TSTP Solution File: SEU308+2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU308+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:10:02 EDT 2022
% Result : Theorem 22.23s 22.39s
% Output : CNFRefutation 37.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 59
% Number of leaves : 468
% Syntax : Number of formulae : 5830 (1857 unt; 231 typ; 0 def)
% Number of atoms : 65135 (24937 equ; 0 cnn)
% Maximal formula atoms : 26 ( 11 avg)
% Number of connectives : 161347 (25860 ~;24975 |; 875 &;109101 @)
% ( 132 <=>; 404 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 414 ( 414 >; 0 *; 0 +; 0 <<)
% Number of symbols : 234 ( 231 usr; 22 con; 0-7 aty)
% Number of variables : 21414 ( 0 ^21286 !; 128 ?;21414 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_antisymmetric,type,
antisymmetric: $i > $o ).
thf(tp_apply,type,
apply: $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_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_subset,type,
cast_to_subset: $i > $i ).
thf(tp_complements_of_subsets,type,
complements_of_subsets: $i > $i > $i ).
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_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_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_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_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_commut,type,
join_commut: $i > $i > $i > $i ).
thf(tp_join_commutative,type,
join_commutative: $i > $o ).
thf(tp_join_semilatt_str,type,
join_semilatt_str: $i > $o ).
thf(tp_latt_str,type,
latt_str: $i > $o ).
thf(tp_meet,type,
meet: $i > $i > $i > $i ).
thf(tp_meet_absorbing,type,
meet_absorbing: $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_subsets,type,
meet_of_subsets: $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_ordered_pair,type,
ordered_pair: $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_powerset,type,
powerset: $i > $i ).
thf(tp_preboolean,type,
preboolean: $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_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_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_sK100_B,type,
sK100_B: $i > $i ).
thf(tp_sK101_E,type,
sK101_E: $i > $i > $i > $i > $i ).
thf(tp_sK102_D,type,
sK102_D: $i > $i > $i > $i ).
thf(tp_sK103_E,type,
sK103_E: $i > $i > $i > $i > $i ).
thf(tp_sK104_D,type,
sK104_D: $i > $i > $i > $i ).
thf(tp_sK105_C,type,
sK105_C: $i > $i > $i ).
thf(tp_sK106_B,type,
sK106_B: $i > $i ).
thf(tp_sK107_B,type,
sK107_B: $i > $i ).
thf(tp_sK108_C,type,
sK108_C: $i > $i > $i ).
thf(tp_sK109_E,type,
sK109_E: $i > $i > $i > $i ).
thf(tp_sK10_SY601,type,
sK10_SY601: $i ).
thf(tp_sK110_SY756,type,
sK110_SY756: $i > $i > $i > $i ).
thf(tp_sK111_D,type,
sK111_D: $i > $i > $i > $i ).
thf(tp_sK112_F,type,
sK112_F: $i > $i > $i > $i > $i ).
thf(tp_sK113_SY768,type,
sK113_SY768: $i > $i > $i > $i > $i ).
thf(tp_sK114_SY771,type,
sK114_SY771: $i > $i > $i > $i > $i ).
thf(tp_sK115_I,type,
sK115_I: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK116_B,type,
sK116_B: $i > $i ).
thf(tp_sK117_A,type,
sK117_A: $i ).
thf(tp_sK118_B,type,
sK118_B: $i > $i ).
thf(tp_sK119_B,type,
sK119_B: $i > $i ).
thf(tp_sK11_SY603,type,
sK11_SY603: $i ).
thf(tp_sK120_B,type,
sK120_B: $i > $i ).
thf(tp_sK121_B,type,
sK121_B: $i > $i ).
thf(tp_sK122_A,type,
sK122_A: $i ).
thf(tp_sK123_D,type,
sK123_D: $i > $i > $i > $i ).
thf(tp_sK124_C,type,
sK124_C: $i > $i > $i ).
thf(tp_sK125_C,type,
sK125_C: $i > $i > $i ).
thf(tp_sK12_REN,type,
sK12_REN: $o ).
thf(tp_sK13_C,type,
sK13_C: $i > $i > $i ).
thf(tp_sK14_J,type,
sK14_J: $i > $i > $i > $i ).
thf(tp_sK15_SY612,type,
sK15_SY612: $i > $i > $i > $i ).
thf(tp_sK16_E,type,
sK16_E: $i > $i > $i > $i ).
thf(tp_sK17_C,type,
sK17_C: $i > $i ).
thf(tp_sK18_SY613,type,
sK18_SY613: $i > $i ).
thf(tp_sK19_SY619,type,
sK19_SY619: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_SY626,type,
sK20_SY626: $i > $i ).
thf(tp_sK21_SY628,type,
sK21_SY628: $i > $i ).
thf(tp_sK22_SY620,type,
sK22_SY620: $i > $i ).
thf(tp_sK23_SY629,type,
sK23_SY629: $i > $i ).
thf(tp_sK24_B,type,
sK24_B: $i > $i ).
thf(tp_sK25_D,type,
sK25_D: $i > $i > $i ).
thf(tp_sK26_B,type,
sK26_B: $i > $i ).
thf(tp_sK27_SY634,type,
sK27_SY634: $i > $i ).
thf(tp_sK28_SY636,type,
sK28_SY636: $i > $i ).
thf(tp_sK29_D,type,
sK29_D: $i > $i > $i > $i ).
thf(tp_sK2_SY588,type,
sK2_SY588: $i ).
thf(tp_sK30_O,type,
sK30_O: $i > $i > $i > $i > $i ).
thf(tp_sK31_SY649,type,
sK31_SY649: $i > $i > $i > $i > $i ).
thf(tp_sK32_SY652,type,
sK32_SY652: $i > $i > $i > $i > $i ).
thf(tp_sK33_F,type,
sK33_F: $i > $i > $i > $i > $i ).
thf(tp_sK34_R,type,
sK34_R: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sK35_D,type,
sK35_D: $i > $i > $i ).
thf(tp_sK36_SY655,type,
sK36_SY655: $i > $i > $i ).
thf(tp_sK37_SY665,type,
sK37_SY665: $i > $i > $i ).
thf(tp_sK38_SY678,type,
sK38_SY678: $i > $i > $i ).
thf(tp_sK39_SY682,type,
sK39_SY682: $i > $i > $i ).
thf(tp_sK3_B,type,
sK3_B: $i > $i ).
thf(tp_sK40_SY685,type,
sK40_SY685: $i > $i > $i ).
thf(tp_sK41_SY666,type,
sK41_SY666: $i > $i > $i ).
thf(tp_sK42_SY688,type,
sK42_SY688: $i > $i > $i ).
thf(tp_sK43_SY691,type,
sK43_SY691: $i > $i > $i ).
thf(tp_sK44_C,type,
sK44_C: $i > $i > $i ).
thf(tp_sK45_E,type,
sK45_E: $i > $i > $i > $i ).
thf(tp_sK46_SY702,type,
sK46_SY702: $i > $i > $i > $i ).
thf(tp_sK47_K,type,
sK47_K: $i > $i > $i > $i > $i > $i ).
thf(tp_sK48_C,type,
sK48_C: $i > $i > $i ).
thf(tp_sK49_SY705,type,
sK49_SY705: $i > $i > $i ).
thf(tp_sK4_SY591,type,
sK4_SY591: $i > $i > $i ).
thf(tp_sK50_SY711,type,
sK50_SY711: $i > $i > $i ).
thf(tp_sK51_SY718,type,
sK51_SY718: $i > $i > $i ).
thf(tp_sK52_SY712,type,
sK52_SY712: $i > $i > $i ).
thf(tp_sK53_A,type,
sK53_A: $i ).
thf(tp_sK54_A,type,
sK54_A: $i ).
thf(tp_sK55_A,type,
sK55_A: $i ).
thf(tp_sK56_C,type,
sK56_C: $i > $i > $i ).
thf(tp_sK57_A,type,
sK57_A: $i ).
thf(tp_sK58_A,type,
sK58_A: $i ).
thf(tp_sK59_A,type,
sK59_A: $i ).
thf(tp_sK5_C,type,
sK5_C: $i > $i > $i ).
thf(tp_sK60_A,type,
sK60_A: $i ).
thf(tp_sK61_A,type,
sK61_A: $i ).
thf(tp_sK62_C,type,
sK62_C: $i > $i > $i ).
thf(tp_sK63_C,type,
sK63_C: $i > $i > $i ).
thf(tp_sK64_A,type,
sK64_A: $i ).
thf(tp_sK65_A,type,
sK65_A: $i ).
thf(tp_sK66_D,type,
sK66_D: $i > $i > $i > $i ).
thf(tp_sK67_D,type,
sK67_D: $i > $i > $i > $i ).
thf(tp_sK68_C,type,
sK68_C: $i > $i > $i ).
thf(tp_sK69_SY723,type,
sK69_SY723: $i > $i > $i ).
thf(tp_sK6_C,type,
sK6_C: $i > $i > $i ).
thf(tp_sK70_D,type,
sK70_D: $i > $i > $i > $i ).
thf(tp_sK71_C,type,
sK71_C: $i > $i > $i ).
thf(tp_sK72_C,type,
sK72_C: $i > $i > $i ).
thf(tp_sK73_SY724,type,
sK73_SY724: $i > $i > $i ).
thf(tp_sK74_B,type,
sK74_B: $i > $i ).
thf(tp_sK75_SY725,type,
sK75_SY725: $i > $i ).
thf(tp_sK76_E,type,
sK76_E: $i > $i > $i > $i > $i ).
thf(tp_sK77_SY726,type,
sK77_SY726: $i > $i > $i > $i > $i ).
thf(tp_sK78_D,type,
sK78_D: $i > $i > $i > $i ).
thf(tp_sK79_SY729,type,
sK79_SY729: $i > $i > $i > $i ).
thf(tp_sK7_B,type,
sK7_B: $i > $i ).
thf(tp_sK80_SY731,type,
sK80_SY731: $i > $i > $i > $i ).
thf(tp_sK81_D,type,
sK81_D: $i > $i > $i > $i ).
thf(tp_sK82_D,type,
sK82_D: $i > $i > $i > $i ).
thf(tp_sK83_C,type,
sK83_C: $i > $i > $i ).
thf(tp_sK84_SY732,type,
sK84_SY732: $i > $i > $i ).
thf(tp_sK85_B,type,
sK85_B: $i > $i ).
thf(tp_sK86_B,type,
sK86_B: $i > $i ).
thf(tp_sK87_C,type,
sK87_C: $i > $i > $i ).
thf(tp_sK88_D,type,
sK88_D: $i > $i > $i > $i ).
thf(tp_sK89_C,type,
sK89_C: $i > $i > $i ).
thf(tp_sK8_D,type,
sK8_D: $i > $i > $i ).
thf(tp_sK90_SY733,type,
sK90_SY733: $i > $i > $i ).
thf(tp_sK91_C,type,
sK91_C: $i > $i > $i ).
thf(tp_sK92_SY735,type,
sK92_SY735: $i > $i > $i ).
thf(tp_sK93_B,type,
sK93_B: $i > $i ).
thf(tp_sK94_E,type,
sK94_E: $i > $i > $i > $i > $i ).
thf(tp_sK95_B,type,
sK95_B: $i > $i ).
thf(tp_sK96_SY738,type,
sK96_SY738: $i > $i ).
thf(tp_sK97_C,type,
sK97_C: $i > $i > $i ).
thf(tp_sK98_C,type,
sK98_C: $i > $i > $i ).
thf(tp_sK99_B,type,
sK99_B: $i > $i ).
thf(tp_sK9_B,type,
sK9_B: $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_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_succ,type,
succ: $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_transitive,type,
transitive: $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_int_1,type,
v1_int_1: $i > $o ).
thf(tp_v1_membered,type,
v1_membered: $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_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(1,axiom,
! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
( ( subset @ E @ C )
=> ( in @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_tarski) ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ( in @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).
thf(4,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(5,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(8,axiom,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(10,axiom,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(13,axiom,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(15,axiom,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(20,axiom,
! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( B = C )
& ( ordinal @ C )
& ( B = D )
& ( ordinal @ D ) )
=> ( C = D ) )
=> ? [B: $i] :
! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ D @ A )
& ( D = C )
& ( ordinal @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e6_22__wellord2__1) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i,E: $i] :
( ( ( C = D )
& ? [F: $i,G: $i] :
( ( ( ordered_pair @ F @ G )
= D )
& ( in @ F @ A )
& ( G
= ( singleton @ F ) ) )
& ( C = E )
& ? [H: $i,I: $i] :
( ( ( ordered_pair @ H @ I )
= E )
& ( in @ H @ A )
& ( I
= ( singleton @ H ) ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ E @ ( cartesian_product2 @ A @ B ) )
& ( E = D )
& ? [J: $i,K: $i] :
( ( ( ordered_pair @ J @ K )
= D )
& ( in @ J @ A )
& ( K
= ( singleton @ J ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e16_22__wellord2__2) ).
thf(25,axiom,
! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( in @ B @ A )
& ( C
= ( singleton @ B ) )
& ( in @ B @ A )
& ( D
= ( singleton @ B ) ) )
=> ( C = D ) )
=> ? [B: $i] :
! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ D @ A )
& ( in @ D @ A )
& ( C
= ( singleton @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e16_22__wellord2__1) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ( relation @ B ) )
=> ! [C: $i] :
( ! [D: $i,E: $i,F: $i] :
( ( ( D = E )
& ? [G: $i,H: $i] :
( ( ( ordered_pair @ G @ H )
= E )
& ( in @ G @ A )
& ? [I: $i] :
( ( G = I )
& ( in @ H @ I )
& ! [J: $i] :
( ( in @ J @ I )
=> ( in @ ( ordered_pair @ H @ J ) @ B ) ) ) )
& ( D = F )
& ? [K: $i,L: $i] :
( ( ( ordered_pair @ K @ L )
= F )
& ( in @ K @ A )
& ? [M: $i] :
( ( K = M )
& ( in @ L @ M )
& ! [N: $i] :
( ( in @ N @ M )
=> ( in @ ( ordered_pair @ L @ N ) @ B ) ) ) ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ? [F: $i] :
( ( in @ F @ ( cartesian_product2 @ A @ C ) )
& ( F = E )
& ? [O: $i,P: $i] :
( ( ( ordered_pair @ O @ P )
= E )
& ( in @ O @ A )
& ? [Q: $i] :
( ( O = Q )
& ( in @ P @ Q )
& ! [R: $i] :
( ( in @ R @ Q )
=> ( in @ ( ordered_pair @ P @ R ) @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e10_24__wellord2__2) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ( relation @ B ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( in @ C @ A )
& ? [F: $i] :
( ( C = F )
& ( in @ D @ F )
& ! [G: $i] :
( ( in @ G @ F )
=> ( in @ ( ordered_pair @ D @ G ) @ B ) ) )
& ( in @ C @ A )
& ? [H: $i] :
( ( C = H )
& ( in @ E @ H )
& ! [I: $i] :
( ( in @ I @ H )
=> ( in @ ( ordered_pair @ E @ I ) @ B ) ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ E @ A )
& ( in @ E @ A )
& ? [J: $i] :
( ( E = J )
& ( in @ D @ J )
& ! [K: $i] :
( ( in @ K @ J )
=> ( in @ ( ordered_pair @ D @ K ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e10_24__wellord2__1) ).
thf(29,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
<=> ( relation_of2 @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( meet_of_subsets @ A @ B )
= ( set_meet @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ C )
= ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( union_of_subsets @ A @ B )
= ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( relation_rng_as_subset @ A @ B @ C )
= ( relation_rng @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_relset_1) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( relation_dom_as_subset @ A @ B @ C )
= ( relation_dom @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
thf(43,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(45,axiom,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(46,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(49,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(50,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(51,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(52,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(53,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( relation_of2 @ C @ A @ B )
& ( relation @ C )
& ( function @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(55,axiom,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(57,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(58,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(59,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(65,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(66,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
thf(70,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k5_subset_1) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ A @ B ) )
& ( relation @ ( relation_composition @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_relat_1) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_finset_1) ).
thf(77,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(78,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(79,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(81,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(83,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(84,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(89,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(90,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(91,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_relat_1) ).
thf(94,axiom,
! [A: $i,B: $i] :
( ( v3_membered @ A )
=> ( ( v1_membered @ ( set_difference @ A @ B ) )
& ( v2_membered @ ( set_difference @ A @ B ) )
& ( v3_membered @ ( set_difference @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc39_membered) ).
thf(95,axiom,
! [A: $i,B: $i] :
( ( v2_membered @ A )
=> ( ( v1_membered @ ( set_difference @ A @ B ) )
& ( v2_membered @ ( set_difference @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc38_membered) ).
thf(96,axiom,
! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc37_membered) ).
thf(101,axiom,
! [A: $i,B: $i] :
( ( v3_membered @ A )
=> ( ( v1_membered @ ( set_intersection2 @ B @ A ) )
& ( v2_membered @ ( set_intersection2 @ B @ A ) )
& ( v3_membered @ ( set_intersection2 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc32_membered) ).
thf(102,axiom,
! [A: $i,B: $i] :
( ( v3_membered @ A )
=> ( ( v1_membered @ ( set_intersection2 @ A @ B ) )
& ( v2_membered @ ( set_intersection2 @ A @ B ) )
& ( v3_membered @ ( set_intersection2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc31_membered) ).
thf(103,axiom,
! [A: $i,B: $i] :
( ( v2_membered @ A )
=> ( ( v1_membered @ ( set_intersection2 @ B @ A ) )
& ( v2_membered @ ( set_intersection2 @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc30_membered) ).
thf(104,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(105,axiom,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(106,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_relat_1) ).
thf(110,axiom,
! [A: $i,B: $i] :
( ( v2_membered @ A )
=> ( ( v1_membered @ ( set_intersection2 @ A @ B ) )
& ( v2_membered @ ( set_intersection2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc29_membered) ).
thf(111,axiom,
! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( set_intersection2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc28_membered) ).
thf(112,axiom,
! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc27_membered) ).
thf(113,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(114,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(115,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(116,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(117,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(119,axiom,
! [A: $i] :
~ ( empty @ ( succ @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_ordinal1) ).
thf(122,axiom,
! [A: $i] :
( ~ ( empty @ ( singleton @ A ) )
& ( finite @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_finset_1) ).
thf(125,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(126,axiom,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_finset_1) ).
thf(127,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_inverse @ A ) )
& ( relation @ ( relation_inverse @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_relat_1) ).
thf(128,axiom,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_finset_1) ).
thf(129,axiom,
! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ B @ A ) )
& ( relation @ ( relation_composition @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_relat_1) ).
thf(130,axiom,
! [A: $i,B: $i] :
( ( finite @ B )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_finset_1) ).
thf(131,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(132,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(133,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(135,axiom,
? [A: $i] : ( join_semilatt_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_lattices) ).
thf(136,axiom,
? [A: $i] : ( one_sorted_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(137,axiom,
? [A: $i] : ( meet_semilatt_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_lattices) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(144,axiom,
! [A: $i] :
( ( latt_str @ A )
=> ( ( meet_semilatt_str @ A )
& ( join_semilatt_str @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
thf(145,axiom,
! [A: $i] :
( ( join_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_lattices) ).
thf(147,axiom,
! [A: $i] :
( ( meet_semilatt_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_lattices) ).
thf(149,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
thf(150,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
thf(151,axiom,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(153,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
thf(154,axiom,
! [A: $i] : ( relation @ ( identity_relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(155,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_intersection2 @ A @ B @ C ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_subset_1) ).
thf(156,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_rng_as_subset @ A @ B @ C ) @ ( powerset @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relset_1) ).
thf(158,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(162,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_dom_as_subset @ A @ B @ C ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relset_1) ).
thf(163,axiom,
! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(167,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(172,axiom,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_wellord1) ).
thf(174,axiom,
! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_subset_1) ).
thf(176,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( meet @ A @ B @ C ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattices) ).
thf(183,axiom,
! [A: $i] : ( relation @ ( inclusion_relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_wellord2) ).
thf(190,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( join @ A @ B @ C ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattices) ).
thf(197,axiom,
! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
thf(198,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( powerset @ A ) ) )
=> ( ( C
= ( complements_of_subsets @ A @ B ) )
<=> ! [D: $i] :
( ( element @ D @ ( powerset @ A ) )
=> ( ( in @ D @ C )
<=> ( in @ ( subset_complement @ A @ D ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_setfam_1) ).
thf(203,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(206,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation_restriction @ A @ B )
= ( set_intersection2 @ A @ ( cartesian_product2 @ B @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_wellord1) ).
thf(209,axiom,
! [A: $i] :
( ( being_limit_ordinal @ A )
<=> ( A
= ( union @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_ordinal1) ).
thf(212,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
thf(216,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(219,axiom,
! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
thf(220,axiom,
! [A: $i] :
( ( cast_to_subset @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).
thf(225,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(227,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(228,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_relat_1) ).
thf(229,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_pre_topc) ).
thf(230,axiom,
! [A: $i] :
( ( epsilon_connected @ A )
<=> ! [B: $i,C: $i] :
~ ( ( in @ B @ A )
& ( in @ C @ A )
& ~ ( in @ B @ C )
& ( B != C )
& ~ ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_ordinal1) ).
thf(232,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(233,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(235,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
thf(236,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
thf(237,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( A = B )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
<=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_relat_1) ).
thf(238,axiom,
! [A: $i] :
( ( epsilon_transitive @ A )
<=> ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
thf(241,axiom,
! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(242,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(245,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(246,axiom,
! [A: $i,B: $i] :
( ( ( A != empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ C @ D ) ) ) ) )
& ( ( A = empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ( B = empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_setfam_1) ).
thf(247,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
<=> ( subset @ C @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relset_1) ).
thf(249,axiom,
! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
thf(253,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( ( ( ( B = empty_set )
=> ( A = empty_set ) )
=> ( ( quasi_total @ C @ A @ B )
<=> ( A
= ( relation_dom_as_subset @ A @ B @ C ) ) ) )
& ( ( B = empty_set )
=> ( ( A = empty_set )
| ( ( quasi_total @ C @ A @ B )
<=> ( C = empty_set ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_2) ).
thf(256,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( unordered_triple @ A @ B @ C ) )
<=> ! [E: $i] :
( ( in @ E @ D )
<=> ~ ( ( E != A )
& ( E != B )
& ( E != C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_enumset1) ).
thf(266,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(269,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ C )
= ( subset_intersection2 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k5_subset_1) ).
thf(271,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(275,axiom,
! [A: $i] :
( ( v2_membered @ A )
=> ( v1_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_membered) ).
thf(277,axiom,
! [A: $i] :
( ( v3_membered @ A )
=> ( v2_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_membered) ).
thf(283,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(287,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(290,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(292,axiom,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(295,axiom,
! [A: $i] :
( ( v3_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc18_membered) ).
thf(296,axiom,
! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc17_membered) ).
thf(297,axiom,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc16_membered) ).
thf(302,axiom,
! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc11_membered) ).
thf(303,axiom,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( v1_xcmplx_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc10_membered) ).
thf(305,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(306,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(308,axiom,
! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(311,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(313,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(314,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(317,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_relat_1) ).
thf(319,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_difference @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(320,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(327,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(330,axiom,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
thf(332,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(335,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(337,axiom,
! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(342,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_relat_1) ).
thf(345,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).
thf(348,axiom,
! [A: $i] :
( ( A != empty_set )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ A )
=> ( ~ ( in @ C @ B )
=> ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).
thf(349,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(352,axiom,
! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(353,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( B != empty_set )
=> ( ( union_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= ( subset_difference @ A @ ( cast_to_subset @ A ) @ ( meet_of_subsets @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_setfam_1) ).
thf(354,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( B != empty_set )
=> ( ( subset_difference @ A @ ( cast_to_subset @ A ) @ ( union_of_subsets @ A @ B ) )
= ( meet_of_subsets @ A @ ( complements_of_subsets @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_setfam_1) ).
thf(356,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_zfmisc_1) ).
thf(357,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_setfam_1) ).
thf(360,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(363,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ( ( disjoint @ B @ C )
<=> ( subset @ B @ ( subset_complement @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_subset_1) ).
thf(366,axiom,
! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_1) ).
thf(367,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(368,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(370,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( in @ B @ C )
& ( in @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_ordinal1) ).
thf(371,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(372,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
thf(374,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(375,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(376,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(378,axiom,
! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(382,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(387,axiom,
! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ( ( ordinal @ B )
& ( subset @ B @ A ) ) )
=> ( ordinal @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_ordinal1) ).
thf(389,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(391,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(393,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(394,axiom,
! [A: $i] :
? [B: $i] :
( ( relation @ B )
& ( well_orders @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_wellord2) ).
thf(401,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ~ ( ~ ( in @ A @ B )
& ( A != B )
& ~ ( in @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).
thf(403,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
~ ( in @ ( ordered_pair @ E @ D ) @ C ) )
<=> ( ( relation_rng_as_subset @ A @ B @ C )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_relset_1) ).
thf(404,axiom,
! [A: $i,B: $i] :
( ( ordinal @ B )
=> ( ( in @ A @ B )
=> ( ordinal @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_ordinal1) ).
thf(408,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ B @ A )
=> ( ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
~ ( in @ ( ordered_pair @ D @ E ) @ C ) )
<=> ( ( relation_dom_as_subset @ B @ A @ C )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_relset_1) ).
thf(417,axiom,
( ( powerset @ empty_set )
= ( singleton @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(418,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(419,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(422,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
( ( ( in @ D @ B )
& ( subset @ C @ D ) )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_finset_1) ).
thf(423,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(426,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( subset @ A @ B )
=> ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t178_relat_1) ).
thf(428,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_restriction @ C @ B ) )
<=> ( ( in @ A @ C )
& ( in @ A @ ( cartesian_product2 @ B @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_wellord1) ).
thf(429,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( relation_of2_as_subset @ D @ C @ A )
=> ( ( subset @ A @ B )
=> ( relation_of2_as_subset @ D @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_1) ).
thf(433,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( subset_intersection2 @ ( the_carrier @ A ) @ B @ ( cast_as_carrier_subset @ A ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_pre_topc) ).
thf(434,axiom,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_finset_1) ).
thf(435,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( relation_of2_as_subset @ D @ C @ A )
=> ( ( subset @ ( relation_rng @ D ) @ B )
=> ( relation_of2_as_subset @ D @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relset_1) ).
thf(444,axiom,
! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( finite @ B ) )
=> ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_finset_1) ).
thf(445,axiom,
! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(446,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(448,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_pre_topc) ).
thf(449,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(451,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(453,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_relat_1) ).
thf(457,axiom,
! [A: $i] : ( in @ A @ ( succ @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).
thf(458,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(465,axiom,
! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( in @ C @ B )
<=> ( ( in @ C @ A )
& ( ordinal @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e6_22__wellord2) ).
thf(469,axiom,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ ( cartesian_product2 @ A @ B ) )
& ? [E: $i,F: $i] :
( ( ( ordered_pair @ E @ F )
= D )
& ( in @ E @ A )
& ( F
= ( singleton @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e16_22__wellord2__1) ).
thf(470,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ( relation @ B ) )
=> ! [C: $i] :
? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ( ( in @ E @ ( cartesian_product2 @ A @ C ) )
& ? [F: $i,G: $i] :
( ( ( ordered_pair @ F @ G )
= E )
& ( in @ F @ A )
& ? [H: $i] :
( ( F = H )
& ( in @ G @ H )
& ! [I: $i] :
( ( in @ I @ H )
=> ( in @ ( ordered_pair @ G @ I ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e10_24__wellord2__1) ).
thf(477,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l71_subset_1) ).
thf(478,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
thf(479,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(480,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
thf(482,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_zfmisc_1) ).
thf(484,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_subset_1) ).
thf(485,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_xboole_1) ).
thf(487,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(490,axiom,
! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
thf(491,axiom,
! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).
thf(492,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l23_zfmisc_1) ).
thf(493,axiom,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(495,conjecture,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( subset_complement @ ( the_carrier @ A ) @ B )
= ( subset_difference @ ( the_carrier @ A ) @ ( cast_as_carrier_subset @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_pre_topc) ).
thf(496,negated_conjecture,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( subset_complement @ ( the_carrier @ A ) @ B )
= ( subset_difference @ ( the_carrier @ A ) @ ( cast_as_carrier_subset @ A ) @ B ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[495]) ).
thf(497,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( subset_complement @ ( the_carrier @ A ) @ B )
= ( subset_difference @ ( the_carrier @ A ) @ ( cast_as_carrier_subset @ A ) @ B ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[496]) ).
thf(498,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
( ( subset @ E @ C )
=> ( in @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(499,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(500,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ( in @ D @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(501,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(502,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(503,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(504,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(505,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(506,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(507,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(508,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(509,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( B = C )
& ( ordinal @ C )
& ( B = D )
& ( ordinal @ D ) )
=> ( C = D ) )
=> ? [B: $i] :
! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ D @ A )
& ( D = C )
& ( ordinal @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(510,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i,E: $i] :
( ( ( C = D )
& ? [F: $i,G: $i] :
( ( ( ordered_pair @ F @ G )
= D )
& ( in @ F @ A )
& ( G
= ( singleton @ F ) ) )
& ( C = E )
& ? [H: $i,I: $i] :
( ( ( ordered_pair @ H @ I )
= E )
& ( in @ H @ A )
& ( I
= ( singleton @ H ) ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ E @ ( cartesian_product2 @ A @ B ) )
& ( E = D )
& ? [J: $i,K: $i] :
( ( ( ordered_pair @ J @ K )
= D )
& ( in @ J @ A )
& ( K
= ( singleton @ J ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(511,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i,D: $i] :
( ( ( in @ B @ A )
& ( C
= ( singleton @ B ) )
& ( in @ B @ A )
& ( D
= ( singleton @ B ) ) )
=> ( C = D ) )
=> ? [B: $i] :
! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ D @ A )
& ( in @ D @ A )
& ( C
= ( singleton @ D ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(512,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ( relation @ B ) )
=> ! [C: $i] :
( ! [D: $i,E: $i,F: $i] :
( ( ( D = E )
& ? [G: $i,H: $i] :
( ( ( ordered_pair @ G @ H )
= E )
& ( in @ G @ A )
& ? [I: $i] :
( ( G = I )
& ( in @ H @ I )
& ! [J: $i] :
( ( in @ J @ I )
=> ( in @ ( ordered_pair @ H @ J ) @ B ) ) ) )
& ( D = F )
& ? [K: $i,L: $i] :
( ( ( ordered_pair @ K @ L )
= F )
& ( in @ K @ A )
& ? [M: $i] :
( ( K = M )
& ( in @ L @ M )
& ! [N: $i] :
( ( in @ N @ M )
=> ( in @ ( ordered_pair @ L @ N ) @ B ) ) ) ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ? [F: $i] :
( ( in @ F @ ( cartesian_product2 @ A @ C ) )
& ( F = E )
& ? [O: $i,P: $i] :
( ( ( ordered_pair @ O @ P )
= E )
& ( in @ O @ A )
& ? [Q: $i] :
( ( O = Q )
& ( in @ P @ Q )
& ! [R: $i] :
( ( in @ R @ Q )
=> ( in @ ( ordered_pair @ P @ R ) @ B ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(513,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ( relation @ B ) )
=> ( ! [C: $i,D: $i,E: $i] :
( ( ( in @ C @ A )
& ? [F: $i] :
( ( C = F )
& ( in @ D @ F )
& ! [G: $i] :
( ( in @ G @ F )
=> ( in @ ( ordered_pair @ D @ G ) @ B ) ) )
& ( in @ C @ A )
& ? [H: $i] :
( ( C = H )
& ( in @ E @ H )
& ! [I: $i] :
( ( in @ I @ H )
=> ( in @ ( ordered_pair @ E @ I ) @ B ) ) ) )
=> ( D = E ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ E @ A )
& ( in @ E @ A )
& ? [J: $i] :
( ( E = J )
& ( in @ D @ J )
& ! [K: $i] :
( ( in @ K @ J )
=> ( in @ ( ordered_pair @ D @ K ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(514,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(515,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
<=> ( relation_of2 @ C @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(516,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( relation_rng_as_subset @ A @ B @ C )
= ( relation_rng @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(517,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( relation_dom_as_subset @ A @ B @ C )
= ( relation_dom @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(518,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(519,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(520,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(521,plain,
( ( ! [A: $i,B: $i] :
? [C: $i] :
( ( relation_of2 @ C @ A @ B )
& ( relation @ C )
& ( function @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(522,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(523,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(524,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(525,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(526,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(527,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(528,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(529,plain,
( ( ! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ A @ B ) )
& ( relation @ ( relation_composition @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(530,plain,
( ( ! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(531,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(532,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(533,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(534,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(535,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(536,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(537,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(538,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(539,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(540,plain,
( ( ! [A: $i,B: $i] :
( ( v3_membered @ A )
=> ( ( v1_membered @ ( set_difference @ A @ B ) )
& ( v2_membered @ ( set_difference @ A @ B ) )
& ( v3_membered @ ( set_difference @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(541,plain,
( ( ! [A: $i,B: $i] :
( ( v2_membered @ A )
=> ( ( v1_membered @ ( set_difference @ A @ B ) )
& ( v2_membered @ ( set_difference @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(542,plain,
( ( ! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(543,plain,
( ( ! [A: $i,B: $i] :
( ( v3_membered @ A )
=> ( ( v1_membered @ ( set_intersection2 @ B @ A ) )
& ( v2_membered @ ( set_intersection2 @ B @ A ) )
& ( v3_membered @ ( set_intersection2 @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(544,plain,
( ( ! [A: $i,B: $i] :
( ( v3_membered @ A )
=> ( ( v1_membered @ ( set_intersection2 @ A @ B ) )
& ( v2_membered @ ( set_intersection2 @ A @ B ) )
& ( v3_membered @ ( set_intersection2 @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(545,plain,
( ( ! [A: $i,B: $i] :
( ( v2_membered @ A )
=> ( ( v1_membered @ ( set_intersection2 @ B @ A ) )
& ( v2_membered @ ( set_intersection2 @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(546,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(547,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(548,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(549,plain,
( ( ! [A: $i,B: $i] :
( ( v2_membered @ A )
=> ( ( v1_membered @ ( set_intersection2 @ A @ B ) )
& ( v2_membered @ ( set_intersection2 @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(550,plain,
( ( ! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( set_intersection2 @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(551,plain,
( ( ! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(552,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(553,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(554,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(555,plain,
( ( ! [A: $i] :
~ ( empty @ ( succ @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(556,plain,
( ( ! [A: $i] :
( ~ ( empty @ ( singleton @ A ) )
& ( finite @ ( singleton @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(557,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(558,plain,
( ( ! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(559,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_inverse @ A ) )
& ( relation @ ( relation_inverse @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(560,plain,
( ( ! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(561,plain,
( ( ! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ B @ A ) )
& ( relation @ ( relation_composition @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(562,plain,
( ( ! [A: $i,B: $i] :
( ( finite @ B )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(563,plain,
( ( ! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(564,plain,
( ( ! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(565,plain,
( ( ? [A: $i] : ( join_semilatt_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(566,plain,
( ( ? [A: $i] : ( meet_semilatt_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(567,plain,
( ( ! [A: $i] :
( ( latt_str @ A )
=> ( ( meet_semilatt_str @ A )
& ( join_semilatt_str @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(568,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(569,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(570,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(571,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(572,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(573,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(574,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( meet_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( meet @ A @ B @ C ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(575,plain,
( ( ! [A: $i] : ( relation @ ( inclusion_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(576,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty_carrier @ A )
& ( join_semilatt_str @ A )
& ( element @ B @ ( the_carrier @ A ) )
& ( element @ C @ ( the_carrier @ A ) ) )
=> ( element @ ( join @ A @ B @ C ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(577,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(578,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(579,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation_restriction @ A @ B )
= ( set_intersection2 @ A @ ( cartesian_product2 @ B @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(580,plain,
( ( ! [A: $i] :
( ( being_limit_ordinal @ A )
<=> ( A
= ( union @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(581,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(582,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(583,plain,
( ( ! [A: $i] :
( ( cast_to_subset @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(584,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(585,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(586,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(587,plain,
( ( ! [A: $i] :
( ( epsilon_connected @ A )
<=> ! [B: $i,C: $i] :
~ ( ( in @ B @ A )
& ( in @ C @ A )
& ~ ( in @ B @ C )
& ( B != C )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(588,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(589,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(590,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(591,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( A = B )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
<=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(592,plain,
( ( ! [A: $i] :
( ( epsilon_transitive @ A )
<=> ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(593,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(594,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(595,plain,
( ( ! [A: $i,B: $i] :
( ( ( A != empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ C @ D ) ) ) ) )
& ( ( A = empty_set )
=> ( ( B
= ( set_meet @ A ) )
<=> ( B = empty_set ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(596,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
<=> ( subset @ C @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(597,plain,
( ( ! [A: $i] :
( ( relation @ A )
<=> ! [B: $i] :
~ ( ( in @ B @ A )
& ! [C: $i,D: $i] :
( B
!= ( ordered_pair @ C @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(598,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( ( ( ( B = empty_set )
=> ( A = empty_set ) )
=> ( ( quasi_total @ C @ A @ B )
<=> ( A
= ( relation_dom_as_subset @ A @ B @ C ) ) ) )
& ( ( B = empty_set )
=> ( ( A = empty_set )
| ( ( quasi_total @ C @ A @ B )
<=> ( C = empty_set ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(599,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( D
= ( unordered_triple @ A @ B @ C ) )
<=> ! [E: $i] :
( ( in @ E @ D )
<=> ~ ( ( E != A )
& ( E != B )
& ( E != C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(600,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(601,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(602,plain,
( ( ! [A: $i] :
( ( v2_membered @ A )
=> ( v1_membered @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(603,plain,
( ( ! [A: $i] :
( ( v3_membered @ A )
=> ( v2_membered @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277]) ).
thf(604,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(605,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(606,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(607,plain,
( ( ! [A: $i] :
( ( v3_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(608,plain,
( ( ! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(609,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(610,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(611,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(612,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(613,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(614,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(615,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(616,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(617,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(618,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[330]) ).
thf(619,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(620,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(621,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(622,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(623,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(624,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(625,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( B != empty_set )
=> ( ( union_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= ( subset_difference @ A @ ( cast_to_subset @ A ) @ ( meet_of_subsets @ A @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(626,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( B != empty_set )
=> ( ( subset_difference @ A @ ( cast_to_subset @ A ) @ ( union_of_subsets @ A @ B ) )
= ( meet_of_subsets @ A @ ( complements_of_subsets @ A @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(627,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(628,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(629,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366]) ).
thf(630,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(631,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368]) ).
thf(632,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( in @ B @ C )
& ( in @ C @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[370]) ).
thf(633,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371]) ).
thf(634,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[372]) ).
thf(635,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374]) ).
thf(636,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[375]) ).
thf(637,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[376]) ).
thf(638,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[378]) ).
thf(639,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[382]) ).
thf(640,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ( ( ordinal @ B )
& ( subset @ B @ A ) ) )
=> ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387]) ).
thf(641,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[389]) ).
thf(642,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391]) ).
thf(643,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[393]) ).
thf(644,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( relation @ B )
& ( well_orders @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(645,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ~ ( ~ ( in @ A @ B )
& ( A != B )
& ~ ( in @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[401]) ).
thf(646,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
~ ( in @ ( ordered_pair @ E @ D ) @ C ) )
<=> ( ( relation_rng_as_subset @ A @ B @ C )
= B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[403]) ).
thf(647,plain,
( ( ! [A: $i,B: $i] :
( ( ordinal @ B )
=> ( ( in @ A @ B )
=> ( ordinal @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[404]) ).
thf(648,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ B @ A )
=> ( ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
~ ( in @ ( ordered_pair @ D @ E ) @ C ) )
<=> ( ( relation_dom_as_subset @ B @ A @ C )
= B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[408]) ).
thf(649,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[418]) ).
thf(650,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[419]) ).
thf(651,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
( ( ( in @ D @ B )
& ( subset @ C @ D ) )
=> ( D = C ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[422]) ).
thf(652,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[423]) ).
thf(653,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( subset @ A @ B )
=> ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[426]) ).
thf(654,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_restriction @ C @ B ) )
<=> ( ( in @ A @ C )
& ( in @ A @ ( cartesian_product2 @ B @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[428]) ).
thf(655,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( relation_of2_as_subset @ D @ C @ A )
=> ( ( subset @ A @ B )
=> ( relation_of2_as_subset @ D @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[429]) ).
thf(656,plain,
( ( ! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[434]) ).
thf(657,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( relation_of2_as_subset @ D @ C @ A )
=> ( ( subset @ ( relation_rng @ D ) @ B )
=> ( relation_of2_as_subset @ D @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[435]) ).
thf(658,plain,
( ( ! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( finite @ B ) )
=> ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[444]) ).
thf(659,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[445]) ).
thf(660,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446]) ).
thf(661,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(662,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[451]) ).
thf(663,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[453]) ).
thf(664,plain,
( ( ! [A: $i] : ( in @ A @ ( succ @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(665,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[458]) ).
thf(666,plain,
( ( ! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( in @ C @ B )
<=> ( ( in @ C @ A )
& ( ordinal @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[465]) ).
thf(667,plain,
( ( ! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ ( cartesian_product2 @ A @ B ) )
& ? [E: $i,F: $i] :
( ( ( ordered_pair @ E @ F )
= D )
& ( in @ E @ A )
& ( F
= ( singleton @ E ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[469]) ).
thf(668,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ( relation @ B ) )
=> ! [C: $i] :
? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ( ( in @ E @ ( cartesian_product2 @ A @ C ) )
& ? [F: $i,G: $i] :
( ( ( ordered_pair @ F @ G )
= E )
& ( in @ F @ A )
& ? [H: $i] :
( ( F = H )
& ( in @ G @ H )
& ! [I: $i] :
( ( in @ I @ H )
=> ( in @ ( ordered_pair @ G @ I ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[470]) ).
thf(669,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[478]) ).
thf(670,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[479]) ).
thf(671,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[480]) ).
thf(672,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[482]) ).
thf(673,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[485]) ).
thf(674,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[487]) ).
thf(675,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[490]) ).
thf(676,plain,
( ( ! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[491]) ).
thf(677,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[492]) ).
thf(678,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[493]) ).
thf(679,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(680,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(681,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(682,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(683,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(684,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(685,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( meet_of_subsets @ A @ B )
= ( set_meet @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(686,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ C )
= ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(687,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( union_of_subsets @ A @ B )
= ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(688,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(689,plain,
( ( ? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(690,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(691,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(692,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(693,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(694,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(695,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(696,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(697,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(698,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(699,plain,
( ( ? [A: $i] : ( one_sorted_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(700,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(701,plain,
( ( ! [A: $i] :
( ( join_semilatt_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(702,plain,
( ( ! [A: $i] :
( ( meet_semilatt_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(703,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(704,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(705,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(706,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( element @ ( subset_intersection2 @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(707,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(708,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_rng_as_subset @ A @ B @ C ) @ ( powerset @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(709,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( element @ ( relation_dom_as_subset @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(710,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(711,plain,
( ( ! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(712,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(713,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ ( powerset @ A ) ) )
=> ( ( C
= ( complements_of_subsets @ A @ B ) )
<=> ! [D: $i] :
( ( element @ D @ ( powerset @ A ) )
=> ( ( in @ D @ C )
<=> ( in @ ( subset_complement @ A @ D ) @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(714,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(715,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(716,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(717,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(718,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ A ) )
& ( element @ C @ ( powerset @ A ) ) )
=> ( ( subset_intersection2 @ A @ B @ C )
= ( subset_intersection2 @ A @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[269]) ).
thf(719,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(720,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(721,plain,
( ( ! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(722,plain,
( ( ! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(723,plain,
( ( ! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( v1_xcmplx_0 @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(724,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(725,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ~ ( ( in @ B @ ( subset_complement @ A @ C ) )
& ( in @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(726,plain,
( ( ! [A: $i] :
( ( A != empty_set )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ A )
=> ( ~ ( in @ C @ B )
=> ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(727,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
=> ~ ( ( B != empty_set )
& ( ( complements_of_subsets @ A @ B )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357]) ).
thf(728,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( powerset @ A ) )
=> ( ( disjoint @ B @ C )
<=> ( subset @ B @ ( subset_complement @ A @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[363]) ).
thf(729,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[417]) ).
thf(730,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( subset_intersection2 @ ( the_carrier @ A ) @ B @ ( cast_as_carrier_subset @ A ) )
= B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[433]) ).
thf(731,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[448]) ).
thf(732,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[477]) ).
thf(733,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[484]) ).
thf(734,plain,
( ( ( one_sorted_str @ sK1_A )
=> ! [SY588: $i] :
( ( element @ SY588 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
=> ( ( subset_complement @ ( the_carrier @ sK1_A ) @ SY588 )
= ( subset_difference @ ( the_carrier @ sK1_A ) @ ( cast_as_carrier_subset @ sK1_A ) @ SY588 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[497]) ).
thf(735,plain,
( ( one_sorted_str @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[734]) ).
thf(736,plain,
( ( ! [SY588: $i] :
( ( element @ SY588 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
=> ( ( subset_complement @ ( the_carrier @ sK1_A ) @ SY588 )
= ( subset_difference @ ( the_carrier @ sK1_A ) @ ( cast_as_carrier_subset @ sK1_A ) @ SY588 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[734]) ).
thf(737,plain,
( ( ~ ! [SY588: $i] :
( ( element @ SY588 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
=> ( ( subset_complement @ ( the_carrier @ sK1_A ) @ SY588 )
= ( subset_difference @ ( the_carrier @ sK1_A ) @ ( cast_as_carrier_subset @ sK1_A ) @ SY588 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[736]) ).
thf(738,plain,
( ( ( element @ sK2_SY588 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
& ( ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY588 )
!= ( subset_difference @ ( the_carrier @ sK1_A ) @ ( cast_as_carrier_subset @ sK1_A ) @ sK2_SY588 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[737]) ).
thf(739,plain,
( ( ! [A: $i] :
( ! [SY589: $i] :
( ~ ( subset @ SY589 @ ( sK3_B @ A ) )
| ( are_equipotent @ SY589 @ ( sK3_B @ A ) )
| ( in @ SY589 @ ( sK3_B @ A ) ) )
& ! [SY590: $i] :
( ( ! [SY595: $i] :
( ~ ( subset @ SY595 @ SY590 )
| ( in @ SY595 @ ( sK4_SY591 @ SY590 @ A ) ) )
& ( in @ ( sK4_SY591 @ SY590 @ A ) @ ( sK3_B @ A ) ) )
| ~ ( in @ SY590 @ ( sK3_B @ A ) ) )
& ! [SY593: $i,SY594: $i] :
( ~ ( in @ SY593 @ ( sK3_B @ A ) )
| ~ ( subset @ SY594 @ SY593 )
| ( in @ SY594 @ ( sK3_B @ A ) ) )
& ( in @ A @ ( sK3_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[498]) ).
thf(740,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[499]) ).
thf(741,plain,
( ( ! [A: $i,B: $i] :
( ( ! [SY596: $i] :
( ~ ( in @ SY596 @ B )
| ~ ( in @ SY596 @ ( sK5_C @ B @ A ) ) )
& ( in @ ( sK5_C @ B @ A ) @ B ) )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[500]) ).
thf(742,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[501]) ).
thf(743,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[502]) ).
thf(744,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK6_C @ B @ A ) @ A )
| ~ ( in @ ( sK6_C @ B @ A ) @ B ) )
& ( ( in @ ( sK6_C @ B @ A ) @ A )
| ( in @ ( sK6_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[505]) ).
thf(745,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[508]) ).
thf(746,plain,
( ( ( sK12_REN
| ! [A: $i] :
( ! [SY597: $i] :
( ! [D: $i] :
( ( D != SY597 )
| ~ ( in @ D @ A ) )
| ~ ( ordinal @ SY597 )
| ( in @ SY597 @ ( sK7_B @ A ) ) )
& ! [SY599: $i] :
( ~ ( in @ SY599 @ ( sK7_B @ A ) )
| ( ( ( sK8_D @ SY599 @ A )
= SY599 )
& ( in @ ( sK8_D @ SY599 @ A ) @ A )
& ( ordinal @ SY599 ) ) ) ) )
& ( sK12_REN
=> ( ( sK9_B = sK10_SY601 )
& ( ordinal @ sK10_SY601 )
& ( sK9_B = sK11_SY603 )
& ( ordinal @ sK11_SY603 )
& ( sK10_SY601 != sK11_SY603 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[509]) ).
thf(747,plain,
( ( ! [A: $i] :
( ( ( ( sK17_C @ A )
= ( sK18_SY613 @ A ) )
& ( ( ordered_pair @ ( sK22_SY620 @ A ) @ ( sK23_SY629 @ A ) )
= ( sK18_SY613 @ A ) )
& ( in @ ( sK22_SY620 @ A ) @ A )
& ( ( sK23_SY629 @ A )
= ( singleton @ ( sK22_SY620 @ A ) ) )
& ( ( sK17_C @ A )
= ( sK19_SY619 @ A ) )
& ( ( ordered_pair @ ( sK20_SY626 @ A ) @ ( sK21_SY628 @ A ) )
= ( sK19_SY619 @ A ) )
& ( in @ ( sK20_SY626 @ A ) @ A )
& ( ( sK21_SY628 @ A )
= ( singleton @ ( sK20_SY626 @ A ) ) )
& ( ( sK18_SY613 @ A )
!= ( sK19_SY619 @ A ) ) )
| ! [B: $i] :
( ! [SY604: $i] :
( ! [E: $i] :
( ( E != SY604 )
| ~ ( in @ E @ ( cartesian_product2 @ A @ B ) ) )
| ! [J: $i,K: $i] :
( ( ( ordered_pair @ J @ K )
!= SY604 )
| ~ ( in @ J @ A )
| ( K
!= ( singleton @ J ) ) )
| ( in @ SY604 @ ( sK13_C @ B @ A ) ) )
& ! [SY608: $i] :
( ~ ( in @ SY608 @ ( sK13_C @ B @ A ) )
| ( ( ( sK16_E @ SY608 @ B @ A )
= SY608 )
& ( in @ ( sK16_E @ SY608 @ B @ A ) @ ( cartesian_product2 @ A @ B ) )
& ( ( ordered_pair @ ( sK14_J @ SY608 @ B @ A ) @ ( sK15_SY612 @ SY608 @ B @ A ) )
= SY608 )
& ( in @ ( sK14_J @ SY608 @ B @ A ) @ A )
& ( ( sK15_SY612 @ SY608 @ B @ A )
= ( singleton @ ( sK14_J @ SY608 @ B @ A ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[510]) ).
thf(748,plain,
( ( ! [A: $i] :
( ( ( ( sK27_SY634 @ A )
= ( singleton @ ( sK26_B @ A ) ) )
& ( in @ ( sK26_B @ A ) @ A )
& ( in @ ( sK26_B @ A ) @ A )
& ( ( sK28_SY636 @ A )
= ( singleton @ ( sK26_B @ A ) ) )
& ( ( sK27_SY634 @ A )
!= ( sK28_SY636 @ A ) ) )
| ( ! [SY630: $i] :
( ! [D: $i] :
( ~ ( in @ D @ A )
| ( SY630
!= ( singleton @ D ) ) )
| ( in @ SY630 @ ( sK24_B @ A ) ) )
& ! [SY632: $i] :
( ~ ( in @ SY632 @ ( sK24_B @ A ) )
| ( ( in @ ( sK25_D @ SY632 @ A ) @ A )
& ( SY632
= ( singleton @ ( sK25_D @ SY632 @ A ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[511]) ).
thf(749,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ~ ( relation @ B )
| ( ( ( sK35_D @ B @ A )
= ( sK36_SY655 @ B @ A ) )
& ( ( ordered_pair @ ( sK41_SY666 @ B @ A ) @ ( sK42_SY688 @ B @ A ) )
= ( sK36_SY655 @ B @ A ) )
& ( in @ ( sK41_SY666 @ B @ A ) @ A )
& ! [SY693: $i] :
( ~ ( in @ SY693 @ ( sK43_SY691 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK42_SY688 @ B @ A ) @ SY693 ) @ B ) )
& ( ( sK41_SY666 @ B @ A )
= ( sK43_SY691 @ B @ A ) )
& ( in @ ( sK42_SY688 @ B @ A ) @ ( sK43_SY691 @ B @ A ) )
& ( ( sK35_D @ B @ A )
= ( sK37_SY665 @ B @ A ) )
& ( ( ordered_pair @ ( sK38_SY678 @ B @ A ) @ ( sK39_SY682 @ B @ A ) )
= ( sK37_SY665 @ B @ A ) )
& ( in @ ( sK38_SY678 @ B @ A ) @ A )
& ! [SY687: $i] :
( ~ ( in @ SY687 @ ( sK40_SY685 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK39_SY682 @ B @ A ) @ SY687 ) @ B ) )
& ( ( sK38_SY678 @ B @ A )
= ( sK40_SY685 @ B @ A ) )
& ( in @ ( sK39_SY682 @ B @ A ) @ ( sK40_SY685 @ B @ A ) )
& ( ( sK36_SY655 @ B @ A )
!= ( sK37_SY665 @ B @ A ) ) )
| ! [C: $i] :
( ! [SY637: $i] :
( ! [F: $i] :
( ( F != SY637 )
| ~ ( in @ F @ ( cartesian_product2 @ A @ C ) ) )
| ! [O: $i,P: $i] :
( ( ( ordered_pair @ O @ P )
!= SY637 )
| ~ ( in @ O @ A )
| ! [Q: $i] :
( ( ( in @ ( sK34_R @ Q @ P @ O @ SY637 @ C @ B @ A ) @ Q )
& ~ ( in @ ( ordered_pair @ P @ ( sK34_R @ Q @ P @ O @ SY637 @ C @ B @ A ) ) @ B ) )
| ( O != Q )
| ~ ( in @ P @ Q ) ) )
| ( in @ SY637 @ ( sK29_D @ C @ B @ A ) ) )
& ! [SY643: $i] :
( ~ ( in @ SY643 @ ( sK29_D @ C @ B @ A ) )
| ( ( ( sK33_F @ SY643 @ C @ B @ A )
= SY643 )
& ( in @ ( sK33_F @ SY643 @ C @ B @ A ) @ ( cartesian_product2 @ A @ C ) )
& ( ( ordered_pair @ ( sK30_O @ SY643 @ C @ B @ A ) @ ( sK31_SY649 @ SY643 @ C @ B @ A ) )
= SY643 )
& ( in @ ( sK30_O @ SY643 @ C @ B @ A ) @ A )
& ! [SY654: $i] :
( ~ ( in @ SY654 @ ( sK32_SY652 @ SY643 @ C @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY643 @ C @ B @ A ) @ SY654 ) @ B ) )
& ( ( sK30_O @ SY643 @ C @ B @ A )
= ( sK32_SY652 @ SY643 @ C @ B @ A ) )
& ( in @ ( sK31_SY649 @ SY643 @ C @ B @ A ) @ ( sK32_SY652 @ SY643 @ C @ B @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[512]) ).
thf(750,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ~ ( relation @ B )
| ( ! [SY721: $i] :
( ~ ( in @ SY721 @ ( sK52_SY712 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK49_SY705 @ B @ A ) @ SY721 ) @ B ) )
& ( ( sK48_C @ B @ A )
= ( sK52_SY712 @ B @ A ) )
& ( in @ ( sK49_SY705 @ B @ A ) @ ( sK52_SY712 @ B @ A ) )
& ( in @ ( sK48_C @ B @ A ) @ A )
& ( in @ ( sK48_C @ B @ A ) @ A )
& ! [SY720: $i] :
( ~ ( in @ SY720 @ ( sK51_SY718 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK50_SY711 @ B @ A ) @ SY720 ) @ B ) )
& ( ( sK48_C @ B @ A )
= ( sK51_SY718 @ B @ A ) )
& ( in @ ( sK50_SY711 @ B @ A ) @ ( sK51_SY718 @ B @ A ) )
& ( ( sK49_SY705 @ B @ A )
!= ( sK50_SY711 @ B @ A ) ) )
| ( ! [SY694: $i] :
( ! [E: $i] :
( ~ ( in @ E @ A )
| ! [J: $i] :
( ( ( in @ ( sK47_K @ J @ E @ SY694 @ B @ A ) @ J )
& ~ ( in @ ( ordered_pair @ SY694 @ ( sK47_K @ J @ E @ SY694 @ B @ A ) ) @ B ) )
| ( E != J )
| ~ ( in @ SY694 @ J ) ) )
| ( in @ SY694 @ ( sK44_C @ B @ A ) ) )
& ! [SY698: $i] :
( ~ ( in @ SY698 @ ( sK44_C @ B @ A ) )
| ( ( in @ ( sK45_E @ SY698 @ B @ A ) @ A )
& ! [SY704: $i] :
( ~ ( in @ SY704 @ ( sK46_SY702 @ SY698 @ B @ A ) )
| ( in @ ( ordered_pair @ SY698 @ SY704 ) @ B ) )
& ( ( sK45_E @ SY698 @ B @ A )
= ( sK46_SY702 @ SY698 @ B @ A ) )
& ( in @ SY698 @ ( sK46_SY702 @ SY698 @ B @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[513]) ).
thf(751,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[514]) ).
thf(752,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( relation_of2_as_subset @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[515]) ).
thf(753,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( ( relation_rng_as_subset @ A @ B @ C )
= ( relation_rng @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[516]) ).
thf(754,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( ( relation_dom_as_subset @ A @ B @ C )
= ( relation_dom @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[517]) ).
thf(755,plain,
( ( ( relation @ sK53_A )
& ( relation_empty_yielding @ sK53_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[518]) ).
thf(756,plain,
( ( ~ ( empty @ sK54_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[519]) ).
thf(757,plain,
( ( ~ ( empty @ sK55_A )
& ( relation @ sK55_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[520]) ).
thf(758,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ ( sK56_C @ B @ A ) )
& ( relation_of2 @ ( sK56_C @ B @ A ) @ A @ B )
& ( function @ ( sK56_C @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[521]) ).
thf(759,plain,
( ( ( empty @ sK57_A )
& ( relation @ sK57_A )
& ( function @ sK57_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[522]) ).
thf(760,plain,
( ( empty @ sK58_A )
= $true ),
inference(extcnf_combined,[status(esa)],[523]) ).
thf(761,plain,
( ( ( empty @ sK59_A )
& ( relation @ sK59_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[524]) ).
thf(762,plain,
( ( ( function @ sK60_A )
& ( relation @ sK60_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[525]) ).
thf(763,plain,
( ( ~ ( empty @ sK61_A )
& ( finite @ sK61_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[526]) ).
thf(764,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[527]) ).
thf(765,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[528]) ).
thf(766,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( empty @ ( relation_composition @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[529]) ).
thf(767,plain,
( ( ! [A: $i,B: $i] :
( ~ ( finite @ A )
| ~ ( finite @ B )
| ( finite @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[530]) ).
thf(768,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[531]) ).
thf(769,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[532]) ).
thf(770,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[533]) ).
thf(771,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[534]) ).
thf(772,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[535]) ).
thf(773,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[537]) ).
thf(774,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[539]) ).
thf(775,plain,
( ( ! [A: $i] :
( ~ ( v3_membered @ A )
| ! [B: $i] : ( v1_membered @ ( set_difference @ A @ B ) ) )
& ! [A: $i] :
( ~ ( v3_membered @ A )
| ! [B: $i] : ( v2_membered @ ( set_difference @ A @ B ) ) )
& ! [A: $i] :
( ~ ( v3_membered @ A )
| ! [B: $i] : ( v3_membered @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[540]) ).
thf(776,plain,
( ( ! [A: $i] :
( ~ ( v2_membered @ A )
| ! [B: $i] : ( v1_membered @ ( set_difference @ A @ B ) ) )
& ! [A: $i] :
( ~ ( v2_membered @ A )
| ! [B: $i] : ( v2_membered @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[541]) ).
