%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU368+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 : Wed Oct 7 10:44:09 AM UTC 2026
% Result : Theorem 5.76s 1.61s
% Output : CNFRefutation 5.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 57
% Syntax : Number of formulae : 517 ( 379 unt; 0 typ; 0 def)
% Number of atoms : 2209 ( 782 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 2756 ( 415 ~; 412 |; 32 &;1855 @)
% ( 2 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 199 ( 196 usr; 9 con; 0-6 aty)
% Number of variables : 762 ( 0 ^; 748 !; 14 ?; 762 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a_1_0_filter_1,type,
a_1_0_filter_1: $i > $i ).
thf(tp_a_2_2_lattice3,type,
a_2_2_lattice3: $i > $i > $i ).
thf(tp_a_2_3_lattice3,type,
a_2_3_lattice3: $i > $i > $i ).
thf(tp_antisymmetric,type,
antisymmetric: $i > $o ).
thf(tp_antisymmetric_relstr,type,
antisymmetric_relstr: $i > $o ).
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_apply_as_element,type,
apply_as_element: $i > $i > $i > $i > $i ).
thf(tp_apply_binary,type,
apply_binary: $i > $i > $i > $i ).
thf(tp_apply_binary_as_element,type,
apply_binary_as_element: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_apply_netmap,type,
apply_netmap: $i > $i > $i > $i ).
thf(tp_apply_on_structs,type,
apply_on_structs: $i > $i > $i > $i > $i ).
thf(tp_are_equipotent,type,
are_equipotent: $i > $i > $o ).
thf(tp_being_limit_ordinal,type,
being_limit_ordinal: $i > $o ).
thf(tp_below,type,
below: $i > $i > $i > $o ).
thf(tp_below_refl,type,
below_refl: $i > $i > $i > $o ).
thf(tp_bijective,type,
bijective: $i > $i > $i > $o ).
thf(tp_boole_lattice,type,
boole_lattice: $i > $i ).
thf(tp_bottom_of_relstr,type,
bottom_of_relstr: $i > $i ).
thf(tp_bottom_of_semilattstr,type,
bottom_of_semilattstr: $i > $i ).
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_cast_as_carrier_subset,type,
cast_as_carrier_subset: $i > $i ).
thf(tp_cast_to_el_of_LattPOSet,type,
cast_to_el_of_LattPOSet: $i > $i > $i ).
thf(tp_cast_to_el_of_lattice,type,
cast_to_el_of_lattice: $i > $i > $i ).
thf(tp_cast_to_subset,type,
cast_to_subset: $i > $i ).
thf(tp_centered,type,
centered: $i > $o ).
thf(tp_closed_subset,type,
closed_subset: $i > $i > $o ).
thf(tp_closed_subsets,type,
closed_subsets: $i > $i > $o ).
thf(tp_compact_top_space,type,
compact_top_space: $i > $o ).
thf(tp_complements_of_subsets,type,
complements_of_subsets: $i > $i > $i ).
thf(tp_complete_latt_str,type,
complete_latt_str: $i > $o ).
thf(tp_connected,type,
connected: $i > $o ).
thf(tp_cup_closed,type,
cup_closed: $i > $o ).
thf(tp_diff_closed,type,
diff_closed: $i > $o ).
thf(tp_directed_subset,type,
directed_subset: $i > $i > $o ).
thf(tp_disjoint,type,
disjoint: $i > $i > $o ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_carrier,type,
empty_carrier: $i > $o ).
thf(tp_empty_carrier_subset,type,
empty_carrier_subset: $i > $i ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_epsilon_connected,type,
epsilon_connected: $i > $o ).
thf(tp_epsilon_transitive,type,
epsilon_transitive: $i > $o ).
thf(tp_equipotent,type,
equipotent: $i > $i > $o ).
thf(tp_ex_inf_of_relstr_set,type,
ex_inf_of_relstr_set: $i > $i > $o ).
thf(tp_ex_sup_of_relstr_set,type,
ex_sup_of_relstr_set: $i > $i > $o ).
thf(tp_fiber,type,
fiber: $i > $i > $i ).
thf(tp_finite,type,
finite: $i > $o ).
thf(tp_full_subrelstr,type,
full_subrelstr: $i > $i > $o ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_function_inverse,type,
function_inverse: $i > $i ).
thf(tp_identity_as_relation_of,type,
identity_as_relation_of: $i > $i ).
thf(tp_identity_on_carrier,type,
identity_on_carrier: $i > $i ).
thf(tp_identity_relation,type,
identity_relation: $i > $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_incl_POSet,type,
incl_POSet: $i > $i ).
thf(tp_inclusion_order,type,
inclusion_order: $i > $i ).
thf(tp_inclusion_relation,type,
inclusion_relation: $i > $i ).
thf(tp_interior,type,
interior: $i > $i > $i ).
thf(tp_is_a_cover_of_carrier,type,
is_a_cover_of_carrier: $i > $i > $o ).
thf(tp_is_antisymmetric_in,type,
is_antisymmetric_in: $i > $i > $o ).
thf(tp_is_connected_in,type,
is_connected_in: $i > $i > $o ).
thf(tp_is_eventually_in,type,
is_eventually_in: $i > $i > $i > $o ).
thf(tp_is_often_in,type,
is_often_in: $i > $i > $i > $o ).
thf(tp_is_reflexive_in,type,
is_reflexive_in: $i > $i > $o ).
thf(tp_is_transitive_in,type,
is_transitive_in: $i > $i > $o ).
thf(tp_is_well_founded_in,type,
is_well_founded_in: $i > $i > $o ).
thf(tp_join,type,
join: $i > $i > $i > $i ).
thf(tp_join_absorbing,type,
join_absorbing: $i > $o ).
thf(tp_join_associative,type,
join_associative: $i > $o ).
thf(tp_join_commut,type,
join_commut: $i > $i > $i > $i ).
thf(tp_join_commutative,type,
join_commutative: $i > $o ).
thf(tp_join_of_latt_set,type,
join_of_latt_set: $i > $i > $i ).
thf(tp_join_on_relstr,type,
join_on_relstr: $i > $i > $i ).
thf(tp_join_semilatt_str,type,
join_semilatt_str: $i > $o ).
thf(tp_k10_filter_1,type,
k10_filter_1: $i > $i > $i > $i > $i ).
thf(tp_k1_pcomps_1,type,
k1_pcomps_1: $i > $i ).
thf(tp_k2_lattice3,type,
k2_lattice3: $i > $i ).
thf(tp_k8_filter_1,type,
k8_filter_1: $i > $i > $i ).
thf(tp_latt_element_smaller,type,
latt_element_smaller: $i > $i > $i > $o ).
thf(tp_latt_set_smaller,type,
latt_set_smaller: $i > $i > $i > $o ).
thf(tp_latt_str,type,
latt_str: $i > $o ).
thf(tp_latt_str_of,type,
latt_str_of: $i > $i > $i > $i ).
thf(tp_lattice,type,
lattice: $i > $o ).
thf(tp_lower_bounded_relstr,type,
lower_bounded_relstr: $i > $o ).
thf(tp_lower_bounded_semilattstr,type,
lower_bounded_semilattstr: $i > $o ).
thf(tp_meet,type,
meet: $i > $i > $i > $i ).
thf(tp_meet_absorbing,type,
meet_absorbing: $i > $o ).
thf(tp_meet_associative,type,
meet_associative: $i > $o ).
thf(tp_meet_commut,type,
meet_commut: $i > $i > $i > $i ).
thf(tp_meet_commutative,type,
meet_commutative: $i > $o ).
thf(tp_meet_of_latt_set,type,
meet_of_latt_set: $i > $i > $i ).
thf(tp_meet_of_subsets,type,
meet_of_subsets: $i > $i > $i ).
thf(tp_meet_on_relstr,type,
meet_on_relstr: $i > $i > $i ).
thf(tp_meet_semilatt_str,type,
meet_semilatt_str: $i > $o ).
thf(tp_natural,type,
natural: $i > $o ).
thf(tp_net_str,type,
net_str: $i > $i > $o ).
thf(tp_omega,type,
omega: $i ).
thf(tp_one_sorted_str,type,
one_sorted_str: $i > $o ).
thf(tp_one_to_one,type,
one_to_one: $i > $o ).
thf(tp_onto,type,
onto: $i > $i > $i > $o ).
thf(tp_open_subset,type,
open_subset: $i > $i > $o ).
thf(tp_open_subsets,type,
open_subsets: $i > $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_ordered_pair_as_product_element,type,
ordered_pair_as_product_element: $i > $i > $i > $i > $i ).
thf(tp_ordinal,type,
ordinal: $i > $o ).
thf(tp_ordinal_subset,type,
ordinal_subset: $i > $i > $o ).
thf(tp_pair_first,type,
pair_first: $i > $i ).
thf(tp_pair_second,type,
pair_second: $i > $i ).
thf(tp_point_neighbourhood,type,
point_neighbourhood: $i > $i > $i > $o ).
thf(tp_poset_of_lattice,type,
poset_of_lattice: $i > $i ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_preboolean,type,
preboolean: $i > $o ).
thf(tp_proper_element,type,
proper_element: $i > $i > $o ).
thf(tp_proper_subset,type,
proper_subset: $i > $i > $o ).
thf(tp_quasi_total,type,
quasi_total: $i > $i > $i > $o ).
thf(tp_reflexive,type,
reflexive: $i > $o ).
thf(tp_reflexive_relstr,type,
reflexive_relstr: $i > $o ).
thf(tp_rel_str,type,
rel_str: $i > $o ).
thf(tp_rel_str_of,type,
rel_str_of: $i > $i > $i ).
thf(tp_related,type,
related: $i > $i > $i > $o ).
thf(tp_related_reflexive,type,
related_reflexive: $i > $i > $i > $o ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_composition,type,
relation_composition: $i > $i > $i ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_dom_as_subset,type,
relation_dom_as_subset: $i > $i > $i > $i ).
thf(tp_relation_dom_restriction,type,
relation_dom_restriction: $i > $i > $i ).
thf(tp_relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
thf(tp_relation_field,type,
relation_field: $i > $i ).
thf(tp_relation_image,type,
relation_image: $i > $i > $i ).
thf(tp_relation_inverse,type,
relation_inverse: $i > $i ).
thf(tp_relation_inverse_image,type,
relation_inverse_image: $i > $i > $i ).
thf(tp_relation_isomorphism,type,
relation_isomorphism: $i > $i > $i > $o ).
thf(tp_relation_of2,type,
relation_of2: $i > $i > $i > $o ).
thf(tp_relation_of2_as_subset,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(tp_relation_of_lattice,type,
relation_of_lattice: $i > $i ).
thf(tp_relation_restriction,type,
relation_restriction: $i > $i > $i ).
thf(tp_relation_restriction_as_relation_of,type,
relation_restriction_as_relation_of: $i > $i > $i ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_relation_rng_as_subset,type,
relation_rng_as_subset: $i > $i > $i > $i ).
thf(tp_relation_rng_restriction,type,
relation_rng_restriction: $i > $i > $i ).
thf(tp_relstr_element_smaller,type,
relstr_element_smaller: $i > $i > $i > $o ).
thf(tp_relstr_set_smaller,type,
relstr_set_smaller: $i > $i > $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_A,type,
sK2_A: $i ).
thf(tp_sK3_A,type,
sK3_A: $i ).
thf(tp_sK4_C,type,
sK4_C: $i > $i > $i ).
thf(tp_sK5_B,type,
sK5_B: $i > $i ).
thf(tp_sK6_B,type,
sK6_B: $i > $i ).
thf(tp_sK7_A,type,
sK7_A: $i ).
thf(tp_sK8_A,type,
sK8_A: $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(tp_set_meet,type,
set_meet: $i > $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_strict_latt_str,type,
strict_latt_str: $i > $o ).
thf(tp_strict_rel_str,type,
strict_rel_str: $i > $o ).
thf(tp_subrelstr,type,
subrelstr: $i > $i > $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subset_complement,type,
subset_complement: $i > $i > $i ).
thf(tp_subset_difference,type,
subset_difference: $i > $i > $i > $i ).
thf(tp_subset_intersection2,type,
subset_intersection2: $i > $i > $i > $i ).
thf(tp_subset_union2,type,
subset_union2: $i > $i > $i > $i ).
thf(tp_succ,type,
succ: $i > $i ).
thf(tp_symmetric,type,
symmetric: $i > $o ).
thf(tp_the_InternalRel,type,
the_InternalRel: $i > $i ).
thf(tp_the_L_join,type,
the_L_join: $i > $i ).
thf(tp_the_L_meet,type,
the_L_meet: $i > $i ).
thf(tp_the_carrier,type,
the_carrier: $i > $i ).
