%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU359+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 : n018.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 10:44:07 AM UTC 2026
% Result : Theorem 8.45s 1.65s
% Output : CNFRefutation 8.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 42
% Syntax : Number of formulae : 586 ( 173 unt; 0 typ; 0 def)
% Number of atoms : 7253 (2069 equ; 0 cnn)
% Maximal formula atoms : 15 ( 12 avg)
% Number of connectives : 15382 (2819 ~;2804 |; 78 &;9520 @)
% ( 12 <=>; 149 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 193 ( 190 usr; 10 con; 0-6 aty)
% Number of variables : 1484 ( 0 ^;1469 !; 15 ?;1484 :)
% 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_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_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_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_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_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_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_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_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_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_sK10_SY99,type,
sK10_SY99: $i > $i > $i ).
thf(tp_sK11_SY96,type,
sK11_SY96: $i > $i > $i > $i ).
thf(tp_sK12_SY109,type,
sK12_SY109: $i > $i > $i > $i ).
thf(tp_sK13_SY115,type,
sK13_SY115: $i > $i > $i > $i ).
thf(tp_sK14_SY114,type,
sK14_SY114: $i > $i > $i > $i ).
thf(tp_sK15_SY110,type,
sK15_SY110: $i > $i > $i > $i ).
thf(tp_sK16_SY110,type,
sK16_SY110: $i > $i > $i > $i ).
thf(tp_sK17_SY110,type,
sK17_SY110: $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK5_SY55,type,
sK5_SY55: $i > $i ).
thf(tp_sK6_SY76,type,
sK6_SY76: $i ).
thf(tp_sK7_SY79,type,
sK7_SY79: $i > $i > $i ).
thf(tp_sK8_SY98,type,
sK8_SY98: $i > $i > $i > $i ).
thf(tp_sK9_SY93,type,
sK9_SY93: $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_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_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_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(14,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(92,axiom,
? [A: $i] :
( ( rel_str @ A )
& ( strict_rel_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_orders_2) ).
thf(188,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(195,axiom,
? [A: $i] : ( rel_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(198,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(203,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(204,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(208,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(210,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(212,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_relat_1) ).
thf(229,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_ordinal2) ).
thf(232,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(233,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(239,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(240,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(242,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_relat_1) ).
thf(245,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(246,axiom,
! [A: $i,B: $i] :
( ( rel_str @ A )
=> ( element @ ( meet_on_relstr @ A @ B ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_yellow_0) ).
thf(247,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(249,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(251,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(253,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_mcart_1) ).
thf(258,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(259,axiom,
! [A: $i,B: $i] :
( ( rel_str @ A )
=> ( element @ ( join_on_relstr @ A @ B ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_yellow_0) ).
thf(260,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(262,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord1) ).
thf(264,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(265,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_setfam_1) ).
thf(266,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(269,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_ordinal1) ).
thf(270,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_mcart_1) ).
thf(273,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_funct_1) ).
thf(274,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_enumset1) ).
thf(276,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_binop_1) ).
thf(279,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_relat_1) ).
thf(283,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ex_sup_of_relstr_set @ A @ B )
=> ( ( C
= ( join_on_relstr @ A @ B ) )
<=> ( ( relstr_set_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ D )
=> ( related @ A @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_yellow_0) ).
thf(286,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ C )
<=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ B )
=> ( related @ A @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_lattice3) ).
thf(298,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( ex_sup_of_relstr_set @ A @ B )
<=> ? [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
& ( relstr_set_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ D )
=> ( related @ A @ C @ D ) ) )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( relstr_set_smaller @ A @ B @ D )
& ! [E: $i] :
( ( element @ E @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ E )
=> ( related @ A @ D @ E ) ) ) )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_yellow_0) ).
thf(557,axiom,
! [A: $i] :
( ( ( transitive_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( related @ A @ B @ C )
& ( related @ A @ C @ D ) )
=> ( related @ A @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_orders_2) ).
thf(563,axiom,
! [A: $i] :
( ( ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( related @ A @ B @ C )
& ( related @ A @ C @ B ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_orders_2) ).
thf(603,axiom,
! [A: $i] :
( ( ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( ex_sup_of_relstr_set @ A @ B )
<=> ? [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
& ( relstr_set_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ D )
=> ( related @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_yellow_0) ).
thf(682,conjecture,
! [A: $i] :
( ( ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( ( ( B
= ( join_on_relstr @ A @ C ) )
& ( ex_sup_of_relstr_set @ A @ C ) )
=> ( ( relstr_set_smaller @ A @ C @ B )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ C @ D )
=> ( related @ A @ B @ D ) ) ) ) )
& ( ( ( relstr_set_smaller @ A @ C @ B )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ C @ D )
=> ( related @ A @ B @ D ) ) ) )
=> ( ( B
= ( join_on_relstr @ A @ C ) )
& ( ex_sup_of_relstr_set @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_yellow_0) ).
thf(683,negated_conjecture,
( ( ! [A: $i] :
( ( ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( ( ( B
= ( join_on_relstr @ A @ C ) )
& ( ex_sup_of_relstr_set @ A @ C ) )
=> ( ( relstr_set_smaller @ A @ C @ B )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ C @ D )
=> ( related @ A @ B @ D ) ) ) ) )
& ( ( ( relstr_set_smaller @ A @ C @ B )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ C @ D )
=> ( related @ A @ B @ D ) ) ) )
=> ( ( B
= ( join_on_relstr @ A @ C ) )
& ( ex_sup_of_relstr_set @ A @ C ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[682]) ).
thf(684,plain,
( ( ! [A: $i] :
( ( ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( ( ( B
= ( join_on_relstr @ A @ C ) )
& ( ex_sup_of_relstr_set @ A @ C ) )
=> ( ( relstr_set_smaller @ A @ C @ B )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ C @ D )
=> ( related @ A @ B @ D ) ) ) ) )
& ( ( ( relstr_set_smaller @ A @ C @ B )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ C @ D )
=> ( related @ A @ B @ D ) ) ) )
=> ( ( B
= ( join_on_relstr @ A @ C ) )
& ( ex_sup_of_relstr_set @ A @ C ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[683]) ).
thf(685,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(686,plain,
( ( ? [A: $i] :
( ( rel_str @ A )
& ( strict_rel_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(687,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(688,plain,
( ( ? [A: $i] : ( rel_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(689,plain,
$true = $true,
inference(unfold_def,[status(thm)],[198]) ).
thf(690,plain,
$true = $true,
inference(unfold_def,[status(thm)],[203]) ).
thf(691,plain,
$true = $true,
inference(unfold_def,[status(thm)],[204]) ).
thf(692,plain,
$true = $true,
inference(unfold_def,[status(thm)],[208]) ).
thf(693,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(694,plain,
$true = $true,
inference(unfold_def,[status(thm)],[212]) ).
thf(695,plain,
$true = $true,
inference(unfold_def,[status(thm)],[229]) ).
thf(696,plain,
$true = $true,
inference(unfold_def,[status(thm)],[232]) ).
thf(697,plain,
$true = $true,
inference(unfold_def,[status(thm)],[233]) ).
thf(698,plain,
$true = $true,
inference(unfold_def,[status(thm)],[239]) ).
thf(699,plain,
$true = $true,
inference(unfold_def,[status(thm)],[240]) ).
thf(700,plain,
$true = $true,
inference(unfold_def,[status(thm)],[242]) ).
thf(701,plain,
$true = $true,
inference(unfold_def,[status(thm)],[245]) ).
thf(702,plain,
( ( ! [A: $i,B: $i] :
( ( rel_str @ A )
=> ( element @ ( meet_on_relstr @ A @ B ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(703,plain,
$true = $true,
inference(unfold_def,[status(thm)],[247]) ).
thf(704,plain,
$true = $true,
inference(unfold_def,[status(thm)],[249]) ).
thf(705,plain,
$true = $true,
inference(unfold_def,[status(thm)],[251]) ).
thf(706,plain,
$true = $true,
inference(unfold_def,[status(thm)],[253]) ).
thf(707,plain,
$true = $true,
inference(unfold_def,[status(thm)],[258]) ).
thf(708,plain,
( ( ! [A: $i,B: $i] :
( ( rel_str @ A )
=> ( element @ ( join_on_relstr @ A @ B ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(709,plain,
$true = $true,
inference(unfold_def,[status(thm)],[260]) ).
thf(710,plain,
$true = $true,
inference(unfold_def,[status(thm)],[262]) ).
thf(711,plain,
$true = $true,
inference(unfold_def,[status(thm)],[264]) ).
thf(712,plain,
$true = $true,
inference(unfold_def,[status(thm)],[265]) ).
thf(713,plain,
$true = $true,
inference(unfold_def,[status(thm)],[266]) ).
thf(714,plain,
$true = $true,
inference(unfold_def,[status(thm)],[269]) ).
thf(715,plain,
$true = $true,
inference(unfold_def,[status(thm)],[270]) ).
thf(716,plain,
$true = $true,
inference(unfold_def,[status(thm)],[273]) ).
thf(717,plain,
$true = $true,
inference(unfold_def,[status(thm)],[274]) ).
thf(718,plain,
$true = $true,
inference(unfold_def,[status(thm)],[276]) ).
thf(719,plain,
$true = $true,
inference(unfold_def,[status(thm)],[279]) ).
thf(720,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ex_sup_of_relstr_set @ A @ B )
=> ( ( C
= ( join_on_relstr @ A @ B ) )
<=> ( ( relstr_set_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ D )
=> ( related @ A @ C @ D ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(721,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ C )
<=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ B )
=> ( related @ A @ D @ C ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(722,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( ex_sup_of_relstr_set @ A @ B )
<=> ? [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
& ( relstr_set_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ D )
=> ( related @ A @ C @ D ) ) )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( relstr_set_smaller @ A @ B @ D )
& ! [E: $i] :
( ( element @ E @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ E )
=> ( related @ A @ D @ E ) ) ) )
=> ( D = C ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(723,plain,
( ( ! [A: $i] :
( ( ( transitive_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( related @ A @ B @ C )
& ( related @ A @ C @ D ) )
=> ( related @ A @ B @ D ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[557]) ).
thf(724,plain,
( ( ! [A: $i] :
( ( ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( related @ A @ B @ C )
& ( related @ A @ C @ B ) )
=> ( B = C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[563]) ).
thf(725,plain,
( ( ! [A: $i] :
( ( ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( ex_sup_of_relstr_set @ A @ B )
<=> ? [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
& ( relstr_set_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ D )
=> ( related @ A @ C @ D ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[603]) ).
thf(726,plain,
( ( ( ( antisymmetric_relstr @ sK1_A )
& ( rel_str @ sK1_A ) )
=> ! [SY41: $i] :
( ( element @ SY41 @ ( the_carrier @ sK1_A ) )
=> ! [SY42: $i] :
( ( ( ( SY41
= ( join_on_relstr @ sK1_A @ SY42 ) )
& ( ex_sup_of_relstr_set @ sK1_A @ SY42 ) )
=> ( ( relstr_set_smaller @ sK1_A @ SY42 @ SY41 )
& ! [SY43: $i] :
( ( element @ SY43 @ ( the_carrier @ sK1_A ) )
=> ( ( relstr_set_smaller @ sK1_A @ SY42 @ SY43 )
=> ( related @ sK1_A @ SY41 @ SY43 ) ) ) ) )
& ( ( ( relstr_set_smaller @ sK1_A @ SY42 @ SY41 )
& ! [SY44: $i] :
( ( element @ SY44 @ ( the_carrier @ sK1_A ) )
=> ( ( relstr_set_smaller @ sK1_A @ SY42 @ SY44 )
=> ( related @ sK1_A @ SY41 @ SY44 ) ) ) )
=> ( ( SY41
= ( join_on_relstr @ sK1_A @ SY42 ) )
& ( ex_sup_of_relstr_set @ sK1_A @ SY42 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[684]) ).
thf(727,plain,
( ( antisymmetric_relstr @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[726]) ).
thf(728,plain,
( ( rel_str @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[726]) ).
thf(729,plain,
( ( ! [SY41: $i] :
( ( element @ SY41 @ ( the_carrier @ sK1_A ) )
=> ! [SY42: $i] :
( ( ( ( SY41
= ( join_on_relstr @ sK1_A @ SY42 ) )
& ( ex_sup_of_relstr_set @ sK1_A @ SY42 ) )
=> ( ( relstr_set_smaller @ sK1_A @ SY42 @ SY41 )
& ! [SY43: $i] :
( ( element @ SY43 @ ( the_carrier @ sK1_A ) )
=> ( ( relstr_set_smaller @ sK1_A @ SY42 @ SY43 )
=> ( related @ sK1_A @ SY41 @ SY43 ) ) ) ) )
& ( ( ( relstr_set_smaller @ sK1_A @ SY42 @ SY41 )
& ! [SY44: $i] :
( ( element @ SY44 @ ( the_carrier @ sK1_A ) )
=> ( ( relstr_set_smaller @ sK1_A @ SY42 @ SY44 )
=> ( related @ sK1_A @ SY41 @ SY44 ) ) ) )
=> ( ( SY41
= ( join_on_relstr @ sK1_A @ SY42 ) )
& ( ex_sup_of_relstr_set @ sK1_A @ SY42 ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[726]) ).
thf(730,plain,
( ( ~ ! [SY41: $i] :
( ( element @ SY41 @ ( the_carrier @ sK1_A ) )
=> ! [SY42: $i] :
( ( ( ( SY41
= ( join_on_relstr @ sK1_A @ SY42 ) )
& ( ex_sup_of_relstr_set @ sK1_A @ SY42 ) )
=> ( ( relstr_set_smaller @ sK1_A @ SY42 @ SY41 )
& ! [SY43: $i] :
( ( element @ SY43 @ ( the_carrier @ sK1_A ) )
=> ( ( relstr_set_smaller @ sK1_A @ SY42 @ SY43 )
=> ( related @ sK1_A @ SY41 @ SY43 ) ) ) ) )
& ( ( ( relstr_set_smaller @ sK1_A @ SY42 @ SY41 )
& ! [SY44: $i] :
( ( element @ SY44 @ ( the_carrier @ sK1_A ) )
=> ( ( relstr_set_smaller @ sK1_A @ SY42 @ SY44 )
=> ( related @ sK1_A @ SY41 @ SY44 ) ) ) )
=> ( ( SY41
= ( join_on_relstr @ sK1_A @ SY42 ) )
& ( ex_sup_of_relstr_set @ sK1_A @ SY42 ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[729]) ).
thf(731,plain,
( ( ! [A: $i] :
( ( ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( ex_sup_of_relstr_set @ A @ B )
<=> ? [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
& ( relstr_set_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ D )
=> ( related @ A @ C @ D ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[725]) ).
thf(732,plain,
( ( ! [A: $i] :
( ( ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( related @ A @ B @ C )
& ( related @ A @ C @ B ) )
=> ( B = C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[724]) ).
thf(733,plain,
( ( ! [A: $i] :
( ( ( transitive_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( related @ A @ B @ C )
& ( related @ A @ C @ D ) )
=> ( related @ A @ B @ D ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[723]) ).
thf(734,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( ex_sup_of_relstr_set @ A @ B )
<=> ? [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
& ( relstr_set_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ D )
=> ( related @ A @ C @ D ) ) )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( relstr_set_smaller @ A @ B @ D )
& ! [E: $i] :
( ( element @ E @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ E )
=> ( related @ A @ D @ E ) ) ) )
=> ( D = C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[722]) ).
thf(735,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ C )
<=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ B )
=> ( related @ A @ D @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[721]) ).
thf(736,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ex_sup_of_relstr_set @ A @ B )
=> ( ( C
= ( join_on_relstr @ A @ B ) )
<=> ( ( relstr_set_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ D )
=> ( related @ A @ C @ D ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[720]) ).
thf(737,plain,
$true = $true,
inference(copy,[status(thm)],[719]) ).
thf(738,plain,
$true = $true,
inference(copy,[status(thm)],[718]) ).
thf(739,plain,
$true = $true,
inference(copy,[status(thm)],[717]) ).
thf(740,plain,
$true = $true,
inference(copy,[status(thm)],[716]) ).
thf(741,plain,
$true = $true,
inference(copy,[status(thm)],[715]) ).
thf(742,plain,
$true = $true,
inference(copy,[status(thm)],[714]) ).
thf(743,plain,
$true = $true,
inference(copy,[status(thm)],[713]) ).
thf(744,plain,
$true = $true,
inference(copy,[status(thm)],[712]) ).
thf(745,plain,
$true = $true,
inference(copy,[status(thm)],[711]) ).
thf(746,plain,
$true = $true,
inference(copy,[status(thm)],[710]) ).
thf(747,plain,
$true = $true,
inference(copy,[status(thm)],[709]) ).
thf(748,plain,
( ( ! [A: $i,B: $i] :
( ( rel_str @ A )
=> ( element @ ( join_on_relstr @ A @ B ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[708]) ).
thf(749,plain,
$true = $true,
inference(copy,[status(thm)],[707]) ).
thf(750,plain,
$true = $true,
inference(copy,[status(thm)],[706]) ).
thf(751,plain,
$true = $true,
inference(copy,[status(thm)],[705]) ).
thf(752,plain,
$true = $true,
inference(copy,[status(thm)],[704]) ).
thf(753,plain,
$true = $true,
inference(copy,[status(thm)],[703]) ).
thf(754,plain,
( ( ! [A: $i,B: $i] :
( ( rel_str @ A )
=> ( element @ ( meet_on_relstr @ A @ B ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[702]) ).
thf(755,plain,
$true = $true,
inference(copy,[status(thm)],[701]) ).
thf(756,plain,
$true = $true,
inference(copy,[status(thm)],[700]) ).
thf(757,plain,
$true = $true,
inference(copy,[status(thm)],[699]) ).
thf(758,plain,
$true = $true,
inference(copy,[status(thm)],[698]) ).
thf(759,plain,
$true = $true,
inference(copy,[status(thm)],[697]) ).
thf(760,plain,
$true = $true,
inference(copy,[status(thm)],[696]) ).
thf(761,plain,
$true = $true,
inference(copy,[status(thm)],[695]) ).
thf(762,plain,
$true = $true,
inference(copy,[status(thm)],[694]) ).
thf(763,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[693]) ).
thf(764,plain,
$true = $true,
inference(copy,[status(thm)],[692]) ).
thf(765,plain,
$true = $true,
inference(copy,[status(thm)],[691]) ).
thf(766,plain,
$true = $true,
inference(copy,[status(thm)],[690]) ).
thf(767,plain,
$true = $true,
inference(copy,[status(thm)],[689]) ).
thf(768,plain,
( ( ? [A: $i] : ( rel_str @ A ) )
= $true ),
inference(copy,[status(thm)],[688]) ).
thf(769,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(copy,[status(thm)],[687]) ).
thf(770,plain,
( ( ? [A: $i] :
( ( rel_str @ A )
& ( strict_rel_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[686]) ).
thf(771,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[685]) ).
thf(772,plain,
( ( rel_str @ sK1_A )
= $true ),
inference(copy,[status(thm)],[728]) ).
thf(773,plain,
( ( antisymmetric_relstr @ sK1_A )
= $true ),
inference(copy,[status(thm)],[727]) ).
thf(774,plain,
( ( ~ ! [SY41: $i] :
( ( element @ SY41 @ ( the_carrier @ sK1_A ) )
=> ! [SY42: $i] :
( ( ( ( SY41
= ( join_on_relstr @ sK1_A @ SY42 ) )
& ( ex_sup_of_relstr_set @ sK1_A @ SY42 ) )
=> ( ( relstr_set_smaller @ sK1_A @ SY42 @ SY41 )
& ! [SY43: $i] :
( ( element @ SY43 @ ( the_carrier @ sK1_A ) )
=> ( ( relstr_set_smaller @ sK1_A @ SY42 @ SY43 )
=> ( related @ sK1_A @ SY41 @ SY43 ) ) ) ) )
& ( ( ( relstr_set_smaller @ sK1_A @ SY42 @ SY41 )
& ! [SY44: $i] :
( ( element @ SY44 @ ( the_carrier @ sK1_A ) )
=> ( ( relstr_set_smaller @ sK1_A @ SY42 @ SY44 )
=> ( related @ sK1_A @ SY41 @ SY44 ) ) ) )
=> ( ( SY41
= ( join_on_relstr @ sK1_A @ SY42 ) )
& ( ex_sup_of_relstr_set @ sK1_A @ SY42 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[730]) ).
thf(775,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[771]) ).
thf(776,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( rel_str @ SX0 )
| ~ ( strict_rel_str @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[770]) ).
thf(777,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ~ ( ex_sup_of_relstr_set @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_set_smaller @ SX0 @ SX1 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( element @ SX3 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_set_smaller @ SX0 @ SX1 @ SX3 )
| ( related @ SX0 @ SX2 @ SX3 ) ) )
| ~ ! [SX3: $i] :
( ~ ( element @ SX3 @ ( the_carrier @ SX0 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SX0 @ SX1 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( element @ SX4 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_set_smaller @ SX0 @ SX1 @ SX4 )
| ( related @ SX0 @ SX3 @ SX4 ) ) )
| ( SX3 = SX2 ) ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_set_smaller @ SX0 @ SX1 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( element @ SX3 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_set_smaller @ SX0 @ SX1 @ SX3 )
| ( related @ SX0 @ SX2 @ SX3 ) ) )
| ~ ! [SX3: $i] :
( ~ ( element @ SX3 @ ( the_carrier @ SX0 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SX0 @ SX1 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( element @ SX4 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_set_smaller @ SX0 @ SX1 @ SX4 )
| ( related @ SX0 @ SX3 @ SX4 ) ) )
| ( SX3 = SX2 ) ) )
| ( ex_sup_of_relstr_set @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[734]) ).
thf(778,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( element @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[769]) ).
thf(779,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( one_sorted_str @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[763]) ).
thf(780,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 ) )
| ! [SX1: $i] :
~ ( ~ ( ~ ( ex_sup_of_relstr_set @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_set_smaller @ SX0 @ SX1 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( element @ SX3 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_set_smaller @ SX0 @ SX1 @ SX3 )
| ( related @ SX0 @ SX2 @ SX3 ) ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_set_smaller @ SX0 @ SX1 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( element @ SX3 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_set_smaller @ SX0 @ SX1 @ SX3 )
| ( related @ SX0 @ SX2 @ SX3 ) ) )
| ( ex_sup_of_relstr_set @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[731]) ).
thf(781,plain,
( ( ~ ! [SX0: $i] :
~ ( rel_str @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[768]) ).
thf(782,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( ex_sup_of_relstr_set @ SX0 @ SX1 )
| ~ ( ~ ( ( SX2
!= ( join_on_relstr @ SX0 @ SX1 ) )
| ~ ( ~ ( relstr_set_smaller @ SX0 @ SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( element @ SX3 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_set_smaller @ SX0 @ SX1 @ SX3 )
| ( related @ SX0 @ SX2 @ SX3 ) ) ) )
| ~ ( ~ ~ ( ~ ( relstr_set_smaller @ SX0 @ SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( element @ SX3 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_set_smaller @ SX0 @ SX1 @ SX3 )
| ( related @ SX0 @ SX2 @ SX3 ) ) )
| ( SX2
= ( join_on_relstr @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[736]) ).