thf(777,plain,
( ( ! [A: $i] :
( ~ ( v1_membered @ A )
| ! [B: $i] : ( v1_membered @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[542]) ).
thf(778,plain,
( ( ! [A: $i] :
( ~ ( v3_membered @ A )
| ! [B: $i] : ( v1_membered @ ( set_intersection2 @ B @ A ) ) )
& ! [A: $i] :
( ~ ( v3_membered @ A )
| ! [B: $i] : ( v2_membered @ ( set_intersection2 @ B @ A ) ) )
& ! [A: $i] :
( ~ ( v3_membered @ A )
| ! [B: $i] : ( v3_membered @ ( set_intersection2 @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[543]) ).
thf(779,plain,
( ( ! [A: $i] :
( ~ ( v3_membered @ A )
| ! [B: $i] : ( v1_membered @ ( set_intersection2 @ A @ B ) ) )
& ! [A: $i] :
( ~ ( v3_membered @ A )
| ! [B: $i] : ( v2_membered @ ( set_intersection2 @ A @ B ) ) )
& ! [A: $i] :
( ~ ( v3_membered @ A )
| ! [B: $i] : ( v3_membered @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[544]) ).
thf(780,plain,
( ( ! [A: $i] :
( ~ ( v2_membered @ A )
| ! [B: $i] : ( v1_membered @ ( set_intersection2 @ B @ A ) ) )
& ! [A: $i] :
( ~ ( v2_membered @ A )
| ! [B: $i] : ( v2_membered @ ( set_intersection2 @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[545]) ).
thf(781,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[546]) ).
thf(782,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[548]) ).
thf(783,plain,
( ( ! [A: $i] :
( ~ ( v2_membered @ A )
| ! [B: $i] : ( v1_membered @ ( set_intersection2 @ A @ B ) ) )
& ! [A: $i] :
( ~ ( v2_membered @ A )
| ! [B: $i] : ( v2_membered @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[549]) ).
thf(784,plain,
( ( ! [A: $i] :
( ~ ( v1_membered @ A )
| ! [B: $i] : ( v1_membered @ ( set_intersection2 @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[550]) ).
thf(785,plain,
( ( ! [A: $i] :
( ~ ( v1_membered @ A )
| ! [B: $i] : ( v1_membered @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[551]) ).
thf(786,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[554]) ).
thf(787,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) )
& ! [A: $i] : ( finite @ ( singleton @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[556]) ).
thf(788,plain,
( ( ! [A: $i] :
( ~ ( finite @ A )
| ! [B: $i] : ( finite @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[558]) ).
thf(789,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_inverse @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[559]) ).
thf(790,plain,
( ( ! [A: $i] :
( ~ ( finite @ A )
| ! [B: $i] : ( finite @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[560]) ).
thf(791,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( empty @ ( relation_composition @ B @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[561]) ).
thf(792,plain,
( ( ! [A: $i,B: $i] :
( ~ ( finite @ B )
| ( finite @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[562]) ).
thf(793,plain,
( ( ! [A: $i,B: $i] : ( relation_of2_as_subset @ ( sK62_C @ B @ A ) @ A @ B ) )
= $true ),
inference(extcnf_combined,[status(esa)],[563]) ).
thf(794,plain,
( ( ! [A: $i,B: $i] : ( relation_of2 @ ( sK63_C @ B @ A ) @ A @ B ) )
= $true ),
inference(extcnf_combined,[status(esa)],[564]) ).
thf(795,plain,
( ( join_semilatt_str @ sK64_A )
= $true ),
inference(extcnf_combined,[status(esa)],[565]) ).
thf(796,plain,
( ( meet_semilatt_str @ sK65_A )
= $true ),
inference(extcnf_combined,[status(esa)],[566]) ).
thf(797,plain,
( ( ! [A: $i] :
( ~ ( latt_str @ A )
| ( join_semilatt_str @ A ) )
& ! [A: $i] :
( ~ ( latt_str @ A )
| ( meet_semilatt_str @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[567]) ).
thf(798,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[568]) ).
thf(799,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[569]) ).
thf(800,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[571]) ).
thf(801,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[572]) ).
thf(802,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_restriction @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[573]) ).
thf(803,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( empty_carrier @ A )
| ~ ( meet_semilatt_str @ A )
| ~ ( element @ B @ ( the_carrier @ A ) )
| ~ ( element @ C @ ( the_carrier @ A ) )
| ( element @ ( meet @ A @ B @ C ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[574]) ).
thf(804,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( empty_carrier @ A )
| ~ ( join_semilatt_str @ A )
| ~ ( element @ B @ ( the_carrier @ A ) )
| ~ ( element @ C @ ( the_carrier @ A ) )
| ( element @ ( join @ A @ B @ C ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[576]) ).
thf(805,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ( proper_subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( A != B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[577]) ).
thf(806,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_intersection2 @ A @ B )
!= empty_set )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[578]) ).
thf(807,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( relation_restriction @ A @ B )
= ( set_intersection2 @ A @ ( cartesian_product2 @ B @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[579]) ).
thf(808,plain,
( ( ! [A: $i] :
( ( A
!= ( union @ A ) )
| ( being_limit_ordinal @ A ) )
& ! [A: $i] :
( ~ ( being_limit_ordinal @ A )
| ( A
= ( union @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[580]) ).
thf(809,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK66_D @ C @ B @ A ) @ A )
| ( in @ ( sK66_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK66_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK66_D @ C @ B @ A ) @ A )
| ( in @ ( sK66_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK66_D @ C @ B @ A ) @ B )
| ( in @ ( sK66_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_difference @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_difference @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ~ ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[581]) ).
thf(810,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY722: $i] :
( ~ ( in @ ( sK68_C @ B @ A ) @ SY722 )
| ~ ( in @ SY722 @ A ) )
| ~ ( in @ ( sK68_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK68_C @ B @ A ) @ ( sK69_SY723 @ B @ A ) )
& ( in @ ( sK69_SY723 @ B @ A ) @ A ) )
| ( in @ ( sK68_C @ B @ A ) @ B ) ) )
| ( B
= ( union @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( union @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
( ~ ( in @ C @ D )
| ~ ( in @ D @ A ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( ( in @ C @ ( sK67_D @ C @ B @ A ) )
& ( in @ ( sK67_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[582]) ).
thf(811,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK70_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK70_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK70_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK70_D @ C @ B @ A ) @ A )
| ( in @ ( sK70_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK70_D @ C @ B @ A ) @ B )
| ( in @ ( sK70_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_intersection2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_intersection2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ~ ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[584]) ).
thf(812,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK71_C @ B @ A ) @ A )
& ~ ( in @ ( sK71_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[585]) ).
thf(813,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( in @ ( ordered_pair @ ( sK72_C @ B @ A ) @ ( sK73_SY724 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK72_C @ B @ A ) @ ( sK73_SY724 @ B @ A ) ) @ B ) )
| ( subset @ A @ B ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[586]) ).
thf(814,plain,
( ( ! [A: $i] :
( ( ( ( sK74_B @ A )
!= ( sK75_SY725 @ A ) )
& ( in @ ( sK74_B @ A ) @ A )
& ( in @ ( sK75_SY725 @ A ) @ A )
& ~ ( in @ ( sK74_B @ A ) @ ( sK75_SY725 @ A ) )
& ~ ( in @ ( sK75_SY725 @ A ) @ ( sK74_B @ A ) ) )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( epsilon_connected @ A )
| ! [B: $i,C: $i] :
( ( B = C )
| ~ ( in @ B @ A )
| ~ ( in @ C @ A )
| ( in @ B @ C )
| ( in @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[587]) ).
thf(815,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY727: $i,SY728: $i] :
( ~ ( in @ SY727 @ A )
| ~ ( in @ SY728 @ B )
| ( ( sK78_D @ C @ B @ A )
!= ( ordered_pair @ SY727 @ SY728 ) ) )
| ~ ( in @ ( sK78_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK79_SY729 @ C @ B @ A ) @ A )
& ( in @ ( sK80_SY731 @ C @ B @ A ) @ B )
& ( ( sK78_D @ C @ B @ A )
= ( ordered_pair @ ( sK79_SY729 @ C @ B @ A ) @ ( sK80_SY731 @ C @ B @ A ) ) ) )
| ( in @ ( sK78_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( cartesian_product2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( cartesian_product2 @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i,F: $i] :
( ~ ( in @ E @ A )
| ~ ( in @ F @ B )
| ( D
!= ( ordered_pair @ E @ F ) ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( sK76_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK77_SY726 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK76_E @ D @ C @ B @ A ) @ ( sK77_SY726 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[588]) ).
thf(816,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK81_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK81_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK81_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK81_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK81_D @ C @ B @ A ) @ C )
| ( in @ ( sK81_D @ C @ B @ A ) @ A )
| ( in @ ( sK81_D @ C @ B @ A ) @ B ) ) )
| ( C
= ( set_union2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A )
| ( in @ D @ B ) )
& ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[589]) ).
thf(817,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK82_D @ C @ B @ A ) @ C )
| ( ( sK82_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK82_D @ C @ B @ A ) @ C )
| ( ( sK82_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK82_D @ C @ B @ A ) @ C )
| ( ( sK82_D @ C @ B @ A )
= A )
| ( ( sK82_D @ C @ B @ A )
= B ) ) )
| ( C
= ( unordered_pair @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( unordered_pair @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( D = A )
| ( D = B ) )
& ! [D: $i] :
( ( D != A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ( D != B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[590]) ).
thf(818,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK83_C @ B @ A ) @ ( sK84_SY732 @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK83_C @ B @ A ) @ ( sK84_SY732 @ B @ A ) ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK83_C @ B @ A ) @ ( sK84_SY732 @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK83_C @ B @ A ) @ ( sK84_SY732 @ B @ A ) ) @ B ) ) )
| ( A = B ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ( A != B )
| ( ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ B )
| ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[591]) ).
thf(819,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK85_B @ A ) @ A )
& ~ ( subset @ ( sK85_B @ A ) @ A ) )
| ( epsilon_transitive @ A ) )
& ! [A: $i] :
( ~ ( epsilon_transitive @ A )
| ! [B: $i] :
( ~ ( in @ B @ A )
| ( subset @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[592]) ).
thf(820,plain,
( ( ! [A: $i] :
( ( in @ ( sK86_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[593]) ).
thf(821,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK87_C @ B @ A )
!= A )
| ~ ( in @ ( sK87_C @ B @ A ) @ B ) )
& ( ( ( sK87_C @ B @ A )
= A )
| ( in @ ( sK87_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[594]) ).
thf(822,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( ( ( ( in @ ( sK90_SY733 @ B @ A ) @ A )
& ~ ( in @ ( sK89_C @ B @ A ) @ ( sK90_SY733 @ B @ A ) ) )
| ~ ( in @ ( sK89_C @ B @ A ) @ B ) )
& ( ! [SY734: $i] :
( ~ ( in @ SY734 @ A )
| ( in @ ( sK89_C @ B @ A ) @ SY734 ) )
| ( in @ ( sK89_C @ B @ A ) @ B ) ) )
| ( B
= ( set_meet @ A ) ) ) )
& ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( ! [C: $i] :
( ( ( in @ ( sK88_D @ C @ B @ A ) @ A )
& ~ ( in @ C @ ( sK88_D @ C @ B @ A ) ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ C @ D ) ) ) ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( B = empty_set ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
( ( B != empty_set )
| ( B
= ( set_meet @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[595]) ).
thf(823,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( subset @ C @ ( cartesian_product2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ C @ ( cartesian_product2 @ A @ B ) )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[596]) ).
thf(824,plain,
( ( ! [A: $i] :
( ( ! [SY736: $i,SY737: $i] :
( ( sK93_B @ A )
!= ( ordered_pair @ SY736 @ SY737 ) )
& ( in @ ( sK93_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK91_C @ B @ A ) @ ( sK92_SY735 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[597]) ).
thf(825,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( B = empty_set )
| ( A
!= ( relation_dom_as_subset @ A @ B @ C ) )
| ( quasi_total @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( B = empty_set )
| ~ ( quasi_total @ C @ A @ B )
| ( A
= ( relation_dom_as_subset @ A @ B @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( A != empty_set )
| ( A
!= ( relation_dom_as_subset @ A @ B @ C ) )
| ( quasi_total @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( A != empty_set )
| ~ ( quasi_total @ C @ A @ B )
| ( A
= ( relation_dom_as_subset @ A @ B @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( B != empty_set )
| ( C != empty_set )
| ( quasi_total @ C @ A @ B )
| ( A = empty_set ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( B != empty_set )
| ~ ( quasi_total @ C @ A @ B )
| ( C = empty_set )
| ( A = empty_set ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[598]) ).
thf(826,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( ~ ( in @ ( sK94_E @ D @ C @ B @ A ) @ D )
| ( ( sK94_E @ D @ C @ B @ A )
!= C ) )
& ( ~ ( in @ ( sK94_E @ D @ C @ B @ A ) @ D )
| ( ( sK94_E @ D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK94_E @ D @ C @ B @ A ) @ D )
| ( ( sK94_E @ D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK94_E @ D @ C @ B @ A ) @ D )
| ( ( sK94_E @ D @ C @ B @ A )
= C )
| ( ( sK94_E @ D @ C @ B @ A )
= A )
| ( ( sK94_E @ D @ C @ B @ A )
= B ) ) )
| ( D
= ( unordered_triple @ A @ B @ C ) ) )
& ! [C: $i,D: $i] :
( ( D
!= ( unordered_triple @ A @ B @ C ) )
| ( ! [E: $i] :
( ~ ( in @ E @ D )
| ( E = C )
| ( E = A )
| ( E = B ) )
& ! [E: $i] :
( ( E != C )
| ( in @ E @ D ) )
& ! [E: $i] :
( ( E != A )
| ( in @ E @ D ) )
& ! [E: $i] :
( ( E != B )
| ( in @ E @ D ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[599]) ).
thf(827,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[600]) ).
thf(828,plain,
( ( ! [A: $i] :
( ~ ( v2_membered @ A )
| ( v1_membered @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[602]) ).
thf(829,plain,
( ( ! [A: $i] :
( ~ ( v3_membered @ A )
| ( v2_membered @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[603]) ).
thf(830,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[604]) ).
thf(831,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[605]) ).
thf(832,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( finite @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[606]) ).
thf(833,plain,
( ( ! [A: $i] :
( ~ ( v3_membered @ A )
| ( ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( v1_membered @ B ) )
& ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( v2_membered @ B ) )
& ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( v3_membered @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[607]) ).
thf(834,plain,
( ( ! [A: $i] :
( ~ ( v2_membered @ A )
| ( ! [B: $i] :
( ~ ( element @ B @ A )
| ( v1_xcmplx_0 @ B ) )
& ! [B: $i] :
( ~ ( element @ B @ A )
| ( v1_xreal_0 @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[608]) ).
thf(835,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[609]) ).
thf(836,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[610]) ).
thf(837,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[611]) ).
thf(838,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[612]) ).
thf(839,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[613]) ).
thf(840,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[614]) ).
thf(841,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= A )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[615]) ).
thf(842,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[617]) ).
thf(843,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
!= A )
| ~ ( in @ B @ A ) )
& ! [A: $i,B: $i] :
( ( in @ B @ A )
| ( ( set_difference @ A @ ( singleton @ B ) )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[619]) ).
thf(844,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[620]) ).
thf(845,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[621]) ).
thf(846,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK95_B @ A ) @ ( sK96_SY738 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[622]) ).
thf(847,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK97_C @ B @ A ) @ ( set_intersection2 @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[623]) ).
thf(848,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( B = empty_set )
| ( ( union_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= ( subset_difference @ A @ ( cast_to_subset @ A ) @ ( meet_of_subsets @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[625]) ).
thf(849,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( B = empty_set )
| ( ( subset_difference @ A @ ( cast_to_subset @ A ) @ ( union_of_subsets @ A @ B ) )
= ( meet_of_subsets @ A @ ( complements_of_subsets @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[626]) ).
thf(850,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[627]) ).
thf(851,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[628]) ).
thf(852,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[630]) ).
thf(853,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK98_C @ B @ A ) @ A )
& ( in @ ( sK98_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[631]) ).
thf(854,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ C )
| ~ ( in @ C @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[632]) ).
thf(855,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[633]) ).
thf(856,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ C )
| ( subset @ ( unordered_pair @ A @ B ) @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ A @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[635]) ).
thf(857,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[636]) ).
thf(858,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[637]) ).
thf(859,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[639]) ).
thf(860,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK99_B @ A ) @ A )
& ( ~ ( ordinal @ ( sK99_B @ A ) )
| ~ ( subset @ ( sK99_B @ A ) @ A ) ) )
| ( ordinal @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[640]) ).
thf(861,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[642]) ).
thf(862,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[643]) ).
thf(863,plain,
( ( ! [A: $i] :
( ( relation @ ( sK100_B @ A ) )
& ( well_orders @ ( sK100_B @ A ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[644]) ).
thf(864,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ! [B: $i] :
( ~ ( ordinal @ B )
| ( in @ A @ B )
| ( A = B )
| ( in @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[645]) ).
thf(865,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( ! [SY739: $i] :
~ ( in @ ( ordered_pair @ SY739 @ ( sK102_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK102_D @ C @ B @ A ) @ B ) )
| ( ( relation_rng_as_subset @ A @ B @ C )
= B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( ( relation_rng_as_subset @ A @ B @ C )
!= B )
| ! [D: $i] :
( ( in @ ( ordered_pair @ ( sK101_E @ D @ C @ B @ A ) @ D ) @ C )
| ~ ( in @ D @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[646]) ).
thf(866,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ordinal @ B )
| ~ ( in @ A @ B )
| ( ordinal @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[647]) ).
thf(867,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ B @ A )
| ( ! [SY740: $i] :
~ ( in @ ( ordered_pair @ ( sK104_D @ C @ B @ A ) @ SY740 ) @ C )
& ( in @ ( sK104_D @ C @ B @ A ) @ B ) )
| ( ( relation_dom_as_subset @ B @ A @ C )
= B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ B @ A )
| ( ( relation_dom_as_subset @ B @ A @ C )
!= B )
| ! [D: $i] :
( ( in @ ( ordered_pair @ D @ ( sK103_E @ D @ C @ B @ A ) ) @ C )
| ~ ( in @ D @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[648]) ).
thf(868,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[649]) ).
thf(869,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[650]) ).
thf(870,plain,
( ( ! [A: $i] :
( ~ ( finite @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ! [SY741: $i] :
( ~ ( in @ SY741 @ B )
| ~ ( subset @ ( sK105_C @ B @ A ) @ SY741 )
| ( SY741
= ( sK105_C @ B @ A ) ) )
& ( in @ ( sK105_C @ B @ A ) @ B ) )
| ( B = empty_set ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[651]) ).
thf(871,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[653]) ).
thf(872,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ C )
| ~ ( in @ A @ ( cartesian_product2 @ B @ B ) )
| ( in @ A @ ( relation_restriction @ C @ B ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_restriction @ C @ B ) )
| ( in @ A @ C ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_restriction @ C @ B ) )
| ( in @ A @ ( cartesian_product2 @ B @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[654]) ).
thf(873,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( relation_of2_as_subset @ D @ C @ A )
| ~ ( subset @ A @ B )
| ( relation_of2_as_subset @ D @ C @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[655]) ).
thf(874,plain,
( ( ! [A: $i] :
( ~ ( finite @ A )
| ! [B: $i] : ( finite @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[656]) ).
thf(875,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( relation_of2_as_subset @ D @ C @ A )
| ~ ( subset @ ( relation_rng @ D ) @ B )
| ( relation_of2_as_subset @ D @ C @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[657]) ).
thf(876,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ~ ( finite @ B )
| ~ ( subset @ A @ B ) )
| ( finite @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[658]) ).
thf(877,plain,
( ( ! [A: $i] :
( ! [SY742: $i] :
( ~ ( subset @ SY742 @ ( sK106_B @ A ) )
| ( are_equipotent @ SY742 @ ( sK106_B @ A ) )
| ( in @ SY742 @ ( sK106_B @ A ) ) )
& ! [SY743: $i] :
( ~ ( in @ SY743 @ ( sK106_B @ A ) )
| ( in @ ( powerset @ SY743 ) @ ( sK106_B @ A ) ) )
& ! [SY744: $i,SY745: $i] :
( ~ ( in @ SY744 @ ( sK106_B @ A ) )
| ~ ( subset @ SY745 @ SY744 )
| ( in @ SY745 @ ( sK106_B @ A ) ) )
& ( in @ A @ ( sK106_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[659]) ).
thf(878,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[660]) ).
thf(879,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ D )
| ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[661]) ).
thf(880,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) )
& ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[662]) ).
thf(881,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[663]) ).
thf(882,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) )
& ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ A @ C ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ B @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[665]) ).
thf(883,plain,
( ( ! [A: $i] :
( ! [SY746: $i] :
( ~ ( in @ SY746 @ A )
| ~ ( ordinal @ SY746 )
| ( in @ SY746 @ ( sK107_B @ A ) ) )
& ! [SY747: $i] :
( ~ ( in @ SY747 @ ( sK107_B @ A ) )
| ( in @ SY747 @ A ) )
& ! [SY748: $i] :
( ~ ( in @ SY748 @ ( sK107_B @ A ) )
| ( ordinal @ SY748 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[666]) ).
thf(884,plain,
( ( ! [A: $i,B: $i] :
( ! [SY749: $i] :
( ! [E: $i,F: $i] :
( ( ( ordered_pair @ E @ F )
!= SY749 )
| ~ ( in @ E @ A )
| ( F
!= ( singleton @ E ) ) )
| ~ ( in @ SY749 @ ( cartesian_product2 @ A @ B ) )
| ( in @ SY749 @ ( sK108_C @ B @ A ) ) )
& ! [SY752: $i] :
( ~ ( in @ SY752 @ ( sK108_C @ B @ A ) )
| ( ( ( ordered_pair @ ( sK109_E @ SY752 @ B @ A ) @ ( sK110_SY756 @ SY752 @ B @ A ) )
= SY752 )
& ( in @ ( sK109_E @ SY752 @ B @ A ) @ A )
& ( ( sK110_SY756 @ SY752 @ B @ A )
= ( singleton @ ( sK109_E @ SY752 @ B @ A ) ) ) ) )
& ! [SY755: $i] :
( ~ ( in @ SY755 @ ( sK108_C @ B @ A ) )
| ( in @ SY755 @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[667]) ).
thf(885,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ~ ( relation @ B )
| ! [C: $i] :
( ! [SY757: $i] :
( ! [F: $i,G: $i] :
( ( ( ordered_pair @ F @ G )
!= SY757 )
| ~ ( in @ F @ A )
| ! [H: $i] :
( ( ( in @ ( sK115_I @ H @ G @ F @ SY757 @ C @ B @ A ) @ H )
& ~ ( in @ ( ordered_pair @ G @ ( sK115_I @ H @ G @ F @ SY757 @ C @ B @ A ) ) @ B ) )
| ( F != H )
| ~ ( in @ G @ H ) ) )
| ~ ( in @ SY757 @ ( cartesian_product2 @ A @ C ) )
| ( in @ SY757 @ ( sK111_D @ C @ B @ A ) ) )
& ! [SY762: $i] :
( ~ ( in @ SY762 @ ( sK111_D @ C @ B @ A ) )
| ( ( ( ordered_pair @ ( sK112_F @ SY762 @ C @ B @ A ) @ ( sK113_SY768 @ SY762 @ C @ B @ A ) )
= SY762 )
& ( in @ ( sK112_F @ SY762 @ C @ B @ A ) @ A )
& ! [SY773: $i] :
( ~ ( in @ SY773 @ ( sK114_SY771 @ SY762 @ C @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK113_SY768 @ SY762 @ C @ B @ A ) @ SY773 ) @ B ) )
& ( ( sK112_F @ SY762 @ C @ B @ A )
= ( sK114_SY771 @ SY762 @ C @ B @ A ) )
& ( in @ ( sK113_SY768 @ SY762 @ C @ B @ A ) @ ( sK114_SY771 @ SY762 @ C @ B @ A ) ) ) )
& ! [SY767: $i] :
( ~ ( in @ SY767 @ ( sK111_D @ C @ B @ A ) )
| ( in @ SY767 @ ( cartesian_product2 @ A @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[668]) ).
thf(886,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) )
& ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ A @ C ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ B @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[669]) ).
thf(887,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[670]) ).
thf(888,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[671]) ).
thf(889,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[672]) ).
thf(890,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[673]) ).
thf(891,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[674]) ).
thf(892,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[675]) ).
thf(893,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[676]) ).
thf(894,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[677]) ).
thf(895,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(extcnf_combined,[status(esa)],[678]) ).
thf(896,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[679]) ).
thf(897,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[680]) ).
thf(898,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[681]) ).
thf(899,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[682]) ).
thf(900,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[683]) ).
thf(901,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( element @ C @ ( powerset @ A ) )
| ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[684]) ).
thf(902,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ( meet_of_subsets @ A @ B )
= ( set_meet @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[685]) ).
thf(903,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( element @ C @ ( powerset @ A ) )
| ( ( subset_intersection2 @ A @ B @ C )
= ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[686]) ).
thf(904,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ( union_of_subsets @ A @ B )
= ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[687]) ).
thf(905,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ( ( element @ ( sK116_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ ( sK116_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[688]) ).
thf(906,plain,
( ( ( one_sorted_str @ sK117_A )
& ~ ( empty_carrier @ sK117_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[689]) ).
thf(907,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK118_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK118_B @ A ) )
& ( finite @ ( sK118_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[690]) ).
thf(908,plain,
( ( ! [A: $i] :
( ( element @ ( sK119_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK119_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[691]) ).
thf(909,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK120_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK120_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[692]) ).
thf(910,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[693]) ).
thf(911,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[694]) ).
thf(912,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
~ ( element @ C @ ( powerset @ A ) )
| ( ( subset_intersection2 @ A @ B @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[695]) ).
thf(913,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[697]) ).
thf(914,plain,
( ( ! [A: $i] : ( element @ ( sK121_B @ A ) @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[698]) ).
thf(915,plain,
( ( one_sorted_str @ sK122_A )
= $true ),
inference(extcnf_combined,[status(esa)],[699]) ).
thf(916,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[700]) ).
thf(917,plain,
( ( ! [A: $i] :
( ~ ( join_semilatt_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[701]) ).
thf(918,plain,
( ( ! [A: $i] :
( ~ ( meet_semilatt_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[702]) ).
thf(919,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[703]) ).
thf(920,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( element @ C @ ( powerset @ A ) )
| ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[704]) ).
thf(921,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[705]) ).
thf(922,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( element @ C @ ( powerset @ A ) )
| ( element @ ( subset_intersection2 @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[706]) ).
thf(923,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[707]) ).
thf(924,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( element @ ( relation_rng_as_subset @ A @ B @ C ) @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[708]) ).
thf(925,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( element @ ( relation_dom_as_subset @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[709]) ).
thf(926,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[710]) ).
thf(927,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[712]) ).
thf(928,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ! [C: $i] :
( ~ ( element @ C @ ( powerset @ ( powerset @ A ) ) )
| ( ( element @ ( sK123_D @ C @ B @ A ) @ ( powerset @ A ) )
& ( ~ ( in @ ( sK123_D @ C @ B @ A ) @ C )
| ~ ( in @ ( subset_complement @ A @ ( sK123_D @ C @ B @ A ) ) @ B ) )
& ( ( in @ ( sK123_D @ C @ B @ A ) @ C )
| ( in @ ( subset_complement @ A @ ( sK123_D @ C @ B @ A ) ) @ B ) ) )
| ( C
= ( complements_of_subsets @ A @ B ) ) )
& ! [C: $i] :
( ~ ( element @ C @ ( powerset @ ( powerset @ A ) ) )
| ( C
!= ( complements_of_subsets @ A @ B ) )
| ( ! [D: $i] :
( ~ ( element @ D @ ( powerset @ A ) )
| ~ ( in @ D @ C )
| ( in @ ( subset_complement @ A @ D ) @ B ) )
& ! [D: $i] :
( ~ ( element @ D @ ( powerset @ A ) )
| ~ ( in @ ( subset_complement @ A @ D ) @ B )
| ( in @ D @ C ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[713]) ).
thf(929,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[714]) ).
thf(930,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[715]) ).
thf(931,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( in @ B @ A ) ) )
& ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( in @ B @ A )
| ( element @ B @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( empty @ B ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( empty @ B )
| ( element @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[716]) ).
thf(932,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK124_C @ B @ A ) @ B )
| ~ ( subset @ ( sK124_C @ B @ A ) @ A ) )
& ( ( in @ ( sK124_C @ B @ A ) @ B )
| ( subset @ ( sK124_C @ B @ A ) @ A ) ) )
| ( B
= ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( in @ C @ B )
| ( subset @ C @ A ) )
& ! [C: $i] :
( ~ ( subset @ C @ A )
| ( in @ C @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[717]) ).
thf(933,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( element @ C @ ( powerset @ A ) )
| ( ( subset_intersection2 @ A @ B @ C )
= ( subset_intersection2 @ A @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[718]) ).
thf(934,plain,
( ( ! [A: $i] :
( ~ ( finite @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( finite @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[719]) ).
thf(935,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
| ( relation @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[720]) ).
thf(936,plain,
( ( ! [A: $i] :
( ~ ( v2_membered @ A )
| ( ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( v1_membered @ B ) )
& ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( v2_membered @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[721]) ).
thf(937,plain,
( ( ! [A: $i] :
( ~ ( v1_membered @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( v1_membered @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[722]) ).
thf(938,plain,
( ( ! [A: $i] :
( ~ ( v1_membered @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( v1_xcmplx_0 @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[723]) ).
thf(939,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( in @ B @ ( subset_complement @ A @ C ) )
| ~ ( in @ B @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[725]) ).
thf(940,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( element @ C @ A )
| ( in @ C @ B )
| ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[726]) ).
thf(941,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( B = empty_set )
| ( ( complements_of_subsets @ A @ B )
!= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[727]) ).
thf(942,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( disjoint @ B @ C )
| ( subset @ B @ ( subset_complement @ A @ C ) ) )
& ! [C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( subset @ B @ ( subset_complement @ A @ C ) )
| ( disjoint @ B @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[728]) ).
thf(943,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ( ( subset_intersection2 @ ( the_carrier @ A ) @ B @ ( cast_as_carrier_subset @ A ) )
= B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[730]) ).
thf(944,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[731]) ).
thf(945,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK125_C @ B @ A ) @ A )
& ~ ( in @ ( sK125_C @ B @ A ) @ B ) )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[732]) ).
thf(946,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[733]) ).
thf(947,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[946]) ).
thf(948,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK125_C @ B @ A ) @ A )
& ~ ( in @ ( sK125_C @ B @ A ) @ B ) )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[945]) ).
thf(949,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[944]) ).
thf(950,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ( ( subset_intersection2 @ ( the_carrier @ A ) @ B @ ( cast_as_carrier_subset @ A ) )
= B ) ) ) )
= $true ),
inference(copy,[status(thm)],[943]) ).
thf(951,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[729]) ).
thf(952,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( disjoint @ B @ C )
| ( subset @ B @ ( subset_complement @ A @ C ) ) )
& ! [C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( subset @ B @ ( subset_complement @ A @ C ) )
| ( disjoint @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[942]) ).
thf(953,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( B = empty_set )
| ( ( complements_of_subsets @ A @ B )
!= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[941]) ).
thf(954,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
( ~ ( element @ C @ A )
| ( in @ C @ B )
| ( in @ C @ ( subset_complement @ A @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[940]) ).
thf(955,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ A ) )
| ~ ( in @ B @ ( subset_complement @ A @ C ) )
| ~ ( in @ B @ C ) ) )
= $true ),
inference(copy,[status(thm)],[939]) ).
thf(956,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[724]) ).
thf(957,plain,
( ( ! [A: $i] :
( ~ ( v1_membered @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( v1_xcmplx_0 @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[938]) ).
thf(958,plain,
( ( ! [A: $i] :
( ~ ( v1_membered @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( v1_membered @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[937]) ).
thf(959,plain,
( ( ! [A: $i] :
( ~ ( v2_membered @ A )
| ( ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( v1_membered @ B ) )
& ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( v2_membered @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[936]) ).
thf(960,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
| ( relation @ C ) ) )
= $true ),
inference(copy,[status(thm)],[935]) ).
thf(961,plain,
( ( ! [A: $i] :
( ~ ( finite @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[934]) ).
thf(962,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( element @ C @ ( powerset @ A ) )
| ( ( subset_intersection2 @ A @ B @ C )
= ( subset_intersection2 @ A @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[933]) ).
thf(963,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK124_C @ B @ A ) @ B )
| ~ ( subset @ ( sK124_C @ B @ A ) @ A ) )
& ( ( in @ ( sK124_C @ B @ A ) @ B )
| ( subset @ ( sK124_C @ B @ A ) @ A ) ) )
| ( B
= ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( in @ C @ B )
| ( subset @ C @ A ) )
& ! [C: $i] :
( ~ ( subset @ C @ A )
| ( in @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[932]) ).
thf(964,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( in @ B @ A ) ) )
& ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( in @ B @ A )
| ( element @ B @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( empty @ B ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( empty @ B )
| ( element @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[931]) ).
thf(965,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( ( cast_as_carrier_subset @ A )
= ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[930]) ).
thf(966,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ( subset_complement @ A @ B )
= ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[929]) ).
thf(967,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ! [C: $i] :
( ~ ( element @ C @ ( powerset @ ( powerset @ A ) ) )
| ( ( element @ ( sK123_D @ C @ B @ A ) @ ( powerset @ A ) )
& ( ~ ( in @ ( sK123_D @ C @ B @ A ) @ C )
| ~ ( in @ ( subset_complement @ A @ ( sK123_D @ C @ B @ A ) ) @ B ) )
& ( ( in @ ( sK123_D @ C @ B @ A ) @ C )
| ( in @ ( subset_complement @ A @ ( sK123_D @ C @ B @ A ) ) @ B ) ) )
| ( C
= ( complements_of_subsets @ A @ B ) ) )
& ! [C: $i] :
( ~ ( element @ C @ ( powerset @ ( powerset @ A ) ) )
| ( C
!= ( complements_of_subsets @ A @ B ) )
| ( ! [D: $i] :
( ~ ( element @ D @ ( powerset @ A ) )
| ~ ( in @ D @ C )
| ( in @ ( subset_complement @ A @ D ) @ B ) )
& ! [D: $i] :
( ~ ( element @ D @ ( powerset @ A ) )
| ~ ( in @ ( subset_complement @ A @ D ) @ B )
| ( in @ D @ C ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[928]) ).
thf(968,plain,
( ( ! [A: $i] :
( ~ ( one_sorted_str @ A )
| ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[927]) ).
thf(969,plain,
( ( ! [A: $i] : ( element @ ( cast_to_subset @ A ) @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[711]) ).
thf(970,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[926]) ).
thf(971,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( element @ ( relation_dom_as_subset @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[925]) ).
thf(972,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( element @ ( relation_rng_as_subset @ A @ B @ C ) @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[924]) ).
thf(973,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( union_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[923]) ).
thf(974,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( element @ C @ ( powerset @ A ) )
| ( element @ ( subset_intersection2 @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[922]) ).
thf(975,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( meet_of_subsets @ A @ B ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[921]) ).
thf(976,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( element @ C @ ( powerset @ A ) )
| ( element @ ( subset_difference @ A @ B @ C ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[920]) ).
thf(977,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[919]) ).
thf(978,plain,
( ( ! [A: $i] :
( ~ ( meet_semilatt_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[918]) ).
thf(979,plain,
( ( ! [A: $i] :
( ~ ( join_semilatt_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[917]) ).
thf(980,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[916]) ).
thf(981,plain,
( ( one_sorted_str @ sK122_A )
= $true ),
inference(copy,[status(thm)],[915]) ).
thf(982,plain,
( ( ! [A: $i] : ( element @ ( sK121_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[914]) ).
thf(983,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[913]) ).
thf(984,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[696]) ).
thf(985,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ! [C: $i] :
~ ( element @ C @ ( powerset @ A ) )
| ( ( subset_intersection2 @ A @ B @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[912]) ).
thf(986,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[911]) ).
thf(987,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[910]) ).
thf(988,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK120_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK120_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[909]) ).
thf(989,plain,
( ( ! [A: $i] :
( ( element @ ( sK119_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK119_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[908]) ).
thf(990,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK118_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK118_B @ A ) )
& ( finite @ ( sK118_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[907]) ).
thf(991,plain,
( ( ( one_sorted_str @ sK117_A )
& ~ ( empty_carrier @ sK117_A ) )
= $true ),
inference(copy,[status(thm)],[906]) ).
thf(992,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ( ( element @ ( sK116_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ ( sK116_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[905]) ).
thf(993,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ( union_of_subsets @ A @ B )
= ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[904]) ).
thf(994,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( element @ C @ ( powerset @ A ) )
| ( ( subset_intersection2 @ A @ B @ C )
= ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[903]) ).
thf(995,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ( meet_of_subsets @ A @ B )
= ( set_meet @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[902]) ).
thf(996,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( element @ C @ ( powerset @ A ) )
| ( ( subset_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[901]) ).
thf(997,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[900]) ).
thf(998,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[899]) ).
thf(999,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[898]) ).
thf(1000,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[897]) ).
thf(1001,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[896]) ).
thf(1002,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[895]) ).
thf(1003,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[894]) ).
thf(1004,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[893]) ).
thf(1005,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[892]) ).
thf(1006,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[891]) ).
thf(1007,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[890]) ).
thf(1008,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[889]) ).
thf(1009,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[888]) ).
thf(1010,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[887]) ).
thf(1011,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) )
& ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ A @ C ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[886]) ).
thf(1012,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ~ ( relation @ B )
| ! [C: $i] :
( ! [SY757: $i] :
( ! [F: $i,G: $i] :
( ( ( ordered_pair @ F @ G )
!= SY757 )
| ~ ( in @ F @ A )
| ! [H: $i] :
( ( ( in @ ( sK115_I @ H @ G @ F @ SY757 @ C @ B @ A ) @ H )
& ~ ( in @ ( ordered_pair @ G @ ( sK115_I @ H @ G @ F @ SY757 @ C @ B @ A ) ) @ B ) )
| ( F != H )
| ~ ( in @ G @ H ) ) )
| ~ ( in @ SY757 @ ( cartesian_product2 @ A @ C ) )
| ( in @ SY757 @ ( sK111_D @ C @ B @ A ) ) )
& ! [SY762: $i] :
( ~ ( in @ SY762 @ ( sK111_D @ C @ B @ A ) )
| ( ( ( ordered_pair @ ( sK112_F @ SY762 @ C @ B @ A ) @ ( sK113_SY768 @ SY762 @ C @ B @ A ) )
= SY762 )
& ( in @ ( sK112_F @ SY762 @ C @ B @ A ) @ A )
& ! [SY773: $i] :
( ~ ( in @ SY773 @ ( sK114_SY771 @ SY762 @ C @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK113_SY768 @ SY762 @ C @ B @ A ) @ SY773 ) @ B ) )
& ( ( sK112_F @ SY762 @ C @ B @ A )
= ( sK114_SY771 @ SY762 @ C @ B @ A ) )
& ( in @ ( sK113_SY768 @ SY762 @ C @ B @ A ) @ ( sK114_SY771 @ SY762 @ C @ B @ A ) ) ) )
& ! [SY767: $i] :
( ~ ( in @ SY767 @ ( sK111_D @ C @ B @ A ) )
| ( in @ SY767 @ ( cartesian_product2 @ A @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[885]) ).
thf(1013,plain,
( ( ! [A: $i,B: $i] :
( ! [SY749: $i] :
( ! [E: $i,F: $i] :
( ( ( ordered_pair @ E @ F )
!= SY749 )
| ~ ( in @ E @ A )
| ( F
!= ( singleton @ E ) ) )
| ~ ( in @ SY749 @ ( cartesian_product2 @ A @ B ) )
| ( in @ SY749 @ ( sK108_C @ B @ A ) ) )
& ! [SY752: $i] :
( ~ ( in @ SY752 @ ( sK108_C @ B @ A ) )
| ( ( ( ordered_pair @ ( sK109_E @ SY752 @ B @ A ) @ ( sK110_SY756 @ SY752 @ B @ A ) )
= SY752 )
& ( in @ ( sK109_E @ SY752 @ B @ A ) @ A )
& ( ( sK110_SY756 @ SY752 @ B @ A )
= ( singleton @ ( sK109_E @ SY752 @ B @ A ) ) ) ) )
& ! [SY755: $i] :
( ~ ( in @ SY755 @ ( sK108_C @ B @ A ) )
| ( in @ SY755 @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[884]) ).
thf(1014,plain,
( ( ! [A: $i] :
( ! [SY746: $i] :
( ~ ( in @ SY746 @ A )
| ~ ( ordinal @ SY746 )
| ( in @ SY746 @ ( sK107_B @ A ) ) )
& ! [SY747: $i] :
( ~ ( in @ SY747 @ ( sK107_B @ A ) )
| ( in @ SY747 @ A ) )
& ! [SY748: $i] :
( ~ ( in @ SY748 @ ( sK107_B @ A ) )
| ( ordinal @ SY748 ) ) ) )
= $true ),
inference(copy,[status(thm)],[883]) ).
thf(1015,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) )
& ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ A @ C ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[882]) ).
thf(1016,plain,
( ( ! [A: $i] : ( in @ A @ ( succ @ A ) ) )
= $true ),
inference(copy,[status(thm)],[664]) ).
thf(1017,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[881]) ).
thf(1018,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) )
& ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[880]) ).
thf(1019,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ D )
| ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[879]) ).
thf(1020,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[878]) ).
thf(1021,plain,
( ( ! [A: $i] :
( ! [SY742: $i] :
( ~ ( subset @ SY742 @ ( sK106_B @ A ) )
| ( are_equipotent @ SY742 @ ( sK106_B @ A ) )
| ( in @ SY742 @ ( sK106_B @ A ) ) )
& ! [SY743: $i] :
( ~ ( in @ SY743 @ ( sK106_B @ A ) )
| ( in @ ( powerset @ SY743 ) @ ( sK106_B @ A ) ) )
& ! [SY744: $i,SY745: $i] :
( ~ ( in @ SY744 @ ( sK106_B @ A ) )
| ~ ( subset @ SY745 @ SY744 )
| ( in @ SY745 @ ( sK106_B @ A ) ) )
& ( in @ A @ ( sK106_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[877]) ).
thf(1022,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ~ ( finite @ B )
| ~ ( subset @ A @ B ) )
| ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[876]) ).
thf(1023,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( relation_of2_as_subset @ D @ C @ A )
| ~ ( subset @ ( relation_rng @ D ) @ B )
| ( relation_of2_as_subset @ D @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[875]) ).
thf(1024,plain,
( ( ! [A: $i] :
( ~ ( finite @ A )
| ! [B: $i] : ( finite @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[874]) ).
thf(1025,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( relation_of2_as_subset @ D @ C @ A )
| ~ ( subset @ A @ B )
| ( relation_of2_as_subset @ D @ C @ B ) ) )
= $true ),
inference(copy,[status(thm)],[873]) ).
thf(1026,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ C )
| ~ ( in @ A @ ( cartesian_product2 @ B @ B ) )
| ( in @ A @ ( relation_restriction @ C @ B ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_restriction @ C @ B ) )
| ( in @ A @ C ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_restriction @ C @ B ) )
| ( in @ A @ ( cartesian_product2 @ B @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[872]) ).
thf(1027,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( subset @ A @ B )
| ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[871]) ).
thf(1028,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[652]) ).
thf(1029,plain,
( ( ! [A: $i] :
( ~ ( finite @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( ! [SY741: $i] :
( ~ ( in @ SY741 @ B )
| ~ ( subset @ ( sK105_C @ B @ A ) @ SY741 )
| ( SY741
= ( sK105_C @ B @ A ) ) )
& ( in @ ( sK105_C @ B @ A ) @ B ) )
| ( B = empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[870]) ).
thf(1030,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[869]) ).
thf(1031,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[868]) ).
thf(1032,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ B @ A )
| ( ! [SY740: $i] :
~ ( in @ ( ordered_pair @ ( sK104_D @ C @ B @ A ) @ SY740 ) @ C )
& ( in @ ( sK104_D @ C @ B @ A ) @ B ) )
| ( ( relation_dom_as_subset @ B @ A @ C )
= B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ B @ A )
| ( ( relation_dom_as_subset @ B @ A @ C )
!= B )
| ! [D: $i] :
( ( in @ ( ordered_pair @ D @ ( sK103_E @ D @ C @ B @ A ) ) @ C )
| ~ ( in @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[867]) ).
thf(1033,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ordinal @ B )
| ~ ( in @ A @ B )
| ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[866]) ).
thf(1034,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( ! [SY739: $i] :
~ ( in @ ( ordered_pair @ SY739 @ ( sK102_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK102_D @ C @ B @ A ) @ B ) )
| ( ( relation_rng_as_subset @ A @ B @ C )
= B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( ( relation_rng_as_subset @ A @ B @ C )
!= B )
| ! [D: $i] :
( ( in @ ( ordered_pair @ ( sK101_E @ D @ C @ B @ A ) @ D ) @ C )
| ~ ( in @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[865]) ).
thf(1035,plain,
( ( ! [A: $i] :
( ~ ( ordinal @ A )
| ! [B: $i] :
( ~ ( ordinal @ B )
| ( in @ A @ B )
| ( A = B )
| ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[864]) ).
thf(1036,plain,
( ( ! [A: $i] :
( ( relation @ ( sK100_B @ A ) )
& ( well_orders @ ( sK100_B @ A ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[863]) ).
thf(1037,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[862]) ).
thf(1038,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[861]) ).
thf(1039,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[641]) ).
thf(1040,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK99_B @ A ) @ A )
& ( ~ ( ordinal @ ( sK99_B @ A ) )
| ~ ( subset @ ( sK99_B @ A ) @ A ) ) )
| ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[860]) ).
thf(1041,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[859]) ).
thf(1042,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[638]) ).
thf(1043,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[858]) ).
thf(1044,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[857]) ).
thf(1045,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ C )
| ( subset @ ( unordered_pair @ A @ B ) @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ A @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[856]) ).
thf(1046,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[634]) ).
thf(1047,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[855]) ).
thf(1048,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ C )
| ~ ( in @ C @ A ) ) )
= $true ),
inference(copy,[status(thm)],[854]) ).
thf(1049,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK98_C @ B @ A ) @ A )
& ( in @ ( sK98_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[853]) ).
thf(1050,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[852]) ).
thf(1051,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[629]) ).
thf(1052,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[851]) ).
thf(1053,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[850]) ).
thf(1054,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( B = empty_set )
| ( ( subset_difference @ A @ ( cast_to_subset @ A ) @ ( union_of_subsets @ A @ B ) )
= ( meet_of_subsets @ A @ ( complements_of_subsets @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[849]) ).
thf(1055,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ ( powerset @ A ) ) )
| ( B = empty_set )
| ( ( union_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
= ( subset_difference @ A @ ( cast_to_subset @ A ) @ ( meet_of_subsets @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[848]) ).
thf(1056,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[624]) ).
thf(1057,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK97_C @ B @ A ) @ ( set_intersection2 @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[847]) ).
thf(1058,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK95_B @ A ) @ ( sK96_SY738 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[846]) ).
thf(1059,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[845]) ).
thf(1060,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[844]) ).
thf(1061,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
!= A )
| ~ ( in @ B @ A ) )
& ! [A: $i,B: $i] :
( ( in @ B @ A )
| ( ( set_difference @ A @ ( singleton @ B ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[843]) ).
thf(1062,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[618]) ).
thf(1063,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[842]) ).
thf(1064,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[616]) ).
thf(1065,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= A )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[841]) ).
thf(1066,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[840]) ).
thf(1067,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[839]) ).
thf(1068,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[838]) ).
thf(1069,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[837]) ).
thf(1070,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[836]) ).
thf(1071,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[835]) ).
thf(1072,plain,
( ( ! [A: $i] :
( ~ ( v2_membered @ A )
| ( ! [B: $i] :
( ~ ( element @ B @ A )
| ( v1_xcmplx_0 @ B ) )
& ! [B: $i] :
( ~ ( element @ B @ A )
| ( v1_xreal_0 @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[834]) ).
thf(1073,plain,
( ( ! [A: $i] :
( ~ ( v3_membered @ A )
| ( ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( v1_membered @ B ) )
& ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( v2_membered @ B ) )
& ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( v3_membered @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[833]) ).
thf(1074,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[832]) ).
thf(1075,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[831]) ).
thf(1076,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[830]) ).
thf(1077,plain,
( ( ! [A: $i] :
( ~ ( v3_membered @ A )
| ( v2_membered @ A ) ) )
= $true ),
inference(copy,[status(thm)],[829]) ).
thf(1078,plain,
( ( ! [A: $i] :
( ~ ( v2_membered @ A )
| ( v1_membered @ A ) ) )
= $true ),
inference(copy,[status(thm)],[828]) ).
thf(1079,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[601]) ).
thf(1080,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[827]) ).
thf(1081,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( ~ ( in @ ( sK94_E @ D @ C @ B @ A ) @ D )
| ( ( sK94_E @ D @ C @ B @ A )
!= C ) )
& ( ~ ( in @ ( sK94_E @ D @ C @ B @ A ) @ D )
| ( ( sK94_E @ D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK94_E @ D @ C @ B @ A ) @ D )
| ( ( sK94_E @ D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK94_E @ D @ C @ B @ A ) @ D )
| ( ( sK94_E @ D @ C @ B @ A )
= C )
| ( ( sK94_E @ D @ C @ B @ A )
= A )
| ( ( sK94_E @ D @ C @ B @ A )
= B ) ) )
| ( D
= ( unordered_triple @ A @ B @ C ) ) )
& ! [C: $i,D: $i] :
( ( D
!= ( unordered_triple @ A @ B @ C ) )
| ( ! [E: $i] :
( ~ ( in @ E @ D )
| ( E = C )
| ( E = A )
| ( E = B ) )
& ! [E: $i] :
( ( E != C )
| ( in @ E @ D ) )
& ! [E: $i] :
( ( E != A )
| ( in @ E @ D ) )
& ! [E: $i] :
( ( E != B )
| ( in @ E @ D ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[826]) ).
thf(1082,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( B = empty_set )
| ( A
!= ( relation_dom_as_subset @ A @ B @ C ) )
| ( quasi_total @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( B = empty_set )
| ~ ( quasi_total @ C @ A @ B )
| ( A
= ( relation_dom_as_subset @ A @ B @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( A != empty_set )
| ( A
!= ( relation_dom_as_subset @ A @ B @ C ) )
| ( quasi_total @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( A != empty_set )
| ~ ( quasi_total @ C @ A @ B )
| ( A
= ( relation_dom_as_subset @ A @ B @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( B != empty_set )
| ( C != empty_set )
| ( quasi_total @ C @ A @ B )
| ( A = empty_set ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( B != empty_set )
| ~ ( quasi_total @ C @ A @ B )
| ( C = empty_set )
| ( A = empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[825]) ).
thf(1083,plain,
( ( ! [A: $i] :
( ( ! [SY736: $i,SY737: $i] :
( ( sK93_B @ A )
!= ( ordered_pair @ SY736 @ SY737 ) )
& ( in @ ( sK93_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK91_C @ B @ A ) @ ( sK92_SY735 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[824]) ).
thf(1084,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( subset @ C @ ( cartesian_product2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ C @ ( cartesian_product2 @ A @ B ) )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[823]) ).
thf(1085,plain,
( ( ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( ( ( ( in @ ( sK90_SY733 @ B @ A ) @ A )
& ~ ( in @ ( sK89_C @ B @ A ) @ ( sK90_SY733 @ B @ A ) ) )
| ~ ( in @ ( sK89_C @ B @ A ) @ B ) )
& ( ! [SY734: $i] :
( ~ ( in @ SY734 @ A )
| ( in @ ( sK89_C @ B @ A ) @ SY734 ) )
| ( in @ ( sK89_C @ B @ A ) @ B ) ) )
| ( B
= ( set_meet @ A ) ) ) )
& ! [A: $i] :
( ( A = empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( ! [C: $i] :
( ( ( in @ ( sK88_D @ C @ B @ A ) @ A )
& ~ ( in @ C @ ( sK88_D @ C @ B @ A ) ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ C @ D ) ) ) ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
( ( B
!= ( set_meet @ A ) )
| ( B = empty_set ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
( ( B != empty_set )
| ( B
= ( set_meet @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[822]) ).
thf(1086,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK87_C @ B @ A )
!= A )
| ~ ( in @ ( sK87_C @ B @ A ) @ B ) )
& ( ( ( sK87_C @ B @ A )
= A )
| ( in @ ( sK87_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[821]) ).
thf(1087,plain,
( ( ! [A: $i] :
( ( in @ ( sK86_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[820]) ).
thf(1088,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK85_B @ A ) @ A )
& ~ ( subset @ ( sK85_B @ A ) @ A ) )
| ( epsilon_transitive @ A ) )
& ! [A: $i] :
( ~ ( epsilon_transitive @ A )
| ! [B: $i] :
( ~ ( in @ B @ A )
| ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[819]) ).
thf(1089,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK83_C @ B @ A ) @ ( sK84_SY732 @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK83_C @ B @ A ) @ ( sK84_SY732 @ B @ A ) ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK83_C @ B @ A ) @ ( sK84_SY732 @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK83_C @ B @ A ) @ ( sK84_SY732 @ B @ A ) ) @ B ) ) )
| ( A = B ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ( A != B )
| ( ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ B )
| ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[818]) ).
thf(1090,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK82_D @ C @ B @ A ) @ C )
| ( ( sK82_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK82_D @ C @ B @ A ) @ C )
| ( ( sK82_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK82_D @ C @ B @ A ) @ C )
| ( ( sK82_D @ C @ B @ A )
= A )
| ( ( sK82_D @ C @ B @ A )
= B ) ) )
| ( C
= ( unordered_pair @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( unordered_pair @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( D = A )
| ( D = B ) )
& ! [D: $i] :
( ( D != A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ( D != B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[817]) ).
thf(1091,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK81_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK81_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK81_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK81_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK81_D @ C @ B @ A ) @ C )
| ( in @ ( sK81_D @ C @ B @ A ) @ A )
| ( in @ ( sK81_D @ C @ B @ A ) @ B ) ) )
| ( C
= ( set_union2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A )
| ( in @ D @ B ) )
& ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[816]) ).
thf(1092,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY727: $i,SY728: $i] :
( ~ ( in @ SY727 @ A )
| ~ ( in @ SY728 @ B )
| ( ( sK78_D @ C @ B @ A )
!= ( ordered_pair @ SY727 @ SY728 ) ) )
| ~ ( in @ ( sK78_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK79_SY729 @ C @ B @ A ) @ A )
& ( in @ ( sK80_SY731 @ C @ B @ A ) @ B )
& ( ( sK78_D @ C @ B @ A )
= ( ordered_pair @ ( sK79_SY729 @ C @ B @ A ) @ ( sK80_SY731 @ C @ B @ A ) ) ) )
| ( in @ ( sK78_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( cartesian_product2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( cartesian_product2 @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i,F: $i] :
( ~ ( in @ E @ A )
| ~ ( in @ F @ B )
| ( D
!= ( ordered_pair @ E @ F ) ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( sK76_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK77_SY726 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK76_E @ D @ C @ B @ A ) @ ( sK77_SY726 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[815]) ).
thf(1093,plain,
( ( ! [A: $i] :
( ( ( ( sK74_B @ A )
!= ( sK75_SY725 @ A ) )
& ( in @ ( sK74_B @ A ) @ A )
& ( in @ ( sK75_SY725 @ A ) @ A )
& ~ ( in @ ( sK74_B @ A ) @ ( sK75_SY725 @ A ) )
& ~ ( in @ ( sK75_SY725 @ A ) @ ( sK74_B @ A ) ) )
| ( epsilon_connected @ A ) )
& ! [A: $i] :
( ~ ( epsilon_connected @ A )
| ! [B: $i,C: $i] :
( ( B = C )
| ~ ( in @ B @ A )
| ~ ( in @ C @ A )
| ( in @ B @ C )
| ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[814]) ).
thf(1094,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( in @ ( ordered_pair @ ( sK72_C @ B @ A ) @ ( sK73_SY724 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK72_C @ B @ A ) @ ( sK73_SY724 @ B @ A ) ) @ B ) )
| ( subset @ A @ B ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ~ ( subset @ A @ B )
| ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[813]) ).
thf(1095,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK71_C @ B @ A ) @ A )
& ~ ( in @ ( sK71_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[812]) ).
thf(1096,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK70_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK70_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK70_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK70_D @ C @ B @ A ) @ A )
| ( in @ ( sK70_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK70_D @ C @ B @ A ) @ B )
| ( in @ ( sK70_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_intersection2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_intersection2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ~ ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[811]) ).
thf(1097,plain,
( ( ! [A: $i] :
( ( cast_to_subset @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[583]) ).
thf(1098,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY722: $i] :
( ~ ( in @ ( sK68_C @ B @ A ) @ SY722 )
| ~ ( in @ SY722 @ A ) )
| ~ ( in @ ( sK68_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK68_C @ B @ A ) @ ( sK69_SY723 @ B @ A ) )
& ( in @ ( sK69_SY723 @ B @ A ) @ A ) )
| ( in @ ( sK68_C @ B @ A ) @ B ) ) )
| ( B
= ( union @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( union @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
( ~ ( in @ C @ D )
| ~ ( in @ D @ A ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( ( in @ C @ ( sK67_D @ C @ B @ A ) )
& ( in @ ( sK67_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[810]) ).
thf(1099,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK66_D @ C @ B @ A ) @ A )
| ( in @ ( sK66_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK66_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK66_D @ C @ B @ A ) @ A )
| ( in @ ( sK66_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK66_D @ C @ B @ A ) @ B )
| ( in @ ( sK66_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_difference @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_difference @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ~ ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[809]) ).
thf(1100,plain,
( ( ! [A: $i] :
( ( A
!= ( union @ A ) )
| ( being_limit_ordinal @ A ) )
& ! [A: $i] :
( ~ ( being_limit_ordinal @ A )
| ( A
= ( union @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[808]) ).
thf(1101,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( relation_restriction @ A @ B )
= ( set_intersection2 @ A @ ( cartesian_product2 @ B @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[807]) ).
thf(1102,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_intersection2 @ A @ B )
!= empty_set )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[806]) ).
thf(1103,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ( proper_subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( A != B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[805]) ).
thf(1104,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( empty_carrier @ A )
| ~ ( join_semilatt_str @ A )
| ~ ( element @ B @ ( the_carrier @ A ) )
| ~ ( element @ C @ ( the_carrier @ A ) )
| ( element @ ( join @ A @ B @ C ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[804]) ).
thf(1105,plain,
( ( ! [A: $i] : ( relation @ ( inclusion_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[575]) ).
thf(1106,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( empty_carrier @ A )
| ~ ( meet_semilatt_str @ A )
| ~ ( element @ B @ ( the_carrier @ A ) )
| ~ ( element @ C @ ( the_carrier @ A ) )
| ( element @ ( meet @ A @ B @ C ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[803]) ).
thf(1107,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[802]) ).
thf(1108,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[801]) ).
thf(1109,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[800]) ).
thf(1110,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[570]) ).
thf(1111,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] : ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[799]) ).
thf(1112,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[798]) ).
thf(1113,plain,
( ( ! [A: $i] :
( ~ ( latt_str @ A )
| ( join_semilatt_str @ A ) )
& ! [A: $i] :
( ~ ( latt_str @ A )
| ( meet_semilatt_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[797]) ).
thf(1114,plain,
( ( meet_semilatt_str @ sK65_A )
= $true ),
inference(copy,[status(thm)],[796]) ).