thf(tp_the_mapping,type,
the_mapping: $i > $i > $i ).
thf(tp_the_topology,type,
the_topology: $i > $i ).
thf(tp_top_str,type,
top_str: $i > $o ).
thf(tp_topological_space,type,
topological_space: $i > $o ).
thf(tp_topstr_closure,type,
topstr_closure: $i > $i > $i ).
thf(tp_transitive,type,
transitive: $i > $o ).
thf(tp_transitive_relstr,type,
transitive_relstr: $i > $o ).
thf(tp_union,type,
union: $i > $i ).
thf(tp_union_of_subsets,type,
union_of_subsets: $i > $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(tp_unordered_pair_as_carrier_subset,type,
unordered_pair_as_carrier_subset: $i > $i > $i > $i ).
thf(tp_unordered_triple,type,
unordered_triple: $i > $i > $i > $i ).
thf(tp_v1_binop_1,type,
v1_binop_1: $i > $i > $o ).
thf(tp_v1_int_1,type,
v1_int_1: $i > $o ).
thf(tp_v1_membered,type,
v1_membered: $i > $o ).
thf(tp_v1_partfun1,type,
v1_partfun1: $i > $i > $i > $o ).
thf(tp_v1_rat_1,type,
v1_rat_1: $i > $o ).
thf(tp_v1_xcmplx_0,type,
v1_xcmplx_0: $i > $o ).
thf(tp_v1_xreal_0,type,
v1_xreal_0: $i > $o ).
thf(tp_v2_binop_1,type,
v2_binop_1: $i > $i > $o ).
thf(tp_v2_membered,type,
v2_membered: $i > $o ).
thf(tp_v3_membered,type,
v3_membered: $i > $o ).
thf(tp_v4_membered,type,
v4_membered: $i > $o ).
thf(tp_v5_membered,type,
v5_membered: $i > $o ).
thf(tp_well_founded_relation,type,
well_founded_relation: $i > $o ).
thf(tp_well_ordering,type,
well_ordering: $i > $o ).
thf(tp_well_orders,type,
well_orders: $i > $i > $o ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
<=> ( relation_of2 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(59,axiom,
! [A: $i] :
( ( inclusion_order @ A )
= ( inclusion_relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_yellow_1) ).
thf(72,axiom,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(97,axiom,
? [A: $i] :
( ( rel_str @ A )
& ( strict_rel_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_orders_2) ).
thf(112,axiom,
! [A: $i,B: $i] :
( ( relation_of2 @ B @ A @ A )
=> ! [C: $i,D: $i] :
( ( ( rel_str_of @ A @ B )
= ( rel_str_of @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_orders_2) ).
thf(195,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(196,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ? [B: $i] : ( subrelstr @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_yellow_0) ).
thf(202,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] : ( net_str @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_waybel_0) ).
thf(203,axiom,
? [A: $i] : ( one_sorted_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(205,axiom,
? [A: $i] : ( rel_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(209,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(211,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_orders_2) ).
thf(214,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( subrelstr @ B @ A )
=> ( rel_str @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_yellow_0) ).
thf(215,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(216,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(219,axiom,
! [A: $i] :
( ( join_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(220,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ( rel_str @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_waybel_0) ).
thf(221,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(222,axiom,
! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(223,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(224,axiom,
! [A: $i] :
( ( meet_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(225,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_relat_1) ).
thf(242,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_ordinal2) ).
thf(245,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(246,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(253,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(255,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(257,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_relat_1) ).
thf(260,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(261,axiom,
! [A: $i] :
( ( strict_rel_str @ ( incl_POSet @ A ) )
& ( rel_str @ ( incl_POSet @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_yellow_1) ).
thf(263,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(265,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(268,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(270,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_mcart_1) ).
thf(275,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(278,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(279,axiom,
! [A: $i] : ( relation @ ( inclusion_relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord2) ).
thf(280,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord1) ).
thf(284,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(285,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_setfam_1) ).
thf(286,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(289,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_ordinal1) ).
thf(290,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_mcart_1) ).
thf(293,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_funct_1) ).
thf(294,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_enumset1) ).
thf(296,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_binop_1) ).
thf(299,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_relat_1) ).
thf(302,axiom,
! [A: $i,B: $i] :
( ( relation_of2 @ B @ A @ A )
=> ( ( strict_rel_str @ ( rel_str_of @ A @ B ) )
& ( rel_str @ ( rel_str_of @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g1_orders_2) ).
thf(352,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pre_topc) ).
thf(374,axiom,
! [A: $i] :
( ( incl_POSet @ A )
= ( rel_str_of @ A @ ( inclusion_order @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_yellow_1) ).
thf(471,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( strict_rel_str @ A )
=> ( A
= ( rel_str_of @ ( the_carrier @ A ) @ ( the_InternalRel @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
thf(511,axiom,
! [A: $i] : ( antisymmetric @ ( inclusion_relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_wellord2) ).
thf(555,axiom,
! [A: $i] : ( transitive @ ( inclusion_relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_wellord2) ).
thf(583,axiom,
! [A: $i] : ( reflexive @ ( inclusion_relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_wellord2) ).
thf(636,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( relation_of2_as_subset @ D @ C @ A )
=> ( ( subset @ A @ B )
=> ( relation_of2_as_subset @ D @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_relset_1) ).
thf(659,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_pre_topc) ).
thf(721,conjecture,
! [A: $i] :
( ( ( the_carrier @ ( incl_POSet @ A ) )
= A )
& ( ( the_InternalRel @ ( incl_POSet @ A ) )
= ( inclusion_order @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_yellow_1) ).
thf(722,negated_conjecture,
( ( ! [A: $i] :
( ( ( the_carrier @ ( incl_POSet @ A ) )
= A )
& ( ( the_InternalRel @ ( incl_POSet @ A ) )
= ( inclusion_order @ A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[721]) ).
thf(723,plain,
( ( ! [A: $i] :
( ( ( the_carrier @ ( incl_POSet @ A ) )
= A )
& ( ( the_InternalRel @ ( incl_POSet @ A ) )
= ( inclusion_order @ A ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[722]) ).
thf(724,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
<=> ( relation_of2 @ C @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(725,plain,
( ( ? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(726,plain,
( ( ? [A: $i] :
( ( rel_str @ A )
& ( strict_rel_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(727,plain,
( ( ! [A: $i,B: $i] :
( ( relation_of2 @ B @ A @ A )
=> ! [C: $i,D: $i] :
( ( ( rel_str_of @ A @ B )
= ( rel_str_of @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(728,plain,
( ( ! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(729,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ? [B: $i] : ( subrelstr @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(730,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] : ( net_str @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(731,plain,
( ( ? [A: $i] : ( one_sorted_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(732,plain,
( ( ? [A: $i] : ( rel_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(733,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( subrelstr @ B @ A )
=> ( rel_str @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(734,plain,
( ( ! [A: $i] :
( ( join_semilatt_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(735,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ( rel_str @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(736,plain,
( ( ! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(737,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(738,plain,
( ( ! [A: $i] :
( ( meet_semilatt_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(739,plain,
( ( ! [A: $i] : ( relation @ ( inclusion_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(740,plain,
( ( ! [A: $i,B: $i] :
( ( relation_of2 @ B @ A @ A )
=> ( ( strict_rel_str @ ( rel_str_of @ A @ B ) )
& ( rel_str @ ( rel_str_of @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(741,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( ( strict_rel_str @ A )
=> ( A
= ( rel_str_of @ ( the_carrier @ A ) @ ( the_InternalRel @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471]) ).
thf(742,plain,
( ( ! [A: $i] : ( antisymmetric @ ( inclusion_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[511]) ).
thf(743,plain,
( ( ! [A: $i] : ( transitive @ ( inclusion_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[555]) ).
thf(744,plain,
( ( ! [A: $i] : ( reflexive @ ( inclusion_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[583]) ).
thf(745,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( relation_of2_as_subset @ D @ C @ A )
=> ( ( subset @ A @ B )
=> ( relation_of2_as_subset @ D @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[636]) ).
thf(746,plain,
( ( ! [A: $i] :
( ( inclusion_order @ A )
= ( inclusion_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(747,plain,
$true = $true,
inference(unfold_def,[status(thm)],[209]) ).
thf(748,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(749,plain,
$true = $true,
inference(unfold_def,[status(thm)],[215]) ).
thf(750,plain,
$true = $true,
inference(unfold_def,[status(thm)],[216]) ).
thf(751,plain,
$true = $true,
inference(unfold_def,[status(thm)],[221]) ).
thf(752,plain,
$true = $true,
inference(unfold_def,[status(thm)],[225]) ).
thf(753,plain,
$true = $true,
inference(unfold_def,[status(thm)],[242]) ).
thf(754,plain,
$true = $true,
inference(unfold_def,[status(thm)],[245]) ).
thf(755,plain,
$true = $true,
inference(unfold_def,[status(thm)],[246]) ).
thf(756,plain,
$true = $true,
inference(unfold_def,[status(thm)],[253]) ).
thf(757,plain,
$true = $true,
inference(unfold_def,[status(thm)],[255]) ).
thf(758,plain,
$true = $true,
inference(unfold_def,[status(thm)],[257]) ).
thf(759,plain,
$true = $true,
inference(unfold_def,[status(thm)],[260]) ).
thf(760,plain,
( ( ! [A: $i] :
( ( strict_rel_str @ ( incl_POSet @ A ) )
& ( rel_str @ ( incl_POSet @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(761,plain,
$true = $true,
inference(unfold_def,[status(thm)],[263]) ).
thf(762,plain,
$true = $true,
inference(unfold_def,[status(thm)],[265]) ).
thf(763,plain,
$true = $true,
inference(unfold_def,[status(thm)],[268]) ).
thf(764,plain,
$true = $true,
inference(unfold_def,[status(thm)],[270]) ).
thf(765,plain,
$true = $true,
inference(unfold_def,[status(thm)],[275]) ).
thf(766,plain,
$true = $true,
inference(unfold_def,[status(thm)],[278]) ).
thf(767,plain,
$true = $true,
inference(unfold_def,[status(thm)],[280]) ).
thf(768,plain,
$true = $true,
inference(unfold_def,[status(thm)],[284]) ).
thf(769,plain,
$true = $true,
inference(unfold_def,[status(thm)],[285]) ).
thf(770,plain,
$true = $true,
inference(unfold_def,[status(thm)],[286]) ).
thf(771,plain,
$true = $true,
inference(unfold_def,[status(thm)],[289]) ).
thf(772,plain,
$true = $true,
inference(unfold_def,[status(thm)],[290]) ).
thf(773,plain,
$true = $true,
inference(unfold_def,[status(thm)],[293]) ).
thf(774,plain,
$true = $true,
inference(unfold_def,[status(thm)],[294]) ).
thf(775,plain,
$true = $true,
inference(unfold_def,[status(thm)],[296]) ).
thf(776,plain,
$true = $true,
inference(unfold_def,[status(thm)],[299]) ).
thf(777,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(778,plain,
( ( ! [A: $i] :
( ( incl_POSet @ A )
= ( rel_str_of @ A @ ( inclusion_order @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374]) ).
thf(779,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[659]) ).
thf(780,plain,
( ( ( ( the_carrier @ ( incl_POSet @ sK1_A ) )
= sK1_A )
& ( ( the_InternalRel @ ( incl_POSet @ sK1_A ) )
= ( inclusion_order @ sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[723]) ).
thf(781,plain,
( ( ( the_carrier @ ( incl_POSet @ sK1_A ) )
= sK1_A )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[780]) ).
thf(782,plain,
( ( ( the_InternalRel @ ( incl_POSet @ sK1_A ) )
= ( inclusion_order @ sK1_A ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[780]) ).
thf(783,plain,
( ( ( the_carrier @ ( incl_POSet @ sK1_A ) )
!= sK1_A )
= $true ),
inference(polarity_switch,[status(thm)],[781]) ).
thf(784,plain,
( ( ( the_InternalRel @ ( incl_POSet @ sK1_A ) )
!= ( inclusion_order @ sK1_A ) )
= $true ),
inference(polarity_switch,[status(thm)],[782]) ).
thf(785,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( relation_of2_as_subset @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[724]) ).
thf(786,plain,
( ( ( one_sorted_str @ sK2_A )
& ~ ( empty_carrier @ sK2_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[725]) ).
thf(787,plain,
( ( ( rel_str @ sK3_A )
& ( strict_rel_str @ sK3_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[726]) ).
thf(788,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation_of2 @ B @ A @ A )
| ( ! [C: $i] :
( ! [D: $i] :
( ( rel_str_of @ A @ B )
!= ( rel_str_of @ C @ D ) )
| ( A = C ) )
& ! [C: $i,D: $i] :
( ( ( rel_str_of @ A @ B )
!= ( rel_str_of @ C @ D ) )
| ( B = D ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[727]) ).
