward_subsumption_resolution,[],[f15702,f4975]) ).
fof(f15706,plain,
( $false
| spl501_2
| spl501_63
| ~ spl501_67
| ~ spl501_68
| ~ spl501_69 ),
inference(forward_subsumption_resolution,[],[f15704,f4972]) ).
fof(f15707,plain,
( spl501_2
| spl501_63
| ~ spl501_67
| ~ spl501_68
| ~ spl501_69 ),
inference(avatar_contradiction_clause,[],[f15706]) ).
cnf(s1,plain,
( spl501_1
| spl501_2 ),
inference(sat_conversion,[],[f4591]) ).
cnf(s2,plain,
( ~ spl501_1
| ~ spl501_2 ),
inference(sat_conversion,[],[f4592]) ).
cnf(s55,plain,
( ~ spl501_2
| spl501_63
| ~ spl501_67
| ~ spl501_68
| spl501_69 ),
inference(sat_conversion,[],[f5001]) ).
cnf(s56,plain,
~ spl501_63,
inference(sat_conversion,[],[f5006]) ).
cnf(s61,plain,
spl501_68,
inference(sat_conversion,[],[f5073]) ).
cnf(s63,plain,
spl501_67,
inference(sat_conversion,[],[f5105]) ).
cnf(s64,plain,
( ~ spl501_79
| ~ spl501_80 ),
inference(sat_conversion,[],[f5141]) ).
cnf(s65,plain,
spl501_79,
inference(sat_conversion,[],[f5165]) ).
cnf(s112,plain,
( ~ spl501_67
| ~ spl501_69
| spl501_128 ),
inference(sat_conversion,[],[f9488]) ).
cnf(s148,plain,
( spl501_80
| ~ spl501_128
| spl501_132 ),
inference(sat_conversion,[],[f15237]) ).
cnf(s150,plain,
( spl501_1
| ~ spl501_67
| ~ spl501_132 ),
inference(sat_conversion,[],[f15404]) ).
cnf(s152,plain,
( ~ spl501_1
| ~ spl501_67
| spl501_69
| spl501_80 ),
inference(sat_conversion,[],[f15675]) ).
cnf(s153,plain,
( spl501_2
| spl501_63
| ~ spl501_67
| ~ spl501_68
| ~ spl501_69 ),
inference(sat_conversion,[],[f15707]) ).
cnf(s171,plain,
~ spl501_80,
inference(rat,[],[s64,s65]) ).
cnf(s177,plain,
( ~ spl501_2
| spl501_69 ),
inference(rat,[],[s55,s61,s63,s56]) ).
cnf(s182,plain,
spl501_1,
inference(rat,[],[s112,s177,s148,s1,s150,s63,s171]) ).
cnf(s183,plain,
spl501_69,
inference(rat,[],[s152,s171,s63,s182]) ).
cnf(s186,plain,
~ spl501_2,
inference(rat,[],[s2,s182]) ).
cnf(s189,plain,
$false,
inference(rat,[],[s153,s56,s61,s63,s183,s186]) ).
fof(f15709,plain,
$false,
inference(avatar_sat_refutation,[],[s189]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU346+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 04:49:31 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 11.09/2.72 % (1437928)Detected formulas, will run a generic FOF schedule.
% 11.09/2.72 % (1437933)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=3622473105:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 11.09/2.72 % (1437936)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2074622873:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 11.09/2.72 % (1437939)dis-21_1_sil=8000:lcm=predicate:random_seed=2046450895: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)
% 11.09/2.72 % (1437935)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=2525388028:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 11.09/2.72 % (1437937)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4151538480:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 11.09/2.72 % (1437934)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=897727531:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 11.09/2.72 % (1437938)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1524837592:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 11.09/2.72 % (1437936)Instruction limit reached!