thf(783,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rel_str @ SX0 )
| ( element @ ( meet_on_relstr @ SX0 @ SX1 ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[754]) ).
thf(784,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( ~ ( ~ ( relstr_set_smaller @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( element @ SX3 @ ( the_carrier @ SX0 ) )
| ~ ( in @ SX3 @ SX1 )
| ( related @ SX0 @ SX3 @ SX2 ) ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( element @ SX3 @ ( the_carrier @ SX0 ) )
| ~ ( in @ SX3 @ SX1 )
| ( related @ SX0 @ SX3 @ SX2 ) )
| ( relstr_set_smaller @ SX0 @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[735]) ).
thf(785,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 ) )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ SX0 ) )
| ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ~ ( ~ ( related @ SX0 @ SX1 @ SX2 )
| ~ ( related @ SX0 @ SX2 @ SX1 ) )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[732]) ).
thf(786,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( rel_str @ SX0 )
| ( element @ ( join_on_relstr @ SX0 @ SX1 ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[748]) ).
thf(787,plain,
( ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ ( the_carrier @ sK1_A ) )
| ! [SX1: $i] :
~ ( ~ ( ~ ~ ( ( SX0
!= ( join_on_relstr @ sK1_A @ SX1 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ SX1 ) )
| ~ ( ~ ( relstr_set_smaller @ sK1_A @ SX1 @ SX0 )
| ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ SX1 @ SX2 )
| ( related @ sK1_A @ SX0 @ SX2 ) ) ) )
| ~ ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ SX1 @ SX0 )
| ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ SX1 @ SX2 )
| ( related @ sK1_A @ SX0 @ SX2 ) ) )
| ~ ( ( SX0
!= ( join_on_relstr @ sK1_A @ SX1 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[774]) ).
thf(788,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( transitive_relstr @ SX0 )
| ~ ( rel_str @ SX0 ) )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ SX0 ) )
| ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ! [SX3: $i] :
( ~ ( element @ SX3 @ ( the_carrier @ SX0 ) )
| ~ ~ ( ~ ( related @ SX0 @ SX1 @ SX2 )
| ~ ( related @ SX0 @ SX2 @ SX3 ) )
| ( related @ SX0 @ SX1 @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[733]) ).
thf(789,plain,
! [SV1: $i] :
( ( ! [SY45: $i] :
( ~ ( in @ SV1 @ SY45 )
| ( element @ SV1 @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(790,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( rel_str @ SX0 )
| ~ ( strict_rel_str @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[776]) ).
thf(791,plain,
! [SV2: $i] :
( ( ~ ( rel_str @ SV2 )
| ! [SY46: $i] :
~ ( ~ ( ~ ( ex_sup_of_relstr_set @ SV2 @ SY46 )
| ~ ! [SY47: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY47 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SY46 @ SY47 ) )
| ~ ! [SY48: $i] :
( ~ ( element @ SY48 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SY46 @ SY48 )
| ( related @ SV2 @ SY47 @ SY48 ) ) )
| ~ ! [SY49: $i] :
( ~ ( element @ SY49 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SY46 @ SY49 )
| ~ ! [SY50: $i] :
( ~ ( element @ SY50 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SY46 @ SY50 )
| ( related @ SV2 @ SY49 @ SY50 ) ) )
| ( SY49 = SY47 ) ) ) )
| ~ ( ~ ~ ! [SY51: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY51 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SY46 @ SY51 ) )
| ~ ! [SY52: $i] :
( ~ ( element @ SY52 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SY46 @ SY52 )
| ( related @ SV2 @ SY51 @ SY52 ) ) )
| ~ ! [SY53: $i] :
( ~ ( element @ SY53 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SY46 @ SY53 )
| ~ ! [SY54: $i] :
( ~ ( element @ SY54 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SY46 @ SY54 )
| ( related @ SV2 @ SY53 @ SY54 ) ) )
| ( SY53 = SY51 ) ) )
| ( ex_sup_of_relstr_set @ SV2 @ SY46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(792,plain,
! [SV3: $i] :
( ( ~ ! [SY55: $i] :
~ ( element @ SY55 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(793,plain,
! [SV4: $i] :
( ( ~ ( rel_str @ SV4 )
| ( one_sorted_str @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(794,plain,
! [SV5: $i] :
( ( ~ ~ ( ~ ( antisymmetric_relstr @ SV5 )
| ~ ( rel_str @ SV5 ) )
| ! [SY56: $i] :
~ ( ~ ( ~ ( ex_sup_of_relstr_set @ SV5 @ SY56 )
| ~ ! [SY57: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY57 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SY56 @ SY57 ) )
| ~ ! [SY58: $i] :
( ~ ( element @ SY58 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SY56 @ SY58 )
| ( related @ SV5 @ SY57 @ SY58 ) ) ) )
| ~ ( ~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY59 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SY56 @ SY59 ) )
| ~ ! [SY60: $i] :
( ~ ( element @ SY60 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SY56 @ SY60 )
| ( related @ SV5 @ SY59 @ SY60 ) ) )
| ( ex_sup_of_relstr_set @ SV5 @ SY56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(795,plain,
( ( ! [SX0: $i] :
~ ( rel_str @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[781]) ).
thf(796,plain,
! [SV6: $i] :
( ( ~ ( rel_str @ SV6 )
| ! [SY61: $i,SY62: $i] :
( ~ ( element @ SY62 @ ( the_carrier @ SV6 ) )
| ~ ( ex_sup_of_relstr_set @ SV6 @ SY61 )
| ~ ( ~ ( ( SY62
!= ( join_on_relstr @ SV6 @ SY61 ) )
| ~ ( ~ ( relstr_set_smaller @ SV6 @ SY61 @ SY62 )
| ~ ! [SY63: $i] :
( ~ ( element @ SY63 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SY61 @ SY63 )
| ( related @ SV6 @ SY62 @ SY63 ) ) ) )
| ~ ( ~ ~ ( ~ ( relstr_set_smaller @ SV6 @ SY61 @ SY62 )
| ~ ! [SY64: $i] :
( ~ ( element @ SY64 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SY61 @ SY64 )
| ( related @ SV6 @ SY62 @ SY64 ) ) )
| ( SY62
= ( join_on_relstr @ SV6 @ SY61 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(797,plain,
! [SV7: $i] :
( ( ! [SY65: $i] :
( ~ ( rel_str @ SV7 )
| ( element @ ( meet_on_relstr @ SV7 @ SY65 ) @ ( the_carrier @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(798,plain,
! [SV8: $i] :
( ( ~ ( rel_str @ SV8 )
| ! [SY66: $i,SY67: $i] :
( ~ ( element @ SY67 @ ( the_carrier @ SV8 ) )
| ~ ( ~ ( ~ ( relstr_set_smaller @ SV8 @ SY66 @ SY67 )
| ! [SY68: $i] :
( ~ ( element @ SY68 @ ( the_carrier @ SV8 ) )
| ~ ( in @ SY68 @ SY66 )
| ( related @ SV8 @ SY68 @ SY67 ) ) )
| ~ ( ~ ! [SY69: $i] :
( ~ ( element @ SY69 @ ( the_carrier @ SV8 ) )
| ~ ( in @ SY69 @ SY66 )
| ( related @ SV8 @ SY69 @ SY67 ) )
| ( relstr_set_smaller @ SV8 @ SY66 @ SY67 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(799,plain,
! [SV9: $i] :
( ( ~ ~ ( ~ ( antisymmetric_relstr @ SV9 )
| ~ ( rel_str @ SV9 ) )
| ! [SY70: $i] :
( ~ ( element @ SY70 @ ( the_carrier @ SV9 ) )
| ! [SY71: $i] :
( ~ ( element @ SY71 @ ( the_carrier @ SV9 ) )
| ~ ~ ( ~ ( related @ SV9 @ SY70 @ SY71 )
| ~ ( related @ SV9 @ SY71 @ SY70 ) )
| ( SY70 = SY71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(800,plain,
! [SV10: $i] :
( ( ! [SY72: $i] :
( ~ ( rel_str @ SV10 )
| ( element @ ( join_on_relstr @ SV10 @ SY72 ) @ ( the_carrier @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(801,plain,
( ( ! [SX0: $i] :
( ~ ( element @ SX0 @ ( the_carrier @ sK1_A ) )
| ! [SX1: $i] :
~ ( ~ ( ~ ~ ( ( SX0
!= ( join_on_relstr @ sK1_A @ SX1 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ SX1 ) )
| ~ ( ~ ( relstr_set_smaller @ sK1_A @ SX1 @ SX0 )
| ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ SX1 @ SX2 )
| ( related @ sK1_A @ SX0 @ SX2 ) ) ) )
| ~ ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ SX1 @ SX0 )
| ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ SX1 @ SX2 )
| ( related @ sK1_A @ SX0 @ SX2 ) ) )
| ~ ( ( SX0
!= ( join_on_relstr @ sK1_A @ SX1 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[787]) ).
thf(802,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ( transitive_relstr @ SV11 )
| ~ ( rel_str @ SV11 ) )
| ! [SY73: $i] :
( ~ ( element @ SY73 @ ( the_carrier @ SV11 ) )
| ! [SY74: $i] :
( ~ ( element @ SY74 @ ( the_carrier @ SV11 ) )
| ! [SY75: $i] :
( ~ ( element @ SY75 @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( related @ SV11 @ SY73 @ SY74 )
| ~ ( related @ SV11 @ SY74 @ SY75 ) )
| ( related @ SV11 @ SY73 @ SY75 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(803,plain,
! [SV12: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV12 )
| ( element @ SV1 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(804,plain,
( ( ~ ~ ( ~ ( rel_str @ sK2_SX0 )
| ~ ( strict_rel_str @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[790]) ).
thf(805,plain,
! [SV2: $i] :
( ( ( ~ ( rel_str @ SV2 ) )
= $true )
| ( ( ! [SY46: $i] :
~ ( ~ ( ~ ( ex_sup_of_relstr_set @ SV2 @ SY46 )
| ~ ! [SY47: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY47 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SY46 @ SY47 ) )
| ~ ! [SY48: $i] :
( ~ ( element @ SY48 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SY46 @ SY48 )
| ( related @ SV2 @ SY47 @ SY48 ) ) )
| ~ ! [SY49: $i] :
( ~ ( element @ SY49 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SY46 @ SY49 )
| ~ ! [SY50: $i] :
( ~ ( element @ SY50 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SY46 @ SY50 )
| ( related @ SV2 @ SY49 @ SY50 ) ) )
| ( SY49 = SY47 ) ) ) )
| ~ ( ~ ~ ! [SY51: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY51 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SY46 @ SY51 ) )
| ~ ! [SY52: $i] :
( ~ ( element @ SY52 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SY46 @ SY52 )
| ( related @ SV2 @ SY51 @ SY52 ) ) )
| ~ ! [SY53: $i] :
( ~ ( element @ SY53 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SY46 @ SY53 )
| ~ ! [SY54: $i] :
( ~ ( element @ SY54 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SY46 @ SY54 )
| ( related @ SV2 @ SY53 @ SY54 ) ) )
| ( SY53 = SY51 ) ) )
| ( ex_sup_of_relstr_set @ SV2 @ SY46 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[791]) ).
thf(806,plain,
! [SV3: $i] :
( ( ! [SY55: $i] :
~ ( element @ SY55 @ SV3 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[792]) ).
thf(807,plain,
! [SV4: $i] :
( ( ( ~ ( rel_str @ SV4 ) )
= $true )
| ( ( one_sorted_str @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[793]) ).
thf(808,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ~ ( antisymmetric_relstr @ SV5 )
| ~ ( rel_str @ SV5 ) ) )
= $true )
| ( ( ! [SY56: $i] :
~ ( ~ ( ~ ( ex_sup_of_relstr_set @ SV5 @ SY56 )
| ~ ! [SY57: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY57 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SY56 @ SY57 ) )
| ~ ! [SY58: $i] :
( ~ ( element @ SY58 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SY56 @ SY58 )
| ( related @ SV5 @ SY57 @ SY58 ) ) ) )
| ~ ( ~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY59 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SY56 @ SY59 ) )
| ~ ! [SY60: $i] :
( ~ ( element @ SY60 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SY56 @ SY60 )
| ( related @ SV5 @ SY59 @ SY60 ) ) )
| ( ex_sup_of_relstr_set @ SV5 @ SY56 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[794]) ).
thf(809,plain,
( ( ~ ( rel_str @ sK3_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[795]) ).
thf(810,plain,
! [SV6: $i] :
( ( ( ~ ( rel_str @ SV6 ) )
= $true )
| ( ( ! [SY61: $i,SY62: $i] :
( ~ ( element @ SY62 @ ( the_carrier @ SV6 ) )
| ~ ( ex_sup_of_relstr_set @ SV6 @ SY61 )
| ~ ( ~ ( ( SY62
!= ( join_on_relstr @ SV6 @ SY61 ) )
| ~ ( ~ ( relstr_set_smaller @ SV6 @ SY61 @ SY62 )
| ~ ! [SY63: $i] :
( ~ ( element @ SY63 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SY61 @ SY63 )
| ( related @ SV6 @ SY62 @ SY63 ) ) ) )
| ~ ( ~ ~ ( ~ ( relstr_set_smaller @ SV6 @ SY61 @ SY62 )
| ~ ! [SY64: $i] :
( ~ ( element @ SY64 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SY61 @ SY64 )
| ( related @ SV6 @ SY62 @ SY64 ) ) )
| ( SY62
= ( join_on_relstr @ SV6 @ SY61 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[796]) ).
thf(811,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ( rel_str @ SV7 )
| ( element @ ( meet_on_relstr @ SV7 @ SV13 ) @ ( the_carrier @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(812,plain,
! [SV8: $i] :
( ( ( ~ ( rel_str @ SV8 ) )
= $true )
| ( ( ! [SY66: $i,SY67: $i] :
( ~ ( element @ SY67 @ ( the_carrier @ SV8 ) )
| ~ ( ~ ( ~ ( relstr_set_smaller @ SV8 @ SY66 @ SY67 )
| ! [SY68: $i] :
( ~ ( element @ SY68 @ ( the_carrier @ SV8 ) )
| ~ ( in @ SY68 @ SY66 )
| ( related @ SV8 @ SY68 @ SY67 ) ) )
| ~ ( ~ ! [SY69: $i] :
( ~ ( element @ SY69 @ ( the_carrier @ SV8 ) )
| ~ ( in @ SY69 @ SY66 )
| ( related @ SV8 @ SY69 @ SY67 ) )
| ( relstr_set_smaller @ SV8 @ SY66 @ SY67 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[798]) ).
thf(813,plain,
! [SV9: $i] :
( ( ( ~ ~ ( ~ ( antisymmetric_relstr @ SV9 )
| ~ ( rel_str @ SV9 ) ) )
= $true )
| ( ( ! [SY70: $i] :
( ~ ( element @ SY70 @ ( the_carrier @ SV9 ) )
| ! [SY71: $i] :
( ~ ( element @ SY71 @ ( the_carrier @ SV9 ) )
| ~ ~ ( ~ ( related @ SV9 @ SY70 @ SY71 )
| ~ ( related @ SV9 @ SY71 @ SY70 ) )
| ( SY70 = SY71 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[799]) ).
thf(814,plain,
! [SV14: $i,SV10: $i] :
( ( ~ ( rel_str @ SV10 )
| ( element @ ( join_on_relstr @ SV10 @ SV14 ) @ ( the_carrier @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(815,plain,
( ( ~ ( element @ sK4_SX0 @ ( the_carrier @ sK1_A ) )
| ! [SY76: $i] :
~ ( ~ ( ~ ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ SY76 ) )
| ~ ( ~ ( relstr_set_smaller @ sK1_A @ SY76 @ sK4_SX0 )
| ~ ! [SY77: $i] :
( ~ ( element @ SY77 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ SY76 @ SY77 )
| ( related @ sK1_A @ sK4_SX0 @ SY77 ) ) ) )
| ~ ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ SY76 @ sK4_SX0 )
| ~ ! [SY78: $i] :
( ~ ( element @ SY78 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ SY76 @ SY78 )
| ( related @ sK1_A @ sK4_SX0 @ SY78 ) ) )
| ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ SY76 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[801]) ).
thf(816,plain,
! [SV11: $i] :
( ( ( ~ ~ ( ~ ( transitive_relstr @ SV11 )
| ~ ( rel_str @ SV11 ) ) )
= $true )
| ( ( ! [SY73: $i] :
( ~ ( element @ SY73 @ ( the_carrier @ SV11 ) )
| ! [SY74: $i] :
( ~ ( element @ SY74 @ ( the_carrier @ SV11 ) )
| ! [SY75: $i] :
( ~ ( element @ SY75 @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( related @ SV11 @ SY73 @ SY74 )
| ~ ( related @ SV11 @ SY74 @ SY75 ) )
| ( related @ SV11 @ SY73 @ SY75 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[802]) ).
thf(817,plain,
! [SV12: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV12 ) )
= $true )
| ( ( element @ SV1 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[803]) ).
thf(818,plain,
( ( ~ ( ~ ( rel_str @ sK2_SX0 )
| ~ ( strict_rel_str @ sK2_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[804]) ).
thf(819,plain,
! [SV2: $i] :
( ( ( rel_str @ SV2 )
= $false )
| ( ( ! [SY46: $i] :
~ ( ~ ( ~ ( ex_sup_of_relstr_set @ SV2 @ SY46 )
| ~ ! [SY47: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY47 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SY46 @ SY47 ) )
| ~ ! [SY48: $i] :
( ~ ( element @ SY48 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SY46 @ SY48 )
| ( related @ SV2 @ SY47 @ SY48 ) ) )
| ~ ! [SY49: $i] :
( ~ ( element @ SY49 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SY46 @ SY49 )
| ~ ! [SY50: $i] :
( ~ ( element @ SY50 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SY46 @ SY50 )
| ( related @ SV2 @ SY49 @ SY50 ) ) )
| ( SY49 = SY47 ) ) ) )
| ~ ( ~ ~ ! [SY51: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY51 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SY46 @ SY51 ) )
| ~ ! [SY52: $i] :
( ~ ( element @ SY52 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SY46 @ SY52 )
| ( related @ SV2 @ SY51 @ SY52 ) ) )
| ~ ! [SY53: $i] :
( ~ ( element @ SY53 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SY46 @ SY53 )
| ~ ! [SY54: $i] :
( ~ ( element @ SY54 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SY46 @ SY54 )
| ( related @ SV2 @ SY53 @ SY54 ) ) )
| ( SY53 = SY51 ) ) )
| ( ex_sup_of_relstr_set @ SV2 @ SY46 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(820,plain,
! [SV3: $i] :
( ( ~ ( element @ ( sK5_SY55 @ SV3 ) @ SV3 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[806]) ).
thf(821,plain,
! [SV4: $i] :
( ( ( rel_str @ SV4 )
= $false )
| ( ( one_sorted_str @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[807]) ).
thf(822,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ( antisymmetric_relstr @ SV5 )
| ~ ( rel_str @ SV5 ) ) )
= $false )
| ( ( ! [SY56: $i] :
~ ( ~ ( ~ ( ex_sup_of_relstr_set @ SV5 @ SY56 )
| ~ ! [SY57: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY57 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SY56 @ SY57 ) )
| ~ ! [SY58: $i] :
( ~ ( element @ SY58 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SY56 @ SY58 )
| ( related @ SV5 @ SY57 @ SY58 ) ) ) )
| ~ ( ~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY59 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SY56 @ SY59 ) )
| ~ ! [SY60: $i] :
( ~ ( element @ SY60 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SY56 @ SY60 )
| ( related @ SV5 @ SY59 @ SY60 ) ) )
| ( ex_sup_of_relstr_set @ SV5 @ SY56 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[808]) ).
thf(823,plain,
( ( rel_str @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[809]) ).
thf(824,plain,
! [SV6: $i] :
( ( ( rel_str @ SV6 )
= $false )
| ( ( ! [SY61: $i,SY62: $i] :
( ~ ( element @ SY62 @ ( the_carrier @ SV6 ) )
| ~ ( ex_sup_of_relstr_set @ SV6 @ SY61 )
| ~ ( ~ ( ( SY62
!= ( join_on_relstr @ SV6 @ SY61 ) )
| ~ ( ~ ( relstr_set_smaller @ SV6 @ SY61 @ SY62 )
| ~ ! [SY63: $i] :
( ~ ( element @ SY63 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SY61 @ SY63 )
| ( related @ SV6 @ SY62 @ SY63 ) ) ) )
| ~ ( ~ ~ ( ~ ( relstr_set_smaller @ SV6 @ SY61 @ SY62 )
| ~ ! [SY64: $i] :
( ~ ( element @ SY64 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SY61 @ SY64 )
| ( related @ SV6 @ SY62 @ SY64 ) ) )
| ( SY62
= ( join_on_relstr @ SV6 @ SY61 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[810]) ).
thf(825,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( rel_str @ SV7 ) )
= $true )
| ( ( element @ ( meet_on_relstr @ SV7 @ SV13 ) @ ( the_carrier @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[811]) ).
thf(826,plain,
! [SV8: $i] :
( ( ( rel_str @ SV8 )
= $false )
| ( ( ! [SY66: $i,SY67: $i] :
( ~ ( element @ SY67 @ ( the_carrier @ SV8 ) )
| ~ ( ~ ( ~ ( relstr_set_smaller @ SV8 @ SY66 @ SY67 )
| ! [SY68: $i] :
( ~ ( element @ SY68 @ ( the_carrier @ SV8 ) )
| ~ ( in @ SY68 @ SY66 )
| ( related @ SV8 @ SY68 @ SY67 ) ) )
| ~ ( ~ ! [SY69: $i] :
( ~ ( element @ SY69 @ ( the_carrier @ SV8 ) )
| ~ ( in @ SY69 @ SY66 )
| ( related @ SV8 @ SY69 @ SY67 ) )
| ( relstr_set_smaller @ SV8 @ SY66 @ SY67 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[812]) ).
thf(827,plain,
! [SV9: $i] :
( ( ( ~ ( ~ ( antisymmetric_relstr @ SV9 )
| ~ ( rel_str @ SV9 ) ) )
= $false )
| ( ( ! [SY70: $i] :
( ~ ( element @ SY70 @ ( the_carrier @ SV9 ) )
| ! [SY71: $i] :
( ~ ( element @ SY71 @ ( the_carrier @ SV9 ) )
| ~ ~ ( ~ ( related @ SV9 @ SY70 @ SY71 )
| ~ ( related @ SV9 @ SY71 @ SY70 ) )
| ( SY70 = SY71 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[813]) ).