thf(789,plain,
( ( ! [A: $i,B: $i] : ( relation_of2_as_subset @ ( sK4_C @ B @ A ) @ A @ B ) )
= $true ),
inference(extcnf_combined,[status(esa)],[728]) ).
thf(790,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( subrelstr @ ( sK5_B @ A ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[729]) ).
thf(791,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( net_str @ ( sK6_B @ A ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[730]) ).
thf(792,plain,
( ( one_sorted_str @ sK7_A )
= $true ),
inference(extcnf_combined,[status(esa)],[731]) ).
thf(793,plain,
( ( rel_str @ sK8_A )
= $true ),
inference(extcnf_combined,[status(esa)],[732]) ).
thf(794,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ! [B: $i] :
( ~ ( subrelstr @ B @ A )
| ( rel_str @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[733]) ).
thf(795,plain,
( ( ! [A: $i] :
( ~ ( join_semilatt_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[734]) ).
thf(796,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ! [B: $i] :
( ~ ( net_str @ B @ A )
| ( rel_str @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[735]) ).
thf(797,plain,
( ( ! [A: $i] :
( ~ ( top_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[736]) ).
thf(798,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[737]) ).
thf(799,plain,
( ( ! [A: $i] :
( ~ ( meet_semilatt_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[738]) ).
thf(800,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation_of2 @ B @ A @ A )
| ( rel_str @ ( rel_str_of @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( relation_of2 @ B @ A @ A )
| ( strict_rel_str @ ( rel_str_of @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[740]) ).
thf(801,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( strict_rel_str @ A )
| ( A
= ( rel_str_of @ ( the_carrier @ A ) @ ( the_InternalRel @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[741]) ).
thf(802,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( relation_of2_as_subset @ D @ C @ A )
| ~ ( subset @ A @ B )
| ( relation_of2_as_subset @ D @ C @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[745]) ).
thf(803,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[748]) ).
thf(804,plain,
( ( ! [A: $i] : ( rel_str @ ( incl_POSet @ A ) )
& ! [A: $i] : ( strict_rel_str @ ( incl_POSet @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[760]) ).
thf(805,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[777]) ).
thf(806,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[779]) ).
thf(807,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[806]) ).
thf(808,plain,
( ( ! [A: $i] :
( ( incl_POSet @ A )
= ( rel_str_of @ A @ ( inclusion_order @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[778]) ).
thf(809,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[805]) ).
thf(810,plain,
$true = $true,
inference(copy,[status(thm)],[776]) ).
thf(811,plain,
$true = $true,
inference(copy,[status(thm)],[775]) ).
thf(812,plain,
$true = $true,
inference(copy,[status(thm)],[774]) ).
thf(813,plain,
$true = $true,
inference(copy,[status(thm)],[773]) ).
thf(814,plain,
$true = $true,
inference(copy,[status(thm)],[772]) ).
thf(815,plain,
$true = $true,
inference(copy,[status(thm)],[771]) ).
thf(816,plain,
$true = $true,
inference(copy,[status(thm)],[770]) ).
thf(817,plain,
$true = $true,
inference(copy,[status(thm)],[769]) ).
thf(818,plain,
$true = $true,
inference(copy,[status(thm)],[768]) ).
thf(819,plain,
$true = $true,
inference(copy,[status(thm)],[767]) ).
thf(820,plain,
$true = $true,
inference(copy,[status(thm)],[766]) ).
thf(821,plain,
$true = $true,
inference(copy,[status(thm)],[765]) ).
thf(822,plain,
$true = $true,
inference(copy,[status(thm)],[764]) ).
thf(823,plain,
$true = $true,
inference(copy,[status(thm)],[763]) ).
thf(824,plain,
$true = $true,
inference(copy,[status(thm)],[762]) ).
thf(825,plain,
$true = $true,
inference(copy,[status(thm)],[761]) ).
thf(826,plain,
( ( ! [A: $i] : ( rel_str @ ( incl_POSet @ A ) )
& ! [A: $i] : ( strict_rel_str @ ( incl_POSet @ A ) ) )
= $true ),
inference(copy,[status(thm)],[804]) ).
thf(827,plain,
$true = $true,
inference(copy,[status(thm)],[759]) ).
thf(828,plain,
$true = $true,
inference(copy,[status(thm)],[758]) ).
thf(829,plain,
$true = $true,
inference(copy,[status(thm)],[757]) ).
thf(830,plain,
$true = $true,
inference(copy,[status(thm)],[756]) ).
thf(831,plain,
$true = $true,
inference(copy,[status(thm)],[755]) ).
thf(832,plain,
$true = $true,
inference(copy,[status(thm)],[754]) ).
thf(833,plain,
$true = $true,
inference(copy,[status(thm)],[753]) ).
thf(834,plain,
$true = $true,
inference(copy,[status(thm)],[752]) ).
thf(835,plain,
$true = $true,
inference(copy,[status(thm)],[751]) ).
thf(836,plain,
$true = $true,
inference(copy,[status(thm)],[750]) ).
thf(837,plain,
$true = $true,
inference(copy,[status(thm)],[749]) ).
thf(838,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[803]) ).
thf(839,plain,
$true = $true,
inference(copy,[status(thm)],[747]) ).
thf(840,plain,
( ( ! [A: $i] :
( ( inclusion_order @ A )
= ( inclusion_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[746]) ).
thf(841,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( relation_of2_as_subset @ D @ C @ A )
| ~ ( subset @ A @ B )
| ( relation_of2_as_subset @ D @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[802]) ).
thf(842,plain,
( ( ! [A: $i] : ( reflexive @ ( inclusion_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[744]) ).
thf(843,plain,
( ( ! [A: $i] : ( transitive @ ( inclusion_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[743]) ).
thf(844,plain,
( ( ! [A: $i] : ( antisymmetric @ ( inclusion_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[742]) ).
thf(845,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( strict_rel_str @ A )
| ( A
= ( rel_str_of @ ( the_carrier @ A ) @ ( the_InternalRel @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[801]) ).
thf(846,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation_of2 @ B @ A @ A )
| ( rel_str @ ( rel_str_of @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( relation_of2 @ B @ A @ A )
| ( strict_rel_str @ ( rel_str_of @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[800]) ).
thf(847,plain,
( ( ! [A: $i] : ( relation @ ( inclusion_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[739]) ).
thf(848,plain,
( ( ! [A: $i] :
( ~ ( meet_semilatt_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[799]) ).
thf(849,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[798]) ).
thf(850,plain,
( ( ! [A: $i] :
( ~ ( top_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[797]) ).
thf(851,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ! [B: $i] :
( ~ ( net_str @ B @ A )
| ( rel_str @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[796]) ).
thf(852,plain,
( ( ! [A: $i] :
( ~ ( join_semilatt_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[795]) ).
thf(853,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ! [B: $i] :
( ~ ( subrelstr @ B @ A )
| ( rel_str @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[794]) ).
thf(854,plain,
( ( rel_str @ sK8_A )
= $true ),
inference(copy,[status(thm)],[793]) ).
thf(855,plain,
( ( one_sorted_str @ sK7_A )
= $true ),
inference(copy,[status(thm)],[792]) ).
thf(856,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( net_str @ ( sK6_B @ A ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[791]) ).
thf(857,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( subrelstr @ ( sK5_B @ A ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[790]) ).
thf(858,plain,
( ( ! [A: $i,B: $i] : ( relation_of2_as_subset @ ( sK4_C @ B @ A ) @ A @ B ) )
= $true ),
inference(copy,[status(thm)],[789]) ).
thf(859,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation_of2 @ B @ A @ A )
| ( ! [C: $i] :
( ! [D: $i] :
( ( rel_str_of @ A @ B )
!= ( rel_str_of @ C @ D ) )
| ( A = C ) )
& ! [C: $i,D: $i] :
( ( ( rel_str_of @ A @ B )
!= ( rel_str_of @ C @ D ) )
| ( B = D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[788]) ).
thf(860,plain,
( ( ( rel_str @ sK3_A )
& ( strict_rel_str @ sK3_A ) )
= $true ),
inference(copy,[status(thm)],[787]) ).
thf(861,plain,
( ( ( one_sorted_str @ sK2_A )
& ~ ( empty_carrier @ sK2_A ) )
= $true ),
inference(copy,[status(thm)],[786]) ).
thf(862,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( relation_of2_as_subset @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[785]) ).
thf(863,plain,
( ( ( the_carrier @ ( incl_POSet @ sK1_A ) )
!= sK1_A )
= $true ),
inference(copy,[status(thm)],[783]) ).
thf(864,plain,
( ( ~ ( ~ ( one_sorted_str @ sK2_A )
| ~ ~ ( empty_carrier @ sK2_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[861]) ).
thf(865,plain,
( ( ~ ( ~ ( rel_str @ sK3_A )
| ~ ( strict_rel_str @ sK3_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[860]) ).
thf(866,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2 @ SX2 @ SX0 @ SX1 )
| ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( relation_of2 @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[862]) ).
thf(867,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ( rel_str_of @ SX0 @ SX1 )
!= ( rel_str_of @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( ( rel_str_of @ SX0 @ SX1 )
!= ( rel_str_of @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[859]) ).
thf(868,plain,
( ( ~ ( ~ ! [SX0: $i] : ( rel_str @ ( incl_POSet @ SX0 ) )
| ~ ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[826]) ).
thf(869,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[846]) ).
thf(870,plain,
! [SV1: $i] :
( ( ~ ( one_sorted_str @ SV1 )
| ( ( cast_as_carrier_subset @ SV1 )
= ( the_carrier @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(871,plain,
! [SV2: $i] :
( ( ( incl_POSet @ SV2 )
= ( rel_str_of @ SV2 @ ( inclusion_order @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(872,plain,
! [SV3: $i] :
( ( ~ ( one_sorted_str @ SV3 )
| ( ( cast_as_carrier_subset @ SV3 )
= ( the_carrier @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(873,plain,
! [SV4: $i] :
( ( ~ ( rel_str @ SV4 )
| ( relation_of2_as_subset @ ( the_InternalRel @ SV4 ) @ ( the_carrier @ SV4 ) @ ( the_carrier @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(874,plain,
! [SV5: $i] :
( ( ( inclusion_order @ SV5 )
= ( inclusion_relation @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(875,plain,
! [SV6: $i] :
( ( ! [SY44: $i,SY45: $i,SY46: $i] :
( ~ ( relation_of2_as_subset @ SY46 @ SY45 @ SV6 )
| ~ ( subset @ SV6 @ SY44 )
| ( relation_of2_as_subset @ SY46 @ SY45 @ SY44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(876,plain,
! [SV7: $i] :
( ( reflexive @ ( inclusion_relation @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(877,plain,
! [SV8: $i] :
( ( transitive @ ( inclusion_relation @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(878,plain,
! [SV9: $i] :
( ( antisymmetric @ ( inclusion_relation @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(879,plain,
! [SV10: $i] :
( ( ~ ( rel_str @ SV10 )
| ~ ( strict_rel_str @ SV10 )
| ( SV10
= ( rel_str_of @ ( the_carrier @ SV10 ) @ ( the_InternalRel @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(880,plain,
! [SV11: $i] :
( ( relation @ ( inclusion_relation @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(881,plain,
! [SV12: $i] :
( ( ~ ( meet_semilatt_str @ SV12 )
| ( one_sorted_str @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(882,plain,
! [SV13: $i] :
( ( ~ ( rel_str @ SV13 )
| ( one_sorted_str @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(883,plain,
! [SV14: $i] :
( ( ~ ( top_str @ SV14 )
| ( one_sorted_str @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(884,plain,
! [SV15: $i] :
( ( ~ ( one_sorted_str @ SV15 )
| ! [SY47: $i] :
( ~ ( net_str @ SY47 @ SV15 )
| ( rel_str @ SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(885,plain,
! [SV16: $i] :
( ( ~ ( join_semilatt_str @ SV16 )
| ( one_sorted_str @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(886,plain,
! [SV17: $i] :
( ( ~ ( rel_str @ SV17 )
| ! [SY48: $i] :
( ~ ( subrelstr @ SY48 @ SV17 )
| ( rel_str @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(887,plain,
! [SV18: $i] :
( ( ~ ( one_sorted_str @ SV18 )
| ( net_str @ ( sK6_B @ SV18 ) @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(888,plain,
! [SV19: $i] :
( ( ~ ( rel_str @ SV19 )
| ( subrelstr @ ( sK5_B @ SV19 ) @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(889,plain,
! [SV20: $i] :
( ( ! [SY49: $i] : ( relation_of2_as_subset @ ( sK4_C @ SY49 @ SV20 ) @ SV20 @ SY49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(890,plain,
( ( ( the_carrier @ ( incl_POSet @ sK1_A ) )
= sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[863]) ).