thf(1115,plain,
( ( join_semilatt_str @ sK64_A )
= $true ),
inference(copy,[status(thm)],[795]) ).
thf(1116,plain,
( ( ! [A: $i,B: $i] : ( relation_of2 @ ( sK63_C @ B @ A ) @ A @ B ) )
= $true ),
inference(copy,[status(thm)],[794]) ).
thf(1117,plain,
( ( ! [A: $i,B: $i] : ( relation_of2_as_subset @ ( sK62_C @ B @ A ) @ A @ B ) )
= $true ),
inference(copy,[status(thm)],[793]) ).
thf(1118,plain,
( ( ! [A: $i,B: $i] :
( ~ ( finite @ B )
| ( finite @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[792]) ).
thf(1119,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( empty @ ( relation_composition @ B @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[791]) ).
thf(1120,plain,
( ( ! [A: $i] :
( ~ ( finite @ A )
| ! [B: $i] : ( finite @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[790]) ).
thf(1121,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_inverse @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[789]) ).
thf(1122,plain,
( ( ! [A: $i] :
( ~ ( finite @ A )
| ! [B: $i] : ( finite @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[788]) ).
thf(1123,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[557]) ).
thf(1124,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) )
& ! [A: $i] : ( finite @ ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[787]) ).
thf(1125,plain,
( ( ! [A: $i] :
~ ( empty @ ( succ @ A ) ) )
= $true ),
inference(copy,[status(thm)],[555]) ).
thf(1126,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[786]) ).
thf(1127,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[553]) ).
thf(1128,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[552]) ).
thf(1129,plain,
( ( ! [A: $i] :
( ~ ( v1_membered @ A )
| ! [B: $i] : ( v1_membered @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[785]) ).
thf(1130,plain,
( ( ! [A: $i] :
( ~ ( v1_membered @ A )
| ! [B: $i] : ( v1_membered @ ( set_intersection2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[784]) ).
thf(1131,plain,
( ( ! [A: $i] :
( ~ ( v2_membered @ A )
| ! [B: $i] : ( v1_membered @ ( set_intersection2 @ A @ B ) ) )
& ! [A: $i] :
( ~ ( v2_membered @ A )
| ! [B: $i] : ( v2_membered @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[783]) ).
thf(1132,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[782]) ).
thf(1133,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[547]) ).
thf(1134,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[781]) ).
thf(1135,plain,
( ( ! [A: $i] :
( ~ ( v2_membered @ A )
| ! [B: $i] : ( v1_membered @ ( set_intersection2 @ B @ A ) ) )
& ! [A: $i] :
( ~ ( v2_membered @ A )
| ! [B: $i] : ( v2_membered @ ( set_intersection2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[780]) ).
thf(1136,plain,
( ( ! [A: $i] :
( ~ ( v3_membered @ A )
| ! [B: $i] : ( v1_membered @ ( set_intersection2 @ A @ B ) ) )
& ! [A: $i] :
( ~ ( v3_membered @ A )
| ! [B: $i] : ( v2_membered @ ( set_intersection2 @ A @ B ) ) )
& ! [A: $i] :
( ~ ( v3_membered @ A )
| ! [B: $i] : ( v3_membered @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[779]) ).
thf(1137,plain,
( ( ! [A: $i] :
( ~ ( v3_membered @ A )
| ! [B: $i] : ( v1_membered @ ( set_intersection2 @ B @ A ) ) )
& ! [A: $i] :
( ~ ( v3_membered @ A )
| ! [B: $i] : ( v2_membered @ ( set_intersection2 @ B @ A ) ) )
& ! [A: $i] :
( ~ ( v3_membered @ A )
| ! [B: $i] : ( v3_membered @ ( set_intersection2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[778]) ).
thf(1138,plain,
( ( ! [A: $i] :
( ~ ( v1_membered @ A )
| ! [B: $i] : ( v1_membered @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[777]) ).
thf(1139,plain,
( ( ! [A: $i] :
( ~ ( v2_membered @ A )
| ! [B: $i] : ( v1_membered @ ( set_difference @ A @ B ) ) )
& ! [A: $i] :
( ~ ( v2_membered @ A )
| ! [B: $i] : ( v2_membered @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[776]) ).
thf(1140,plain,
( ( ! [A: $i] :
( ~ ( v3_membered @ A )
| ! [B: $i] : ( v1_membered @ ( set_difference @ A @ B ) ) )
& ! [A: $i] :
( ~ ( v3_membered @ A )
| ! [B: $i] : ( v2_membered @ ( set_difference @ A @ B ) ) )
& ! [A: $i] :
( ~ ( v3_membered @ A )
| ! [B: $i] : ( v3_membered @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[775]) ).
thf(1141,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[774]) ).
thf(1142,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[538]) ).
thf(1143,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[773]) ).
thf(1144,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[536]) ).
thf(1145,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[772]) ).
thf(1146,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[771]) ).
thf(1147,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[770]) ).
thf(1148,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[769]) ).
thf(1149,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[768]) ).
thf(1150,plain,
( ( ! [A: $i,B: $i] :
( ~ ( finite @ A )
| ~ ( finite @ B )
| ( finite @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[767]) ).
thf(1151,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( empty @ ( relation_composition @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[766]) ).
thf(1152,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[765]) ).
thf(1153,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[764]) ).
thf(1154,plain,
( ( ~ ( empty @ sK61_A )
& ( finite @ sK61_A ) )
= $true ),
inference(copy,[status(thm)],[763]) ).
thf(1155,plain,
( ( ( function @ sK60_A )
& ( relation @ sK60_A ) )
= $true ),
inference(copy,[status(thm)],[762]) ).
thf(1156,plain,
( ( ( empty @ sK59_A )
& ( relation @ sK59_A ) )
= $true ),
inference(copy,[status(thm)],[761]) ).
thf(1157,plain,
( ( empty @ sK58_A )
= $true ),
inference(copy,[status(thm)],[760]) ).
thf(1158,plain,
( ( ( empty @ sK57_A )
& ( relation @ sK57_A )
& ( function @ sK57_A ) )
= $true ),
inference(copy,[status(thm)],[759]) ).
thf(1159,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ ( sK56_C @ B @ A ) )
& ( relation_of2 @ ( sK56_C @ B @ A ) @ A @ B )
& ( function @ ( sK56_C @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[758]) ).
thf(1160,plain,
( ( ~ ( empty @ sK55_A )
& ( relation @ sK55_A ) )
= $true ),
inference(copy,[status(thm)],[757]) ).
thf(1161,plain,
( ( ~ ( empty @ sK54_A ) )
= $true ),
inference(copy,[status(thm)],[756]) ).
thf(1162,plain,
( ( ( relation @ sK53_A )
& ( relation_empty_yielding @ sK53_A ) )
= $true ),
inference(copy,[status(thm)],[755]) ).
thf(1163,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( ( relation_dom_as_subset @ A @ B @ C )
= ( relation_dom @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[754]) ).
thf(1164,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( ( relation_rng_as_subset @ A @ B @ C )
= ( relation_rng @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[753]) ).
thf(1165,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( relation_of2_as_subset @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[752]) ).
thf(1166,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[751]) ).
thf(1167,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ~ ( relation @ B )
| ( ! [SY721: $i] :
( ~ ( in @ SY721 @ ( sK52_SY712 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK49_SY705 @ B @ A ) @ SY721 ) @ B ) )
& ( ( sK48_C @ B @ A )
= ( sK52_SY712 @ B @ A ) )
& ( in @ ( sK49_SY705 @ B @ A ) @ ( sK52_SY712 @ B @ A ) )
& ( in @ ( sK48_C @ B @ A ) @ A )
& ( in @ ( sK48_C @ B @ A ) @ A )
& ! [SY720: $i] :
( ~ ( in @ SY720 @ ( sK51_SY718 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK50_SY711 @ B @ A ) @ SY720 ) @ B ) )
& ( ( sK48_C @ B @ A )
= ( sK51_SY718 @ B @ A ) )
& ( in @ ( sK50_SY711 @ B @ A ) @ ( sK51_SY718 @ B @ A ) )
& ( ( sK49_SY705 @ B @ A )
!= ( sK50_SY711 @ B @ A ) ) )
| ( ! [SY694: $i] :
( ! [E: $i] :
( ~ ( in @ E @ A )
| ! [J: $i] :
( ( ( in @ ( sK47_K @ J @ E @ SY694 @ B @ A ) @ J )
& ~ ( in @ ( ordered_pair @ SY694 @ ( sK47_K @ J @ E @ SY694 @ B @ A ) ) @ B ) )
| ( E != J )
| ~ ( in @ SY694 @ J ) ) )
| ( in @ SY694 @ ( sK44_C @ B @ A ) ) )
& ! [SY698: $i] :
( ~ ( in @ SY698 @ ( sK44_C @ B @ A ) )
| ( ( in @ ( sK45_E @ SY698 @ B @ A ) @ A )
& ! [SY704: $i] :
( ~ ( in @ SY704 @ ( sK46_SY702 @ SY698 @ B @ A ) )
| ( in @ ( ordered_pair @ SY698 @ SY704 ) @ B ) )
& ( ( sK45_E @ SY698 @ B @ A )
= ( sK46_SY702 @ SY698 @ B @ A ) )
& ( in @ SY698 @ ( sK46_SY702 @ SY698 @ B @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[750]) ).
thf(1168,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ~ ( relation @ B )
| ( ( ( sK35_D @ B @ A )
= ( sK36_SY655 @ B @ A ) )
& ( ( ordered_pair @ ( sK41_SY666 @ B @ A ) @ ( sK42_SY688 @ B @ A ) )
= ( sK36_SY655 @ B @ A ) )
& ( in @ ( sK41_SY666 @ B @ A ) @ A )
& ! [SY693: $i] :
( ~ ( in @ SY693 @ ( sK43_SY691 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK42_SY688 @ B @ A ) @ SY693 ) @ B ) )
& ( ( sK41_SY666 @ B @ A )
= ( sK43_SY691 @ B @ A ) )
& ( in @ ( sK42_SY688 @ B @ A ) @ ( sK43_SY691 @ B @ A ) )
& ( ( sK35_D @ B @ A )
= ( sK37_SY665 @ B @ A ) )
& ( ( ordered_pair @ ( sK38_SY678 @ B @ A ) @ ( sK39_SY682 @ B @ A ) )
= ( sK37_SY665 @ B @ A ) )
& ( in @ ( sK38_SY678 @ B @ A ) @ A )
& ! [SY687: $i] :
( ~ ( in @ SY687 @ ( sK40_SY685 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK39_SY682 @ B @ A ) @ SY687 ) @ B ) )
& ( ( sK38_SY678 @ B @ A )
= ( sK40_SY685 @ B @ A ) )
& ( in @ ( sK39_SY682 @ B @ A ) @ ( sK40_SY685 @ B @ A ) )
& ( ( sK36_SY655 @ B @ A )
!= ( sK37_SY665 @ B @ A ) ) )
| ! [C: $i] :
( ! [SY637: $i] :
( ! [F: $i] :
( ( F != SY637 )
| ~ ( in @ F @ ( cartesian_product2 @ A @ C ) ) )
| ! [O: $i,P: $i] :
( ( ( ordered_pair @ O @ P )
!= SY637 )
| ~ ( in @ O @ A )
| ! [Q: $i] :
( ( ( in @ ( sK34_R @ Q @ P @ O @ SY637 @ C @ B @ A ) @ Q )
& ~ ( in @ ( ordered_pair @ P @ ( sK34_R @ Q @ P @ O @ SY637 @ C @ B @ A ) ) @ B ) )
| ( O != Q )
| ~ ( in @ P @ Q ) ) )
| ( in @ SY637 @ ( sK29_D @ C @ B @ A ) ) )
& ! [SY643: $i] :
( ~ ( in @ SY643 @ ( sK29_D @ C @ B @ A ) )
| ( ( ( sK33_F @ SY643 @ C @ B @ A )
= SY643 )
& ( in @ ( sK33_F @ SY643 @ C @ B @ A ) @ ( cartesian_product2 @ A @ C ) )
& ( ( ordered_pair @ ( sK30_O @ SY643 @ C @ B @ A ) @ ( sK31_SY649 @ SY643 @ C @ B @ A ) )
= SY643 )
& ( in @ ( sK30_O @ SY643 @ C @ B @ A ) @ A )
& ! [SY654: $i] :
( ~ ( in @ SY654 @ ( sK32_SY652 @ SY643 @ C @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY643 @ C @ B @ A ) @ SY654 ) @ B ) )
& ( ( sK30_O @ SY643 @ C @ B @ A )
= ( sK32_SY652 @ SY643 @ C @ B @ A ) )
& ( in @ ( sK31_SY649 @ SY643 @ C @ B @ A ) @ ( sK32_SY652 @ SY643 @ C @ B @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[749]) ).
thf(1169,plain,
( ( ! [A: $i] :
( ( ( ( sK27_SY634 @ A )
= ( singleton @ ( sK26_B @ A ) ) )
& ( in @ ( sK26_B @ A ) @ A )
& ( in @ ( sK26_B @ A ) @ A )
& ( ( sK28_SY636 @ A )
= ( singleton @ ( sK26_B @ A ) ) )
& ( ( sK27_SY634 @ A )
!= ( sK28_SY636 @ A ) ) )
| ( ! [SY630: $i] :
( ! [D: $i] :
( ~ ( in @ D @ A )
| ( SY630
!= ( singleton @ D ) ) )
| ( in @ SY630 @ ( sK24_B @ A ) ) )
& ! [SY632: $i] :
( ~ ( in @ SY632 @ ( sK24_B @ A ) )
| ( ( in @ ( sK25_D @ SY632 @ A ) @ A )
& ( SY632
= ( singleton @ ( sK25_D @ SY632 @ A ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[748]) ).
thf(1170,plain,
( ( ! [A: $i] :
( ( ( ( sK17_C @ A )
= ( sK18_SY613 @ A ) )
& ( ( ordered_pair @ ( sK22_SY620 @ A ) @ ( sK23_SY629 @ A ) )
= ( sK18_SY613 @ A ) )
& ( in @ ( sK22_SY620 @ A ) @ A )
& ( ( sK23_SY629 @ A )
= ( singleton @ ( sK22_SY620 @ A ) ) )
& ( ( sK17_C @ A )
= ( sK19_SY619 @ A ) )
& ( ( ordered_pair @ ( sK20_SY626 @ A ) @ ( sK21_SY628 @ A ) )
= ( sK19_SY619 @ A ) )
& ( in @ ( sK20_SY626 @ A ) @ A )
& ( ( sK21_SY628 @ A )
= ( singleton @ ( sK20_SY626 @ A ) ) )
& ( ( sK18_SY613 @ A )
!= ( sK19_SY619 @ A ) ) )
| ! [B: $i] :
( ! [SY604: $i] :
( ! [E: $i] :
( ( E != SY604 )
| ~ ( in @ E @ ( cartesian_product2 @ A @ B ) ) )
| ! [J: $i,K: $i] :
( ( ( ordered_pair @ J @ K )
!= SY604 )
| ~ ( in @ J @ A )
| ( K
!= ( singleton @ J ) ) )
| ( in @ SY604 @ ( sK13_C @ B @ A ) ) )
& ! [SY608: $i] :
( ~ ( in @ SY608 @ ( sK13_C @ B @ A ) )
| ( ( ( sK16_E @ SY608 @ B @ A )
= SY608 )
& ( in @ ( sK16_E @ SY608 @ B @ A ) @ ( cartesian_product2 @ A @ B ) )
& ( ( ordered_pair @ ( sK14_J @ SY608 @ B @ A ) @ ( sK15_SY612 @ SY608 @ B @ A ) )
= SY608 )
& ( in @ ( sK14_J @ SY608 @ B @ A ) @ A )
& ( ( sK15_SY612 @ SY608 @ B @ A )
= ( singleton @ ( sK14_J @ SY608 @ B @ A ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[747]) ).
thf(1171,plain,
( ( ( sK12_REN
| ! [A: $i] :
( ! [SY597: $i] :
( ! [D: $i] :
( ( D != SY597 )
| ~ ( in @ D @ A ) )
| ~ ( ordinal @ SY597 )
| ( in @ SY597 @ ( sK7_B @ A ) ) )
& ! [SY599: $i] :
( ~ ( in @ SY599 @ ( sK7_B @ A ) )
| ( ( ( sK8_D @ SY599 @ A )
= SY599 )
& ( in @ ( sK8_D @ SY599 @ A ) @ A )
& ( ordinal @ SY599 ) ) ) ) )
& ( sK12_REN
=> ( ( sK9_B = sK10_SY601 )
& ( ordinal @ sK10_SY601 )
& ( sK9_B = sK11_SY603 )
& ( ordinal @ sK11_SY603 )
& ( sK10_SY601 != sK11_SY603 ) ) ) )
= $true ),
inference(copy,[status(thm)],[746]) ).
thf(1172,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[745]) ).
thf(1173,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[507]) ).
thf(1174,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[506]) ).
thf(1175,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK6_C @ B @ A ) @ A )
| ~ ( in @ ( sK6_C @ B @ A ) @ B ) )
& ( ( in @ ( sK6_C @ B @ A ) @ A )
| ( in @ ( sK6_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[744]) ).
thf(1176,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[504]) ).
thf(1177,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[503]) ).
thf(1178,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[743]) ).
thf(1179,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[742]) ).
thf(1180,plain,
( ( ! [A: $i,B: $i] :
( ( ! [SY596: $i] :
( ~ ( in @ SY596 @ B )
| ~ ( in @ SY596 @ ( sK5_C @ B @ A ) ) )
& ( in @ ( sK5_C @ B @ A ) @ B ) )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[741]) ).
thf(1181,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[740]) ).
thf(1182,plain,
( ( ! [A: $i] :
( ! [SY589: $i] :
( ~ ( subset @ SY589 @ ( sK3_B @ A ) )
| ( are_equipotent @ SY589 @ ( sK3_B @ A ) )
| ( in @ SY589 @ ( sK3_B @ A ) ) )
& ! [SY590: $i] :
( ( ! [SY595: $i] :
( ~ ( subset @ SY595 @ SY590 )
| ( in @ SY595 @ ( sK4_SY591 @ SY590 @ A ) ) )
& ( in @ ( sK4_SY591 @ SY590 @ A ) @ ( sK3_B @ A ) ) )
| ~ ( in @ SY590 @ ( sK3_B @ A ) ) )
& ! [SY593: $i,SY594: $i] :
( ~ ( in @ SY593 @ ( sK3_B @ A ) )
| ~ ( subset @ SY594 @ SY593 )
| ( in @ SY594 @ ( sK3_B @ A ) ) )
& ( in @ A @ ( sK3_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[739]) ).
thf(1183,plain,
( ( one_sorted_str @ sK1_A )
= $true ),
inference(copy,[status(thm)],[735]) ).
thf(1184,plain,
( ( ( element @ sK2_SY588 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
& ( ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY588 )
!= ( subset_difference @ ( the_carrier @ sK1_A ) @ ( cast_as_carrier_subset @ sK1_A ) @ sK2_SY588 ) ) )
= $true ),
inference(copy,[status(thm)],[738]) ).
thf(1185,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1103]) ).
thf(1186,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1102]) ).
thf(1187,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK17_C @ SX0 )
!= ( sK18_SY613 @ SX0 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK22_SY620 @ SX0 ) @ ( sK23_SY629 @ SX0 ) )
!= ( sK18_SY613 @ SX0 ) )
| ~ ( in @ ( sK22_SY620 @ SX0 ) @ SX0 ) )
| ( ( sK23_SY629 @ SX0 )
!= ( singleton @ ( sK22_SY620 @ SX0 ) ) ) ) )
| ( ( sK17_C @ SX0 )
!= ( sK19_SY619 @ SX0 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK20_SY626 @ SX0 ) @ ( sK21_SY628 @ SX0 ) )
!= ( sK19_SY619 @ SX0 ) )
| ~ ( in @ ( sK20_SY626 @ SX0 ) @ SX0 ) )
| ( ( sK21_SY628 @ SX0 )
!= ( singleton @ ( sK20_SY626 @ SX0 ) ) ) ) )
| ~ ( ( ( sK18_SY613 @ SX0 )
!= ( sK19_SY619 @ SX0 ) ) ) )
| ! [SX1: $i] :
~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ( SX3 != SX2 )
| ~ ( in @ SX3 @ ( cartesian_product2 @ SX0 @ SX1 ) ) )
| ! [SX3: $i,SX4: $i] :
( ( ( ordered_pair @ SX3 @ SX4 )
!= SX2 )
| ~ ( in @ SX3 @ SX0 )
| ( SX4
!= ( singleton @ SX3 ) ) )
| ( in @ SX2 @ ( sK13_C @ SX1 @ SX0 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK13_C @ SX1 @ SX0 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SX2 @ SX1 @ SX0 )
!= SX2 )
| ~ ( in @ ( sK16_E @ SX2 @ SX1 @ SX0 ) @ ( cartesian_product2 @ SX0 @ SX1 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SX2 @ SX1 @ SX0 ) @ ( sK15_SY612 @ SX2 @ SX1 @ SX0 ) )
!= SX2 )
| ~ ( in @ ( sK14_J @ SX2 @ SX1 @ SX0 ) @ SX0 ) )
| ( ( sK15_SY612 @ SX2 @ SX1 @ SX0 )
!= ( singleton @ ( sK14_J @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1170]) ).
thf(1188,plain,
( ( ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 )
| ~ ( ~ ( element @ ( sK116_B @ SX0 ) @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ~ ( empty @ ( sK116_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[992]) ).
thf(1189,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_intersection2 @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_intersection2 @ SX1 @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v3_membered @ ( set_intersection2 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1137]) ).
thf(1190,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK99_B @ SX0 ) @ SX0 )
| ~ ( ~ ( ordinal @ ( sK99_B @ SX0 ) )
| ~ ( subset @ ( sK99_B @ SX0 ) @ SX0 ) ) )
| ( ordinal @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1040]) ).
thf(1191,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX2 )
| ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1045]) ).
thf(1192,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK70_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK70_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK70_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK70_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK70_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( sK70_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK70_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1096]) ).
thf(1193,plain,
( ( ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ~ ( ~ ~ ( ~ ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( v1_membered @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( v2_membered @ SX1 ) ) )
| ~ ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( v3_membered @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1073]) ).
thf(1194,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK52_SY712 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK49_SY705 @ SX1 @ SX0 ) @ SX2 ) @ SX1 ) )
| ~ ~ ( ( ( sK48_C @ SX1 @ SX0 )
!= ( sK52_SY712 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK49_SY705 @ SX1 @ SX0 ) @ ( sK52_SY712 @ SX1 @ SX0 ) ) ) )
| ~ ( in @ ( sK48_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( in @ ( sK48_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK51_SY718 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK50_SY711 @ SX1 @ SX0 ) @ SX2 ) @ SX1 ) )
| ~ ~ ( ( ( sK48_C @ SX1 @ SX0 )
!= ( sK51_SY718 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK50_SY711 @ SX1 @ SX0 ) @ ( sK51_SY718 @ SX1 @ SX0 ) ) ) ) )
| ~ ( ( ( sK49_SY705 @ SX1 @ SX0 )
!= ( sK50_SY711 @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX4 )
| ~ ~ ( in @ ( ordered_pair @ SX2 @ ( sK47_K @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( SX3 != SX4 )
| ~ ( in @ SX2 @ SX4 ) ) )
| ( in @ SX2 @ ( sK44_C @ SX1 @ SX0 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK44_C @ SX1 @ SX0 ) )
| ~ ( ~ ( in @ ( sK45_E @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ ( sK46_SY702 @ SX2 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) )
| ~ ~ ( ( ( sK45_E @ SX2 @ SX1 @ SX0 )
!= ( sK46_SY702 @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ SX2 @ ( sK46_SY702 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1167]) ).
thf(1195,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1080]) ).
thf(1196,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( sK5_C @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1180]) ).
thf(1197,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK85_B @ SX0 ) @ SX0 )
| ~ ~ ( subset @ ( sK85_B @ SX0 ) @ SX0 ) )
| ( epsilon_transitive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( epsilon_transitive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1088]) ).
thf(1198,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK66_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK66_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK66_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK66_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK66_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( in @ ( sK66_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK66_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( set_difference @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_difference @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( in @ SX3 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1099]) ).
thf(1199,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( in @ ( sK86_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1087]) ).
thf(1200,plain,
( ( ! [SX0: $i] :
( ~ ( finite @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( subset @ ( sK105_C @ SX1 @ SX0 ) @ SX2 )
| ( SX2
= ( sK105_C @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK105_C @ SX1 @ SX0 ) @ SX1 ) )
| ( SX1 = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1029]) ).
thf(1201,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1065]) ).
thf(1202,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1061]) ).
thf(1203,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK68_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK68_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK68_C @ SX1 @ SX0 ) @ ( sK69_SY723 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK69_SY723 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK68_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK67_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK67_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1098]) ).
thf(1204,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[999]) ).
thf(1205,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1121]) ).
thf(1206,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[964]) ).
thf(1207,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK124_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK124_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK124_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK124_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[963]) ).
thf(1208,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ~ ( ~ ( element @ ( sK118_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK118_B @ SX0 ) ) )
| ~ ( finite @ ( sK118_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[990]) ).
thf(1209,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ~ ( ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ ( sK102_D @ SX2 @ SX1 @ SX0 ) ) @ SX2 )
| ~ ( in @ ( sK102_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( relation_rng_as_subset @ SX0 @ SX1 @ SX2 )
= SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( ( relation_rng_as_subset @ SX0 @ SX1 @ SX2 )
!= SX1 )
| ! [SX3: $i] :
( ( in @ ( ordered_pair @ ( sK101_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX2 )
| ~ ( in @ SX3 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1034]) ).
thf(1210,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK94_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 )
| ( ( sK94_E @ SX3 @ SX2 @ SX1 @ SX0 )
!= SX2 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK94_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 )
| ( ( sK94_E @ SX3 @ SX2 @ SX1 @ SX0 )
!= SX0 ) )
| ~ ( ~ ( in @ ( sK94_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 )
| ( ( sK94_E @ SX3 @ SX2 @ SX1 @ SX0 )
!= SX1 ) ) ) )
| ~ ( ( in @ ( sK94_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 )
| ( ( sK94_E @ SX3 @ SX2 @ SX1 @ SX0 )
= SX2 )
| ( ( sK94_E @ SX3 @ SX2 @ SX1 @ SX0 )
= SX0 )
| ( ( sK94_E @ SX3 @ SX2 @ SX1 @ SX0 )
= SX1 ) ) )
| ( SX3
= ( unordered_triple @ SX0 @ SX1 @ SX2 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( SX3
!= ( unordered_triple @ SX0 @ SX1 @ SX2 ) )
| ~ ( ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( SX4 = SX2 )
| ( SX4 = SX0 )
| ( SX4 = SX1 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SX2 )
| ( in @ SX4 @ SX3 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SX0 )
| ( in @ SX4 @ SX3 ) )
| ~ ! [SX4: $i] :
( ( SX4 != SX1 )
| ( in @ SX4 @ SX3 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1081]) ).
thf(1211,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX1 @ ( sK106_B @ SX0 ) )
| ( are_equipotent @ SX1 @ ( sK106_B @ SX0 ) )
| ( in @ SX1 @ ( sK106_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK106_B @ SX0 ) )
| ( in @ ( powerset @ SX1 ) @ ( sK106_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK106_B @ SX0 ) )
| ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK106_B @ SX0 ) ) )
| ~ ( in @ SX0 @ ( sK106_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1021]) ).
thf(1212,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ~ ( ordinal @ SX1 )
| ( in @ SX1 @ ( sK107_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK107_B @ SX0 ) )
| ( in @ SX1 @ SX0 ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK107_B @ SX0 ) )
| ( ordinal @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1014]) ).
thf(1213,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK72_C @ SX1 @ SX0 ) @ ( sK73_SY724 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( in @ ( ordered_pair @ ( sK72_C @ SX1 @ SX0 ) @ ( sK73_SY724 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1094]) ).
thf(1214,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ ( powerset @ SX0 ) ) )
| ~ ( ~ ( element @ ( sK123_D @ SX2 @ SX1 @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK123_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( subset_complement @ SX0 @ ( sK123_D @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK123_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( in @ ( subset_complement @ SX0 @ ( sK123_D @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX2
= ( complements_of_subsets @ SX0 @ SX1 ) ) )
| ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ ( powerset @ SX0 ) ) )
| ( SX2
!= ( complements_of_subsets @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( element @ SX3 @ ( powerset @ SX0 ) )
| ~ ( in @ SX3 @ SX2 )
| ( in @ ( subset_complement @ SX0 @ SX3 ) @ SX1 ) )
| ~ ! [SX3: $i] :
( ~ ( element @ SX3 @ ( powerset @ SX0 ) )
| ~ ( in @ ( subset_complement @ SX0 @ SX3 ) @ SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[967]) ).
thf(1215,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1009]) ).
thf(1216,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1047]) ).
thf(1217,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1043]) ).
thf(1218,plain,
( ( ! [SX0: $i] :
( ~ ( v2_membered @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( v1_membered @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( v2_membered @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[959]) ).
thf(1219,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1151]) ).
thf(1220,plain,
( ( ~ ( ~ ( sK12_REN
| ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
( ( SX2 != SX1 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( ordinal @ SX1 )
| ( in @ SX1 @ ( sK7_B @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK7_B @ SX0 ) )
| ~ ( ~ ~ ( ( ( sK8_D @ SX1 @ SX0 )
!= SX1 )
| ~ ( in @ ( sK8_D @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ordinal @ SX1 ) ) ) ) )
| ~ ( ~ sK12_REN
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK9_B != sK10_SY601 )
| ~ ( ordinal @ sK10_SY601 ) )
| ( sK9_B != sK11_SY603 ) )
| ~ ( ordinal @ sK11_SY603 ) )
| ~ ( ( sK10_SY601 != sK11_SY603 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1171]) ).
thf(1221,plain,
( ( ~ ( ~ ( element @ sK2_SY588 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( ( ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY588 )
!= ( subset_difference @ ( the_carrier @ sK1_A ) @ ( cast_as_carrier_subset @ sK1_A ) @ sK2_SY588 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1184]) ).
thf(1222,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX0 @ ( cartesian_product2 @ SX1 @ SX1 ) )
| ( in @ SX0 @ ( relation_restriction @ SX2 @ SX1 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_restriction @ SX2 @ SX1 ) )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_restriction @ SX2 @ SX1 ) )
| ( in @ SX0 @ ( cartesian_product2 @ SX1 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1026]) ).
thf(1223,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1123]) ).
thf(1224,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( SX1 = empty_set )
| ( SX0
!= ( relation_dom_as_subset @ SX0 @ SX1 @ SX2 ) )
| ( quasi_total @ SX2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( SX1 = empty_set )
| ~ ( quasi_total @ SX2 @ SX0 @ SX1 )
| ( SX0
= ( relation_dom_as_subset @ SX0 @ SX1 @ SX2 ) ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( SX0 != empty_set )
| ( SX0
!= ( relation_dom_as_subset @ SX0 @ SX1 @ SX2 ) )
| ( quasi_total @ SX2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( SX0 != empty_set )
| ~ ( quasi_total @ SX2 @ SX0 @ SX1 )
| ( SX0
= ( relation_dom_as_subset @ SX0 @ SX1 @ SX2 ) ) ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( SX1 != empty_set )
| ( SX2 != empty_set )
| ( quasi_total @ SX2 @ SX0 @ SX1 )
| ( SX0 = empty_set ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( SX1 != empty_set )
| ~ ( quasi_total @ SX2 @ SX0 @ SX1 )
| ( SX2 = empty_set )
| ( SX0 = empty_set ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1082]) ).
thf(1225,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK90_SY733 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK89_C @ SX1 @ SX0 ) @ ( sK90_SY733 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK89_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK89_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK89_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK88_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK88_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1085]) ).
thf(1226,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK82_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK82_D @ SX2 @ SX1 @ SX0 )
!= SX0 ) )
| ~ ( ~ ( in @ ( sK82_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK82_D @ SX2 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ( ( in @ ( sK82_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK82_D @ SX2 @ SX1 @ SX0 )
= SX0 )
| ( ( sK82_D @ SX2 @ SX1 @ SX0 )
= SX1 ) ) )
| ( SX2
= ( unordered_pair @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( unordered_pair @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ( SX3 != SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1090]) ).
thf(1227,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1119]) ).
thf(1228,plain,
( ( ! [SX0: $i] :
( ~ ( v2_membered @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( v1_xcmplx_0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( v1_xreal_0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1072]) ).
thf(1229,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( latt_str @ SX0 )
| ( join_semilatt_str @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( latt_str @ SX0 )
| ( meet_semilatt_str @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1113]) ).
thf(1230,plain,
( ( ~ ( ~ ( relation @ sK53_A )
| ~ ( relation_empty_yielding @ sK53_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1162]) ).
thf(1231,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK93_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK93_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK91_C @ SX1 @ SX0 ) @ ( sK92_SY735 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1083]) ).
thf(1232,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1149]) ).
thf(1233,plain,
( ( ! [SX0: $i] :
~ ( ~ ( relation @ ( sK100_B @ SX0 ) )
| ~ ( well_orders @ ( sK100_B @ SX0 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1036]) ).
thf(1234,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ SX0 ) )
| ~ ( disjoint @ SX1 @ SX2 )
| ( subset @ SX1 @ ( subset_complement @ SX0 @ SX2 ) ) )
| ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ SX0 ) )
| ~ ( subset @ SX1 @ ( subset_complement @ SX0 @ SX2 ) )
| ( disjoint @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[952]) ).
thf(1235,plain,
( ( ~ ( ~ ( one_sorted_str @ sK117_A )
| ~ ~ ( empty_carrier @ sK117_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[991]) ).
thf(1236,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1006]) ).
thf(1237,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2 @ SX2 @ SX0 @ SX1 )
| ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( relation_of2 @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1165]) ).
thf(1238,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK87_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK87_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK87_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK87_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1086]) ).
thf(1239,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i,SX4: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX4 @ SX1 )
| ( ( sK78_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ SX3 @ SX4 ) ) )
| ~ ( in @ ( sK78_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK79_SY729 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK80_SY731 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( sK78_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ ( sK79_SY729 @ SX2 @ SX1 @ SX0 ) @ ( sK80_SY731 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( in @ ( sK78_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ( SX2
= ( cartesian_product2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( cartesian_product2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i,SX5: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ~ ( ~ ( in @ ( sK76_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK77_SY726 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( SX3
!= ( ordered_pair @ ( sK76_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK77_SY726 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1092]) ).
thf(1240,plain,
( ( ~ ( ~ ( empty @ sK59_A )
| ~ ( relation @ sK59_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1156]) ).
thf(1241,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK71_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK71_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1095]) ).
thf(1242,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2 @ SX2 @ SX0 @ SX1 )
| ( subset @ SX2 @ ( cartesian_product2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ ( cartesian_product2 @ SX0 @ SX1 ) )
| ( relation_of2 @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1084]) ).
thf(1243,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX1 @ ( sK3_B @ SX0 ) )
| ( are_equipotent @ SX1 @ ( sK3_B @ SX0 ) )
| ( in @ SX1 @ ( sK3_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK4_SY591 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK4_SY591 @ SX1 @ SX0 ) @ ( sK3_B @ SX0 ) ) )
| ~ ( in @ SX1 @ ( sK3_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK3_B @ SX0 ) )
| ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK3_B @ SX0 ) ) )
| ~ ( in @ SX0 @ ( sK3_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1182]) ).
thf(1244,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX1 @ SX0 )
| ~ ( ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ ( sK104_D @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX2 )
| ~ ( in @ ( sK104_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( relation_dom_as_subset @ SX1 @ SX0 @ SX2 )
= SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX1 @ SX0 )
| ( ( relation_dom_as_subset @ SX1 @ SX0 @ SX2 )
!= SX1 )
| ! [SX3: $i] :
( ( in @ ( ordered_pair @ SX3 @ ( sK103_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX2 )
| ~ ( in @ SX3 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1032]) ).
thf(1245,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK27_SY634 @ SX0 )
!= ( singleton @ ( sK26_B @ SX0 ) ) )
| ~ ( in @ ( sK26_B @ SX0 ) @ SX0 ) )
| ~ ( in @ ( sK26_B @ SX0 ) @ SX0 ) )
| ( ( sK28_SY636 @ SX0 )
!= ( singleton @ ( sK26_B @ SX0 ) ) ) )
| ~ ( ( ( sK27_SY634 @ SX0 )
!= ( sK28_SY636 @ SX0 ) ) ) )
| ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1
!= ( singleton @ SX2 ) ) )
| ( in @ SX1 @ ( sK24_B @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK24_B @ SX0 ) )
| ~ ( ~ ( in @ ( sK25_D @ SX1 @ SX0 ) @ SX0 )
| ( SX1
!= ( singleton @ ( sK25_D @ SX1 @ SX0 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1169]) ).
thf(1246,plain,
( ( ~ ( ~ ( function @ sK60_A )
| ~ ( relation @ sK60_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1155]) ).
thf(1247,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ sK57_A )
| ~ ( relation @ sK57_A ) )
| ~ ( function @ sK57_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1158]) ).
thf(1248,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ( in @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1015]) ).
thf(1249,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ! [SX2: $i] :
~ ( ~ ! [SX3: $i] :
( ! [SX4: $i,SX5: $i] :
( ( ( ordered_pair @ SX4 @ SX5 )
!= SX3 )
| ~ ( in @ SX4 @ SX0 )
| ! [SX6: $i] :
( ~ ( ~ ( in @ ( sK115_I @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX6 )
| ~ ~ ( in @ ( ordered_pair @ SX5 @ ( sK115_I @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( SX4 != SX6 )
| ~ ( in @ SX5 @ SX6 ) ) )
| ~ ( in @ SX3 @ ( cartesian_product2 @ SX0 @ SX2 ) )
| ( in @ SX3 @ ( sK111_D @ SX2 @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ ( sK111_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( ~ ~ ( ( ( ordered_pair @ ( sK112_F @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK113_SY768 @ SX3 @ SX2 @ SX1 @ SX0 ) )
!= SX3 )
| ~ ( in @ ( sK112_F @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ ( sK114_SY771 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK113_SY768 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX4 ) @ SX1 ) )
| ~ ~ ( ( ( sK112_F @ SX3 @ SX2 @ SX1 @ SX0 )
!= ( sK114_SY771 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK113_SY768 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK114_SY771 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ ( sK111_D @ SX2 @ SX1 @ SX0 ) )
| ( in @ SX3 @ ( cartesian_product2 @ SX0 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1012]) ).
thf(1250,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( ( ( sK74_B @ SX0 )
!= ( sK75_SY725 @ SX0 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK74_B @ SX0 ) @ SX0 )
| ~ ( in @ ( sK75_SY725 @ SX0 ) @ SX0 ) )
| ~ ~ ( in @ ( sK74_B @ SX0 ) @ ( sK75_SY725 @ SX0 ) ) ) )
| ~ ~ ( in @ ( sK75_SY725 @ SX0 ) @ ( sK74_B @ SX0 ) ) )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( epsilon_connected @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( SX1 = SX2 )
| ~ ( in @ SX1 @ SX0 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ SX2 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1093]) ).
thf(1251,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_difference @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_difference @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v3_membered @ ( set_difference @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1140]) ).
thf(1252,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK83_C @ SX1 @ SX0 ) @ ( sK84_SY732 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK83_C @ SX1 @ SX0 ) @ ( sK84_SY732 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK83_C @ SX1 @ SX0 ) @ ( sK84_SY732 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK83_C @ SX1 @ SX0 ) @ ( sK84_SY732 @ SX1 @ SX0 ) ) @ SX1 ) ) )
| ( SX0 = SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1089]) ).
thf(1253,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1144]) ).
thf(1254,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK98_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK98_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1049]) ).
thf(1255,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1044]) ).
thf(1256,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK97_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1057]) ).
thf(1257,plain,
( ( ~ ( ~ ! [SX0: $i] :
~ ( empty @ ( singleton @ SX0 ) )
| ~ ! [SX0: $i] : ( finite @ ( singleton @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1124]) ).
thf(1258,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK35_D @ SX1 @ SX0 )
!= ( sK36_SY655 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK41_SY666 @ SX1 @ SX0 ) @ ( sK42_SY688 @ SX1 @ SX0 ) )
!= ( sK36_SY655 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK41_SY666 @ SX1 @ SX0 ) @ SX0 ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK43_SY691 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK42_SY688 @ SX1 @ SX0 ) @ SX2 ) @ SX1 ) )
| ~ ~ ( ( ( sK41_SY666 @ SX1 @ SX0 )
!= ( sK43_SY691 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK42_SY688 @ SX1 @ SX0 ) @ ( sK43_SY691 @ SX1 @ SX0 ) ) ) ) ) )
| ( ( sK35_D @ SX1 @ SX0 )
!= ( sK37_SY665 @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK38_SY678 @ SX1 @ SX0 ) @ ( sK39_SY682 @ SX1 @ SX0 ) )
!= ( sK37_SY665 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK38_SY678 @ SX1 @ SX0 ) @ SX0 ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK40_SY685 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK39_SY682 @ SX1 @ SX0 ) @ SX2 ) @ SX1 ) )
| ~ ~ ( ( ( sK38_SY678 @ SX1 @ SX0 )
!= ( sK40_SY685 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK39_SY682 @ SX1 @ SX0 ) @ ( sK40_SY685 @ SX1 @ SX0 ) ) ) ) ) )
| ~ ( ( ( sK36_SY655 @ SX1 @ SX0 )
!= ( sK37_SY665 @ SX1 @ SX0 ) ) ) )
| ! [SX2: $i] :
~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
( ( SX4 != SX3 )
| ~ ( in @ SX4 @ ( cartesian_product2 @ SX0 @ SX2 ) ) )
| ! [SX4: $i,SX5: $i] :
( ( ( ordered_pair @ SX4 @ SX5 )
!= SX3 )
| ~ ( in @ SX4 @ SX0 )
| ! [SX6: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX6 )
| ~ ~ ( in @ ( ordered_pair @ SX5 @ ( sK34_R @ SX6 @ SX5 @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( SX4 != SX6 )
| ~ ( in @ SX5 @ SX6 ) ) )
| ( in @ SX3 @ ( sK29_D @ SX2 @ SX1 @ SX0 ) ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ ( sK29_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SX3 @ SX2 @ SX1 @ SX0 )
!= SX3 )
| ~ ( in @ ( sK33_F @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( cartesian_product2 @ SX0 @ SX2 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK31_SY649 @ SX3 @ SX2 @ SX1 @ SX0 ) )
!= SX3 )
| ~ ( in @ ( sK30_O @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ ( sK32_SY652 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX4 ) @ SX1 ) )
| ~ ~ ( ( ( sK30_O @ SX3 @ SX2 @ SX1 @ SX0 )
!= ( sK32_SY652 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK31_SY649 @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK32_SY652 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1168]) ).
thf(1259,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0
!= ( union @ SX0 ) )
| ( being_limit_ordinal @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( being_limit_ordinal @ SX0 )
| ( SX0
= ( union @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1100]) ).
thf(1260,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( v2_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_intersection2 @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( v2_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_intersection2 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1135]) ).
thf(1261,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ( in @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1011]) ).
thf(1262,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ( ~ ( relation @ ( sK56_C @ SX1 @ SX0 ) )
| ~ ( relation_of2 @ ( sK56_C @ SX1 @ SX0 ) @ SX0 @ SX1 ) )
| ~ ( function @ ( sK56_C @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1159]) ).
thf(1263,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1148]) ).
thf(1264,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( v2_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_difference @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( v2_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_difference @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1139]) ).
thf(1265,plain,
( ( ! [SX0: $i] :
~ ( ~ ( element @ ( sK119_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ( empty @ ( sK119_B @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[989]) ).
thf(1266,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v3_membered @ ( set_intersection2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1136]) ).
thf(1267,plain,
( ( ~ ( ~ ~ ( empty @ sK61_A )
| ~ ( finite @ sK61_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1154]) ).
thf(1268,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( v2_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( v2_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_intersection2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1131]) ).
thf(1269,plain,
( ( ~ ( ~ ~ ( empty @ sK55_A )
| ~ ( relation @ sK55_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1160]) ).
thf(1270,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1007]) ).
thf(1271,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i] :
( ! [SX3: $i,SX4: $i] :
( ( ( ordered_pair @ SX3 @ SX4 )
!= SX2 )
| ~ ( in @ SX3 @ SX0 )
| ( SX4
!= ( singleton @ SX3 ) ) )
| ~ ( in @ SX2 @ ( cartesian_product2 @ SX0 @ SX1 ) )
| ( in @ SX2 @ ( sK108_C @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK108_C @ SX1 @ SX0 ) )
| ~ ( ~ ~ ( ( ( ordered_pair @ ( sK109_E @ SX2 @ SX1 @ SX0 ) @ ( sK110_SY756 @ SX2 @ SX1 @ SX0 ) )
!= SX2 )
| ~ ( in @ ( sK109_E @ SX2 @ SX1 @ SX0 ) @ SX0 ) )
| ( ( sK110_SY756 @ SX2 @ SX1 @ SX0 )
!= ( singleton @ ( sK109_E @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK108_C @ SX1 @ SX0 ) )
| ( in @ SX2 @ ( cartesian_product2 @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1013]) ).
thf(1272,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK125_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK125_C @ SX1 @ SX0 ) @ SX1 ) )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[948]) ).
thf(1273,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1175]) ).
thf(1274,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] : ( subset @ ( cartesian_product2 @ SX0 @ SX2 ) @ ( cartesian_product2 @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] : ( subset @ ( cartesian_product2 @ SX2 @ SX0 ) @ ( cartesian_product2 @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1018]) ).
thf(1275,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK81_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK81_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ~ ( in @ ( sK81_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK81_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ( ( in @ ( sK81_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( in @ ( sK81_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK81_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX2
= ( set_union2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_union2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1091]) ).
thf(1276,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ( element @ ( sK120_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK120_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[988]) ).
thf(1277,plain,
! [SV1: $i] :
( ( ! [SY774: $i] :
( ~ ( element @ SY774 @ ( powerset @ SV1 ) )
| ! [SY775: $i] :
( ~ ( in @ SY775 @ SY774 )
| ( in @ SY775 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1278,plain,
! [SV2: $i] :
( ( ~ ( one_sorted_str @ SV2 )
| ( ( cast_as_carrier_subset @ SV2 )
= ( the_carrier @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(1279,plain,
! [SV3: $i] :
( ( ~ ( one_sorted_str @ SV3 )
| ! [SY776: $i] :
( ~ ( element @ SY776 @ ( powerset @ ( the_carrier @ SV3 ) ) )
| ( ( subset_intersection2 @ ( the_carrier @ SV3 ) @ SY776 @ ( cast_as_carrier_subset @ SV3 ) )
= SY776 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1280,plain,
! [SV4: $i] :
( ( ! [SY777: $i] :
( ~ ( element @ SY777 @ ( powerset @ ( powerset @ SV4 ) ) )
| ( SY777 = empty_set )
| ( ( complements_of_subsets @ SV4 @ SY777 )
!= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1281,plain,
! [SV5: $i] :
( ( ( SV5 = empty_set )
| ! [SY778: $i] :
( ~ ( element @ SY778 @ ( powerset @ SV5 ) )
| ! [SY779: $i] :
( ~ ( element @ SY779 @ SV5 )
| ( in @ SY779 @ SY778 )
| ( in @ SY779 @ ( subset_complement @ SV5 @ SY778 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1282,plain,
! [SV6: $i] :
( ( ! [SY780: $i,SY781: $i] :
( ~ ( element @ SY781 @ ( powerset @ SV6 ) )
| ~ ( in @ SY780 @ ( subset_complement @ SV6 @ SY781 ) )
| ~ ( in @ SY780 @ SY781 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1283,plain,
! [SV7: $i] :
( ( ( union @ ( powerset @ SV7 ) )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1284,plain,
! [SV8: $i] :
( ( ~ ( v1_membered @ SV8 )
| ! [SY782: $i] :
( ~ ( element @ SY782 @ SV8 )
| ( v1_xcmplx_0 @ SY782 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1285,plain,
! [SV9: $i] :
( ( ~ ( v1_membered @ SV9 )
| ! [SY783: $i] :
( ~ ( element @ SY783 @ ( powerset @ SV9 ) )
| ( v1_membered @ SY783 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1286,plain,
! [SV10: $i] :
( ( ! [SY784: $i,SY785: $i] :
( ~ ( element @ SY785 @ ( powerset @ ( cartesian_product2 @ SV10 @ SY784 ) ) )
| ( relation @ SY785 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1287,plain,
! [SV11: $i] :
( ( ~ ( finite @ SV11 )
| ! [SY786: $i] :
( ~ ( element @ SY786 @ ( powerset @ SV11 ) )
| ( finite @ SY786 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1288,plain,
! [SV12: $i] :
( ( ! [SY787: $i,SY788: $i] :
( ~ ( element @ SY787 @ ( powerset @ SV12 ) )
| ~ ( element @ SY788 @ ( powerset @ SV12 ) )
| ( ( subset_intersection2 @ SV12 @ SY787 @ SY788 )
= ( subset_intersection2 @ SV12 @ SY788 @ SY787 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1289,plain,
! [SV13: $i] :
( ( ~ ( one_sorted_str @ SV13 )
| ( ( cast_as_carrier_subset @ SV13 )
= ( the_carrier @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1290,plain,
! [SV14: $i] :
( ( ! [SY789: $i] :
( ~ ( element @ SY789 @ ( powerset @ SV14 ) )
| ( ( subset_complement @ SV14 @ SY789 )
= ( set_difference @ SV14 @ SY789 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1291,plain,
! [SV15: $i] :
( ( ~ ( one_sorted_str @ SV15 )
| ( element @ ( cast_as_carrier_subset @ SV15 ) @ ( powerset @ ( the_carrier @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1292,plain,
! [SV16: $i] :
( ( element @ ( cast_to_subset @ SV16 ) @ ( powerset @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1293,plain,
! [SV17: $i] :
( ( ! [SY790: $i] :
( ~ ( element @ SY790 @ ( powerset @ SV17 ) )
| ( element @ ( subset_complement @ SV17 @ SY790 ) @ ( powerset @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1294,plain,
! [SV18: $i] :
( ( ! [SY791: $i,SY792: $i] :
( ~ ( relation_of2 @ SY792 @ SV18 @ SY791 )
| ( element @ ( relation_dom_as_subset @ SV18 @ SY791 @ SY792 ) @ ( powerset @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1295,plain,
! [SV19: $i] :
( ( ! [SY793: $i,SY794: $i] :
( ~ ( relation_of2 @ SY794 @ SV19 @ SY793 )
| ( element @ ( relation_rng_as_subset @ SV19 @ SY793 @ SY794 ) @ ( powerset @ SY793 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1296,plain,
! [SV20: $i] :
( ( ! [SY795: $i] :
( ~ ( element @ SY795 @ ( powerset @ ( powerset @ SV20 ) ) )
| ( element @ ( union_of_subsets @ SV20 @ SY795 ) @ ( powerset @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1297,plain,
! [SV21: $i] :
( ( ! [SY796: $i,SY797: $i] :
( ~ ( element @ SY796 @ ( powerset @ SV21 ) )
| ~ ( element @ SY797 @ ( powerset @ SV21 ) )
| ( element @ ( subset_intersection2 @ SV21 @ SY796 @ SY797 ) @ ( powerset @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1298,plain,
! [SV22: $i] :
( ( ! [SY798: $i] :
( ~ ( element @ SY798 @ ( powerset @ ( powerset @ SV22 ) ) )
| ( element @ ( meet_of_subsets @ SV22 @ SY798 ) @ ( powerset @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1299,plain,
! [SV23: $i] :
( ( ! [SY799: $i,SY800: $i] :
( ~ ( element @ SY799 @ ( powerset @ SV23 ) )
| ~ ( element @ SY800 @ ( powerset @ SV23 ) )
| ( element @ ( subset_difference @ SV23 @ SY799 @ SY800 ) @ ( powerset @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1300,plain,
! [SV24: $i] :
( ( ! [SY801: $i] :
( ~ ( element @ SY801 @ ( powerset @ ( powerset @ SV24 ) ) )
| ( element @ ( complements_of_subsets @ SV24 @ SY801 ) @ ( powerset @ ( powerset @ SV24 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1301,plain,
! [SV25: $i] :
( ( ~ ( meet_semilatt_str @ SV25 )
| ( one_sorted_str @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1302,plain,
! [SV26: $i] :
( ( ~ ( join_semilatt_str @ SV26 )
| ( one_sorted_str @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1303,plain,
! [SV27: $i] :
( ( ! [SY802: $i,SY803: $i] :
( ~ ( relation_of2_as_subset @ SY803 @ SV27 @ SY802 )
| ( element @ SY803 @ ( powerset @ ( cartesian_product2 @ SV27 @ SY802 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1304,plain,
! [SV28: $i] :
( ( element @ ( sK121_B @ SV28 ) @ SV28 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1305,plain,
! [SV29: $i] :
( ( ( empty_carrier @ SV29 )
| ~ ( one_sorted_str @ SV29 )
| ~ ( empty @ ( the_carrier @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1306,plain,
! [SV30: $i] :
( ( ~ ( empty @ ( powerset @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1307,plain,
! [SV31: $i] :
( ( ! [SY804: $i] :
( ~ ( element @ SY804 @ ( powerset @ SV31 ) )
| ! [SY805: $i] :
~ ( element @ SY805 @ ( powerset @ SV31 ) )
| ( ( subset_intersection2 @ SV31 @ SY804 @ SY804 )
= SY804 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1308,plain,
! [SV32: $i] :
( ( ! [SY806: $i] :
( ~ ( element @ SY806 @ ( powerset @ SV32 ) )
| ( ( subset_complement @ SV32 @ ( subset_complement @ SV32 @ SY806 ) )
= SY806 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1309,plain,
! [SV33: $i] :
( ( ! [SY807: $i] :
( ~ ( element @ SY807 @ ( powerset @ ( powerset @ SV33 ) ) )
| ( ( complements_of_subsets @ SV33 @ ( complements_of_subsets @ SV33 @ SY807 ) )
= SY807 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1310,plain,
! [SV34: $i] :
( ( ! [SY808: $i] :
( ~ ( element @ SY808 @ ( powerset @ ( powerset @ SV34 ) ) )
| ( ( union_of_subsets @ SV34 @ SY808 )
= ( union @ SY808 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1311,plain,
! [SV35: $i] :
( ( ! [SY809: $i,SY810: $i] :
( ~ ( element @ SY809 @ ( powerset @ SV35 ) )
| ~ ( element @ SY810 @ ( powerset @ SV35 ) )
| ( ( subset_intersection2 @ SV35 @ SY809 @ SY810 )
= ( set_intersection2 @ SY809 @ SY810 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1312,plain,
! [SV36: $i] :
( ( ! [SY811: $i] :
( ~ ( element @ SY811 @ ( powerset @ ( powerset @ SV36 ) ) )
| ( ( meet_of_subsets @ SV36 @ SY811 )
= ( set_meet @ SY811 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1313,plain,
! [SV37: $i] :
( ( ! [SY812: $i,SY813: $i] :
( ~ ( element @ SY812 @ ( powerset @ SV37 ) )
| ~ ( element @ SY813 @ ( powerset @ SV37 ) )
| ( ( subset_difference @ SV37 @ SY812 @ SY813 )
= ( set_difference @ SY812 @ SY813 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1314,plain,
! [SV38: $i] :
( ( ! [SY814: $i] :
( ~ ( in @ SV38 @ SY814 )
| ( element @ SV38 @ SY814 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1315,plain,
! [SV39: $i] :
( ( ! [SY815: $i] :
( ~ ( element @ SV39 @ SY815 )
| ( empty @ SY815 )
| ( in @ SV39 @ SY815 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1316,plain,
! [SV40: $i] :
( ( ! [SY816: $i,SY817: $i] :
( ~ ( element @ SY816 @ ( powerset @ SY817 ) )
| ~ ( in @ SV40 @ SY816 )
| ( element @ SV40 @ SY817 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1317,plain,
! [SV41: $i] :
( ( ! [SY818: $i,SY819: $i] :
( ~ ( element @ SY818 @ ( powerset @ SY819 ) )
| ~ ( in @ SV41 @ SY818 )
| ~ ( empty @ SY819 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1318,plain,
! [SV42: $i] :
( ( ( ( singleton @ SV42 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1319,plain,
! [SV43: $i] :
( ( ! [SY820: $i] :
( ~ ( in @ SV43 @ SY820 )
| ( ( set_union2 @ ( singleton @ SV43 ) @ SY820 )
= SY820 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1320,plain,
! [SV44: $i] :
( ( ! [SY821: $i] :
( ~ ( disjoint @ ( singleton @ SV44 ) @ SY821 )
| ~ ( in @ SV44 @ SY821 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1321,plain,
! [SV45: $i] :
( ( ! [SY822: $i] :
( ( in @ SV45 @ SY822 )
| ( disjoint @ ( singleton @ SV45 ) @ SY822 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1322,plain,
! [SV46: $i] :
( ( ! [SY823: $i] :
( ~ ( subset @ SV46 @ SY823 )
| ! [SY824: $i] :
( ( in @ SY824 @ SV46 )
| ( subset @ SV46 @ ( set_difference @ SY823 @ ( singleton @ SY824 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1323,plain,
! [SV47: $i] :
( ( ! [SY825: $i] :
( ~ ( in @ SV47 @ SY825 )
| ( subset @ SV47 @ ( union @ SY825 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1324,plain,
! [SV48: $i] :
( ( in @ SV48 @ ( succ @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1325,plain,
! [SV49: $i] :
( ( ! [SY826: $i] :
( ~ ( relation @ SY826 )
| ( subset @ ( relation_rng_restriction @ SV49 @ SY826 ) @ SY826 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1326,plain,
! [SV50: $i] :
( ( ! [SY827: $i,SY828: $i,SY829: $i] :
( ~ ( subset @ SV50 @ SY827 )
| ~ ( subset @ SY828 @ SY829 )
| ( subset @ ( cartesian_product2 @ SV50 @ SY828 ) @ ( cartesian_product2 @ SY827 @ SY829 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1327,plain,
! [SV51: $i] :
( ( ! [SY830: $i] :
( ~ ( subset @ SV51 @ SY830 )
| ( ( set_union2 @ SV51 @ SY830 )
= SY830 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1328,plain,
! [SV52: $i] :
( ( ! [SY831: $i] :
( ~ ( finite @ SY831 )
| ~ ( subset @ SV52 @ SY831 ) )
| ( finite @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1329,plain,
! [SV53: $i] :
( ( ! [SY832: $i,SY833: $i,SY834: $i] :
( ~ ( relation_of2_as_subset @ SY834 @ SY833 @ SV53 )
| ~ ( subset @ ( relation_rng @ SY834 ) @ SY832 )
| ( relation_of2_as_subset @ SY834 @ SY833 @ SY832 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1330,plain,
! [SV54: $i] :
( ( ~ ( finite @ SV54 )
| ! [SY835: $i] : ( finite @ ( set_intersection2 @ SV54 @ SY835 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1331,plain,
! [SV55: $i] :
( ( ! [SY836: $i,SY837: $i,SY838: $i] :
( ~ ( relation_of2_as_subset @ SY838 @ SY837 @ SV55 )
| ~ ( subset @ SV55 @ SY836 )
| ( relation_of2_as_subset @ SY838 @ SY837 @ SY836 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1332,plain,
! [SV56: $i] :
( ( ! [SY839: $i,SY840: $i] :
( ~ ( relation @ SY840 )
| ~ ( subset @ SV56 @ SY839 )
| ( subset @ ( relation_inverse_image @ SY840 @ SV56 ) @ ( relation_inverse_image @ SY840 @ SY839 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1333,plain,
! [SV57: $i] :
( ( ! [SY841: $i] : ( subset @ ( set_intersection2 @ SV57 @ SY841 ) @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1334,plain,
! [SV58: $i] :
( ( ! [SY842: $i,SY843: $i] :
( ~ ( subset @ SV58 @ SY842 )
| ~ ( subset @ SV58 @ SY843 )
| ( subset @ SV58 @ ( set_intersection2 @ SY842 @ SY843 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1030]) ).