thf(828,plain,
! [SV14: $i,SV10: $i] :
( ( ( ~ ( rel_str @ SV10 ) )
= $true )
| ( ( element @ ( join_on_relstr @ SV10 @ SV14 ) @ ( the_carrier @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[814]) ).
thf(829,plain,
( ( ~ ( element @ sK4_SX0 @ ( the_carrier @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[815]) ).
thf(830,plain,
( ( ! [SY76: $i] :
~ ( ~ ( ~ ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ SY76 ) )
| ~ ( ~ ( relstr_set_smaller @ sK1_A @ SY76 @ sK4_SX0 )
| ~ ! [SY77: $i] :
( ~ ( element @ SY77 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ SY76 @ SY77 )
| ( related @ sK1_A @ sK4_SX0 @ SY77 ) ) ) )
| ~ ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ SY76 @ sK4_SX0 )
| ~ ! [SY78: $i] :
( ~ ( element @ SY78 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ SY76 @ SY78 )
| ( related @ sK1_A @ sK4_SX0 @ SY78 ) ) )
| ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ SY76 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[815]) ).
thf(831,plain,
! [SV11: $i] :
( ( ( ~ ( ~ ( transitive_relstr @ SV11 )
| ~ ( rel_str @ SV11 ) ) )
= $false )
| ( ( ! [SY73: $i] :
( ~ ( element @ SY73 @ ( the_carrier @ SV11 ) )
| ! [SY74: $i] :
( ~ ( element @ SY74 @ ( the_carrier @ SV11 ) )
| ! [SY75: $i] :
( ~ ( element @ SY75 @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( related @ SV11 @ SY73 @ SY74 )
| ~ ( related @ SV11 @ SY74 @ SY75 ) )
| ( related @ SV11 @ SY73 @ SY75 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[816]) ).
thf(832,plain,
! [SV12: $i,SV1: $i] :
( ( ( in @ SV1 @ SV12 )
= $false )
| ( ( element @ SV1 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[817]) ).
thf(833,plain,
( ( ~ ( rel_str @ sK2_SX0 )
| ~ ( strict_rel_str @ sK2_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[818]) ).
thf(834,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ( ~ ( ~ ( ex_sup_of_relstr_set @ SV2 @ SV15 )
| ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY79 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY79 ) )
| ~ ! [SY80: $i] :
( ~ ( element @ SY80 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY80 )
| ( related @ SV2 @ SY79 @ SY80 ) ) )
| ~ ! [SY81: $i] :
( ~ ( element @ SY81 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY81 )
| ~ ! [SY82: $i] :
( ~ ( element @ SY82 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY82 )
| ( related @ SV2 @ SY81 @ SY82 ) ) )
| ( SY81 = SY79 ) ) ) )
| ~ ( ~ ~ ! [SY83: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY83 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY83 ) )
| ~ ! [SY84: $i] :
( ~ ( element @ SY84 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY84 )
| ( related @ SV2 @ SY83 @ SY84 ) ) )
| ~ ! [SY85: $i] :
( ~ ( element @ SY85 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY85 )
| ~ ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY86 )
| ( related @ SV2 @ SY85 @ SY86 ) ) )
| ( SY85 = SY83 ) ) )
| ( ex_sup_of_relstr_set @ SV2 @ SV15 ) ) ) )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(835,plain,
! [SV3: $i] :
( ( element @ ( sK5_SY55 @ SV3 ) @ SV3 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[820]) ).
thf(836,plain,
! [SV5: $i] :
( ( ( ~ ( antisymmetric_relstr @ SV5 )
| ~ ( rel_str @ SV5 ) )
= $true )
| ( ( ! [SY56: $i] :
~ ( ~ ( ~ ( ex_sup_of_relstr_set @ SV5 @ SY56 )
| ~ ! [SY57: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY57 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SY56 @ SY57 ) )
| ~ ! [SY58: $i] :
( ~ ( element @ SY58 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SY56 @ SY58 )
| ( related @ SV5 @ SY57 @ SY58 ) ) ) )
| ~ ( ~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY59 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SY56 @ SY59 ) )
| ~ ! [SY60: $i] :
( ~ ( element @ SY60 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SY56 @ SY60 )
| ( related @ SV5 @ SY59 @ SY60 ) ) )
| ( ex_sup_of_relstr_set @ SV5 @ SY56 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[822]) ).
thf(837,plain,
! [SV16: $i,SV6: $i] :
( ( ( ! [SY87: $i] :
( ~ ( element @ SY87 @ ( the_carrier @ SV6 ) )
| ~ ( ex_sup_of_relstr_set @ SV6 @ SV16 )
| ~ ( ~ ( ( SY87
!= ( join_on_relstr @ SV6 @ SV16 ) )
| ~ ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY87 )
| ~ ! [SY88: $i] :
( ~ ( element @ SY88 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY88 )
| ( related @ SV6 @ SY87 @ SY88 ) ) ) )
| ~ ( ~ ~ ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY87 )
| ~ ! [SY89: $i] :
( ~ ( element @ SY89 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY89 )
| ( related @ SV6 @ SY87 @ SY89 ) ) )
| ( SY87
= ( join_on_relstr @ SV6 @ SV16 ) ) ) ) ) )
= $true )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(838,plain,
! [SV13: $i,SV7: $i] :
( ( ( rel_str @ SV7 )
= $false )
| ( ( element @ ( meet_on_relstr @ SV7 @ SV13 ) @ ( the_carrier @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[825]) ).
thf(839,plain,
! [SV17: $i,SV8: $i] :
( ( ( ! [SY90: $i] :
( ~ ( element @ SY90 @ ( the_carrier @ SV8 ) )
| ~ ( ~ ( ~ ( relstr_set_smaller @ SV8 @ SV17 @ SY90 )
| ! [SY91: $i] :
( ~ ( element @ SY91 @ ( the_carrier @ SV8 ) )
| ~ ( in @ SY91 @ SV17 )
| ( related @ SV8 @ SY91 @ SY90 ) ) )
| ~ ( ~ ! [SY92: $i] :
( ~ ( element @ SY92 @ ( the_carrier @ SV8 ) )
| ~ ( in @ SY92 @ SV17 )
| ( related @ SV8 @ SY92 @ SY90 ) )
| ( relstr_set_smaller @ SV8 @ SV17 @ SY90 ) ) ) ) )
= $true )
| ( ( rel_str @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(840,plain,
! [SV9: $i] :
( ( ( ~ ( antisymmetric_relstr @ SV9 )
| ~ ( rel_str @ SV9 ) )
= $true )
| ( ( ! [SY70: $i] :
( ~ ( element @ SY70 @ ( the_carrier @ SV9 ) )
| ! [SY71: $i] :
( ~ ( element @ SY71 @ ( the_carrier @ SV9 ) )
| ~ ~ ( ~ ( related @ SV9 @ SY70 @ SY71 )
| ~ ( related @ SV9 @ SY71 @ SY70 ) )
| ( SY70 = SY71 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[827]) ).
thf(841,plain,
! [SV14: $i,SV10: $i] :
( ( ( rel_str @ SV10 )
= $false )
| ( ( element @ ( join_on_relstr @ SV10 @ SV14 ) @ ( the_carrier @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[828]) ).
thf(842,plain,
( ( element @ sK4_SX0 @ ( the_carrier @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[829]) ).
thf(843,plain,
( ( ~ ( ~ ( ~ ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) )
| ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY93: $i] :
( ~ ( element @ SY93 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY93 )
| ( related @ sK1_A @ sK4_SX0 @ SY93 ) ) ) )
| ~ ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
| ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[830]) ).
thf(844,plain,
! [SV11: $i] :
( ( ( ~ ( transitive_relstr @ SV11 )
| ~ ( rel_str @ SV11 ) )
= $true )
| ( ( ! [SY73: $i] :
( ~ ( element @ SY73 @ ( the_carrier @ SV11 ) )
| ! [SY74: $i] :
( ~ ( element @ SY74 @ ( the_carrier @ SV11 ) )
| ! [SY75: $i] :
( ~ ( element @ SY75 @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( related @ SV11 @ SY73 @ SY74 )
| ~ ( related @ SV11 @ SY74 @ SY75 ) )
| ( related @ SV11 @ SY73 @ SY75 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[831]) ).
thf(845,plain,
( ( ~ ( rel_str @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[833]) ).
thf(846,plain,
( ( ~ ( strict_rel_str @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[833]) ).
thf(847,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ( ~ ( ex_sup_of_relstr_set @ SV2 @ SV15 )
| ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY79 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY79 ) )
| ~ ! [SY80: $i] :
( ~ ( element @ SY80 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY80 )
| ( related @ SV2 @ SY79 @ SY80 ) ) )
| ~ ! [SY81: $i] :
( ~ ( element @ SY81 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY81 )
| ~ ! [SY82: $i] :
( ~ ( element @ SY82 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY82 )
| ( related @ SV2 @ SY81 @ SY82 ) ) )
| ( SY81 = SY79 ) ) ) )
| ~ ( ~ ~ ! [SY83: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY83 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY83 ) )
| ~ ! [SY84: $i] :
( ~ ( element @ SY84 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY84 )
| ( related @ SV2 @ SY83 @ SY84 ) ) )
| ~ ! [SY85: $i] :
( ~ ( element @ SY85 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY85 )
| ~ ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY86 )
| ( related @ SV2 @ SY85 @ SY86 ) ) )
| ( SY85 = SY83 ) ) )
| ( ex_sup_of_relstr_set @ SV2 @ SV15 ) ) )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(848,plain,
! [SV5: $i] :
( ( ( ~ ( antisymmetric_relstr @ SV5 ) )
= $true )
| ( ( ~ ( rel_str @ SV5 ) )
= $true )
| ( ( ! [SY56: $i] :
~ ( ~ ( ~ ( ex_sup_of_relstr_set @ SV5 @ SY56 )
| ~ ! [SY57: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY57 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SY56 @ SY57 ) )
| ~ ! [SY58: $i] :
( ~ ( element @ SY58 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SY56 @ SY58 )
| ( related @ SV5 @ SY57 @ SY58 ) ) ) )
| ~ ( ~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY59 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SY56 @ SY59 ) )
| ~ ! [SY60: $i] :
( ~ ( element @ SY60 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SY56 @ SY60 )
| ( related @ SV5 @ SY59 @ SY60 ) ) )
| ( ex_sup_of_relstr_set @ SV5 @ SY56 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[836]) ).
thf(849,plain,
! [SV16: $i,SV6: $i,SV18: $i] :
( ( ( ~ ( element @ SV18 @ ( the_carrier @ SV6 ) )
| ~ ( ex_sup_of_relstr_set @ SV6 @ SV16 )
| ~ ( ~ ( ( SV18
!= ( join_on_relstr @ SV6 @ SV16 ) )
| ~ ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
| ~ ! [SY95: $i] :
( ~ ( element @ SY95 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY95 )
| ( related @ SV6 @ SV18 @ SY95 ) ) ) )
| ~ ( ~ ~ ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
| ~ ! [SY96: $i] :
( ~ ( element @ SY96 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY96 )
| ( related @ SV6 @ SV18 @ SY96 ) ) )
| ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) ) ) ) )
= $true )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(850,plain,
! [SV17: $i,SV8: $i,SV19: $i] :
( ( ( ~ ( element @ SV19 @ ( the_carrier @ SV8 ) )
| ~ ( ~ ( ~ ( relstr_set_smaller @ SV8 @ SV17 @ SV19 )
| ! [SY97: $i] :
( ~ ( element @ SY97 @ ( the_carrier @ SV8 ) )
| ~ ( in @ SY97 @ SV17 )
| ( related @ SV8 @ SY97 @ SV19 ) ) )
| ~ ( ~ ! [SY98: $i] :
( ~ ( element @ SY98 @ ( the_carrier @ SV8 ) )
| ~ ( in @ SY98 @ SV17 )
| ( related @ SV8 @ SY98 @ SV19 ) )
| ( relstr_set_smaller @ SV8 @ SV17 @ SV19 ) ) ) )
= $true )
| ( ( rel_str @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(851,plain,
! [SV9: $i] :
( ( ( ~ ( antisymmetric_relstr @ SV9 ) )
= $true )
| ( ( ~ ( rel_str @ SV9 ) )
= $true )
| ( ( ! [SY70: $i] :
( ~ ( element @ SY70 @ ( the_carrier @ SV9 ) )
| ! [SY71: $i] :
( ~ ( element @ SY71 @ ( the_carrier @ SV9 ) )
| ~ ~ ( ~ ( related @ SV9 @ SY70 @ SY71 )
| ~ ( related @ SV9 @ SY71 @ SY70 ) )
| ( SY70 = SY71 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[840]) ).
thf(852,plain,
( ( ~ ( ~ ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) )
| ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY93: $i] :
( ~ ( element @ SY93 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY93 )
| ( related @ sK1_A @ sK4_SX0 @ SY93 ) ) ) )
| ~ ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
| ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[843]) ).
thf(853,plain,
! [SV11: $i] :
( ( ( ~ ( transitive_relstr @ SV11 ) )
= $true )
| ( ( ~ ( rel_str @ SV11 ) )
= $true )
| ( ( ! [SY73: $i] :
( ~ ( element @ SY73 @ ( the_carrier @ SV11 ) )
| ! [SY74: $i] :
( ~ ( element @ SY74 @ ( the_carrier @ SV11 ) )
| ! [SY75: $i] :
( ~ ( element @ SY75 @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( related @ SV11 @ SY73 @ SY74 )
| ~ ( related @ SV11 @ SY74 @ SY75 ) )
| ( related @ SV11 @ SY73 @ SY75 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[844]) ).
thf(854,plain,
( ( rel_str @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[845]) ).
thf(855,plain,
( ( strict_rel_str @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[846]) ).
thf(856,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ( ~ ( ex_sup_of_relstr_set @ SV2 @ SV15 )
| ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY79 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY79 ) )
| ~ ! [SY80: $i] :
( ~ ( element @ SY80 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY80 )
| ( related @ SV2 @ SY79 @ SY80 ) ) )
| ~ ! [SY81: $i] :
( ~ ( element @ SY81 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY81 )
| ~ ! [SY82: $i] :
( ~ ( element @ SY82 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY82 )
| ( related @ SV2 @ SY81 @ SY82 ) ) )
| ( SY81 = SY79 ) ) ) ) )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[847]) ).
thf(857,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ( ~ ~ ! [SY83: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY83 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY83 ) )
| ~ ! [SY84: $i] :
( ~ ( element @ SY84 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY84 )
| ( related @ SV2 @ SY83 @ SY84 ) ) )
| ~ ! [SY85: $i] :
( ~ ( element @ SY85 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY85 )
| ~ ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY86 )
| ( related @ SV2 @ SY85 @ SY86 ) ) )
| ( SY85 = SY83 ) ) )
| ( ex_sup_of_relstr_set @ SV2 @ SV15 ) ) )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[847]) ).
thf(858,plain,
! [SV5: $i] :
( ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( ~ ( rel_str @ SV5 ) )
= $true )
| ( ( ! [SY56: $i] :
~ ( ~ ( ~ ( ex_sup_of_relstr_set @ SV5 @ SY56 )
| ~ ! [SY57: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY57 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SY56 @ SY57 ) )
| ~ ! [SY58: $i] :
( ~ ( element @ SY58 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SY56 @ SY58 )
| ( related @ SV5 @ SY57 @ SY58 ) ) ) )
| ~ ( ~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY59 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SY56 @ SY59 ) )
| ~ ! [SY60: $i] :
( ~ ( element @ SY60 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SY56 @ SY60 )
| ( related @ SV5 @ SY59 @ SY60 ) ) )
| ( ex_sup_of_relstr_set @ SV5 @ SY56 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[848]) ).
thf(859,plain,
! [SV16: $i,SV6: $i,SV18: $i] :
( ( ( ~ ( element @ SV18 @ ( the_carrier @ SV6 ) ) )
= $true )
| ( ( ~ ( ex_sup_of_relstr_set @ SV6 @ SV16 )
| ~ ( ~ ( ( SV18
!= ( join_on_relstr @ SV6 @ SV16 ) )
| ~ ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
| ~ ! [SY95: $i] :
( ~ ( element @ SY95 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY95 )
| ( related @ SV6 @ SV18 @ SY95 ) ) ) )
| ~ ( ~ ~ ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
| ~ ! [SY96: $i] :
( ~ ( element @ SY96 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY96 )
| ( related @ SV6 @ SV18 @ SY96 ) ) )
| ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) ) ) ) )
= $true )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[849]) ).
thf(860,plain,
! [SV17: $i,SV8: $i,SV19: $i] :
( ( ( ~ ( element @ SV19 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( relstr_set_smaller @ SV8 @ SV17 @ SV19 )
| ! [SY97: $i] :
( ~ ( element @ SY97 @ ( the_carrier @ SV8 ) )
| ~ ( in @ SY97 @ SV17 )
| ( related @ SV8 @ SY97 @ SV19 ) ) )
| ~ ( ~ ! [SY98: $i] :
( ~ ( element @ SY98 @ ( the_carrier @ SV8 ) )
| ~ ( in @ SY98 @ SV17 )
| ( related @ SV8 @ SY98 @ SV19 ) )
| ( relstr_set_smaller @ SV8 @ SV17 @ SV19 ) ) ) )
= $true )
| ( ( rel_str @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[850]) ).
thf(861,plain,
! [SV9: $i] :
( ( ( antisymmetric_relstr @ SV9 )
= $false )
| ( ( ~ ( rel_str @ SV9 ) )
= $true )
| ( ( ! [SY70: $i] :
( ~ ( element @ SY70 @ ( the_carrier @ SV9 ) )
| ! [SY71: $i] :
( ~ ( element @ SY71 @ ( the_carrier @ SV9 ) )
| ~ ~ ( ~ ( related @ SV9 @ SY70 @ SY71 )
| ~ ( related @ SV9 @ SY71 @ SY70 ) )
| ( SY70 = SY71 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[851]) ).
thf(862,plain,
( ( ( ~ ( ~ ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) )
| ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY93: $i] :
( ~ ( element @ SY93 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY93 )
| ( related @ sK1_A @ sK4_SX0 @ SY93 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
| ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[852]) ).
thf(863,plain,
! [SV11: $i] :
( ( ( transitive_relstr @ SV11 )
= $false )
| ( ( ~ ( rel_str @ SV11 ) )
= $true )
| ( ( ! [SY73: $i] :
( ~ ( element @ SY73 @ ( the_carrier @ SV11 ) )
| ! [SY74: $i] :
( ~ ( element @ SY74 @ ( the_carrier @ SV11 ) )
| ! [SY75: $i] :
( ~ ( element @ SY75 @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( related @ SV11 @ SY73 @ SY74 )
| ~ ( related @ SV11 @ SY74 @ SY75 ) )
| ( related @ SV11 @ SY73 @ SY75 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[853]) ).
thf(864,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ( ex_sup_of_relstr_set @ SV2 @ SV15 )
| ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY79 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY79 ) )
| ~ ! [SY80: $i] :
( ~ ( element @ SY80 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY80 )
| ( related @ SV2 @ SY79 @ SY80 ) ) )
| ~ ! [SY81: $i] :
( ~ ( element @ SY81 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY81 )
| ~ ! [SY82: $i] :
( ~ ( element @ SY82 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY82 )
| ( related @ SV2 @ SY81 @ SY82 ) ) )
| ( SY81 = SY79 ) ) ) )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[856]) ).
thf(865,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ~ ! [SY83: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY83 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY83 ) )
| ~ ! [SY84: $i] :
( ~ ( element @ SY84 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY84 )
| ( related @ SV2 @ SY83 @ SY84 ) ) )
| ~ ! [SY85: $i] :
( ~ ( element @ SY85 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY85 )
| ~ ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY86 )
| ( related @ SV2 @ SY85 @ SY86 ) ) )
| ( SY85 = SY83 ) ) )
| ( ex_sup_of_relstr_set @ SV2 @ SV15 ) )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[857]) ).
thf(866,plain,
! [SV5: $i] :
( ( ( rel_str @ SV5 )
= $false )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( ! [SY56: $i] :
~ ( ~ ( ~ ( ex_sup_of_relstr_set @ SV5 @ SY56 )
| ~ ! [SY57: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY57 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SY56 @ SY57 ) )
| ~ ! [SY58: $i] :
( ~ ( element @ SY58 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SY56 @ SY58 )
| ( related @ SV5 @ SY57 @ SY58 ) ) ) )
| ~ ( ~ ~ ! [SY59: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY59 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SY56 @ SY59 ) )
| ~ ! [SY60: $i] :
( ~ ( element @ SY60 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SY56 @ SY60 )
| ( related @ SV5 @ SY59 @ SY60 ) ) )
| ( ex_sup_of_relstr_set @ SV5 @ SY56 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[858]) ).
thf(867,plain,
! [SV16: $i,SV6: $i,SV18: $i] :
( ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( ~ ( ex_sup_of_relstr_set @ SV6 @ SV16 )
| ~ ( ~ ( ( SV18
!= ( join_on_relstr @ SV6 @ SV16 ) )
| ~ ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
| ~ ! [SY95: $i] :
( ~ ( element @ SY95 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY95 )
| ( related @ SV6 @ SV18 @ SY95 ) ) ) )
| ~ ( ~ ~ ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
| ~ ! [SY96: $i] :
( ~ ( element @ SY96 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY96 )
| ( related @ SV6 @ SV18 @ SY96 ) ) )
| ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) ) ) ) )
= $true )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[859]) ).
thf(868,plain,
! [SV17: $i,SV8: $i,SV19: $i] :
( ( ( element @ SV19 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( relstr_set_smaller @ SV8 @ SV17 @ SV19 )
| ! [SY97: $i] :
( ~ ( element @ SY97 @ ( the_carrier @ SV8 ) )
| ~ ( in @ SY97 @ SV17 )
| ( related @ SV8 @ SY97 @ SV19 ) ) )
| ~ ( ~ ! [SY98: $i] :
( ~ ( element @ SY98 @ ( the_carrier @ SV8 ) )
| ~ ( in @ SY98 @ SV17 )
| ( related @ SV8 @ SY98 @ SV19 ) )
| ( relstr_set_smaller @ SV8 @ SV17 @ SV19 ) ) ) )
= $true )
| ( ( rel_str @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(869,plain,
! [SV9: $i] :
( ( ( rel_str @ SV9 )
= $false )
| ( ( antisymmetric_relstr @ SV9 )
= $false )
| ( ( ! [SY70: $i] :
( ~ ( element @ SY70 @ ( the_carrier @ SV9 ) )
| ! [SY71: $i] :
( ~ ( element @ SY71 @ ( the_carrier @ SV9 ) )
| ~ ~ ( ~ ( related @ SV9 @ SY70 @ SY71 )
| ~ ( related @ SV9 @ SY71 @ SY70 ) )
| ( SY70 = SY71 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[861]) ).