% 11.09/2.72 % (1437936)------------------------------
% 11.09/2.72 % (1437936)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.09/2.72 % (1437936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.09/2.72 % (1437936)CaDiCaL version: 2.1.3
% 11.09/2.72 % (1437936)Termination reason: Instruction limit
% 11.09/2.72 % (1437936)Termination phase: Saturation
% 11.09/2.72 % (1437936)Time elapsed: 0.058 s
% 11.09/2.72 % (1437936)Peak memory usage: 91 MB
% 11.09/2.72 % (1437936)Instructions burned: 110 (million)
% 11.09/2.72 % (1437939)Instruction limit reached!
% 11.09/2.72 % (1437939)------------------------------
% 11.09/2.72 % (1437939)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.09/2.72 % (1437939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.09/2.72 % (1437939)CaDiCaL version: 2.1.3
% 11.09/2.72 % (1437939)Termination reason: Instruction limit
% 11.09/2.72 % (1437939)Termination phase: Saturation
% 11.09/2.72 % (1437939)Time elapsed: 0.065 s
% 11.09/2.72 % (1437939)Peak memory usage: 91 MB
% 11.09/2.72 % (1437939)Instructions burned: 129 (million)
% 11.09/2.72 % (1437937)Instruction limit reached!
% 11.09/2.72 % (1437937)------------------------------
% 11.09/2.72 % (1437937)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.09/2.72 % (1437937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.09/2.72 % (1437937)CaDiCaL version: 2.1.3
% 11.09/2.72 % (1437937)Termination reason: Instruction limit
% 11.09/2.72 % (1437937)Termination phase: Saturation
% 11.09/2.72 % (1437937)Time elapsed: 0.075 s
% 11.09/2.72 % (1437937)Peak memory usage: 91 MB
% 11.09/2.72 % (1437937)Instructions burned: 120 (million)
% 11.09/2.72 % (1437938)Instruction limit reached!
% 11.09/2.72 % (1437938)------------------------------
% 11.09/2.72 % (1437938)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.09/2.72 % (1437938)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.09/2.72 % (1437938)CaDiCaL version: 2.1.3
% 11.09/2.72 % (1437938)Termination reason: Instruction limit
% 11.09/2.72 % (1437938)Termination phase: Saturation
% 11.09/2.72 % (1437938)Time elapsed: 0.087 s
% 11.09/2.72 % (1437938)Peak memory usage: 92 MB
% 11.09/2.72 % (1437938)Instructions burned: 139 (million)
% 11.09/2.72 % (1437948)lrs+10_1_sil=8000:sp=occurrence:random_seed=3079014005:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 11.09/2.72 % (1437949)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2864143474:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 11.09/2.72 % (1437949)Refutation not found, incomplete strategy
% 11.09/2.72 % (1437949)------------------------------
% 11.09/2.72 % (1437949)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.09/2.72 % (1437949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.09/2.72 % (1437949)CaDiCaL version: 2.1.3
% 11.09/2.72 % (1437949)Termination reason: Refutation not found, incomplete strategy
% 11.09/2.72 % (1437949)Time elapsed: 0.010 s
% 11.09/2.72 % (1437949)Peak memory usage: 90 MB
% 11.09/2.72 % (1437949)Instructions burned: 14 (million)
% 11.09/2.72 % (1437950)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1691501992:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 11.09/2.72 % (1437951)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=2611337634:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 11.09/2.72 % (1437948)Instruction limit reached!
% 11.09/2.72 % (1437948)------------------------------
% 11.09/2.72 % (1437948)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.09/2.72 % (1437948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.09/2.72 % (1437948)CaDiCaL version: 2.1.3
% 11.09/2.72 % (1437948)Termination reason: Instruction limit
% 11.09/2.72 % (1437948)Termination phase: Saturation
% 11.09/2.72 % (1437948)Time elapsed: 0.181 s
% 11.09/2.72 % (1437948)Peak memory usage: 95 MB
% 11.09/2.72 % (1437948)Instructions burned: 286 (million)
% 11.09/2.72 % (1437951)Instruction limit reached!