thf(891,plain,
( ( ~ ( one_sorted_str @ sK2_A )
| ~ ~ ( empty_carrier @ sK2_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[864]) ).
thf(892,plain,
( ( ~ ( rel_str @ sK3_A )
| ~ ( strict_rel_str @ sK3_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(893,plain,
! [SV21: $i] :
( ( ~ ( ~ ! [SY50: $i,SY51: $i] :
( ~ ( relation_of2 @ SY51 @ SV21 @ SY50 )
| ( relation_of2_as_subset @ SY51 @ SV21 @ SY50 ) )
| ~ ! [SY52: $i,SY53: $i] :
( ~ ( relation_of2_as_subset @ SY53 @ SV21 @ SY52 )
| ( relation_of2 @ SY53 @ SV21 @ SY52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(894,plain,
! [SV22: $i] :
( ( ! [SY54: $i] :
( ~ ( relation_of2 @ SY54 @ SV22 @ SV22 )
| ~ ( ~ ! [SY55: $i] :
( ! [SY56: $i] :
( ( rel_str_of @ SV22 @ SY54 )
!= ( rel_str_of @ SY55 @ SY56 ) )
| ( SV22 = SY55 ) )
| ~ ! [SY57: $i,SY58: $i] :
( ( ( rel_str_of @ SV22 @ SY54 )
!= ( rel_str_of @ SY57 @ SY58 ) )
| ( SY54 = SY58 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(895,plain,
( ( ~ ! [SX0: $i] : ( rel_str @ ( incl_POSet @ SX0 ) )
| ~ ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[868]) ).
thf(896,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[869]) ).
thf(897,plain,
! [SV1: $i] :
( ( ( ~ ( one_sorted_str @ SV1 ) )
= $true )
| ( ( ( cast_as_carrier_subset @ SV1 )
= ( the_carrier @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[870]) ).
thf(898,plain,
! [SV3: $i] :
( ( ( ~ ( one_sorted_str @ SV3 ) )
= $true )
| ( ( ( cast_as_carrier_subset @ SV3 )
= ( the_carrier @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[872]) ).
thf(899,plain,
! [SV4: $i] :
( ( ( ~ ( rel_str @ SV4 ) )
= $true )
| ( ( relation_of2_as_subset @ ( the_InternalRel @ SV4 ) @ ( the_carrier @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[873]) ).
thf(900,plain,
! [SV23: $i,SV6: $i] :
( ( ! [SY59: $i,SY60: $i] :
( ~ ( relation_of2_as_subset @ SY60 @ SY59 @ SV6 )
| ~ ( subset @ SV6 @ SV23 )
| ( relation_of2_as_subset @ SY60 @ SY59 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(901,plain,
! [SV10: $i] :
( ( ( ~ ( rel_str @ SV10 ) )
= $true )
| ( ( ~ ( strict_rel_str @ SV10 )
| ( SV10
= ( rel_str_of @ ( the_carrier @ SV10 ) @ ( the_InternalRel @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[879]) ).
thf(902,plain,
! [SV12: $i] :
( ( ( ~ ( meet_semilatt_str @ SV12 ) )
= $true )
| ( ( one_sorted_str @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[881]) ).
thf(903,plain,
! [SV13: $i] :
( ( ( ~ ( rel_str @ SV13 ) )
= $true )
| ( ( one_sorted_str @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[882]) ).
thf(904,plain,
! [SV14: $i] :
( ( ( ~ ( top_str @ SV14 ) )
= $true )
| ( ( one_sorted_str @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[883]) ).
thf(905,plain,
! [SV15: $i] :
( ( ( ~ ( one_sorted_str @ SV15 ) )
= $true )
| ( ( ! [SY47: $i] :
( ~ ( net_str @ SY47 @ SV15 )
| ( rel_str @ SY47 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[884]) ).
thf(906,plain,
! [SV16: $i] :
( ( ( ~ ( join_semilatt_str @ SV16 ) )
= $true )
| ( ( one_sorted_str @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[885]) ).
thf(907,plain,
! [SV17: $i] :
( ( ( ~ ( rel_str @ SV17 ) )
= $true )
| ( ( ! [SY48: $i] :
( ~ ( subrelstr @ SY48 @ SV17 )
| ( rel_str @ SY48 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[886]) ).
thf(908,plain,
! [SV18: $i] :
( ( ( ~ ( one_sorted_str @ SV18 ) )
= $true )
| ( ( net_str @ ( sK6_B @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[887]) ).
thf(909,plain,
! [SV19: $i] :
( ( ( ~ ( rel_str @ SV19 ) )
= $true )
| ( ( subrelstr @ ( sK5_B @ SV19 ) @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[888]) ).
thf(910,plain,
! [SV20: $i,SV24: $i] :
( ( relation_of2_as_subset @ ( sK4_C @ SV24 @ SV20 ) @ SV20 @ SV24 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(911,plain,
( ( ~ ( one_sorted_str @ sK2_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[891]) ).
thf(912,plain,
( ( ~ ~ ( empty_carrier @ sK2_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[891]) ).
thf(913,plain,
( ( ~ ( rel_str @ sK3_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[892]) ).
thf(914,plain,
( ( ~ ( strict_rel_str @ sK3_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[892]) ).
thf(915,plain,
! [SV21: $i] :
( ( ~ ! [SY50: $i,SY51: $i] :
( ~ ( relation_of2 @ SY51 @ SV21 @ SY50 )
| ( relation_of2_as_subset @ SY51 @ SV21 @ SY50 ) )
| ~ ! [SY52: $i,SY53: $i] :
( ~ ( relation_of2_as_subset @ SY53 @ SV21 @ SY52 )
| ( relation_of2 @ SY53 @ SV21 @ SY52 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[893]) ).
thf(916,plain,
! [SV22: $i,SV25: $i] :
( ( ~ ( relation_of2 @ SV25 @ SV22 @ SV22 )
| ~ ( ~ ! [SY61: $i] :
( ! [SY62: $i] :
( ( rel_str_of @ SV22 @ SV25 )
!= ( rel_str_of @ SY61 @ SY62 ) )
| ( SV22 = SY61 ) )
| ~ ! [SY63: $i,SY64: $i] :
( ( ( rel_str_of @ SV22 @ SV25 )
!= ( rel_str_of @ SY63 @ SY64 ) )
| ( SV25 = SY64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(917,plain,
( ( ~ ! [SX0: $i] : ( rel_str @ ( incl_POSet @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[895]) ).
thf(918,plain,
( ( ~ ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[895]) ).
thf(919,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[896]) ).
thf(920,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[896]) ).
thf(921,plain,
! [SV1: $i] :
( ( ( one_sorted_str @ SV1 )
= $false )
| ( ( ( cast_as_carrier_subset @ SV1 )
= ( the_carrier @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[897]) ).
thf(922,plain,
! [SV3: $i] :
( ( ( one_sorted_str @ SV3 )
= $false )
| ( ( ( cast_as_carrier_subset @ SV3 )
= ( the_carrier @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[898]) ).
thf(923,plain,
! [SV4: $i] :
( ( ( rel_str @ SV4 )
= $false )
| ( ( relation_of2_as_subset @ ( the_InternalRel @ SV4 ) @ ( the_carrier @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[899]) ).
thf(924,plain,
! [SV23: $i,SV6: $i,SV26: $i] :
( ( ! [SY65: $i] :
( ~ ( relation_of2_as_subset @ SY65 @ SV26 @ SV6 )
| ~ ( subset @ SV6 @ SV23 )
| ( relation_of2_as_subset @ SY65 @ SV26 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(925,plain,
! [SV10: $i] :
( ( ( rel_str @ SV10 )
= $false )
| ( ( ~ ( strict_rel_str @ SV10 )
| ( SV10
= ( rel_str_of @ ( the_carrier @ SV10 ) @ ( the_InternalRel @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[901]) ).
thf(926,plain,
! [SV12: $i] :
( ( ( meet_semilatt_str @ SV12 )
= $false )
| ( ( one_sorted_str @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(927,plain,
! [SV13: $i] :
( ( ( rel_str @ SV13 )
= $false )
| ( ( one_sorted_str @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[903]) ).
thf(928,plain,
! [SV14: $i] :
( ( ( top_str @ SV14 )
= $false )
| ( ( one_sorted_str @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[904]) ).
thf(929,plain,
! [SV15: $i] :
( ( ( one_sorted_str @ SV15 )
= $false )
| ( ( ! [SY47: $i] :
( ~ ( net_str @ SY47 @ SV15 )
| ( rel_str @ SY47 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[905]) ).
thf(930,plain,
! [SV16: $i] :
( ( ( join_semilatt_str @ SV16 )
= $false )
| ( ( one_sorted_str @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[906]) ).
thf(931,plain,
! [SV17: $i] :
( ( ( rel_str @ SV17 )
= $false )
| ( ( ! [SY48: $i] :
( ~ ( subrelstr @ SY48 @ SV17 )
| ( rel_str @ SY48 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[907]) ).
thf(932,plain,
! [SV18: $i] :
( ( ( one_sorted_str @ SV18 )
= $false )
| ( ( net_str @ ( sK6_B @ SV18 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[908]) ).
thf(933,plain,
! [SV19: $i] :
( ( ( rel_str @ SV19 )
= $false )
| ( ( subrelstr @ ( sK5_B @ SV19 ) @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[909]) ).
thf(934,plain,
( ( one_sorted_str @ sK2_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[911]) ).
thf(935,plain,
( ( ~ ( empty_carrier @ sK2_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[912]) ).
thf(936,plain,
( ( rel_str @ sK3_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[913]) ).
thf(937,plain,
( ( strict_rel_str @ sK3_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[914]) ).
thf(938,plain,
! [SV21: $i] :
( ( ~ ! [SY50: $i,SY51: $i] :
( ~ ( relation_of2 @ SY51 @ SV21 @ SY50 )
| ( relation_of2_as_subset @ SY51 @ SV21 @ SY50 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[915]) ).
thf(939,plain,
! [SV21: $i] :
( ( ~ ! [SY52: $i,SY53: $i] :
( ~ ( relation_of2_as_subset @ SY53 @ SV21 @ SY52 )
| ( relation_of2 @ SY53 @ SV21 @ SY52 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[915]) ).
thf(940,plain,
! [SV22: $i,SV25: $i] :
( ( ( ~ ( relation_of2 @ SV25 @ SV22 @ SV22 ) )
= $true )
| ( ( ~ ( ~ ! [SY61: $i] :
( ! [SY62: $i] :
( ( rel_str_of @ SV22 @ SV25 )
!= ( rel_str_of @ SY61 @ SY62 ) )
| ( SV22 = SY61 ) )
| ~ ! [SY63: $i,SY64: $i] :
( ( ( rel_str_of @ SV22 @ SV25 )
!= ( rel_str_of @ SY63 @ SY64 ) )
| ( SV25 = SY64 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[916]) ).
thf(941,plain,
( ( ! [SX0: $i] : ( rel_str @ ( incl_POSet @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[917]) ).
thf(942,plain,
( ( ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[918]) ).
thf(943,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[919]) ).
thf(944,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[920]) ).
thf(945,plain,
! [SV23: $i,SV6: $i,SV26: $i,SV27: $i] :
( ( ~ ( relation_of2_as_subset @ SV27 @ SV26 @ SV6 )
| ~ ( subset @ SV6 @ SV23 )
| ( relation_of2_as_subset @ SV27 @ SV26 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(946,plain,
! [SV10: $i] :
( ( ( ~ ( strict_rel_str @ SV10 ) )
= $true )
| ( ( SV10
= ( rel_str_of @ ( the_carrier @ SV10 ) @ ( the_InternalRel @ SV10 ) ) )
= $true )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[925]) ).
thf(947,plain,
! [SV15: $i,SV28: $i] :
( ( ( ~ ( net_str @ SV28 @ SV15 )
| ( rel_str @ SV28 ) )
= $true )
| ( ( one_sorted_str @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(948,plain,
! [SV17: $i,SV29: $i] :
( ( ( ~ ( subrelstr @ SV29 @ SV17 )
| ( rel_str @ SV29 ) )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(949,plain,
( ( empty_carrier @ sK2_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[935]) ).
thf(950,plain,
! [SV21: $i] :
( ( ! [SY50: $i,SY51: $i] :
( ~ ( relation_of2 @ SY51 @ SV21 @ SY50 )
| ( relation_of2_as_subset @ SY51 @ SV21 @ SY50 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[938]) ).
thf(951,plain,
! [SV21: $i] :
( ( ! [SY52: $i,SY53: $i] :
( ~ ( relation_of2_as_subset @ SY53 @ SV21 @ SY52 )
| ( relation_of2 @ SY53 @ SV21 @ SY52 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[939]) ).