thf(1335,plain,
! [SV59: $i] :
( ( ! [SY844: $i,SY845: $i] :
( ~ ( subset @ SV59 @ SY844 )
| ~ ( subset @ SY844 @ SY845 )
| ( subset @ SV59 @ SY845 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1336,plain,
! [SV60: $i] :
( ( ! [SY846: $i] :
( ~ ( ordinal @ SY846 )
| ~ ( in @ SV60 @ SY846 )
| ( ordinal @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1337,plain,
! [SV61: $i] :
( ( ~ ( ordinal @ SV61 )
| ! [SY847: $i] :
( ~ ( ordinal @ SY847 )
| ( in @ SV61 @ SY847 )
| ( SV61 = SY847 )
| ( in @ SY847 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1338,plain,
! [SV62: $i] :
( ( ! [SY848: $i] :
( ~ ( subset @ SV62 @ SY848 )
| ! [SY849: $i] : ( subset @ ( set_intersection2 @ SV62 @ SY849 ) @ ( set_intersection2 @ SY848 @ SY849 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1339,plain,
! [SV63: $i] :
( ( ! [SY850: $i] :
( ~ ( subset @ SV63 @ SY850 )
| ( ( set_intersection2 @ SV63 @ SY850 )
= SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1340,plain,
! [SV64: $i] :
( ( subset @ empty_set @ SV64 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1341,plain,
! [SV65: $i] :
( ( ! [SY851: $i] :
( ~ ( subset @ SV65 @ SY851 )
| ! [SY852: $i] : ( subset @ ( set_difference @ SV65 @ SY852 ) @ ( set_difference @ SY851 @ SY852 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1342,plain,
! [SV66: $i] :
( ( ! [SY853: $i] : ( subset @ ( set_difference @ SV66 @ SY853 ) @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1343,plain,
! [SV67: $i] :
( ( ! [SY854: $i] :
( ( set_union2 @ SV67 @ ( set_difference @ SY854 @ SV67 ) )
= ( set_union2 @ SV67 @ SY854 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1344,plain,
! [SV68: $i] :
( ( ! [SY855: $i,SY856: $i] :
( ~ ( in @ SV68 @ SY855 )
| ~ ( in @ SY855 @ SY856 )
| ~ ( in @ SY856 @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1345,plain,
! [SV69: $i] :
( ( ~ ( subset @ SV69 @ empty_set )
| ( SV69 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1346,plain,
! [SV70: $i] :
( ( ! [SY857: $i] :
( ( set_difference @ ( set_union2 @ SV70 @ SY857 ) @ SY857 )
= ( set_difference @ SV70 @ SY857 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1347,plain,
! [SV71: $i] :
( ( ! [SY858: $i] :
( ~ ( subset @ SV71 @ SY858 )
| ( SY858
= ( set_union2 @ SV71 @ ( set_difference @ SY858 @ SV71 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1348,plain,
! [SV72: $i] :
( ( ! [SY859: $i] :
( ~ ( in @ SV72 @ SY859 )
| ( ( set_union2 @ ( singleton @ SV72 ) @ SY859 )
= SY859 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1349,plain,
! [SV73: $i] :
( ( ! [SY860: $i] :
( ~ ( element @ SY860 @ ( powerset @ ( powerset @ SV73 ) ) )
| ( SY860 = empty_set )
| ( ( subset_difference @ SV73 @ ( cast_to_subset @ SV73 ) @ ( union_of_subsets @ SV73 @ SY860 ) )
= ( meet_of_subsets @ SV73 @ ( complements_of_subsets @ SV73 @ SY860 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1350,plain,
! [SV74: $i] :
( ( ! [SY861: $i] :
( ~ ( element @ SY861 @ ( powerset @ ( powerset @ SV74 ) ) )
| ( SY861 = empty_set )
| ( ( union_of_subsets @ SV74 @ ( complements_of_subsets @ SV74 @ SY861 ) )
= ( subset_difference @ SV74 @ ( cast_to_subset @ SV74 ) @ ( meet_of_subsets @ SV74 @ SY861 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1351,plain,
! [SV75: $i] :
( ( ! [SY862: $i] :
( ( set_difference @ SV75 @ ( set_difference @ SV75 @ SY862 ) )
= ( set_intersection2 @ SV75 @ SY862 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1352,plain,
! [SV76: $i] :
( ( ~ ( relation @ SV76 )
| ( in @ ( ordered_pair @ ( sK95_B @ SV76 ) @ ( sK96_SY738 @ SV76 ) ) @ SV76 )
| ( SV76 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1353,plain,
! [SV77: $i] :
( ( ! [SY863: $i] :
( ~ ( proper_subset @ SY863 @ SV77 )
| ~ ( subset @ SV77 @ SY863 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1354,plain,
! [SV78: $i] :
( ( ! [SY864: $i,SY865: $i] :
( ~ ( disjoint @ SY864 @ SY865 )
| ~ ( subset @ SV78 @ SY864 )
| ( disjoint @ SV78 @ SY865 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1355,plain,
! [SV79: $i] :
( ( ( unordered_pair @ SV79 @ SV79 )
= ( singleton @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1356,plain,
! [SV80: $i] :
( ( ! [SY866: $i] :
( ~ ( subset @ ( singleton @ SV80 ) @ ( singleton @ SY866 ) )
| ( SV80 = SY866 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1357,plain,
! [SV81: $i] :
( ( ! [SY867: $i] : ( subset @ SV81 @ ( set_union2 @ SV81 @ SY867 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1358,plain,
! [SV82: $i] :
( ( ! [SY868: $i] :
( ~ ( relation @ SY868 )
| ( subset @ ( relation_dom_restriction @ SY868 @ SV82 ) @ SY868 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1359,plain,
! [SV83: $i] :
( ( ! [SY869: $i,SY870: $i] :
( ~ ( subset @ SV83 @ SY869 )
| ~ ( subset @ SY870 @ SY869 )
| ( subset @ ( set_union2 @ SV83 @ SY870 ) @ SY869 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1360,plain,
! [SV84: $i] :
( ( ! [SY871: $i] :
( ! [SY872: $i] :
( ( singleton @ SV84 )
!= ( unordered_pair @ SY871 @ SY872 ) )
| ( SV84 = SY871 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1361,plain,
! [SV85: $i] :
( ( ! [SY873: $i] :
( ~ ( in @ SV85 @ SY873 )
| ( subset @ SV85 @ ( union @ SY873 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1069]) ).
thf(1362,plain,
! [SV86: $i] :
( ( ! [SY874: $i,SY875: $i] :
( ( ( singleton @ SV86 )
!= ( unordered_pair @ SY874 @ SY875 ) )
| ( SY874 = SY875 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1363,plain,
! [SV87: $i] :
( ( ! [SY876: $i] :
( ~ ( in @ SV87 @ SY876 )
| ~ ( in @ SY876 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1364,plain,
! [SV88: $i] :
( ( ~ ( empty @ SV88 )
| ( finite @ SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1365,plain,
! [SV89: $i] :
( ( ~ ( empty @ SV89 )
| ( function @ SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1366,plain,
! [SV90: $i] :
( ( ~ ( empty @ SV90 )
| ( relation @ SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1367,plain,
! [SV91: $i] :
( ( ~ ( v3_membered @ SV91 )
| ( v2_membered @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1077]) ).
thf(1368,plain,
! [SV92: $i] :
( ( ~ ( v2_membered @ SV92 )
| ( v1_membered @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1369,plain,
! [SV93: $i] :
( ( ! [SY877: $i] :
( ( set_intersection2 @ SV93 @ SY877 )
= ( set_intersection2 @ SY877 @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1370,plain,
! [SV94: $i] :
( ( ( cast_to_subset @ SV94 )
= SV94 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1371,plain,
! [SV95: $i] :
( ( ~ ( relation @ SV95 )
| ! [SY878: $i] :
( ( relation_restriction @ SV95 @ SY878 )
= ( set_intersection2 @ SV95 @ ( cartesian_product2 @ SY878 @ SY878 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1372,plain,
! [SV96: $i] :
( ( ! [SY879: $i,SY880: $i] :
( ( empty_carrier @ SV96 )
| ~ ( join_semilatt_str @ SV96 )
| ~ ( element @ SY879 @ ( the_carrier @ SV96 ) )
| ~ ( element @ SY880 @ ( the_carrier @ SV96 ) )
| ( element @ ( join @ SV96 @ SY879 @ SY880 ) @ ( the_carrier @ SV96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1373,plain,
! [SV97: $i] :
( ( relation @ ( inclusion_relation @ SV97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1374,plain,
! [SV98: $i] :
( ( ! [SY881: $i,SY882: $i] :
( ( empty_carrier @ SV98 )
| ~ ( meet_semilatt_str @ SV98 )
| ~ ( element @ SY881 @ ( the_carrier @ SV98 ) )
| ~ ( element @ SY882 @ ( the_carrier @ SV98 ) )
| ( element @ ( meet @ SV98 @ SY881 @ SY882 ) @ ( the_carrier @ SV98 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1106]) ).
thf(1375,plain,
! [SV99: $i] :
( ( ~ ( relation @ SV99 )
| ! [SY883: $i] : ( relation @ ( relation_restriction @ SV99 @ SY883 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1376,plain,
! [SV100: $i] :
( ( ~ ( relation @ SV100 )
| ( relation @ ( relation_inverse @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1377,plain,
! [SV101: $i] :
( ( ! [SY884: $i] :
( ~ ( relation @ SV101 )
| ~ ( relation @ SY884 )
| ( relation @ ( relation_composition @ SV101 @ SY884 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1378,plain,
! [SV102: $i] :
( ( relation @ ( identity_relation @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1379,plain,
! [SV103: $i] :
( ( ~ ( relation @ SV103 )
| ! [SY885: $i] : ( relation @ ( relation_dom_restriction @ SV103 @ SY885 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1380,plain,
! [SV104: $i] :
( ( ! [SY886: $i] :
( ~ ( relation @ SY886 )
| ( relation @ ( relation_rng_restriction @ SV104 @ SY886 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1381,plain,
! [SV105: $i] :
( ( ! [SY887: $i] : ( relation_of2 @ ( sK63_C @ SY887 @ SV105 ) @ SV105 @ SY887 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1382,plain,
! [SV106: $i] :
( ( ! [SY888: $i] : ( relation_of2_as_subset @ ( sK62_C @ SY888 @ SV106 ) @ SV106 @ SY888 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1383,plain,
! [SV107: $i] :
( ( ! [SY889: $i] :
( ~ ( finite @ SY889 )
| ( finite @ ( set_intersection2 @ SV107 @ SY889 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1384,plain,
! [SV108: $i] :
( ( ~ ( finite @ SV108 )
| ! [SY890: $i] : ( finite @ ( set_intersection2 @ SV108 @ SY890 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1385,plain,
! [SV109: $i] :
( ( ~ ( finite @ SV109 )
| ! [SY891: $i] : ( finite @ ( set_difference @ SV109 @ SY891 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1386,plain,
! [SV110: $i] :
( ( ~ ( empty @ ( succ @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1125]) ).
thf(1387,plain,
! [SV111: $i] :
( ( ! [SY892: $i] :
( ~ ( relation @ SV111 )
| ~ ( relation @ SY892 )
| ( relation @ ( set_intersection2 @ SV111 @ SY892 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1388,plain,
! [SV112: $i] :
( ( ! [SY893: $i] :
~ ( empty @ ( ordered_pair @ SV112 @ SY893 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1389,plain,
! [SV113: $i] :
( ( ~ ( v1_membered @ SV113 )
| ! [SY894: $i] : ( v1_membered @ ( set_intersection2 @ SV113 @ SY894 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1390,plain,
! [SV114: $i] :
( ( ~ ( v1_membered @ SV114 )
| ! [SY895: $i] : ( v1_membered @ ( set_intersection2 @ SY895 @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1391,plain,
! [SV115: $i] :
( ( ! [SY896: $i] :
( ~ ( relation @ SV115 )
| ~ ( relation @ SY896 )
| ( relation @ ( set_union2 @ SV115 @ SY896 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1392,plain,
! [SV116: $i] :
( ( ~ ( empty @ ( singleton @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1393,plain,
! [SV117: $i] :
( ( ( empty @ SV117 )
| ! [SY897: $i] :
~ ( empty @ ( set_union2 @ SV117 @ SY897 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1394,plain,
! [SV118: $i] :
( ( ~ ( v1_membered @ SV118 )
| ! [SY898: $i] : ( v1_membered @ ( set_difference @ SV118 @ SY898 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1395,plain,
! [SV119: $i] :
( ( ! [SY899: $i] :
( ~ ( relation @ SV119 )
| ~ ( relation @ SY899 )
| ( relation @ ( set_difference @ SV119 @ SY899 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1396,plain,
! [SV120: $i] :
( ( ! [SY900: $i] :
~ ( empty @ ( unordered_pair @ SV120 @ SY900 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1397,plain,
! [SV121: $i] :
( ( ( empty @ SV121 )
| ! [SY901: $i] :
~ ( empty @ ( set_union2 @ SY901 @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1398,plain,
! [SV122: $i] :
( ( ! [SY902: $i] :
( ( empty @ SV122 )
| ( empty @ SY902 )
| ~ ( empty @ ( cartesian_product2 @ SV122 @ SY902 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1399,plain,
! [SV123: $i] :
( ( ( empty @ SV123 )
| ~ ( relation @ SV123 )
| ~ ( empty @ ( relation_dom @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1400,plain,
! [SV124: $i] :
( ( ( empty @ SV124 )
| ~ ( relation @ SV124 )
| ~ ( empty @ ( relation_rng @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1401,plain,
! [SV125: $i] :
( ( ! [SY903: $i] :
( ~ ( finite @ SV125 )
| ~ ( finite @ SY903 )
| ( finite @ ( set_union2 @ SV125 @ SY903 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1150]) ).
thf(1402,plain,
! [SV126: $i] :
( ( ( set_intersection2 @ SV126 @ SV126 )
= SV126 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1403,plain,
! [SV127: $i] :
( ( ~ ( relation @ SV127 )
| ( ( relation_inverse @ ( relation_inverse @ SV127 ) )
= SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1404,plain,
( ( empty @ sK54_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1161]) ).
thf(1405,plain,
! [SV128: $i] :
( ( ! [SY904: $i,SY905: $i] :
( ~ ( relation_of2 @ SY905 @ SV128 @ SY904 )
| ( ( relation_dom_as_subset @ SV128 @ SY904 @ SY905 )
= ( relation_dom @ SY905 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1406,plain,
! [SV129: $i] :
( ( ! [SY906: $i,SY907: $i] :
( ~ ( relation_of2 @ SY907 @ SV129 @ SY906 )
| ( ( relation_rng_as_subset @ SV129 @ SY906 @ SY907 )
= ( relation_rng @ SY907 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1407,plain,
! [SV130: $i] :
( ( subset @ SV130 @ SV130 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1408,plain,
! [SV131: $i] :
( ( ! [SY908: $i] :
( ~ ( disjoint @ SV131 @ SY908 )
| ( disjoint @ SY908 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1409,plain,
! [SV132: $i] :
( ( ( set_union2 @ SV132 @ empty_set )
= SV132 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1410,plain,
! [SV133: $i] :
( ( ( set_intersection2 @ SV133 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1411,plain,
! [SV134: $i] :
( ( ( set_difference @ SV134 @ empty_set )
= SV134 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1176]) ).
thf(1412,plain,
! [SV135: $i] :
( ( ( set_difference @ empty_set @ SV135 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1413,plain,
! [SV136: $i] :
( ( ~ ( empty @ SV136 )
| ( SV136 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1414,plain,
! [SV137: $i] :
( ( ! [SY909: $i] :
( ~ ( empty @ SY909 )
| ~ ( in @ SV137 @ SY909 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1415,plain,
! [SV138: $i] :
( ( ! [SY910: $i] :
( ( SV138 = SY910 )
| ~ ( empty @ SV138 )
| ~ ( empty @ SY910 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1416,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1185]) ).
thf(1417,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1186]) ).
thf(1418,plain,
! [SV139: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK17_C @ SV139 )
!= ( sK18_SY613 @ SV139 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
!= ( sK18_SY613 @ SV139 ) )
| ~ ( in @ ( sK22_SY620 @ SV139 ) @ SV139 ) )
| ( ( sK23_SY629 @ SV139 )
!= ( singleton @ ( sK22_SY620 @ SV139 ) ) ) ) )
| ( ( sK17_C @ SV139 )
!= ( sK19_SY619 @ SV139 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
!= ( sK19_SY619 @ SV139 ) )
| ~ ( in @ ( sK20_SY626 @ SV139 ) @ SV139 ) )
| ( ( sK21_SY628 @ SV139 )
!= ( singleton @ ( sK20_SY626 @ SV139 ) ) ) ) )
| ~ ( ( ( sK18_SY613 @ SV139 )
!= ( sK19_SY619 @ SV139 ) ) ) )
| ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1419,plain,
! [SV140: $i] :
( ( ( empty_carrier @ SV140 )
| ~ ( one_sorted_str @ SV140 )
| ~ ( ~ ( element @ ( sK116_B @ SV140 ) @ ( powerset @ ( the_carrier @ SV140 ) ) )
| ~ ~ ( empty @ ( sK116_B @ SV140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1420,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_intersection2 @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_intersection2 @ SX1 @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v3_membered @ ( set_intersection2 @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1189]) ).
thf(1421,plain,
! [SV141: $i] :
( ( ~ ( ~ ( in @ ( sK99_B @ SV141 ) @ SV141 )
| ~ ( ~ ( ordinal @ ( sK99_B @ SV141 ) )
| ~ ( subset @ ( sK99_B @ SV141 ) @ SV141 ) ) )
| ( ordinal @ SV141 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1190]) ).
thf(1422,plain,
! [SV142: $i] :
( ( ~ ( ~ ! [SY917: $i,SY918: $i] :
( ~ ( in @ SV142 @ SY918 )
| ~ ( in @ SY917 @ SY918 )
| ( subset @ ( unordered_pair @ SV142 @ SY917 ) @ SY918 ) )
| ~ ~ ( ~ ! [SY919: $i,SY920: $i] :
( ~ ( subset @ ( unordered_pair @ SV142 @ SY919 ) @ SY920 )
| ( in @ SV142 @ SY920 ) )
| ~ ! [SY921: $i,SY922: $i] :
( ~ ( subset @ ( unordered_pair @ SV142 @ SY921 ) @ SY922 )
| ( in @ SY921 @ SY922 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1191]) ).
thf(1423,plain,
! [SV143: $i] :
( ( ~ ( ~ ! [SY923: $i,SY924: $i] :
( ~ ( ~ ( ~ ( in @ ( sK70_D @ SY924 @ SY923 @ SV143 ) @ SV143 )
| ~ ( in @ ( sK70_D @ SY924 @ SY923 @ SV143 ) @ SY923 )
| ~ ( in @ ( sK70_D @ SY924 @ SY923 @ SV143 ) @ SY924 ) )
| ~ ~ ( ~ ( ( in @ ( sK70_D @ SY924 @ SY923 @ SV143 ) @ SV143 )
| ( in @ ( sK70_D @ SY924 @ SY923 @ SV143 ) @ SY924 ) )
| ~ ( ( in @ ( sK70_D @ SY924 @ SY923 @ SV143 ) @ SY923 )
| ( in @ ( sK70_D @ SY924 @ SY923 @ SV143 ) @ SY924 ) ) ) )
| ( SY924
= ( set_intersection2 @ SV143 @ SY923 ) ) )
| ~ ! [SY925: $i,SY926: $i] :
( ( SY926
!= ( set_intersection2 @ SV143 @ SY925 ) )
| ~ ( ~ ! [SY927: $i] :
( ~ ( in @ SY927 @ SV143 )
| ~ ( in @ SY927 @ SY925 )
| ( in @ SY927 @ SY926 ) )
| ~ ~ ( ~ ! [SY928: $i] :
( ~ ( in @ SY928 @ SY926 )
| ( in @ SY928 @ SV143 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY926 )
| ( in @ SX3 @ SY925 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1192]) ).
thf(1424,plain,
! [SV144: $i] :
( ( ~ ( v3_membered @ SV144 )
| ~ ( ~ ~ ( ~ ! [SY930: $i] :
( ~ ( element @ SY930 @ ( powerset @ SV144 ) )
| ( v1_membered @ SY930 ) )
| ~ ! [SY931: $i] :
( ~ ( element @ SY931 @ ( powerset @ SV144 ) )
| ( v2_membered @ SY931 ) ) )
| ~ ! [SY932: $i] :
( ~ ( element @ SY932 @ ( powerset @ SV144 ) )
| ( v3_membered @ SY932 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1193]) ).
thf(1425,plain,
! [SV145: $i] :
( ( ! [SY933: $i] :
( ( empty @ SV145 )
| ~ ( relation @ SY933 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY934: $i] :
( ~ ( in @ SY934 @ ( sK52_SY712 @ SY933 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK49_SY705 @ SY933 @ SV145 ) @ SY934 ) @ SY933 ) )
| ~ ~ ( ( ( sK48_C @ SY933 @ SV145 )
!= ( sK52_SY712 @ SY933 @ SV145 ) )
| ~ ( in @ ( sK49_SY705 @ SY933 @ SV145 ) @ ( sK52_SY712 @ SY933 @ SV145 ) ) ) )
| ~ ( in @ ( sK48_C @ SY933 @ SV145 ) @ SV145 ) )
| ~ ( in @ ( sK48_C @ SY933 @ SV145 ) @ SV145 ) )
| ~ ~ ( ~ ! [SY935: $i] :
( ~ ( in @ SY935 @ ( sK51_SY718 @ SY933 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK50_SY711 @ SY933 @ SV145 ) @ SY935 ) @ SY933 ) )
| ~ ~ ( ( ( sK48_C @ SY933 @ SV145 )
!= ( sK51_SY718 @ SY933 @ SV145 ) )
| ~ ( in @ ( sK50_SY711 @ SY933 @ SV145 ) @ ( sK51_SY718 @ SY933 @ SV145 ) ) ) ) )
| ~ ( ( ( sK49_SY705 @ SY933 @ SV145 )
!= ( sK50_SY711 @ SY933 @ SV145 ) ) ) )
| ~ ( ~ ! [SY936: $i] :
( ! [SY937: $i] :
( ~ ( in @ SY937 @ SV145 )
| ! [SY938: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY938 @ SY937 @ SY936 @ SY933 @ SV145 ) @ SY938 )
| ~ ~ ( in @ ( ordered_pair @ SY936 @ ( sK47_K @ SY938 @ SY937 @ SY936 @ SY933 @ SV145 ) ) @ SY933 ) )
| ( SY937 != SY938 )
| ~ ( in @ SY936 @ SY938 ) ) )
| ( in @ SY936 @ ( sK44_C @ SY933 @ SV145 ) ) )
| ~ ! [SY939: $i] :
( ~ ( in @ SY939 @ ( sK44_C @ SY933 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY939 @ SY933 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY940: $i] :
( ~ ( in @ SY940 @ ( sK46_SY702 @ SY939 @ SY933 @ SV145 ) )
| ( in @ ( ordered_pair @ SY939 @ SY940 ) @ SY933 ) )
| ~ ~ ( ( ( sK45_E @ SY939 @ SY933 @ SV145 )
!= ( sK46_SY702 @ SY939 @ SY933 @ SV145 ) )
| ~ ( in @ SY939 @ ( sK46_SY702 @ SY939 @ SY933 @ SV145 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1426,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1195]) ).
thf(1427,plain,
! [SV146: $i] :
( ( ! [SY941: $i] :
( ~ ( ~ ! [SY942: $i] :
( ~ ( in @ SY942 @ SY941 )
| ~ ( in @ SY942 @ ( sK5_C @ SY941 @ SV146 ) ) )
| ~ ( in @ ( sK5_C @ SY941 @ SV146 ) @ SY941 ) )
| ~ ( in @ SV146 @ SY941 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1428,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK85_B @ SX0 ) @ SX0 )
| ~ ~ ( subset @ ( sK85_B @ SX0 ) @ SX0 ) )
| ( epsilon_transitive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( epsilon_transitive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1197]) ).
thf(1429,plain,
! [SV147: $i] :
( ( ~ ( ~ ! [SY943: $i,SY944: $i] :
( ~ ( ~ ( ~ ( in @ ( sK66_D @ SY944 @ SY943 @ SV147 ) @ SV147 )
| ( in @ ( sK66_D @ SY944 @ SY943 @ SV147 ) @ SY943 )
| ~ ( in @ ( sK66_D @ SY944 @ SY943 @ SV147 ) @ SY944 ) )
| ~ ~ ( ~ ( ( in @ ( sK66_D @ SY944 @ SY943 @ SV147 ) @ SV147 )
| ( in @ ( sK66_D @ SY944 @ SY943 @ SV147 ) @ SY944 ) )
| ~ ( ~ ( in @ ( sK66_D @ SY944 @ SY943 @ SV147 ) @ SY943 )
| ( in @ ( sK66_D @ SY944 @ SY943 @ SV147 ) @ SY944 ) ) ) )
| ( SY944
= ( set_difference @ SV147 @ SY943 ) ) )
| ~ ! [SY945: $i,SY946: $i] :
( ( SY946
!= ( set_difference @ SV147 @ SY945 ) )
| ~ ( ~ ! [SY947: $i] :
( ~ ( in @ SY947 @ SV147 )
| ( in @ SY947 @ SY945 )
| ( in @ SY947 @ SY946 ) )
| ~ ~ ( ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ SY946 )
| ( in @ SY948 @ SV147 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY946 )
| ~ ( in @ SX3 @ SY945 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1430,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK86_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1199]) ).
thf(1431,plain,
! [SV148: $i] :
( ( ~ ( finite @ SV148 )
| ! [SY950: $i] :
( ~ ( element @ SY950 @ ( powerset @ ( powerset @ SV148 ) ) )
| ~ ( ~ ! [SY951: $i] :
( ~ ( in @ SY951 @ SY950 )
| ~ ( subset @ ( sK105_C @ SY950 @ SV148 ) @ SY951 )
| ( SY951
= ( sK105_C @ SY950 @ SV148 ) ) )
| ~ ( in @ ( sK105_C @ SY950 @ SV148 ) @ SY950 ) )
| ( SY950 = empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1432,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1201]) ).
thf(1433,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1202]) ).
thf(1434,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK68_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK68_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK68_C @ SX1 @ SX0 ) @ ( sK69_SY723 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK69_SY723 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK68_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK67_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK67_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1203]) ).
thf(1435,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1204]) ).
thf(1436,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1205]) ).
thf(1437,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1206]) ).
thf(1438,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK124_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK124_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK124_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK124_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1207]) ).
thf(1439,plain,
! [SV149: $i] :
( ( ( empty @ SV149 )
| ~ ( ~ ~ ( ~ ( element @ ( sK118_B @ SV149 ) @ ( powerset @ SV149 ) )
| ~ ~ ( empty @ ( sK118_B @ SV149 ) ) )
| ~ ( finite @ ( sK118_B @ SV149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1208]) ).
thf(1440,plain,
! [SV150: $i] :
( ( ~ ( ~ ! [SY952: $i,SY953: $i] :
( ~ ( relation_of2_as_subset @ SY953 @ SV150 @ SY952 )
| ~ ( ~ ! [SY954: $i] :
~ ( in @ ( ordered_pair @ SY954 @ ( sK102_D @ SY953 @ SY952 @ SV150 ) ) @ SY953 )
| ~ ( in @ ( sK102_D @ SY953 @ SY952 @ SV150 ) @ SY952 ) )
| ( ( relation_rng_as_subset @ SV150 @ SY952 @ SY953 )
= SY952 ) )
| ~ ! [SY955: $i,SY956: $i] :
( ~ ( relation_of2_as_subset @ SY956 @ SV150 @ SY955 )
| ( ( relation_rng_as_subset @ SV150 @ SY955 @ SY956 )
!= SY955 )
| ! [SY957: $i] :
( ( in @ ( ordered_pair @ ( sK101_E @ SY957 @ SY956 @ SY955 @ SV150 ) @ SY957 ) @ SY956 )
| ~ ( in @ SY957 @ SY955 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1209]) ).
thf(1441,plain,
! [SV151: $i] :
( ( ! [SY958: $i] :
~ ( ~ ! [SY959: $i,SY960: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK94_E @ SY960 @ SY959 @ SY958 @ SV151 ) @ SY960 )
| ( ( sK94_E @ SY960 @ SY959 @ SY958 @ SV151 )
!= SY959 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK94_E @ SY960 @ SY959 @ SY958 @ SV151 ) @ SY960 )
| ( ( sK94_E @ SY960 @ SY959 @ SY958 @ SV151 )
!= SV151 ) )
| ~ ( ~ ( in @ ( sK94_E @ SY960 @ SY959 @ SY958 @ SV151 ) @ SY960 )
| ( ( sK94_E @ SY960 @ SY959 @ SY958 @ SV151 )
!= SY958 ) ) ) )
| ~ ( ( in @ ( sK94_E @ SY960 @ SY959 @ SY958 @ SV151 ) @ SY960 )
| ( ( sK94_E @ SY960 @ SY959 @ SY958 @ SV151 )
= SY959 )
| ( ( sK94_E @ SY960 @ SY959 @ SY958 @ SV151 )
= SV151 )
| ( ( sK94_E @ SY960 @ SY959 @ SY958 @ SV151 )
= SY958 ) ) )
| ( SY960
= ( unordered_triple @ SV151 @ SY958 @ SY959 ) ) )
| ~ ! [SY961: $i,SY962: $i] :
( ( SY962
!= ( unordered_triple @ SV151 @ SY958 @ SY961 ) )
| ~ ( ~ ! [SY963: $i] :
( ~ ( in @ SY963 @ SY962 )
| ( SY963 = SY961 )
| ( SY963 = SV151 )
| ( SY963 = SY958 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SY961 )
| ( in @ SX4 @ SY962 ) )
| ~ ~ ( ~ ! [SY965: $i] :
( ( SY965 != SV151 )
| ( in @ SY965 @ SY962 ) )
| ~ ! [SX4: $i] :
( ( SX4 != SY958 )
| ( in @ SX4 @ SY962 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1442,plain,
! [SV152: $i] :
( ( ~ ( ~ ! [SY967: $i] :
( ~ ( subset @ SY967 @ ( sK106_B @ SV152 ) )
| ( are_equipotent @ SY967 @ ( sK106_B @ SV152 ) )
| ( in @ SY967 @ ( sK106_B @ SV152 ) ) )
| ~ ~ ( ~ ! [SY968: $i] :
( ~ ( in @ SY968 @ ( sK106_B @ SV152 ) )
| ( in @ ( powerset @ SY968 ) @ ( sK106_B @ SV152 ) ) )
| ~ ~ ( ~ ! [SY969: $i,SY970: $i] :
( ~ ( in @ SY969 @ ( sK106_B @ SV152 ) )
| ~ ( subset @ SY970 @ SY969 )
| ( in @ SY970 @ ( sK106_B @ SV152 ) ) )
| ~ ( in @ SV152 @ ( sK106_B @ SV152 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1443,plain,
! [SV153: $i] :
( ( ~ ( ~ ! [SY971: $i] :
( ~ ( in @ SY971 @ SV153 )
| ~ ( ordinal @ SY971 )
| ( in @ SY971 @ ( sK107_B @ SV153 ) ) )
| ~ ~ ( ~ ! [SY972: $i] :
( ~ ( in @ SY972 @ ( sK107_B @ SV153 ) )
| ( in @ SY972 @ SV153 ) )
| ~ ! [SY973: $i] :
( ~ ( in @ SY973 @ ( sK107_B @ SV153 ) )
| ( ordinal @ SY973 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1444,plain,
! [SV154: $i] :
( ( ~ ( relation @ SV154 )
| ~ ( ~ ! [SY974: $i] :
( ~ ( relation @ SY974 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK72_C @ SY974 @ SV154 ) @ ( sK73_SY724 @ SY974 @ SV154 ) ) @ SV154 )
| ~ ~ ( in @ ( ordered_pair @ ( sK72_C @ SY974 @ SV154 ) @ ( sK73_SY724 @ SY974 @ SV154 ) ) @ SY974 ) )
| ( subset @ SV154 @ SY974 ) )
| ~ ! [SY975: $i] :
( ~ ( relation @ SY975 )
| ~ ( subset @ SV154 @ SY975 )
| ! [SY976: $i,SY977: $i] :
( ~ ( in @ ( ordered_pair @ SY976 @ SY977 ) @ SV154 )
| ( in @ ( ordered_pair @ SY976 @ SY977 ) @ SY975 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1445,plain,
! [SV155: $i] :
( ( ! [SY978: $i] :
( ~ ( element @ SY978 @ ( powerset @ ( powerset @ SV155 ) ) )
| ~ ( ~ ! [SY979: $i] :
( ~ ( element @ SY979 @ ( powerset @ ( powerset @ SV155 ) ) )
| ~ ( ~ ( element @ ( sK123_D @ SY979 @ SY978 @ SV155 ) @ ( powerset @ SV155 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK123_D @ SY979 @ SY978 @ SV155 ) @ SY979 )
| ~ ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SY979 @ SY978 @ SV155 ) ) @ SY978 ) )
| ~ ( ( in @ ( sK123_D @ SY979 @ SY978 @ SV155 ) @ SY979 )
| ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SY979 @ SY978 @ SV155 ) ) @ SY978 ) ) ) )
| ( SY979
= ( complements_of_subsets @ SV155 @ SY978 ) ) )
| ~ ! [SY980: $i] :
( ~ ( element @ SY980 @ ( powerset @ ( powerset @ SV155 ) ) )
| ( SY980
!= ( complements_of_subsets @ SV155 @ SY978 ) )
| ~ ( ~ ! [SY981: $i] :
( ~ ( element @ SY981 @ ( powerset @ SV155 ) )
| ~ ( in @ SY981 @ SY980 )
| ( in @ ( subset_complement @ SV155 @ SY981 ) @ SY978 ) )
| ~ ! [SY982: $i] :
( ~ ( element @ SY982 @ ( powerset @ SV155 ) )
| ~ ( in @ ( subset_complement @ SV155 @ SY982 ) @ SY978 )
| ( in @ SY982 @ SY980 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1446,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1215]) ).
thf(1447,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1448,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1217]) ).
thf(1449,plain,
! [SV156: $i] :
( ( ~ ( v2_membered @ SV156 )
| ~ ( ~ ! [SY983: $i] :
( ~ ( element @ SY983 @ ( powerset @ SV156 ) )
| ( v1_membered @ SY983 ) )
| ~ ! [SY984: $i] :
( ~ ( element @ SY984 @ ( powerset @ SV156 ) )
| ( v2_membered @ SY984 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1218]) ).
thf(1450,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1219]) ).
thf(1451,plain,
( ( ~ ( sK12_REN
| ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
( ( SX2 != SX1 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( ordinal @ SX1 )
| ( in @ SX1 @ ( sK7_B @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK7_B @ SX0 ) )
| ~ ( ~ ~ ( ( ( sK8_D @ SX1 @ SX0 )
!= SX1 )
| ~ ( in @ ( sK8_D @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ordinal @ SX1 ) ) ) ) )
| ~ ( ~ sK12_REN
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK9_B != sK10_SY601 )
| ~ ( ordinal @ sK10_SY601 ) )
| ( sK9_B != sK11_SY603 ) )
| ~ ( ordinal @ sK11_SY603 ) )
| ~ ( ( sK10_SY601 != sK11_SY603 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1220]) ).
thf(1452,plain,
( ( ~ ( element @ sK2_SY588 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( ( ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY588 )
!= ( subset_difference @ ( the_carrier @ sK1_A ) @ ( cast_as_carrier_subset @ sK1_A ) @ sK2_SY588 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1221]) ).
thf(1453,plain,
! [SV157: $i] :
( ( ~ ( ~ ! [SY985: $i,SY986: $i] :
( ~ ( relation @ SY986 )
| ~ ( in @ SV157 @ SY986 )
| ~ ( in @ SV157 @ ( cartesian_product2 @ SY985 @ SY985 ) )
| ( in @ SV157 @ ( relation_restriction @ SY986 @ SY985 ) ) )
| ~ ~ ( ~ ! [SY987: $i,SY988: $i] :
( ~ ( relation @ SY988 )
| ~ ( in @ SV157 @ ( relation_restriction @ SY988 @ SY987 ) )
| ( in @ SV157 @ SY988 ) )
| ~ ! [SY989: $i,SY990: $i] :
( ~ ( relation @ SY990 )
| ~ ( in @ SV157 @ ( relation_restriction @ SY990 @ SY989 ) )
| ( in @ SV157 @ ( cartesian_product2 @ SY989 @ SY989 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1454,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1223]) ).
thf(1455,plain,
! [SV158: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY991: $i,SY992: $i] :
( ~ ( relation_of2_as_subset @ SY992 @ SV158 @ SY991 )
| ( SY991 = empty_set )
| ( SV158
!= ( relation_dom_as_subset @ SV158 @ SY991 @ SY992 ) )
| ( quasi_total @ SY992 @ SV158 @ SY991 ) )
| ~ ! [SY993: $i,SY994: $i] :
( ~ ( relation_of2_as_subset @ SY994 @ SV158 @ SY993 )
| ( SY993 = empty_set )
| ~ ( quasi_total @ SY994 @ SV158 @ SY993 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SY993 @ SY994 ) ) ) )
| ~ ~ ( ~ ! [SY995: $i,SY996: $i] :
( ~ ( relation_of2_as_subset @ SY996 @ SV158 @ SY995 )
| ( SV158 != empty_set )
| ( SV158
!= ( relation_dom_as_subset @ SV158 @ SY995 @ SY996 ) )
| ( quasi_total @ SY996 @ SV158 @ SY995 ) )
| ~ ! [SY997: $i,SY998: $i] :
( ~ ( relation_of2_as_subset @ SY998 @ SV158 @ SY997 )
| ( SV158 != empty_set )
| ~ ( quasi_total @ SY998 @ SV158 @ SY997 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SY997 @ SY998 ) ) ) ) )
| ~ ~ ( ~ ! [SY999: $i,SY1000: $i] :
( ~ ( relation_of2_as_subset @ SY1000 @ SV158 @ SY999 )
| ( SY999 != empty_set )
| ( SY1000 != empty_set )
| ( quasi_total @ SY1000 @ SV158 @ SY999 )
| ( SV158 = empty_set ) )
| ~ ! [SY1001: $i,SY1002: $i] :
( ~ ( relation_of2_as_subset @ SY1002 @ SV158 @ SY1001 )
| ( SY1001 != empty_set )
| ~ ( quasi_total @ SY1002 @ SV158 @ SY1001 )
| ( SY1002 = empty_set )
| ( SV158 = empty_set ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1456,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK90_SY733 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK89_C @ SX1 @ SX0 ) @ ( sK90_SY733 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK89_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK89_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK89_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK88_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK88_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1225]) ).
thf(1457,plain,
! [SV159: $i] :
( ( ~ ( ~ ! [SY1003: $i,SY1004: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK82_D @ SY1004 @ SY1003 @ SV159 ) @ SY1004 )
| ( ( sK82_D @ SY1004 @ SY1003 @ SV159 )
!= SV159 ) )
| ~ ( ~ ( in @ ( sK82_D @ SY1004 @ SY1003 @ SV159 ) @ SY1004 )
| ( ( sK82_D @ SY1004 @ SY1003 @ SV159 )
!= SY1003 ) ) )
| ~ ( ( in @ ( sK82_D @ SY1004 @ SY1003 @ SV159 ) @ SY1004 )
| ( ( sK82_D @ SY1004 @ SY1003 @ SV159 )
= SV159 )
| ( ( sK82_D @ SY1004 @ SY1003 @ SV159 )
= SY1003 ) ) )
| ( SY1004
= ( unordered_pair @ SV159 @ SY1003 ) ) )
| ~ ! [SY1005: $i,SY1006: $i] :
( ( SY1006
!= ( unordered_pair @ SV159 @ SY1005 ) )
| ~ ( ~ ! [SY1007: $i] :
( ~ ( in @ SY1007 @ SY1006 )
| ( SY1007 = SV159 )
| ( SY1007 = SY1005 ) )
| ~ ~ ( ~ ! [SY1008: $i] :
( ( SY1008 != SV159 )
| ( in @ SY1008 @ SY1006 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY1005 )
| ( in @ SX3 @ SY1006 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1458,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1227]) ).
thf(1459,plain,
! [SV160: $i] :
( ( ~ ( v2_membered @ SV160 )
| ~ ( ~ ! [SY1010: $i] :
( ~ ( element @ SY1010 @ SV160 )
| ( v1_xcmplx_0 @ SY1010 ) )
| ~ ! [SY1011: $i] :
( ~ ( element @ SY1011 @ SV160 )
| ( v1_xreal_0 @ SY1011 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1228]) ).
thf(1460,plain,
( ( ~ ! [SX0: $i] :
( ~ ( latt_str @ SX0 )
| ( join_semilatt_str @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( latt_str @ SX0 )
| ( meet_semilatt_str @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1229]) ).
thf(1461,plain,
( ( ~ ( relation @ sK53_A )
| ~ ( relation_empty_yielding @ sK53_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1230]) ).
thf(1462,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK93_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK93_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK91_C @ SX1 @ SX0 ) @ ( sK92_SY735 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1231]) ).
thf(1463,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1232]) ).
thf(1464,plain,
! [SV161: $i] :
( ( ~ ( ~ ( relation @ ( sK100_B @ SV161 ) )
| ~ ( well_orders @ ( sK100_B @ SV161 ) @ SV161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1233]) ).
thf(1465,plain,
! [SV162: $i] :
( ( ! [SY1012: $i] :
( ~ ( element @ SY1012 @ ( powerset @ SV162 ) )
| ~ ( ~ ! [SY1013: $i] :
( ~ ( element @ SY1013 @ ( powerset @ SV162 ) )
| ~ ( disjoint @ SY1012 @ SY1013 )
| ( subset @ SY1012 @ ( subset_complement @ SV162 @ SY1013 ) ) )
| ~ ! [SY1014: $i] :
( ~ ( element @ SY1014 @ ( powerset @ SV162 ) )
| ~ ( subset @ SY1012 @ ( subset_complement @ SV162 @ SY1014 ) )
| ( disjoint @ SY1012 @ SY1014 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1234]) ).
thf(1466,plain,
( ( ~ ( one_sorted_str @ sK117_A )
| ~ ~ ( empty_carrier @ sK117_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1235]) ).
thf(1467,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1236]) ).
thf(1468,plain,
! [SV163: $i] :
( ( ~ ( ~ ! [SY1015: $i,SY1016: $i] :
( ~ ( relation_of2 @ SY1016 @ SV163 @ SY1015 )
| ( relation_of2_as_subset @ SY1016 @ SV163 @ SY1015 ) )
| ~ ! [SY1017: $i,SY1018: $i] :
( ~ ( relation_of2_as_subset @ SY1018 @ SV163 @ SY1017 )
| ( relation_of2 @ SY1018 @ SV163 @ SY1017 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1237]) ).
thf(1469,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK87_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK87_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK87_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK87_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1238]) ).
thf(1470,plain,
! [SV164: $i] :
( ( ~ ( ~ ! [SY1019: $i,SY1020: $i] :
( ~ ( ~ ( ! [SY1021: $i,SY1022: $i] :
( ~ ( in @ SY1021 @ SV164 )
| ~ ( in @ SY1022 @ SY1019 )
| ( ( sK78_D @ SY1020 @ SY1019 @ SV164 )
!= ( ordered_pair @ SY1021 @ SY1022 ) ) )
| ~ ( in @ ( sK78_D @ SY1020 @ SY1019 @ SV164 ) @ SY1020 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK79_SY729 @ SY1020 @ SY1019 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK80_SY731 @ SY1020 @ SY1019 @ SV164 ) @ SY1019 ) )
| ( ( sK78_D @ SY1020 @ SY1019 @ SV164 )
!= ( ordered_pair @ ( sK79_SY729 @ SY1020 @ SY1019 @ SV164 ) @ ( sK80_SY731 @ SY1020 @ SY1019 @ SV164 ) ) ) )
| ( in @ ( sK78_D @ SY1020 @ SY1019 @ SV164 ) @ SY1020 ) ) )
| ( SY1020
= ( cartesian_product2 @ SV164 @ SY1019 ) ) )
| ~ ! [SY1023: $i,SY1024: $i] :
( ( SY1024
!= ( cartesian_product2 @ SV164 @ SY1023 ) )
| ~ ( ~ ! [SY1025: $i] :
( ! [SY1026: $i,SY1027: $i] :
( ~ ( in @ SY1026 @ SV164 )
| ~ ( in @ SY1027 @ SY1023 )
| ( SY1025
!= ( ordered_pair @ SY1026 @ SY1027 ) ) )
| ( in @ SY1025 @ SY1024 ) )
| ~ ! [SY1028: $i] :
( ~ ( in @ SY1028 @ SY1024 )
| ~ ( ~ ~ ( ~ ( in @ ( sK76_E @ SY1028 @ SY1024 @ SY1023 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK77_SY726 @ SY1028 @ SY1024 @ SY1023 @ SV164 ) @ SY1023 ) )
| ( SY1028
!= ( ordered_pair @ ( sK76_E @ SY1028 @ SY1024 @ SY1023 @ SV164 ) @ ( sK77_SY726 @ SY1028 @ SY1024 @ SY1023 @ SV164 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1239]) ).
thf(1471,plain,
( ( ~ ( empty @ sK59_A )
| ~ ( relation @ sK59_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1240]) ).
thf(1472,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK71_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK71_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1241]) ).
thf(1473,plain,
! [SV165: $i] :
( ( ~ ( ~ ! [SY1029: $i,SY1030: $i] :
( ~ ( relation_of2 @ SY1030 @ SV165 @ SY1029 )
| ( subset @ SY1030 @ ( cartesian_product2 @ SV165 @ SY1029 ) ) )
| ~ ! [SY1031: $i,SY1032: $i] :
( ~ ( subset @ SY1032 @ ( cartesian_product2 @ SV165 @ SY1031 ) )
| ( relation_of2 @ SY1032 @ SV165 @ SY1031 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1242]) ).
thf(1474,plain,
! [SV166: $i] :
( ( ~ ( ~ ! [SY1033: $i] :
( ~ ( subset @ SY1033 @ ( sK3_B @ SV166 ) )
| ( are_equipotent @ SY1033 @ ( sK3_B @ SV166 ) )
| ( in @ SY1033 @ ( sK3_B @ SV166 ) ) )
| ~ ~ ( ~ ! [SY1034: $i] :
( ~ ( ~ ! [SY1035: $i] :
( ~ ( subset @ SY1035 @ SY1034 )
| ( in @ SY1035 @ ( sK4_SY591 @ SY1034 @ SV166 ) ) )
| ~ ( in @ ( sK4_SY591 @ SY1034 @ SV166 ) @ ( sK3_B @ SV166 ) ) )
| ~ ( in @ SY1034 @ ( sK3_B @ SV166 ) ) )
| ~ ~ ( ~ ! [SY1036: $i,SY1037: $i] :
( ~ ( in @ SY1036 @ ( sK3_B @ SV166 ) )
| ~ ( subset @ SY1037 @ SY1036 )
| ( in @ SY1037 @ ( sK3_B @ SV166 ) ) )
| ~ ( in @ SV166 @ ( sK3_B @ SV166 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(1475,plain,
! [SV167: $i] :
( ( ~ ( ~ ! [SY1038: $i,SY1039: $i] :
( ~ ( relation_of2_as_subset @ SY1039 @ SY1038 @ SV167 )
| ~ ( ~ ! [SY1040: $i] :
~ ( in @ ( ordered_pair @ ( sK104_D @ SY1039 @ SY1038 @ SV167 ) @ SY1040 ) @ SY1039 )
| ~ ( in @ ( sK104_D @ SY1039 @ SY1038 @ SV167 ) @ SY1038 ) )
| ( ( relation_dom_as_subset @ SY1038 @ SV167 @ SY1039 )
= SY1038 ) )
| ~ ! [SY1041: $i,SY1042: $i] :
( ~ ( relation_of2_as_subset @ SY1042 @ SY1041 @ SV167 )
| ( ( relation_dom_as_subset @ SY1041 @ SV167 @ SY1042 )
!= SY1041 )
| ! [SY1043: $i] :
( ( in @ ( ordered_pair @ SY1043 @ ( sK103_E @ SY1043 @ SY1042 @ SY1041 @ SV167 ) ) @ SY1042 )
| ~ ( in @ SY1043 @ SY1041 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(1476,plain,
! [SV168: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK27_SY634 @ SV168 )
!= ( singleton @ ( sK26_B @ SV168 ) ) )
| ~ ( in @ ( sK26_B @ SV168 ) @ SV168 ) )
| ~ ( in @ ( sK26_B @ SV168 ) @ SV168 ) )
| ( ( sK28_SY636 @ SV168 )
!= ( singleton @ ( sK26_B @ SV168 ) ) ) )
| ~ ( ( ( sK27_SY634 @ SV168 )
!= ( sK28_SY636 @ SV168 ) ) ) )
| ~ ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) )
| ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1477,plain,
( ( ~ ( function @ sK60_A )
| ~ ( relation @ sK60_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1246]) ).
thf(1478,plain,
( ( ~ ~ ( ~ ( empty @ sK57_A )
| ~ ( relation @ sK57_A ) )
| ~ ( function @ sK57_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1247]) ).
thf(1479,plain,
! [SV169: $i] :
( ( ! [SY1047: $i] :
~ ( ~ ! [SY1048: $i,SY1049: $i] :
( ~ ( in @ SV169 @ SY1048 )
| ~ ( in @ SY1047 @ SY1049 )
| ( in @ ( ordered_pair @ SV169 @ SY1047 ) @ ( cartesian_product2 @ SY1048 @ SY1049 ) ) )
| ~ ~ ( ~ ! [SY1050: $i] :
( ! [SY1051: $i] :
~ ( in @ ( ordered_pair @ SV169 @ SY1047 ) @ ( cartesian_product2 @ SY1050 @ SY1051 ) )
| ( in @ SV169 @ SY1050 ) )
| ~ ! [SY1052: $i,SY1053: $i] :
( ~ ( in @ ( ordered_pair @ SV169 @ SY1047 ) @ ( cartesian_product2 @ SY1052 @ SY1053 ) )
| ( in @ SY1047 @ SY1053 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1480,plain,
! [SV170: $i] :
( ( ! [SY1054: $i] :
( ( empty @ SV170 )
| ~ ( relation @ SY1054 )
| ! [SY1055: $i] :
~ ( ~ ! [SY1056: $i] :
( ! [SY1057: $i,SY1058: $i] :
( ( ( ordered_pair @ SY1057 @ SY1058 )
!= SY1056 )
| ~ ( in @ SY1057 @ SV170 )
| ! [SY1059: $i] :
( ~ ( ~ ( in @ ( sK115_I @ SY1059 @ SY1058 @ SY1057 @ SY1056 @ SY1055 @ SY1054 @ SV170 ) @ SY1059 )
| ~ ~ ( in @ ( ordered_pair @ SY1058 @ ( sK115_I @ SY1059 @ SY1058 @ SY1057 @ SY1056 @ SY1055 @ SY1054 @ SV170 ) ) @ SY1054 ) )
| ( SY1057 != SY1059 )
| ~ ( in @ SY1058 @ SY1059 ) ) )
| ~ ( in @ SY1056 @ ( cartesian_product2 @ SV170 @ SY1055 ) )
| ( in @ SY1056 @ ( sK111_D @ SY1055 @ SY1054 @ SV170 ) ) )
| ~ ~ ( ~ ! [SY1060: $i] :
( ~ ( in @ SY1060 @ ( sK111_D @ SY1055 @ SY1054 @ SV170 ) )
| ~ ( ~ ~ ( ( ( ordered_pair @ ( sK112_F @ SY1060 @ SY1055 @ SY1054 @ SV170 ) @ ( sK113_SY768 @ SY1060 @ SY1055 @ SY1054 @ SV170 ) )
!= SY1060 )
| ~ ( in @ ( sK112_F @ SY1060 @ SY1055 @ SY1054 @ SV170 ) @ SV170 ) )
| ~ ~ ( ~ ! [SY1061: $i] :
( ~ ( in @ SY1061 @ ( sK114_SY771 @ SY1060 @ SY1055 @ SY1054 @ SV170 ) )
| ( in @ ( ordered_pair @ ( sK113_SY768 @ SY1060 @ SY1055 @ SY1054 @ SV170 ) @ SY1061 ) @ SY1054 ) )
| ~ ~ ( ( ( sK112_F @ SY1060 @ SY1055 @ SY1054 @ SV170 )
!= ( sK114_SY771 @ SY1060 @ SY1055 @ SY1054 @ SV170 ) )
| ~ ( in @ ( sK113_SY768 @ SY1060 @ SY1055 @ SY1054 @ SV170 ) @ ( sK114_SY771 @ SY1060 @ SY1055 @ SY1054 @ SV170 ) ) ) ) ) )
| ~ ! [SY1062: $i] :
( ~ ( in @ SY1062 @ ( sK111_D @ SY1055 @ SY1054 @ SV170 ) )
| ( in @ SY1062 @ ( cartesian_product2 @ SV170 @ SY1055 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(1481,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( ( ( sK74_B @ SX0 )
!= ( sK75_SY725 @ SX0 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK74_B @ SX0 ) @ SX0 )
| ~ ( in @ ( sK75_SY725 @ SX0 ) @ SX0 ) )
| ~ ~ ( in @ ( sK74_B @ SX0 ) @ ( sK75_SY725 @ SX0 ) ) ) )
| ~ ~ ( in @ ( sK75_SY725 @ SX0 ) @ ( sK74_B @ SX0 ) ) )
| ( epsilon_connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( epsilon_connected @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( SX1 = SX2 )
| ~ ( in @ SX1 @ SX0 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ SX2 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1250]) ).
thf(1482,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_difference @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_difference @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v3_membered @ ( set_difference @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1251]) ).
thf(1483,plain,
! [SV171: $i] :
( ( ~ ( relation @ SV171 )
| ~ ( ~ ! [SY1063: $i] :
( ~ ( relation @ SY1063 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK83_C @ SY1063 @ SV171 ) @ ( sK84_SY732 @ SY1063 @ SV171 ) ) @ SV171 )
| ~ ( in @ ( ordered_pair @ ( sK83_C @ SY1063 @ SV171 ) @ ( sK84_SY732 @ SY1063 @ SV171 ) ) @ SY1063 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK83_C @ SY1063 @ SV171 ) @ ( sK84_SY732 @ SY1063 @ SV171 ) ) @ SV171 )
| ( in @ ( ordered_pair @ ( sK83_C @ SY1063 @ SV171 ) @ ( sK84_SY732 @ SY1063 @ SV171 ) ) @ SY1063 ) ) )
| ( SV171 = SY1063 ) )
| ~ ! [SY1064: $i] :
( ~ ( relation @ SY1064 )
| ( SV171 != SY1064 )
| ~ ( ~ ! [SY1065: $i,SY1066: $i] :
( ~ ( in @ ( ordered_pair @ SY1065 @ SY1066 ) @ SV171 )
| ( in @ ( ordered_pair @ SY1065 @ SY1066 ) @ SY1064 ) )
| ~ ! [SY1067: $i,SY1068: $i] :
( ~ ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SY1064 )
| ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SV171 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1484,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1253]) ).
thf(1485,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK98_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK98_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1254]) ).
thf(1486,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1255]) ).
thf(1487,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK97_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1256]) ).
thf(1488,plain,
( ( ~ ! [SX0: $i] :
~ ( empty @ ( singleton @ SX0 ) )
| ~ ! [SX0: $i] : ( finite @ ( singleton @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1257]) ).
thf(1489,plain,
! [SV172: $i] :
( ( ! [SY1069: $i] :
( ( empty @ SV172 )
| ~ ( relation @ SY1069 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK35_D @ SY1069 @ SV172 )
!= ( sK36_SY655 @ SY1069 @ SV172 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK41_SY666 @ SY1069 @ SV172 ) @ ( sK42_SY688 @ SY1069 @ SV172 ) )
!= ( sK36_SY655 @ SY1069 @ SV172 ) )
| ~ ( in @ ( sK41_SY666 @ SY1069 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1070: $i] :
( ~ ( in @ SY1070 @ ( sK43_SY691 @ SY1069 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK42_SY688 @ SY1069 @ SV172 ) @ SY1070 ) @ SY1069 ) )
| ~ ~ ( ( ( sK41_SY666 @ SY1069 @ SV172 )
!= ( sK43_SY691 @ SY1069 @ SV172 ) )
| ~ ( in @ ( sK42_SY688 @ SY1069 @ SV172 ) @ ( sK43_SY691 @ SY1069 @ SV172 ) ) ) ) ) )
| ( ( sK35_D @ SY1069 @ SV172 )
!= ( sK37_SY665 @ SY1069 @ SV172 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK38_SY678 @ SY1069 @ SV172 ) @ ( sK39_SY682 @ SY1069 @ SV172 ) )
!= ( sK37_SY665 @ SY1069 @ SV172 ) )
| ~ ( in @ ( sK38_SY678 @ SY1069 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1071: $i] :
( ~ ( in @ SY1071 @ ( sK40_SY685 @ SY1069 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK39_SY682 @ SY1069 @ SV172 ) @ SY1071 ) @ SY1069 ) )
| ~ ~ ( ( ( sK38_SY678 @ SY1069 @ SV172 )
!= ( sK40_SY685 @ SY1069 @ SV172 ) )
| ~ ( in @ ( sK39_SY682 @ SY1069 @ SV172 ) @ ( sK40_SY685 @ SY1069 @ SV172 ) ) ) ) ) )
| ~ ( ( ( sK36_SY655 @ SY1069 @ SV172 )
!= ( sK37_SY665 @ SY1069 @ SV172 ) ) ) )
| ! [SY1072: $i] :
~ ( ~ ! [SY1073: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1073 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1072 ) ) )
| ! [SY1075: $i,SY1076: $i] :
( ( ( ordered_pair @ SY1075 @ SY1076 )
!= SY1073 )
| ~ ( in @ SY1075 @ SV172 )
| ! [SY1077: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1077 @ SY1076 @ SY1075 @ SY1073 @ SY1072 @ SY1069 @ SV172 ) @ SY1077 )
| ~ ~ ( in @ ( ordered_pair @ SY1076 @ ( sK34_R @ SY1077 @ SY1076 @ SY1075 @ SY1073 @ SY1072 @ SY1069 @ SV172 ) ) @ SY1069 ) )
| ( SY1075 != SY1077 )
| ~ ( in @ SY1076 @ SY1077 ) ) )
| ( in @ SY1073 @ ( sK29_D @ SY1072 @ SY1069 @ SV172 ) ) )
| ~ ! [SY1078: $i] :
( ~ ( in @ SY1078 @ ( sK29_D @ SY1072 @ SY1069 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1078 @ SY1072 @ SY1069 @ SV172 )
!= SY1078 )
| ~ ( in @ ( sK33_F @ SY1078 @ SY1072 @ SY1069 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1072 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1078 @ SY1072 @ SY1069 @ SV172 ) @ ( sK31_SY649 @ SY1078 @ SY1072 @ SY1069 @ SV172 ) )
!= SY1078 )
| ~ ( in @ ( sK30_O @ SY1078 @ SY1072 @ SY1069 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1079: $i] :
( ~ ( in @ SY1079 @ ( sK32_SY652 @ SY1078 @ SY1072 @ SY1069 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1078 @ SY1072 @ SY1069 @ SV172 ) @ SY1079 ) @ SY1069 ) )
| ~ ~ ( ( ( sK30_O @ SY1078 @ SY1072 @ SY1069 @ SV172 )
!= ( sK32_SY652 @ SY1078 @ SY1072 @ SY1069 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1078 @ SY1072 @ SY1069 @ SV172 ) @ ( sK32_SY652 @ SY1078 @ SY1072 @ SY1069 @ SV172 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1258]) ).