% 11.09/2.72 % (1437951)------------------------------
% 11.09/2.72 % (1437951)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.09/2.72 % (1437951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.09/2.72 % (1437951)CaDiCaL version: 2.1.3
% 11.09/2.72 % (1437951)Termination reason: Instruction limit
% 11.09/2.72 % (1437951)Termination phase: Saturation
% 11.09/2.72 % (1437951)Time elapsed: 0.152 s
% 11.09/2.72 % (1437951)Peak memory usage: 94 MB
% 11.09/2.72 % (1437951)Instructions burned: 248 (million)
% 11.09/2.72 % (1437950)Instruction limit reached!
% 11.09/2.72 % (1437950)------------------------------
% 11.09/2.72 % (1437950)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.09/2.72 % (1437950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.09/2.72 % (1437950)CaDiCaL version: 2.1.3
% 11.09/2.72 % (1437950)Termination reason: Instruction limit
% 11.09/2.72 % (1437950)Termination phase: Saturation
% 11.09/2.72 % (1437950)Time elapsed: 0.219 s
% 11.09/2.72 % (1437950)Peak memory usage: 95 MB
% 11.09/2.72 % (1437950)Instructions burned: 326 (million)
% 11.09/2.72 % (1437949)------------------------------
% 11.09/2.72 % (1437949)------------------------------
% 11.09/2.72 % (1437956)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=164928205:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 11.09/2.72 % (1437957)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1866282231:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 11.09/2.72 % (1437958)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3822444988:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 11.09/2.72 % (1437959)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=516011803:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 11.09/2.72 % (1437958)Instruction limit reached!
% 11.09/2.72 % (1437958)------------------------------
% 11.09/2.72 % (1437958)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.09/2.72 % (1437958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.09/2.72 % (1437958)CaDiCaL version: 2.1.3
% 11.09/2.72 % (1437958)Termination reason: Instruction limit
% 11.09/2.72 % (1437958)Termination phase: Saturation
% 11.09/2.72 % (1437958)Time elapsed: 0.065 s
% 11.09/2.72 % (1437958)Peak memory usage: 92 MB
% 11.09/2.72 % (1437958)Instructions burned: 113 (million)
% 11.09/2.72 % (1437959)Instruction limit reached!
% 11.09/2.72 % (1437959)------------------------------
% 11.09/2.72 % (1437959)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.09/2.72 % (1437959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.09/2.72 % (1437959)CaDiCaL version: 2.1.3
% 11.09/2.72 % (1437959)Termination reason: Instruction limit
% 11.09/2.72 % (1437959)Termination phase: Saturation
% 11.09/2.72 % (1437959)Time elapsed: 0.070 s
% 11.09/2.72 % (1437959)Peak memory usage: 91 MB
% 11.09/2.72 % (1437959)Instructions burned: 128 (million)
% 11.09/2.72 % (1437956)Instruction limit reached!
% 11.09/2.72 % (1437956)------------------------------
% 11.09/2.72 % (1437956)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.09/2.72 % (1437956)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.09/2.72 % (1437956)CaDiCaL version: 2.1.3
% 11.09/2.72 % (1437956)Termination reason: Instruction limit
% 11.09/2.72 % (1437956)Termination phase: Saturation
% 11.09/2.72 % (1437956)Time elapsed: 0.183 s
% 11.09/2.72 % (1437956)Peak memory usage: 93 MB
% 11.09/2.72 % (1437956)Instructions burned: 295 (million)
% 11.09/2.72 % (1437964)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=745634866:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 11.09/2.72 % (1437965)lrs+10_1_sil=8000:sp=occurrence:random_seed=427570965:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2990 on theBenchmark for (2990ds/907Mi)
% 11.09/2.72 % (1437966)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2161874934:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 11.09/2.72 % (1437964)Instruction limit reached!