thf(870,plain,
( ( ( ~ ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) )
| ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY93: $i] :
( ~ ( element @ SY93 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY93 )
| ( related @ sK1_A @ sK4_SX0 @ SY93 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
| ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[862]) ).
thf(871,plain,
! [SV11: $i] :
( ( ( rel_str @ SV11 )
= $false )
| ( ( transitive_relstr @ SV11 )
= $false )
| ( ( ! [SY73: $i] :
( ~ ( element @ SY73 @ ( the_carrier @ SV11 ) )
| ! [SY74: $i] :
( ~ ( element @ SY74 @ ( the_carrier @ SV11 ) )
| ! [SY75: $i] :
( ~ ( element @ SY75 @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( related @ SV11 @ SY73 @ SY74 )
| ~ ( related @ SV11 @ SY74 @ SY75 ) )
| ( related @ SV11 @ SY73 @ SY75 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[863]) ).
thf(872,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ( ex_sup_of_relstr_set @ SV2 @ SV15 ) )
= $true )
| ( ( ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY79 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY79 ) )
| ~ ! [SY80: $i] :
( ~ ( element @ SY80 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY80 )
| ( related @ SV2 @ SY79 @ SY80 ) ) )
| ~ ! [SY81: $i] :
( ~ ( element @ SY81 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY81 )
| ~ ! [SY82: $i] :
( ~ ( element @ SY82 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY82 )
| ( related @ SV2 @ SY81 @ SY82 ) ) )
| ( SY81 = SY79 ) ) ) )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[864]) ).
thf(873,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ~ ! [SY83: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY83 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY83 ) )
| ~ ! [SY84: $i] :
( ~ ( element @ SY84 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY84 )
| ( related @ SV2 @ SY83 @ SY84 ) ) )
| ~ ! [SY85: $i] :
( ~ ( element @ SY85 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY85 )
| ~ ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY86 )
| ( related @ SV2 @ SY85 @ SY86 ) ) )
| ( SY85 = SY83 ) ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[865]) ).
thf(874,plain,
! [SV20: $i,SV5: $i] :
( ( ( ~ ( ~ ( ~ ( ex_sup_of_relstr_set @ SV5 @ SV20 )
| ~ ! [SY99: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY99 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY99 ) )
| ~ ! [SY100: $i] :
( ~ ( element @ SY100 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY100 )
| ( related @ SV5 @ SY99 @ SY100 ) ) ) )
| ~ ( ~ ~ ! [SY101: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY101 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( element @ SY102 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY102 )
| ( related @ SV5 @ SY101 @ SY102 ) ) )
| ( ex_sup_of_relstr_set @ SV5 @ SV20 ) ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(875,plain,
! [SV18: $i,SV16: $i,SV6: $i] :
( ( ( ~ ( ex_sup_of_relstr_set @ SV6 @ SV16 ) )
= $true )
| ( ( ~ ( ~ ( ( SV18
!= ( join_on_relstr @ SV6 @ SV16 ) )
| ~ ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
| ~ ! [SY95: $i] :
( ~ ( element @ SY95 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY95 )
| ( related @ SV6 @ SV18 @ SY95 ) ) ) )
| ~ ( ~ ~ ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
| ~ ! [SY96: $i] :
( ~ ( element @ SY96 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY96 )
| ( related @ SV6 @ SV18 @ SY96 ) ) )
| ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) ) ) ) )
= $true )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[867]) ).
thf(876,plain,
! [SV19: $i,SV17: $i,SV8: $i] :
( ( ( ~ ( ~ ( relstr_set_smaller @ SV8 @ SV17 @ SV19 )
| ! [SY97: $i] :
( ~ ( element @ SY97 @ ( the_carrier @ SV8 ) )
| ~ ( in @ SY97 @ SV17 )
| ( related @ SV8 @ SY97 @ SV19 ) ) )
| ~ ( ~ ! [SY98: $i] :
( ~ ( element @ SY98 @ ( the_carrier @ SV8 ) )
| ~ ( in @ SY98 @ SV17 )
| ( related @ SV8 @ SY98 @ SV19 ) )
| ( relstr_set_smaller @ SV8 @ SV17 @ SV19 ) ) )
= $false )
| ( ( element @ SV19 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( rel_str @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[868]) ).
thf(877,plain,
! [SV9: $i,SV21: $i] :
( ( ( ~ ( element @ SV21 @ ( the_carrier @ SV9 ) )
| ! [SY103: $i] :
( ~ ( element @ SY103 @ ( the_carrier @ SV9 ) )
| ~ ~ ( ~ ( related @ SV9 @ SV21 @ SY103 )
| ~ ( related @ SV9 @ SY103 @ SV21 ) )
| ( SV21 = SY103 ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV9 )
= $false )
| ( ( rel_str @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(878,plain,
( ( ( ~ ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
| ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[870]) ).
thf(879,plain,
( ( ( ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY93: $i] :
( ~ ( element @ SY93 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY93 )
| ( related @ sK1_A @ sK4_SX0 @ SY93 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
| ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[870]) ).
thf(880,plain,
! [SV11: $i,SV22: $i] :
( ( ( ~ ( element @ SV22 @ ( the_carrier @ SV11 ) )
| ! [SY104: $i] :
( ~ ( element @ SY104 @ ( the_carrier @ SV11 ) )
| ! [SY105: $i] :
( ~ ( element @ SY105 @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( related @ SV11 @ SV22 @ SY104 )
| ~ ( related @ SV11 @ SY104 @ SY105 ) )
| ( related @ SV11 @ SV22 @ SY105 ) ) ) )
= $true )
| ( ( transitive_relstr @ SV11 )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(881,plain,
! [SV15: $i,SV2: $i] :
( ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY79 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY79 ) )
| ~ ! [SY80: $i] :
( ~ ( element @ SY80 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY80 )
| ( related @ SV2 @ SY79 @ SY80 ) ) )
| ~ ! [SY81: $i] :
( ~ ( element @ SY81 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY81 )
| ~ ! [SY82: $i] :
( ~ ( element @ SY82 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY82 )
| ( related @ SV2 @ SY81 @ SY82 ) ) )
| ( SY81 = SY79 ) ) ) )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[872]) ).
thf(882,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ! [SY83: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY83 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY83 ) )
| ~ ! [SY84: $i] :
( ~ ( element @ SY84 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY84 )
| ( related @ SV2 @ SY83 @ SY84 ) ) )
| ~ ! [SY85: $i] :
( ~ ( element @ SY85 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY85 )
| ~ ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY86 )
| ( related @ SV2 @ SY85 @ SY86 ) ) )
| ( SY85 = SY83 ) ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[873]) ).
thf(883,plain,
! [SV20: $i,SV5: $i] :
( ( ( ~ ( ~ ( ex_sup_of_relstr_set @ SV5 @ SV20 )
| ~ ! [SY99: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY99 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY99 ) )
| ~ ! [SY100: $i] :
( ~ ( element @ SY100 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY100 )
| ( related @ SV5 @ SY99 @ SY100 ) ) ) )
| ~ ( ~ ~ ! [SY101: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY101 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( element @ SY102 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY102 )
| ( related @ SV5 @ SY101 @ SY102 ) ) )
| ( ex_sup_of_relstr_set @ SV5 @ SV20 ) ) )
= $false )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[874]) ).
thf(884,plain,
! [SV18: $i,SV16: $i,SV6: $i] :
( ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( ~ ( ~ ( ( SV18
!= ( join_on_relstr @ SV6 @ SV16 ) )
| ~ ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
| ~ ! [SY95: $i] :
( ~ ( element @ SY95 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY95 )
| ( related @ SV6 @ SV18 @ SY95 ) ) ) )
| ~ ( ~ ~ ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
| ~ ! [SY96: $i] :
( ~ ( element @ SY96 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY96 )
| ( related @ SV6 @ SV18 @ SY96 ) ) )
| ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) ) ) ) )
= $true )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[875]) ).
thf(885,plain,
! [SV19: $i,SV17: $i,SV8: $i] :
( ( ( ~ ( ~ ( relstr_set_smaller @ SV8 @ SV17 @ SV19 )
| ! [SY97: $i] :
( ~ ( element @ SY97 @ ( the_carrier @ SV8 ) )
| ~ ( in @ SY97 @ SV17 )
| ( related @ SV8 @ SY97 @ SV19 ) ) ) )
= $false )
| ( ( element @ SV19 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( rel_str @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[876]) ).
thf(886,plain,
! [SV19: $i,SV17: $i,SV8: $i] :
( ( ( ~ ( ~ ! [SY98: $i] :
( ~ ( element @ SY98 @ ( the_carrier @ SV8 ) )
| ~ ( in @ SY98 @ SV17 )
| ( related @ SV8 @ SY98 @ SV19 ) )
| ( relstr_set_smaller @ SV8 @ SV17 @ SV19 ) ) )
= $false )
| ( ( element @ SV19 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( rel_str @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[876]) ).
thf(887,plain,
! [SV9: $i,SV21: $i] :
( ( ( ~ ( element @ SV21 @ ( the_carrier @ SV9 ) ) )
= $true )
| ( ( ! [SY103: $i] :
( ~ ( element @ SY103 @ ( the_carrier @ SV9 ) )
| ~ ~ ( ~ ( related @ SV9 @ SV21 @ SY103 )
| ~ ( related @ SV9 @ SY103 @ SV21 ) )
| ( SV21 = SY103 ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV9 )
= $false )
| ( ( rel_str @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[877]) ).
thf(888,plain,
( ( ( ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
| ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[878]) ).
thf(889,plain,
( ( ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY93: $i] :
( ~ ( element @ SY93 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY93 )
| ( related @ sK1_A @ sK4_SX0 @ SY93 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
| ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[879]) ).
thf(890,plain,
! [SV11: $i,SV22: $i] :
( ( ( ~ ( element @ SV22 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ! [SY104: $i] :
( ~ ( element @ SY104 @ ( the_carrier @ SV11 ) )
| ! [SY105: $i] :
( ~ ( element @ SY105 @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( related @ SV11 @ SV22 @ SY104 )
| ~ ( related @ SV11 @ SY104 @ SY105 ) )
| ( related @ SV11 @ SV22 @ SY105 ) ) ) )
= $true )
| ( ( transitive_relstr @ SV11 )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[880]) ).
thf(891,plain,
! [SV15: $i,SV2: $i] :
( ( ( ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY79 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY79 ) )
| ~ ! [SY80: $i] :
( ~ ( element @ SY80 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY80 )
| ( related @ SV2 @ SY79 @ SY80 ) ) )
| ~ ! [SY81: $i] :
( ~ ( element @ SY81 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY81 )
| ~ ! [SY82: $i] :
( ~ ( element @ SY82 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY82 )
| ( related @ SV2 @ SY81 @ SY82 ) ) )
| ( SY81 = SY79 ) ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[881]) ).
thf(892,plain,
! [SV15: $i,SV2: $i] :
( ( ( ! [SY83: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SY83 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY83 ) )
| ~ ! [SY84: $i] :
( ~ ( element @ SY84 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY84 )
| ( related @ SV2 @ SY83 @ SY84 ) ) )
| ~ ! [SY85: $i] :
( ~ ( element @ SY85 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY85 )
| ~ ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY86 )
| ( related @ SV2 @ SY85 @ SY86 ) ) )
| ( SY85 = SY83 ) ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[882]) ).
thf(893,plain,
! [SV20: $i,SV5: $i] :
( ( ( ~ ( ~ ( ex_sup_of_relstr_set @ SV5 @ SV20 )
| ~ ! [SY99: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY99 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY99 ) )
| ~ ! [SY100: $i] :
( ~ ( element @ SY100 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY100 )
| ( related @ SV5 @ SY99 @ SY100 ) ) ) ) )
= $false )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[883]) ).
thf(894,plain,
! [SV20: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ! [SY101: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY101 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( element @ SY102 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY102 )
| ( related @ SV5 @ SY101 @ SY102 ) ) )
| ( ex_sup_of_relstr_set @ SV5 @ SV20 ) ) )
= $false )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[883]) ).
thf(895,plain,
! [SV16: $i,SV6: $i,SV18: $i] :
( ( ( ~ ( ( SV18
!= ( join_on_relstr @ SV6 @ SV16 ) )
| ~ ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
| ~ ! [SY95: $i] :
( ~ ( element @ SY95 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY95 )
| ( related @ SV6 @ SV18 @ SY95 ) ) ) )
| ~ ( ~ ~ ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
| ~ ! [SY96: $i] :
( ~ ( element @ SY96 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY96 )
| ( related @ SV6 @ SV18 @ SY96 ) ) )
| ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[884]) ).
thf(896,plain,
! [SV19: $i,SV17: $i,SV8: $i] :
( ( ( ~ ( relstr_set_smaller @ SV8 @ SV17 @ SV19 )
| ! [SY97: $i] :
( ~ ( element @ SY97 @ ( the_carrier @ SV8 ) )
| ~ ( in @ SY97 @ SV17 )
| ( related @ SV8 @ SY97 @ SV19 ) ) )
= $true )
| ( ( element @ SV19 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( rel_str @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[885]) ).
thf(897,plain,
! [SV19: $i,SV17: $i,SV8: $i] :
( ( ( ~ ! [SY98: $i] :
( ~ ( element @ SY98 @ ( the_carrier @ SV8 ) )
| ~ ( in @ SY98 @ SV17 )
| ( related @ SV8 @ SY98 @ SV19 ) )
| ( relstr_set_smaller @ SV8 @ SV17 @ SV19 ) )
= $true )
| ( ( element @ SV19 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( rel_str @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[886]) ).
thf(898,plain,
! [SV9: $i,SV21: $i] :
( ( ( element @ SV21 @ ( the_carrier @ SV9 ) )
= $false )
| ( ( ! [SY103: $i] :
( ~ ( element @ SY103 @ ( the_carrier @ SV9 ) )
| ~ ~ ( ~ ( related @ SV9 @ SV21 @ SY103 )
| ~ ( related @ SV9 @ SY103 @ SV21 ) )
| ( SV21 = SY103 ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV9 )
= $false )
| ( ( rel_str @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[887]) ).
thf(899,plain,
( ( ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
| ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[888]) ).
thf(900,plain,
( ( ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 ) )
= $true )
| ( ( ~ ! [SY93: $i] :
( ~ ( element @ SY93 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY93 )
| ( related @ sK1_A @ sK4_SX0 @ SY93 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
| ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[889]) ).
thf(901,plain,
! [SV11: $i,SV22: $i] :
( ( ( element @ SV22 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( ! [SY104: $i] :
( ~ ( element @ SY104 @ ( the_carrier @ SV11 ) )
| ! [SY105: $i] :
( ~ ( element @ SY105 @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( related @ SV11 @ SV22 @ SY104 )
| ~ ( related @ SV11 @ SY104 @ SY105 ) )
| ( related @ SV11 @ SV22 @ SY105 ) ) ) )
= $true )
| ( ( transitive_relstr @ SV11 )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[890]) ).
thf(902,plain,
! [SV2: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK7_SY79 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK7_SY79 @ SV15 @ SV2 ) ) )
| ~ ! [SY106: $i] :
( ~ ( element @ SY106 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY106 )
| ( related @ SV2 @ ( sK7_SY79 @ SV15 @ SV2 ) @ SY106 ) ) )
| ~ ! [SY107: $i] :
( ~ ( element @ SY107 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY107 )
| ~ ! [SY82: $i] :
( ~ ( element @ SY82 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY82 )
| ( related @ SV2 @ SY107 @ SY82 ) ) )
| ( SY107
= ( sK7_SY79 @ SV15 @ SV2 ) ) ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[891]) ).
thf(903,plain,
! [SV15: $i,SV2: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SV23 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV23 ) )
| ~ ! [SY109: $i] :
( ~ ( element @ SY109 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY109 )
| ( related @ SV2 @ SV23 @ SY109 ) ) )
| ~ ! [SY110: $i] :
( ~ ( element @ SY110 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY110 )
| ~ ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY86 )
| ( related @ SV2 @ SY110 @ SY86 ) ) )
| ( SY110 = SV23 ) ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(904,plain,
! [SV20: $i,SV5: $i] :
( ( ( ~ ( ex_sup_of_relstr_set @ SV5 @ SV20 )
| ~ ! [SY99: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY99 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY99 ) )
| ~ ! [SY100: $i] :
( ~ ( element @ SY100 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY100 )
| ( related @ SV5 @ SY99 @ SY100 ) ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[893]) ).
thf(905,plain,
! [SV20: $i,SV5: $i] :
( ( ( ~ ~ ! [SY101: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY101 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( element @ SY102 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY102 )
| ( related @ SV5 @ SY101 @ SY102 ) ) )
| ( ex_sup_of_relstr_set @ SV5 @ SV20 ) )
= $true )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[894]) ).
thf(906,plain,
! [SV16: $i,SV6: $i,SV18: $i] :
( ( ( ~ ( ( SV18
!= ( join_on_relstr @ SV6 @ SV16 ) )
| ~ ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
| ~ ! [SY95: $i] :
( ~ ( element @ SY95 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY95 )
| ( related @ SV6 @ SV18 @ SY95 ) ) ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[895]) ).
thf(907,plain,
! [SV18: $i,SV16: $i,SV6: $i] :
( ( ( ~ ( ~ ~ ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
| ~ ! [SY96: $i] :
( ~ ( element @ SY96 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY96 )
| ( related @ SV6 @ SV18 @ SY96 ) ) )
| ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[895]) ).
thf(908,plain,
! [SV19: $i,SV17: $i,SV8: $i] :
( ( ( ~ ( relstr_set_smaller @ SV8 @ SV17 @ SV19 ) )
= $true )
| ( ( ! [SY97: $i] :
( ~ ( element @ SY97 @ ( the_carrier @ SV8 ) )
| ~ ( in @ SY97 @ SV17 )
| ( related @ SV8 @ SY97 @ SV19 ) ) )
= $true )
| ( ( element @ SV19 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( rel_str @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[896]) ).
thf(909,plain,
! [SV19: $i,SV17: $i,SV8: $i] :
( ( ( ~ ! [SY98: $i] :
( ~ ( element @ SY98 @ ( the_carrier @ SV8 ) )
| ~ ( in @ SY98 @ SV17 )
| ( related @ SV8 @ SY98 @ SV19 ) ) )
= $true )
| ( ( relstr_set_smaller @ SV8 @ SV17 @ SV19 )
= $true )
| ( ( element @ SV19 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( rel_str @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[897]) ).
thf(910,plain,
! [SV21: $i,SV9: $i,SV24: $i] :
( ( ( ~ ( element @ SV24 @ ( the_carrier @ SV9 ) )
| ~ ~ ( ~ ( related @ SV9 @ SV21 @ SV24 )
| ~ ( related @ SV9 @ SV24 @ SV21 ) )
| ( SV21 = SV24 ) )
= $true )
| ( ( element @ SV21 @ ( the_carrier @ SV9 ) )
= $false )
| ( ( antisymmetric_relstr @ SV9 )
= $false )
| ( ( rel_str @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(911,plain,
( ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
| ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[899]) ).
thf(912,plain,
( ( ( ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
| ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[899]) ).
thf(913,plain,
( ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( ~ ! [SY93: $i] :
( ~ ( element @ SY93 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY93 )
| ( related @ sK1_A @ sK4_SX0 @ SY93 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
| ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[900]) ).
thf(914,plain,
! [SV22: $i,SV11: $i,SV25: $i] :
( ( ( ~ ( element @ SV25 @ ( the_carrier @ SV11 ) )
| ! [SY112: $i] :
( ~ ( element @ SY112 @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( related @ SV11 @ SV22 @ SV25 )
| ~ ( related @ SV11 @ SV25 @ SY112 ) )
| ( related @ SV11 @ SV22 @ SY112 ) ) )
= $true )
| ( ( element @ SV22 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( transitive_relstr @ SV11 )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(915,plain,
! [SV2: $i,SV15: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK7_SY79 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK7_SY79 @ SV15 @ SV2 ) ) )
| ~ ! [SY106: $i] :
( ~ ( element @ SY106 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY106 )
| ( related @ SV2 @ ( sK7_SY79 @ SV15 @ SV2 ) @ SY106 ) ) )
| ~ ! [SY107: $i] :
( ~ ( element @ SY107 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY107 )
| ~ ! [SY82: $i] :
( ~ ( element @ SY82 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY82 )
| ( related @ SV2 @ SY107 @ SY82 ) ) )
| ( SY107
= ( sK7_SY79 @ SV15 @ SV2 ) ) ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[902]) ).
thf(916,plain,
! [SV15: $i,SV2: $i,SV23: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ SV23 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV23 ) )
| ~ ! [SY109: $i] :
( ~ ( element @ SY109 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY109 )
| ( related @ SV2 @ SV23 @ SY109 ) ) )
| ~ ! [SY110: $i] :
( ~ ( element @ SY110 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY110 )
| ~ ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY86 )
| ( related @ SV2 @ SY110 @ SY86 ) ) )
| ( SY110 = SV23 ) ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[903]) ).
thf(917,plain,
! [SV20: $i,SV5: $i] :
( ( ( ~ ( ex_sup_of_relstr_set @ SV5 @ SV20 ) )
= $true )
| ( ( ~ ! [SY99: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY99 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY99 ) )
| ~ ! [SY100: $i] :
( ~ ( element @ SY100 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY100 )
| ( related @ SV5 @ SY99 @ SY100 ) ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[904]) ).
thf(918,plain,
! [SV20: $i,SV5: $i] :
( ( ( ~ ~ ! [SY101: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY101 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( element @ SY102 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY102 )
| ( related @ SV5 @ SY101 @ SY102 ) ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $true )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[905]) ).
thf(919,plain,
! [SV16: $i,SV6: $i,SV18: $i] :
( ( ( ( SV18
!= ( join_on_relstr @ SV6 @ SV16 ) )
| ~ ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
| ~ ! [SY95: $i] :
( ~ ( element @ SY95 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY95 )
| ( related @ SV6 @ SV18 @ SY95 ) ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[906]) ).
thf(920,plain,
! [SV18: $i,SV16: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
| ~ ! [SY96: $i] :
( ~ ( element @ SY96 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY96 )
| ( related @ SV6 @ SV18 @ SY96 ) ) )
| ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[907]) ).
thf(921,plain,
! [SV19: $i,SV17: $i,SV8: $i] :
( ( ( relstr_set_smaller @ SV8 @ SV17 @ SV19 )
= $false )
| ( ( ! [SY97: $i] :
( ~ ( element @ SY97 @ ( the_carrier @ SV8 ) )
| ~ ( in @ SY97 @ SV17 )
| ( related @ SV8 @ SY97 @ SV19 ) ) )
= $true )
| ( ( element @ SV19 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( rel_str @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[908]) ).