thf(1490,plain,
( ( ~ ! [SX0: $i] :
( ( SX0
!= ( union @ SX0 ) )
| ( being_limit_ordinal @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( being_limit_ordinal @ SX0 )
| ( SX0
= ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1259]) ).
thf(1491,plain,
( ( ~ ! [SX0: $i] :
( ~ ( v2_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_intersection2 @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( v2_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_intersection2 @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1260]) ).
thf(1492,plain,
! [SV173: $i] :
( ( ! [SY1080: $i] :
~ ( ~ ! [SY1081: $i,SY1082: $i] :
( ~ ( in @ SV173 @ SY1081 )
| ~ ( in @ SY1080 @ SY1082 )
| ( in @ ( ordered_pair @ SV173 @ SY1080 ) @ ( cartesian_product2 @ SY1081 @ SY1082 ) ) )
| ~ ~ ( ~ ! [SY1083: $i] :
( ! [SY1084: $i] :
~ ( in @ ( ordered_pair @ SV173 @ SY1080 ) @ ( cartesian_product2 @ SY1083 @ SY1084 ) )
| ( in @ SV173 @ SY1083 ) )
| ~ ! [SY1085: $i,SY1086: $i] :
( ~ ( in @ ( ordered_pair @ SV173 @ SY1080 ) @ ( cartesian_product2 @ SY1085 @ SY1086 ) )
| ( in @ SY1080 @ SY1086 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1493,plain,
! [SV174: $i] :
( ( ! [SY1087: $i] :
~ ( ~ ~ ( ~ ( relation @ ( sK56_C @ SY1087 @ SV174 ) )
| ~ ( relation_of2 @ ( sK56_C @ SY1087 @ SV174 ) @ SV174 @ SY1087 ) )
| ~ ( function @ ( sK56_C @ SY1087 @ SV174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1494,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1263]) ).
thf(1495,plain,
( ( ~ ! [SX0: $i] :
( ~ ( v2_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_difference @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( v2_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_difference @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1264]) ).
thf(1496,plain,
! [SV175: $i] :
( ( ~ ( ~ ( element @ ( sK119_B @ SV175 ) @ ( powerset @ SV175 ) )
| ~ ( empty @ ( sK119_B @ SV175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1497,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v3_membered @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1266]) ).
thf(1498,plain,
( ( ~ ~ ( empty @ sK61_A )
| ~ ( finite @ sK61_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1267]) ).
thf(1499,plain,
( ( ~ ! [SX0: $i] :
( ~ ( v2_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( v2_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1268]) ).
thf(1500,plain,
( ( ~ ~ ( empty @ sK55_A )
| ~ ( relation @ sK55_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1269]) ).
thf(1501,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1270]) ).
thf(1502,plain,
! [SV176: $i] :
( ( ! [SY1088: $i] :
~ ( ~ ! [SY1089: $i] :
( ! [SY1090: $i,SY1091: $i] :
( ( ( ordered_pair @ SY1090 @ SY1091 )
!= SY1089 )
| ~ ( in @ SY1090 @ SV176 )
| ( SY1091
!= ( singleton @ SY1090 ) ) )
| ~ ( in @ SY1089 @ ( cartesian_product2 @ SV176 @ SY1088 ) )
| ( in @ SY1089 @ ( sK108_C @ SY1088 @ SV176 ) ) )
| ~ ~ ( ~ ! [SY1092: $i] :
( ~ ( in @ SY1092 @ ( sK108_C @ SY1088 @ SV176 ) )
| ~ ( ~ ~ ( ( ( ordered_pair @ ( sK109_E @ SY1092 @ SY1088 @ SV176 ) @ ( sK110_SY756 @ SY1092 @ SY1088 @ SV176 ) )
!= SY1092 )
| ~ ( in @ ( sK109_E @ SY1092 @ SY1088 @ SV176 ) @ SV176 ) )
| ( ( sK110_SY756 @ SY1092 @ SY1088 @ SV176 )
!= ( singleton @ ( sK109_E @ SY1092 @ SY1088 @ SV176 ) ) ) ) )
| ~ ! [SY1093: $i] :
( ~ ( in @ SY1093 @ ( sK108_C @ SY1088 @ SV176 ) )
| ( in @ SY1093 @ ( cartesian_product2 @ SV176 @ SY1088 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1271]) ).
thf(1503,plain,
! [SV177: $i] :
( ( ! [SY1094: $i] :
( ~ ( ~ ( in @ ( sK125_C @ SY1094 @ SV177 ) @ SV177 )
| ~ ~ ( in @ ( sK125_C @ SY1094 @ SV177 ) @ SY1094 ) )
| ( element @ SV177 @ ( powerset @ SY1094 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1504,plain,
! [SV178: $i] :
( ( ! [SY1095: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_C @ SY1095 @ SV178 ) @ SV178 )
| ~ ( in @ ( sK6_C @ SY1095 @ SV178 ) @ SY1095 ) )
| ~ ( ( in @ ( sK6_C @ SY1095 @ SV178 ) @ SV178 )
| ( in @ ( sK6_C @ SY1095 @ SV178 ) @ SY1095 ) ) )
| ( SV178 = SY1095 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1273]) ).
thf(1505,plain,
! [SV179: $i] :
( ( ~ ( ~ ! [SY1096: $i] :
( ~ ( subset @ SV179 @ SY1096 )
| ! [SY1097: $i] : ( subset @ ( cartesian_product2 @ SV179 @ SY1097 ) @ ( cartesian_product2 @ SY1096 @ SY1097 ) ) )
| ~ ! [SY1098: $i] :
( ~ ( subset @ SV179 @ SY1098 )
| ! [SY1099: $i] : ( subset @ ( cartesian_product2 @ SY1099 @ SV179 ) @ ( cartesian_product2 @ SY1099 @ SY1098 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1274]) ).
thf(1506,plain,
! [SV180: $i] :
( ( ~ ( ~ ! [SY1100: $i,SY1101: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK81_D @ SY1101 @ SY1100 @ SV180 ) @ SY1101 )
| ~ ( in @ ( sK81_D @ SY1101 @ SY1100 @ SV180 ) @ SV180 ) )
| ~ ( ~ ( in @ ( sK81_D @ SY1101 @ SY1100 @ SV180 ) @ SY1101 )
| ~ ( in @ ( sK81_D @ SY1101 @ SY1100 @ SV180 ) @ SY1100 ) ) )
| ~ ( ( in @ ( sK81_D @ SY1101 @ SY1100 @ SV180 ) @ SY1101 )
| ( in @ ( sK81_D @ SY1101 @ SY1100 @ SV180 ) @ SV180 )
| ( in @ ( sK81_D @ SY1101 @ SY1100 @ SV180 ) @ SY1100 ) ) )
| ( SY1101
= ( set_union2 @ SV180 @ SY1100 ) ) )
| ~ ! [SY1102: $i,SY1103: $i] :
( ( SY1103
!= ( set_union2 @ SV180 @ SY1102 ) )
| ~ ( ~ ! [SY1104: $i] :
( ~ ( in @ SY1104 @ SY1103 )
| ( in @ SY1104 @ SV180 )
| ( in @ SY1104 @ SY1102 ) )
| ~ ~ ( ~ ! [SY1105: $i] :
( ~ ( in @ SY1105 @ SV180 )
| ( in @ SY1105 @ SY1103 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1102 )
| ( in @ SX3 @ SY1103 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1275]) ).
thf(1507,plain,
! [SV181: $i] :
( ( ( empty @ SV181 )
| ~ ( ~ ( element @ ( sK120_B @ SV181 ) @ ( powerset @ SV181 ) )
| ~ ~ ( empty @ ( sK120_B @ SV181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1508,plain,
! [SV1: $i,SV182: $i] :
( ( ~ ( element @ SV182 @ ( powerset @ SV1 ) )
| ! [SY1107: $i] :
( ~ ( in @ SY1107 @ SV182 )
| ( in @ SY1107 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1509,plain,
! [SV2: $i] :
( ( ( ~ ( one_sorted_str @ SV2 ) )
= $true )
| ( ( ( cast_as_carrier_subset @ SV2 )
= ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1278]) ).
thf(1510,plain,
! [SV3: $i] :
( ( ( ~ ( one_sorted_str @ SV3 ) )
= $true )
| ( ( ! [SY776: $i] :
( ~ ( element @ SY776 @ ( powerset @ ( the_carrier @ SV3 ) ) )
| ( ( subset_intersection2 @ ( the_carrier @ SV3 ) @ SY776 @ ( cast_as_carrier_subset @ SV3 ) )
= SY776 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1279]) ).
thf(1511,plain,
! [SV4: $i,SV183: $i] :
( ( ~ ( element @ SV183 @ ( powerset @ ( powerset @ SV4 ) ) )
| ( SV183 = empty_set )
| ( ( complements_of_subsets @ SV4 @ SV183 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1280]) ).
thf(1512,plain,
! [SV5: $i] :
( ( ( SV5 = empty_set )
= $true )
| ( ( ! [SY778: $i] :
( ~ ( element @ SY778 @ ( powerset @ SV5 ) )
| ! [SY779: $i] :
( ~ ( element @ SY779 @ SV5 )
| ( in @ SY779 @ SY778 )
| ( in @ SY779 @ ( subset_complement @ SV5 @ SY778 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1281]) ).
thf(1513,plain,
! [SV184: $i,SV6: $i] :
( ( ! [SY1108: $i] :
( ~ ( element @ SY1108 @ ( powerset @ SV6 ) )
| ~ ( in @ SV184 @ ( subset_complement @ SV6 @ SY1108 ) )
| ~ ( in @ SV184 @ SY1108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1514,plain,
! [SV8: $i] :
( ( ( ~ ( v1_membered @ SV8 ) )
= $true )
| ( ( ! [SY782: $i] :
( ~ ( element @ SY782 @ SV8 )
| ( v1_xcmplx_0 @ SY782 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1284]) ).
thf(1515,plain,
! [SV9: $i] :
( ( ( ~ ( v1_membered @ SV9 ) )
= $true )
| ( ( ! [SY783: $i] :
( ~ ( element @ SY783 @ ( powerset @ SV9 ) )
| ( v1_membered @ SY783 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1285]) ).
thf(1516,plain,
! [SV185: $i,SV10: $i] :
( ( ! [SY1109: $i] :
( ~ ( element @ SY1109 @ ( powerset @ ( cartesian_product2 @ SV10 @ SV185 ) ) )
| ( relation @ SY1109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1286]) ).
thf(1517,plain,
! [SV11: $i] :
( ( ( ~ ( finite @ SV11 ) )
= $true )
| ( ( ! [SY786: $i] :
( ~ ( element @ SY786 @ ( powerset @ SV11 ) )
| ( finite @ SY786 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1287]) ).
thf(1518,plain,
! [SV12: $i,SV186: $i] :
( ( ! [SY1110: $i] :
( ~ ( element @ SV186 @ ( powerset @ SV12 ) )
| ~ ( element @ SY1110 @ ( powerset @ SV12 ) )
| ( ( subset_intersection2 @ SV12 @ SV186 @ SY1110 )
= ( subset_intersection2 @ SV12 @ SY1110 @ SV186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1519,plain,
! [SV13: $i] :
( ( ( ~ ( one_sorted_str @ SV13 ) )
= $true )
| ( ( ( cast_as_carrier_subset @ SV13 )
= ( the_carrier @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1289]) ).
thf(1520,plain,
! [SV14: $i,SV187: $i] :
( ( ~ ( element @ SV187 @ ( powerset @ SV14 ) )
| ( ( subset_complement @ SV14 @ SV187 )
= ( set_difference @ SV14 @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1290]) ).
thf(1521,plain,
! [SV15: $i] :
( ( ( ~ ( one_sorted_str @ SV15 ) )
= $true )
| ( ( element @ ( cast_as_carrier_subset @ SV15 ) @ ( powerset @ ( the_carrier @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1291]) ).
thf(1522,plain,
! [SV17: $i,SV188: $i] :
( ( ~ ( element @ SV188 @ ( powerset @ SV17 ) )
| ( element @ ( subset_complement @ SV17 @ SV188 ) @ ( powerset @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1523,plain,
! [SV189: $i,SV18: $i] :
( ( ! [SY1111: $i] :
( ~ ( relation_of2 @ SY1111 @ SV18 @ SV189 )
| ( element @ ( relation_dom_as_subset @ SV18 @ SV189 @ SY1111 ) @ ( powerset @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1524,plain,
! [SV190: $i,SV19: $i] :
( ( ! [SY1112: $i] :
( ~ ( relation_of2 @ SY1112 @ SV19 @ SV190 )
| ( element @ ( relation_rng_as_subset @ SV19 @ SV190 @ SY1112 ) @ ( powerset @ SV190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1295]) ).
thf(1525,plain,
! [SV20: $i,SV191: $i] :
( ( ~ ( element @ SV191 @ ( powerset @ ( powerset @ SV20 ) ) )
| ( element @ ( union_of_subsets @ SV20 @ SV191 ) @ ( powerset @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1296]) ).
thf(1526,plain,
! [SV21: $i,SV192: $i] :
( ( ! [SY1113: $i] :
( ~ ( element @ SV192 @ ( powerset @ SV21 ) )
| ~ ( element @ SY1113 @ ( powerset @ SV21 ) )
| ( element @ ( subset_intersection2 @ SV21 @ SV192 @ SY1113 ) @ ( powerset @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1297]) ).
thf(1527,plain,
! [SV22: $i,SV193: $i] :
( ( ~ ( element @ SV193 @ ( powerset @ ( powerset @ SV22 ) ) )
| ( element @ ( meet_of_subsets @ SV22 @ SV193 ) @ ( powerset @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1298]) ).
thf(1528,plain,
! [SV23: $i,SV194: $i] :
( ( ! [SY1114: $i] :
( ~ ( element @ SV194 @ ( powerset @ SV23 ) )
| ~ ( element @ SY1114 @ ( powerset @ SV23 ) )
| ( element @ ( subset_difference @ SV23 @ SV194 @ SY1114 ) @ ( powerset @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1299]) ).
thf(1529,plain,
! [SV24: $i,SV195: $i] :
( ( ~ ( element @ SV195 @ ( powerset @ ( powerset @ SV24 ) ) )
| ( element @ ( complements_of_subsets @ SV24 @ SV195 ) @ ( powerset @ ( powerset @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1530,plain,
! [SV25: $i] :
( ( ( ~ ( meet_semilatt_str @ SV25 ) )
= $true )
| ( ( one_sorted_str @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1301]) ).
thf(1531,plain,
! [SV26: $i] :
( ( ( ~ ( join_semilatt_str @ SV26 ) )
= $true )
| ( ( one_sorted_str @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1302]) ).
thf(1532,plain,
! [SV196: $i,SV27: $i] :
( ( ! [SY1115: $i] :
( ~ ( relation_of2_as_subset @ SY1115 @ SV27 @ SV196 )
| ( element @ SY1115 @ ( powerset @ ( cartesian_product2 @ SV27 @ SV196 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1303]) ).
thf(1533,plain,
! [SV29: $i] :
( ( ( ( empty_carrier @ SV29 )
| ~ ( one_sorted_str @ SV29 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1305]) ).
thf(1534,plain,
! [SV30: $i] :
( ( empty @ ( powerset @ SV30 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1306]) ).
thf(1535,plain,
! [SV31: $i,SV197: $i] :
( ( ~ ( element @ SV197 @ ( powerset @ SV31 ) )
| ! [SY805: $i] :
~ ( element @ SY805 @ ( powerset @ SV31 ) )
| ( ( subset_intersection2 @ SV31 @ SV197 @ SV197 )
= SV197 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1536,plain,
! [SV32: $i,SV198: $i] :
( ( ~ ( element @ SV198 @ ( powerset @ SV32 ) )
| ( ( subset_complement @ SV32 @ ( subset_complement @ SV32 @ SV198 ) )
= SV198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1308]) ).
thf(1537,plain,
! [SV33: $i,SV199: $i] :
( ( ~ ( element @ SV199 @ ( powerset @ ( powerset @ SV33 ) ) )
| ( ( complements_of_subsets @ SV33 @ ( complements_of_subsets @ SV33 @ SV199 ) )
= SV199 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1309]) ).
thf(1538,plain,
! [SV34: $i,SV200: $i] :
( ( ~ ( element @ SV200 @ ( powerset @ ( powerset @ SV34 ) ) )
| ( ( union_of_subsets @ SV34 @ SV200 )
= ( union @ SV200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1310]) ).
thf(1539,plain,
! [SV35: $i,SV201: $i] :
( ( ! [SY1117: $i] :
( ~ ( element @ SV201 @ ( powerset @ SV35 ) )
| ~ ( element @ SY1117 @ ( powerset @ SV35 ) )
| ( ( subset_intersection2 @ SV35 @ SV201 @ SY1117 )
= ( set_intersection2 @ SV201 @ SY1117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1540,plain,
! [SV36: $i,SV202: $i] :
( ( ~ ( element @ SV202 @ ( powerset @ ( powerset @ SV36 ) ) )
| ( ( meet_of_subsets @ SV36 @ SV202 )
= ( set_meet @ SV202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1312]) ).
thf(1541,plain,
! [SV37: $i,SV203: $i] :
( ( ! [SY1118: $i] :
( ~ ( element @ SV203 @ ( powerset @ SV37 ) )
| ~ ( element @ SY1118 @ ( powerset @ SV37 ) )
| ( ( subset_difference @ SV37 @ SV203 @ SY1118 )
= ( set_difference @ SV203 @ SY1118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1313]) ).
thf(1542,plain,
! [SV204: $i,SV38: $i] :
( ( ~ ( in @ SV38 @ SV204 )
| ( element @ SV38 @ SV204 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1543,plain,
! [SV205: $i,SV39: $i] :
( ( ~ ( element @ SV39 @ SV205 )
| ( empty @ SV205 )
| ( in @ SV39 @ SV205 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1544,plain,
! [SV40: $i,SV206: $i] :
( ( ! [SY1119: $i] :
( ~ ( element @ SV206 @ ( powerset @ SY1119 ) )
| ~ ( in @ SV40 @ SV206 )
| ( element @ SV40 @ SY1119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1545,plain,
! [SV41: $i,SV207: $i] :
( ( ! [SY1120: $i] :
( ~ ( element @ SV207 @ ( powerset @ SY1120 ) )
| ~ ( in @ SV41 @ SV207 )
| ~ ( empty @ SY1120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1317]) ).
thf(1546,plain,
! [SV42: $i] :
( ( ( singleton @ SV42 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1318]) ).
thf(1547,plain,
! [SV208: $i,SV43: $i] :
( ( ~ ( in @ SV43 @ SV208 )
| ( ( set_union2 @ ( singleton @ SV43 ) @ SV208 )
= SV208 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1319]) ).
thf(1548,plain,
! [SV209: $i,SV44: $i] :
( ( ~ ( disjoint @ ( singleton @ SV44 ) @ SV209 )
| ~ ( in @ SV44 @ SV209 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1320]) ).
thf(1549,plain,
! [SV210: $i,SV45: $i] :
( ( ( in @ SV45 @ SV210 )
| ( disjoint @ ( singleton @ SV45 ) @ SV210 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1550,plain,
! [SV211: $i,SV46: $i] :
( ( ~ ( subset @ SV46 @ SV211 )
| ! [SY1121: $i] :
( ( in @ SY1121 @ SV46 )
| ( subset @ SV46 @ ( set_difference @ SV211 @ ( singleton @ SY1121 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1551,plain,
! [SV212: $i,SV47: $i] :
( ( ~ ( in @ SV47 @ SV212 )
| ( subset @ SV47 @ ( union @ SV212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1323]) ).
thf(1552,plain,
! [SV49: $i,SV213: $i] :
( ( ~ ( relation @ SV213 )
| ( subset @ ( relation_rng_restriction @ SV49 @ SV213 ) @ SV213 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1553,plain,
! [SV214: $i,SV50: $i] :
( ( ! [SY1122: $i,SY1123: $i] :
( ~ ( subset @ SV50 @ SV214 )
| ~ ( subset @ SY1122 @ SY1123 )
| ( subset @ ( cartesian_product2 @ SV50 @ SY1122 ) @ ( cartesian_product2 @ SV214 @ SY1123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1326]) ).
thf(1554,plain,
! [SV215: $i,SV51: $i] :
( ( ~ ( subset @ SV51 @ SV215 )
| ( ( set_union2 @ SV51 @ SV215 )
= SV215 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1327]) ).
thf(1555,plain,
! [SV52: $i] :
( ( ( ! [SY831: $i] :
( ~ ( finite @ SY831 )
| ~ ( subset @ SV52 @ SY831 ) ) )
= $true )
| ( ( finite @ SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1328]) ).
thf(1556,plain,
! [SV216: $i,SV53: $i] :
( ( ! [SY1124: $i,SY1125: $i] :
( ~ ( relation_of2_as_subset @ SY1125 @ SY1124 @ SV53 )
| ~ ( subset @ ( relation_rng @ SY1125 ) @ SV216 )
| ( relation_of2_as_subset @ SY1125 @ SY1124 @ SV216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1329]) ).
thf(1557,plain,
! [SV54: $i] :
( ( ( ~ ( finite @ SV54 ) )
= $true )
| ( ( ! [SY835: $i] : ( finite @ ( set_intersection2 @ SV54 @ SY835 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1330]) ).
thf(1558,plain,
! [SV217: $i,SV55: $i] :
( ( ! [SY1126: $i,SY1127: $i] :
( ~ ( relation_of2_as_subset @ SY1127 @ SY1126 @ SV55 )
| ~ ( subset @ SV55 @ SV217 )
| ( relation_of2_as_subset @ SY1127 @ SY1126 @ SV217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1331]) ).
thf(1559,plain,
! [SV218: $i,SV56: $i] :
( ( ! [SY1128: $i] :
( ~ ( relation @ SY1128 )
| ~ ( subset @ SV56 @ SV218 )
| ( subset @ ( relation_inverse_image @ SY1128 @ SV56 ) @ ( relation_inverse_image @ SY1128 @ SV218 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1332]) ).
thf(1560,plain,
! [SV219: $i,SV57: $i] :
( ( subset @ ( set_intersection2 @ SV57 @ SV219 ) @ SV57 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1333]) ).
thf(1561,plain,
! [SV220: $i,SV58: $i] :
( ( ! [SY1129: $i] :
( ~ ( subset @ SV58 @ SV220 )
| ~ ( subset @ SV58 @ SY1129 )
| ( subset @ SV58 @ ( set_intersection2 @ SV220 @ SY1129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1334]) ).
thf(1562,plain,
! [SV221: $i,SV59: $i] :
( ( ! [SY1130: $i] :
( ~ ( subset @ SV59 @ SV221 )
| ~ ( subset @ SV221 @ SY1130 )
| ( subset @ SV59 @ SY1130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1335]) ).
thf(1563,plain,
! [SV60: $i,SV222: $i] :
( ( ~ ( ordinal @ SV222 )
| ~ ( in @ SV60 @ SV222 )
| ( ordinal @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1564,plain,
! [SV61: $i] :
( ( ( ~ ( ordinal @ SV61 ) )
= $true )
| ( ( ! [SY847: $i] :
( ~ ( ordinal @ SY847 )
| ( in @ SV61 @ SY847 )
| ( SV61 = SY847 )
| ( in @ SY847 @ SV61 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1337]) ).
thf(1565,plain,
! [SV223: $i,SV62: $i] :
( ( ~ ( subset @ SV62 @ SV223 )
| ! [SY1131: $i] : ( subset @ ( set_intersection2 @ SV62 @ SY1131 ) @ ( set_intersection2 @ SV223 @ SY1131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1338]) ).
thf(1566,plain,
! [SV224: $i,SV63: $i] :
( ( ~ ( subset @ SV63 @ SV224 )
| ( ( set_intersection2 @ SV63 @ SV224 )
= SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1339]) ).
thf(1567,plain,
! [SV225: $i,SV65: $i] :
( ( ~ ( subset @ SV65 @ SV225 )
| ! [SY1132: $i] : ( subset @ ( set_difference @ SV65 @ SY1132 ) @ ( set_difference @ SV225 @ SY1132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1341]) ).
thf(1568,plain,
! [SV226: $i,SV66: $i] :
( ( subset @ ( set_difference @ SV66 @ SV226 ) @ SV66 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(1569,plain,
! [SV227: $i,SV67: $i] :
( ( ( set_union2 @ SV67 @ ( set_difference @ SV227 @ SV67 ) )
= ( set_union2 @ SV67 @ SV227 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1343]) ).
thf(1570,plain,
! [SV228: $i,SV68: $i] :
( ( ! [SY1133: $i] :
( ~ ( in @ SV68 @ SV228 )
| ~ ( in @ SV228 @ SY1133 )
| ~ ( in @ SY1133 @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1344]) ).
thf(1571,plain,
! [SV69: $i] :
( ( ( ~ ( subset @ SV69 @ empty_set ) )
= $true )
| ( ( SV69 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1345]) ).
thf(1572,plain,
! [SV229: $i,SV70: $i] :
( ( ( set_difference @ ( set_union2 @ SV70 @ SV229 ) @ SV229 )
= ( set_difference @ SV70 @ SV229 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1346]) ).
thf(1573,plain,
! [SV230: $i,SV71: $i] :
( ( ~ ( subset @ SV71 @ SV230 )
| ( SV230
= ( set_union2 @ SV71 @ ( set_difference @ SV230 @ SV71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1347]) ).
thf(1574,plain,
! [SV231: $i,SV72: $i] :
( ( ~ ( in @ SV72 @ SV231 )
| ( ( set_union2 @ ( singleton @ SV72 ) @ SV231 )
= SV231 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1348]) ).
thf(1575,plain,
! [SV73: $i,SV232: $i] :
( ( ~ ( element @ SV232 @ ( powerset @ ( powerset @ SV73 ) ) )
| ( SV232 = empty_set )
| ( ( subset_difference @ SV73 @ ( cast_to_subset @ SV73 ) @ ( union_of_subsets @ SV73 @ SV232 ) )
= ( meet_of_subsets @ SV73 @ ( complements_of_subsets @ SV73 @ SV232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1349]) ).
thf(1576,plain,
! [SV74: $i,SV233: $i] :
( ( ~ ( element @ SV233 @ ( powerset @ ( powerset @ SV74 ) ) )
| ( SV233 = empty_set )
| ( ( union_of_subsets @ SV74 @ ( complements_of_subsets @ SV74 @ SV233 ) )
= ( subset_difference @ SV74 @ ( cast_to_subset @ SV74 ) @ ( meet_of_subsets @ SV74 @ SV233 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1350]) ).
thf(1577,plain,
! [SV234: $i,SV75: $i] :
( ( ( set_difference @ SV75 @ ( set_difference @ SV75 @ SV234 ) )
= ( set_intersection2 @ SV75 @ SV234 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1351]) ).
thf(1578,plain,
! [SV76: $i] :
( ( ( ~ ( relation @ SV76 ) )
= $true )
| ( ( ( in @ ( ordered_pair @ ( sK95_B @ SV76 ) @ ( sK96_SY738 @ SV76 ) ) @ SV76 )
| ( SV76 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1352]) ).
thf(1579,plain,
! [SV77: $i,SV235: $i] :
( ( ~ ( proper_subset @ SV235 @ SV77 )
| ~ ( subset @ SV77 @ SV235 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1353]) ).
thf(1580,plain,
! [SV78: $i,SV236: $i] :
( ( ! [SY1134: $i] :
( ~ ( disjoint @ SV236 @ SY1134 )
| ~ ( subset @ SV78 @ SV236 )
| ( disjoint @ SV78 @ SY1134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1354]) ).
thf(1581,plain,
! [SV237: $i,SV80: $i] :
( ( ~ ( subset @ ( singleton @ SV80 ) @ ( singleton @ SV237 ) )
| ( SV80 = SV237 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1356]) ).
thf(1582,plain,
! [SV238: $i,SV81: $i] :
( ( subset @ SV81 @ ( set_union2 @ SV81 @ SV238 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1357]) ).
thf(1583,plain,
! [SV82: $i,SV239: $i] :
( ( ~ ( relation @ SV239 )
| ( subset @ ( relation_dom_restriction @ SV239 @ SV82 ) @ SV239 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1358]) ).
thf(1584,plain,
! [SV240: $i,SV83: $i] :
( ( ! [SY1135: $i] :
( ~ ( subset @ SV83 @ SV240 )
| ~ ( subset @ SY1135 @ SV240 )
| ( subset @ ( set_union2 @ SV83 @ SY1135 ) @ SV240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1359]) ).
thf(1585,plain,
! [SV241: $i,SV84: $i] :
( ( ! [SY1136: $i] :
( ( singleton @ SV84 )
!= ( unordered_pair @ SV241 @ SY1136 ) )
| ( SV84 = SV241 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1360]) ).
thf(1586,plain,
! [SV242: $i,SV85: $i] :
( ( ~ ( in @ SV85 @ SV242 )
| ( subset @ SV85 @ ( union @ SV242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1361]) ).
thf(1587,plain,
! [SV243: $i,SV86: $i] :
( ( ! [SY1137: $i] :
( ( ( singleton @ SV86 )
!= ( unordered_pair @ SV243 @ SY1137 ) )
| ( SV243 = SY1137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1362]) ).
thf(1588,plain,
! [SV244: $i,SV87: $i] :
( ( ~ ( in @ SV87 @ SV244 )
| ~ ( in @ SV244 @ SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1363]) ).
thf(1589,plain,
! [SV88: $i] :
( ( ( ~ ( empty @ SV88 ) )
= $true )
| ( ( finite @ SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1364]) ).
thf(1590,plain,
! [SV89: $i] :
( ( ( ~ ( empty @ SV89 ) )
= $true )
| ( ( function @ SV89 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1365]) ).
thf(1591,plain,
! [SV90: $i] :
( ( ( ~ ( empty @ SV90 ) )
= $true )
| ( ( relation @ SV90 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1366]) ).
thf(1592,plain,
! [SV91: $i] :
( ( ( ~ ( v3_membered @ SV91 ) )
= $true )
| ( ( v2_membered @ SV91 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1367]) ).
thf(1593,plain,
! [SV92: $i] :
( ( ( ~ ( v2_membered @ SV92 ) )
= $true )
| ( ( v1_membered @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1368]) ).
thf(1594,plain,
! [SV245: $i,SV93: $i] :
( ( ( set_intersection2 @ SV93 @ SV245 )
= ( set_intersection2 @ SV245 @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(1595,plain,
! [SV95: $i] :
( ( ( ~ ( relation @ SV95 ) )
= $true )
| ( ( ! [SY878: $i] :
( ( relation_restriction @ SV95 @ SY878 )
= ( set_intersection2 @ SV95 @ ( cartesian_product2 @ SY878 @ SY878 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1371]) ).
thf(1596,plain,
! [SV246: $i,SV96: $i] :
( ( ! [SY1138: $i] :
( ( empty_carrier @ SV96 )
| ~ ( join_semilatt_str @ SV96 )
| ~ ( element @ SV246 @ ( the_carrier @ SV96 ) )
| ~ ( element @ SY1138 @ ( the_carrier @ SV96 ) )
| ( element @ ( join @ SV96 @ SV246 @ SY1138 ) @ ( the_carrier @ SV96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1372]) ).
thf(1597,plain,
! [SV247: $i,SV98: $i] :
( ( ! [SY1139: $i] :
( ( empty_carrier @ SV98 )
| ~ ( meet_semilatt_str @ SV98 )
| ~ ( element @ SV247 @ ( the_carrier @ SV98 ) )
| ~ ( element @ SY1139 @ ( the_carrier @ SV98 ) )
| ( element @ ( meet @ SV98 @ SV247 @ SY1139 ) @ ( the_carrier @ SV98 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1374]) ).
thf(1598,plain,
! [SV99: $i] :
( ( ( ~ ( relation @ SV99 ) )
= $true )
| ( ( ! [SY883: $i] : ( relation @ ( relation_restriction @ SV99 @ SY883 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1375]) ).
thf(1599,plain,
! [SV100: $i] :
( ( ( ~ ( relation @ SV100 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1376]) ).
thf(1600,plain,
! [SV248: $i,SV101: $i] :
( ( ~ ( relation @ SV101 )
| ~ ( relation @ SV248 )
| ( relation @ ( relation_composition @ SV101 @ SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1377]) ).
thf(1601,plain,
! [SV103: $i] :
( ( ( ~ ( relation @ SV103 ) )
= $true )
| ( ( ! [SY885: $i] : ( relation @ ( relation_dom_restriction @ SV103 @ SY885 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1379]) ).
thf(1602,plain,
! [SV104: $i,SV249: $i] :
( ( ~ ( relation @ SV249 )
| ( relation @ ( relation_rng_restriction @ SV104 @ SV249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1380]) ).
thf(1603,plain,
! [SV105: $i,SV250: $i] :
( ( relation_of2 @ ( sK63_C @ SV250 @ SV105 ) @ SV105 @ SV250 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1381]) ).
thf(1604,plain,
! [SV106: $i,SV251: $i] :
( ( relation_of2_as_subset @ ( sK62_C @ SV251 @ SV106 ) @ SV106 @ SV251 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1382]) ).
thf(1605,plain,
! [SV107: $i,SV252: $i] :
( ( ~ ( finite @ SV252 )
| ( finite @ ( set_intersection2 @ SV107 @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1383]) ).
thf(1606,plain,
! [SV108: $i] :
( ( ( ~ ( finite @ SV108 ) )
= $true )
| ( ( ! [SY890: $i] : ( finite @ ( set_intersection2 @ SV108 @ SY890 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1384]) ).
thf(1607,plain,
! [SV109: $i] :
( ( ( ~ ( finite @ SV109 ) )
= $true )
| ( ( ! [SY891: $i] : ( finite @ ( set_difference @ SV109 @ SY891 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1385]) ).
thf(1608,plain,
! [SV110: $i] :
( ( empty @ ( succ @ SV110 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1386]) ).
thf(1609,plain,
! [SV253: $i,SV111: $i] :
( ( ~ ( relation @ SV111 )
| ~ ( relation @ SV253 )
| ( relation @ ( set_intersection2 @ SV111 @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1387]) ).
thf(1610,plain,
! [SV254: $i,SV112: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV112 @ SV254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1388]) ).
thf(1611,plain,
! [SV113: $i] :
( ( ( ~ ( v1_membered @ SV113 ) )
= $true )
| ( ( ! [SY894: $i] : ( v1_membered @ ( set_intersection2 @ SV113 @ SY894 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1389]) ).
thf(1612,plain,
! [SV114: $i] :
( ( ( ~ ( v1_membered @ SV114 ) )
= $true )
| ( ( ! [SY895: $i] : ( v1_membered @ ( set_intersection2 @ SY895 @ SV114 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1390]) ).
thf(1613,plain,
! [SV255: $i,SV115: $i] :
( ( ~ ( relation @ SV115 )
| ~ ( relation @ SV255 )
| ( relation @ ( set_union2 @ SV115 @ SV255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1391]) ).
thf(1614,plain,
! [SV116: $i] :
( ( empty @ ( singleton @ SV116 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1392]) ).
thf(1615,plain,
! [SV117: $i] :
( ( ( empty @ SV117 )
= $true )
| ( ( ! [SY897: $i] :
~ ( empty @ ( set_union2 @ SV117 @ SY897 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1393]) ).
thf(1616,plain,
! [SV118: $i] :
( ( ( ~ ( v1_membered @ SV118 ) )
= $true )
| ( ( ! [SY898: $i] : ( v1_membered @ ( set_difference @ SV118 @ SY898 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1394]) ).
thf(1617,plain,
! [SV256: $i,SV119: $i] :
( ( ~ ( relation @ SV119 )
| ~ ( relation @ SV256 )
| ( relation @ ( set_difference @ SV119 @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1395]) ).
thf(1618,plain,
! [SV257: $i,SV120: $i] :
( ( ~ ( empty @ ( unordered_pair @ SV120 @ SV257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1396]) ).
thf(1619,plain,
! [SV121: $i] :
( ( ( empty @ SV121 )
= $true )
| ( ( ! [SY901: $i] :
~ ( empty @ ( set_union2 @ SY901 @ SV121 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1397]) ).
thf(1620,plain,
! [SV258: $i,SV122: $i] :
( ( ( empty @ SV122 )
| ( empty @ SV258 )
| ~ ( empty @ ( cartesian_product2 @ SV122 @ SV258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1398]) ).
thf(1621,plain,
! [SV123: $i] :
( ( ( ( empty @ SV123 )
| ~ ( relation @ SV123 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV123 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1399]) ).
thf(1622,plain,
! [SV124: $i] :
( ( ( ( empty @ SV124 )
| ~ ( relation @ SV124 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV124 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1400]) ).
thf(1623,plain,
! [SV259: $i,SV125: $i] :
( ( ~ ( finite @ SV125 )
| ~ ( finite @ SV259 )
| ( finite @ ( set_union2 @ SV125 @ SV259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1401]) ).
thf(1624,plain,
! [SV127: $i] :
( ( ( ~ ( relation @ SV127 ) )
= $true )
| ( ( ( relation_inverse @ ( relation_inverse @ SV127 ) )
= SV127 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1403]) ).
thf(1625,plain,
! [SV260: $i,SV128: $i] :
( ( ! [SY1140: $i] :
( ~ ( relation_of2 @ SY1140 @ SV128 @ SV260 )
| ( ( relation_dom_as_subset @ SV128 @ SV260 @ SY1140 )
= ( relation_dom @ SY1140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1405]) ).
thf(1626,plain,
! [SV261: $i,SV129: $i] :
( ( ! [SY1141: $i] :
( ~ ( relation_of2 @ SY1141 @ SV129 @ SV261 )
| ( ( relation_rng_as_subset @ SV129 @ SV261 @ SY1141 )
= ( relation_rng @ SY1141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1406]) ).
thf(1627,plain,
! [SV262: $i,SV131: $i] :
( ( ~ ( disjoint @ SV131 @ SV262 )
| ( disjoint @ SV262 @ SV131 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1408]) ).
thf(1628,plain,
! [SV136: $i] :
( ( ( ~ ( empty @ SV136 ) )
= $true )
| ( ( SV136 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1413]) ).
thf(1629,plain,
! [SV137: $i,SV263: $i] :
( ( ~ ( empty @ SV263 )
| ~ ( in @ SV137 @ SV263 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1414]) ).
thf(1630,plain,
! [SV264: $i,SV138: $i] :
( ( ( SV138 = SV264 )
| ~ ( empty @ SV138 )
| ~ ( empty @ SV264 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1415]) ).
thf(1631,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1416]) ).
thf(1632,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1416]) ).
thf(1633,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1417]) ).
thf(1634,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1417]) ).
thf(1635,plain,
! [SV139: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK17_C @ SV139 )
!= ( sK18_SY613 @ SV139 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
!= ( sK18_SY613 @ SV139 ) )
| ~ ( in @ ( sK22_SY620 @ SV139 ) @ SV139 ) )
| ( ( sK23_SY629 @ SV139 )
!= ( singleton @ ( sK22_SY620 @ SV139 ) ) ) ) )
| ( ( sK17_C @ SV139 )
!= ( sK19_SY619 @ SV139 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
!= ( sK19_SY619 @ SV139 ) )
| ~ ( in @ ( sK20_SY626 @ SV139 ) @ SV139 ) )
| ( ( sK21_SY628 @ SV139 )
!= ( singleton @ ( sK20_SY626 @ SV139 ) ) ) ) )
| ~ ( ( ( sK18_SY613 @ SV139 )
!= ( sK19_SY619 @ SV139 ) ) ) ) )
= $true )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1418]) ).
thf(1636,plain,
! [SV140: $i] :
( ( ( ( empty_carrier @ SV140 )
| ~ ( one_sorted_str @ SV140 ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK116_B @ SV140 ) @ ( powerset @ ( the_carrier @ SV140 ) ) )
| ~ ~ ( empty @ ( sK116_B @ SV140 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1419]) ).
thf(1637,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_intersection2 @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_intersection2 @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1420]) ).
thf(1638,plain,
( ( ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v3_membered @ ( set_intersection2 @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1420]) ).
thf(1639,plain,
! [SV141: $i] :
( ( ( ~ ( ~ ( in @ ( sK99_B @ SV141 ) @ SV141 )
| ~ ( ~ ( ordinal @ ( sK99_B @ SV141 ) )
| ~ ( subset @ ( sK99_B @ SV141 ) @ SV141 ) ) ) )
= $true )
| ( ( ordinal @ SV141 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1421]) ).
thf(1640,plain,
! [SV142: $i] :
( ( ~ ! [SY917: $i,SY918: $i] :
( ~ ( in @ SV142 @ SY918 )
| ~ ( in @ SY917 @ SY918 )
| ( subset @ ( unordered_pair @ SV142 @ SY917 ) @ SY918 ) )
| ~ ~ ( ~ ! [SY919: $i,SY920: $i] :
( ~ ( subset @ ( unordered_pair @ SV142 @ SY919 ) @ SY920 )
| ( in @ SV142 @ SY920 ) )
| ~ ! [SY921: $i,SY922: $i] :
( ~ ( subset @ ( unordered_pair @ SV142 @ SY921 ) @ SY922 )
| ( in @ SY921 @ SY922 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1422]) ).
thf(1641,plain,
! [SV143: $i] :
( ( ~ ! [SY923: $i,SY924: $i] :
( ~ ( ~ ( ~ ( in @ ( sK70_D @ SY924 @ SY923 @ SV143 ) @ SV143 )
| ~ ( in @ ( sK70_D @ SY924 @ SY923 @ SV143 ) @ SY923 )
| ~ ( in @ ( sK70_D @ SY924 @ SY923 @ SV143 ) @ SY924 ) )
| ~ ~ ( ~ ( ( in @ ( sK70_D @ SY924 @ SY923 @ SV143 ) @ SV143 )
| ( in @ ( sK70_D @ SY924 @ SY923 @ SV143 ) @ SY924 ) )
| ~ ( ( in @ ( sK70_D @ SY924 @ SY923 @ SV143 ) @ SY923 )
| ( in @ ( sK70_D @ SY924 @ SY923 @ SV143 ) @ SY924 ) ) ) )
| ( SY924
= ( set_intersection2 @ SV143 @ SY923 ) ) )
| ~ ! [SY925: $i,SY926: $i] :
( ( SY926
!= ( set_intersection2 @ SV143 @ SY925 ) )
| ~ ( ~ ! [SY927: $i] :
( ~ ( in @ SY927 @ SV143 )
| ~ ( in @ SY927 @ SY925 )
| ( in @ SY927 @ SY926 ) )
| ~ ~ ( ~ ! [SY928: $i] :
( ~ ( in @ SY928 @ SY926 )
| ( in @ SY928 @ SV143 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY926 )
| ( in @ SX3 @ SY925 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1423]) ).
thf(1642,plain,
! [SV144: $i] :
( ( ( ~ ( v3_membered @ SV144 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY930: $i] :
( ~ ( element @ SY930 @ ( powerset @ SV144 ) )
| ( v1_membered @ SY930 ) )
| ~ ! [SY931: $i] :
( ~ ( element @ SY931 @ ( powerset @ SV144 ) )
| ( v2_membered @ SY931 ) ) )
| ~ ! [SY932: $i] :
( ~ ( element @ SY932 @ ( powerset @ SV144 ) )
| ( v3_membered @ SY932 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1424]) ).
thf(1643,plain,
! [SV265: $i,SV145: $i] :
( ( ( empty @ SV145 )
| ~ ( relation @ SV265 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1142: $i] :
( ~ ( in @ SY1142 @ ( sK52_SY712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SY1142 ) @ SV265 ) )
| ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK52_SY712 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) ) ) )
| ~ ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 ) )
| ~ ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 ) )
| ~ ~ ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ ( sK51_SY718 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SY1143 ) @ SV265 ) )
| ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK51_SY718 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) ) ) ) )
| ~ ( ( ( sK49_SY705 @ SV265 @ SV145 )
!= ( sK50_SY711 @ SV265 @ SV145 ) ) ) )
| ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1425]) ).
thf(1644,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1426]) ).
thf(1645,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1426]) ).
thf(1646,plain,
! [SV146: $i,SV266: $i] :
( ( ~ ( ~ ! [SY1149: $i] :
( ~ ( in @ SY1149 @ SV266 )
| ~ ( in @ SY1149 @ ( sK5_C @ SV266 @ SV146 ) ) )
| ~ ( in @ ( sK5_C @ SV266 @ SV146 ) @ SV266 ) )
| ~ ( in @ SV146 @ SV266 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1427]) ).
thf(1647,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK85_B @ SX0 ) @ SX0 )
| ~ ~ ( subset @ ( sK85_B @ SX0 ) @ SX0 ) )
| ( epsilon_transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1428]) ).
thf(1648,plain,
( ( ~ ! [SX0: $i] :
( ~ ( epsilon_transitive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1428]) ).
thf(1649,plain,
! [SV147: $i] :
( ( ~ ! [SY943: $i,SY944: $i] :
( ~ ( ~ ( ~ ( in @ ( sK66_D @ SY944 @ SY943 @ SV147 ) @ SV147 )
| ( in @ ( sK66_D @ SY944 @ SY943 @ SV147 ) @ SY943 )
| ~ ( in @ ( sK66_D @ SY944 @ SY943 @ SV147 ) @ SY944 ) )
| ~ ~ ( ~ ( ( in @ ( sK66_D @ SY944 @ SY943 @ SV147 ) @ SV147 )
| ( in @ ( sK66_D @ SY944 @ SY943 @ SV147 ) @ SY944 ) )
| ~ ( ~ ( in @ ( sK66_D @ SY944 @ SY943 @ SV147 ) @ SY943 )
| ( in @ ( sK66_D @ SY944 @ SY943 @ SV147 ) @ SY944 ) ) ) )
| ( SY944
= ( set_difference @ SV147 @ SY943 ) ) )
| ~ ! [SY945: $i,SY946: $i] :
( ( SY946
!= ( set_difference @ SV147 @ SY945 ) )
| ~ ( ~ ! [SY947: $i] :
( ~ ( in @ SY947 @ SV147 )
| ( in @ SY947 @ SY945 )
| ( in @ SY947 @ SY946 ) )
| ~ ~ ( ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ SY946 )
| ( in @ SY948 @ SV147 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY946 )
| ~ ( in @ SX3 @ SY945 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1429]) ).
thf(1650,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK86_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1430]) ).
thf(1651,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1430]) ).
thf(1652,plain,
! [SV148: $i] :
( ( ( ~ ( finite @ SV148 ) )
= $true )
| ( ( ! [SY950: $i] :
( ~ ( element @ SY950 @ ( powerset @ ( powerset @ SV148 ) ) )
| ~ ( ~ ! [SY951: $i] :
( ~ ( in @ SY951 @ SY950 )
| ~ ( subset @ ( sK105_C @ SY950 @ SV148 ) @ SY951 )
| ( SY951
= ( sK105_C @ SY950 @ SV148 ) ) )
| ~ ( in @ ( sK105_C @ SY950 @ SV148 ) @ SY950 ) )
| ( SY950 = empty_set ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1431]) ).
thf(1653,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1432]) ).
thf(1654,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1432]) ).
thf(1655,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1433]) ).
thf(1656,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1433]) ).
thf(1657,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK68_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK68_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK68_C @ SX1 @ SX0 ) @ ( sK69_SY723 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK69_SY723 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK68_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1434]) ).
thf(1658,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK67_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK67_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1434]) ).
thf(1659,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1435]) ).
thf(1660,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1435]) ).
thf(1661,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1436]) ).
thf(1662,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1436]) ).
thf(1663,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1437]) ).
thf(1664,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1437]) ).
thf(1665,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK124_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK124_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK124_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK124_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1438]) ).
thf(1666,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1438]) ).
thf(1667,plain,
! [SV149: $i] :
( ( ( empty @ SV149 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( element @ ( sK118_B @ SV149 ) @ ( powerset @ SV149 ) )
| ~ ~ ( empty @ ( sK118_B @ SV149 ) ) )
| ~ ( finite @ ( sK118_B @ SV149 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1439]) ).
thf(1668,plain,
! [SV150: $i] :
( ( ~ ! [SY952: $i,SY953: $i] :
( ~ ( relation_of2_as_subset @ SY953 @ SV150 @ SY952 )
| ~ ( ~ ! [SY954: $i] :
~ ( in @ ( ordered_pair @ SY954 @ ( sK102_D @ SY953 @ SY952 @ SV150 ) ) @ SY953 )
| ~ ( in @ ( sK102_D @ SY953 @ SY952 @ SV150 ) @ SY952 ) )
| ( ( relation_rng_as_subset @ SV150 @ SY952 @ SY953 )
= SY952 ) )
| ~ ! [SY955: $i,SY956: $i] :
( ~ ( relation_of2_as_subset @ SY956 @ SV150 @ SY955 )
| ( ( relation_rng_as_subset @ SV150 @ SY955 @ SY956 )
!= SY955 )
| ! [SY957: $i] :
( ( in @ ( ordered_pair @ ( sK101_E @ SY957 @ SY956 @ SY955 @ SV150 ) @ SY957 ) @ SY956 )
| ~ ( in @ SY957 @ SY955 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1440]) ).
thf(1669,plain,
! [SV151: $i,SV267: $i] :
( ( ~ ( ~ ! [SY1150: $i,SY1151: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 ) @ SY1151 )
| ( ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 )
!= SY1150 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 ) @ SY1151 )
| ( ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 )
!= SV151 ) )
| ~ ( ~ ( in @ ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 ) @ SY1151 )
| ( ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 )
!= SV267 ) ) ) )
| ~ ( ( in @ ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 ) @ SY1151 )
| ( ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 )
= SY1150 )
| ( ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 )
= SV151 )
| ( ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 )
= SV267 ) ) )
| ( SY1151
= ( unordered_triple @ SV151 @ SV267 @ SY1150 ) ) )
| ~ ! [SY1152: $i,SY1153: $i] :
( ( SY1153
!= ( unordered_triple @ SV151 @ SV267 @ SY1152 ) )
| ~ ( ~ ! [SY1154: $i] :
( ~ ( in @ SY1154 @ SY1153 )
| ( SY1154 = SY1152 )
| ( SY1154 = SV151 )
| ( SY1154 = SV267 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SY1152 )
| ( in @ SX4 @ SY1153 ) )
| ~ ~ ( ~ ! [SY965: $i] :
( ( SY965 != SV151 )
| ( in @ SY965 @ SY1153 ) )
| ~ ! [SY1157: $i] :
( ( SY1157 != SV267 )
| ( in @ SY1157 @ SY1153 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(1670,plain,
! [SV152: $i] :
( ( ~ ! [SY967: $i] :
( ~ ( subset @ SY967 @ ( sK106_B @ SV152 ) )
| ( are_equipotent @ SY967 @ ( sK106_B @ SV152 ) )
| ( in @ SY967 @ ( sK106_B @ SV152 ) ) )
| ~ ~ ( ~ ! [SY968: $i] :
( ~ ( in @ SY968 @ ( sK106_B @ SV152 ) )
| ( in @ ( powerset @ SY968 ) @ ( sK106_B @ SV152 ) ) )
| ~ ~ ( ~ ! [SY969: $i,SY970: $i] :
( ~ ( in @ SY969 @ ( sK106_B @ SV152 ) )
| ~ ( subset @ SY970 @ SY969 )
| ( in @ SY970 @ ( sK106_B @ SV152 ) ) )
| ~ ( in @ SV152 @ ( sK106_B @ SV152 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1442]) ).
thf(1671,plain,
! [SV153: $i] :
( ( ~ ! [SY971: $i] :
( ~ ( in @ SY971 @ SV153 )
| ~ ( ordinal @ SY971 )
| ( in @ SY971 @ ( sK107_B @ SV153 ) ) )
| ~ ~ ( ~ ! [SY972: $i] :
( ~ ( in @ SY972 @ ( sK107_B @ SV153 ) )
| ( in @ SY972 @ SV153 ) )
| ~ ! [SY973: $i] :
( ~ ( in @ SY973 @ ( sK107_B @ SV153 ) )
| ( ordinal @ SY973 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1443]) ).
thf(1672,plain,
! [SV154: $i] :
( ( ( ~ ( relation @ SV154 ) )
= $true )
| ( ( ~ ( ~ ! [SY974: $i] :
( ~ ( relation @ SY974 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK72_C @ SY974 @ SV154 ) @ ( sK73_SY724 @ SY974 @ SV154 ) ) @ SV154 )
| ~ ~ ( in @ ( ordered_pair @ ( sK72_C @ SY974 @ SV154 ) @ ( sK73_SY724 @ SY974 @ SV154 ) ) @ SY974 ) )
| ( subset @ SV154 @ SY974 ) )
| ~ ! [SY975: $i] :
( ~ ( relation @ SY975 )
| ~ ( subset @ SV154 @ SY975 )
| ! [SY976: $i,SY977: $i] :
( ~ ( in @ ( ordered_pair @ SY976 @ SY977 ) @ SV154 )
| ( in @ ( ordered_pair @ SY976 @ SY977 ) @ SY975 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1444]) ).
thf(1673,plain,
! [SV155: $i,SV268: $i] :
( ( ~ ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
| ~ ( ~ ! [SY1158: $i] :
( ~ ( element @ SY1158 @ ( powerset @ ( powerset @ SV155 ) ) )
| ~ ( ~ ( element @ ( sK123_D @ SY1158 @ SV268 @ SV155 ) @ ( powerset @ SV155 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK123_D @ SY1158 @ SV268 @ SV155 ) @ SY1158 )
| ~ ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SY1158 @ SV268 @ SV155 ) ) @ SV268 ) )
| ~ ( ( in @ ( sK123_D @ SY1158 @ SV268 @ SV155 ) @ SY1158 )
| ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SY1158 @ SV268 @ SV155 ) ) @ SV268 ) ) ) )
| ( SY1158
= ( complements_of_subsets @ SV155 @ SV268 ) ) )
| ~ ! [SY1159: $i] :
( ~ ( element @ SY1159 @ ( powerset @ ( powerset @ SV155 ) ) )
| ( SY1159
!= ( complements_of_subsets @ SV155 @ SV268 ) )
| ~ ( ~ ! [SY1160: $i] :
( ~ ( element @ SY1160 @ ( powerset @ SV155 ) )
| ~ ( in @ SY1160 @ SY1159 )
| ( in @ ( subset_complement @ SV155 @ SY1160 ) @ SV268 ) )
| ~ ! [SY1161: $i] :
( ~ ( element @ SY1161 @ ( powerset @ SV155 ) )
| ~ ( in @ ( subset_complement @ SV155 @ SY1161 ) @ SV268 )
| ( in @ SY1161 @ SY1159 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(1674,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1446]) ).
thf(1675,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1446]) ).
thf(1676,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1447]) ).
thf(1677,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1447]) ).
thf(1678,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1448]) ).
thf(1679,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1448]) ).
thf(1680,plain,
! [SV156: $i] :
( ( ( ~ ( v2_membered @ SV156 ) )
= $true )
| ( ( ~ ( ~ ! [SY983: $i] :
( ~ ( element @ SY983 @ ( powerset @ SV156 ) )
| ( v1_membered @ SY983 ) )
| ~ ! [SY984: $i] :
( ~ ( element @ SY984 @ ( powerset @ SV156 ) )
| ( v2_membered @ SY984 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1449]) ).
thf(1681,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1450]) ).
thf(1682,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1450]) ).
thf(1683,plain,
( ( ~ ( sK12_REN
| ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
( ( SX2 != SX1 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( ordinal @ SX1 )
| ( in @ SX1 @ ( sK7_B @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK7_B @ SX0 ) )
| ~ ( ~ ~ ( ( ( sK8_D @ SX1 @ SX0 )
!= SX1 )
| ~ ( in @ ( sK8_D @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ordinal @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1451]) ).
thf(1684,plain,
( ( ~ ( ~ sK12_REN
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK9_B != sK10_SY601 )
| ~ ( ordinal @ sK10_SY601 ) )
| ( sK9_B != sK11_SY603 ) )
| ~ ( ordinal @ sK11_SY603 ) )
| ~ ( ( sK10_SY601 != sK11_SY603 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1451]) ).
thf(1685,plain,
( ( ~ ( element @ sK2_SY588 @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1452]) ).
thf(1686,plain,
( ( ~ ( ( ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY588 )
!= ( subset_difference @ ( the_carrier @ sK1_A ) @ ( cast_as_carrier_subset @ sK1_A ) @ sK2_SY588 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1452]) ).
thf(1687,plain,
! [SV157: $i] :
( ( ~ ! [SY985: $i,SY986: $i] :
( ~ ( relation @ SY986 )
| ~ ( in @ SV157 @ SY986 )
| ~ ( in @ SV157 @ ( cartesian_product2 @ SY985 @ SY985 ) )
| ( in @ SV157 @ ( relation_restriction @ SY986 @ SY985 ) ) )
| ~ ~ ( ~ ! [SY987: $i,SY988: $i] :
( ~ ( relation @ SY988 )
| ~ ( in @ SV157 @ ( relation_restriction @ SY988 @ SY987 ) )
| ( in @ SV157 @ SY988 ) )
| ~ ! [SY989: $i,SY990: $i] :
( ~ ( relation @ SY990 )
| ~ ( in @ SV157 @ ( relation_restriction @ SY990 @ SY989 ) )
| ( in @ SV157 @ ( cartesian_product2 @ SY989 @ SY989 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1453]) ).
thf(1688,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1454]) ).
thf(1689,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1454]) ).
thf(1690,plain,
! [SV158: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY991: $i,SY992: $i] :
( ~ ( relation_of2_as_subset @ SY992 @ SV158 @ SY991 )
| ( SY991 = empty_set )
| ( SV158
!= ( relation_dom_as_subset @ SV158 @ SY991 @ SY992 ) )
| ( quasi_total @ SY992 @ SV158 @ SY991 ) )
| ~ ! [SY993: $i,SY994: $i] :
( ~ ( relation_of2_as_subset @ SY994 @ SV158 @ SY993 )
| ( SY993 = empty_set )
| ~ ( quasi_total @ SY994 @ SV158 @ SY993 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SY993 @ SY994 ) ) ) )
| ~ ~ ( ~ ! [SY995: $i,SY996: $i] :
( ~ ( relation_of2_as_subset @ SY996 @ SV158 @ SY995 )
| ( SV158 != empty_set )
| ( SV158
!= ( relation_dom_as_subset @ SV158 @ SY995 @ SY996 ) )
| ( quasi_total @ SY996 @ SV158 @ SY995 ) )
| ~ ! [SY997: $i,SY998: $i] :
( ~ ( relation_of2_as_subset @ SY998 @ SV158 @ SY997 )
| ( SV158 != empty_set )
| ~ ( quasi_total @ SY998 @ SV158 @ SY997 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SY997 @ SY998 ) ) ) ) )
| ~ ~ ( ~ ! [SY999: $i,SY1000: $i] :
( ~ ( relation_of2_as_subset @ SY1000 @ SV158 @ SY999 )
| ( SY999 != empty_set )
| ( SY1000 != empty_set )
| ( quasi_total @ SY1000 @ SV158 @ SY999 )
| ( SV158 = empty_set ) )
| ~ ! [SY1001: $i,SY1002: $i] :
( ~ ( relation_of2_as_subset @ SY1002 @ SV158 @ SY1001 )
| ( SY1001 != empty_set )
| ~ ( quasi_total @ SY1002 @ SV158 @ SY1001 )
| ( SY1002 = empty_set )
| ( SV158 = empty_set ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1455]) ).