thf(952,plain,
! [SV22: $i,SV25: $i] :
( ( ( relation_of2 @ SV25 @ SV22 @ SV22 )
= $false )
| ( ( ~ ( ~ ! [SY61: $i] :
( ! [SY62: $i] :
( ( rel_str_of @ SV22 @ SV25 )
!= ( rel_str_of @ SY61 @ SY62 ) )
| ( SV22 = SY61 ) )
| ~ ! [SY63: $i,SY64: $i] :
( ( ( rel_str_of @ SV22 @ SV25 )
!= ( rel_str_of @ SY63 @ SY64 ) )
| ( SV25 = SY64 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[940]) ).
thf(953,plain,
! [SV30: $i] :
( ( rel_str @ ( incl_POSet @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(954,plain,
! [SV31: $i] :
( ( strict_rel_str @ ( incl_POSet @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(955,plain,
! [SV32: $i] :
( ( ! [SY66: $i] :
( ~ ( relation_of2 @ SY66 @ SV32 @ SV32 )
| ( rel_str @ ( rel_str_of @ SV32 @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(956,plain,
! [SV33: $i] :
( ( ! [SY67: $i] :
( ~ ( relation_of2 @ SY67 @ SV33 @ SV33 )
| ( strict_rel_str @ ( rel_str_of @ SV33 @ SY67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(957,plain,
! [SV23: $i,SV6: $i,SV26: $i,SV27: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV27 @ SV26 @ SV6 ) )
= $true )
| ( ( ~ ( subset @ SV6 @ SV23 )
| ( relation_of2_as_subset @ SV27 @ SV26 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[945]) ).
thf(958,plain,
! [SV10: $i] :
( ( ( strict_rel_str @ SV10 )
= $false )
| ( ( SV10
= ( rel_str_of @ ( the_carrier @ SV10 ) @ ( the_InternalRel @ SV10 ) ) )
= $true )
| ( ( rel_str @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[946]) ).
thf(959,plain,
! [SV15: $i,SV28: $i] :
( ( ( ~ ( net_str @ SV28 @ SV15 ) )
= $true )
| ( ( rel_str @ SV28 )
= $true )
| ( ( one_sorted_str @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[947]) ).
thf(960,plain,
! [SV17: $i,SV29: $i] :
( ( ( ~ ( subrelstr @ SV29 @ SV17 ) )
= $true )
| ( ( rel_str @ SV29 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[948]) ).
thf(961,plain,
! [SV34: $i,SV21: $i] :
( ( ! [SY68: $i] :
( ~ ( relation_of2 @ SY68 @ SV21 @ SV34 )
| ( relation_of2_as_subset @ SY68 @ SV21 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(962,plain,
! [SV35: $i,SV21: $i] :
( ( ! [SY69: $i] :
( ~ ( relation_of2_as_subset @ SY69 @ SV21 @ SV35 )
| ( relation_of2 @ SY69 @ SV21 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(963,plain,
! [SV25: $i,SV22: $i] :
( ( ( ~ ! [SY61: $i] :
( ! [SY62: $i] :
( ( rel_str_of @ SV22 @ SV25 )
!= ( rel_str_of @ SY61 @ SY62 ) )
| ( SV22 = SY61 ) )
| ~ ! [SY63: $i,SY64: $i] :
( ( ( rel_str_of @ SV22 @ SV25 )
!= ( rel_str_of @ SY63 @ SY64 ) )
| ( SV25 = SY64 ) ) )
= $false )
| ( ( relation_of2 @ SV25 @ SV22 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[952]) ).
thf(964,plain,
! [SV32: $i,SV36: $i] :
( ( ~ ( relation_of2 @ SV36 @ SV32 @ SV32 )
| ( rel_str @ ( rel_str_of @ SV32 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(965,plain,
! [SV33: $i,SV37: $i] :
( ( ~ ( relation_of2 @ SV37 @ SV33 @ SV33 )
| ( strict_rel_str @ ( rel_str_of @ SV33 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(966,plain,
! [SV23: $i,SV6: $i,SV26: $i,SV27: $i] :
( ( ( relation_of2_as_subset @ SV27 @ SV26 @ SV6 )
= $false )
| ( ( ~ ( subset @ SV6 @ SV23 )
| ( relation_of2_as_subset @ SV27 @ SV26 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[957]) ).
thf(967,plain,
! [SV15: $i,SV28: $i] :
( ( ( net_str @ SV28 @ SV15 )
= $false )
| ( ( rel_str @ SV28 )
= $true )
| ( ( one_sorted_str @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[959]) ).
thf(968,plain,
! [SV17: $i,SV29: $i] :
( ( ( subrelstr @ SV29 @ SV17 )
= $false )
| ( ( rel_str @ SV29 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[960]) ).
thf(969,plain,
! [SV34: $i,SV21: $i,SV38: $i] :
( ( ~ ( relation_of2 @ SV38 @ SV21 @ SV34 )
| ( relation_of2_as_subset @ SV38 @ SV21 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(970,plain,
! [SV35: $i,SV21: $i,SV39: $i] :
( ( ~ ( relation_of2_as_subset @ SV39 @ SV21 @ SV35 )
| ( relation_of2 @ SV39 @ SV21 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(971,plain,
! [SV25: $i,SV22: $i] :
( ( ( ~ ! [SY61: $i] :
( ! [SY62: $i] :
( ( rel_str_of @ SV22 @ SV25 )
!= ( rel_str_of @ SY61 @ SY62 ) )
| ( SV22 = SY61 ) ) )
= $false )
| ( ( relation_of2 @ SV25 @ SV22 @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[963]) ).
thf(972,plain,
! [SV25: $i,SV22: $i] :
( ( ( ~ ! [SY63: $i,SY64: $i] :
( ( ( rel_str_of @ SV22 @ SV25 )
!= ( rel_str_of @ SY63 @ SY64 ) )
| ( SV25 = SY64 ) ) )
= $false )
| ( ( relation_of2 @ SV25 @ SV22 @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[963]) ).
thf(973,plain,
! [SV32: $i,SV36: $i] :
( ( ( ~ ( relation_of2 @ SV36 @ SV32 @ SV32 ) )
= $true )
| ( ( rel_str @ ( rel_str_of @ SV32 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[964]) ).
thf(974,plain,
! [SV33: $i,SV37: $i] :
( ( ( ~ ( relation_of2 @ SV37 @ SV33 @ SV33 ) )
= $true )
| ( ( strict_rel_str @ ( rel_str_of @ SV33 @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[965]) ).
thf(975,plain,
! [SV26: $i,SV27: $i,SV23: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV23 ) )
= $true )
| ( ( relation_of2_as_subset @ SV27 @ SV26 @ SV23 )
= $true )
| ( ( relation_of2_as_subset @ SV27 @ SV26 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[966]) ).
thf(976,plain,
! [SV34: $i,SV21: $i,SV38: $i] :
( ( ( ~ ( relation_of2 @ SV38 @ SV21 @ SV34 ) )
= $true )
| ( ( relation_of2_as_subset @ SV38 @ SV21 @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[969]) ).
thf(977,plain,
! [SV35: $i,SV21: $i,SV39: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV39 @ SV21 @ SV35 ) )
= $true )
| ( ( relation_of2 @ SV39 @ SV21 @ SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[970]) ).
thf(978,plain,
! [SV25: $i,SV22: $i] :
( ( ( ! [SY61: $i] :
( ! [SY62: $i] :
( ( rel_str_of @ SV22 @ SV25 )
!= ( rel_str_of @ SY61 @ SY62 ) )
| ( SV22 = SY61 ) ) )
= $true )
| ( ( relation_of2 @ SV25 @ SV22 @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[971]) ).
thf(979,plain,
! [SV25: $i,SV22: $i] :
( ( ( ! [SY63: $i,SY64: $i] :
( ( ( rel_str_of @ SV22 @ SV25 )
!= ( rel_str_of @ SY63 @ SY64 ) )
| ( SV25 = SY64 ) ) )
= $true )
| ( ( relation_of2 @ SV25 @ SV22 @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[972]) ).
thf(980,plain,
! [SV32: $i,SV36: $i] :
( ( ( relation_of2 @ SV36 @ SV32 @ SV32 )
= $false )
| ( ( rel_str @ ( rel_str_of @ SV32 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[973]) ).
thf(981,plain,
! [SV33: $i,SV37: $i] :
( ( ( relation_of2 @ SV37 @ SV33 @ SV33 )
= $false )
| ( ( strict_rel_str @ ( rel_str_of @ SV33 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[974]) ).
thf(982,plain,
! [SV26: $i,SV27: $i,SV23: $i,SV6: $i] :
( ( ( subset @ SV6 @ SV23 )
= $false )
| ( ( relation_of2_as_subset @ SV27 @ SV26 @ SV23 )
= $true )
| ( ( relation_of2_as_subset @ SV27 @ SV26 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[975]) ).
thf(983,plain,
! [SV34: $i,SV21: $i,SV38: $i] :
( ( ( relation_of2 @ SV38 @ SV21 @ SV34 )
= $false )
| ( ( relation_of2_as_subset @ SV38 @ SV21 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[976]) ).
thf(984,plain,
! [SV35: $i,SV21: $i,SV39: $i] :
( ( ( relation_of2_as_subset @ SV39 @ SV21 @ SV35 )
= $false )
| ( ( relation_of2 @ SV39 @ SV21 @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(985,plain,
! [SV40: $i,SV25: $i,SV22: $i] :
( ( ( ! [SY70: $i] :
( ( rel_str_of @ SV22 @ SV25 )
!= ( rel_str_of @ SV40 @ SY70 ) )
| ( SV22 = SV40 ) )
= $true )
| ( ( relation_of2 @ SV25 @ SV22 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(986,plain,
! [SV41: $i,SV25: $i,SV22: $i] :
( ( ( ! [SY71: $i] :
( ( ( rel_str_of @ SV22 @ SV25 )
!= ( rel_str_of @ SV41 @ SY71 ) )
| ( SV25 = SY71 ) ) )
= $true )
| ( ( relation_of2 @ SV25 @ SV22 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(987,plain,
! [SV40: $i,SV25: $i,SV22: $i] :
( ( ( ! [SY70: $i] :
( ( rel_str_of @ SV22 @ SV25 )
!= ( rel_str_of @ SV40 @ SY70 ) ) )
= $true )
| ( ( SV22 = SV40 )
= $true )
| ( ( relation_of2 @ SV25 @ SV22 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[985]) ).
thf(988,plain,
! [SV42: $i,SV41: $i,SV25: $i,SV22: $i] :
( ( ( ( ( rel_str_of @ SV22 @ SV25 )
!= ( rel_str_of @ SV41 @ SV42 ) )
| ( SV25 = SV42 ) )
= $true )
| ( ( relation_of2 @ SV25 @ SV22 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(989,plain,
! [SV43: $i,SV40: $i,SV25: $i,SV22: $i] :
( ( ( ( rel_str_of @ SV22 @ SV25 )
!= ( rel_str_of @ SV40 @ SV43 ) )
= $true )
| ( ( SV22 = SV40 )
= $true )
| ( ( relation_of2 @ SV25 @ SV22 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(990,plain,
! [SV42: $i,SV41: $i,SV25: $i,SV22: $i] :
( ( ( ( rel_str_of @ SV22 @ SV25 )
!= ( rel_str_of @ SV41 @ SV42 ) )
= $true )
| ( ( SV25 = SV42 )
= $true )
| ( ( relation_of2 @ SV25 @ SV22 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[988]) ).
thf(991,plain,
! [SV43: $i,SV40: $i,SV25: $i,SV22: $i] :
( ( ( ( rel_str_of @ SV22 @ SV25 )
= ( rel_str_of @ SV40 @ SV43 ) )
= $false )
| ( ( SV22 = SV40 )
= $true )
| ( ( relation_of2 @ SV25 @ SV22 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(992,plain,
! [SV42: $i,SV41: $i,SV25: $i,SV22: $i] :
( ( ( ( rel_str_of @ SV22 @ SV25 )
= ( rel_str_of @ SV41 @ SV42 ) )
= $false )
| ( ( SV25 = SV42 )
= $true )
| ( ( relation_of2 @ SV25 @ SV22 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[990]) ).
thf(993,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[810,992,991,984,983,982,981,980,968,967,958,954,953,949,937,936,934,933,932,930,928,927,926,923,922,921,910,890,880,878,877,876,874,871,855,854,839,837,836,835,834,833,832,831,830,829,828,827,825,824,823,822,821,820,819,818,817,816,815,814,813,812,811]) ).
thf(994,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[806]) ).