thf(922,plain,
! [SV19: $i,SV17: $i,SV8: $i] :
( ( ( ! [SY98: $i] :
( ~ ( element @ SY98 @ ( the_carrier @ SV8 ) )
| ~ ( in @ SY98 @ SV17 )
| ( related @ SV8 @ SY98 @ SV19 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV8 @ SV17 @ SV19 )
= $true )
| ( ( element @ SV19 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( rel_str @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[909]) ).
thf(923,plain,
! [SV21: $i,SV9: $i,SV24: $i] :
( ( ( ~ ( element @ SV24 @ ( the_carrier @ SV9 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( related @ SV9 @ SV21 @ SV24 )
| ~ ( related @ SV9 @ SV24 @ SV21 ) )
| ( SV21 = SV24 ) )
= $true )
| ( ( element @ SV21 @ ( the_carrier @ SV9 ) )
= $false )
| ( ( antisymmetric_relstr @ SV9 )
= $false )
| ( ( rel_str @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[910]) ).
thf(924,plain,
( ( ( sK4_SX0
= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
| ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[911]) ).
thf(925,plain,
( ( ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
| ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[912]) ).
thf(926,plain,
( ( ( ! [SY93: $i] :
( ~ ( element @ SY93 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY93 )
| ( related @ sK1_A @ sK4_SX0 @ SY93 ) ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
| ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[913]) ).
thf(927,plain,
! [SV22: $i,SV11: $i,SV25: $i] :
( ( ( ~ ( element @ SV25 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ! [SY112: $i] :
( ~ ( element @ SY112 @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( related @ SV11 @ SV22 @ SV25 )
| ~ ( related @ SV11 @ SV25 @ SY112 ) )
| ( related @ SV11 @ SV22 @ SY112 ) ) )
= $true )
| ( ( element @ SV22 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( transitive_relstr @ SV11 )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[914]) ).
thf(928,plain,
! [SV2: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK7_SY79 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK7_SY79 @ SV15 @ SV2 ) ) )
| ~ ! [SY106: $i] :
( ~ ( element @ SY106 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY106 )
| ( related @ SV2 @ ( sK7_SY79 @ SV15 @ SV2 ) @ SY106 ) ) )
| ~ ! [SY107: $i] :
( ~ ( element @ SY107 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY107 )
| ~ ! [SY82: $i] :
( ~ ( element @ SY82 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY82 )
| ( related @ SV2 @ SY107 @ SY82 ) ) )
| ( SY107
= ( sK7_SY79 @ SV15 @ SV2 ) ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[915]) ).
thf(929,plain,
! [SV15: $i,SV2: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ SV23 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV23 ) )
| ~ ! [SY109: $i] :
( ~ ( element @ SY109 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY109 )
| ( related @ SV2 @ SV23 @ SY109 ) ) )
| ~ ! [SY110: $i] :
( ~ ( element @ SY110 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY110 )
| ~ ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY86 )
| ( related @ SV2 @ SY110 @ SY86 ) ) )
| ( SY110 = SV23 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[916]) ).
thf(930,plain,
! [SV20: $i,SV5: $i] :
( ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $false )
| ( ( ~ ! [SY99: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY99 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY99 ) )
| ~ ! [SY100: $i] :
( ~ ( element @ SY100 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY100 )
| ( related @ SV5 @ SY99 @ SY100 ) ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[917]) ).
thf(931,plain,
! [SV20: $i,SV5: $i] :
( ( ( ~ ! [SY101: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY101 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( element @ SY102 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY102 )
| ( related @ SV5 @ SY101 @ SY102 ) ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $true )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[918]) ).
thf(932,plain,
! [SV16: $i,SV6: $i,SV18: $i] :
( ( ( SV18
!= ( join_on_relstr @ SV6 @ SV16 ) )
= $true )
| ( ( ~ ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
| ~ ! [SY95: $i] :
( ~ ( element @ SY95 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY95 )
| ( related @ SV6 @ SV18 @ SY95 ) ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[919]) ).
thf(933,plain,
! [SV18: $i,SV16: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
| ~ ! [SY96: $i] :
( ~ ( element @ SY96 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY96 )
| ( related @ SV6 @ SV18 @ SY96 ) ) ) )
= $true )
| ( ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[920]) ).
thf(934,plain,
! [SV19: $i,SV17: $i,SV8: $i,SV26: $i] :
( ( ( ~ ( element @ SV26 @ ( the_carrier @ SV8 ) )
| ~ ( in @ SV26 @ SV17 )
| ( related @ SV8 @ SV26 @ SV19 ) )
= $true )
| ( ( relstr_set_smaller @ SV8 @ SV17 @ SV19 )
= $false )
| ( ( element @ SV19 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( rel_str @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(935,plain,
! [SV8: $i,SV17: $i,SV19: $i] :
( ( ( ~ ( element @ ( sK8_SY98 @ SV19 @ SV17 @ SV8 ) @ ( the_carrier @ SV8 ) )
| ~ ( in @ ( sK8_SY98 @ SV19 @ SV17 @ SV8 ) @ SV17 )
| ( related @ SV8 @ ( sK8_SY98 @ SV19 @ SV17 @ SV8 ) @ SV19 ) )
= $false )
| ( ( relstr_set_smaller @ SV8 @ SV17 @ SV19 )
= $true )
| ( ( element @ SV19 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( rel_str @ SV8 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[922]) ).
thf(936,plain,
! [SV21: $i,SV9: $i,SV24: $i] :
( ( ( element @ SV24 @ ( the_carrier @ SV9 ) )
= $false )
| ( ( ~ ~ ( ~ ( related @ SV9 @ SV21 @ SV24 )
| ~ ( related @ SV9 @ SV24 @ SV21 ) )
| ( SV21 = SV24 ) )
= $true )
| ( ( element @ SV21 @ ( the_carrier @ SV9 ) )
= $false )
| ( ( antisymmetric_relstr @ SV9 )
= $false )
| ( ( rel_str @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[923]) ).
thf(937,plain,
( ( ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
| ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) )
= $false )
| ( ( sK4_SX0
= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[924]) ).
thf(938,plain,
( ( ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
| ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[925]) ).
thf(939,plain,
( ( ( ~ ( element @ sK9_SY93 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK9_SY93 )
| ( related @ sK1_A @ sK4_SX0 @ sK9_SY93 ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
| ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[926]) ).
thf(940,plain,
! [SV22: $i,SV11: $i,SV25: $i] :
( ( ( element @ SV25 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( ! [SY112: $i] :
( ~ ( element @ SY112 @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( related @ SV11 @ SV22 @ SV25 )
| ~ ( related @ SV11 @ SV25 @ SY112 ) )
| ( related @ SV11 @ SV22 @ SY112 ) ) )
= $true )
| ( ( element @ SV22 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( transitive_relstr @ SV11 )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[927]) ).
thf(941,plain,
! [SV2: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK7_SY79 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK7_SY79 @ SV15 @ SV2 ) ) )
| ~ ! [SY106: $i] :
( ~ ( element @ SY106 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY106 )
| ( related @ SV2 @ ( sK7_SY79 @ SV15 @ SV2 ) @ SY106 ) ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[928]) ).
thf(942,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ! [SY107: $i] :
( ~ ( element @ SY107 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY107 )
| ~ ! [SY82: $i] :
( ~ ( element @ SY82 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY82 )
| ( related @ SV2 @ SY107 @ SY82 ) ) )
| ( SY107
= ( sK7_SY79 @ SV15 @ SV2 ) ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[928]) ).
thf(943,plain,
! [SV15: $i,SV2: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ SV23 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV23 ) )
| ~ ! [SY109: $i] :
( ~ ( element @ SY109 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY109 )
| ( related @ SV2 @ SV23 @ SY109 ) ) ) )
= $true )
| ( ( ~ ! [SY110: $i] :
( ~ ( element @ SY110 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY110 )
| ~ ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY86 )
| ( related @ SV2 @ SY110 @ SY86 ) ) )
| ( SY110 = SV23 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[929]) ).
thf(944,plain,
! [SV20: $i,SV5: $i] :
( ( ( ! [SY99: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY99 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY99 ) )
| ~ ! [SY100: $i] :
( ~ ( element @ SY100 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY100 )
| ( related @ SV5 @ SY99 @ SY100 ) ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $false )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[930]) ).
thf(945,plain,
! [SV20: $i,SV5: $i] :
( ( ( ! [SY101: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY101 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY101 ) )
| ~ ! [SY102: $i] :
( ~ ( element @ SY102 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY102 )
| ( related @ SV5 @ SY101 @ SY102 ) ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $true )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[931]) ).
thf(946,plain,
! [SV16: $i,SV6: $i,SV18: $i] :
( ( ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) )
= $false )
| ( ( ~ ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
| ~ ! [SY95: $i] :
( ~ ( element @ SY95 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY95 )
| ( related @ SV6 @ SV18 @ SY95 ) ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[932]) ).
thf(947,plain,
! [SV18: $i,SV16: $i,SV6: $i] :
( ( ( ~ ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
| ~ ! [SY96: $i] :
( ~ ( element @ SY96 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY96 )
| ( related @ SV6 @ SV18 @ SY96 ) ) ) )
= $false )
| ( ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[933]) ).
thf(948,plain,
! [SV19: $i,SV17: $i,SV8: $i,SV26: $i] :
( ( ( ~ ( element @ SV26 @ ( the_carrier @ SV8 ) ) )
= $true )
| ( ( ~ ( in @ SV26 @ SV17 )
| ( related @ SV8 @ SV26 @ SV19 ) )
= $true )
| ( ( relstr_set_smaller @ SV8 @ SV17 @ SV19 )
= $false )
| ( ( element @ SV19 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( rel_str @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[934]) ).
thf(949,plain,
! [SV8: $i,SV17: $i,SV19: $i] :
( ( ( ~ ( element @ ( sK8_SY98 @ SV19 @ SV17 @ SV8 ) @ ( the_carrier @ SV8 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV8 @ SV17 @ SV19 )
= $true )
| ( ( element @ SV19 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( rel_str @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[935]) ).
thf(950,plain,
! [SV8: $i,SV17: $i,SV19: $i] :
( ( ( ~ ( in @ ( sK8_SY98 @ SV19 @ SV17 @ SV8 ) @ SV17 )
| ( related @ SV8 @ ( sK8_SY98 @ SV19 @ SV17 @ SV8 ) @ SV19 ) )
= $false )
| ( ( relstr_set_smaller @ SV8 @ SV17 @ SV19 )
= $true )
| ( ( element @ SV19 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( rel_str @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[935]) ).
thf(951,plain,
! [SV24: $i,SV21: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( related @ SV9 @ SV21 @ SV24 )
| ~ ( related @ SV9 @ SV24 @ SV21 ) ) )
= $true )
| ( ( SV21 = SV24 )
= $true )
| ( ( element @ SV24 @ ( the_carrier @ SV9 ) )
= $false )
| ( ( element @ SV21 @ ( the_carrier @ SV9 ) )
= $false )
| ( ( antisymmetric_relstr @ SV9 )
= $false )
| ( ( rel_str @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[936]) ).
thf(952,plain,
( ( ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) ) )
= $false )
| ( ( sK4_SX0
= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[937]) ).
thf(953,plain,
( ( ( ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) )
= $false )
| ( ( sK4_SX0
= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[937]) ).
thf(954,plain,
( ( ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[938]) ).
thf(955,plain,
( ( ( ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[938]) ).
thf(956,plain,
( ( ( ~ ( element @ sK9_SY93 @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
| ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[939]) ).
thf(957,plain,
( ( ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK9_SY93 )
| ( related @ sK1_A @ sK4_SX0 @ sK9_SY93 ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
| ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[939]) ).
thf(958,plain,
! [SV25: $i,SV22: $i,SV11: $i,SV27: $i] :
( ( ( ~ ( element @ SV27 @ ( the_carrier @ SV11 ) )
| ~ ~ ( ~ ( related @ SV11 @ SV22 @ SV25 )
| ~ ( related @ SV11 @ SV25 @ SV27 ) )
| ( related @ SV11 @ SV22 @ SV27 ) )
= $true )
| ( ( element @ SV25 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( transitive_relstr @ SV11 )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(959,plain,
! [SV2: $i,SV15: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ ( sK7_SY79 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK7_SY79 @ SV15 @ SV2 ) ) )
| ~ ! [SY106: $i] :
( ~ ( element @ SY106 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY106 )
| ( related @ SV2 @ ( sK7_SY79 @ SV15 @ SV2 ) @ SY106 ) ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[941]) ).
thf(960,plain,
! [SV15: $i,SV2: $i] :
( ( ( ! [SY107: $i] :
( ~ ( element @ SY107 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY107 )
| ~ ! [SY82: $i] :
( ~ ( element @ SY82 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY82 )
| ( related @ SV2 @ SY107 @ SY82 ) ) )
| ( SY107
= ( sK7_SY79 @ SV15 @ SV2 ) ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[942]) ).
thf(961,plain,
! [SV15: $i,SV2: $i,SV23: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ SV23 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV23 ) )
| ~ ! [SY109: $i] :
( ~ ( element @ SY109 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY109 )
| ( related @ SV2 @ SV23 @ SY109 ) ) ) )
= $false )
| ( ( ~ ! [SY110: $i] :
( ~ ( element @ SY110 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY110 )
| ~ ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY86 )
| ( related @ SV2 @ SY110 @ SY86 ) ) )
| ( SY110 = SV23 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[943]) ).
thf(962,plain,
! [SV5: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK10_SY99 @ SV20 @ SV5 ) @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ ( sK10_SY99 @ SV20 @ SV5 ) ) )
| ~ ! [SY113: $i] :
( ~ ( element @ SY113 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY113 )
| ( related @ SV5 @ ( sK10_SY99 @ SV20 @ SV5 ) @ SY113 ) ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $false )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[944]) ).
thf(963,plain,
! [SV20: $i,SV5: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ SV28 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SV28 ) )
| ~ ! [SY114: $i] :
( ~ ( element @ SY114 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY114 )
| ( related @ SV5 @ SV28 @ SY114 ) ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $true )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(964,plain,
! [SV18: $i,SV16: $i,SV6: $i] :
( ( ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
| ~ ! [SY95: $i] :
( ~ ( element @ SY95 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY95 )
| ( related @ SV6 @ SV18 @ SY95 ) ) )
= $false )
| ( ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[946]) ).
thf(965,plain,
! [SV18: $i,SV16: $i,SV6: $i] :
( ( ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
| ~ ! [SY96: $i] :
( ~ ( element @ SY96 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY96 )
| ( related @ SV6 @ SV18 @ SY96 ) ) )
= $true )
| ( ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[947]) ).
thf(966,plain,
! [SV19: $i,SV17: $i,SV8: $i,SV26: $i] :
( ( ( element @ SV26 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( ~ ( in @ SV26 @ SV17 )
| ( related @ SV8 @ SV26 @ SV19 ) )
= $true )
| ( ( relstr_set_smaller @ SV8 @ SV17 @ SV19 )
= $false )
| ( ( element @ SV19 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( rel_str @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[948]) ).
thf(967,plain,
! [SV8: $i,SV17: $i,SV19: $i] :
( ( ( element @ ( sK8_SY98 @ SV19 @ SV17 @ SV8 ) @ ( the_carrier @ SV8 ) )
= $true )
| ( ( relstr_set_smaller @ SV8 @ SV17 @ SV19 )
= $true )
| ( ( element @ SV19 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( rel_str @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[949]) ).
thf(968,plain,
! [SV8: $i,SV17: $i,SV19: $i] :
( ( ( ~ ( in @ ( sK8_SY98 @ SV19 @ SV17 @ SV8 ) @ SV17 ) )
= $false )
| ( ( relstr_set_smaller @ SV8 @ SV17 @ SV19 )
= $true )
| ( ( element @ SV19 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( rel_str @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[950]) ).
thf(969,plain,
! [SV17: $i,SV19: $i,SV8: $i] :
( ( ( related @ SV8 @ ( sK8_SY98 @ SV19 @ SV17 @ SV8 ) @ SV19 )
= $false )
| ( ( relstr_set_smaller @ SV8 @ SV17 @ SV19 )
= $true )
| ( ( element @ SV19 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( rel_str @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[950]) ).
thf(970,plain,
! [SV24: $i,SV21: $i,SV9: $i] :
( ( ( ~ ( ~ ( related @ SV9 @ SV21 @ SV24 )
| ~ ( related @ SV9 @ SV24 @ SV21 ) ) )
= $false )
| ( ( SV21 = SV24 )
= $true )
| ( ( element @ SV24 @ ( the_carrier @ SV9 ) )
= $false )
| ( ( element @ SV21 @ ( the_carrier @ SV9 ) )
= $false )
| ( ( antisymmetric_relstr @ SV9 )
= $false )
| ( ( rel_str @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[951]) ).
thf(971,plain,
( ( ( ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) ) )
= $true )
| ( ( sK4_SX0
= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[952]) ).
thf(972,plain,
( ( ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) )
= $true )
| ( ( sK4_SX0
= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[953]) ).
thf(973,plain,
( ( ( ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[954]) ).
thf(974,plain,
( ( ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[955]) ).
thf(975,plain,
( ( ( element @ sK9_SY93 @ ( the_carrier @ sK1_A ) )
= $true )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
| ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[956]) ).
thf(976,plain,
( ( ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK9_SY93 ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
| ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[957]) ).
thf(977,plain,
( ( ( related @ sK1_A @ sK4_SX0 @ sK9_SY93 )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
| ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[957]) ).
thf(978,plain,
! [SV25: $i,SV22: $i,SV11: $i,SV27: $i] :
( ( ( ~ ( element @ SV27 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( related @ SV11 @ SV22 @ SV25 )
| ~ ( related @ SV11 @ SV25 @ SV27 ) )
| ( related @ SV11 @ SV22 @ SV27 ) )
= $true )
| ( ( element @ SV25 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( transitive_relstr @ SV11 )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[958]) ).
thf(979,plain,
! [SV2: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK7_SY79 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK7_SY79 @ SV15 @ SV2 ) ) )
| ~ ! [SY106: $i] :
( ~ ( element @ SY106 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY106 )
| ( related @ SV2 @ ( sK7_SY79 @ SV15 @ SV2 ) @ SY106 ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[959]) ).
thf(980,plain,
! [SV15: $i,SV2: $i,SV29: $i] :
( ( ( ~ ( element @ SV29 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV29 )
| ~ ! [SY115: $i] :
( ~ ( element @ SY115 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY115 )
| ( related @ SV2 @ SV29 @ SY115 ) ) )
| ( SV29
= ( sK7_SY79 @ SV15 @ SV2 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(981,plain,
! [SV15: $i,SV2: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( element @ SV23 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV23 ) )
| ~ ! [SY109: $i] :
( ~ ( element @ SY109 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY109 )
| ( related @ SV2 @ SV23 @ SY109 ) ) )
= $true )
| ( ( ~ ! [SY110: $i] :
( ~ ( element @ SY110 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY110 )
| ~ ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY86 )
| ( related @ SV2 @ SY110 @ SY86 ) ) )
| ( SY110 = SV23 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[961]) ).
thf(982,plain,
! [SV5: $i,SV20: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ ( sK10_SY99 @ SV20 @ SV5 ) @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ ( sK10_SY99 @ SV20 @ SV5 ) ) )
| ~ ! [SY113: $i] :
( ~ ( element @ SY113 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY113 )
| ( related @ SV5 @ ( sK10_SY99 @ SV20 @ SV5 ) @ SY113 ) ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $false )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[962]) ).
thf(983,plain,
! [SV20: $i,SV5: $i,SV28: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ SV28 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SV28 ) )
| ~ ! [SY114: $i] :
( ~ ( element @ SY114 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY114 )
| ( related @ SV5 @ SV28 @ SY114 ) ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $true )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[963]) ).
thf(984,plain,
! [SV18: $i,SV16: $i,SV6: $i] :
( ( ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ SV18 ) )
= $false )
| ( ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[964]) ).
thf(985,plain,
! [SV18: $i,SV16: $i,SV6: $i] :
( ( ( ~ ! [SY95: $i] :
( ~ ( element @ SY95 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY95 )
| ( related @ SV6 @ SV18 @ SY95 ) ) )
= $false )
| ( ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[964]) ).
thf(986,plain,
! [SV18: $i,SV16: $i,SV6: $i] :
( ( ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ SV18 ) )
= $true )
| ( ( ~ ! [SY96: $i] :
( ~ ( element @ SY96 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY96 )
| ( related @ SV6 @ SV18 @ SY96 ) ) )
= $true )
| ( ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[965]) ).
thf(987,plain,
! [SV19: $i,SV8: $i,SV17: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ SV17 ) )
= $true )
| ( ( related @ SV8 @ SV26 @ SV19 )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( relstr_set_smaller @ SV8 @ SV17 @ SV19 )
= $false )
| ( ( element @ SV19 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( rel_str @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[966]) ).
thf(988,plain,
! [SV8: $i,SV17: $i,SV19: $i] :
( ( ( in @ ( sK8_SY98 @ SV19 @ SV17 @ SV8 ) @ SV17 )
= $true )
| ( ( relstr_set_smaller @ SV8 @ SV17 @ SV19 )
= $true )
| ( ( element @ SV19 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( rel_str @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[968]) ).
thf(989,plain,
! [SV24: $i,SV21: $i,SV9: $i] :
( ( ( ~ ( related @ SV9 @ SV21 @ SV24 )
| ~ ( related @ SV9 @ SV24 @ SV21 ) )
= $true )
| ( ( SV21 = SV24 )
= $true )
| ( ( element @ SV24 @ ( the_carrier @ SV9 ) )
= $false )
| ( ( element @ SV21 @ ( the_carrier @ SV9 ) )
= $false )
| ( ( antisymmetric_relstr @ SV9 )
= $false )
| ( ( rel_str @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[970]) ).
thf(990,plain,
( ( ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
= $false )
| ( ( sK4_SX0
= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[971]) ).
thf(991,plain,
( ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $true )
| ( ( ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) )
= $true )
| ( ( sK4_SX0
= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[972]) ).
thf(992,plain,
( ( ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[973]) ).
thf(993,plain,
( ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $true )
| ( ( ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[974]) ).
thf(994,plain,
( ( ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
| ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( element @ sK9_SY93 @ ( the_carrier @ sK1_A ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[975]) ).
thf(995,plain,
( ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK9_SY93 )
= $true )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
| ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[976]) ).
thf(996,plain,
( ( ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
| ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( related @ sK1_A @ sK4_SX0 @ sK9_SY93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(997,plain,
! [SV25: $i,SV22: $i,SV11: $i,SV27: $i] :
( ( ( element @ SV27 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( ~ ~ ( ~ ( related @ SV11 @ SV22 @ SV25 )
| ~ ( related @ SV11 @ SV25 @ SV27 ) )
| ( related @ SV11 @ SV22 @ SV27 ) )
= $true )
| ( ( element @ SV25 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( transitive_relstr @ SV11 )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[978]) ).