thf(1691,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK90_SY733 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK89_C @ SX1 @ SX0 ) @ ( sK90_SY733 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK89_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK89_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK89_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK88_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK88_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1456]) ).
thf(1692,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1456]) ).
thf(1693,plain,
! [SV159: $i] :
( ( ~ ! [SY1003: $i,SY1004: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK82_D @ SY1004 @ SY1003 @ SV159 ) @ SY1004 )
| ( ( sK82_D @ SY1004 @ SY1003 @ SV159 )
!= SV159 ) )
| ~ ( ~ ( in @ ( sK82_D @ SY1004 @ SY1003 @ SV159 ) @ SY1004 )
| ( ( sK82_D @ SY1004 @ SY1003 @ SV159 )
!= SY1003 ) ) )
| ~ ( ( in @ ( sK82_D @ SY1004 @ SY1003 @ SV159 ) @ SY1004 )
| ( ( sK82_D @ SY1004 @ SY1003 @ SV159 )
= SV159 )
| ( ( sK82_D @ SY1004 @ SY1003 @ SV159 )
= SY1003 ) ) )
| ( SY1004
= ( unordered_pair @ SV159 @ SY1003 ) ) )
| ~ ! [SY1005: $i,SY1006: $i] :
( ( SY1006
!= ( unordered_pair @ SV159 @ SY1005 ) )
| ~ ( ~ ! [SY1007: $i] :
( ~ ( in @ SY1007 @ SY1006 )
| ( SY1007 = SV159 )
| ( SY1007 = SY1005 ) )
| ~ ~ ( ~ ! [SY1008: $i] :
( ( SY1008 != SV159 )
| ( in @ SY1008 @ SY1006 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY1005 )
| ( in @ SX3 @ SY1006 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1457]) ).
thf(1694,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1458]) ).
thf(1695,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1458]) ).
thf(1696,plain,
! [SV160: $i] :
( ( ( ~ ( v2_membered @ SV160 ) )
= $true )
| ( ( ~ ( ~ ! [SY1010: $i] :
( ~ ( element @ SY1010 @ SV160 )
| ( v1_xcmplx_0 @ SY1010 ) )
| ~ ! [SY1011: $i] :
( ~ ( element @ SY1011 @ SV160 )
| ( v1_xreal_0 @ SY1011 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1459]) ).
thf(1697,plain,
( ( ~ ! [SX0: $i] :
( ~ ( latt_str @ SX0 )
| ( join_semilatt_str @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1460]) ).
thf(1698,plain,
( ( ~ ! [SX0: $i] :
( ~ ( latt_str @ SX0 )
| ( meet_semilatt_str @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1460]) ).
thf(1699,plain,
( ( ~ ( relation @ sK53_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1461]) ).
thf(1700,plain,
( ( ~ ( relation_empty_yielding @ sK53_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1461]) ).
thf(1701,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK93_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK93_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1462]) ).
thf(1702,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK91_C @ SX1 @ SX0 ) @ ( sK92_SY735 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1462]) ).
thf(1703,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1463]) ).
thf(1704,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1463]) ).
thf(1705,plain,
! [SV161: $i] :
( ( ~ ( relation @ ( sK100_B @ SV161 ) )
| ~ ( well_orders @ ( sK100_B @ SV161 ) @ SV161 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1464]) ).
thf(1706,plain,
! [SV162: $i,SV269: $i] :
( ( ~ ( element @ SV269 @ ( powerset @ SV162 ) )
| ~ ( ~ ! [SY1162: $i] :
( ~ ( element @ SY1162 @ ( powerset @ SV162 ) )
| ~ ( disjoint @ SV269 @ SY1162 )
| ( subset @ SV269 @ ( subset_complement @ SV162 @ SY1162 ) ) )
| ~ ! [SY1163: $i] :
( ~ ( element @ SY1163 @ ( powerset @ SV162 ) )
| ~ ( subset @ SV269 @ ( subset_complement @ SV162 @ SY1163 ) )
| ( disjoint @ SV269 @ SY1163 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1465]) ).
thf(1707,plain,
( ( ~ ( one_sorted_str @ sK117_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1466]) ).
thf(1708,plain,
( ( ~ ~ ( empty_carrier @ sK117_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1466]) ).
thf(1709,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1467]) ).
thf(1710,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1467]) ).
thf(1711,plain,
! [SV163: $i] :
( ( ~ ! [SY1015: $i,SY1016: $i] :
( ~ ( relation_of2 @ SY1016 @ SV163 @ SY1015 )
| ( relation_of2_as_subset @ SY1016 @ SV163 @ SY1015 ) )
| ~ ! [SY1017: $i,SY1018: $i] :
( ~ ( relation_of2_as_subset @ SY1018 @ SV163 @ SY1017 )
| ( relation_of2 @ SY1018 @ SV163 @ SY1017 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1468]) ).
thf(1712,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK87_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK87_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK87_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK87_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1469]) ).
thf(1713,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1469]) ).
thf(1714,plain,
! [SV164: $i] :
( ( ~ ! [SY1019: $i,SY1020: $i] :
( ~ ( ~ ( ! [SY1021: $i,SY1022: $i] :
( ~ ( in @ SY1021 @ SV164 )
| ~ ( in @ SY1022 @ SY1019 )
| ( ( sK78_D @ SY1020 @ SY1019 @ SV164 )
!= ( ordered_pair @ SY1021 @ SY1022 ) ) )
| ~ ( in @ ( sK78_D @ SY1020 @ SY1019 @ SV164 ) @ SY1020 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK79_SY729 @ SY1020 @ SY1019 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK80_SY731 @ SY1020 @ SY1019 @ SV164 ) @ SY1019 ) )
| ( ( sK78_D @ SY1020 @ SY1019 @ SV164 )
!= ( ordered_pair @ ( sK79_SY729 @ SY1020 @ SY1019 @ SV164 ) @ ( sK80_SY731 @ SY1020 @ SY1019 @ SV164 ) ) ) )
| ( in @ ( sK78_D @ SY1020 @ SY1019 @ SV164 ) @ SY1020 ) ) )
| ( SY1020
= ( cartesian_product2 @ SV164 @ SY1019 ) ) )
| ~ ! [SY1023: $i,SY1024: $i] :
( ( SY1024
!= ( cartesian_product2 @ SV164 @ SY1023 ) )
| ~ ( ~ ! [SY1025: $i] :
( ! [SY1026: $i,SY1027: $i] :
( ~ ( in @ SY1026 @ SV164 )
| ~ ( in @ SY1027 @ SY1023 )
| ( SY1025
!= ( ordered_pair @ SY1026 @ SY1027 ) ) )
| ( in @ SY1025 @ SY1024 ) )
| ~ ! [SY1028: $i] :
( ~ ( in @ SY1028 @ SY1024 )
| ~ ( ~ ~ ( ~ ( in @ ( sK76_E @ SY1028 @ SY1024 @ SY1023 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK77_SY726 @ SY1028 @ SY1024 @ SY1023 @ SV164 ) @ SY1023 ) )
| ( SY1028
!= ( ordered_pair @ ( sK76_E @ SY1028 @ SY1024 @ SY1023 @ SV164 ) @ ( sK77_SY726 @ SY1028 @ SY1024 @ SY1023 @ SV164 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1470]) ).
thf(1715,plain,
( ( ~ ( empty @ sK59_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1471]) ).
thf(1716,plain,
( ( ~ ( relation @ sK59_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1471]) ).
thf(1717,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK71_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK71_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1718,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1719,plain,
! [SV165: $i] :
( ( ~ ! [SY1029: $i,SY1030: $i] :
( ~ ( relation_of2 @ SY1030 @ SV165 @ SY1029 )
| ( subset @ SY1030 @ ( cartesian_product2 @ SV165 @ SY1029 ) ) )
| ~ ! [SY1031: $i,SY1032: $i] :
( ~ ( subset @ SY1032 @ ( cartesian_product2 @ SV165 @ SY1031 ) )
| ( relation_of2 @ SY1032 @ SV165 @ SY1031 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1473]) ).
thf(1720,plain,
! [SV166: $i] :
( ( ~ ! [SY1033: $i] :
( ~ ( subset @ SY1033 @ ( sK3_B @ SV166 ) )
| ( are_equipotent @ SY1033 @ ( sK3_B @ SV166 ) )
| ( in @ SY1033 @ ( sK3_B @ SV166 ) ) )
| ~ ~ ( ~ ! [SY1034: $i] :
( ~ ( ~ ! [SY1035: $i] :
( ~ ( subset @ SY1035 @ SY1034 )
| ( in @ SY1035 @ ( sK4_SY591 @ SY1034 @ SV166 ) ) )
| ~ ( in @ ( sK4_SY591 @ SY1034 @ SV166 ) @ ( sK3_B @ SV166 ) ) )
| ~ ( in @ SY1034 @ ( sK3_B @ SV166 ) ) )
| ~ ~ ( ~ ! [SY1036: $i,SY1037: $i] :
( ~ ( in @ SY1036 @ ( sK3_B @ SV166 ) )
| ~ ( subset @ SY1037 @ SY1036 )
| ( in @ SY1037 @ ( sK3_B @ SV166 ) ) )
| ~ ( in @ SV166 @ ( sK3_B @ SV166 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1474]) ).
thf(1721,plain,
! [SV167: $i] :
( ( ~ ! [SY1038: $i,SY1039: $i] :
( ~ ( relation_of2_as_subset @ SY1039 @ SY1038 @ SV167 )
| ~ ( ~ ! [SY1040: $i] :
~ ( in @ ( ordered_pair @ ( sK104_D @ SY1039 @ SY1038 @ SV167 ) @ SY1040 ) @ SY1039 )
| ~ ( in @ ( sK104_D @ SY1039 @ SY1038 @ SV167 ) @ SY1038 ) )
| ( ( relation_dom_as_subset @ SY1038 @ SV167 @ SY1039 )
= SY1038 ) )
| ~ ! [SY1041: $i,SY1042: $i] :
( ~ ( relation_of2_as_subset @ SY1042 @ SY1041 @ SV167 )
| ( ( relation_dom_as_subset @ SY1041 @ SV167 @ SY1042 )
!= SY1041 )
| ! [SY1043: $i] :
( ( in @ ( ordered_pair @ SY1043 @ ( sK103_E @ SY1043 @ SY1042 @ SY1041 @ SV167 ) ) @ SY1042 )
| ~ ( in @ SY1043 @ SY1041 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1475]) ).
thf(1722,plain,
! [SV168: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK27_SY634 @ SV168 )
!= ( singleton @ ( sK26_B @ SV168 ) ) )
| ~ ( in @ ( sK26_B @ SV168 ) @ SV168 ) )
| ~ ( in @ ( sK26_B @ SV168 ) @ SV168 ) )
| ( ( sK28_SY636 @ SV168 )
!= ( singleton @ ( sK26_B @ SV168 ) ) ) )
| ~ ( ( ( sK27_SY634 @ SV168 )
!= ( sK28_SY636 @ SV168 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) )
| ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1476]) ).
thf(1723,plain,
( ( ~ ( function @ sK60_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1477]) ).
thf(1724,plain,
( ( ~ ( relation @ sK60_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1477]) ).
thf(1725,plain,
( ( ~ ~ ( ~ ( empty @ sK57_A )
| ~ ( relation @ sK57_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1478]) ).
thf(1726,plain,
( ( ~ ( function @ sK57_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1478]) ).
thf(1727,plain,
! [SV270: $i,SV169: $i] :
( ( ~ ( ~ ! [SY1164: $i,SY1165: $i] :
( ~ ( in @ SV169 @ SY1164 )
| ~ ( in @ SV270 @ SY1165 )
| ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SY1164 @ SY1165 ) ) )
| ~ ~ ( ~ ! [SY1166: $i] :
( ! [SY1167: $i] :
~ ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SY1166 @ SY1167 ) )
| ( in @ SV169 @ SY1166 ) )
| ~ ! [SY1168: $i,SY1169: $i] :
( ~ ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SY1168 @ SY1169 ) )
| ( in @ SV270 @ SY1169 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(1728,plain,
! [SV271: $i,SV170: $i] :
( ( ( empty @ SV170 )
| ~ ( relation @ SV271 )
| ! [SY1170: $i] :
~ ( ~ ! [SY1171: $i] :
( ! [SY1172: $i,SY1173: $i] :
( ( ( ordered_pair @ SY1172 @ SY1173 )
!= SY1171 )
| ~ ( in @ SY1172 @ SV170 )
| ! [SY1174: $i] :
( ~ ( ~ ( in @ ( sK115_I @ SY1174 @ SY1173 @ SY1172 @ SY1171 @ SY1170 @ SV271 @ SV170 ) @ SY1174 )
| ~ ~ ( in @ ( ordered_pair @ SY1173 @ ( sK115_I @ SY1174 @ SY1173 @ SY1172 @ SY1171 @ SY1170 @ SV271 @ SV170 ) ) @ SV271 ) )
| ( SY1172 != SY1174 )
| ~ ( in @ SY1173 @ SY1174 ) ) )
| ~ ( in @ SY1171 @ ( cartesian_product2 @ SV170 @ SY1170 ) )
| ( in @ SY1171 @ ( sK111_D @ SY1170 @ SV271 @ SV170 ) ) )
| ~ ~ ( ~ ! [SY1175: $i] :
( ~ ( in @ SY1175 @ ( sK111_D @ SY1170 @ SV271 @ SV170 ) )
| ~ ( ~ ~ ( ( ( ordered_pair @ ( sK112_F @ SY1175 @ SY1170 @ SV271 @ SV170 ) @ ( sK113_SY768 @ SY1175 @ SY1170 @ SV271 @ SV170 ) )
!= SY1175 )
| ~ ( in @ ( sK112_F @ SY1175 @ SY1170 @ SV271 @ SV170 ) @ SV170 ) )
| ~ ~ ( ~ ! [SY1176: $i] :
( ~ ( in @ SY1176 @ ( sK114_SY771 @ SY1175 @ SY1170 @ SV271 @ SV170 ) )
| ( in @ ( ordered_pair @ ( sK113_SY768 @ SY1175 @ SY1170 @ SV271 @ SV170 ) @ SY1176 ) @ SV271 ) )
| ~ ~ ( ( ( sK112_F @ SY1175 @ SY1170 @ SV271 @ SV170 )
!= ( sK114_SY771 @ SY1175 @ SY1170 @ SV271 @ SV170 ) )
| ~ ( in @ ( sK113_SY768 @ SY1175 @ SY1170 @ SV271 @ SV170 ) @ ( sK114_SY771 @ SY1175 @ SY1170 @ SV271 @ SV170 ) ) ) ) ) )
| ~ ! [SY1177: $i] :
( ~ ( in @ SY1177 @ ( sK111_D @ SY1170 @ SV271 @ SV170 ) )
| ( in @ SY1177 @ ( cartesian_product2 @ SV170 @ SY1170 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1480]) ).
thf(1729,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( ( ( sK74_B @ SX0 )
!= ( sK75_SY725 @ SX0 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK74_B @ SX0 ) @ SX0 )
| ~ ( in @ ( sK75_SY725 @ SX0 ) @ SX0 ) )
| ~ ~ ( in @ ( sK74_B @ SX0 ) @ ( sK75_SY725 @ SX0 ) ) ) )
| ~ ~ ( in @ ( sK75_SY725 @ SX0 ) @ ( sK74_B @ SX0 ) ) )
| ( epsilon_connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1481]) ).
thf(1730,plain,
( ( ~ ! [SX0: $i] :
( ~ ( epsilon_connected @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( SX1 = SX2 )
| ~ ( in @ SX1 @ SX0 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ SX2 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1481]) ).
thf(1731,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_difference @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_difference @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1482]) ).
thf(1732,plain,
( ( ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v3_membered @ ( set_difference @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1482]) ).
thf(1733,plain,
! [SV171: $i] :
( ( ( ~ ( relation @ SV171 ) )
= $true )
| ( ( ~ ( ~ ! [SY1063: $i] :
( ~ ( relation @ SY1063 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK83_C @ SY1063 @ SV171 ) @ ( sK84_SY732 @ SY1063 @ SV171 ) ) @ SV171 )
| ~ ( in @ ( ordered_pair @ ( sK83_C @ SY1063 @ SV171 ) @ ( sK84_SY732 @ SY1063 @ SV171 ) ) @ SY1063 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK83_C @ SY1063 @ SV171 ) @ ( sK84_SY732 @ SY1063 @ SV171 ) ) @ SV171 )
| ( in @ ( ordered_pair @ ( sK83_C @ SY1063 @ SV171 ) @ ( sK84_SY732 @ SY1063 @ SV171 ) ) @ SY1063 ) ) )
| ( SV171 = SY1063 ) )
| ~ ! [SY1064: $i] :
( ~ ( relation @ SY1064 )
| ( SV171 != SY1064 )
| ~ ( ~ ! [SY1065: $i,SY1066: $i] :
( ~ ( in @ ( ordered_pair @ SY1065 @ SY1066 ) @ SV171 )
| ( in @ ( ordered_pair @ SY1065 @ SY1066 ) @ SY1064 ) )
| ~ ! [SY1067: $i,SY1068: $i] :
( ~ ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SY1064 )
| ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SV171 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1483]) ).
thf(1734,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1484]) ).
thf(1735,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1484]) ).
thf(1736,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK98_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK98_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1485]) ).
thf(1737,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1485]) ).
thf(1738,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1486]) ).
thf(1739,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1486]) ).
thf(1740,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK97_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1487]) ).
thf(1741,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1487]) ).
thf(1742,plain,
( ( ~ ! [SX0: $i] :
~ ( empty @ ( singleton @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1488]) ).
thf(1743,plain,
( ( ~ ! [SX0: $i] : ( finite @ ( singleton @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1488]) ).
thf(1744,plain,
! [SV272: $i,SV172: $i] :
( ( ( empty @ SV172 )
| ~ ( relation @ SV272 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK35_D @ SV272 @ SV172 )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1178: $i] :
( ~ ( in @ SY1178 @ ( sK43_SY691 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SY1178 ) @ SV272 ) )
| ~ ~ ( ( ( sK41_SY666 @ SV272 @ SV172 )
!= ( sK43_SY691 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) ) ) ) ) )
| ( ( sK35_D @ SV272 @ SV172 )
!= ( sK37_SY665 @ SV272 @ SV172 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
!= ( sK37_SY665 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1179: $i] :
( ~ ( in @ SY1179 @ ( sK40_SY685 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SY1179 ) @ SV272 ) )
| ~ ~ ( ( ( sK38_SY678 @ SV272 @ SV172 )
!= ( sK40_SY685 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) ) ) ) ) )
| ~ ( ( ( sK36_SY655 @ SV272 @ SV172 )
!= ( sK37_SY665 @ SV272 @ SV172 ) ) ) )
| ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1489]) ).
thf(1745,plain,
( ( ~ ! [SX0: $i] :
( ( SX0
!= ( union @ SX0 ) )
| ( being_limit_ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1490]) ).
thf(1746,plain,
( ( ~ ! [SX0: $i] :
( ~ ( being_limit_ordinal @ SX0 )
| ( SX0
= ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1490]) ).
thf(1747,plain,
( ( ~ ! [SX0: $i] :
( ~ ( v2_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_intersection2 @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1491]) ).
thf(1748,plain,
( ( ~ ! [SX0: $i] :
( ~ ( v2_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_intersection2 @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1491]) ).
thf(1749,plain,
! [SV273: $i,SV173: $i] :
( ( ~ ( ~ ! [SY1188: $i,SY1189: $i] :
( ~ ( in @ SV173 @ SY1188 )
| ~ ( in @ SV273 @ SY1189 )
| ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SY1188 @ SY1189 ) ) )
| ~ ~ ( ~ ! [SY1190: $i] :
( ! [SY1191: $i] :
~ ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SY1190 @ SY1191 ) )
| ( in @ SV173 @ SY1190 ) )
| ~ ! [SY1192: $i,SY1193: $i] :
( ~ ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SY1192 @ SY1193 ) )
| ( in @ SV273 @ SY1193 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1492]) ).
thf(1750,plain,
! [SV174: $i,SV274: $i] :
( ( ~ ( ~ ~ ( ~ ( relation @ ( sK56_C @ SV274 @ SV174 ) )
| ~ ( relation_of2 @ ( sK56_C @ SV274 @ SV174 ) @ SV174 @ SV274 ) )
| ~ ( function @ ( sK56_C @ SV274 @ SV174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(1751,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1494]) ).
thf(1752,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1494]) ).
thf(1753,plain,
( ( ~ ! [SX0: $i] :
( ~ ( v2_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_difference @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1495]) ).
thf(1754,plain,
( ( ~ ! [SX0: $i] :
( ~ ( v2_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_difference @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1495]) ).
thf(1755,plain,
! [SV175: $i] :
( ( ~ ( element @ ( sK119_B @ SV175 ) @ ( powerset @ SV175 ) )
| ~ ( empty @ ( sK119_B @ SV175 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1496]) ).
thf(1756,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_intersection2 @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1497]) ).
thf(1757,plain,
( ( ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v3_membered @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1497]) ).
thf(1758,plain,
( ( ~ ~ ( empty @ sK61_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1498]) ).
thf(1759,plain,
( ( ~ ( finite @ sK61_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1498]) ).
thf(1760,plain,
( ( ~ ! [SX0: $i] :
( ~ ( v2_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1499]) ).
thf(1761,plain,
( ( ~ ! [SX0: $i] :
( ~ ( v2_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1499]) ).
thf(1762,plain,
( ( ~ ~ ( empty @ sK55_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1500]) ).
thf(1763,plain,
( ( ~ ( relation @ sK55_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1500]) ).
thf(1764,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1501]) ).
thf(1765,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1501]) ).
thf(1766,plain,
! [SV275: $i,SV176: $i] :
( ( ~ ( ~ ! [SY1194: $i] :
( ! [SY1090: $i,SY1091: $i] :
( ( ( ordered_pair @ SY1090 @ SY1091 )
!= SY1194 )
| ~ ( in @ SY1090 @ SV176 )
| ( SY1091
!= ( singleton @ SY1090 ) ) )
| ~ ( in @ SY1194 @ ( cartesian_product2 @ SV176 @ SV275 ) )
| ( in @ SY1194 @ ( sK108_C @ SV275 @ SV176 ) ) )
| ~ ~ ( ~ ! [SY1197: $i] :
( ~ ( in @ SY1197 @ ( sK108_C @ SV275 @ SV176 ) )
| ~ ( ~ ~ ( ( ( ordered_pair @ ( sK109_E @ SY1197 @ SV275 @ SV176 ) @ ( sK110_SY756 @ SY1197 @ SV275 @ SV176 ) )
!= SY1197 )
| ~ ( in @ ( sK109_E @ SY1197 @ SV275 @ SV176 ) @ SV176 ) )
| ( ( sK110_SY756 @ SY1197 @ SV275 @ SV176 )
!= ( singleton @ ( sK109_E @ SY1197 @ SV275 @ SV176 ) ) ) ) )
| ~ ! [SY1198: $i] :
( ~ ( in @ SY1198 @ ( sK108_C @ SV275 @ SV176 ) )
| ( in @ SY1198 @ ( cartesian_product2 @ SV176 @ SV275 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1502]) ).
thf(1767,plain,
! [SV177: $i,SV276: $i] :
( ( ~ ( ~ ( in @ ( sK125_C @ SV276 @ SV177 ) @ SV177 )
| ~ ~ ( in @ ( sK125_C @ SV276 @ SV177 ) @ SV276 ) )
| ( element @ SV177 @ ( powerset @ SV276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1503]) ).
thf(1768,plain,
! [SV178: $i,SV277: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK6_C @ SV277 @ SV178 ) @ SV178 )
| ~ ( in @ ( sK6_C @ SV277 @ SV178 ) @ SV277 ) )
| ~ ( ( in @ ( sK6_C @ SV277 @ SV178 ) @ SV178 )
| ( in @ ( sK6_C @ SV277 @ SV178 ) @ SV277 ) ) )
| ( SV178 = SV277 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1504]) ).
thf(1769,plain,
! [SV179: $i] :
( ( ~ ! [SY1096: $i] :
( ~ ( subset @ SV179 @ SY1096 )
| ! [SY1097: $i] : ( subset @ ( cartesian_product2 @ SV179 @ SY1097 ) @ ( cartesian_product2 @ SY1096 @ SY1097 ) ) )
| ~ ! [SY1098: $i] :
( ~ ( subset @ SV179 @ SY1098 )
| ! [SY1099: $i] : ( subset @ ( cartesian_product2 @ SY1099 @ SV179 ) @ ( cartesian_product2 @ SY1099 @ SY1098 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1505]) ).
thf(1770,plain,
! [SV180: $i] :
( ( ~ ! [SY1100: $i,SY1101: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK81_D @ SY1101 @ SY1100 @ SV180 ) @ SY1101 )
| ~ ( in @ ( sK81_D @ SY1101 @ SY1100 @ SV180 ) @ SV180 ) )
| ~ ( ~ ( in @ ( sK81_D @ SY1101 @ SY1100 @ SV180 ) @ SY1101 )
| ~ ( in @ ( sK81_D @ SY1101 @ SY1100 @ SV180 ) @ SY1100 ) ) )
| ~ ( ( in @ ( sK81_D @ SY1101 @ SY1100 @ SV180 ) @ SY1101 )
| ( in @ ( sK81_D @ SY1101 @ SY1100 @ SV180 ) @ SV180 )
| ( in @ ( sK81_D @ SY1101 @ SY1100 @ SV180 ) @ SY1100 ) ) )
| ( SY1101
= ( set_union2 @ SV180 @ SY1100 ) ) )
| ~ ! [SY1102: $i,SY1103: $i] :
( ( SY1103
!= ( set_union2 @ SV180 @ SY1102 ) )
| ~ ( ~ ! [SY1104: $i] :
( ~ ( in @ SY1104 @ SY1103 )
| ( in @ SY1104 @ SV180 )
| ( in @ SY1104 @ SY1102 ) )
| ~ ~ ( ~ ! [SY1105: $i] :
( ~ ( in @ SY1105 @ SV180 )
| ( in @ SY1105 @ SY1103 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1102 )
| ( in @ SX3 @ SY1103 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1506]) ).
thf(1771,plain,
! [SV181: $i] :
( ( ( empty @ SV181 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK120_B @ SV181 ) @ ( powerset @ SV181 ) )
| ~ ~ ( empty @ ( sK120_B @ SV181 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1507]) ).
thf(1772,plain,
! [SV1: $i,SV182: $i] :
( ( ( ~ ( element @ SV182 @ ( powerset @ SV1 ) ) )
= $true )
| ( ( ! [SY1107: $i] :
( ~ ( in @ SY1107 @ SV182 )
| ( in @ SY1107 @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1508]) ).
thf(1773,plain,
! [SV2: $i] :
( ( ( one_sorted_str @ SV2 )
= $false )
| ( ( ( cast_as_carrier_subset @ SV2 )
= ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1509]) ).
thf(1774,plain,
! [SV3: $i] :
( ( ( one_sorted_str @ SV3 )
= $false )
| ( ( ! [SY776: $i] :
( ~ ( element @ SY776 @ ( powerset @ ( the_carrier @ SV3 ) ) )
| ( ( subset_intersection2 @ ( the_carrier @ SV3 ) @ SY776 @ ( cast_as_carrier_subset @ SV3 ) )
= SY776 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1510]) ).
thf(1775,plain,
! [SV4: $i,SV183: $i] :
( ( ( ~ ( element @ SV183 @ ( powerset @ ( powerset @ SV4 ) ) ) )
= $true )
| ( ( ( SV183 = empty_set )
| ( ( complements_of_subsets @ SV4 @ SV183 )
!= empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1511]) ).
thf(1776,plain,
! [SV5: $i,SV278: $i] :
( ( ( ~ ( element @ SV278 @ ( powerset @ SV5 ) )
| ! [SY1199: $i] :
( ~ ( element @ SY1199 @ SV5 )
| ( in @ SY1199 @ SV278 )
| ( in @ SY1199 @ ( subset_complement @ SV5 @ SV278 ) ) ) )
= $true )
| ( ( SV5 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1512]) ).
thf(1777,plain,
! [SV184: $i,SV6: $i,SV279: $i] :
( ( ~ ( element @ SV279 @ ( powerset @ SV6 ) )
| ~ ( in @ SV184 @ ( subset_complement @ SV6 @ SV279 ) )
| ~ ( in @ SV184 @ SV279 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(1778,plain,
! [SV8: $i] :
( ( ( v1_membered @ SV8 )
= $false )
| ( ( ! [SY782: $i] :
( ~ ( element @ SY782 @ SV8 )
| ( v1_xcmplx_0 @ SY782 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1514]) ).
thf(1779,plain,
! [SV9: $i] :
( ( ( v1_membered @ SV9 )
= $false )
| ( ( ! [SY783: $i] :
( ~ ( element @ SY783 @ ( powerset @ SV9 ) )
| ( v1_membered @ SY783 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1515]) ).
thf(1780,plain,
! [SV185: $i,SV10: $i,SV280: $i] :
( ( ~ ( element @ SV280 @ ( powerset @ ( cartesian_product2 @ SV10 @ SV185 ) ) )
| ( relation @ SV280 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1516]) ).
thf(1781,plain,
! [SV11: $i] :
( ( ( finite @ SV11 )
= $false )
| ( ( ! [SY786: $i] :
( ~ ( element @ SY786 @ ( powerset @ SV11 ) )
| ( finite @ SY786 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1517]) ).
thf(1782,plain,
! [SV281: $i,SV12: $i,SV186: $i] :
( ( ~ ( element @ SV186 @ ( powerset @ SV12 ) )
| ~ ( element @ SV281 @ ( powerset @ SV12 ) )
| ( ( subset_intersection2 @ SV12 @ SV186 @ SV281 )
= ( subset_intersection2 @ SV12 @ SV281 @ SV186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(1783,plain,
! [SV13: $i] :
( ( ( one_sorted_str @ SV13 )
= $false )
| ( ( ( cast_as_carrier_subset @ SV13 )
= ( the_carrier @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1519]) ).
thf(1784,plain,
! [SV14: $i,SV187: $i] :
( ( ( ~ ( element @ SV187 @ ( powerset @ SV14 ) ) )
= $true )
| ( ( ( subset_complement @ SV14 @ SV187 )
= ( set_difference @ SV14 @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1520]) ).
thf(1785,plain,
! [SV15: $i] :
( ( ( one_sorted_str @ SV15 )
= $false )
| ( ( element @ ( cast_as_carrier_subset @ SV15 ) @ ( powerset @ ( the_carrier @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1521]) ).
thf(1786,plain,
! [SV17: $i,SV188: $i] :
( ( ( ~ ( element @ SV188 @ ( powerset @ SV17 ) ) )
= $true )
| ( ( element @ ( subset_complement @ SV17 @ SV188 ) @ ( powerset @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1522]) ).
thf(1787,plain,
! [SV189: $i,SV18: $i,SV282: $i] :
( ( ~ ( relation_of2 @ SV282 @ SV18 @ SV189 )
| ( element @ ( relation_dom_as_subset @ SV18 @ SV189 @ SV282 ) @ ( powerset @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(1788,plain,
! [SV190: $i,SV19: $i,SV283: $i] :
( ( ~ ( relation_of2 @ SV283 @ SV19 @ SV190 )
| ( element @ ( relation_rng_as_subset @ SV19 @ SV190 @ SV283 ) @ ( powerset @ SV190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1524]) ).
thf(1789,plain,
! [SV20: $i,SV191: $i] :
( ( ( ~ ( element @ SV191 @ ( powerset @ ( powerset @ SV20 ) ) ) )
= $true )
| ( ( element @ ( union_of_subsets @ SV20 @ SV191 ) @ ( powerset @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1525]) ).
thf(1790,plain,
! [SV284: $i,SV21: $i,SV192: $i] :
( ( ~ ( element @ SV192 @ ( powerset @ SV21 ) )
| ~ ( element @ SV284 @ ( powerset @ SV21 ) )
| ( element @ ( subset_intersection2 @ SV21 @ SV192 @ SV284 ) @ ( powerset @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(1791,plain,
! [SV22: $i,SV193: $i] :
( ( ( ~ ( element @ SV193 @ ( powerset @ ( powerset @ SV22 ) ) ) )
= $true )
| ( ( element @ ( meet_of_subsets @ SV22 @ SV193 ) @ ( powerset @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1527]) ).
thf(1792,plain,
! [SV285: $i,SV23: $i,SV194: $i] :
( ( ~ ( element @ SV194 @ ( powerset @ SV23 ) )
| ~ ( element @ SV285 @ ( powerset @ SV23 ) )
| ( element @ ( subset_difference @ SV23 @ SV194 @ SV285 ) @ ( powerset @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(1793,plain,
! [SV24: $i,SV195: $i] :
( ( ( ~ ( element @ SV195 @ ( powerset @ ( powerset @ SV24 ) ) ) )
= $true )
| ( ( element @ ( complements_of_subsets @ SV24 @ SV195 ) @ ( powerset @ ( powerset @ SV24 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1529]) ).
thf(1794,plain,
! [SV25: $i] :
( ( ( meet_semilatt_str @ SV25 )
= $false )
| ( ( one_sorted_str @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1530]) ).
thf(1795,plain,
! [SV26: $i] :
( ( ( join_semilatt_str @ SV26 )
= $false )
| ( ( one_sorted_str @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1531]) ).
thf(1796,plain,
! [SV196: $i,SV27: $i,SV286: $i] :
( ( ~ ( relation_of2_as_subset @ SV286 @ SV27 @ SV196 )
| ( element @ SV286 @ ( powerset @ ( cartesian_product2 @ SV27 @ SV196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(1797,plain,
! [SV29: $i] :
( ( ( empty_carrier @ SV29 )
= $true )
| ( ( ~ ( one_sorted_str @ SV29 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1533]) ).
thf(1798,plain,
! [SV31: $i,SV197: $i] :
( ( ( ~ ( element @ SV197 @ ( powerset @ SV31 ) )
| ! [SY805: $i] :
~ ( element @ SY805 @ ( powerset @ SV31 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV31 @ SV197 @ SV197 )
= SV197 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1535]) ).
thf(1799,plain,
! [SV32: $i,SV198: $i] :
( ( ( ~ ( element @ SV198 @ ( powerset @ SV32 ) ) )
= $true )
| ( ( ( subset_complement @ SV32 @ ( subset_complement @ SV32 @ SV198 ) )
= SV198 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1536]) ).
thf(1800,plain,
! [SV33: $i,SV199: $i] :
( ( ( ~ ( element @ SV199 @ ( powerset @ ( powerset @ SV33 ) ) ) )
= $true )
| ( ( ( complements_of_subsets @ SV33 @ ( complements_of_subsets @ SV33 @ SV199 ) )
= SV199 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1537]) ).
thf(1801,plain,
! [SV34: $i,SV200: $i] :
( ( ( ~ ( element @ SV200 @ ( powerset @ ( powerset @ SV34 ) ) ) )
= $true )
| ( ( ( union_of_subsets @ SV34 @ SV200 )
= ( union @ SV200 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1538]) ).
thf(1802,plain,
! [SV287: $i,SV35: $i,SV201: $i] :
( ( ~ ( element @ SV201 @ ( powerset @ SV35 ) )
| ~ ( element @ SV287 @ ( powerset @ SV35 ) )
| ( ( subset_intersection2 @ SV35 @ SV201 @ SV287 )
= ( set_intersection2 @ SV201 @ SV287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1539]) ).
thf(1803,plain,
! [SV36: $i,SV202: $i] :
( ( ( ~ ( element @ SV202 @ ( powerset @ ( powerset @ SV36 ) ) ) )
= $true )
| ( ( ( meet_of_subsets @ SV36 @ SV202 )
= ( set_meet @ SV202 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1540]) ).
thf(1804,plain,
! [SV288: $i,SV37: $i,SV203: $i] :
( ( ~ ( element @ SV203 @ ( powerset @ SV37 ) )
| ~ ( element @ SV288 @ ( powerset @ SV37 ) )
| ( ( subset_difference @ SV37 @ SV203 @ SV288 )
= ( set_difference @ SV203 @ SV288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1541]) ).
thf(1805,plain,
! [SV204: $i,SV38: $i] :
( ( ( ~ ( in @ SV38 @ SV204 ) )
= $true )
| ( ( element @ SV38 @ SV204 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1542]) ).
thf(1806,plain,
! [SV205: $i,SV39: $i] :
( ( ( ~ ( element @ SV39 @ SV205 ) )
= $true )
| ( ( ( empty @ SV205 )
| ( in @ SV39 @ SV205 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1543]) ).
thf(1807,plain,
! [SV40: $i,SV289: $i,SV206: $i] :
( ( ~ ( element @ SV206 @ ( powerset @ SV289 ) )
| ~ ( in @ SV40 @ SV206 )
| ( element @ SV40 @ SV289 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1544]) ).
thf(1808,plain,
! [SV41: $i,SV290: $i,SV207: $i] :
( ( ~ ( element @ SV207 @ ( powerset @ SV290 ) )
| ~ ( in @ SV41 @ SV207 )
| ~ ( empty @ SV290 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(1809,plain,
! [SV208: $i,SV43: $i] :
( ( ( ~ ( in @ SV43 @ SV208 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV43 ) @ SV208 )
= SV208 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1547]) ).
thf(1810,plain,
! [SV209: $i,SV44: $i] :
( ( ( ~ ( disjoint @ ( singleton @ SV44 ) @ SV209 ) )
= $true )
| ( ( ~ ( in @ SV44 @ SV209 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1548]) ).
thf(1811,plain,
! [SV210: $i,SV45: $i] :
( ( ( in @ SV45 @ SV210 )
= $true )
| ( ( disjoint @ ( singleton @ SV45 ) @ SV210 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1549]) ).
thf(1812,plain,
! [SV211: $i,SV46: $i] :
( ( ( ~ ( subset @ SV46 @ SV211 ) )
= $true )
| ( ( ! [SY1121: $i] :
( ( in @ SY1121 @ SV46 )
| ( subset @ SV46 @ ( set_difference @ SV211 @ ( singleton @ SY1121 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1550]) ).
thf(1813,plain,
! [SV212: $i,SV47: $i] :
( ( ( ~ ( in @ SV47 @ SV212 ) )
= $true )
| ( ( subset @ SV47 @ ( union @ SV212 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1551]) ).
thf(1814,plain,
! [SV49: $i,SV213: $i] :
( ( ( ~ ( relation @ SV213 ) )
= $true )
| ( ( subset @ ( relation_rng_restriction @ SV49 @ SV213 ) @ SV213 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1552]) ).
thf(1815,plain,
! [SV291: $i,SV214: $i,SV50: $i] :
( ( ! [SY1200: $i] :
( ~ ( subset @ SV50 @ SV214 )
| ~ ( subset @ SV291 @ SY1200 )
| ( subset @ ( cartesian_product2 @ SV50 @ SV291 ) @ ( cartesian_product2 @ SV214 @ SY1200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1553]) ).
thf(1816,plain,
! [SV215: $i,SV51: $i] :
( ( ( ~ ( subset @ SV51 @ SV215 ) )
= $true )
| ( ( ( set_union2 @ SV51 @ SV215 )
= SV215 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1554]) ).
thf(1817,plain,
! [SV52: $i,SV292: $i] :
( ( ( ~ ( finite @ SV292 )
| ~ ( subset @ SV52 @ SV292 ) )
= $true )
| ( ( finite @ SV52 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1555]) ).
thf(1818,plain,
! [SV216: $i,SV53: $i,SV293: $i] :
( ( ! [SY1201: $i] :
( ~ ( relation_of2_as_subset @ SY1201 @ SV293 @ SV53 )
| ~ ( subset @ ( relation_rng @ SY1201 ) @ SV216 )
| ( relation_of2_as_subset @ SY1201 @ SV293 @ SV216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1556]) ).
thf(1819,plain,
! [SV54: $i] :
( ( ( finite @ SV54 )
= $false )
| ( ( ! [SY835: $i] : ( finite @ ( set_intersection2 @ SV54 @ SY835 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1557]) ).
thf(1820,plain,
! [SV217: $i,SV55: $i,SV294: $i] :
( ( ! [SY1202: $i] :
( ~ ( relation_of2_as_subset @ SY1202 @ SV294 @ SV55 )
| ~ ( subset @ SV55 @ SV217 )
| ( relation_of2_as_subset @ SY1202 @ SV294 @ SV217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1558]) ).
thf(1821,plain,
! [SV218: $i,SV56: $i,SV295: $i] :
( ( ~ ( relation @ SV295 )
| ~ ( subset @ SV56 @ SV218 )
| ( subset @ ( relation_inverse_image @ SV295 @ SV56 ) @ ( relation_inverse_image @ SV295 @ SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1559]) ).
thf(1822,plain,
! [SV296: $i,SV220: $i,SV58: $i] :
( ( ~ ( subset @ SV58 @ SV220 )
| ~ ( subset @ SV58 @ SV296 )
| ( subset @ SV58 @ ( set_intersection2 @ SV220 @ SV296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1561]) ).
thf(1823,plain,
! [SV297: $i,SV221: $i,SV59: $i] :
( ( ~ ( subset @ SV59 @ SV221 )
| ~ ( subset @ SV221 @ SV297 )
| ( subset @ SV59 @ SV297 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1562]) ).
thf(1824,plain,
! [SV60: $i,SV222: $i] :
( ( ( ~ ( ordinal @ SV222 ) )
= $true )
| ( ( ~ ( in @ SV60 @ SV222 )
| ( ordinal @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1563]) ).
thf(1825,plain,
! [SV61: $i] :
( ( ( ordinal @ SV61 )
= $false )
| ( ( ! [SY847: $i] :
( ~ ( ordinal @ SY847 )
| ( in @ SV61 @ SY847 )
| ( SV61 = SY847 )
| ( in @ SY847 @ SV61 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1564]) ).
thf(1826,plain,
! [SV223: $i,SV62: $i] :
( ( ( ~ ( subset @ SV62 @ SV223 ) )
= $true )
| ( ( ! [SY1131: $i] : ( subset @ ( set_intersection2 @ SV62 @ SY1131 ) @ ( set_intersection2 @ SV223 @ SY1131 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1565]) ).
thf(1827,plain,
! [SV224: $i,SV63: $i] :
( ( ( ~ ( subset @ SV63 @ SV224 ) )
= $true )
| ( ( ( set_intersection2 @ SV63 @ SV224 )
= SV63 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1566]) ).
thf(1828,plain,
! [SV225: $i,SV65: $i] :
( ( ( ~ ( subset @ SV65 @ SV225 ) )
= $true )
| ( ( ! [SY1132: $i] : ( subset @ ( set_difference @ SV65 @ SY1132 ) @ ( set_difference @ SV225 @ SY1132 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1567]) ).
thf(1829,plain,
! [SV298: $i,SV228: $i,SV68: $i] :
( ( ~ ( in @ SV68 @ SV228 )
| ~ ( in @ SV228 @ SV298 )
| ~ ( in @ SV298 @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1570]) ).
thf(1830,plain,
! [SV69: $i] :
( ( ( subset @ SV69 @ empty_set )
= $false )
| ( ( SV69 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1571]) ).
thf(1831,plain,
! [SV230: $i,SV71: $i] :
( ( ( ~ ( subset @ SV71 @ SV230 ) )
= $true )
| ( ( SV230
= ( set_union2 @ SV71 @ ( set_difference @ SV230 @ SV71 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1573]) ).
thf(1832,plain,
! [SV231: $i,SV72: $i] :
( ( ( ~ ( in @ SV72 @ SV231 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV72 ) @ SV231 )
= SV231 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1574]) ).
thf(1833,plain,
! [SV73: $i,SV232: $i] :
( ( ( ~ ( element @ SV232 @ ( powerset @ ( powerset @ SV73 ) ) ) )
= $true )
| ( ( ( SV232 = empty_set )
| ( ( subset_difference @ SV73 @ ( cast_to_subset @ SV73 ) @ ( union_of_subsets @ SV73 @ SV232 ) )
= ( meet_of_subsets @ SV73 @ ( complements_of_subsets @ SV73 @ SV232 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1575]) ).
thf(1834,plain,
! [SV74: $i,SV233: $i] :
( ( ( ~ ( element @ SV233 @ ( powerset @ ( powerset @ SV74 ) ) ) )
= $true )
| ( ( ( SV233 = empty_set )
| ( ( union_of_subsets @ SV74 @ ( complements_of_subsets @ SV74 @ SV233 ) )
= ( subset_difference @ SV74 @ ( cast_to_subset @ SV74 ) @ ( meet_of_subsets @ SV74 @ SV233 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1576]) ).
thf(1835,plain,
! [SV76: $i] :
( ( ( relation @ SV76 )
= $false )
| ( ( ( in @ ( ordered_pair @ ( sK95_B @ SV76 ) @ ( sK96_SY738 @ SV76 ) ) @ SV76 )
| ( SV76 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1578]) ).
thf(1836,plain,
! [SV77: $i,SV235: $i] :
( ( ( ~ ( proper_subset @ SV235 @ SV77 ) )
= $true )
| ( ( ~ ( subset @ SV77 @ SV235 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1579]) ).
thf(1837,plain,
! [SV78: $i,SV299: $i,SV236: $i] :
( ( ~ ( disjoint @ SV236 @ SV299 )
| ~ ( subset @ SV78 @ SV236 )
| ( disjoint @ SV78 @ SV299 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1580]) ).
thf(1838,plain,
! [SV237: $i,SV80: $i] :
( ( ( ~ ( subset @ ( singleton @ SV80 ) @ ( singleton @ SV237 ) ) )
= $true )
| ( ( SV80 = SV237 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1581]) ).
thf(1839,plain,
! [SV82: $i,SV239: $i] :
( ( ( ~ ( relation @ SV239 ) )
= $true )
| ( ( subset @ ( relation_dom_restriction @ SV239 @ SV82 ) @ SV239 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1583]) ).
thf(1840,plain,
! [SV300: $i,SV240: $i,SV83: $i] :
( ( ~ ( subset @ SV83 @ SV240 )
| ~ ( subset @ SV300 @ SV240 )
| ( subset @ ( set_union2 @ SV83 @ SV300 ) @ SV240 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1584]) ).
thf(1841,plain,
! [SV241: $i,SV84: $i] :
( ( ( ! [SY1136: $i] :
( ( singleton @ SV84 )
!= ( unordered_pair @ SV241 @ SY1136 ) ) )
= $true )
| ( ( SV84 = SV241 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1585]) ).
thf(1842,plain,
! [SV242: $i,SV85: $i] :
( ( ( ~ ( in @ SV85 @ SV242 ) )
= $true )
| ( ( subset @ SV85 @ ( union @ SV242 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1586]) ).
thf(1843,plain,
! [SV301: $i,SV243: $i,SV86: $i] :
( ( ( ( singleton @ SV86 )
!= ( unordered_pair @ SV243 @ SV301 ) )
| ( SV243 = SV301 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1587]) ).
thf(1844,plain,
! [SV244: $i,SV87: $i] :
( ( ( ~ ( in @ SV87 @ SV244 ) )
= $true )
| ( ( ~ ( in @ SV244 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1588]) ).
thf(1845,plain,
! [SV88: $i] :
( ( ( empty @ SV88 )
= $false )
| ( ( finite @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1589]) ).
thf(1846,plain,
! [SV89: $i] :
( ( ( empty @ SV89 )
= $false )
| ( ( function @ SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1590]) ).
thf(1847,plain,
! [SV90: $i] :
( ( ( empty @ SV90 )
= $false )
| ( ( relation @ SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1591]) ).
thf(1848,plain,
! [SV91: $i] :
( ( ( v3_membered @ SV91 )
= $false )
| ( ( v2_membered @ SV91 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1592]) ).
thf(1849,plain,
! [SV92: $i] :
( ( ( v2_membered @ SV92 )
= $false )
| ( ( v1_membered @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1593]) ).
thf(1850,plain,
! [SV95: $i] :
( ( ( relation @ SV95 )
= $false )
| ( ( ! [SY878: $i] :
( ( relation_restriction @ SV95 @ SY878 )
= ( set_intersection2 @ SV95 @ ( cartesian_product2 @ SY878 @ SY878 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1595]) ).
thf(1851,plain,
! [SV302: $i,SV246: $i,SV96: $i] :
( ( ( empty_carrier @ SV96 )
| ~ ( join_semilatt_str @ SV96 )
| ~ ( element @ SV246 @ ( the_carrier @ SV96 ) )
| ~ ( element @ SV302 @ ( the_carrier @ SV96 ) )
| ( element @ ( join @ SV96 @ SV246 @ SV302 ) @ ( the_carrier @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1596]) ).
thf(1852,plain,
! [SV303: $i,SV247: $i,SV98: $i] :
( ( ( empty_carrier @ SV98 )
| ~ ( meet_semilatt_str @ SV98 )
| ~ ( element @ SV247 @ ( the_carrier @ SV98 ) )
| ~ ( element @ SV303 @ ( the_carrier @ SV98 ) )
| ( element @ ( meet @ SV98 @ SV247 @ SV303 ) @ ( the_carrier @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1597]) ).
thf(1853,plain,
! [SV99: $i] :
( ( ( relation @ SV99 )
= $false )
| ( ( ! [SY883: $i] : ( relation @ ( relation_restriction @ SV99 @ SY883 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1598]) ).
thf(1854,plain,
! [SV100: $i] :
( ( ( relation @ SV100 )
= $false )
| ( ( relation @ ( relation_inverse @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1599]) ).
thf(1855,plain,
! [SV248: $i,SV101: $i] :
( ( ( ~ ( relation @ SV101 )
| ~ ( relation @ SV248 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV101 @ SV248 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1600]) ).
thf(1856,plain,
! [SV103: $i] :
( ( ( relation @ SV103 )
= $false )
| ( ( ! [SY885: $i] : ( relation @ ( relation_dom_restriction @ SV103 @ SY885 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1601]) ).
thf(1857,plain,
! [SV104: $i,SV249: $i] :
( ( ( ~ ( relation @ SV249 ) )
= $true )
| ( ( relation @ ( relation_rng_restriction @ SV104 @ SV249 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1602]) ).
thf(1858,plain,
! [SV107: $i,SV252: $i] :
( ( ( ~ ( finite @ SV252 ) )
= $true )
| ( ( finite @ ( set_intersection2 @ SV107 @ SV252 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1605]) ).
thf(1859,plain,
! [SV108: $i] :
( ( ( finite @ SV108 )
= $false )
| ( ( ! [SY890: $i] : ( finite @ ( set_intersection2 @ SV108 @ SY890 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1606]) ).
thf(1860,plain,
! [SV109: $i] :
( ( ( finite @ SV109 )
= $false )
| ( ( ! [SY891: $i] : ( finite @ ( set_difference @ SV109 @ SY891 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1607]) ).
thf(1861,plain,
! [SV253: $i,SV111: $i] :
( ( ( ~ ( relation @ SV111 )
| ~ ( relation @ SV253 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV111 @ SV253 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1609]) ).
thf(1862,plain,
! [SV254: $i,SV112: $i] :
( ( empty @ ( ordered_pair @ SV112 @ SV254 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1610]) ).
thf(1863,plain,
! [SV113: $i] :
( ( ( v1_membered @ SV113 )
= $false )
| ( ( ! [SY894: $i] : ( v1_membered @ ( set_intersection2 @ SV113 @ SY894 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1611]) ).
thf(1864,plain,
! [SV114: $i] :
( ( ( v1_membered @ SV114 )
= $false )
| ( ( ! [SY895: $i] : ( v1_membered @ ( set_intersection2 @ SY895 @ SV114 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1612]) ).
thf(1865,plain,
! [SV255: $i,SV115: $i] :
( ( ( ~ ( relation @ SV115 )
| ~ ( relation @ SV255 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV115 @ SV255 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1613]) ).
thf(1866,plain,
! [SV304: $i,SV117: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV117 @ SV304 ) ) )
= $true )
| ( ( empty @ SV117 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1615]) ).
thf(1867,plain,
! [SV118: $i] :
( ( ( v1_membered @ SV118 )
= $false )
| ( ( ! [SY898: $i] : ( v1_membered @ ( set_difference @ SV118 @ SY898 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1616]) ).
thf(1868,plain,
! [SV256: $i,SV119: $i] :
( ( ( ~ ( relation @ SV119 )
| ~ ( relation @ SV256 ) )
= $true )
| ( ( relation @ ( set_difference @ SV119 @ SV256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1617]) ).
thf(1869,plain,
! [SV257: $i,SV120: $i] :
( ( empty @ ( unordered_pair @ SV120 @ SV257 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1618]) ).
thf(1870,plain,
! [SV121: $i,SV305: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV305 @ SV121 ) ) )
= $true )
| ( ( empty @ SV121 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1619]) ).
thf(1871,plain,
! [SV258: $i,SV122: $i] :
( ( ( ( empty @ SV122 )
| ( empty @ SV258 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV122 @ SV258 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1620]) ).
thf(1872,plain,
! [SV123: $i] :
( ( ( empty @ SV123 )
= $true )
| ( ( ~ ( relation @ SV123 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV123 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1621]) ).
thf(1873,plain,
! [SV124: $i] :
( ( ( empty @ SV124 )
= $true )
| ( ( ~ ( relation @ SV124 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV124 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1622]) ).
thf(1874,plain,
! [SV259: $i,SV125: $i] :
( ( ( ~ ( finite @ SV125 )
| ~ ( finite @ SV259 ) )
= $true )
| ( ( finite @ ( set_union2 @ SV125 @ SV259 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1623]) ).
thf(1875,plain,
! [SV127: $i] :
( ( ( relation @ SV127 )
= $false )
| ( ( ( relation_inverse @ ( relation_inverse @ SV127 ) )
= SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1624]) ).
thf(1876,plain,
! [SV260: $i,SV128: $i,SV306: $i] :
( ( ~ ( relation_of2 @ SV306 @ SV128 @ SV260 )
| ( ( relation_dom_as_subset @ SV128 @ SV260 @ SV306 )
= ( relation_dom @ SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1625]) ).
thf(1877,plain,
! [SV261: $i,SV129: $i,SV307: $i] :
( ( ~ ( relation_of2 @ SV307 @ SV129 @ SV261 )
| ( ( relation_rng_as_subset @ SV129 @ SV261 @ SV307 )
= ( relation_rng @ SV307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1626]) ).
thf(1878,plain,
! [SV262: $i,SV131: $i] :
( ( ( ~ ( disjoint @ SV131 @ SV262 ) )
= $true )
| ( ( disjoint @ SV262 @ SV131 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1627]) ).
thf(1879,plain,
! [SV136: $i] :
( ( ( empty @ SV136 )
= $false )
| ( ( SV136 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1628]) ).
thf(1880,plain,
! [SV137: $i,SV263: $i] :
( ( ( ~ ( empty @ SV263 ) )
= $true )
| ( ( ~ ( in @ SV137 @ SV263 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1629]) ).
thf(1881,plain,
! [SV264: $i,SV138: $i] :
( ( ( ( SV138 = SV264 )
| ~ ( empty @ SV138 ) )
= $true )
| ( ( ~ ( empty @ SV264 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1630]) ).
thf(1882,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1631]) ).
thf(1883,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1632]) ).
thf(1884,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1633]) ).
thf(1885,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1634]) ).
thf(1886,plain,
! [SV139: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK17_C @ SV139 )
!= ( sK18_SY613 @ SV139 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
!= ( sK18_SY613 @ SV139 ) )
| ~ ( in @ ( sK22_SY620 @ SV139 ) @ SV139 ) )
| ( ( sK23_SY629 @ SV139 )
!= ( singleton @ ( sK22_SY620 @ SV139 ) ) ) ) )
| ( ( sK17_C @ SV139 )
!= ( sK19_SY619 @ SV139 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
!= ( sK19_SY619 @ SV139 ) )
| ~ ( in @ ( sK20_SY626 @ SV139 ) @ SV139 ) )
| ( ( sK21_SY628 @ SV139 )
!= ( singleton @ ( sK20_SY626 @ SV139 ) ) ) ) )
| ~ ( ( ( sK18_SY613 @ SV139 )
!= ( sK19_SY619 @ SV139 ) ) ) )
= $false )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1635]) ).
thf(1887,plain,
! [SV140: $i] :
( ( ( empty_carrier @ SV140 )
= $true )
| ( ( ~ ( one_sorted_str @ SV140 ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK116_B @ SV140 ) @ ( powerset @ ( the_carrier @ SV140 ) ) )
| ~ ~ ( empty @ ( sK116_B @ SV140 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1636]) ).
thf(1888,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_intersection2 @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_intersection2 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1637]) ).
thf(1889,plain,
( ( ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v3_membered @ ( set_intersection2 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1638]) ).
thf(1890,plain,
! [SV141: $i] :
( ( ( ~ ( in @ ( sK99_B @ SV141 ) @ SV141 )
| ~ ( ~ ( ordinal @ ( sK99_B @ SV141 ) )
| ~ ( subset @ ( sK99_B @ SV141 ) @ SV141 ) ) )
= $false )
| ( ( ordinal @ SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1639]) ).
thf(1891,plain,
! [SV142: $i] :
( ( ~ ! [SY917: $i,SY918: $i] :
( ~ ( in @ SV142 @ SY918 )
| ~ ( in @ SY917 @ SY918 )
| ( subset @ ( unordered_pair @ SV142 @ SY917 ) @ SY918 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1640]) ).
thf(1892,plain,
! [SV142: $i] :
( ( ~ ~ ( ~ ! [SY919: $i,SY920: $i] :
( ~ ( subset @ ( unordered_pair @ SV142 @ SY919 ) @ SY920 )
| ( in @ SV142 @ SY920 ) )
| ~ ! [SY921: $i,SY922: $i] :
( ~ ( subset @ ( unordered_pair @ SV142 @ SY921 ) @ SY922 )
| ( in @ SY921 @ SY922 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1640]) ).
thf(1893,plain,
! [SV143: $i] :
( ( ~ ! [SY923: $i,SY924: $i] :
( ~ ( ~ ( ~ ( in @ ( sK70_D @ SY924 @ SY923 @ SV143 ) @ SV143 )
| ~ ( in @ ( sK70_D @ SY924 @ SY923 @ SV143 ) @ SY923 )
| ~ ( in @ ( sK70_D @ SY924 @ SY923 @ SV143 ) @ SY924 ) )
| ~ ~ ( ~ ( ( in @ ( sK70_D @ SY924 @ SY923 @ SV143 ) @ SV143 )
| ( in @ ( sK70_D @ SY924 @ SY923 @ SV143 ) @ SY924 ) )
| ~ ( ( in @ ( sK70_D @ SY924 @ SY923 @ SV143 ) @ SY923 )
| ( in @ ( sK70_D @ SY924 @ SY923 @ SV143 ) @ SY924 ) ) ) )
| ( SY924
= ( set_intersection2 @ SV143 @ SY923 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1641]) ).
thf(1894,plain,
! [SV143: $i] :
( ( ~ ! [SY925: $i,SY926: $i] :
( ( SY926
!= ( set_intersection2 @ SV143 @ SY925 ) )
| ~ ( ~ ! [SY927: $i] :
( ~ ( in @ SY927 @ SV143 )
| ~ ( in @ SY927 @ SY925 )
| ( in @ SY927 @ SY926 ) )
| ~ ~ ( ~ ! [SY928: $i] :
( ~ ( in @ SY928 @ SY926 )
| ( in @ SY928 @ SV143 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY926 )
| ( in @ SX3 @ SY925 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1641]) ).