thf(995,plain,
( ( ! [A: $i] :
( ( incl_POSet @ A )
= ( rel_str_of @ A @ ( inclusion_order @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[778]) ).
thf(996,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[805]) ).
thf(997,plain,
$true = $true,
inference(copy,[status(thm)],[776]) ).
thf(998,plain,
$true = $true,
inference(copy,[status(thm)],[775]) ).
thf(999,plain,
$true = $true,
inference(copy,[status(thm)],[774]) ).
thf(1000,plain,
$true = $true,
inference(copy,[status(thm)],[773]) ).
thf(1001,plain,
$true = $true,
inference(copy,[status(thm)],[772]) ).
thf(1002,plain,
$true = $true,
inference(copy,[status(thm)],[771]) ).
thf(1003,plain,
$true = $true,
inference(copy,[status(thm)],[770]) ).
thf(1004,plain,
$true = $true,
inference(copy,[status(thm)],[769]) ).
thf(1005,plain,
$true = $true,
inference(copy,[status(thm)],[768]) ).
thf(1006,plain,
$true = $true,
inference(copy,[status(thm)],[767]) ).
thf(1007,plain,
$true = $true,
inference(copy,[status(thm)],[766]) ).
thf(1008,plain,
$true = $true,
inference(copy,[status(thm)],[765]) ).
thf(1009,plain,
$true = $true,
inference(copy,[status(thm)],[764]) ).
thf(1010,plain,
$true = $true,
inference(copy,[status(thm)],[763]) ).
thf(1011,plain,
$true = $true,
inference(copy,[status(thm)],[762]) ).
thf(1012,plain,
$true = $true,
inference(copy,[status(thm)],[761]) ).
thf(1013,plain,
( ( ! [A: $i] : ( rel_str @ ( incl_POSet @ A ) )
& ! [A: $i] : ( strict_rel_str @ ( incl_POSet @ A ) ) )
= $true ),
inference(copy,[status(thm)],[804]) ).
thf(1014,plain,
$true = $true,
inference(copy,[status(thm)],[759]) ).
thf(1015,plain,
$true = $true,
inference(copy,[status(thm)],[758]) ).
thf(1016,plain,
$true = $true,
inference(copy,[status(thm)],[757]) ).
thf(1017,plain,
$true = $true,
inference(copy,[status(thm)],[756]) ).
thf(1018,plain,
$true = $true,
inference(copy,[status(thm)],[755]) ).
thf(1019,plain,
$true = $true,
inference(copy,[status(thm)],[754]) ).
thf(1020,plain,
$true = $true,
inference(copy,[status(thm)],[753]) ).
thf(1021,plain,
$true = $true,
inference(copy,[status(thm)],[752]) ).
thf(1022,plain,
$true = $true,
inference(copy,[status(thm)],[751]) ).
thf(1023,plain,
$true = $true,
inference(copy,[status(thm)],[750]) ).
thf(1024,plain,
$true = $true,
inference(copy,[status(thm)],[749]) ).
thf(1025,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[803]) ).
thf(1026,plain,
$true = $true,
inference(copy,[status(thm)],[747]) ).
thf(1027,plain,
( ( ! [A: $i] :
( ( inclusion_order @ A )
= ( inclusion_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[746]) ).
thf(1028,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( relation_of2_as_subset @ D @ C @ A )
| ~ ( subset @ A @ B )
| ( relation_of2_as_subset @ D @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[802]) ).
thf(1029,plain,
( ( ! [A: $i] : ( reflexive @ ( inclusion_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[744]) ).
thf(1030,plain,
( ( ! [A: $i] : ( transitive @ ( inclusion_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[743]) ).
thf(1031,plain,
( ( ! [A: $i] : ( antisymmetric @ ( inclusion_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[742]) ).
thf(1032,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( strict_rel_str @ A )
| ( A
= ( rel_str_of @ ( the_carrier @ A ) @ ( the_InternalRel @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[801]) ).
thf(1033,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation_of2 @ B @ A @ A )
| ( rel_str @ ( rel_str_of @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( relation_of2 @ B @ A @ A )
| ( strict_rel_str @ ( rel_str_of @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[800]) ).
thf(1034,plain,
( ( ! [A: $i] : ( relation @ ( inclusion_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[739]) ).
thf(1035,plain,
( ( ! [A: $i] :
( ~ ( meet_semilatt_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[799]) ).
thf(1036,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[798]) ).
thf(1037,plain,
( ( ! [A: $i] :
( ~ ( top_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[797]) ).
thf(1038,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ! [B: $i] :
( ~ ( net_str @ B @ A )
| ( rel_str @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[796]) ).
thf(1039,plain,
( ( ! [A: $i] :
( ~ ( join_semilatt_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[795]) ).
thf(1040,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ! [B: $i] :
( ~ ( subrelstr @ B @ A )
| ( rel_str @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[794]) ).
thf(1041,plain,
( ( rel_str @ sK8_A )
= $true ),
inference(copy,[status(thm)],[793]) ).
thf(1042,plain,
( ( one_sorted_str @ sK7_A )
= $true ),
inference(copy,[status(thm)],[792]) ).
thf(1043,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( net_str @ ( sK6_B @ A ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[791]) ).
thf(1044,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( subrelstr @ ( sK5_B @ A ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[790]) ).
thf(1045,plain,
( ( ! [A: $i,B: $i] : ( relation_of2_as_subset @ ( sK4_C @ B @ A ) @ A @ B ) )
= $true ),
inference(copy,[status(thm)],[789]) ).
thf(1046,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation_of2 @ B @ A @ A )
| ( ! [C: $i] :
( ! [D: $i] :
( ( rel_str_of @ A @ B )
!= ( rel_str_of @ C @ D ) )
| ( A = C ) )
& ! [C: $i,D: $i] :
( ( ( rel_str_of @ A @ B )
!= ( rel_str_of @ C @ D ) )
| ( B = D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[788]) ).
thf(1047,plain,
( ( ( rel_str @ sK3_A )
& ( strict_rel_str @ sK3_A ) )
= $true ),
inference(copy,[status(thm)],[787]) ).
thf(1048,plain,
( ( ( one_sorted_str @ sK2_A )
& ~ ( empty_carrier @ sK2_A ) )
= $true ),
inference(copy,[status(thm)],[786]) ).
thf(1049,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( relation_of2_as_subset @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[785]) ).
thf(1050,plain,
( ( ( the_InternalRel @ ( incl_POSet @ sK1_A ) )
!= ( inclusion_order @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[784]) ).
thf(1051,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1033]) ).
thf(1052,plain,
( ( ~ ( ~ ( rel_str @ sK3_A )
| ~ ( strict_rel_str @ sK3_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1047]) ).
thf(1053,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ( rel_str_of @ SX0 @ SX1 )
!= ( rel_str_of @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( ( rel_str_of @ SX0 @ SX1 )
!= ( rel_str_of @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1046]) ).
thf(1054,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2 @ SX2 @ SX0 @ SX1 )
| ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( relation_of2 @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1049]) ).
thf(1055,plain,
( ( ~ ( ~ ( one_sorted_str @ sK2_A )
| ~ ~ ( empty_carrier @ sK2_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1048]) ).
thf(1056,plain,
( ( ~ ( ~ ! [SX0: $i] : ( rel_str @ ( incl_POSet @ SX0 ) )
| ~ ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1013]) ).
thf(1057,plain,
! [SV44: $i] :
( ( ~ ( one_sorted_str @ SV44 )
| ( ( cast_as_carrier_subset @ SV44 )
= ( the_carrier @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1058,plain,
! [SV45: $i] :
( ( ( incl_POSet @ SV45 )
= ( rel_str_of @ SV45 @ ( inclusion_order @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1059,plain,
! [SV46: $i] :
( ( ~ ( one_sorted_str @ SV46 )
| ( ( cast_as_carrier_subset @ SV46 )
= ( the_carrier @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1060,plain,
! [SV47: $i] :
( ( ~ ( rel_str @ SV47 )
| ( relation_of2_as_subset @ ( the_InternalRel @ SV47 ) @ ( the_carrier @ SV47 ) @ ( the_carrier @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1061,plain,
! [SV48: $i] :
( ( ( inclusion_order @ SV48 )
= ( inclusion_relation @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1062,plain,
! [SV49: $i] :
( ( ! [SY72: $i,SY73: $i,SY74: $i] :
( ~ ( relation_of2_as_subset @ SY74 @ SY73 @ SV49 )
| ~ ( subset @ SV49 @ SY72 )
| ( relation_of2_as_subset @ SY74 @ SY73 @ SY72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1063,plain,
! [SV50: $i] :
( ( reflexive @ ( inclusion_relation @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1064,plain,
! [SV51: $i] :
( ( transitive @ ( inclusion_relation @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1030]) ).
thf(1065,plain,
! [SV52: $i] :
( ( antisymmetric @ ( inclusion_relation @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1066,plain,
! [SV53: $i] :
( ( ~ ( rel_str @ SV53 )
| ~ ( strict_rel_str @ SV53 )
| ( SV53
= ( rel_str_of @ ( the_carrier @ SV53 ) @ ( the_InternalRel @ SV53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1067,plain,
! [SV54: $i] :
( ( relation @ ( inclusion_relation @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1034]) ).
thf(1068,plain,
! [SV55: $i] :
( ( ~ ( meet_semilatt_str @ SV55 )
| ( one_sorted_str @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1069,plain,
! [SV56: $i] :
( ( ~ ( rel_str @ SV56 )
| ( one_sorted_str @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1036]) ).
thf(1070,plain,
! [SV57: $i] :
( ( ~ ( top_str @ SV57 )
| ( one_sorted_str @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1071,plain,
! [SV58: $i] :
( ( ~ ( one_sorted_str @ SV58 )
| ! [SY75: $i] :
( ~ ( net_str @ SY75 @ SV58 )
| ( rel_str @ SY75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1072,plain,
! [SV59: $i] :
( ( ~ ( join_semilatt_str @ SV59 )
| ( one_sorted_str @ SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1073,plain,
! [SV60: $i] :
( ( ~ ( rel_str @ SV60 )
| ! [SY76: $i] :
( ~ ( subrelstr @ SY76 @ SV60 )
| ( rel_str @ SY76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1074,plain,
! [SV61: $i] :
( ( ~ ( one_sorted_str @ SV61 )
| ( net_str @ ( sK6_B @ SV61 ) @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1075,plain,
! [SV62: $i] :
( ( ~ ( rel_str @ SV62 )
| ( subrelstr @ ( sK5_B @ SV62 ) @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1076,plain,
! [SV63: $i] :
( ( ! [SY77: $i] : ( relation_of2_as_subset @ ( sK4_C @ SY77 @ SV63 ) @ SV63 @ SY77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1077,plain,
( ( ( the_InternalRel @ ( incl_POSet @ sK1_A ) )
= ( inclusion_order @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1050]) ).
thf(1078,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1051]) ).
thf(1079,plain,
( ( ~ ( rel_str @ sK3_A )
| ~ ( strict_rel_str @ sK3_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1052]) ).
thf(1080,plain,
! [SV64: $i] :
( ( ! [SY78: $i] :
( ~ ( relation_of2 @ SY78 @ SV64 @ SV64 )
| ~ ( ~ ! [SY79: $i] :
( ! [SY80: $i] :
( ( rel_str_of @ SV64 @ SY78 )
!= ( rel_str_of @ SY79 @ SY80 ) )
| ( SV64 = SY79 ) )
| ~ ! [SY81: $i,SY82: $i] :
( ( ( rel_str_of @ SV64 @ SY78 )
!= ( rel_str_of @ SY81 @ SY82 ) )
| ( SY78 = SY82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1081,plain,
! [SV65: $i] :
( ( ~ ( ~ ! [SY83: $i,SY84: $i] :
( ~ ( relation_of2 @ SY84 @ SV65 @ SY83 )
| ( relation_of2_as_subset @ SY84 @ SV65 @ SY83 ) )
| ~ ! [SY85: $i,SY86: $i] :
( ~ ( relation_of2_as_subset @ SY86 @ SV65 @ SY85 )
| ( relation_of2 @ SY86 @ SV65 @ SY85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1082,plain,
( ( ~ ( one_sorted_str @ sK2_A )
| ~ ~ ( empty_carrier @ sK2_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1055]) ).
thf(1083,plain,
( ( ~ ! [SX0: $i] : ( rel_str @ ( incl_POSet @ SX0 ) )
| ~ ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1056]) ).
thf(1084,plain,
! [SV44: $i] :
( ( ( ~ ( one_sorted_str @ SV44 ) )
= $true )
| ( ( ( cast_as_carrier_subset @ SV44 )
= ( the_carrier @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1057]) ).
thf(1085,plain,
! [SV46: $i] :
( ( ( ~ ( one_sorted_str @ SV46 ) )
= $true )
| ( ( ( cast_as_carrier_subset @ SV46 )
= ( the_carrier @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1059]) ).