thf(998,plain,
! [SV2: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK7_SY79 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK7_SY79 @ SV15 @ SV2 ) ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[979]) ).
thf(999,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ! [SY106: $i] :
( ~ ( element @ SY106 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY106 )
| ( related @ SV2 @ ( sK7_SY79 @ SV15 @ SV2 ) @ SY106 ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[979]) ).
thf(1000,plain,
! [SV15: $i,SV2: $i,SV29: $i] :
( ( ( ~ ( element @ SV29 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV29 )
| ~ ! [SY115: $i] :
( ~ ( element @ SY115 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY115 )
| ( related @ SV2 @ SV29 @ SY115 ) ) )
| ( SV29
= ( sK7_SY79 @ SV15 @ SV2 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[980]) ).
thf(1001,plain,
! [SV15: $i,SV2: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( element @ SV23 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV23 ) ) )
= $true )
| ( ( ~ ! [SY109: $i] :
( ~ ( element @ SY109 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY109 )
| ( related @ SV2 @ SV23 @ SY109 ) ) )
= $true )
| ( ( ~ ! [SY110: $i] :
( ~ ( element @ SY110 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY110 )
| ~ ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY86 )
| ( related @ SV2 @ SY110 @ SY86 ) ) )
| ( SY110 = SV23 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[981]) ).
thf(1002,plain,
! [SV5: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK10_SY99 @ SV20 @ SV5 ) @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ ( sK10_SY99 @ SV20 @ SV5 ) ) )
| ~ ! [SY113: $i] :
( ~ ( element @ SY113 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY113 )
| ( related @ SV5 @ ( sK10_SY99 @ SV20 @ SV5 ) @ SY113 ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $false )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1003,plain,
! [SV20: $i,SV5: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( element @ SV28 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SV28 ) )
| ~ ! [SY114: $i] :
( ~ ( element @ SY114 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY114 )
| ( related @ SV5 @ SV28 @ SY114 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $true )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[983]) ).
thf(1004,plain,
! [SV18: $i,SV16: $i,SV6: $i] :
( ( ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
= $true )
| ( ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[984]) ).
thf(1005,plain,
! [SV18: $i,SV16: $i,SV6: $i] :
( ( ( ! [SY95: $i] :
( ~ ( element @ SY95 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY95 )
| ( related @ SV6 @ SV18 @ SY95 ) ) )
= $true )
| ( ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[985]) ).
thf(1006,plain,
! [SV18: $i,SV16: $i,SV6: $i] :
( ( ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
= $false )
| ( ( ~ ! [SY96: $i] :
( ~ ( element @ SY96 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY96 )
| ( related @ SV6 @ SV18 @ SY96 ) ) )
= $true )
| ( ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[986]) ).
thf(1007,plain,
! [SV19: $i,SV8: $i,SV17: $i,SV26: $i] :
( ( ( in @ SV26 @ SV17 )
= $false )
| ( ( related @ SV8 @ SV26 @ SV19 )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( relstr_set_smaller @ SV8 @ SV17 @ SV19 )
= $false )
| ( ( element @ SV19 @ ( the_carrier @ SV8 ) )
= $false )
| ( ( rel_str @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[987]) ).
thf(1008,plain,
! [SV24: $i,SV21: $i,SV9: $i] :
( ( ( ~ ( related @ SV9 @ SV21 @ SV24 ) )
= $true )
| ( ( ~ ( related @ SV9 @ SV24 @ SV21 ) )
= $true )
| ( ( SV21 = SV24 )
= $true )
| ( ( element @ SV24 @ ( the_carrier @ SV9 ) )
= $false )
| ( ( element @ SV21 @ ( the_carrier @ SV9 ) )
= $false )
| ( ( antisymmetric_relstr @ SV9 )
= $false )
| ( ( rel_str @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[989]) ).
thf(1009,plain,
( ( ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 ) )
= $false )
| ( ( sK4_SX0
= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[990]) ).
thf(1010,plain,
( ( ( ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
= $false )
| ( ( sK4_SX0
= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[990]) ).
thf(1011,plain,
( ( ( sK4_SX0
= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $false )
| ( ( ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) )
= $true )
| ( ( sK4_SX0
= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[991]) ).
thf(1012,plain,
( ( ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[992]) ).
thf(1013,plain,
( ( ( ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[992]) ).
thf(1014,plain,
( ( ( sK4_SX0
= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $false )
| ( ( ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[993]) ).
thf(1015,plain,
( ( ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( element @ sK9_SY93 @ ( the_carrier @ sK1_A ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[994]) ).
thf(1016,plain,
( ( ( ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( element @ sK9_SY93 @ ( the_carrier @ sK1_A ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[994]) ).
thf(1017,plain,
( ( ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
| ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK9_SY93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[995]) ).
thf(1018,plain,
( ( ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( related @ sK1_A @ sK4_SX0 @ sK9_SY93 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[996]) ).
thf(1019,plain,
( ( ( ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( related @ sK1_A @ sK4_SX0 @ sK9_SY93 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[996]) ).
thf(1020,plain,
! [SV27: $i,SV25: $i,SV22: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( related @ SV11 @ SV22 @ SV25 )
| ~ ( related @ SV11 @ SV25 @ SV27 ) ) )
= $true )
| ( ( related @ SV11 @ SV22 @ SV27 )
= $true )
| ( ( element @ SV27 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( element @ SV25 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( transitive_relstr @ SV11 )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[997]) ).
thf(1021,plain,
! [SV2: $i,SV15: $i] :
( ( ( ~ ( ~ ( element @ ( sK7_SY79 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK7_SY79 @ SV15 @ SV2 ) ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[998]) ).
thf(1022,plain,
! [SV15: $i,SV2: $i] :
( ( ( ! [SY106: $i] :
( ~ ( element @ SY106 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY106 )
| ( related @ SV2 @ ( sK7_SY79 @ SV15 @ SV2 ) @ SY106 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[999]) ).
thf(1023,plain,
! [SV15: $i,SV2: $i,SV29: $i] :
( ( ( element @ SV29 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV29 )
| ~ ! [SY115: $i] :
( ~ ( element @ SY115 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY115 )
| ( related @ SV2 @ SV29 @ SY115 ) ) )
| ( SV29
= ( sK7_SY79 @ SV15 @ SV2 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1000]) ).
thf(1024,plain,
! [SV15: $i,SV2: $i,SV23: $i] :
( ( ( ~ ( ~ ( element @ SV23 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV23 ) ) )
= $false )
| ( ( ~ ! [SY109: $i] :
( ~ ( element @ SY109 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY109 )
| ( related @ SV2 @ SV23 @ SY109 ) ) )
= $true )
| ( ( ~ ! [SY110: $i] :
( ~ ( element @ SY110 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY110 )
| ~ ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY86 )
| ( related @ SV2 @ SY110 @ SY86 ) ) )
| ( SY110 = SV23 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1001]) ).
thf(1025,plain,
! [SV5: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK10_SY99 @ SV20 @ SV5 ) @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ ( sK10_SY99 @ SV20 @ SV5 ) ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $false )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1002]) ).
thf(1026,plain,
! [SV20: $i,SV5: $i] :
( ( ( ~ ! [SY113: $i] :
( ~ ( element @ SY113 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY113 )
| ( related @ SV5 @ ( sK10_SY99 @ SV20 @ SV5 ) @ SY113 ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $false )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1002]) ).
thf(1027,plain,
! [SV20: $i,SV5: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( element @ SV28 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SV28 ) ) )
= $true )
| ( ( ~ ! [SY114: $i] :
( ~ ( element @ SY114 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY114 )
| ( related @ SV5 @ SV28 @ SY114 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $true )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1003]) ).
thf(1028,plain,
! [SV18: $i,SV16: $i,SV6: $i,SV30: $i] :
( ( ( ~ ( element @ SV30 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ SV30 )
| ( related @ SV6 @ SV18 @ SV30 ) )
= $true )
| ( ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1029,plain,
! [SV18: $i,SV16: $i,SV6: $i] :
( ( ( ! [SY96: $i] :
( ~ ( element @ SY96 @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ SY96 )
| ( related @ SV6 @ SV18 @ SY96 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
= $false )
| ( ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1006]) ).
thf(1030,plain,
! [SV24: $i,SV21: $i,SV9: $i] :
( ( ( related @ SV9 @ SV21 @ SV24 )
= $false )
| ( ( ~ ( related @ SV9 @ SV24 @ SV21 ) )
= $true )
| ( ( SV21 = SV24 )
= $true )
| ( ( element @ SV24 @ ( the_carrier @ SV9 ) )
= $false )
| ( ( element @ SV21 @ ( the_carrier @ SV9 ) )
= $false )
| ( ( antisymmetric_relstr @ SV9 )
= $false )
| ( ( rel_str @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1008]) ).
thf(1031,plain,
( ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $true )
| ( ( sK4_SX0
= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1009]) ).
thf(1032,plain,
( ( ( ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
= $true )
| ( ( sK4_SX0
= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1010]) ).
thf(1033,plain,
( ( ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 )
= $false )
| ( ( sK4_SX0
= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $false )
| ( ( sK4_SX0
= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1011]) ).
thf(1034,plain,
( ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $true )
| ( ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1012]) ).
thf(1035,plain,
( ( ( ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1013]) ).
thf(1036,plain,
( ( ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 )
= $false )
| ( ( sK4_SX0
= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1014]) ).
thf(1037,plain,
( ( ( ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) ) )
= $true )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( element @ sK9_SY93 @ ( the_carrier @ sK1_A ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1015]) ).
thf(1038,plain,
( ( ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) )
= $true )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( element @ sK9_SY93 @ ( the_carrier @ sK1_A ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1016]) ).
thf(1039,plain,
( ( ( ~ ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK9_SY93 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1017]) ).
thf(1040,plain,
( ( ( ~ ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK9_SY93 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1017]) ).
thf(1041,plain,
( ( ( ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) ) )
= $true )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( related @ sK1_A @ sK4_SX0 @ sK9_SY93 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1018]) ).
thf(1042,plain,
( ( ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) )
= $true )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( related @ sK1_A @ sK4_SX0 @ sK9_SY93 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1019]) ).
thf(1043,plain,
! [SV27: $i,SV25: $i,SV22: $i,SV11: $i] :
( ( ( ~ ( ~ ( related @ SV11 @ SV22 @ SV25 )
| ~ ( related @ SV11 @ SV25 @ SV27 ) ) )
= $false )
| ( ( related @ SV11 @ SV22 @ SV27 )
= $true )
| ( ( element @ SV27 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( element @ SV25 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( transitive_relstr @ SV11 )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1020]) ).
thf(1044,plain,
! [SV2: $i,SV15: $i] :
( ( ( ~ ( element @ ( sK7_SY79 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK7_SY79 @ SV15 @ SV2 ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1021]) ).
thf(1045,plain,
! [SV15: $i,SV2: $i,SV31: $i] :
( ( ( ~ ( element @ SV31 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV31 )
| ( related @ SV2 @ ( sK7_SY79 @ SV15 @ SV2 ) @ SV31 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1046,plain,
! [SV29: $i,SV15: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV29 )
| ~ ! [SY115: $i] :
( ~ ( element @ SY115 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY115 )
| ( related @ SV2 @ SV29 @ SY115 ) ) ) )
= $true )
| ( ( SV29
= ( sK7_SY79 @ SV15 @ SV2 ) )
= $true )
| ( ( element @ SV29 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1023]) ).
thf(1047,plain,
! [SV15: $i,SV2: $i,SV23: $i] :
( ( ( ~ ( element @ SV23 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV23 ) )
= $true )
| ( ( ~ ! [SY109: $i] :
( ~ ( element @ SY109 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY109 )
| ( related @ SV2 @ SV23 @ SY109 ) ) )
= $true )
| ( ( ~ ! [SY110: $i] :
( ~ ( element @ SY110 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY110 )
| ~ ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY86 )
| ( related @ SV2 @ SY110 @ SY86 ) ) )
| ( SY110 = SV23 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1024]) ).
thf(1048,plain,
! [SV5: $i,SV20: $i] :
( ( ( ~ ( ~ ( element @ ( sK10_SY99 @ SV20 @ SV5 ) @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ ( sK10_SY99 @ SV20 @ SV5 ) ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $false )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1025]) ).
thf(1049,plain,
! [SV20: $i,SV5: $i] :
( ( ( ! [SY113: $i] :
( ~ ( element @ SY113 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY113 )
| ( related @ SV5 @ ( sK10_SY99 @ SV20 @ SV5 ) @ SY113 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $false )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1026]) ).
thf(1050,plain,
! [SV20: $i,SV5: $i,SV28: $i] :
( ( ( ~ ( ~ ( element @ SV28 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SV28 ) ) )
= $false )
| ( ( ~ ! [SY114: $i] :
( ~ ( element @ SY114 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY114 )
| ( related @ SV5 @ SV28 @ SY114 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $true )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1027]) ).
thf(1051,plain,
! [SV18: $i,SV16: $i,SV6: $i,SV30: $i] :
( ( ( ~ ( element @ SV30 @ ( the_carrier @ SV6 ) ) )
= $true )
| ( ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ SV30 )
| ( related @ SV6 @ SV18 @ SV30 ) )
= $true )
| ( ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1028]) ).
thf(1052,plain,
! [SV6: $i,SV16: $i,SV18: $i] :
( ( ( ~ ( element @ ( sK11_SY96 @ SV18 @ SV16 @ SV6 ) @ ( the_carrier @ SV6 ) )
| ~ ( relstr_set_smaller @ SV6 @ SV16 @ ( sK11_SY96 @ SV18 @ SV16 @ SV6 ) )
| ( related @ SV6 @ SV18 @ ( sK11_SY96 @ SV18 @ SV16 @ SV6 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
= $false )
| ( ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1029]) ).
thf(1053,plain,
! [SV21: $i,SV24: $i,SV9: $i] :
( ( ( related @ SV9 @ SV24 @ SV21 )
= $false )
| ( ( related @ SV9 @ SV21 @ SV24 )
= $false )
| ( ( SV21 = SV24 )
= $true )
| ( ( element @ SV24 @ ( the_carrier @ SV9 ) )
= $false )
| ( ( element @ SV21 @ ( the_carrier @ SV9 ) )
= $false )
| ( ( antisymmetric_relstr @ SV9 )
= $false )
| ( ( rel_str @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1030]) ).
thf(1054,plain,
! [SV32: $i] :
( ( ( ~ ( element @ SV32 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SV32 )
| ( related @ sK1_A @ sK4_SX0 @ SV32 ) )
= $true )
| ( ( sK4_SX0
= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1055,plain,
! [SV33: $i] :
( ( ( ~ ( element @ SV33 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SV33 )
| ( related @ sK1_A @ sK4_SX0 @ SV33 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1056,plain,
( ( ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( element @ sK9_SY93 @ ( the_carrier @ sK1_A ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1037]) ).
thf(1057,plain,
( ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $true )
| ( ( ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) )
= $true )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( element @ sK9_SY93 @ ( the_carrier @ sK1_A ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1038]) ).
thf(1058,plain,
( ( ( ~ ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) ) )
= $true )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK9_SY93 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1039]) ).
thf(1059,plain,
( ( ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
| ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) )
= $true )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK9_SY93 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1040]) ).
thf(1060,plain,
( ( ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( related @ sK1_A @ sK4_SX0 @ sK9_SY93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1041]) ).
thf(1061,plain,
( ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $true )
| ( ( ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) )
= $true )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( related @ sK1_A @ sK4_SX0 @ sK9_SY93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1042]) ).
thf(1062,plain,
! [SV27: $i,SV25: $i,SV22: $i,SV11: $i] :
( ( ( ~ ( related @ SV11 @ SV22 @ SV25 )
| ~ ( related @ SV11 @ SV25 @ SV27 ) )
= $true )
| ( ( related @ SV11 @ SV22 @ SV27 )
= $true )
| ( ( element @ SV27 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( element @ SV25 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( transitive_relstr @ SV11 )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1043]) ).
thf(1063,plain,
! [SV2: $i,SV15: $i] :
( ( ( ~ ( element @ ( sK7_SY79 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1044]) ).
thf(1064,plain,
! [SV15: $i,SV2: $i] :
( ( ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK7_SY79 @ SV15 @ SV2 ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1044]) ).
thf(1065,plain,
! [SV15: $i,SV2: $i,SV31: $i] :
( ( ( ~ ( element @ SV31 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV31 )
| ( related @ SV2 @ ( sK7_SY79 @ SV15 @ SV2 ) @ SV31 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1045]) ).
thf(1066,plain,
! [SV29: $i,SV15: $i,SV2: $i] :
( ( ( ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV29 )
| ~ ! [SY115: $i] :
( ~ ( element @ SY115 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY115 )
| ( related @ SV2 @ SV29 @ SY115 ) ) ) )
= $false )
| ( ( SV29
= ( sK7_SY79 @ SV15 @ SV2 ) )
= $true )
| ( ( element @ SV29 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1046]) ).
thf(1067,plain,
! [SV15: $i,SV2: $i,SV23: $i] :
( ( ( ~ ( element @ SV23 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV23 ) )
= $true )
| ( ( ~ ! [SY109: $i] :
( ~ ( element @ SY109 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY109 )
| ( related @ SV2 @ SV23 @ SY109 ) ) )
= $true )
| ( ( ~ ! [SY110: $i] :
( ~ ( element @ SY110 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY110 )
| ~ ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY86 )
| ( related @ SV2 @ SY110 @ SY86 ) ) )
| ( SY110 = SV23 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1047]) ).
thf(1068,plain,
! [SV5: $i,SV20: $i] :
( ( ( ~ ( element @ ( sK10_SY99 @ SV20 @ SV5 ) @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ ( sK10_SY99 @ SV20 @ SV5 ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $false )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1048]) ).
thf(1069,plain,
! [SV20: $i,SV5: $i,SV34: $i] :
( ( ( ~ ( element @ SV34 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SV34 )
| ( related @ SV5 @ ( sK10_SY99 @ SV20 @ SV5 ) @ SV34 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $false )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1070,plain,
! [SV20: $i,SV5: $i,SV28: $i] :
( ( ( ~ ( element @ SV28 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SV28 ) )
= $true )
| ( ( ~ ! [SY114: $i] :
( ~ ( element @ SY114 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY114 )
| ( related @ SV5 @ SV28 @ SY114 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $true )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1050]) ).
thf(1071,plain,
! [SV18: $i,SV16: $i,SV6: $i,SV30: $i] :
( ( ( element @ SV30 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ SV30 )
| ( related @ SV6 @ SV18 @ SV30 ) )
= $true )
| ( ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1051]) ).
thf(1072,plain,
! [SV6: $i,SV16: $i,SV18: $i] :
( ( ( ~ ( element @ ( sK11_SY96 @ SV18 @ SV16 @ SV6 ) @ ( the_carrier @ SV6 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
= $false )
| ( ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1052]) ).
thf(1073,plain,
! [SV18: $i,SV16: $i,SV6: $i] :
( ( ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ ( sK11_SY96 @ SV18 @ SV16 @ SV6 ) )
| ( related @ SV6 @ SV18 @ ( sK11_SY96 @ SV18 @ SV16 @ SV6 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
= $false )
| ( ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1052]) ).
thf(1074,plain,
! [SV32: $i] :
( ( ( ~ ( element @ SV32 @ ( the_carrier @ sK1_A ) ) )
= $true )
| ( ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SV32 )
| ( related @ sK1_A @ sK4_SX0 @ SV32 ) )
= $true )
| ( ( sK4_SX0
= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1054]) ).
thf(1075,plain,
! [SV33: $i] :
( ( ( ~ ( element @ SV33 @ ( the_carrier @ sK1_A ) ) )
= $true )
| ( ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SV33 )
| ( related @ sK1_A @ sK4_SX0 @ SV33 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1055]) ).
thf(1076,plain,
( ( ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( element @ sK9_SY93 @ ( the_carrier @ sK1_A ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1056]) ).
thf(1077,plain,
( ( ( ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( element @ sK9_SY93 @ ( the_carrier @ sK1_A ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1056]) ).
thf(1078,plain,
( ( ( sK4_SX0
= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $false )
| ( ( ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) )
= $true )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( element @ sK9_SY93 @ ( the_carrier @ sK1_A ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1057]) ).
thf(1079,plain,
( ( ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
| ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK9_SY93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1058]) ).
thf(1080,plain,
( ( ( sK4_SX0
!= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $true )
| ( ( ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) )
= $true )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK9_SY93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1059]) ).
thf(1081,plain,
( ( ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( related @ sK1_A @ sK4_SX0 @ sK9_SY93 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1060]) ).
thf(1082,plain,
( ( ( ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( related @ sK1_A @ sK4_SX0 @ sK9_SY93 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1060]) ).
thf(1083,plain,
( ( ( sK4_SX0
= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $false )
| ( ( ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) )
= $true )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( related @ sK1_A @ sK4_SX0 @ sK9_SY93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1061]) ).
thf(1084,plain,
! [SV27: $i,SV25: $i,SV22: $i,SV11: $i] :
( ( ( ~ ( related @ SV11 @ SV22 @ SV25 ) )
= $true )
| ( ( ~ ( related @ SV11 @ SV25 @ SV27 ) )
= $true )
| ( ( related @ SV11 @ SV22 @ SV27 )
= $true )
| ( ( element @ SV27 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( element @ SV25 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( transitive_relstr @ SV11 )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1062]) ).
thf(1085,plain,
! [SV2: $i,SV15: $i] :
( ( ( element @ ( sK7_SY79 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1063]) ).
thf(1086,plain,
! [SV15: $i,SV2: $i] :
( ( ( relstr_set_smaller @ SV2 @ SV15 @ ( sK7_SY79 @ SV15 @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1064]) ).
thf(1087,plain,
! [SV15: $i,SV2: $i,SV31: $i] :
( ( ( element @ SV31 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV31 )
| ( related @ SV2 @ ( sK7_SY79 @ SV15 @ SV2 ) @ SV31 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1065]) ).
thf(1088,plain,
! [SV29: $i,SV15: $i,SV2: $i] :
( ( ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV29 )
| ~ ! [SY115: $i] :
( ~ ( element @ SY115 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY115 )
| ( related @ SV2 @ SV29 @ SY115 ) ) )
= $true )
| ( ( SV29
= ( sK7_SY79 @ SV15 @ SV2 ) )
= $true )
| ( ( element @ SV29 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1066]) ).