% 11.09/2.72 % (1437964)------------------------------
% 11.09/2.72 % (1437964)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.09/2.72 % (1437964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.09/2.72 % (1437964)CaDiCaL version: 2.1.3
% 11.09/2.72 % (1437964)Termination reason: Instruction limit
% 11.09/2.72 % (1437964)Termination phase: Saturation
% 11.09/2.72 % (1437964)Time elapsed: 0.068 s
% 11.09/2.72 % (1437964)Peak memory usage: 89 MB
% 11.09/2.72 % (1437964)Instructions burned: 115 (million)
% 11.09/2.72 % (1437970)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=210073591:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 11.09/2.72 % (1437966)Instruction limit reached!
% 11.09/2.72 % (1437966)------------------------------
% 11.09/2.72 % (1437966)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.09/2.72 % (1437966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.09/2.72 % (1437966)CaDiCaL version: 2.1.3
% 11.09/2.72 % (1437966)Termination reason: Instruction limit
% 11.09/2.72 % (1437966)Termination phase: Saturation
% 11.09/2.72 % (1437966)Time elapsed: 0.266 s
% 11.09/2.72 % (1437966)Peak memory usage: 95 MB
% 11.09/2.72 % (1437966)Instructions burned: 438 (million)
% 11.09/2.72 % (1437972)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=2774761933:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2986 on theBenchmark for (2986ds/134Mi)
% 11.09/2.72 % (1437972)Instruction limit reached!
% 11.09/2.72 % (1437972)------------------------------
% 11.09/2.72 % (1437972)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.09/2.72 % (1437972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.09/2.72 % (1437972)CaDiCaL version: 2.1.3
% 11.09/2.72 % (1437972)Termination reason: Instruction limit
% 11.09/2.72 % (1437972)Termination phase: Saturation
% 11.09/2.72 % (1437972)Time elapsed: 0.069 s
% 11.09/2.72 % (1437972)Peak memory usage: 92 MB
% 11.09/2.72 % (1437972)Instructions burned: 135 (million)
% 11.09/2.72 % (1437965)Instruction limit reached!
% 11.09/2.72 % (1437965)------------------------------
% 11.09/2.72 % (1437965)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.09/2.72 % (1437965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.09/2.72 % (1437965)CaDiCaL version: 2.1.3
% 11.09/2.72 % (1437965)Termination reason: Instruction limit
% 11.09/2.72 % (1437965)Termination phase: Saturation
% 11.09/2.72 % (1437965)Time elapsed: 0.570 s
% 11.09/2.72 % (1437965)Peak memory usage: 104 MB
% 11.09/2.72 % (1437965)Instructions burned: 907 (million)
% 11.09/2.72 % (1437933)First to succeed.
% 11.09/2.72 % (1437933)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1437928"
% 11.09/2.72 % (1437974)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=4011039527:st=8:i=592:sd=3:ep=RST:ss=axioms_2984 on theBenchmark for (2984ds/592Mi)
% 11.09/2.72 % (1437975)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=2083585405:st=3:i=13193:sd=3:ss=axioms_2983 on theBenchmark for (2983ds/13193Mi)
% 11.09/2.72 % (1437933)Refutation found. Thanks to Tanya!
% 11.09/2.72 % SZS status Theorem for theBenchmark
% 11.09/2.72 % SZS output start Proof for theBenchmark
% See solution above
% 13.75/2.92 % (1437933)------------------------------
% 13.75/2.92 % (1437933)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.75/2.92 % (1437933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.75/2.92 % (1437933)CaDiCaL version: 2.1.3
% 13.75/2.92 % (1437933)Termination reason: Refutation
% 13.75/2.92 % (1437933)Time elapsed: 1.564 s
% 13.75/2.92 % (1437933)Peak memory usage: 167 MB
% 13.75/2.92 % (1437933)Instructions burned: 4498 (million)
% 13.75/2.92 % (1437933)------------------------------
% 13.75/2.92 % (1437933)------------------------------
% 13.75/2.92 % (1437928)Success in time 1.875 s
% 13.75/2.92 % Vampire exiting
%------------------------------------------------------------------------------