thf(1086,plain,
! [SV47: $i] :
( ( ( ~ ( rel_str @ SV47 ) )
= $true )
| ( ( relation_of2_as_subset @ ( the_InternalRel @ SV47 ) @ ( the_carrier @ SV47 ) @ ( the_carrier @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1060]) ).
thf(1087,plain,
! [SV66: $i,SV49: $i] :
( ( ! [SY87: $i,SY88: $i] :
( ~ ( relation_of2_as_subset @ SY88 @ SY87 @ SV49 )
| ~ ( subset @ SV49 @ SV66 )
| ( relation_of2_as_subset @ SY88 @ SY87 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1088,plain,
! [SV53: $i] :
( ( ( ~ ( rel_str @ SV53 ) )
= $true )
| ( ( ~ ( strict_rel_str @ SV53 )
| ( SV53
= ( rel_str_of @ ( the_carrier @ SV53 ) @ ( the_InternalRel @ SV53 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1066]) ).
thf(1089,plain,
! [SV55: $i] :
( ( ( ~ ( meet_semilatt_str @ SV55 ) )
= $true )
| ( ( one_sorted_str @ SV55 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1068]) ).
thf(1090,plain,
! [SV56: $i] :
( ( ( ~ ( rel_str @ SV56 ) )
= $true )
| ( ( one_sorted_str @ SV56 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1069]) ).
thf(1091,plain,
! [SV57: $i] :
( ( ( ~ ( top_str @ SV57 ) )
= $true )
| ( ( one_sorted_str @ SV57 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1070]) ).
thf(1092,plain,
! [SV58: $i] :
( ( ( ~ ( one_sorted_str @ SV58 ) )
= $true )
| ( ( ! [SY75: $i] :
( ~ ( net_str @ SY75 @ SV58 )
| ( rel_str @ SY75 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1071]) ).
thf(1093,plain,
! [SV59: $i] :
( ( ( ~ ( join_semilatt_str @ SV59 ) )
= $true )
| ( ( one_sorted_str @ SV59 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1072]) ).
thf(1094,plain,
! [SV60: $i] :
( ( ( ~ ( rel_str @ SV60 ) )
= $true )
| ( ( ! [SY76: $i] :
( ~ ( subrelstr @ SY76 @ SV60 )
| ( rel_str @ SY76 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1073]) ).
thf(1095,plain,
! [SV61: $i] :
( ( ( ~ ( one_sorted_str @ SV61 ) )
= $true )
| ( ( net_str @ ( sK6_B @ SV61 ) @ SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1074]) ).
thf(1096,plain,
! [SV62: $i] :
( ( ( ~ ( rel_str @ SV62 ) )
= $true )
| ( ( subrelstr @ ( sK5_B @ SV62 ) @ SV62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1075]) ).
thf(1097,plain,
! [SV63: $i,SV67: $i] :
( ( relation_of2_as_subset @ ( sK4_C @ SV67 @ SV63 ) @ SV63 @ SV67 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1098,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1078]) ).
thf(1099,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1078]) ).
thf(1100,plain,
( ( ~ ( rel_str @ sK3_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1079]) ).
thf(1101,plain,
( ( ~ ( strict_rel_str @ sK3_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1079]) ).
thf(1102,plain,
! [SV64: $i,SV68: $i] :
( ( ~ ( relation_of2 @ SV68 @ SV64 @ SV64 )
| ~ ( ~ ! [SY89: $i] :
( ! [SY90: $i] :
( ( rel_str_of @ SV64 @ SV68 )
!= ( rel_str_of @ SY89 @ SY90 ) )
| ( SV64 = SY89 ) )
| ~ ! [SY91: $i,SY92: $i] :
( ( ( rel_str_of @ SV64 @ SV68 )
!= ( rel_str_of @ SY91 @ SY92 ) )
| ( SV68 = SY92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1103,plain,
! [SV65: $i] :
( ( ~ ! [SY83: $i,SY84: $i] :
( ~ ( relation_of2 @ SY84 @ SV65 @ SY83 )
| ( relation_of2_as_subset @ SY84 @ SV65 @ SY83 ) )
| ~ ! [SY85: $i,SY86: $i] :
( ~ ( relation_of2_as_subset @ SY86 @ SV65 @ SY85 )
| ( relation_of2 @ SY86 @ SV65 @ SY85 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1081]) ).
thf(1104,plain,
( ( ~ ( one_sorted_str @ sK2_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1082]) ).
thf(1105,plain,
( ( ~ ~ ( empty_carrier @ sK2_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1082]) ).
thf(1106,plain,
( ( ~ ! [SX0: $i] : ( rel_str @ ( incl_POSet @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1083]) ).
thf(1107,plain,
( ( ~ ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1083]) ).
thf(1108,plain,
! [SV44: $i] :
( ( ( one_sorted_str @ SV44 )
= $false )
| ( ( ( cast_as_carrier_subset @ SV44 )
= ( the_carrier @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1084]) ).
thf(1109,plain,
! [SV46: $i] :
( ( ( one_sorted_str @ SV46 )
= $false )
| ( ( ( cast_as_carrier_subset @ SV46 )
= ( the_carrier @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1085]) ).
thf(1110,plain,
! [SV47: $i] :
( ( ( rel_str @ SV47 )
= $false )
| ( ( relation_of2_as_subset @ ( the_InternalRel @ SV47 ) @ ( the_carrier @ SV47 ) @ ( the_carrier @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1086]) ).
thf(1111,plain,
! [SV66: $i,SV49: $i,SV69: $i] :
( ( ! [SY93: $i] :
( ~ ( relation_of2_as_subset @ SY93 @ SV69 @ SV49 )
| ~ ( subset @ SV49 @ SV66 )
| ( relation_of2_as_subset @ SY93 @ SV69 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1112,plain,
! [SV53: $i] :
( ( ( rel_str @ SV53 )
= $false )
| ( ( ~ ( strict_rel_str @ SV53 )
| ( SV53
= ( rel_str_of @ ( the_carrier @ SV53 ) @ ( the_InternalRel @ SV53 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1088]) ).
thf(1113,plain,
! [SV55: $i] :
( ( ( meet_semilatt_str @ SV55 )
= $false )
| ( ( one_sorted_str @ SV55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1089]) ).
thf(1114,plain,
! [SV56: $i] :
( ( ( rel_str @ SV56 )
= $false )
| ( ( one_sorted_str @ SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1090]) ).
thf(1115,plain,
! [SV57: $i] :
( ( ( top_str @ SV57 )
= $false )
| ( ( one_sorted_str @ SV57 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1091]) ).
thf(1116,plain,
! [SV58: $i] :
( ( ( one_sorted_str @ SV58 )
= $false )
| ( ( ! [SY75: $i] :
( ~ ( net_str @ SY75 @ SV58 )
| ( rel_str @ SY75 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1092]) ).
thf(1117,plain,
! [SV59: $i] :
( ( ( join_semilatt_str @ SV59 )
= $false )
| ( ( one_sorted_str @ SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1093]) ).
thf(1118,plain,
! [SV60: $i] :
( ( ( rel_str @ SV60 )
= $false )
| ( ( ! [SY76: $i] :
( ~ ( subrelstr @ SY76 @ SV60 )
| ( rel_str @ SY76 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1094]) ).
thf(1119,plain,
! [SV61: $i] :
( ( ( one_sorted_str @ SV61 )
= $false )
| ( ( net_str @ ( sK6_B @ SV61 ) @ SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1095]) ).
thf(1120,plain,
! [SV62: $i] :
( ( ( rel_str @ SV62 )
= $false )
| ( ( subrelstr @ ( sK5_B @ SV62 ) @ SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1096]) ).
thf(1121,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1098]) ).
thf(1122,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1099]) ).
thf(1123,plain,
( ( rel_str @ sK3_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1100]) ).
thf(1124,plain,
( ( strict_rel_str @ sK3_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1101]) ).
thf(1125,plain,
! [SV64: $i,SV68: $i] :
( ( ( ~ ( relation_of2 @ SV68 @ SV64 @ SV64 ) )
= $true )
| ( ( ~ ( ~ ! [SY89: $i] :
( ! [SY90: $i] :
( ( rel_str_of @ SV64 @ SV68 )
!= ( rel_str_of @ SY89 @ SY90 ) )
| ( SV64 = SY89 ) )
| ~ ! [SY91: $i,SY92: $i] :
( ( ( rel_str_of @ SV64 @ SV68 )
!= ( rel_str_of @ SY91 @ SY92 ) )
| ( SV68 = SY92 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1102]) ).
thf(1126,plain,
! [SV65: $i] :
( ( ~ ! [SY83: $i,SY84: $i] :
( ~ ( relation_of2 @ SY84 @ SV65 @ SY83 )
| ( relation_of2_as_subset @ SY84 @ SV65 @ SY83 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1103]) ).
thf(1127,plain,
! [SV65: $i] :
( ( ~ ! [SY85: $i,SY86: $i] :
( ~ ( relation_of2_as_subset @ SY86 @ SV65 @ SY85 )
| ( relation_of2 @ SY86 @ SV65 @ SY85 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1103]) ).
thf(1128,plain,
( ( one_sorted_str @ sK2_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1104]) ).
thf(1129,plain,
( ( ~ ( empty_carrier @ sK2_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1105]) ).
thf(1130,plain,
( ( ! [SX0: $i] : ( rel_str @ ( incl_POSet @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1106]) ).
thf(1131,plain,
( ( ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1107]) ).
thf(1132,plain,
! [SV66: $i,SV49: $i,SV69: $i,SV70: $i] :
( ( ~ ( relation_of2_as_subset @ SV70 @ SV69 @ SV49 )
| ~ ( subset @ SV49 @ SV66 )
| ( relation_of2_as_subset @ SV70 @ SV69 @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1133,plain,
! [SV53: $i] :
( ( ( ~ ( strict_rel_str @ SV53 ) )
= $true )
| ( ( SV53
= ( rel_str_of @ ( the_carrier @ SV53 ) @ ( the_InternalRel @ SV53 ) ) )
= $true )
| ( ( rel_str @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1112]) ).
thf(1134,plain,
! [SV58: $i,SV71: $i] :
( ( ( ~ ( net_str @ SV71 @ SV58 )
| ( rel_str @ SV71 ) )
= $true )
| ( ( one_sorted_str @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1135,plain,
! [SV60: $i,SV72: $i] :
( ( ( ~ ( subrelstr @ SV72 @ SV60 )
| ( rel_str @ SV72 ) )
= $true )
| ( ( rel_str @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1136,plain,
! [SV73: $i] :
( ( ! [SY94: $i] :
( ~ ( relation_of2 @ SY94 @ SV73 @ SV73 )
| ( rel_str @ ( rel_str_of @ SV73 @ SY94 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1137,plain,
! [SV74: $i] :
( ( ! [SY95: $i] :
( ~ ( relation_of2 @ SY95 @ SV74 @ SV74 )
| ( strict_rel_str @ ( rel_str_of @ SV74 @ SY95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1138,plain,
! [SV64: $i,SV68: $i] :
( ( ( relation_of2 @ SV68 @ SV64 @ SV64 )
= $false )
| ( ( ~ ( ~ ! [SY89: $i] :
( ! [SY90: $i] :
( ( rel_str_of @ SV64 @ SV68 )
!= ( rel_str_of @ SY89 @ SY90 ) )
| ( SV64 = SY89 ) )
| ~ ! [SY91: $i,SY92: $i] :
( ( ( rel_str_of @ SV64 @ SV68 )
!= ( rel_str_of @ SY91 @ SY92 ) )
| ( SV68 = SY92 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1125]) ).
thf(1139,plain,
! [SV65: $i] :
( ( ! [SY83: $i,SY84: $i] :
( ~ ( relation_of2 @ SY84 @ SV65 @ SY83 )
| ( relation_of2_as_subset @ SY84 @ SV65 @ SY83 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1126]) ).
thf(1140,plain,
! [SV65: $i] :
( ( ! [SY85: $i,SY86: $i] :
( ~ ( relation_of2_as_subset @ SY86 @ SV65 @ SY85 )
| ( relation_of2 @ SY86 @ SV65 @ SY85 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1127]) ).
thf(1141,plain,
( ( empty_carrier @ sK2_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1129]) ).
thf(1142,plain,
! [SV75: $i] :
( ( rel_str @ ( incl_POSet @ SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1143,plain,
! [SV76: $i] :
( ( strict_rel_str @ ( incl_POSet @ SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1144,plain,
! [SV66: $i,SV49: $i,SV69: $i,SV70: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV70 @ SV69 @ SV49 ) )
= $true )
| ( ( ~ ( subset @ SV49 @ SV66 )
| ( relation_of2_as_subset @ SV70 @ SV69 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1132]) ).