thf(1089,plain,
! [SV15: $i,SV2: $i,SV23: $i] :
( ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV23 ) )
= $true )
| ( ( ~ ! [SY109: $i] :
( ~ ( element @ SY109 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY109 )
| ( related @ SV2 @ SV23 @ SY109 ) ) )
= $true )
| ( ( ~ ! [SY110: $i] :
( ~ ( element @ SY110 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY110 )
| ~ ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY86 )
| ( related @ SV2 @ SY110 @ SY86 ) ) )
| ( SY110 = SV23 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1067]) ).
thf(1090,plain,
! [SV5: $i,SV20: $i] :
( ( ( ~ ( element @ ( sK10_SY99 @ SV20 @ SV5 ) @ ( the_carrier @ SV5 ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $false )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1068]) ).
thf(1091,plain,
! [SV20: $i,SV5: $i] :
( ( ( ~ ( relstr_set_smaller @ SV5 @ SV20 @ ( sK10_SY99 @ SV20 @ SV5 ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $false )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1068]) ).
thf(1092,plain,
! [SV20: $i,SV5: $i,SV34: $i] :
( ( ( ~ ( element @ SV34 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ~ ( relstr_set_smaller @ SV5 @ SV20 @ SV34 )
| ( related @ SV5 @ ( sK10_SY99 @ SV20 @ SV5 ) @ SV34 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $false )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1069]) ).
thf(1093,plain,
! [SV20: $i,SV5: $i,SV28: $i] :
( ( ( ~ ( element @ SV28 @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ~ ( relstr_set_smaller @ SV5 @ SV20 @ SV28 ) )
= $true )
| ( ( ~ ! [SY114: $i] :
( ~ ( element @ SY114 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY114 )
| ( related @ SV5 @ SV28 @ SY114 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $true )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1070]) ).
thf(1094,plain,
! [SV18: $i,SV30: $i,SV16: $i,SV6: $i] :
( ( ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ SV30 ) )
= $true )
| ( ( related @ SV6 @ SV18 @ SV30 )
= $true )
| ( ( element @ SV30 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1071]) ).
thf(1095,plain,
! [SV6: $i,SV16: $i,SV18: $i] :
( ( ( element @ ( sK11_SY96 @ SV18 @ SV16 @ SV6 ) @ ( the_carrier @ SV6 ) )
= $true )
| ( ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
= $false )
| ( ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1072]) ).
thf(1096,plain,
! [SV18: $i,SV16: $i,SV6: $i] :
( ( ( ~ ( relstr_set_smaller @ SV6 @ SV16 @ ( sK11_SY96 @ SV18 @ SV16 @ SV6 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
= $false )
| ( ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1073]) ).
thf(1097,plain,
! [SV16: $i,SV18: $i,SV6: $i] :
( ( ( related @ SV6 @ SV18 @ ( sK11_SY96 @ SV18 @ SV16 @ SV6 ) )
= $false )
| ( ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
= $false )
| ( ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1073]) ).
thf(1098,plain,
! [SV32: $i] :
( ( ( element @ SV32 @ ( the_carrier @ sK1_A ) )
= $false )
| ( ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SV32 )
| ( related @ sK1_A @ sK4_SX0 @ SV32 ) )
= $true )
| ( ( sK4_SX0
= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1074]) ).
thf(1099,plain,
! [SV33: $i] :
( ( ( element @ SV33 @ ( the_carrier @ sK1_A ) )
= $false )
| ( ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SV33 )
| ( related @ sK1_A @ sK4_SX0 @ SV33 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1075]) ).
thf(1100,plain,
( ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $true )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( element @ sK9_SY93 @ ( the_carrier @ sK1_A ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1076]) ).
thf(1101,plain,
( ( ( ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
= $true )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( element @ sK9_SY93 @ ( the_carrier @ sK1_A ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1077]) ).
thf(1102,plain,
( ( ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 )
= $false )
| ( ( sK4_SX0
= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( element @ sK9_SY93 @ ( the_carrier @ sK1_A ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1078]) ).
thf(1103,plain,
( ( ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK9_SY93 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1079]) ).
thf(1104,plain,
( ( ( ~ ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK9_SY93 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1079]) ).
thf(1105,plain,
( ( ( sK4_SX0
= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $false )
| ( ( ~ ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 ) )
= $true )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK9_SY93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1080]) ).
thf(1106,plain,
( ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $true )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( related @ sK1_A @ sK4_SX0 @ sK9_SY93 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1081]) ).
thf(1107,plain,
( ( ( ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
= $true )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( related @ sK1_A @ sK4_SX0 @ sK9_SY93 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1082]) ).
thf(1108,plain,
( ( ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 )
= $false )
| ( ( sK4_SX0
= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( related @ sK1_A @ sK4_SX0 @ sK9_SY93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1083]) ).
thf(1109,plain,
! [SV27: $i,SV25: $i,SV22: $i,SV11: $i] :
( ( ( related @ SV11 @ SV22 @ SV25 )
= $false )
| ( ( ~ ( related @ SV11 @ SV25 @ SV27 ) )
= $true )
| ( ( related @ SV11 @ SV22 @ SV27 )
= $true )
| ( ( element @ SV27 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( element @ SV25 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( transitive_relstr @ SV11 )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1084]) ).
thf(1110,plain,
! [SV31: $i,SV15: $i,SV2: $i] :
( ( ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV31 ) )
= $true )
| ( ( related @ SV2 @ ( sK7_SY79 @ SV15 @ SV2 ) @ SV31 )
= $true )
| ( ( element @ SV31 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1087]) ).
thf(1111,plain,
! [SV29: $i,SV15: $i,SV2: $i] :
( ( ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV29 ) )
= $true )
| ( ( ~ ! [SY115: $i] :
( ~ ( element @ SY115 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY115 )
| ( related @ SV2 @ SV29 @ SY115 ) ) )
= $true )
| ( ( SV29
= ( sK7_SY79 @ SV15 @ SV2 ) )
= $true )
| ( ( element @ SV29 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1088]) ).
thf(1112,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( ~ ! [SY109: $i] :
( ~ ( element @ SY109 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY109 )
| ( related @ SV2 @ SV23 @ SY109 ) ) )
= $true )
| ( ( ~ ! [SY110: $i] :
( ~ ( element @ SY110 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY110 )
| ~ ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY86 )
| ( related @ SV2 @ SY110 @ SY86 ) ) )
| ( SY110 = SV23 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1089]) ).
thf(1113,plain,
! [SV5: $i,SV20: $i] :
( ( ( element @ ( sK10_SY99 @ SV20 @ SV5 ) @ ( the_carrier @ SV5 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $false )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1090]) ).
thf(1114,plain,
! [SV20: $i,SV5: $i] :
( ( ( relstr_set_smaller @ SV5 @ SV20 @ ( sK10_SY99 @ SV20 @ SV5 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $false )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1091]) ).
thf(1115,plain,
! [SV20: $i,SV5: $i,SV34: $i] :
( ( ( element @ SV34 @ ( the_carrier @ SV5 ) )
= $false )
| ( ( ~ ( relstr_set_smaller @ SV5 @ SV20 @ SV34 )
| ( related @ SV5 @ ( sK10_SY99 @ SV20 @ SV5 ) @ SV34 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $false )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1092]) ).
thf(1116,plain,
! [SV20: $i,SV5: $i,SV28: $i] :
( ( ( element @ SV28 @ ( the_carrier @ SV5 ) )
= $false )
| ( ( ~ ( relstr_set_smaller @ SV5 @ SV20 @ SV28 ) )
= $true )
| ( ( ~ ! [SY114: $i] :
( ~ ( element @ SY114 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY114 )
| ( related @ SV5 @ SV28 @ SY114 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $true )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1093]) ).
thf(1117,plain,
! [SV18: $i,SV30: $i,SV16: $i,SV6: $i] :
( ( ( relstr_set_smaller @ SV6 @ SV16 @ SV30 )
= $false )
| ( ( related @ SV6 @ SV18 @ SV30 )
= $true )
| ( ( element @ SV30 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1094]) ).
thf(1118,plain,
! [SV18: $i,SV16: $i,SV6: $i] :
( ( ( relstr_set_smaller @ SV6 @ SV16 @ ( sK11_SY96 @ SV18 @ SV16 @ SV6 ) )
= $true )
| ( ( relstr_set_smaller @ SV6 @ SV16 @ SV18 )
= $false )
| ( ( SV18
= ( join_on_relstr @ SV6 @ SV16 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV6 @ SV16 )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV6 ) )
= $false )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1096]) ).
thf(1119,plain,
! [SV32: $i] :
( ( ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SV32 ) )
= $true )
| ( ( related @ sK1_A @ sK4_SX0 @ SV32 )
= $true )
| ( ( element @ SV32 @ ( the_carrier @ sK1_A ) )
= $false )
| ( ( sK4_SX0
= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1098]) ).
thf(1120,plain,
! [SV33: $i] :
( ( ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SV33 ) )
= $true )
| ( ( related @ sK1_A @ sK4_SX0 @ SV33 )
= $true )
| ( ( element @ SV33 @ ( the_carrier @ sK1_A ) )
= $false )
| ( ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1099]) ).
thf(1121,plain,
! [SV35: $i] :
( ( ( ~ ( element @ SV35 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SV35 )
| ( related @ sK1_A @ sK4_SX0 @ SV35 ) )
= $true )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( element @ sK9_SY93 @ ( the_carrier @ sK1_A ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1122,plain,
( ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $true )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK9_SY93 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1103]) ).
thf(1123,plain,
( ( ( ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SY94 )
| ( related @ sK1_A @ sK4_SX0 @ SY94 ) ) )
= $true )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK9_SY93 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1104]) ).
thf(1124,plain,
( ( ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 )
= $false )
| ( ( sK4_SX0
= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK9_SY93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1105]) ).
thf(1125,plain,
! [SV36: $i] :
( ( ( ~ ( element @ SV36 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SV36 )
| ( related @ sK1_A @ sK4_SX0 @ SV36 ) )
= $true )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( related @ sK1_A @ sK4_SX0 @ sK9_SY93 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1126,plain,
! [SV22: $i,SV27: $i,SV25: $i,SV11: $i] :
( ( ( related @ SV11 @ SV25 @ SV27 )
= $false )
| ( ( related @ SV11 @ SV22 @ SV25 )
= $false )
| ( ( related @ SV11 @ SV22 @ SV27 )
= $true )
| ( ( element @ SV27 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( element @ SV25 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( element @ SV22 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( transitive_relstr @ SV11 )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1109]) ).
thf(1127,plain,
! [SV31: $i,SV15: $i,SV2: $i] :
( ( ( relstr_set_smaller @ SV2 @ SV15 @ SV31 )
= $false )
| ( ( related @ SV2 @ ( sK7_SY79 @ SV15 @ SV2 ) @ SV31 )
= $true )
| ( ( element @ SV31 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1110]) ).
thf(1128,plain,
! [SV29: $i,SV15: $i,SV2: $i] :
( ( ( relstr_set_smaller @ SV2 @ SV15 @ SV29 )
= $false )
| ( ( ~ ! [SY115: $i] :
( ~ ( element @ SY115 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY115 )
| ( related @ SV2 @ SV29 @ SY115 ) ) )
= $true )
| ( ( SV29
= ( sK7_SY79 @ SV15 @ SV2 ) )
= $true )
| ( ( element @ SV29 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1111]) ).
thf(1129,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( ! [SY109: $i] :
( ~ ( element @ SY109 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY109 )
| ( related @ SV2 @ SV23 @ SY109 ) ) )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( ~ ! [SY110: $i] :
( ~ ( element @ SY110 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY110 )
| ~ ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY86 )
| ( related @ SV2 @ SY110 @ SY86 ) ) )
| ( SY110 = SV23 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1112]) ).
thf(1130,plain,
! [SV34: $i,SV20: $i,SV5: $i] :
( ( ( ~ ( relstr_set_smaller @ SV5 @ SV20 @ SV34 ) )
= $true )
| ( ( related @ SV5 @ ( sK10_SY99 @ SV20 @ SV5 ) @ SV34 )
= $true )
| ( ( element @ SV34 @ ( the_carrier @ SV5 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $false )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1115]) ).
thf(1131,plain,
! [SV28: $i,SV20: $i,SV5: $i] :
( ( ( relstr_set_smaller @ SV5 @ SV20 @ SV28 )
= $false )
| ( ( element @ SV28 @ ( the_carrier @ SV5 ) )
= $false )
| ( ( ~ ! [SY114: $i] :
( ~ ( element @ SY114 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY114 )
| ( related @ SV5 @ SV28 @ SY114 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $true )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1116]) ).
thf(1132,plain,
! [SV32: $i] :
( ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SV32 )
= $false )
| ( ( related @ sK1_A @ sK4_SX0 @ SV32 )
= $true )
| ( ( element @ SV32 @ ( the_carrier @ sK1_A ) )
= $false )
| ( ( sK4_SX0
= ( join_on_relstr @ sK1_A @ sK6_SY76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1119]) ).
thf(1133,plain,
! [SV33: $i] :
( ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SV33 )
= $false )
| ( ( related @ sK1_A @ sK4_SX0 @ SV33 )
= $true )
| ( ( element @ SV33 @ ( the_carrier @ sK1_A ) )
= $false )
| ( ( ex_sup_of_relstr_set @ sK1_A @ sK6_SY76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1120]) ).
thf(1134,plain,
! [SV35: $i] :
( ( ( ~ ( element @ SV35 @ ( the_carrier @ sK1_A ) ) )
= $true )
| ( ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SV35 )
| ( related @ sK1_A @ sK4_SX0 @ SV35 ) )
= $true )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( element @ sK9_SY93 @ ( the_carrier @ sK1_A ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1121]) ).
thf(1135,plain,
! [SV37: $i] :
( ( ( ~ ( element @ SV37 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SV37 )
| ( related @ sK1_A @ sK4_SX0 @ SV37 ) )
= $true )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK9_SY93 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1136,plain,
! [SV36: $i] :
( ( ( ~ ( element @ SV36 @ ( the_carrier @ sK1_A ) ) )
= $true )
| ( ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SV36 )
| ( related @ sK1_A @ sK4_SX0 @ SV36 ) )
= $true )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( related @ sK1_A @ sK4_SX0 @ sK9_SY93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1125]) ).
thf(1137,plain,
! [SV29: $i,SV15: $i,SV2: $i] :
( ( ( ! [SY115: $i] :
( ~ ( element @ SY115 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY115 )
| ( related @ SV2 @ SV29 @ SY115 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV29 )
= $false )
| ( ( SV29
= ( sK7_SY79 @ SV15 @ SV2 ) )
= $true )
| ( ( element @ SV29 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1128]) ).
thf(1138,plain,
! [SV2: $i,SV15: $i,SV23: $i] :
( ( ( ~ ( element @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
| ( related @ SV2 @ SV23 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) ) )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( ~ ! [SY110: $i] :
( ~ ( element @ SY110 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY110 )
| ~ ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY86 )
| ( related @ SV2 @ SY110 @ SY86 ) ) )
| ( SY110 = SV23 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1129]) ).
thf(1139,plain,
! [SV34: $i,SV20: $i,SV5: $i] :
( ( ( relstr_set_smaller @ SV5 @ SV20 @ SV34 )
= $false )
| ( ( related @ SV5 @ ( sK10_SY99 @ SV20 @ SV5 ) @ SV34 )
= $true )
| ( ( element @ SV34 @ ( the_carrier @ SV5 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $false )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1130]) ).
thf(1140,plain,
! [SV28: $i,SV20: $i,SV5: $i] :
( ( ( ! [SY114: $i] :
( ~ ( element @ SY114 @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ SY114 )
| ( related @ SV5 @ SV28 @ SY114 ) ) )
= $false )
| ( ( element @ SV28 @ ( the_carrier @ SV5 ) )
= $false )
| ( ( relstr_set_smaller @ SV5 @ SV20 @ SV28 )
= $false )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $true )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1131]) ).
thf(1141,plain,
! [SV35: $i] :
( ( ( element @ SV35 @ ( the_carrier @ sK1_A ) )
= $false )
| ( ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SV35 )
| ( related @ sK1_A @ sK4_SX0 @ SV35 ) )
= $true )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( element @ sK9_SY93 @ ( the_carrier @ sK1_A ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1134]) ).
thf(1142,plain,
! [SV37: $i] :
( ( ( ~ ( element @ SV37 @ ( the_carrier @ sK1_A ) ) )
= $true )
| ( ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SV37 )
| ( related @ sK1_A @ sK4_SX0 @ SV37 ) )
= $true )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK9_SY93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1135]) ).
thf(1143,plain,
! [SV36: $i] :
( ( ( element @ SV36 @ ( the_carrier @ sK1_A ) )
= $false )
| ( ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SV36 )
| ( related @ sK1_A @ sK4_SX0 @ SV36 ) )
= $true )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( related @ sK1_A @ sK4_SX0 @ sK9_SY93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1136]) ).
thf(1144,plain,
! [SV2: $i,SV15: $i,SV29: $i] :
( ( ( ~ ( element @ ( sK13_SY115 @ SV29 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK13_SY115 @ SV29 @ SV15 @ SV2 ) )
| ( related @ SV2 @ SV29 @ ( sK13_SY115 @ SV29 @ SV15 @ SV2 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV29 )
= $false )
| ( ( SV29
= ( sK7_SY79 @ SV15 @ SV2 ) )
= $true )
| ( ( element @ SV29 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1137]) ).
thf(1145,plain,
! [SV2: $i,SV15: $i,SV23: $i] :
( ( ( ~ ( element @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) ) )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( ~ ! [SY110: $i] :
( ~ ( element @ SY110 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY110 )
| ~ ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY86 )
| ( related @ SV2 @ SY110 @ SY86 ) ) )
| ( SY110 = SV23 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1138]) ).
thf(1146,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
| ( related @ SV2 @ SV23 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) ) )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( ~ ! [SY110: $i] :
( ~ ( element @ SY110 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY110 )
| ~ ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY86 )
| ( related @ SV2 @ SY110 @ SY86 ) ) )
| ( SY110 = SV23 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1138]) ).
thf(1147,plain,
! [SV5: $i,SV20: $i,SV28: $i] :
( ( ( ~ ( element @ ( sK14_SY114 @ SV28 @ SV20 @ SV5 ) @ ( the_carrier @ SV5 ) )
| ~ ( relstr_set_smaller @ SV5 @ SV20 @ ( sK14_SY114 @ SV28 @ SV20 @ SV5 ) )
| ( related @ SV5 @ SV28 @ ( sK14_SY114 @ SV28 @ SV20 @ SV5 ) ) )
= $false )
| ( ( element @ SV28 @ ( the_carrier @ SV5 ) )
= $false )
| ( ( relstr_set_smaller @ SV5 @ SV20 @ SV28 )
= $false )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $true )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1140]) ).
thf(1148,plain,
! [SV35: $i] :
( ( ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SV35 ) )
= $true )
| ( ( related @ sK1_A @ sK4_SX0 @ SV35 )
= $true )
| ( ( element @ SV35 @ ( the_carrier @ sK1_A ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( element @ sK9_SY93 @ ( the_carrier @ sK1_A ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1141]) ).
thf(1149,plain,
! [SV37: $i] :
( ( ( element @ SV37 @ ( the_carrier @ sK1_A ) )
= $false )
| ( ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SV37 )
| ( related @ sK1_A @ sK4_SX0 @ SV37 ) )
= $true )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK9_SY93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1142]) ).
thf(1150,plain,
! [SV36: $i] :
( ( ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SV36 ) )
= $true )
| ( ( related @ sK1_A @ sK4_SX0 @ SV36 )
= $true )
| ( ( element @ SV36 @ ( the_carrier @ sK1_A ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( related @ sK1_A @ sK4_SX0 @ sK9_SY93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1143]) ).
thf(1151,plain,
! [SV2: $i,SV15: $i,SV29: $i] :
( ( ( ~ ( element @ ( sK13_SY115 @ SV29 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV29 )
= $false )
| ( ( SV29
= ( sK7_SY79 @ SV15 @ SV2 ) )
= $true )
| ( ( element @ SV29 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1144]) ).
thf(1152,plain,
! [SV29: $i,SV15: $i,SV2: $i] :
( ( ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK13_SY115 @ SV29 @ SV15 @ SV2 ) )
| ( related @ SV2 @ SV29 @ ( sK13_SY115 @ SV29 @ SV15 @ SV2 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV29 )
= $false )
| ( ( SV29
= ( sK7_SY79 @ SV15 @ SV2 ) )
= $true )
| ( ( element @ SV29 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1144]) ).
thf(1153,plain,
! [SV2: $i,SV15: $i,SV23: $i] :
( ( ( element @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
= $true )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( ~ ! [SY110: $i] :
( ~ ( element @ SY110 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY110 )
| ~ ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY86 )
| ( related @ SV2 @ SY110 @ SY86 ) ) )
| ( SY110 = SV23 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1145]) ).
thf(1154,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) ) )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( ~ ! [SY110: $i] :
( ~ ( element @ SY110 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY110 )
| ~ ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY86 )
| ( related @ SV2 @ SY110 @ SY86 ) ) )
| ( SY110 = SV23 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1146]) ).
thf(1155,plain,
! [SV15: $i,SV23: $i,SV2: $i] :
( ( ( related @ SV2 @ SV23 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( ~ ! [SY110: $i] :
( ~ ( element @ SY110 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY110 )
| ~ ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY86 )
| ( related @ SV2 @ SY110 @ SY86 ) ) )
| ( SY110 = SV23 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1146]) ).
thf(1156,plain,
! [SV5: $i,SV20: $i,SV28: $i] :
( ( ( ~ ( element @ ( sK14_SY114 @ SV28 @ SV20 @ SV5 ) @ ( the_carrier @ SV5 ) ) )
= $false )
| ( ( element @ SV28 @ ( the_carrier @ SV5 ) )
= $false )
| ( ( relstr_set_smaller @ SV5 @ SV20 @ SV28 )
= $false )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $true )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1147]) ).
thf(1157,plain,
! [SV28: $i,SV20: $i,SV5: $i] :
( ( ( ~ ( relstr_set_smaller @ SV5 @ SV20 @ ( sK14_SY114 @ SV28 @ SV20 @ SV5 ) )
| ( related @ SV5 @ SV28 @ ( sK14_SY114 @ SV28 @ SV20 @ SV5 ) ) )
= $false )
| ( ( element @ SV28 @ ( the_carrier @ SV5 ) )
= $false )
| ( ( relstr_set_smaller @ SV5 @ SV20 @ SV28 )
= $false )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $true )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1147]) ).
thf(1158,plain,
! [SV35: $i] :
( ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SV35 )
= $false )
| ( ( related @ sK1_A @ sK4_SX0 @ SV35 )
= $true )
| ( ( element @ SV35 @ ( the_carrier @ sK1_A ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( element @ sK9_SY93 @ ( the_carrier @ sK1_A ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1159,plain,
! [SV37: $i] :
( ( ( ~ ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SV37 ) )
= $true )
| ( ( related @ sK1_A @ sK4_SX0 @ SV37 )
= $true )
| ( ( element @ SV37 @ ( the_carrier @ sK1_A ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK9_SY93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1149]) ).