thf(1895,plain,
! [SV144: $i] :
( ( ( v3_membered @ SV144 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY930: $i] :
( ~ ( element @ SY930 @ ( powerset @ SV144 ) )
| ( v1_membered @ SY930 ) )
| ~ ! [SY931: $i] :
( ~ ( element @ SY931 @ ( powerset @ SV144 ) )
| ( v2_membered @ SY931 ) ) )
| ~ ! [SY932: $i] :
( ~ ( element @ SY932 @ ( powerset @ SV144 ) )
| ( v3_membered @ SY932 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1642]) ).
thf(1896,plain,
! [SV265: $i,SV145: $i] :
( ( ( ( empty @ SV145 )
| ~ ( relation @ SV265 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1142: $i] :
( ~ ( in @ SY1142 @ ( sK52_SY712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SY1142 ) @ SV265 ) )
| ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK52_SY712 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) ) ) )
| ~ ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 ) )
| ~ ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 ) )
| ~ ~ ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ ( sK51_SY718 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SY1143 ) @ SV265 ) )
| ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK51_SY718 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) ) ) ) )
| ~ ( ( ( sK49_SY705 @ SV265 @ SV145 )
!= ( sK50_SY711 @ SV265 @ SV145 ) ) ) )
| ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1643]) ).
thf(1897,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1644]) ).
thf(1898,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1645]) ).
thf(1899,plain,
! [SV146: $i,SV266: $i] :
( ( ( ~ ( ~ ! [SY1149: $i] :
( ~ ( in @ SY1149 @ SV266 )
| ~ ( in @ SY1149 @ ( sK5_C @ SV266 @ SV146 ) ) )
| ~ ( in @ ( sK5_C @ SV266 @ SV146 ) @ SV266 ) ) )
= $true )
| ( ( ~ ( in @ SV146 @ SV266 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1646]) ).
thf(1900,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ( in @ ( sK85_B @ SX0 ) @ SX0 )
| ~ ~ ( subset @ ( sK85_B @ SX0 ) @ SX0 ) )
| ( epsilon_transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1647]) ).
thf(1901,plain,
( ( ! [SX0: $i] :
( ~ ( epsilon_transitive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1648]) ).
thf(1902,plain,
! [SV147: $i] :
( ( ~ ! [SY943: $i,SY944: $i] :
( ~ ( ~ ( ~ ( in @ ( sK66_D @ SY944 @ SY943 @ SV147 ) @ SV147 )
| ( in @ ( sK66_D @ SY944 @ SY943 @ SV147 ) @ SY943 )
| ~ ( in @ ( sK66_D @ SY944 @ SY943 @ SV147 ) @ SY944 ) )
| ~ ~ ( ~ ( ( in @ ( sK66_D @ SY944 @ SY943 @ SV147 ) @ SV147 )
| ( in @ ( sK66_D @ SY944 @ SY943 @ SV147 ) @ SY944 ) )
| ~ ( ~ ( in @ ( sK66_D @ SY944 @ SY943 @ SV147 ) @ SY943 )
| ( in @ ( sK66_D @ SY944 @ SY943 @ SV147 ) @ SY944 ) ) ) )
| ( SY944
= ( set_difference @ SV147 @ SY943 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1649]) ).
thf(1903,plain,
! [SV147: $i] :
( ( ~ ! [SY945: $i,SY946: $i] :
( ( SY946
!= ( set_difference @ SV147 @ SY945 ) )
| ~ ( ~ ! [SY947: $i] :
( ~ ( in @ SY947 @ SV147 )
| ( in @ SY947 @ SY945 )
| ( in @ SY947 @ SY946 ) )
| ~ ~ ( ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ SY946 )
| ( in @ SY948 @ SV147 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY946 )
| ~ ( in @ SX3 @ SY945 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1649]) ).
thf(1904,plain,
( ( ! [SX0: $i] :
( ( in @ ( sK86_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1650]) ).
thf(1905,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1651]) ).
thf(1906,plain,
! [SV148: $i] :
( ( ( finite @ SV148 )
= $false )
| ( ( ! [SY950: $i] :
( ~ ( element @ SY950 @ ( powerset @ ( powerset @ SV148 ) ) )
| ~ ( ~ ! [SY951: $i] :
( ~ ( in @ SY951 @ SY950 )
| ~ ( subset @ ( sK105_C @ SY950 @ SV148 ) @ SY951 )
| ( SY951
= ( sK105_C @ SY950 @ SV148 ) ) )
| ~ ( in @ ( sK105_C @ SY950 @ SV148 ) @ SY950 ) )
| ( SY950 = empty_set ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1652]) ).
thf(1907,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1653]) ).
thf(1908,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1654]) ).
thf(1909,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1655]) ).
thf(1910,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1656]) ).
thf(1911,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK68_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK68_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK68_C @ SX1 @ SX0 ) @ ( sK69_SY723 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK69_SY723 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK68_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1657]) ).
thf(1912,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK67_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK67_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1658]) ).
thf(1913,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1659]) ).
thf(1914,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1660]) ).
thf(1915,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1661]) ).
thf(1916,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1662]) ).
thf(1917,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1663]) ).
thf(1918,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1664]) ).
thf(1919,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK124_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK124_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK124_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK124_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1665]) ).
thf(1920,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1666]) ).
thf(1921,plain,
! [SV149: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK118_B @ SV149 ) @ ( powerset @ SV149 ) )
| ~ ~ ( empty @ ( sK118_B @ SV149 ) ) )
| ~ ( finite @ ( sK118_B @ SV149 ) ) )
= $false )
| ( ( empty @ SV149 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1667]) ).
thf(1922,plain,
! [SV150: $i] :
( ( ~ ! [SY952: $i,SY953: $i] :
( ~ ( relation_of2_as_subset @ SY953 @ SV150 @ SY952 )
| ~ ( ~ ! [SY954: $i] :
~ ( in @ ( ordered_pair @ SY954 @ ( sK102_D @ SY953 @ SY952 @ SV150 ) ) @ SY953 )
| ~ ( in @ ( sK102_D @ SY953 @ SY952 @ SV150 ) @ SY952 ) )
| ( ( relation_rng_as_subset @ SV150 @ SY952 @ SY953 )
= SY952 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1668]) ).
thf(1923,plain,
! [SV150: $i] :
( ( ~ ! [SY955: $i,SY956: $i] :
( ~ ( relation_of2_as_subset @ SY956 @ SV150 @ SY955 )
| ( ( relation_rng_as_subset @ SV150 @ SY955 @ SY956 )
!= SY955 )
| ! [SY957: $i] :
( ( in @ ( ordered_pair @ ( sK101_E @ SY957 @ SY956 @ SY955 @ SV150 ) @ SY957 ) @ SY956 )
| ~ ( in @ SY957 @ SY955 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1668]) ).
thf(1924,plain,
! [SV151: $i,SV267: $i] :
( ( ~ ! [SY1150: $i,SY1151: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 ) @ SY1151 )
| ( ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 )
!= SY1150 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 ) @ SY1151 )
| ( ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 )
!= SV151 ) )
| ~ ( ~ ( in @ ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 ) @ SY1151 )
| ( ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 )
!= SV267 ) ) ) )
| ~ ( ( in @ ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 ) @ SY1151 )
| ( ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 )
= SY1150 )
| ( ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 )
= SV151 )
| ( ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 )
= SV267 ) ) )
| ( SY1151
= ( unordered_triple @ SV151 @ SV267 @ SY1150 ) ) )
| ~ ! [SY1152: $i,SY1153: $i] :
( ( SY1153
!= ( unordered_triple @ SV151 @ SV267 @ SY1152 ) )
| ~ ( ~ ! [SY1154: $i] :
( ~ ( in @ SY1154 @ SY1153 )
| ( SY1154 = SY1152 )
| ( SY1154 = SV151 )
| ( SY1154 = SV267 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SY1152 )
| ( in @ SX4 @ SY1153 ) )
| ~ ~ ( ~ ! [SY965: $i] :
( ( SY965 != SV151 )
| ( in @ SY965 @ SY1153 ) )
| ~ ! [SY1157: $i] :
( ( SY1157 != SV267 )
| ( in @ SY1157 @ SY1153 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1669]) ).
thf(1925,plain,
! [SV152: $i] :
( ( ~ ! [SY967: $i] :
( ~ ( subset @ SY967 @ ( sK106_B @ SV152 ) )
| ( are_equipotent @ SY967 @ ( sK106_B @ SV152 ) )
| ( in @ SY967 @ ( sK106_B @ SV152 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1670]) ).
thf(1926,plain,
! [SV152: $i] :
( ( ~ ~ ( ~ ! [SY968: $i] :
( ~ ( in @ SY968 @ ( sK106_B @ SV152 ) )
| ( in @ ( powerset @ SY968 ) @ ( sK106_B @ SV152 ) ) )
| ~ ~ ( ~ ! [SY969: $i,SY970: $i] :
( ~ ( in @ SY969 @ ( sK106_B @ SV152 ) )
| ~ ( subset @ SY970 @ SY969 )
| ( in @ SY970 @ ( sK106_B @ SV152 ) ) )
| ~ ( in @ SV152 @ ( sK106_B @ SV152 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1670]) ).
thf(1927,plain,
! [SV153: $i] :
( ( ~ ! [SY971: $i] :
( ~ ( in @ SY971 @ SV153 )
| ~ ( ordinal @ SY971 )
| ( in @ SY971 @ ( sK107_B @ SV153 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1671]) ).
thf(1928,plain,
! [SV153: $i] :
( ( ~ ~ ( ~ ! [SY972: $i] :
( ~ ( in @ SY972 @ ( sK107_B @ SV153 ) )
| ( in @ SY972 @ SV153 ) )
| ~ ! [SY973: $i] :
( ~ ( in @ SY973 @ ( sK107_B @ SV153 ) )
| ( ordinal @ SY973 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1671]) ).
thf(1929,plain,
! [SV154: $i] :
( ( ( relation @ SV154 )
= $false )
| ( ( ~ ( ~ ! [SY974: $i] :
( ~ ( relation @ SY974 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK72_C @ SY974 @ SV154 ) @ ( sK73_SY724 @ SY974 @ SV154 ) ) @ SV154 )
| ~ ~ ( in @ ( ordered_pair @ ( sK72_C @ SY974 @ SV154 ) @ ( sK73_SY724 @ SY974 @ SV154 ) ) @ SY974 ) )
| ( subset @ SV154 @ SY974 ) )
| ~ ! [SY975: $i] :
( ~ ( relation @ SY975 )
| ~ ( subset @ SV154 @ SY975 )
| ! [SY976: $i,SY977: $i] :
( ~ ( in @ ( ordered_pair @ SY976 @ SY977 ) @ SV154 )
| ( in @ ( ordered_pair @ SY976 @ SY977 ) @ SY975 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1672]) ).
thf(1930,plain,
! [SV155: $i,SV268: $i] :
( ( ( ~ ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1158: $i] :
( ~ ( element @ SY1158 @ ( powerset @ ( powerset @ SV155 ) ) )
| ~ ( ~ ( element @ ( sK123_D @ SY1158 @ SV268 @ SV155 ) @ ( powerset @ SV155 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK123_D @ SY1158 @ SV268 @ SV155 ) @ SY1158 )
| ~ ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SY1158 @ SV268 @ SV155 ) ) @ SV268 ) )
| ~ ( ( in @ ( sK123_D @ SY1158 @ SV268 @ SV155 ) @ SY1158 )
| ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SY1158 @ SV268 @ SV155 ) ) @ SV268 ) ) ) )
| ( SY1158
= ( complements_of_subsets @ SV155 @ SV268 ) ) )
| ~ ! [SY1159: $i] :
( ~ ( element @ SY1159 @ ( powerset @ ( powerset @ SV155 ) ) )
| ( SY1159
!= ( complements_of_subsets @ SV155 @ SV268 ) )
| ~ ( ~ ! [SY1160: $i] :
( ~ ( element @ SY1160 @ ( powerset @ SV155 ) )
| ~ ( in @ SY1160 @ SY1159 )
| ( in @ ( subset_complement @ SV155 @ SY1160 ) @ SV268 ) )
| ~ ! [SY1161: $i] :
( ~ ( element @ SY1161 @ ( powerset @ SV155 ) )
| ~ ( in @ ( subset_complement @ SV155 @ SY1161 ) @ SV268 )
| ( in @ SY1161 @ SY1159 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1673]) ).
thf(1931,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1674]) ).
thf(1932,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1675]) ).
thf(1933,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1676]) ).
thf(1934,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1677]) ).
thf(1935,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1678]) ).
thf(1936,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1679]) ).
thf(1937,plain,
! [SV156: $i] :
( ( ( v2_membered @ SV156 )
= $false )
| ( ( ~ ( ~ ! [SY983: $i] :
( ~ ( element @ SY983 @ ( powerset @ SV156 ) )
| ( v1_membered @ SY983 ) )
| ~ ! [SY984: $i] :
( ~ ( element @ SY984 @ ( powerset @ SV156 ) )
| ( v2_membered @ SY984 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1680]) ).
thf(1938,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1681]) ).
thf(1939,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1682]) ).
thf(1940,plain,
( ( sK12_REN
| ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
( ( SX2 != SX1 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( ordinal @ SX1 )
| ( in @ SX1 @ ( sK7_B @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK7_B @ SX0 ) )
| ~ ( ~ ~ ( ( ( sK8_D @ SX1 @ SX0 )
!= SX1 )
| ~ ( in @ ( sK8_D @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ordinal @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1683]) ).
thf(1941,plain,
( ( ~ sK12_REN
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK9_B != sK10_SY601 )
| ~ ( ordinal @ sK10_SY601 ) )
| ( sK9_B != sK11_SY603 ) )
| ~ ( ordinal @ sK11_SY603 ) )
| ~ ( ( sK10_SY601 != sK11_SY603 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1684]) ).
thf(1942,plain,
( ( element @ sK2_SY588 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1685]) ).
thf(1943,plain,
( ( ( ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY588 )
!= ( subset_difference @ ( the_carrier @ sK1_A ) @ ( cast_as_carrier_subset @ sK1_A ) @ sK2_SY588 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1686]) ).
thf(1944,plain,
! [SV157: $i] :
( ( ~ ! [SY985: $i,SY986: $i] :
( ~ ( relation @ SY986 )
| ~ ( in @ SV157 @ SY986 )
| ~ ( in @ SV157 @ ( cartesian_product2 @ SY985 @ SY985 ) )
| ( in @ SV157 @ ( relation_restriction @ SY986 @ SY985 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1687]) ).
thf(1945,plain,
! [SV157: $i] :
( ( ~ ~ ( ~ ! [SY987: $i,SY988: $i] :
( ~ ( relation @ SY988 )
| ~ ( in @ SV157 @ ( relation_restriction @ SY988 @ SY987 ) )
| ( in @ SV157 @ SY988 ) )
| ~ ! [SY989: $i,SY990: $i] :
( ~ ( relation @ SY990 )
| ~ ( in @ SV157 @ ( relation_restriction @ SY990 @ SY989 ) )
| ( in @ SV157 @ ( cartesian_product2 @ SY989 @ SY989 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1687]) ).
thf(1946,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1688]) ).
thf(1947,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1689]) ).
thf(1948,plain,
! [SV158: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY991: $i,SY992: $i] :
( ~ ( relation_of2_as_subset @ SY992 @ SV158 @ SY991 )
| ( SY991 = empty_set )
| ( SV158
!= ( relation_dom_as_subset @ SV158 @ SY991 @ SY992 ) )
| ( quasi_total @ SY992 @ SV158 @ SY991 ) )
| ~ ! [SY993: $i,SY994: $i] :
( ~ ( relation_of2_as_subset @ SY994 @ SV158 @ SY993 )
| ( SY993 = empty_set )
| ~ ( quasi_total @ SY994 @ SV158 @ SY993 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SY993 @ SY994 ) ) ) )
| ~ ~ ( ~ ! [SY995: $i,SY996: $i] :
( ~ ( relation_of2_as_subset @ SY996 @ SV158 @ SY995 )
| ( SV158 != empty_set )
| ( SV158
!= ( relation_dom_as_subset @ SV158 @ SY995 @ SY996 ) )
| ( quasi_total @ SY996 @ SV158 @ SY995 ) )
| ~ ! [SY997: $i,SY998: $i] :
( ~ ( relation_of2_as_subset @ SY998 @ SV158 @ SY997 )
| ( SV158 != empty_set )
| ~ ( quasi_total @ SY998 @ SV158 @ SY997 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SY997 @ SY998 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1690]) ).
thf(1949,plain,
! [SV158: $i] :
( ( ~ ~ ( ~ ! [SY999: $i,SY1000: $i] :
( ~ ( relation_of2_as_subset @ SY1000 @ SV158 @ SY999 )
| ( SY999 != empty_set )
| ( SY1000 != empty_set )
| ( quasi_total @ SY1000 @ SV158 @ SY999 )
| ( SV158 = empty_set ) )
| ~ ! [SY1001: $i,SY1002: $i] :
( ~ ( relation_of2_as_subset @ SY1002 @ SV158 @ SY1001 )
| ( SY1001 != empty_set )
| ~ ( quasi_total @ SY1002 @ SV158 @ SY1001 )
| ( SY1002 = empty_set )
| ( SV158 = empty_set ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1690]) ).
thf(1950,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK90_SY733 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK89_C @ SX1 @ SX0 ) @ ( sK90_SY733 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK89_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK89_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK89_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK88_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK88_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1691]) ).
thf(1951,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1692]) ).
thf(1952,plain,
! [SV159: $i] :
( ( ~ ! [SY1003: $i,SY1004: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK82_D @ SY1004 @ SY1003 @ SV159 ) @ SY1004 )
| ( ( sK82_D @ SY1004 @ SY1003 @ SV159 )
!= SV159 ) )
| ~ ( ~ ( in @ ( sK82_D @ SY1004 @ SY1003 @ SV159 ) @ SY1004 )
| ( ( sK82_D @ SY1004 @ SY1003 @ SV159 )
!= SY1003 ) ) )
| ~ ( ( in @ ( sK82_D @ SY1004 @ SY1003 @ SV159 ) @ SY1004 )
| ( ( sK82_D @ SY1004 @ SY1003 @ SV159 )
= SV159 )
| ( ( sK82_D @ SY1004 @ SY1003 @ SV159 )
= SY1003 ) ) )
| ( SY1004
= ( unordered_pair @ SV159 @ SY1003 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1693]) ).
thf(1953,plain,
! [SV159: $i] :
( ( ~ ! [SY1005: $i,SY1006: $i] :
( ( SY1006
!= ( unordered_pair @ SV159 @ SY1005 ) )
| ~ ( ~ ! [SY1007: $i] :
( ~ ( in @ SY1007 @ SY1006 )
| ( SY1007 = SV159 )
| ( SY1007 = SY1005 ) )
| ~ ~ ( ~ ! [SY1008: $i] :
( ( SY1008 != SV159 )
| ( in @ SY1008 @ SY1006 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY1005 )
| ( in @ SX3 @ SY1006 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1693]) ).
thf(1954,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( empty @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1694]) ).
thf(1955,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 )
| ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1695]) ).
thf(1956,plain,
! [SV160: $i] :
( ( ( v2_membered @ SV160 )
= $false )
| ( ( ~ ( ~ ! [SY1010: $i] :
( ~ ( element @ SY1010 @ SV160 )
| ( v1_xcmplx_0 @ SY1010 ) )
| ~ ! [SY1011: $i] :
( ~ ( element @ SY1011 @ SV160 )
| ( v1_xreal_0 @ SY1011 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1696]) ).
thf(1957,plain,
( ( ! [SX0: $i] :
( ~ ( latt_str @ SX0 )
| ( join_semilatt_str @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1697]) ).
thf(1958,plain,
( ( ! [SX0: $i] :
( ~ ( latt_str @ SX0 )
| ( meet_semilatt_str @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1698]) ).
thf(1959,plain,
( ( relation @ sK53_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1699]) ).
thf(1960,plain,
( ( relation_empty_yielding @ sK53_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1700]) ).
thf(1961,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK93_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK93_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1701]) ).
thf(1962,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK91_C @ SX1 @ SX0 ) @ ( sK92_SY735 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1702]) ).
thf(1963,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1703]) ).
thf(1964,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1704]) ).
thf(1965,plain,
! [SV161: $i] :
( ( ~ ( relation @ ( sK100_B @ SV161 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1705]) ).
thf(1966,plain,
! [SV161: $i] :
( ( ~ ( well_orders @ ( sK100_B @ SV161 ) @ SV161 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1705]) ).
thf(1967,plain,
! [SV162: $i,SV269: $i] :
( ( ( ~ ( element @ SV269 @ ( powerset @ SV162 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1162: $i] :
( ~ ( element @ SY1162 @ ( powerset @ SV162 ) )
| ~ ( disjoint @ SV269 @ SY1162 )
| ( subset @ SV269 @ ( subset_complement @ SV162 @ SY1162 ) ) )
| ~ ! [SY1163: $i] :
( ~ ( element @ SY1163 @ ( powerset @ SV162 ) )
| ~ ( subset @ SV269 @ ( subset_complement @ SV162 @ SY1163 ) )
| ( disjoint @ SV269 @ SY1163 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1706]) ).
thf(1968,plain,
( ( one_sorted_str @ sK117_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1707]) ).
thf(1969,plain,
( ( ~ ( empty_carrier @ sK117_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1708]) ).
thf(1970,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1709]) ).
thf(1971,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1710]) ).
thf(1972,plain,
! [SV163: $i] :
( ( ~ ! [SY1015: $i,SY1016: $i] :
( ~ ( relation_of2 @ SY1016 @ SV163 @ SY1015 )
| ( relation_of2_as_subset @ SY1016 @ SV163 @ SY1015 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1711]) ).
thf(1973,plain,
! [SV163: $i] :
( ( ~ ! [SY1017: $i,SY1018: $i] :
( ~ ( relation_of2_as_subset @ SY1018 @ SV163 @ SY1017 )
| ( relation_of2 @ SY1018 @ SV163 @ SY1017 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1711]) ).
thf(1974,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK87_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK87_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK87_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK87_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1712]) ).
thf(1975,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1713]) ).
thf(1976,plain,
! [SV164: $i] :
( ( ~ ! [SY1019: $i,SY1020: $i] :
( ~ ( ~ ( ! [SY1021: $i,SY1022: $i] :
( ~ ( in @ SY1021 @ SV164 )
| ~ ( in @ SY1022 @ SY1019 )
| ( ( sK78_D @ SY1020 @ SY1019 @ SV164 )
!= ( ordered_pair @ SY1021 @ SY1022 ) ) )
| ~ ( in @ ( sK78_D @ SY1020 @ SY1019 @ SV164 ) @ SY1020 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK79_SY729 @ SY1020 @ SY1019 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK80_SY731 @ SY1020 @ SY1019 @ SV164 ) @ SY1019 ) )
| ( ( sK78_D @ SY1020 @ SY1019 @ SV164 )
!= ( ordered_pair @ ( sK79_SY729 @ SY1020 @ SY1019 @ SV164 ) @ ( sK80_SY731 @ SY1020 @ SY1019 @ SV164 ) ) ) )
| ( in @ ( sK78_D @ SY1020 @ SY1019 @ SV164 ) @ SY1020 ) ) )
| ( SY1020
= ( cartesian_product2 @ SV164 @ SY1019 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1714]) ).
thf(1977,plain,
! [SV164: $i] :
( ( ~ ! [SY1023: $i,SY1024: $i] :
( ( SY1024
!= ( cartesian_product2 @ SV164 @ SY1023 ) )
| ~ ( ~ ! [SY1025: $i] :
( ! [SY1026: $i,SY1027: $i] :
( ~ ( in @ SY1026 @ SV164 )
| ~ ( in @ SY1027 @ SY1023 )
| ( SY1025
!= ( ordered_pair @ SY1026 @ SY1027 ) ) )
| ( in @ SY1025 @ SY1024 ) )
| ~ ! [SY1028: $i] :
( ~ ( in @ SY1028 @ SY1024 )
| ~ ( ~ ~ ( ~ ( in @ ( sK76_E @ SY1028 @ SY1024 @ SY1023 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK77_SY726 @ SY1028 @ SY1024 @ SY1023 @ SV164 ) @ SY1023 ) )
| ( SY1028
!= ( ordered_pair @ ( sK76_E @ SY1028 @ SY1024 @ SY1023 @ SV164 ) @ ( sK77_SY726 @ SY1028 @ SY1024 @ SY1023 @ SV164 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1714]) ).
thf(1978,plain,
( ( empty @ sK59_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1715]) ).
thf(1979,plain,
( ( relation @ sK59_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1716]) ).
thf(1980,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK71_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK71_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1717]) ).
thf(1981,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1718]) ).
thf(1982,plain,
! [SV165: $i] :
( ( ~ ! [SY1029: $i,SY1030: $i] :
( ~ ( relation_of2 @ SY1030 @ SV165 @ SY1029 )
| ( subset @ SY1030 @ ( cartesian_product2 @ SV165 @ SY1029 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1719]) ).
thf(1983,plain,
! [SV165: $i] :
( ( ~ ! [SY1031: $i,SY1032: $i] :
( ~ ( subset @ SY1032 @ ( cartesian_product2 @ SV165 @ SY1031 ) )
| ( relation_of2 @ SY1032 @ SV165 @ SY1031 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1719]) ).
thf(1984,plain,
! [SV166: $i] :
( ( ~ ! [SY1033: $i] :
( ~ ( subset @ SY1033 @ ( sK3_B @ SV166 ) )
| ( are_equipotent @ SY1033 @ ( sK3_B @ SV166 ) )
| ( in @ SY1033 @ ( sK3_B @ SV166 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1720]) ).
thf(1985,plain,
! [SV166: $i] :
( ( ~ ~ ( ~ ! [SY1034: $i] :
( ~ ( ~ ! [SY1035: $i] :
( ~ ( subset @ SY1035 @ SY1034 )
| ( in @ SY1035 @ ( sK4_SY591 @ SY1034 @ SV166 ) ) )
| ~ ( in @ ( sK4_SY591 @ SY1034 @ SV166 ) @ ( sK3_B @ SV166 ) ) )
| ~ ( in @ SY1034 @ ( sK3_B @ SV166 ) ) )
| ~ ~ ( ~ ! [SY1036: $i,SY1037: $i] :
( ~ ( in @ SY1036 @ ( sK3_B @ SV166 ) )
| ~ ( subset @ SY1037 @ SY1036 )
| ( in @ SY1037 @ ( sK3_B @ SV166 ) ) )
| ~ ( in @ SV166 @ ( sK3_B @ SV166 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1720]) ).
thf(1986,plain,
! [SV167: $i] :
( ( ~ ! [SY1038: $i,SY1039: $i] :
( ~ ( relation_of2_as_subset @ SY1039 @ SY1038 @ SV167 )
| ~ ( ~ ! [SY1040: $i] :
~ ( in @ ( ordered_pair @ ( sK104_D @ SY1039 @ SY1038 @ SV167 ) @ SY1040 ) @ SY1039 )
| ~ ( in @ ( sK104_D @ SY1039 @ SY1038 @ SV167 ) @ SY1038 ) )
| ( ( relation_dom_as_subset @ SY1038 @ SV167 @ SY1039 )
= SY1038 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1721]) ).
thf(1987,plain,
! [SV167: $i] :
( ( ~ ! [SY1041: $i,SY1042: $i] :
( ~ ( relation_of2_as_subset @ SY1042 @ SY1041 @ SV167 )
| ( ( relation_dom_as_subset @ SY1041 @ SV167 @ SY1042 )
!= SY1041 )
| ! [SY1043: $i] :
( ( in @ ( ordered_pair @ SY1043 @ ( sK103_E @ SY1043 @ SY1042 @ SY1041 @ SV167 ) ) @ SY1042 )
| ~ ( in @ SY1043 @ SY1041 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1721]) ).
thf(1988,plain,
! [SV168: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK27_SY634 @ SV168 )
!= ( singleton @ ( sK26_B @ SV168 ) ) )
| ~ ( in @ ( sK26_B @ SV168 ) @ SV168 ) )
| ~ ( in @ ( sK26_B @ SV168 ) @ SV168 ) )
| ( ( sK28_SY636 @ SV168 )
!= ( singleton @ ( sK26_B @ SV168 ) ) ) )
| ~ ( ( ( sK27_SY634 @ SV168 )
!= ( sK28_SY636 @ SV168 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) )
| ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1722]) ).
thf(1989,plain,
( ( function @ sK60_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1723]) ).
thf(1990,plain,
( ( relation @ sK60_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1724]) ).
thf(1991,plain,
( ( ~ ( ~ ( empty @ sK57_A )
| ~ ( relation @ sK57_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1725]) ).
thf(1992,plain,
( ( function @ sK57_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1726]) ).
thf(1993,plain,
! [SV270: $i,SV169: $i] :
( ( ~ ! [SY1164: $i,SY1165: $i] :
( ~ ( in @ SV169 @ SY1164 )
| ~ ( in @ SV270 @ SY1165 )
| ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SY1164 @ SY1165 ) ) )
| ~ ~ ( ~ ! [SY1166: $i] :
( ! [SY1167: $i] :
~ ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SY1166 @ SY1167 ) )
| ( in @ SV169 @ SY1166 ) )
| ~ ! [SY1168: $i,SY1169: $i] :
( ~ ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SY1168 @ SY1169 ) )
| ( in @ SV270 @ SY1169 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1727]) ).
thf(1994,plain,
! [SV271: $i,SV170: $i] :
( ( ( ( empty @ SV170 )
| ~ ( relation @ SV271 ) )
= $true )
| ( ( ! [SY1170: $i] :
~ ( ~ ! [SY1171: $i] :
( ! [SY1172: $i,SY1173: $i] :
( ( ( ordered_pair @ SY1172 @ SY1173 )
!= SY1171 )
| ~ ( in @ SY1172 @ SV170 )
| ! [SY1174: $i] :
( ~ ( ~ ( in @ ( sK115_I @ SY1174 @ SY1173 @ SY1172 @ SY1171 @ SY1170 @ SV271 @ SV170 ) @ SY1174 )
| ~ ~ ( in @ ( ordered_pair @ SY1173 @ ( sK115_I @ SY1174 @ SY1173 @ SY1172 @ SY1171 @ SY1170 @ SV271 @ SV170 ) ) @ SV271 ) )
| ( SY1172 != SY1174 )
| ~ ( in @ SY1173 @ SY1174 ) ) )
| ~ ( in @ SY1171 @ ( cartesian_product2 @ SV170 @ SY1170 ) )
| ( in @ SY1171 @ ( sK111_D @ SY1170 @ SV271 @ SV170 ) ) )
| ~ ~ ( ~ ! [SY1175: $i] :
( ~ ( in @ SY1175 @ ( sK111_D @ SY1170 @ SV271 @ SV170 ) )
| ~ ( ~ ~ ( ( ( ordered_pair @ ( sK112_F @ SY1175 @ SY1170 @ SV271 @ SV170 ) @ ( sK113_SY768 @ SY1175 @ SY1170 @ SV271 @ SV170 ) )
!= SY1175 )
| ~ ( in @ ( sK112_F @ SY1175 @ SY1170 @ SV271 @ SV170 ) @ SV170 ) )
| ~ ~ ( ~ ! [SY1176: $i] :
( ~ ( in @ SY1176 @ ( sK114_SY771 @ SY1175 @ SY1170 @ SV271 @ SV170 ) )
| ( in @ ( ordered_pair @ ( sK113_SY768 @ SY1175 @ SY1170 @ SV271 @ SV170 ) @ SY1176 ) @ SV271 ) )
| ~ ~ ( ( ( sK112_F @ SY1175 @ SY1170 @ SV271 @ SV170 )
!= ( sK114_SY771 @ SY1175 @ SY1170 @ SV271 @ SV170 ) )
| ~ ( in @ ( sK113_SY768 @ SY1175 @ SY1170 @ SV271 @ SV170 ) @ ( sK114_SY771 @ SY1175 @ SY1170 @ SV271 @ SV170 ) ) ) ) ) )
| ~ ! [SY1177: $i] :
( ~ ( in @ SY1177 @ ( sK111_D @ SY1170 @ SV271 @ SV170 ) )
| ( in @ SY1177 @ ( cartesian_product2 @ SV170 @ SY1170 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1728]) ).
thf(1995,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( ( ( sK74_B @ SX0 )
!= ( sK75_SY725 @ SX0 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK74_B @ SX0 ) @ SX0 )
| ~ ( in @ ( sK75_SY725 @ SX0 ) @ SX0 ) )
| ~ ~ ( in @ ( sK74_B @ SX0 ) @ ( sK75_SY725 @ SX0 ) ) ) )
| ~ ~ ( in @ ( sK75_SY725 @ SX0 ) @ ( sK74_B @ SX0 ) ) )
| ( epsilon_connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1729]) ).
thf(1996,plain,
( ( ! [SX0: $i] :
( ~ ( epsilon_connected @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( SX1 = SX2 )
| ~ ( in @ SX1 @ SX0 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ SX2 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1730]) ).
thf(1997,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_difference @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_difference @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1731]) ).
thf(1998,plain,
( ( ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v3_membered @ ( set_difference @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1732]) ).
thf(1999,plain,
! [SV171: $i] :
( ( ( relation @ SV171 )
= $false )
| ( ( ~ ( ~ ! [SY1063: $i] :
( ~ ( relation @ SY1063 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK83_C @ SY1063 @ SV171 ) @ ( sK84_SY732 @ SY1063 @ SV171 ) ) @ SV171 )
| ~ ( in @ ( ordered_pair @ ( sK83_C @ SY1063 @ SV171 ) @ ( sK84_SY732 @ SY1063 @ SV171 ) ) @ SY1063 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK83_C @ SY1063 @ SV171 ) @ ( sK84_SY732 @ SY1063 @ SV171 ) ) @ SV171 )
| ( in @ ( ordered_pair @ ( sK83_C @ SY1063 @ SV171 ) @ ( sK84_SY732 @ SY1063 @ SV171 ) ) @ SY1063 ) ) )
| ( SV171 = SY1063 ) )
| ~ ! [SY1064: $i] :
( ~ ( relation @ SY1064 )
| ( SV171 != SY1064 )
| ~ ( ~ ! [SY1065: $i,SY1066: $i] :
( ~ ( in @ ( ordered_pair @ SY1065 @ SY1066 ) @ SV171 )
| ( in @ ( ordered_pair @ SY1065 @ SY1066 ) @ SY1064 ) )
| ~ ! [SY1067: $i,SY1068: $i] :
( ~ ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SY1064 )
| ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SV171 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1733]) ).
thf(2000,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1734]) ).
thf(2001,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1735]) ).
thf(2002,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK98_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK98_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1736]) ).
thf(2003,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1737]) ).
thf(2004,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1738]) ).
thf(2005,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1739]) ).
thf(2006,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK97_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1740]) ).
thf(2007,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1741]) ).
thf(2008,plain,
( ( ! [SX0: $i] :
~ ( empty @ ( singleton @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1742]) ).
thf(2009,plain,
( ( ! [SX0: $i] : ( finite @ ( singleton @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1743]) ).
thf(2010,plain,
! [SV272: $i,SV172: $i] :
( ( ( ( empty @ SV172 )
| ~ ( relation @ SV272 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK35_D @ SV272 @ SV172 )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1178: $i] :
( ~ ( in @ SY1178 @ ( sK43_SY691 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SY1178 ) @ SV272 ) )
| ~ ~ ( ( ( sK41_SY666 @ SV272 @ SV172 )
!= ( sK43_SY691 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) ) ) ) ) )
| ( ( sK35_D @ SV272 @ SV172 )
!= ( sK37_SY665 @ SV272 @ SV172 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
!= ( sK37_SY665 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1179: $i] :
( ~ ( in @ SY1179 @ ( sK40_SY685 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SY1179 ) @ SV272 ) )
| ~ ~ ( ( ( sK38_SY678 @ SV272 @ SV172 )
!= ( sK40_SY685 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) ) ) ) ) )
| ~ ( ( ( sK36_SY655 @ SV272 @ SV172 )
!= ( sK37_SY665 @ SV272 @ SV172 ) ) ) )
| ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1744]) ).
thf(2011,plain,
( ( ! [SX0: $i] :
( ( SX0
!= ( union @ SX0 ) )
| ( being_limit_ordinal @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1745]) ).
thf(2012,plain,
( ( ! [SX0: $i] :
( ~ ( being_limit_ordinal @ SX0 )
| ( SX0
= ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1746]) ).
thf(2013,plain,
( ( ! [SX0: $i] :
( ~ ( v2_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_intersection2 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1747]) ).
thf(2014,plain,
( ( ! [SX0: $i] :
( ~ ( v2_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_intersection2 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1748]) ).
thf(2015,plain,
! [SV273: $i,SV173: $i] :
( ( ~ ! [SY1188: $i,SY1189: $i] :
( ~ ( in @ SV173 @ SY1188 )
| ~ ( in @ SV273 @ SY1189 )
| ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SY1188 @ SY1189 ) ) )
| ~ ~ ( ~ ! [SY1190: $i] :
( ! [SY1191: $i] :
~ ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SY1190 @ SY1191 ) )
| ( in @ SV173 @ SY1190 ) )
| ~ ! [SY1192: $i,SY1193: $i] :
( ~ ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SY1192 @ SY1193 ) )
| ( in @ SV273 @ SY1193 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1749]) ).
thf(2016,plain,
! [SV174: $i,SV274: $i] :
( ( ~ ~ ( ~ ( relation @ ( sK56_C @ SV274 @ SV174 ) )
| ~ ( relation_of2 @ ( sK56_C @ SV274 @ SV174 ) @ SV174 @ SV274 ) )
| ~ ( function @ ( sK56_C @ SV274 @ SV174 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1750]) ).
thf(2017,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1751]) ).
thf(2018,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1752]) ).
thf(2019,plain,
( ( ! [SX0: $i] :
( ~ ( v2_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_difference @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1753]) ).
thf(2020,plain,
( ( ! [SX0: $i] :
( ~ ( v2_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_difference @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1754]) ).
thf(2021,plain,
! [SV175: $i] :
( ( ~ ( element @ ( sK119_B @ SV175 ) @ ( powerset @ SV175 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1755]) ).
thf(2022,plain,
! [SV175: $i] :
( ( ~ ( empty @ ( sK119_B @ SV175 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1755]) ).
thf(2023,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_intersection2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1756]) ).
thf(2024,plain,
( ( ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v3_membered @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1757]) ).
thf(2025,plain,
( ( ~ ( empty @ sK61_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1758]) ).
thf(2026,plain,
( ( finite @ sK61_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1759]) ).
thf(2027,plain,
( ( ! [SX0: $i] :
( ~ ( v2_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1760]) ).
thf(2028,plain,
( ( ! [SX0: $i] :
( ~ ( v2_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1761]) ).
thf(2029,plain,
( ( ~ ( empty @ sK55_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1762]) ).
thf(2030,plain,
( ( relation @ sK55_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1763]) ).
thf(2031,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1764]) ).
thf(2032,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1765]) ).
thf(2033,plain,
! [SV275: $i,SV176: $i] :
( ( ~ ! [SY1194: $i] :
( ! [SY1090: $i,SY1091: $i] :
( ( ( ordered_pair @ SY1090 @ SY1091 )
!= SY1194 )
| ~ ( in @ SY1090 @ SV176 )
| ( SY1091
!= ( singleton @ SY1090 ) ) )
| ~ ( in @ SY1194 @ ( cartesian_product2 @ SV176 @ SV275 ) )
| ( in @ SY1194 @ ( sK108_C @ SV275 @ SV176 ) ) )
| ~ ~ ( ~ ! [SY1197: $i] :
( ~ ( in @ SY1197 @ ( sK108_C @ SV275 @ SV176 ) )
| ~ ( ~ ~ ( ( ( ordered_pair @ ( sK109_E @ SY1197 @ SV275 @ SV176 ) @ ( sK110_SY756 @ SY1197 @ SV275 @ SV176 ) )
!= SY1197 )
| ~ ( in @ ( sK109_E @ SY1197 @ SV275 @ SV176 ) @ SV176 ) )
| ( ( sK110_SY756 @ SY1197 @ SV275 @ SV176 )
!= ( singleton @ ( sK109_E @ SY1197 @ SV275 @ SV176 ) ) ) ) )
| ~ ! [SY1198: $i] :
( ~ ( in @ SY1198 @ ( sK108_C @ SV275 @ SV176 ) )
| ( in @ SY1198 @ ( cartesian_product2 @ SV176 @ SV275 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1766]) ).
thf(2034,plain,
! [SV177: $i,SV276: $i] :
( ( ( ~ ( ~ ( in @ ( sK125_C @ SV276 @ SV177 ) @ SV177 )
| ~ ~ ( in @ ( sK125_C @ SV276 @ SV177 ) @ SV276 ) ) )
= $true )
| ( ( element @ SV177 @ ( powerset @ SV276 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1767]) ).
thf(2035,plain,
! [SV178: $i,SV277: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK6_C @ SV277 @ SV178 ) @ SV178 )
| ~ ( in @ ( sK6_C @ SV277 @ SV178 ) @ SV277 ) )
| ~ ( ( in @ ( sK6_C @ SV277 @ SV178 ) @ SV178 )
| ( in @ ( sK6_C @ SV277 @ SV178 ) @ SV277 ) ) ) )
= $true )
| ( ( SV178 = SV277 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1768]) ).
thf(2036,plain,
! [SV179: $i] :
( ( ~ ! [SY1096: $i] :
( ~ ( subset @ SV179 @ SY1096 )
| ! [SY1097: $i] : ( subset @ ( cartesian_product2 @ SV179 @ SY1097 ) @ ( cartesian_product2 @ SY1096 @ SY1097 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1769]) ).
thf(2037,plain,
! [SV179: $i] :
( ( ~ ! [SY1098: $i] :
( ~ ( subset @ SV179 @ SY1098 )
| ! [SY1099: $i] : ( subset @ ( cartesian_product2 @ SY1099 @ SV179 ) @ ( cartesian_product2 @ SY1099 @ SY1098 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1769]) ).
thf(2038,plain,
! [SV180: $i] :
( ( ~ ! [SY1100: $i,SY1101: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK81_D @ SY1101 @ SY1100 @ SV180 ) @ SY1101 )
| ~ ( in @ ( sK81_D @ SY1101 @ SY1100 @ SV180 ) @ SV180 ) )
| ~ ( ~ ( in @ ( sK81_D @ SY1101 @ SY1100 @ SV180 ) @ SY1101 )
| ~ ( in @ ( sK81_D @ SY1101 @ SY1100 @ SV180 ) @ SY1100 ) ) )
| ~ ( ( in @ ( sK81_D @ SY1101 @ SY1100 @ SV180 ) @ SY1101 )
| ( in @ ( sK81_D @ SY1101 @ SY1100 @ SV180 ) @ SV180 )
| ( in @ ( sK81_D @ SY1101 @ SY1100 @ SV180 ) @ SY1100 ) ) )
| ( SY1101
= ( set_union2 @ SV180 @ SY1100 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1770]) ).
thf(2039,plain,
! [SV180: $i] :
( ( ~ ! [SY1102: $i,SY1103: $i] :
( ( SY1103
!= ( set_union2 @ SV180 @ SY1102 ) )
| ~ ( ~ ! [SY1104: $i] :
( ~ ( in @ SY1104 @ SY1103 )
| ( in @ SY1104 @ SV180 )
| ( in @ SY1104 @ SY1102 ) )
| ~ ~ ( ~ ! [SY1105: $i] :
( ~ ( in @ SY1105 @ SV180 )
| ( in @ SY1105 @ SY1103 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1102 )
| ( in @ SX3 @ SY1103 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1770]) ).
thf(2040,plain,
! [SV181: $i] :
( ( ( ~ ( element @ ( sK120_B @ SV181 ) @ ( powerset @ SV181 ) )
| ~ ~ ( empty @ ( sK120_B @ SV181 ) ) )
= $false )
| ( ( empty @ SV181 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1771]) ).
thf(2041,plain,
! [SV1: $i,SV182: $i] :
( ( ( element @ SV182 @ ( powerset @ SV1 ) )
= $false )
| ( ( ! [SY1107: $i] :
( ~ ( in @ SY1107 @ SV182 )
| ( in @ SY1107 @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1772]) ).
thf(2042,plain,
! [SV3: $i,SV308: $i] :
( ( ( ~ ( element @ SV308 @ ( powerset @ ( the_carrier @ SV3 ) ) )
| ( ( subset_intersection2 @ ( the_carrier @ SV3 ) @ SV308 @ ( cast_as_carrier_subset @ SV3 ) )
= SV308 ) )
= $true )
| ( ( one_sorted_str @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1774]) ).
thf(2043,plain,
! [SV4: $i,SV183: $i] :
( ( ( element @ SV183 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( ( SV183 = empty_set )
| ( ( complements_of_subsets @ SV4 @ SV183 )
!= empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1775]) ).
thf(2044,plain,
! [SV5: $i,SV278: $i] :
( ( ( ~ ( element @ SV278 @ ( powerset @ SV5 ) ) )
= $true )
| ( ( ! [SY1199: $i] :
( ~ ( element @ SY1199 @ SV5 )
| ( in @ SY1199 @ SV278 )
| ( in @ SY1199 @ ( subset_complement @ SV5 @ SV278 ) ) ) )
= $true )
| ( ( SV5 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1776]) ).
thf(2045,plain,
! [SV184: $i,SV6: $i,SV279: $i] :
( ( ( ~ ( element @ SV279 @ ( powerset @ SV6 ) ) )
= $true )
| ( ( ~ ( in @ SV184 @ ( subset_complement @ SV6 @ SV279 ) )
| ~ ( in @ SV184 @ SV279 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1777]) ).
thf(2046,plain,
! [SV8: $i,SV309: $i] :
( ( ( ~ ( element @ SV309 @ SV8 )
| ( v1_xcmplx_0 @ SV309 ) )
= $true )
| ( ( v1_membered @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1778]) ).
thf(2047,plain,
! [SV9: $i,SV310: $i] :
( ( ( ~ ( element @ SV310 @ ( powerset @ SV9 ) )
| ( v1_membered @ SV310 ) )
= $true )
| ( ( v1_membered @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1779]) ).
thf(2048,plain,
! [SV185: $i,SV10: $i,SV280: $i] :
( ( ( ~ ( element @ SV280 @ ( powerset @ ( cartesian_product2 @ SV10 @ SV185 ) ) ) )
= $true )
| ( ( relation @ SV280 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1780]) ).
thf(2049,plain,
! [SV11: $i,SV311: $i] :
( ( ( ~ ( element @ SV311 @ ( powerset @ SV11 ) )
| ( finite @ SV311 ) )
= $true )
| ( ( finite @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1781]) ).
thf(2050,plain,
! [SV281: $i,SV12: $i,SV186: $i] :
( ( ( ~ ( element @ SV186 @ ( powerset @ SV12 ) )
| ~ ( element @ SV281 @ ( powerset @ SV12 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV12 @ SV186 @ SV281 )
= ( subset_intersection2 @ SV12 @ SV281 @ SV186 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1782]) ).
thf(2051,plain,
! [SV14: $i,SV187: $i] :
( ( ( element @ SV187 @ ( powerset @ SV14 ) )
= $false )
| ( ( ( subset_complement @ SV14 @ SV187 )
= ( set_difference @ SV14 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1784]) ).
thf(2052,plain,
! [SV17: $i,SV188: $i] :
( ( ( element @ SV188 @ ( powerset @ SV17 ) )
= $false )
| ( ( element @ ( subset_complement @ SV17 @ SV188 ) @ ( powerset @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1786]) ).
thf(2053,plain,
! [SV189: $i,SV18: $i,SV282: $i] :
( ( ( ~ ( relation_of2 @ SV282 @ SV18 @ SV189 ) )
= $true )
| ( ( element @ ( relation_dom_as_subset @ SV18 @ SV189 @ SV282 ) @ ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1787]) ).
thf(2054,plain,
! [SV190: $i,SV19: $i,SV283: $i] :
( ( ( ~ ( relation_of2 @ SV283 @ SV19 @ SV190 ) )
= $true )
| ( ( element @ ( relation_rng_as_subset @ SV19 @ SV190 @ SV283 ) @ ( powerset @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1788]) ).
thf(2055,plain,
! [SV20: $i,SV191: $i] :
( ( ( element @ SV191 @ ( powerset @ ( powerset @ SV20 ) ) )
= $false )
| ( ( element @ ( union_of_subsets @ SV20 @ SV191 ) @ ( powerset @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1789]) ).
thf(2056,plain,
! [SV284: $i,SV21: $i,SV192: $i] :
( ( ( ~ ( element @ SV192 @ ( powerset @ SV21 ) )
| ~ ( element @ SV284 @ ( powerset @ SV21 ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV21 @ SV192 @ SV284 ) @ ( powerset @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1790]) ).
thf(2057,plain,
! [SV22: $i,SV193: $i] :
( ( ( element @ SV193 @ ( powerset @ ( powerset @ SV22 ) ) )
= $false )
| ( ( element @ ( meet_of_subsets @ SV22 @ SV193 ) @ ( powerset @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1791]) ).
thf(2058,plain,
! [SV285: $i,SV23: $i,SV194: $i] :
( ( ( ~ ( element @ SV194 @ ( powerset @ SV23 ) )
| ~ ( element @ SV285 @ ( powerset @ SV23 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV23 @ SV194 @ SV285 ) @ ( powerset @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1792]) ).
thf(2059,plain,
! [SV24: $i,SV195: $i] :
( ( ( element @ SV195 @ ( powerset @ ( powerset @ SV24 ) ) )
= $false )
| ( ( element @ ( complements_of_subsets @ SV24 @ SV195 ) @ ( powerset @ ( powerset @ SV24 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1793]) ).
thf(2060,plain,
! [SV196: $i,SV27: $i,SV286: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV286 @ SV27 @ SV196 ) )
= $true )
| ( ( element @ SV286 @ ( powerset @ ( cartesian_product2 @ SV27 @ SV196 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1796]) ).
thf(2061,plain,
! [SV29: $i] :
( ( ( one_sorted_str @ SV29 )
= $false )
| ( ( empty_carrier @ SV29 )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1797]) ).
thf(2062,plain,
! [SV31: $i,SV197: $i] :
( ( ( ~ ( element @ SV197 @ ( powerset @ SV31 ) ) )
= $true )
| ( ( ! [SY805: $i] :
~ ( element @ SY805 @ ( powerset @ SV31 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV31 @ SV197 @ SV197 )
= SV197 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1798]) ).
thf(2063,plain,
! [SV32: $i,SV198: $i] :
( ( ( element @ SV198 @ ( powerset @ SV32 ) )
= $false )
| ( ( ( subset_complement @ SV32 @ ( subset_complement @ SV32 @ SV198 ) )
= SV198 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1799]) ).
thf(2064,plain,
! [SV33: $i,SV199: $i] :
( ( ( element @ SV199 @ ( powerset @ ( powerset @ SV33 ) ) )
= $false )
| ( ( ( complements_of_subsets @ SV33 @ ( complements_of_subsets @ SV33 @ SV199 ) )
= SV199 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1800]) ).
thf(2065,plain,
! [SV34: $i,SV200: $i] :
( ( ( element @ SV200 @ ( powerset @ ( powerset @ SV34 ) ) )
= $false )
| ( ( ( union_of_subsets @ SV34 @ SV200 )
= ( union @ SV200 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1801]) ).
thf(2066,plain,
! [SV287: $i,SV35: $i,SV201: $i] :
( ( ( ~ ( element @ SV201 @ ( powerset @ SV35 ) )
| ~ ( element @ SV287 @ ( powerset @ SV35 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV35 @ SV201 @ SV287 )
= ( set_intersection2 @ SV201 @ SV287 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1802]) ).
thf(2067,plain,
! [SV36: $i,SV202: $i] :
( ( ( element @ SV202 @ ( powerset @ ( powerset @ SV36 ) ) )
= $false )
| ( ( ( meet_of_subsets @ SV36 @ SV202 )
= ( set_meet @ SV202 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1803]) ).
thf(2068,plain,
! [SV288: $i,SV37: $i,SV203: $i] :
( ( ( ~ ( element @ SV203 @ ( powerset @ SV37 ) )
| ~ ( element @ SV288 @ ( powerset @ SV37 ) ) )
= $true )
| ( ( ( subset_difference @ SV37 @ SV203 @ SV288 )
= ( set_difference @ SV203 @ SV288 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1804]) ).
thf(2069,plain,
! [SV204: $i,SV38: $i] :
( ( ( in @ SV38 @ SV204 )
= $false )
| ( ( element @ SV38 @ SV204 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1805]) ).
thf(2070,plain,
! [SV205: $i,SV39: $i] :
( ( ( element @ SV39 @ SV205 )
= $false )
| ( ( ( empty @ SV205 )
| ( in @ SV39 @ SV205 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1806]) ).
thf(2071,plain,
! [SV40: $i,SV289: $i,SV206: $i] :
( ( ( ~ ( element @ SV206 @ ( powerset @ SV289 ) )
| ~ ( in @ SV40 @ SV206 ) )
= $true )
| ( ( element @ SV40 @ SV289 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1807]) ).
thf(2072,plain,
! [SV41: $i,SV290: $i,SV207: $i] :
( ( ( ~ ( element @ SV207 @ ( powerset @ SV290 ) )
| ~ ( in @ SV41 @ SV207 ) )
= $true )
| ( ( ~ ( empty @ SV290 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1808]) ).
thf(2073,plain,
! [SV208: $i,SV43: $i] :
( ( ( in @ SV43 @ SV208 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV43 ) @ SV208 )
= SV208 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1809]) ).
thf(2074,plain,
! [SV209: $i,SV44: $i] :
( ( ( disjoint @ ( singleton @ SV44 ) @ SV209 )
= $false )
| ( ( ~ ( in @ SV44 @ SV209 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1810]) ).
thf(2075,plain,
! [SV211: $i,SV46: $i] :
( ( ( subset @ SV46 @ SV211 )
= $false )
| ( ( ! [SY1121: $i] :
( ( in @ SY1121 @ SV46 )
| ( subset @ SV46 @ ( set_difference @ SV211 @ ( singleton @ SY1121 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1812]) ).
thf(2076,plain,
! [SV212: $i,SV47: $i] :
( ( ( in @ SV47 @ SV212 )
= $false )
| ( ( subset @ SV47 @ ( union @ SV212 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1813]) ).
thf(2077,plain,
! [SV49: $i,SV213: $i] :
( ( ( relation @ SV213 )
= $false )
| ( ( subset @ ( relation_rng_restriction @ SV49 @ SV213 ) @ SV213 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1814]) ).
thf(2078,plain,
! [SV312: $i,SV291: $i,SV214: $i,SV50: $i] :
( ( ~ ( subset @ SV50 @ SV214 )
| ~ ( subset @ SV291 @ SV312 )
| ( subset @ ( cartesian_product2 @ SV50 @ SV291 ) @ ( cartesian_product2 @ SV214 @ SV312 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1815]) ).
thf(2079,plain,
! [SV215: $i,SV51: $i] :
( ( ( subset @ SV51 @ SV215 )
= $false )
| ( ( ( set_union2 @ SV51 @ SV215 )
= SV215 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1816]) ).
thf(2080,plain,
! [SV52: $i,SV292: $i] :
( ( ( ~ ( finite @ SV292 ) )
= $true )
| ( ( ~ ( subset @ SV52 @ SV292 ) )
= $true )
| ( ( finite @ SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1817]) ).
thf(2081,plain,
! [SV216: $i,SV53: $i,SV293: $i,SV313: $i] :
( ( ~ ( relation_of2_as_subset @ SV313 @ SV293 @ SV53 )
| ~ ( subset @ ( relation_rng @ SV313 ) @ SV216 )
| ( relation_of2_as_subset @ SV313 @ SV293 @ SV216 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1818]) ).
thf(2082,plain,
! [SV314: $i,SV54: $i] :
( ( ( finite @ ( set_intersection2 @ SV54 @ SV314 ) )
= $true )
| ( ( finite @ SV54 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1819]) ).
thf(2083,plain,
! [SV217: $i,SV55: $i,SV294: $i,SV315: $i] :
( ( ~ ( relation_of2_as_subset @ SV315 @ SV294 @ SV55 )
| ~ ( subset @ SV55 @ SV217 )
| ( relation_of2_as_subset @ SV315 @ SV294 @ SV217 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1820]) ).
thf(2084,plain,
! [SV218: $i,SV56: $i,SV295: $i] :
( ( ( ~ ( relation @ SV295 ) )
= $true )
| ( ( ~ ( subset @ SV56 @ SV218 )
| ( subset @ ( relation_inverse_image @ SV295 @ SV56 ) @ ( relation_inverse_image @ SV295 @ SV218 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1821]) ).
thf(2085,plain,
! [SV296: $i,SV220: $i,SV58: $i] :
( ( ( ~ ( subset @ SV58 @ SV220 )
| ~ ( subset @ SV58 @ SV296 ) )
= $true )
| ( ( subset @ SV58 @ ( set_intersection2 @ SV220 @ SV296 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1822]) ).
thf(2086,plain,
! [SV297: $i,SV221: $i,SV59: $i] :
( ( ( ~ ( subset @ SV59 @ SV221 )
| ~ ( subset @ SV221 @ SV297 ) )
= $true )
| ( ( subset @ SV59 @ SV297 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1823]) ).
thf(2087,plain,
! [SV60: $i,SV222: $i] :
( ( ( ordinal @ SV222 )
= $false )
| ( ( ~ ( in @ SV60 @ SV222 )
| ( ordinal @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1824]) ).
thf(2088,plain,
! [SV61: $i,SV316: $i] :
( ( ( ~ ( ordinal @ SV316 )
| ( in @ SV61 @ SV316 )
| ( SV61 = SV316 )
| ( in @ SV316 @ SV61 ) )
= $true )
| ( ( ordinal @ SV61 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1825]) ).
thf(2089,plain,
! [SV223: $i,SV62: $i] :
( ( ( subset @ SV62 @ SV223 )
= $false )
| ( ( ! [SY1131: $i] : ( subset @ ( set_intersection2 @ SV62 @ SY1131 ) @ ( set_intersection2 @ SV223 @ SY1131 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1826]) ).
thf(2090,plain,
! [SV224: $i,SV63: $i] :
( ( ( subset @ SV63 @ SV224 )
= $false )
| ( ( ( set_intersection2 @ SV63 @ SV224 )
= SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1827]) ).
thf(2091,plain,
! [SV225: $i,SV65: $i] :
( ( ( subset @ SV65 @ SV225 )
= $false )
| ( ( ! [SY1132: $i] : ( subset @ ( set_difference @ SV65 @ SY1132 ) @ ( set_difference @ SV225 @ SY1132 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1828]) ).
thf(2092,plain,
! [SV298: $i,SV228: $i,SV68: $i] :
( ( ( ~ ( in @ SV68 @ SV228 )
| ~ ( in @ SV228 @ SV298 ) )
= $true )
| ( ( ~ ( in @ SV298 @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1829]) ).
thf(2093,plain,
! [SV230: $i,SV71: $i] :
( ( ( subset @ SV71 @ SV230 )
= $false )
| ( ( SV230
= ( set_union2 @ SV71 @ ( set_difference @ SV230 @ SV71 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1831]) ).
thf(2094,plain,
! [SV231: $i,SV72: $i] :
( ( ( in @ SV72 @ SV231 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV72 ) @ SV231 )
= SV231 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1832]) ).