thf(1145,plain,
! [SV53: $i] :
( ( ( strict_rel_str @ SV53 )
= $false )
| ( ( SV53
= ( rel_str_of @ ( the_carrier @ SV53 ) @ ( the_InternalRel @ SV53 ) ) )
= $true )
| ( ( rel_str @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1133]) ).
thf(1146,plain,
! [SV58: $i,SV71: $i] :
( ( ( ~ ( net_str @ SV71 @ SV58 ) )
= $true )
| ( ( rel_str @ SV71 )
= $true )
| ( ( one_sorted_str @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1134]) ).
thf(1147,plain,
! [SV60: $i,SV72: $i] :
( ( ( ~ ( subrelstr @ SV72 @ SV60 ) )
= $true )
| ( ( rel_str @ SV72 )
= $true )
| ( ( rel_str @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1135]) ).
thf(1148,plain,
! [SV73: $i,SV77: $i] :
( ( ~ ( relation_of2 @ SV77 @ SV73 @ SV73 )
| ( rel_str @ ( rel_str_of @ SV73 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1136]) ).
thf(1149,plain,
! [SV74: $i,SV78: $i] :
( ( ~ ( relation_of2 @ SV78 @ SV74 @ SV74 )
| ( strict_rel_str @ ( rel_str_of @ SV74 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1150,plain,
! [SV68: $i,SV64: $i] :
( ( ( ~ ! [SY89: $i] :
( ! [SY90: $i] :
( ( rel_str_of @ SV64 @ SV68 )
!= ( rel_str_of @ SY89 @ SY90 ) )
| ( SV64 = SY89 ) )
| ~ ! [SY91: $i,SY92: $i] :
( ( ( rel_str_of @ SV64 @ SV68 )
!= ( rel_str_of @ SY91 @ SY92 ) )
| ( SV68 = SY92 ) ) )
= $false )
| ( ( relation_of2 @ SV68 @ SV64 @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1138]) ).
thf(1151,plain,
! [SV79: $i,SV65: $i] :
( ( ! [SY96: $i] :
( ~ ( relation_of2 @ SY96 @ SV65 @ SV79 )
| ( relation_of2_as_subset @ SY96 @ SV65 @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1152,plain,
! [SV80: $i,SV65: $i] :
( ( ! [SY97: $i] :
( ~ ( relation_of2_as_subset @ SY97 @ SV65 @ SV80 )
| ( relation_of2 @ SY97 @ SV65 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1153,plain,
! [SV66: $i,SV49: $i,SV69: $i,SV70: $i] :
( ( ( relation_of2_as_subset @ SV70 @ SV69 @ SV49 )
= $false )
| ( ( ~ ( subset @ SV49 @ SV66 )
| ( relation_of2_as_subset @ SV70 @ SV69 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1144]) ).
thf(1154,plain,
! [SV58: $i,SV71: $i] :
( ( ( net_str @ SV71 @ SV58 )
= $false )
| ( ( rel_str @ SV71 )
= $true )
| ( ( one_sorted_str @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1146]) ).
thf(1155,plain,
! [SV60: $i,SV72: $i] :
( ( ( subrelstr @ SV72 @ SV60 )
= $false )
| ( ( rel_str @ SV72 )
= $true )
| ( ( rel_str @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1147]) ).
thf(1156,plain,
! [SV73: $i,SV77: $i] :
( ( ( ~ ( relation_of2 @ SV77 @ SV73 @ SV73 ) )
= $true )
| ( ( rel_str @ ( rel_str_of @ SV73 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1148]) ).
thf(1157,plain,
! [SV74: $i,SV78: $i] :
( ( ( ~ ( relation_of2 @ SV78 @ SV74 @ SV74 ) )
= $true )
| ( ( strict_rel_str @ ( rel_str_of @ SV74 @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1149]) ).
thf(1158,plain,
! [SV68: $i,SV64: $i] :
( ( ( ~ ! [SY89: $i] :
( ! [SY90: $i] :
( ( rel_str_of @ SV64 @ SV68 )
!= ( rel_str_of @ SY89 @ SY90 ) )
| ( SV64 = SY89 ) ) )
= $false )
| ( ( relation_of2 @ SV68 @ SV64 @ SV64 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1150]) ).
thf(1159,plain,
! [SV68: $i,SV64: $i] :
( ( ( ~ ! [SY91: $i,SY92: $i] :
( ( ( rel_str_of @ SV64 @ SV68 )
!= ( rel_str_of @ SY91 @ SY92 ) )
| ( SV68 = SY92 ) ) )
= $false )
| ( ( relation_of2 @ SV68 @ SV64 @ SV64 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1150]) ).
thf(1160,plain,
! [SV79: $i,SV65: $i,SV81: $i] :
( ( ~ ( relation_of2 @ SV81 @ SV65 @ SV79 )
| ( relation_of2_as_subset @ SV81 @ SV65 @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1161,plain,
! [SV80: $i,SV65: $i,SV82: $i] :
( ( ~ ( relation_of2_as_subset @ SV82 @ SV65 @ SV80 )
| ( relation_of2 @ SV82 @ SV65 @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1162,plain,
! [SV69: $i,SV70: $i,SV66: $i,SV49: $i] :
( ( ( ~ ( subset @ SV49 @ SV66 ) )
= $true )
| ( ( relation_of2_as_subset @ SV70 @ SV69 @ SV66 )
= $true )
| ( ( relation_of2_as_subset @ SV70 @ SV69 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1153]) ).
thf(1163,plain,
! [SV73: $i,SV77: $i] :
( ( ( relation_of2 @ SV77 @ SV73 @ SV73 )
= $false )
| ( ( rel_str @ ( rel_str_of @ SV73 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1156]) ).
thf(1164,plain,
! [SV74: $i,SV78: $i] :
( ( ( relation_of2 @ SV78 @ SV74 @ SV74 )
= $false )
| ( ( strict_rel_str @ ( rel_str_of @ SV74 @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1157]) ).
thf(1165,plain,
! [SV68: $i,SV64: $i] :
( ( ( ! [SY89: $i] :
( ! [SY90: $i] :
( ( rel_str_of @ SV64 @ SV68 )
!= ( rel_str_of @ SY89 @ SY90 ) )
| ( SV64 = SY89 ) ) )
= $true )
| ( ( relation_of2 @ SV68 @ SV64 @ SV64 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1158]) ).
thf(1166,plain,
! [SV68: $i,SV64: $i] :
( ( ( ! [SY91: $i,SY92: $i] :
( ( ( rel_str_of @ SV64 @ SV68 )
!= ( rel_str_of @ SY91 @ SY92 ) )
| ( SV68 = SY92 ) ) )
= $true )
| ( ( relation_of2 @ SV68 @ SV64 @ SV64 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1159]) ).
thf(1167,plain,
! [SV79: $i,SV65: $i,SV81: $i] :
( ( ( ~ ( relation_of2 @ SV81 @ SV65 @ SV79 ) )
= $true )
| ( ( relation_of2_as_subset @ SV81 @ SV65 @ SV79 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1160]) ).
thf(1168,plain,
! [SV80: $i,SV65: $i,SV82: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV82 @ SV65 @ SV80 ) )
= $true )
| ( ( relation_of2 @ SV82 @ SV65 @ SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1161]) ).
thf(1169,plain,
! [SV69: $i,SV70: $i,SV66: $i,SV49: $i] :
( ( ( subset @ SV49 @ SV66 )
= $false )
| ( ( relation_of2_as_subset @ SV70 @ SV69 @ SV66 )
= $true )
| ( ( relation_of2_as_subset @ SV70 @ SV69 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1162]) ).
thf(1170,plain,
! [SV83: $i,SV68: $i,SV64: $i] :
( ( ( ! [SY98: $i] :
( ( rel_str_of @ SV64 @ SV68 )
!= ( rel_str_of @ SV83 @ SY98 ) )
| ( SV64 = SV83 ) )
= $true )
| ( ( relation_of2 @ SV68 @ SV64 @ SV64 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1171,plain,
! [SV84: $i,SV68: $i,SV64: $i] :
( ( ( ! [SY99: $i] :
( ( ( rel_str_of @ SV64 @ SV68 )
!= ( rel_str_of @ SV84 @ SY99 ) )
| ( SV68 = SY99 ) ) )
= $true )
| ( ( relation_of2 @ SV68 @ SV64 @ SV64 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1172,plain,
! [SV79: $i,SV65: $i,SV81: $i] :
( ( ( relation_of2 @ SV81 @ SV65 @ SV79 )
= $false )
| ( ( relation_of2_as_subset @ SV81 @ SV65 @ SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1167]) ).
thf(1173,plain,
! [SV80: $i,SV65: $i,SV82: $i] :
( ( ( relation_of2_as_subset @ SV82 @ SV65 @ SV80 )
= $false )
| ( ( relation_of2 @ SV82 @ SV65 @ SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1168]) ).
thf(1174,plain,
! [SV83: $i,SV68: $i,SV64: $i] :
( ( ( ! [SY98: $i] :
( ( rel_str_of @ SV64 @ SV68 )
!= ( rel_str_of @ SV83 @ SY98 ) ) )
= $true )
| ( ( SV64 = SV83 )
= $true )
| ( ( relation_of2 @ SV68 @ SV64 @ SV64 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1170]) ).
thf(1175,plain,
! [SV85: $i,SV84: $i,SV68: $i,SV64: $i] :
( ( ( ( ( rel_str_of @ SV64 @ SV68 )
!= ( rel_str_of @ SV84 @ SV85 ) )
| ( SV68 = SV85 ) )
= $true )
| ( ( relation_of2 @ SV68 @ SV64 @ SV64 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1171]) ).
thf(1176,plain,
! [SV86: $i,SV83: $i,SV68: $i,SV64: $i] :
( ( ( ( rel_str_of @ SV64 @ SV68 )
!= ( rel_str_of @ SV83 @ SV86 ) )
= $true )
| ( ( SV64 = SV83 )
= $true )
| ( ( relation_of2 @ SV68 @ SV64 @ SV64 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1177,plain,
! [SV85: $i,SV84: $i,SV68: $i,SV64: $i] :
( ( ( ( rel_str_of @ SV64 @ SV68 )
!= ( rel_str_of @ SV84 @ SV85 ) )
= $true )
| ( ( SV68 = SV85 )
= $true )
| ( ( relation_of2 @ SV68 @ SV64 @ SV64 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1175]) ).
thf(1178,plain,
! [SV86: $i,SV83: $i,SV68: $i,SV64: $i] :
( ( ( ( rel_str_of @ SV64 @ SV68 )
= ( rel_str_of @ SV83 @ SV86 ) )
= $false )
| ( ( SV64 = SV83 )
= $true )
| ( ( relation_of2 @ SV68 @ SV64 @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1179,plain,
! [SV85: $i,SV84: $i,SV68: $i,SV64: $i] :
( ( ( ( rel_str_of @ SV64 @ SV68 )
= ( rel_str_of @ SV84 @ SV85 ) )
= $false )
| ( ( SV68 = SV85 )
= $true )
| ( ( relation_of2 @ SV68 @ SV64 @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1177]) ).
thf(1180,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[997,1179,1178,1173,1172,1169,1164,1163,1155,1154,1145,1143,1142,1141,1128,1124,1123,1120,1119,1117,1115,1114,1113,1110,1109,1108,1097,1077,1067,1065,1064,1063,1061,1058,1042,1041,1026,1024,1023,1022,1021,1020,1019,1018,1017,1016,1015,1014,1012,1011,1010,1009,1008,1007,1006,1005,1004,1003,1002,1001,1000,999,998]) ).
thf(1181,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1180,993]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU368+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.17 % Computer : n001.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Oct 6 15:22:47 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.76/1.61 .......
% 5.76/1.61
% 5.76/1.61 No.of.Axioms: 720
% 5.76/1.61
% 5.76/1.61 Length.of.Defs: 0
% 5.76/1.61
% 5.76/1.61 Contains.Choice.Funs: false
% 5.76/1.61 ...................
% 5.76/1.61
% 5.76/1.61 ********************************
% 5.76/1.61 * All subproblems solved! *
% 5.76/1.61 ********************************
% 5.76/1.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:56,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1180,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 5.76/1.61
% 5.76/1.61 %**** Beginning of derivation protocol ****
% 5.76/1.61 % SZS output start CNFRefutation
% See solution above
% 5.76/1.61
% 5.76/1.61 %**** End of derivation protocol ****
% 5.76/1.61 %**** no. of clauses in derivation: 517 ****
% 5.76/1.61 %**** clause counter: 1180 ****
% 5.76/1.61
% 5.76/1.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:56,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1180,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------