thf(1160,plain,
! [SV36: $i] :
( ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SV36 )
= $false )
| ( ( related @ sK1_A @ sK4_SX0 @ SV36 )
= $true )
| ( ( element @ SV36 @ ( the_carrier @ sK1_A ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( related @ sK1_A @ sK4_SX0 @ sK9_SY93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1150]) ).
thf(1161,plain,
! [SV2: $i,SV15: $i,SV29: $i] :
( ( ( element @ ( sK13_SY115 @ SV29 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
= $true )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV29 )
= $false )
| ( ( SV29
= ( sK7_SY79 @ SV15 @ SV2 ) )
= $true )
| ( ( element @ SV29 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1151]) ).
thf(1162,plain,
! [SV29: $i,SV15: $i,SV2: $i] :
( ( ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK13_SY115 @ SV29 @ SV15 @ SV2 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV29 )
= $false )
| ( ( SV29
= ( sK7_SY79 @ SV15 @ SV2 ) )
= $true )
| ( ( element @ SV29 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1152]) ).
thf(1163,plain,
! [SV15: $i,SV29: $i,SV2: $i] :
( ( ( related @ SV2 @ SV29 @ ( sK13_SY115 @ SV29 @ SV15 @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV29 )
= $false )
| ( ( SV29
= ( sK7_SY79 @ SV15 @ SV2 ) )
= $true )
| ( ( element @ SV29 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1152]) ).
thf(1164,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( ! [SY110: $i] :
( ~ ( element @ SY110 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY110 )
| ~ ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY86 )
| ( related @ SV2 @ SY110 @ SY86 ) ) )
| ( SY110 = SV23 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1153]) ).
thf(1165,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( relstr_set_smaller @ SV2 @ SV15 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $true )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( ~ ! [SY110: $i] :
( ~ ( element @ SY110 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY110 )
| ~ ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY86 )
| ( related @ SV2 @ SY110 @ SY86 ) ) )
| ( SY110 = SV23 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1154]) ).
thf(1166,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( ! [SY110: $i] :
( ~ ( element @ SY110 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY110 )
| ~ ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY86 )
| ( related @ SV2 @ SY110 @ SY86 ) ) )
| ( SY110 = SV23 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( related @ SV2 @ SV23 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1155]) ).
thf(1167,plain,
! [SV5: $i,SV20: $i,SV28: $i] :
( ( ( element @ ( sK14_SY114 @ SV28 @ SV20 @ SV5 ) @ ( the_carrier @ SV5 ) )
= $true )
| ( ( element @ SV28 @ ( the_carrier @ SV5 ) )
= $false )
| ( ( relstr_set_smaller @ SV5 @ SV20 @ SV28 )
= $false )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $true )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1156]) ).
thf(1168,plain,
! [SV28: $i,SV20: $i,SV5: $i] :
( ( ( ~ ( relstr_set_smaller @ SV5 @ SV20 @ ( sK14_SY114 @ SV28 @ SV20 @ SV5 ) ) )
= $false )
| ( ( element @ SV28 @ ( the_carrier @ SV5 ) )
= $false )
| ( ( relstr_set_smaller @ SV5 @ SV20 @ SV28 )
= $false )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $true )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1157]) ).
thf(1169,plain,
! [SV20: $i,SV28: $i,SV5: $i] :
( ( ( related @ SV5 @ SV28 @ ( sK14_SY114 @ SV28 @ SV20 @ SV5 ) )
= $false )
| ( ( element @ SV28 @ ( the_carrier @ SV5 ) )
= $false )
| ( ( relstr_set_smaller @ SV5 @ SV20 @ SV28 )
= $false )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $true )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1157]) ).
thf(1170,plain,
! [SV37: $i] :
( ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ SV37 )
= $false )
| ( ( related @ sK1_A @ sK4_SX0 @ SV37 )
= $true )
| ( ( element @ SV37 @ ( the_carrier @ sK1_A ) )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK4_SX0 )
= $false )
| ( ( relstr_set_smaller @ sK1_A @ sK6_SY76 @ sK9_SY93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1159]) ).
thf(1171,plain,
! [SV29: $i,SV15: $i,SV2: $i] :
( ( ( relstr_set_smaller @ SV2 @ SV15 @ ( sK13_SY115 @ SV29 @ SV15 @ SV2 ) )
= $true )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV29 )
= $false )
| ( ( SV29
= ( sK7_SY79 @ SV15 @ SV2 ) )
= $true )
| ( ( element @ SV29 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1162]) ).
thf(1172,plain,
! [SV2: $i,SV15: $i,SV23: $i] :
( ( ( ~ ( element @ ( sK15_SY110 @ SV23 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK15_SY110 @ SV23 @ SV15 @ SV2 ) )
| ~ ! [SY116: $i] :
( ~ ( element @ SY116 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY116 )
| ( related @ SV2 @ ( sK15_SY110 @ SV23 @ SV15 @ SV2 ) @ SY116 ) ) )
| ( ( sK15_SY110 @ SV23 @ SV15 @ SV2 )
= SV23 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1164]) ).
thf(1173,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( ! [SY110: $i] :
( ~ ( element @ SY110 @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY110 )
| ~ ! [SY86: $i] :
( ~ ( element @ SY86 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY86 )
| ( related @ SV2 @ SY110 @ SY86 ) ) )
| ( SY110 = SV23 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1165]) ).
thf(1174,plain,
! [SV2: $i,SV15: $i,SV23: $i] :
( ( ( ~ ( element @ ( sK16_SY110 @ SV23 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK16_SY110 @ SV23 @ SV15 @ SV2 ) )
| ~ ! [SY117: $i] :
( ~ ( element @ SY117 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY117 )
| ( related @ SV2 @ ( sK16_SY110 @ SV23 @ SV15 @ SV2 ) @ SY117 ) ) )
| ( ( sK16_SY110 @ SV23 @ SV15 @ SV2 )
= SV23 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( related @ SV2 @ SV23 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1166]) ).
thf(1175,plain,
! [SV28: $i,SV20: $i,SV5: $i] :
( ( ( relstr_set_smaller @ SV5 @ SV20 @ ( sK14_SY114 @ SV28 @ SV20 @ SV5 ) )
= $true )
| ( ( element @ SV28 @ ( the_carrier @ SV5 ) )
= $false )
| ( ( relstr_set_smaller @ SV5 @ SV20 @ SV28 )
= $false )
| ( ( ex_sup_of_relstr_set @ SV5 @ SV20 )
= $true )
| ( ( antisymmetric_relstr @ SV5 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1168]) ).
thf(1176,plain,
! [SV2: $i,SV15: $i,SV23: $i] :
( ( ( ~ ( element @ ( sK15_SY110 @ SV23 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1172]) ).
thf(1177,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK15_SY110 @ SV23 @ SV15 @ SV2 ) )
| ~ ! [SY116: $i] :
( ~ ( element @ SY116 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY116 )
| ( related @ SV2 @ ( sK15_SY110 @ SV23 @ SV15 @ SV2 ) @ SY116 ) ) )
| ( ( sK15_SY110 @ SV23 @ SV15 @ SV2 )
= SV23 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1172]) ).
thf(1178,plain,
! [SV2: $i,SV15: $i,SV23: $i] :
( ( ( ~ ( element @ ( sK17_SY110 @ SV23 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK17_SY110 @ SV23 @ SV15 @ SV2 ) )
| ~ ! [SY118: $i] :
( ~ ( element @ SY118 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY118 )
| ( related @ SV2 @ ( sK17_SY110 @ SV23 @ SV15 @ SV2 ) @ SY118 ) ) )
| ( ( sK17_SY110 @ SV23 @ SV15 @ SV2 )
= SV23 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1173]) ).
thf(1179,plain,
! [SV2: $i,SV15: $i,SV23: $i] :
( ( ( ~ ( element @ ( sK16_SY110 @ SV23 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( related @ SV2 @ SV23 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1174]) ).
thf(1180,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK16_SY110 @ SV23 @ SV15 @ SV2 ) )
| ~ ! [SY117: $i] :
( ~ ( element @ SY117 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY117 )
| ( related @ SV2 @ ( sK16_SY110 @ SV23 @ SV15 @ SV2 ) @ SY117 ) ) )
| ( ( sK16_SY110 @ SV23 @ SV15 @ SV2 )
= SV23 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( related @ SV2 @ SV23 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1174]) ).
thf(1181,plain,
! [SV2: $i,SV15: $i,SV23: $i] :
( ( ( element @ ( sK15_SY110 @ SV23 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
= $true )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1176]) ).
thf(1182,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK15_SY110 @ SV23 @ SV15 @ SV2 ) )
| ~ ! [SY116: $i] :
( ~ ( element @ SY116 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY116 )
| ( related @ SV2 @ ( sK15_SY110 @ SV23 @ SV15 @ SV2 ) @ SY116 ) ) ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1177]) ).
thf(1183,plain,
! [SV2: $i,SV15: $i,SV23: $i] :
( ( ( ( sK15_SY110 @ SV23 @ SV15 @ SV2 )
= SV23 )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1177]) ).
thf(1184,plain,
! [SV2: $i,SV15: $i,SV23: $i] :
( ( ( ~ ( element @ ( sK17_SY110 @ SV23 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1178]) ).
thf(1185,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK17_SY110 @ SV23 @ SV15 @ SV2 ) )
| ~ ! [SY118: $i] :
( ~ ( element @ SY118 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY118 )
| ( related @ SV2 @ ( sK17_SY110 @ SV23 @ SV15 @ SV2 ) @ SY118 ) ) )
| ( ( sK17_SY110 @ SV23 @ SV15 @ SV2 )
= SV23 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1178]) ).
thf(1186,plain,
! [SV2: $i,SV15: $i,SV23: $i] :
( ( ( element @ ( sK16_SY110 @ SV23 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
= $true )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( related @ SV2 @ SV23 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1179]) ).
thf(1187,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK16_SY110 @ SV23 @ SV15 @ SV2 ) )
| ~ ! [SY117: $i] :
( ~ ( element @ SY117 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY117 )
| ( related @ SV2 @ ( sK16_SY110 @ SV23 @ SV15 @ SV2 ) @ SY117 ) ) ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( related @ SV2 @ SV23 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1180]) ).
thf(1188,plain,
! [SV2: $i,SV15: $i,SV23: $i] :
( ( ( ( sK16_SY110 @ SV23 @ SV15 @ SV2 )
= SV23 )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( related @ SV2 @ SV23 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1180]) ).
thf(1189,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK15_SY110 @ SV23 @ SV15 @ SV2 ) )
| ~ ! [SY116: $i] :
( ~ ( element @ SY116 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY116 )
| ( related @ SV2 @ ( sK15_SY110 @ SV23 @ SV15 @ SV2 ) @ SY116 ) ) ) )
= $true )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1182]) ).
thf(1190,plain,
! [SV2: $i,SV15: $i,SV23: $i] :
( ( ( element @ ( sK17_SY110 @ SV23 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
= $true )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1184]) ).
thf(1191,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK17_SY110 @ SV23 @ SV15 @ SV2 ) )
| ~ ! [SY118: $i] :
( ~ ( element @ SY118 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY118 )
| ( related @ SV2 @ ( sK17_SY110 @ SV23 @ SV15 @ SV2 ) @ SY118 ) ) ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1185]) ).
thf(1192,plain,
! [SV2: $i,SV15: $i,SV23: $i] :
( ( ( ( sK17_SY110 @ SV23 @ SV15 @ SV2 )
= SV23 )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1185]) ).
thf(1193,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK16_SY110 @ SV23 @ SV15 @ SV2 ) )
| ~ ! [SY117: $i] :
( ~ ( element @ SY117 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY117 )
| ( related @ SV2 @ ( sK16_SY110 @ SV23 @ SV15 @ SV2 ) @ SY117 ) ) ) )
= $true )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( related @ SV2 @ SV23 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1187]) ).
thf(1194,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK15_SY110 @ SV23 @ SV15 @ SV2 ) )
| ~ ! [SY116: $i] :
( ~ ( element @ SY116 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY116 )
| ( related @ SV2 @ ( sK15_SY110 @ SV23 @ SV15 @ SV2 ) @ SY116 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1189]) ).
thf(1195,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( ~ ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK17_SY110 @ SV23 @ SV15 @ SV2 ) )
| ~ ! [SY118: $i] :
( ~ ( element @ SY118 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY118 )
| ( related @ SV2 @ ( sK17_SY110 @ SV23 @ SV15 @ SV2 ) @ SY118 ) ) ) )
= $true )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1191]) ).
thf(1196,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK16_SY110 @ SV23 @ SV15 @ SV2 ) )
| ~ ! [SY117: $i] :
( ~ ( element @ SY117 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY117 )
| ( related @ SV2 @ ( sK16_SY110 @ SV23 @ SV15 @ SV2 ) @ SY117 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( related @ SV2 @ SV23 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1193]) ).
thf(1197,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK15_SY110 @ SV23 @ SV15 @ SV2 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1194]) ).
thf(1198,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( ~ ! [SY116: $i] :
( ~ ( element @ SY116 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY116 )
| ( related @ SV2 @ ( sK15_SY110 @ SV23 @ SV15 @ SV2 ) @ SY116 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1194]) ).
thf(1199,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK17_SY110 @ SV23 @ SV15 @ SV2 ) )
| ~ ! [SY118: $i] :
( ~ ( element @ SY118 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY118 )
| ( related @ SV2 @ ( sK17_SY110 @ SV23 @ SV15 @ SV2 ) @ SY118 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1195]) ).
thf(1200,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK16_SY110 @ SV23 @ SV15 @ SV2 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( related @ SV2 @ SV23 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1196]) ).
thf(1201,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( ~ ! [SY117: $i] :
( ~ ( element @ SY117 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY117 )
| ( related @ SV2 @ ( sK16_SY110 @ SV23 @ SV15 @ SV2 ) @ SY117 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( related @ SV2 @ SV23 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1196]) ).
thf(1202,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( relstr_set_smaller @ SV2 @ SV15 @ ( sK15_SY110 @ SV23 @ SV15 @ SV2 ) )
= $true )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1197]) ).
thf(1203,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( ! [SY116: $i] :
( ~ ( element @ SY116 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY116 )
| ( related @ SV2 @ ( sK15_SY110 @ SV23 @ SV15 @ SV2 ) @ SY116 ) ) )
= $true )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1198]) ).
thf(1204,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ ( sK17_SY110 @ SV23 @ SV15 @ SV2 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1199]) ).
thf(1205,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( ~ ! [SY118: $i] :
( ~ ( element @ SY118 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY118 )
| ( related @ SV2 @ ( sK17_SY110 @ SV23 @ SV15 @ SV2 ) @ SY118 ) ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1199]) ).
thf(1206,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( relstr_set_smaller @ SV2 @ SV15 @ ( sK16_SY110 @ SV23 @ SV15 @ SV2 ) )
= $true )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( related @ SV2 @ SV23 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1200]) ).
thf(1207,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( ! [SY117: $i] :
( ~ ( element @ SY117 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY117 )
| ( related @ SV2 @ ( sK16_SY110 @ SV23 @ SV15 @ SV2 ) @ SY117 ) ) )
= $true )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( related @ SV2 @ SV23 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1201]) ).
thf(1208,plain,
! [SV23: $i,SV15: $i,SV2: $i,SV38: $i] :
( ( ( ~ ( element @ SV38 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV38 )
| ( related @ SV2 @ ( sK15_SY110 @ SV23 @ SV15 @ SV2 ) @ SV38 ) )
= $true )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1209,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( relstr_set_smaller @ SV2 @ SV15 @ ( sK17_SY110 @ SV23 @ SV15 @ SV2 ) )
= $true )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1204]) ).
thf(1210,plain,
! [SV23: $i,SV15: $i,SV2: $i] :
( ( ( ! [SY118: $i] :
( ~ ( element @ SY118 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SY118 )
| ( related @ SV2 @ ( sK17_SY110 @ SV23 @ SV15 @ SV2 ) @ SY118 ) ) )
= $true )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1205]) ).
thf(1211,plain,
! [SV23: $i,SV15: $i,SV2: $i,SV39: $i] :
( ( ( ~ ( element @ SV39 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV39 )
| ( related @ SV2 @ ( sK16_SY110 @ SV23 @ SV15 @ SV2 ) @ SV39 ) )
= $true )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( related @ SV2 @ SV23 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1212,plain,
! [SV23: $i,SV15: $i,SV2: $i,SV38: $i] :
( ( ( ~ ( element @ SV38 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV38 )
| ( related @ SV2 @ ( sK15_SY110 @ SV23 @ SV15 @ SV2 ) @ SV38 ) )
= $true )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1208]) ).
thf(1213,plain,
! [SV23: $i,SV15: $i,SV2: $i,SV40: $i] :
( ( ( ~ ( element @ SV40 @ ( the_carrier @ SV2 ) )
| ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV40 )
| ( related @ SV2 @ ( sK17_SY110 @ SV23 @ SV15 @ SV2 ) @ SV40 ) )
= $true )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1214,plain,
! [SV23: $i,SV15: $i,SV2: $i,SV39: $i] :
( ( ( ~ ( element @ SV39 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV39 )
| ( related @ SV2 @ ( sK16_SY110 @ SV23 @ SV15 @ SV2 ) @ SV39 ) )
= $true )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( related @ SV2 @ SV23 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1211]) ).
thf(1215,plain,
! [SV23: $i,SV15: $i,SV2: $i,SV38: $i] :
( ( ( element @ SV38 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV38 )
| ( related @ SV2 @ ( sK15_SY110 @ SV23 @ SV15 @ SV2 ) @ SV38 ) )
= $true )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1212]) ).
thf(1216,plain,
! [SV23: $i,SV15: $i,SV2: $i,SV40: $i] :
( ( ( ~ ( element @ SV40 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV40 )
| ( related @ SV2 @ ( sK17_SY110 @ SV23 @ SV15 @ SV2 ) @ SV40 ) )
= $true )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1213]) ).
thf(1217,plain,
! [SV23: $i,SV15: $i,SV2: $i,SV39: $i] :
( ( ( element @ SV39 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV39 )
| ( related @ SV2 @ ( sK16_SY110 @ SV23 @ SV15 @ SV2 ) @ SV39 ) )
= $true )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( related @ SV2 @ SV23 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1214]) ).
thf(1218,plain,
! [SV23: $i,SV38: $i,SV15: $i,SV2: $i] :
( ( ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV38 ) )
= $true )
| ( ( related @ SV2 @ ( sK15_SY110 @ SV23 @ SV15 @ SV2 ) @ SV38 )
= $true )
| ( ( element @ SV38 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1215]) ).
thf(1219,plain,
! [SV23: $i,SV15: $i,SV2: $i,SV40: $i] :
( ( ( element @ SV40 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV40 )
| ( related @ SV2 @ ( sK17_SY110 @ SV23 @ SV15 @ SV2 ) @ SV40 ) )
= $true )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1220,plain,
! [SV23: $i,SV39: $i,SV15: $i,SV2: $i] :
( ( ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV39 ) )
= $true )
| ( ( related @ SV2 @ ( sK16_SY110 @ SV23 @ SV15 @ SV2 ) @ SV39 )
= $true )
| ( ( element @ SV39 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( related @ SV2 @ SV23 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1217]) ).
thf(1221,plain,
! [SV23: $i,SV38: $i,SV15: $i,SV2: $i] :
( ( ( relstr_set_smaller @ SV2 @ SV15 @ SV38 )
= $false )
| ( ( related @ SV2 @ ( sK15_SY110 @ SV23 @ SV15 @ SV2 ) @ SV38 )
= $true )
| ( ( element @ SV38 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) @ ( the_carrier @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1218]) ).
thf(1222,plain,
! [SV23: $i,SV40: $i,SV15: $i,SV2: $i] :
( ( ( ~ ( relstr_set_smaller @ SV2 @ SV15 @ SV40 ) )
= $true )
| ( ( related @ SV2 @ ( sK17_SY110 @ SV23 @ SV15 @ SV2 ) @ SV40 )
= $true )
| ( ( element @ SV40 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1219]) ).
thf(1223,plain,
! [SV23: $i,SV39: $i,SV15: $i,SV2: $i] :
( ( ( relstr_set_smaller @ SV2 @ SV15 @ SV39 )
= $false )
| ( ( related @ SV2 @ ( sK16_SY110 @ SV23 @ SV15 @ SV2 ) @ SV39 )
= $true )
| ( ( element @ SV39 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( related @ SV2 @ SV23 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1220]) ).
thf(1224,plain,
! [SV23: $i,SV40: $i,SV15: $i,SV2: $i] :
( ( ( relstr_set_smaller @ SV2 @ SV15 @ SV40 )
= $false )
| ( ( related @ SV2 @ ( sK17_SY110 @ SV23 @ SV15 @ SV2 ) @ SV40 )
= $true )
| ( ( element @ SV40 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( relstr_set_smaller @ SV2 @ SV15 @ ( sK12_SY109 @ SV23 @ SV15 @ SV2 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV2 @ SV15 )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1222]) ).
thf(1225,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[737,1224,1223,1221,1209,1206,1202,1192,1190,1188,1186,1183,1181,1175,1171,1170,1169,1167,1163,1161,1160,1158,1139,1133,1132,1127,1126,1124,1122,1118,1117,1114,1113,1108,1106,1102,1100,1097,1095,1086,1085,1053,1036,1034,1033,1031,1007,1004,988,969,967,855,854,842,841,838,835,832,823,821,773,772,767,766,765,764,762,761,760,759,758,757,756,755,753,752,751,750,749,747,746,745,744,743,742,741,740,739,738]) ).
thf(1226,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1225]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU359+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
% 0.07/0.17 % Computer : n018.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Oct 6 15:18:59 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.45/1.65 ......
% 8.45/1.65
% 8.45/1.65 No.of.Axioms: 41
% 8.45/1.65
% 8.45/1.65 Length.of.Defs: 0
% 8.45/1.65
% 8.45/1.65 Contains.Choice.Funs: false
% 8.45/1.65 ..........................
% 8.45/1.65
% 8.45/1.65 ********************************
% 8.45/1.65 * All subproblems solved! *
% 8.45/1.65 ********************************
% 8.45/1.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:43,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1225,loop_count:0,foatp_calls:1,translation:fof_full)
% 8.45/1.65
% 8.45/1.65 %**** Beginning of derivation protocol ****
% 8.45/1.65 % SZS output start CNFRefutation
% See solution above
% 8.45/1.66
% 8.45/1.66 %**** End of derivation protocol ****
% 8.45/1.66 %**** no. of clauses in derivation: 586 ****
% 8.45/1.66 %**** clause counter: 1225 ****
% 8.45/1.66
% 8.45/1.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:43,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1225,loop_count:0,foatp_calls:1,translation:fof_full)
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