thf(2095,plain,
! [SV73: $i,SV232: $i] :
( ( ( element @ SV232 @ ( powerset @ ( powerset @ SV73 ) ) )
= $false )
| ( ( ( SV232 = empty_set )
| ( ( subset_difference @ SV73 @ ( cast_to_subset @ SV73 ) @ ( union_of_subsets @ SV73 @ SV232 ) )
= ( meet_of_subsets @ SV73 @ ( complements_of_subsets @ SV73 @ SV232 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1833]) ).
thf(2096,plain,
! [SV74: $i,SV233: $i] :
( ( ( element @ SV233 @ ( powerset @ ( powerset @ SV74 ) ) )
= $false )
| ( ( ( SV233 = empty_set )
| ( ( union_of_subsets @ SV74 @ ( complements_of_subsets @ SV74 @ SV233 ) )
= ( subset_difference @ SV74 @ ( cast_to_subset @ SV74 ) @ ( meet_of_subsets @ SV74 @ SV233 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1834]) ).
thf(2097,plain,
! [SV76: $i] :
( ( ( in @ ( ordered_pair @ ( sK95_B @ SV76 ) @ ( sK96_SY738 @ SV76 ) ) @ SV76 )
= $true )
| ( ( SV76 = empty_set )
= $true )
| ( ( relation @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1835]) ).
thf(2098,plain,
! [SV77: $i,SV235: $i] :
( ( ( proper_subset @ SV235 @ SV77 )
= $false )
| ( ( ~ ( subset @ SV77 @ SV235 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1836]) ).
thf(2099,plain,
! [SV78: $i,SV299: $i,SV236: $i] :
( ( ( ~ ( disjoint @ SV236 @ SV299 )
| ~ ( subset @ SV78 @ SV236 ) )
= $true )
| ( ( disjoint @ SV78 @ SV299 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1837]) ).
thf(2100,plain,
! [SV237: $i,SV80: $i] :
( ( ( subset @ ( singleton @ SV80 ) @ ( singleton @ SV237 ) )
= $false )
| ( ( SV80 = SV237 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1838]) ).
thf(2101,plain,
! [SV82: $i,SV239: $i] :
( ( ( relation @ SV239 )
= $false )
| ( ( subset @ ( relation_dom_restriction @ SV239 @ SV82 ) @ SV239 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1839]) ).
thf(2102,plain,
! [SV300: $i,SV240: $i,SV83: $i] :
( ( ( ~ ( subset @ SV83 @ SV240 )
| ~ ( subset @ SV300 @ SV240 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV83 @ SV300 ) @ SV240 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1840]) ).
thf(2103,plain,
! [SV317: $i,SV241: $i,SV84: $i] :
( ( ( ( ( singleton @ SV84 )
!= ( unordered_pair @ SV241 @ SV317 ) ) )
= $true )
| ( ( SV84 = SV241 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1841]) ).
thf(2104,plain,
! [SV242: $i,SV85: $i] :
( ( ( in @ SV85 @ SV242 )
= $false )
| ( ( subset @ SV85 @ ( union @ SV242 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1842]) ).
thf(2105,plain,
! [SV301: $i,SV243: $i,SV86: $i] :
( ( ( ( ( singleton @ SV86 )
!= ( unordered_pair @ SV243 @ SV301 ) ) )
= $true )
| ( ( SV243 = SV301 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1843]) ).
thf(2106,plain,
! [SV244: $i,SV87: $i] :
( ( ( in @ SV87 @ SV244 )
= $false )
| ( ( ~ ( in @ SV244 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1844]) ).
thf(2107,plain,
! [SV318: $i,SV95: $i] :
( ( ( ( relation_restriction @ SV95 @ SV318 )
= ( set_intersection2 @ SV95 @ ( cartesian_product2 @ SV318 @ SV318 ) ) )
= $true )
| ( ( relation @ SV95 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1850]) ).
thf(2108,plain,
! [SV302: $i,SV246: $i,SV96: $i] :
( ( ( ( empty_carrier @ SV96 )
| ~ ( join_semilatt_str @ SV96 )
| ~ ( element @ SV246 @ ( the_carrier @ SV96 ) )
| ~ ( element @ SV302 @ ( the_carrier @ SV96 ) ) )
= $true )
| ( ( element @ ( join @ SV96 @ SV246 @ SV302 ) @ ( the_carrier @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1851]) ).
thf(2109,plain,
! [SV303: $i,SV247: $i,SV98: $i] :
( ( ( ( empty_carrier @ SV98 )
| ~ ( meet_semilatt_str @ SV98 )
| ~ ( element @ SV247 @ ( the_carrier @ SV98 ) )
| ~ ( element @ SV303 @ ( the_carrier @ SV98 ) ) )
= $true )
| ( ( element @ ( meet @ SV98 @ SV247 @ SV303 ) @ ( the_carrier @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1852]) ).
thf(2110,plain,
! [SV319: $i,SV99: $i] :
( ( ( relation @ ( relation_restriction @ SV99 @ SV319 ) )
= $true )
| ( ( relation @ SV99 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1853]) ).
thf(2111,plain,
! [SV248: $i,SV101: $i] :
( ( ( ~ ( relation @ SV101 ) )
= $true )
| ( ( ~ ( relation @ SV248 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV101 @ SV248 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1855]) ).
thf(2112,plain,
! [SV320: $i,SV103: $i] :
( ( ( relation @ ( relation_dom_restriction @ SV103 @ SV320 ) )
= $true )
| ( ( relation @ SV103 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1856]) ).
thf(2113,plain,
! [SV104: $i,SV249: $i] :
( ( ( relation @ SV249 )
= $false )
| ( ( relation @ ( relation_rng_restriction @ SV104 @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1857]) ).
thf(2114,plain,
! [SV107: $i,SV252: $i] :
( ( ( finite @ SV252 )
= $false )
| ( ( finite @ ( set_intersection2 @ SV107 @ SV252 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1858]) ).
thf(2115,plain,
! [SV321: $i,SV108: $i] :
( ( ( finite @ ( set_intersection2 @ SV108 @ SV321 ) )
= $true )
| ( ( finite @ SV108 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1859]) ).
thf(2116,plain,
! [SV322: $i,SV109: $i] :
( ( ( finite @ ( set_difference @ SV109 @ SV322 ) )
= $true )
| ( ( finite @ SV109 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1860]) ).
thf(2117,plain,
! [SV253: $i,SV111: $i] :
( ( ( ~ ( relation @ SV111 ) )
= $true )
| ( ( ~ ( relation @ SV253 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV111 @ SV253 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1861]) ).
thf(2118,plain,
! [SV323: $i,SV113: $i] :
( ( ( v1_membered @ ( set_intersection2 @ SV113 @ SV323 ) )
= $true )
| ( ( v1_membered @ SV113 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(2119,plain,
! [SV114: $i,SV324: $i] :
( ( ( v1_membered @ ( set_intersection2 @ SV324 @ SV114 ) )
= $true )
| ( ( v1_membered @ SV114 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1864]) ).
thf(2120,plain,
! [SV255: $i,SV115: $i] :
( ( ( ~ ( relation @ SV115 ) )
= $true )
| ( ( ~ ( relation @ SV255 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV115 @ SV255 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1865]) ).
thf(2121,plain,
! [SV304: $i,SV117: $i] :
( ( ( empty @ ( set_union2 @ SV117 @ SV304 ) )
= $false )
| ( ( empty @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1866]) ).
thf(2122,plain,
! [SV325: $i,SV118: $i] :
( ( ( v1_membered @ ( set_difference @ SV118 @ SV325 ) )
= $true )
| ( ( v1_membered @ SV118 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1867]) ).
thf(2123,plain,
! [SV256: $i,SV119: $i] :
( ( ( ~ ( relation @ SV119 ) )
= $true )
| ( ( ~ ( relation @ SV256 ) )
= $true )
| ( ( relation @ ( set_difference @ SV119 @ SV256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1868]) ).
thf(2124,plain,
! [SV121: $i,SV305: $i] :
( ( ( empty @ ( set_union2 @ SV305 @ SV121 ) )
= $false )
| ( ( empty @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1870]) ).
thf(2125,plain,
! [SV258: $i,SV122: $i] :
( ( ( empty @ SV122 )
= $true )
| ( ( empty @ SV258 )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV122 @ SV258 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1871]) ).
thf(2126,plain,
! [SV123: $i] :
( ( ( relation @ SV123 )
= $false )
| ( ( empty @ SV123 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV123 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1872]) ).
thf(2127,plain,
! [SV124: $i] :
( ( ( relation @ SV124 )
= $false )
| ( ( empty @ SV124 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV124 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1873]) ).
thf(2128,plain,
! [SV259: $i,SV125: $i] :
( ( ( ~ ( finite @ SV125 ) )
= $true )
| ( ( ~ ( finite @ SV259 ) )
= $true )
| ( ( finite @ ( set_union2 @ SV125 @ SV259 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1874]) ).
thf(2129,plain,
! [SV260: $i,SV128: $i,SV306: $i] :
( ( ( ~ ( relation_of2 @ SV306 @ SV128 @ SV260 ) )
= $true )
| ( ( ( relation_dom_as_subset @ SV128 @ SV260 @ SV306 )
= ( relation_dom @ SV306 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1876]) ).
thf(2130,plain,
! [SV261: $i,SV129: $i,SV307: $i] :
( ( ( ~ ( relation_of2 @ SV307 @ SV129 @ SV261 ) )
= $true )
| ( ( ( relation_rng_as_subset @ SV129 @ SV261 @ SV307 )
= ( relation_rng @ SV307 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1877]) ).
thf(2131,plain,
! [SV262: $i,SV131: $i] :
( ( ( disjoint @ SV131 @ SV262 )
= $false )
| ( ( disjoint @ SV262 @ SV131 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1878]) ).
thf(2132,plain,
! [SV137: $i,SV263: $i] :
( ( ( empty @ SV263 )
= $false )
| ( ( ~ ( in @ SV137 @ SV263 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1880]) ).
thf(2133,plain,
! [SV264: $i,SV138: $i] :
( ( ( SV138 = SV264 )
= $true )
| ( ( ~ ( empty @ SV138 ) )
= $true )
| ( ( ~ ( empty @ SV264 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1881]) ).
thf(2134,plain,
! [SV326: $i] :
( ( ! [SY1203: $i] :
( ( SV326 = SY1203 )
| ~ ( subset @ SV326 @ SY1203 )
| ( proper_subset @ SV326 @ SY1203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(2135,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1883]) ).
thf(2136,plain,
! [SV327: $i] :
( ( ! [SY1204: $i] :
( ( ( set_intersection2 @ SV327 @ SY1204 )
!= empty_set )
| ( disjoint @ SV327 @ SY1204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1884]) ).
thf(2137,plain,
! [SV328: $i] :
( ( ! [SY1205: $i] :
( ~ ( disjoint @ SV328 @ SY1205 )
| ( ( set_intersection2 @ SV328 @ SY1205 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(2138,plain,
! [SV139: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK17_C @ SV139 )
!= ( sK18_SY613 @ SV139 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
!= ( sK18_SY613 @ SV139 ) )
| ~ ( in @ ( sK22_SY620 @ SV139 ) @ SV139 ) )
| ( ( sK23_SY629 @ SV139 )
!= ( singleton @ ( sK22_SY620 @ SV139 ) ) ) ) )
| ( ( sK17_C @ SV139 )
!= ( sK19_SY619 @ SV139 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
!= ( sK19_SY619 @ SV139 ) )
| ~ ( in @ ( sK20_SY626 @ SV139 ) @ SV139 ) )
| ( ( sK21_SY628 @ SV139 )
!= ( singleton @ ( sK20_SY626 @ SV139 ) ) ) ) ) )
= $false )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1886]) ).
thf(2139,plain,
! [SV139: $i] :
( ( ( ~ ( ( ( sK18_SY613 @ SV139 )
!= ( sK19_SY619 @ SV139 ) ) ) )
= $false )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1886]) ).
thf(2140,plain,
! [SV140: $i] :
( ( ( one_sorted_str @ SV140 )
= $false )
| ( ( empty_carrier @ SV140 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK116_B @ SV140 ) @ ( powerset @ ( the_carrier @ SV140 ) ) )
| ~ ~ ( empty @ ( sK116_B @ SV140 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1887]) ).
thf(2141,plain,
( ( ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_intersection2 @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_intersection2 @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1888]) ).
thf(2142,plain,
! [SV329: $i] :
( ( ~ ( v3_membered @ SV329 )
| ! [SY1206: $i] : ( v3_membered @ ( set_intersection2 @ SY1206 @ SV329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1889]) ).
thf(2143,plain,
! [SV141: $i] :
( ( ( ~ ( in @ ( sK99_B @ SV141 ) @ SV141 ) )
= $false )
| ( ( ordinal @ SV141 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1890]) ).
thf(2144,plain,
! [SV141: $i] :
( ( ( ~ ( ~ ( ordinal @ ( sK99_B @ SV141 ) )
| ~ ( subset @ ( sK99_B @ SV141 ) @ SV141 ) ) )
= $false )
| ( ( ordinal @ SV141 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1890]) ).
thf(2145,plain,
! [SV142: $i] :
( ( ! [SY917: $i,SY918: $i] :
( ~ ( in @ SV142 @ SY918 )
| ~ ( in @ SY917 @ SY918 )
| ( subset @ ( unordered_pair @ SV142 @ SY917 ) @ SY918 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1891]) ).
thf(2146,plain,
! [SV142: $i] :
( ( ~ ( ~ ! [SY919: $i,SY920: $i] :
( ~ ( subset @ ( unordered_pair @ SV142 @ SY919 ) @ SY920 )
| ( in @ SV142 @ SY920 ) )
| ~ ! [SY921: $i,SY922: $i] :
( ~ ( subset @ ( unordered_pair @ SV142 @ SY921 ) @ SY922 )
| ( in @ SY921 @ SY922 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1892]) ).
thf(2147,plain,
! [SV143: $i] :
( ( ! [SY923: $i,SY924: $i] :
( ~ ( ~ ( ~ ( in @ ( sK70_D @ SY924 @ SY923 @ SV143 ) @ SV143 )
| ~ ( in @ ( sK70_D @ SY924 @ SY923 @ SV143 ) @ SY923 )
| ~ ( in @ ( sK70_D @ SY924 @ SY923 @ SV143 ) @ SY924 ) )
| ~ ~ ( ~ ( ( in @ ( sK70_D @ SY924 @ SY923 @ SV143 ) @ SV143 )
| ( in @ ( sK70_D @ SY924 @ SY923 @ SV143 ) @ SY924 ) )
| ~ ( ( in @ ( sK70_D @ SY924 @ SY923 @ SV143 ) @ SY923 )
| ( in @ ( sK70_D @ SY924 @ SY923 @ SV143 ) @ SY924 ) ) ) )
| ( SY924
= ( set_intersection2 @ SV143 @ SY923 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1893]) ).
thf(2148,plain,
! [SV143: $i] :
( ( ! [SY925: $i,SY926: $i] :
( ( SY926
!= ( set_intersection2 @ SV143 @ SY925 ) )
| ~ ( ~ ! [SY927: $i] :
( ~ ( in @ SY927 @ SV143 )
| ~ ( in @ SY927 @ SY925 )
| ( in @ SY927 @ SY926 ) )
| ~ ~ ( ~ ! [SY928: $i] :
( ~ ( in @ SY928 @ SY926 )
| ( in @ SY928 @ SV143 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY926 )
| ( in @ SX3 @ SY925 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1894]) ).
thf(2149,plain,
! [SV144: $i] :
( ( ( ~ ~ ( ~ ! [SY930: $i] :
( ~ ( element @ SY930 @ ( powerset @ SV144 ) )
| ( v1_membered @ SY930 ) )
| ~ ! [SY931: $i] :
( ~ ( element @ SY931 @ ( powerset @ SV144 ) )
| ( v2_membered @ SY931 ) ) )
| ~ ! [SY932: $i] :
( ~ ( element @ SY932 @ ( powerset @ SV144 ) )
| ( v3_membered @ SY932 ) ) )
= $false )
| ( ( v3_membered @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1895]) ).
thf(2150,plain,
! [SV265: $i,SV145: $i] :
( ( ( empty @ SV145 )
= $true )
| ( ( ~ ( relation @ SV265 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1142: $i] :
( ~ ( in @ SY1142 @ ( sK52_SY712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SY1142 ) @ SV265 ) )
| ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK52_SY712 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) ) ) )
| ~ ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 ) )
| ~ ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 ) )
| ~ ~ ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ ( sK51_SY718 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SY1143 ) @ SV265 ) )
| ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK51_SY718 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) ) ) ) )
| ~ ( ( ( sK49_SY705 @ SV265 @ SV145 )
!= ( sK50_SY711 @ SV265 @ SV145 ) ) ) )
| ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1896]) ).
thf(2151,plain,
! [SV330: $i] :
( ( ! [SY1207: $i] :
( ~ ( subset @ SV330 @ SY1207 )
| ~ ( subset @ SY1207 @ SV330 )
| ( SV330 = SY1207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1897]) ).
thf(2152,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1898]) ).
thf(2153,plain,
! [SV146: $i,SV266: $i] :
( ( ( ~ ! [SY1149: $i] :
( ~ ( in @ SY1149 @ SV266 )
| ~ ( in @ SY1149 @ ( sK5_C @ SV266 @ SV146 ) ) )
| ~ ( in @ ( sK5_C @ SV266 @ SV146 ) @ SV266 ) )
= $false )
| ( ( ~ ( in @ SV146 @ SV266 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1899]) ).
thf(2154,plain,
! [SV331: $i] :
( ( ~ ( ~ ( in @ ( sK85_B @ SV331 ) @ SV331 )
| ~ ~ ( subset @ ( sK85_B @ SV331 ) @ SV331 ) )
| ( epsilon_transitive @ SV331 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1900]) ).
thf(2155,plain,
! [SV332: $i] :
( ( ~ ( epsilon_transitive @ SV332 )
| ! [SY1208: $i] :
( ~ ( in @ SY1208 @ SV332 )
| ( subset @ SY1208 @ SV332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1901]) ).
thf(2156,plain,
! [SV147: $i] :
( ( ! [SY943: $i,SY944: $i] :
( ~ ( ~ ( ~ ( in @ ( sK66_D @ SY944 @ SY943 @ SV147 ) @ SV147 )
| ( in @ ( sK66_D @ SY944 @ SY943 @ SV147 ) @ SY943 )
| ~ ( in @ ( sK66_D @ SY944 @ SY943 @ SV147 ) @ SY944 ) )
| ~ ~ ( ~ ( ( in @ ( sK66_D @ SY944 @ SY943 @ SV147 ) @ SV147 )
| ( in @ ( sK66_D @ SY944 @ SY943 @ SV147 ) @ SY944 ) )
| ~ ( ~ ( in @ ( sK66_D @ SY944 @ SY943 @ SV147 ) @ SY943 )
| ( in @ ( sK66_D @ SY944 @ SY943 @ SV147 ) @ SY944 ) ) ) )
| ( SY944
= ( set_difference @ SV147 @ SY943 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1902]) ).
thf(2157,plain,
! [SV147: $i] :
( ( ! [SY945: $i,SY946: $i] :
( ( SY946
!= ( set_difference @ SV147 @ SY945 ) )
| ~ ( ~ ! [SY947: $i] :
( ~ ( in @ SY947 @ SV147 )
| ( in @ SY947 @ SY945 )
| ( in @ SY947 @ SY946 ) )
| ~ ~ ( ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ SY946 )
| ( in @ SY948 @ SV147 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY946 )
| ~ ( in @ SX3 @ SY945 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1903]) ).
thf(2158,plain,
! [SV333: $i] :
( ( ( in @ ( sK86_B @ SV333 ) @ SV333 )
| ( SV333 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1904]) ).
thf(2159,plain,
! [SV334: $i] :
( ( ( SV334 != empty_set )
| ! [SY1209: $i] :
~ ( in @ SY1209 @ SV334 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1905]) ).
thf(2160,plain,
! [SV148: $i,SV335: $i] :
( ( ( ~ ( element @ SV335 @ ( powerset @ ( powerset @ SV148 ) ) )
| ~ ( ~ ! [SY1210: $i] :
( ~ ( in @ SY1210 @ SV335 )
| ~ ( subset @ ( sK105_C @ SV335 @ SV148 ) @ SY1210 )
| ( SY1210
= ( sK105_C @ SV335 @ SV148 ) ) )
| ~ ( in @ ( sK105_C @ SV335 @ SV148 ) @ SV335 ) )
| ( SV335 = empty_set ) )
= $true )
| ( ( finite @ SV148 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1906]) ).
thf(2161,plain,
! [SV336: $i] :
( ( ! [SY1211: $i] :
( ( ( set_difference @ SV336 @ SY1211 )
!= SV336 )
| ( disjoint @ SV336 @ SY1211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1907]) ).
thf(2162,plain,
! [SV337: $i] :
( ( ! [SY1212: $i] :
( ~ ( disjoint @ SV337 @ SY1212 )
| ( ( set_difference @ SV337 @ SY1212 )
= SV337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1908]) ).
thf(2163,plain,
! [SV338: $i] :
( ( ! [SY1213: $i] :
( ( ( set_difference @ SV338 @ ( singleton @ SY1213 ) )
!= SV338 )
| ~ ( in @ SY1213 @ SV338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1909]) ).
thf(2164,plain,
! [SV339: $i] :
( ( ! [SY1214: $i] :
( ( in @ SY1214 @ SV339 )
| ( ( set_difference @ SV339 @ ( singleton @ SY1214 ) )
= SV339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1910]) ).
thf(2165,plain,
! [SV340: $i] :
( ( ! [SY1215: $i] :
( ~ ( ~ ( ! [SY1216: $i] :
( ~ ( in @ ( sK68_C @ SY1215 @ SV340 ) @ SY1216 )
| ~ ( in @ SY1216 @ SV340 ) )
| ~ ( in @ ( sK68_C @ SY1215 @ SV340 ) @ SY1215 ) )
| ~ ( ~ ( ~ ( in @ ( sK68_C @ SY1215 @ SV340 ) @ ( sK69_SY723 @ SY1215 @ SV340 ) )
| ~ ( in @ ( sK69_SY723 @ SY1215 @ SV340 ) @ SV340 ) )
| ( in @ ( sK68_C @ SY1215 @ SV340 ) @ SY1215 ) ) )
| ( SY1215
= ( union @ SV340 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1911]) ).
thf(2166,plain,
! [SV341: $i] :
( ( ! [SY1217: $i] :
( ( SY1217
!= ( union @ SV341 ) )
| ~ ( ~ ! [SY1218: $i] :
( ! [SY1219: $i] :
( ~ ( in @ SY1218 @ SY1219 )
| ~ ( in @ SY1219 @ SV341 ) )
| ( in @ SY1218 @ SY1217 ) )
| ~ ! [SY1220: $i] :
( ~ ( in @ SY1220 @ SY1217 )
| ~ ( ~ ( in @ SY1220 @ ( sK67_D @ SY1220 @ SY1217 @ SV341 ) )
| ~ ( in @ ( sK67_D @ SY1220 @ SY1217 @ SV341 ) @ SV341 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1912]) ).
thf(2167,plain,
! [SV342: $i] :
( ( ! [SY1221: $i] :
( ~ ( element @ SV342 @ ( powerset @ SY1221 ) )
| ( subset @ SV342 @ SY1221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(2168,plain,
! [SV343: $i] :
( ( ! [SY1222: $i] :
( ~ ( subset @ SV343 @ SY1222 )
| ( element @ SV343 @ ( powerset @ SY1222 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1914]) ).
thf(2169,plain,
! [SV344: $i] :
( ( ~ ( empty @ SV344 )
| ( empty @ ( relation_inverse @ SV344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1915]) ).
thf(2170,plain,
! [SV345: $i] :
( ( ~ ( empty @ SV345 )
| ( relation @ ( relation_inverse @ SV345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1916]) ).
thf(2171,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1917]) ).
thf(2172,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1918]) ).
thf(2173,plain,
! [SV346: $i] :
( ( ! [SY1223: $i] :
( ~ ( ~ ( ~ ( in @ ( sK124_C @ SY1223 @ SV346 ) @ SY1223 )
| ~ ( subset @ ( sK124_C @ SY1223 @ SV346 ) @ SV346 ) )
| ~ ( ( in @ ( sK124_C @ SY1223 @ SV346 ) @ SY1223 )
| ( subset @ ( sK124_C @ SY1223 @ SV346 ) @ SV346 ) ) )
| ( SY1223
= ( powerset @ SV346 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1919]) ).
thf(2174,plain,
! [SV347: $i] :
( ( ! [SY1224: $i] :
( ( SY1224
!= ( powerset @ SV347 ) )
| ~ ( ~ ! [SY1225: $i] :
( ~ ( in @ SY1225 @ SY1224 )
| ( subset @ SY1225 @ SV347 ) )
| ~ ! [SY1226: $i] :
( ~ ( subset @ SY1226 @ SV347 )
| ( in @ SY1226 @ SY1224 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1920]) ).
thf(2175,plain,
! [SV149: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK118_B @ SV149 ) @ ( powerset @ SV149 ) )
| ~ ~ ( empty @ ( sK118_B @ SV149 ) ) ) )
= $false )
| ( ( empty @ SV149 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1921]) ).
thf(2176,plain,
! [SV149: $i] :
( ( ( ~ ( finite @ ( sK118_B @ SV149 ) ) )
= $false )
| ( ( empty @ SV149 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1921]) ).
thf(2177,plain,
! [SV150: $i] :
( ( ! [SY952: $i,SY953: $i] :
( ~ ( relation_of2_as_subset @ SY953 @ SV150 @ SY952 )
| ~ ( ~ ! [SY954: $i] :
~ ( in @ ( ordered_pair @ SY954 @ ( sK102_D @ SY953 @ SY952 @ SV150 ) ) @ SY953 )
| ~ ( in @ ( sK102_D @ SY953 @ SY952 @ SV150 ) @ SY952 ) )
| ( ( relation_rng_as_subset @ SV150 @ SY952 @ SY953 )
= SY952 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1922]) ).
thf(2178,plain,
! [SV150: $i] :
( ( ! [SY955: $i,SY956: $i] :
( ~ ( relation_of2_as_subset @ SY956 @ SV150 @ SY955 )
| ( ( relation_rng_as_subset @ SV150 @ SY955 @ SY956 )
!= SY955 )
| ! [SY957: $i] :
( ( in @ ( ordered_pair @ ( sK101_E @ SY957 @ SY956 @ SY955 @ SV150 ) @ SY957 ) @ SY956 )
| ~ ( in @ SY957 @ SY955 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1923]) ).
thf(2179,plain,
! [SV151: $i,SV267: $i] :
( ( ~ ! [SY1150: $i,SY1151: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 ) @ SY1151 )
| ( ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 )
!= SY1150 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 ) @ SY1151 )
| ( ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 )
!= SV151 ) )
| ~ ( ~ ( in @ ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 ) @ SY1151 )
| ( ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 )
!= SV267 ) ) ) )
| ~ ( ( in @ ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 ) @ SY1151 )
| ( ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 )
= SY1150 )
| ( ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 )
= SV151 )
| ( ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 )
= SV267 ) ) )
| ( SY1151
= ( unordered_triple @ SV151 @ SV267 @ SY1150 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1924]) ).
thf(2180,plain,
! [SV267: $i,SV151: $i] :
( ( ~ ! [SY1152: $i,SY1153: $i] :
( ( SY1153
!= ( unordered_triple @ SV151 @ SV267 @ SY1152 ) )
| ~ ( ~ ! [SY1154: $i] :
( ~ ( in @ SY1154 @ SY1153 )
| ( SY1154 = SY1152 )
| ( SY1154 = SV151 )
| ( SY1154 = SV267 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SY1152 )
| ( in @ SX4 @ SY1153 ) )
| ~ ~ ( ~ ! [SY965: $i] :
( ( SY965 != SV151 )
| ( in @ SY965 @ SY1153 ) )
| ~ ! [SY1157: $i] :
( ( SY1157 != SV267 )
| ( in @ SY1157 @ SY1153 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1924]) ).
thf(2181,plain,
! [SV152: $i] :
( ( ! [SY967: $i] :
( ~ ( subset @ SY967 @ ( sK106_B @ SV152 ) )
| ( are_equipotent @ SY967 @ ( sK106_B @ SV152 ) )
| ( in @ SY967 @ ( sK106_B @ SV152 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1925]) ).
thf(2182,plain,
! [SV152: $i] :
( ( ~ ( ~ ! [SY968: $i] :
( ~ ( in @ SY968 @ ( sK106_B @ SV152 ) )
| ( in @ ( powerset @ SY968 ) @ ( sK106_B @ SV152 ) ) )
| ~ ~ ( ~ ! [SY969: $i,SY970: $i] :
( ~ ( in @ SY969 @ ( sK106_B @ SV152 ) )
| ~ ( subset @ SY970 @ SY969 )
| ( in @ SY970 @ ( sK106_B @ SV152 ) ) )
| ~ ( in @ SV152 @ ( sK106_B @ SV152 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1926]) ).
thf(2183,plain,
! [SV153: $i] :
( ( ! [SY971: $i] :
( ~ ( in @ SY971 @ SV153 )
| ~ ( ordinal @ SY971 )
| ( in @ SY971 @ ( sK107_B @ SV153 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1927]) ).
thf(2184,plain,
! [SV153: $i] :
( ( ~ ( ~ ! [SY972: $i] :
( ~ ( in @ SY972 @ ( sK107_B @ SV153 ) )
| ( in @ SY972 @ SV153 ) )
| ~ ! [SY973: $i] :
( ~ ( in @ SY973 @ ( sK107_B @ SV153 ) )
| ( ordinal @ SY973 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1928]) ).
thf(2185,plain,
! [SV154: $i] :
( ( ( ~ ! [SY974: $i] :
( ~ ( relation @ SY974 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK72_C @ SY974 @ SV154 ) @ ( sK73_SY724 @ SY974 @ SV154 ) ) @ SV154 )
| ~ ~ ( in @ ( ordered_pair @ ( sK72_C @ SY974 @ SV154 ) @ ( sK73_SY724 @ SY974 @ SV154 ) ) @ SY974 ) )
| ( subset @ SV154 @ SY974 ) )
| ~ ! [SY975: $i] :
( ~ ( relation @ SY975 )
| ~ ( subset @ SV154 @ SY975 )
| ! [SY976: $i,SY977: $i] :
( ~ ( in @ ( ordered_pair @ SY976 @ SY977 ) @ SV154 )
| ( in @ ( ordered_pair @ SY976 @ SY977 ) @ SY975 ) ) ) )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1929]) ).
thf(2186,plain,
! [SV155: $i,SV268: $i] :
( ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1158: $i] :
( ~ ( element @ SY1158 @ ( powerset @ ( powerset @ SV155 ) ) )
| ~ ( ~ ( element @ ( sK123_D @ SY1158 @ SV268 @ SV155 ) @ ( powerset @ SV155 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK123_D @ SY1158 @ SV268 @ SV155 ) @ SY1158 )
| ~ ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SY1158 @ SV268 @ SV155 ) ) @ SV268 ) )
| ~ ( ( in @ ( sK123_D @ SY1158 @ SV268 @ SV155 ) @ SY1158 )
| ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SY1158 @ SV268 @ SV155 ) ) @ SV268 ) ) ) )
| ( SY1158
= ( complements_of_subsets @ SV155 @ SV268 ) ) )
| ~ ! [SY1159: $i] :
( ~ ( element @ SY1159 @ ( powerset @ ( powerset @ SV155 ) ) )
| ( SY1159
!= ( complements_of_subsets @ SV155 @ SV268 ) )
| ~ ( ~ ! [SY1160: $i] :
( ~ ( element @ SY1160 @ ( powerset @ SV155 ) )
| ~ ( in @ SY1160 @ SY1159 )
| ( in @ ( subset_complement @ SV155 @ SY1160 ) @ SV268 ) )
| ~ ! [SY1161: $i] :
( ~ ( element @ SY1161 @ ( powerset @ SV155 ) )
| ~ ( in @ ( subset_complement @ SV155 @ SY1161 ) @ SV268 )
| ( in @ SY1161 @ SY1159 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1930]) ).
thf(2187,plain,
! [SV348: $i] :
( ( ! [SY1227: $i] :
( ~ ( subset @ SV348 @ ( singleton @ SY1227 ) )
| ( SV348 = empty_set )
| ( SV348
= ( singleton @ SY1227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1931]) ).
thf(2188,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1932]) ).
thf(2189,plain,
! [SV349: $i] :
( ( ! [SY1228: $i] :
( ~ ( subset @ SV349 @ ( singleton @ SY1228 ) )
| ( SV349 = empty_set )
| ( SV349
= ( singleton @ SY1228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1933]) ).
thf(2190,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1934]) ).
thf(2191,plain,
! [SV350: $i] :
( ( ! [SY1229: $i] :
( ( ( set_difference @ SV350 @ SY1229 )
!= empty_set )
| ( subset @ SV350 @ SY1229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(2192,plain,
! [SV351: $i] :
( ( ! [SY1230: $i] :
( ~ ( subset @ SV351 @ SY1230 )
| ( ( set_difference @ SV351 @ SY1230 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1936]) ).
thf(2193,plain,
! [SV156: $i] :
( ( ( ~ ! [SY983: $i] :
( ~ ( element @ SY983 @ ( powerset @ SV156 ) )
| ( v1_membered @ SY983 ) )
| ~ ! [SY984: $i] :
( ~ ( element @ SY984 @ ( powerset @ SV156 ) )
| ( v2_membered @ SY984 ) ) )
= $false )
| ( ( v2_membered @ SV156 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1937]) ).
thf(2194,plain,
! [SV352: $i] :
( ( ! [SY1231: $i] :
( ~ ( empty @ SV352 )
| ~ ( relation @ SY1231 )
| ( empty @ ( relation_composition @ SV352 @ SY1231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2195,plain,
! [SV353: $i] :
( ( ! [SY1232: $i] :
( ~ ( empty @ SV353 )
| ~ ( relation @ SY1232 )
| ( relation @ ( relation_composition @ SV353 @ SY1232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1939]) ).
thf(2196,plain,
( ( sK12_REN = $true )
| ( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
( ( SX2 != SX1 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( ordinal @ SX1 )
| ( in @ SX1 @ ( sK7_B @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK7_B @ SX0 ) )
| ~ ( ~ ~ ( ( ( sK8_D @ SX1 @ SX0 )
!= SX1 )
| ~ ( in @ ( sK8_D @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ordinal @ SX1 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1940]) ).
thf(2197,plain,
( ( ( ~ sK12_REN )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK9_B != sK10_SY601 )
| ~ ( ordinal @ sK10_SY601 ) )
| ( sK9_B != sK11_SY603 ) )
| ~ ( ordinal @ sK11_SY603 ) )
| ~ ( ( sK10_SY601 != sK11_SY603 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1941]) ).
thf(2198,plain,
( ( ( subset_complement @ ( the_carrier @ sK1_A ) @ sK2_SY588 )
= ( subset_difference @ ( the_carrier @ sK1_A ) @ ( cast_as_carrier_subset @ sK1_A ) @ sK2_SY588 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1943]) ).
thf(2199,plain,
! [SV157: $i] :
( ( ! [SY985: $i,SY986: $i] :
( ~ ( relation @ SY986 )
| ~ ( in @ SV157 @ SY986 )
| ~ ( in @ SV157 @ ( cartesian_product2 @ SY985 @ SY985 ) )
| ( in @ SV157 @ ( relation_restriction @ SY986 @ SY985 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1944]) ).
thf(2200,plain,
! [SV157: $i] :
( ( ~ ( ~ ! [SY987: $i,SY988: $i] :
( ~ ( relation @ SY988 )
| ~ ( in @ SV157 @ ( relation_restriction @ SY988 @ SY987 ) )
| ( in @ SV157 @ SY988 ) )
| ~ ! [SY989: $i,SY990: $i] :
( ~ ( relation @ SY990 )
| ~ ( in @ SV157 @ ( relation_restriction @ SY990 @ SY989 ) )
| ( in @ SV157 @ ( cartesian_product2 @ SY989 @ SY989 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1945]) ).
thf(2201,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1946]) ).
thf(2202,plain,
! [SV158: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY991: $i,SY992: $i] :
( ~ ( relation_of2_as_subset @ SY992 @ SV158 @ SY991 )
| ( SY991 = empty_set )
| ( SV158
!= ( relation_dom_as_subset @ SV158 @ SY991 @ SY992 ) )
| ( quasi_total @ SY992 @ SV158 @ SY991 ) )
| ~ ! [SY993: $i,SY994: $i] :
( ~ ( relation_of2_as_subset @ SY994 @ SV158 @ SY993 )
| ( SY993 = empty_set )
| ~ ( quasi_total @ SY994 @ SV158 @ SY993 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SY993 @ SY994 ) ) ) )
| ~ ~ ( ~ ! [SY995: $i,SY996: $i] :
( ~ ( relation_of2_as_subset @ SY996 @ SV158 @ SY995 )
| ( SV158 != empty_set )
| ( SV158
!= ( relation_dom_as_subset @ SV158 @ SY995 @ SY996 ) )
| ( quasi_total @ SY996 @ SV158 @ SY995 ) )
| ~ ! [SY997: $i,SY998: $i] :
( ~ ( relation_of2_as_subset @ SY998 @ SV158 @ SY997 )
| ( SV158 != empty_set )
| ~ ( quasi_total @ SY998 @ SV158 @ SY997 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SY997 @ SY998 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1948]) ).
thf(2203,plain,
! [SV158: $i] :
( ( ~ ( ~ ! [SY999: $i,SY1000: $i] :
( ~ ( relation_of2_as_subset @ SY1000 @ SV158 @ SY999 )
| ( SY999 != empty_set )
| ( SY1000 != empty_set )
| ( quasi_total @ SY1000 @ SV158 @ SY999 )
| ( SV158 = empty_set ) )
| ~ ! [SY1001: $i,SY1002: $i] :
( ~ ( relation_of2_as_subset @ SY1002 @ SV158 @ SY1001 )
| ( SY1001 != empty_set )
| ~ ( quasi_total @ SY1002 @ SV158 @ SY1001 )
| ( SY1002 = empty_set )
| ( SV158 = empty_set ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1949]) ).
thf(2204,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK90_SY733 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK89_C @ SX1 @ SX0 ) @ ( sK90_SY733 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK89_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK89_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK89_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK88_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK88_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1950]) ).
thf(2205,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1951]) ).
thf(2206,plain,
! [SV159: $i] :
( ( ! [SY1003: $i,SY1004: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK82_D @ SY1004 @ SY1003 @ SV159 ) @ SY1004 )
| ( ( sK82_D @ SY1004 @ SY1003 @ SV159 )
!= SV159 ) )
| ~ ( ~ ( in @ ( sK82_D @ SY1004 @ SY1003 @ SV159 ) @ SY1004 )
| ( ( sK82_D @ SY1004 @ SY1003 @ SV159 )
!= SY1003 ) ) )
| ~ ( ( in @ ( sK82_D @ SY1004 @ SY1003 @ SV159 ) @ SY1004 )
| ( ( sK82_D @ SY1004 @ SY1003 @ SV159 )
= SV159 )
| ( ( sK82_D @ SY1004 @ SY1003 @ SV159 )
= SY1003 ) ) )
| ( SY1004
= ( unordered_pair @ SV159 @ SY1003 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1952]) ).
thf(2207,plain,
! [SV159: $i] :
( ( ! [SY1005: $i,SY1006: $i] :
( ( SY1006
!= ( unordered_pair @ SV159 @ SY1005 ) )
| ~ ( ~ ! [SY1007: $i] :
( ~ ( in @ SY1007 @ SY1006 )
| ( SY1007 = SV159 )
| ( SY1007 = SY1005 ) )
| ~ ~ ( ~ ! [SY1008: $i] :
( ( SY1008 != SV159 )
| ( in @ SY1008 @ SY1006 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY1005 )
| ( in @ SX3 @ SY1006 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1953]) ).
thf(2208,plain,
! [SV354: $i] :
( ( ! [SY1233: $i] :
( ~ ( empty @ SV354 )
| ~ ( relation @ SY1233 )
| ( empty @ ( relation_composition @ SY1233 @ SV354 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(2209,plain,
! [SV355: $i] :
( ( ! [SY1234: $i] :
( ~ ( empty @ SV355 )
| ~ ( relation @ SY1234 )
| ( relation @ ( relation_composition @ SY1234 @ SV355 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1955]) ).
thf(2210,plain,
! [SV160: $i] :
( ( ( ~ ! [SY1010: $i] :
( ~ ( element @ SY1010 @ SV160 )
| ( v1_xcmplx_0 @ SY1010 ) )
| ~ ! [SY1011: $i] :
( ~ ( element @ SY1011 @ SV160 )
| ( v1_xreal_0 @ SY1011 ) ) )
= $false )
| ( ( v2_membered @ SV160 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1956]) ).
thf(2211,plain,
! [SV356: $i] :
( ( ~ ( latt_str @ SV356 )
| ( join_semilatt_str @ SV356 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2212,plain,
! [SV357: $i] :
( ( ~ ( latt_str @ SV357 )
| ( meet_semilatt_str @ SV357 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1958]) ).
thf(2213,plain,
! [SV358: $i] :
( ( ~ ( ~ ! [SY1235: $i,SY1236: $i] :
( ( sK93_B @ SV358 )
!= ( ordered_pair @ SY1235 @ SY1236 ) )
| ~ ( in @ ( sK93_B @ SV358 ) @ SV358 ) )
| ( relation @ SV358 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1961]) ).
thf(2214,plain,
! [SV359: $i] :
( ( ~ ( relation @ SV359 )
| ! [SY1237: $i] :
( ( SY1237
= ( ordered_pair @ ( sK91_C @ SY1237 @ SV359 ) @ ( sK92_SY735 @ SY1237 @ SV359 ) ) )
| ~ ( in @ SY1237 @ SV359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(2215,plain,
! [SV360: $i] :
( ( ~ ( empty @ SV360 )
| ( empty @ ( relation_rng @ SV360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1963]) ).
thf(2216,plain,
! [SV361: $i] :
( ( ~ ( empty @ SV361 )
| ( relation @ ( relation_rng @ SV361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1964]) ).
thf(2217,plain,
! [SV161: $i] :
( ( relation @ ( sK100_B @ SV161 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1965]) ).
thf(2218,plain,
! [SV161: $i] :
( ( well_orders @ ( sK100_B @ SV161 ) @ SV161 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1966]) ).
thf(2219,plain,
! [SV162: $i,SV269: $i] :
( ( ( element @ SV269 @ ( powerset @ SV162 ) )
= $false )
| ( ( ~ ( ~ ! [SY1162: $i] :
( ~ ( element @ SY1162 @ ( powerset @ SV162 ) )
| ~ ( disjoint @ SV269 @ SY1162 )
| ( subset @ SV269 @ ( subset_complement @ SV162 @ SY1162 ) ) )
| ~ ! [SY1163: $i] :
( ~ ( element @ SY1163 @ ( powerset @ SV162 ) )
| ~ ( subset @ SV269 @ ( subset_complement @ SV162 @ SY1163 ) )
| ( disjoint @ SV269 @ SY1163 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1967]) ).
thf(2220,plain,
( ( empty_carrier @ sK117_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1969]) ).
thf(2221,plain,
! [SV362: $i] :
( ( ! [SY1238: $i] :
( ~ ( in @ SV362 @ SY1238 )
| ( subset @ ( singleton @ SV362 ) @ SY1238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(2222,plain,
! [SV363: $i] :
( ( ! [SY1239: $i] :
( ~ ( subset @ ( singleton @ SV363 ) @ SY1239 )
| ( in @ SV363 @ SY1239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1971]) ).
thf(2223,plain,
! [SV163: $i] :
( ( ! [SY1015: $i,SY1016: $i] :
( ~ ( relation_of2 @ SY1016 @ SV163 @ SY1015 )
| ( relation_of2_as_subset @ SY1016 @ SV163 @ SY1015 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1972]) ).
thf(2224,plain,
! [SV163: $i] :
( ( ! [SY1017: $i,SY1018: $i] :
( ~ ( relation_of2_as_subset @ SY1018 @ SV163 @ SY1017 )
| ( relation_of2 @ SY1018 @ SV163 @ SY1017 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1973]) ).
thf(2225,plain,
! [SV364: $i] :
( ( ! [SY1240: $i] :
( ~ ( ~ ( ( ( sK87_C @ SY1240 @ SV364 )
!= SV364 )
| ~ ( in @ ( sK87_C @ SY1240 @ SV364 ) @ SY1240 ) )
| ~ ( ( ( sK87_C @ SY1240 @ SV364 )
= SV364 )
| ( in @ ( sK87_C @ SY1240 @ SV364 ) @ SY1240 ) ) )
| ( SY1240
= ( singleton @ SV364 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1974]) ).
thf(2226,plain,
! [SV365: $i] :
( ( ! [SY1241: $i] :
( ( SY1241
!= ( singleton @ SV365 ) )
| ~ ( ~ ! [SY1242: $i] :
( ( SY1242 != SV365 )
| ( in @ SY1242 @ SY1241 ) )
| ~ ! [SY1243: $i] :
( ~ ( in @ SY1243 @ SY1241 )
| ( SY1243 = SV365 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(2227,plain,
! [SV164: $i] :
( ( ! [SY1019: $i,SY1020: $i] :
( ~ ( ~ ( ! [SY1021: $i,SY1022: $i] :
( ~ ( in @ SY1021 @ SV164 )
| ~ ( in @ SY1022 @ SY1019 )
| ( ( sK78_D @ SY1020 @ SY1019 @ SV164 )
!= ( ordered_pair @ SY1021 @ SY1022 ) ) )
| ~ ( in @ ( sK78_D @ SY1020 @ SY1019 @ SV164 ) @ SY1020 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK79_SY729 @ SY1020 @ SY1019 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK80_SY731 @ SY1020 @ SY1019 @ SV164 ) @ SY1019 ) )
| ( ( sK78_D @ SY1020 @ SY1019 @ SV164 )
!= ( ordered_pair @ ( sK79_SY729 @ SY1020 @ SY1019 @ SV164 ) @ ( sK80_SY731 @ SY1020 @ SY1019 @ SV164 ) ) ) )
| ( in @ ( sK78_D @ SY1020 @ SY1019 @ SV164 ) @ SY1020 ) ) )
| ( SY1020
= ( cartesian_product2 @ SV164 @ SY1019 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1976]) ).
thf(2228,plain,
! [SV164: $i] :
( ( ! [SY1023: $i,SY1024: $i] :
( ( SY1024
!= ( cartesian_product2 @ SV164 @ SY1023 ) )
| ~ ( ~ ! [SY1025: $i] :
( ! [SY1026: $i,SY1027: $i] :
( ~ ( in @ SY1026 @ SV164 )
| ~ ( in @ SY1027 @ SY1023 )
| ( SY1025
!= ( ordered_pair @ SY1026 @ SY1027 ) ) )
| ( in @ SY1025 @ SY1024 ) )
| ~ ! [SY1028: $i] :
( ~ ( in @ SY1028 @ SY1024 )
| ~ ( ~ ~ ( ~ ( in @ ( sK76_E @ SY1028 @ SY1024 @ SY1023 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK77_SY726 @ SY1028 @ SY1024 @ SY1023 @ SV164 ) @ SY1023 ) )
| ( SY1028
!= ( ordered_pair @ ( sK76_E @ SY1028 @ SY1024 @ SY1023 @ SV164 ) @ ( sK77_SY726 @ SY1028 @ SY1024 @ SY1023 @ SV164 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1977]) ).
thf(2229,plain,
! [SV366: $i] :
( ( ! [SY1244: $i] :
( ~ ( ~ ( in @ ( sK71_C @ SY1244 @ SV366 ) @ SV366 )
| ~ ~ ( in @ ( sK71_C @ SY1244 @ SV366 ) @ SY1244 ) )
| ( subset @ SV366 @ SY1244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1980]) ).
thf(2230,plain,
! [SV367: $i] :
( ( ! [SY1245: $i] :
( ~ ( subset @ SV367 @ SY1245 )
| ! [SY1246: $i] :
( ~ ( in @ SY1246 @ SV367 )
| ( in @ SY1246 @ SY1245 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1981]) ).
thf(2231,plain,
! [SV165: $i] :
( ( ! [SY1029: $i,SY1030: $i] :
( ~ ( relation_of2 @ SY1030 @ SV165 @ SY1029 )
| ( subset @ SY1030 @ ( cartesian_product2 @ SV165 @ SY1029 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1982]) ).
thf(2232,plain,
! [SV165: $i] :
( ( ! [SY1031: $i,SY1032: $i] :
( ~ ( subset @ SY1032 @ ( cartesian_product2 @ SV165 @ SY1031 ) )
| ( relation_of2 @ SY1032 @ SV165 @ SY1031 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1983]) ).
thf(2233,plain,
! [SV166: $i] :
( ( ! [SY1033: $i] :
( ~ ( subset @ SY1033 @ ( sK3_B @ SV166 ) )
| ( are_equipotent @ SY1033 @ ( sK3_B @ SV166 ) )
| ( in @ SY1033 @ ( sK3_B @ SV166 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1984]) ).
thf(2234,plain,
! [SV166: $i] :
( ( ~ ( ~ ! [SY1034: $i] :
( ~ ( ~ ! [SY1035: $i] :
( ~ ( subset @ SY1035 @ SY1034 )
| ( in @ SY1035 @ ( sK4_SY591 @ SY1034 @ SV166 ) ) )
| ~ ( in @ ( sK4_SY591 @ SY1034 @ SV166 ) @ ( sK3_B @ SV166 ) ) )
| ~ ( in @ SY1034 @ ( sK3_B @ SV166 ) ) )
| ~ ~ ( ~ ! [SY1036: $i,SY1037: $i] :
( ~ ( in @ SY1036 @ ( sK3_B @ SV166 ) )
| ~ ( subset @ SY1037 @ SY1036 )
| ( in @ SY1037 @ ( sK3_B @ SV166 ) ) )
| ~ ( in @ SV166 @ ( sK3_B @ SV166 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1985]) ).
thf(2235,plain,
! [SV167: $i] :
( ( ! [SY1038: $i,SY1039: $i] :
( ~ ( relation_of2_as_subset @ SY1039 @ SY1038 @ SV167 )
| ~ ( ~ ! [SY1040: $i] :
~ ( in @ ( ordered_pair @ ( sK104_D @ SY1039 @ SY1038 @ SV167 ) @ SY1040 ) @ SY1039 )
| ~ ( in @ ( sK104_D @ SY1039 @ SY1038 @ SV167 ) @ SY1038 ) )
| ( ( relation_dom_as_subset @ SY1038 @ SV167 @ SY1039 )
= SY1038 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1986]) ).
thf(2236,plain,
! [SV167: $i] :
( ( ! [SY1041: $i,SY1042: $i] :
( ~ ( relation_of2_as_subset @ SY1042 @ SY1041 @ SV167 )
| ( ( relation_dom_as_subset @ SY1041 @ SV167 @ SY1042 )
!= SY1041 )
| ! [SY1043: $i] :
( ( in @ ( ordered_pair @ SY1043 @ ( sK103_E @ SY1043 @ SY1042 @ SY1041 @ SV167 ) ) @ SY1042 )
| ~ ( in @ SY1043 @ SY1041 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1987]) ).
thf(2237,plain,
! [SV168: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK27_SY634 @ SV168 )
!= ( singleton @ ( sK26_B @ SV168 ) ) )
| ~ ( in @ ( sK26_B @ SV168 ) @ SV168 ) )
| ~ ( in @ ( sK26_B @ SV168 ) @ SV168 ) )
| ( ( sK28_SY636 @ SV168 )
!= ( singleton @ ( sK26_B @ SV168 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) )
| ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1988]) ).
thf(2238,plain,
! [SV168: $i] :
( ( ( ~ ( ( ( sK27_SY634 @ SV168 )
!= ( sK28_SY636 @ SV168 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) )
| ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1988]) ).
thf(2239,plain,
( ( ~ ( empty @ sK57_A )
| ~ ( relation @ sK57_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1991]) ).
thf(2240,plain,
! [SV270: $i,SV169: $i] :
( ( ~ ! [SY1164: $i,SY1165: $i] :
( ~ ( in @ SV169 @ SY1164 )
| ~ ( in @ SV270 @ SY1165 )
| ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SY1164 @ SY1165 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1993]) ).
thf(2241,plain,
! [SV270: $i,SV169: $i] :
( ( ~ ~ ( ~ ! [SY1166: $i] :
( ! [SY1167: $i] :
~ ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SY1166 @ SY1167 ) )
| ( in @ SV169 @ SY1166 ) )
| ~ ! [SY1168: $i,SY1169: $i] :
( ~ ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SY1168 @ SY1169 ) )
| ( in @ SV270 @ SY1169 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1993]) ).
thf(2242,plain,
! [SV271: $i,SV170: $i] :
( ( ( empty @ SV170 )
= $true )
| ( ( ~ ( relation @ SV271 ) )
= $true )
| ( ( ! [SY1170: $i] :
~ ( ~ ! [SY1171: $i] :
( ! [SY1172: $i,SY1173: $i] :
( ( ( ordered_pair @ SY1172 @ SY1173 )
!= SY1171 )
| ~ ( in @ SY1172 @ SV170 )
| ! [SY1174: $i] :
( ~ ( ~ ( in @ ( sK115_I @ SY1174 @ SY1173 @ SY1172 @ SY1171 @ SY1170 @ SV271 @ SV170 ) @ SY1174 )
| ~ ~ ( in @ ( ordered_pair @ SY1173 @ ( sK115_I @ SY1174 @ SY1173 @ SY1172 @ SY1171 @ SY1170 @ SV271 @ SV170 ) ) @ SV271 ) )
| ( SY1172 != SY1174 )
| ~ ( in @ SY1173 @ SY1174 ) ) )
| ~ ( in @ SY1171 @ ( cartesian_product2 @ SV170 @ SY1170 ) )
| ( in @ SY1171 @ ( sK111_D @ SY1170 @ SV271 @ SV170 ) ) )
| ~ ~ ( ~ ! [SY1175: $i] :
( ~ ( in @ SY1175 @ ( sK111_D @ SY1170 @ SV271 @ SV170 ) )
| ~ ( ~ ~ ( ( ( ordered_pair @ ( sK112_F @ SY1175 @ SY1170 @ SV271 @ SV170 ) @ ( sK113_SY768 @ SY1175 @ SY1170 @ SV271 @ SV170 ) )
!= SY1175 )
| ~ ( in @ ( sK112_F @ SY1175 @ SY1170 @ SV271 @ SV170 ) @ SV170 ) )
| ~ ~ ( ~ ! [SY1176: $i] :
( ~ ( in @ SY1176 @ ( sK114_SY771 @ SY1175 @ SY1170 @ SV271 @ SV170 ) )
| ( in @ ( ordered_pair @ ( sK113_SY768 @ SY1175 @ SY1170 @ SV271 @ SV170 ) @ SY1176 ) @ SV271 ) )
| ~ ~ ( ( ( sK112_F @ SY1175 @ SY1170 @ SV271 @ SV170 )
!= ( sK114_SY771 @ SY1175 @ SY1170 @ SV271 @ SV170 ) )
| ~ ( in @ ( sK113_SY768 @ SY1175 @ SY1170 @ SV271 @ SV170 ) @ ( sK114_SY771 @ SY1175 @ SY1170 @ SV271 @ SV170 ) ) ) ) ) )
| ~ ! [SY1177: $i] :
( ~ ( in @ SY1177 @ ( sK111_D @ SY1170 @ SV271 @ SV170 ) )
| ( in @ SY1177 @ ( cartesian_product2 @ SV170 @ SY1170 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1994]) ).
thf(2243,plain,
! [SV368: $i] :
( ( ~ ( ~ ~ ( ~ ( ( ( sK74_B @ SV368 )
!= ( sK75_SY725 @ SV368 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK74_B @ SV368 ) @ SV368 )
| ~ ( in @ ( sK75_SY725 @ SV368 ) @ SV368 ) )
| ~ ~ ( in @ ( sK74_B @ SV368 ) @ ( sK75_SY725 @ SV368 ) ) ) )
| ~ ~ ( in @ ( sK75_SY725 @ SV368 ) @ ( sK74_B @ SV368 ) ) )
| ( epsilon_connected @ SV368 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1995]) ).
thf(2244,plain,
! [SV369: $i] :
( ( ~ ( epsilon_connected @ SV369 )
| ! [SY1247: $i,SY1248: $i] :
( ( SY1247 = SY1248 )
| ~ ( in @ SY1247 @ SV369 )
| ~ ( in @ SY1248 @ SV369 )
| ( in @ SY1247 @ SY1248 )
| ( in @ SY1248 @ SY1247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(2245,plain,
( ( ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_difference @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_difference @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1997]) ).
thf(2246,plain,
! [SV370: $i] :
( ( ~ ( v3_membered @ SV370 )
| ! [SY1249: $i] : ( v3_membered @ ( set_difference @ SV370 @ SY1249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1998]) ).
thf(2247,plain,
! [SV171: $i] :
( ( ( ~ ! [SY1063: $i] :
( ~ ( relation @ SY1063 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK83_C @ SY1063 @ SV171 ) @ ( sK84_SY732 @ SY1063 @ SV171 ) ) @ SV171 )
| ~ ( in @ ( ordered_pair @ ( sK83_C @ SY1063 @ SV171 ) @ ( sK84_SY732 @ SY1063 @ SV171 ) ) @ SY1063 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK83_C @ SY1063 @ SV171 ) @ ( sK84_SY732 @ SY1063 @ SV171 ) ) @ SV171 )
| ( in @ ( ordered_pair @ ( sK83_C @ SY1063 @ SV171 ) @ ( sK84_SY732 @ SY1063 @ SV171 ) ) @ SY1063 ) ) )
| ( SV171 = SY1063 ) )
| ~ ! [SY1064: $i] :
( ~ ( relation @ SY1064 )
| ( SV171 != SY1064 )
| ~ ( ~ ! [SY1065: $i,SY1066: $i] :
( ~ ( in @ ( ordered_pair @ SY1065 @ SY1066 ) @ SV171 )
| ( in @ ( ordered_pair @ SY1065 @ SY1066 ) @ SY1064 ) )
| ~ ! [SY1067: $i,SY1068: $i] :
( ~ ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SY1064 )
| ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SV171 ) ) ) ) )
= $false )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1999]) ).
thf(2248,plain,
! [SV371: $i] :
( ( ! [SY1250: $i] :
( ( disjoint @ SV371 @ SY1250 )
| ~ ( ~ ( in @ ( sK98_C @ SY1250 @ SV371 ) @ SV371 )
| ~ ( in @ ( sK98_C @ SY1250 @ SV371 ) @ SY1250 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2002]) ).
thf(2249,plain,
! [SV372: $i] :
( ( ! [SY1251: $i] :
( ! [SY1252: $i] :
( ~ ( in @ SY1252 @ SV372 )
| ~ ( in @ SY1252 @ SY1251 ) )
| ~ ( disjoint @ SV372 @ SY1251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2003]) ).
thf(2250,plain,
! [SV373: $i] :
( ( ! [SY1253: $i] :
( ~ ( in @ SV373 @ SY1253 )
| ( subset @ ( singleton @ SV373 ) @ SY1253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2004]) ).
thf(2251,plain,
! [SV374: $i] :
( ( ! [SY1254: $i] :
( ~ ( subset @ ( singleton @ SV374 ) @ SY1254 )
| ( in @ SV374 @ SY1254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2005]) ).
thf(2252,plain,
! [SV375: $i] :
( ( ! [SY1255: $i] :
( ( disjoint @ SV375 @ SY1255 )
| ( in @ ( sK97_C @ SY1255 @ SV375 ) @ ( set_intersection2 @ SV375 @ SY1255 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2006]) ).
thf(2253,plain,
! [SV376: $i] :
( ( ! [SY1256: $i] :
( ! [SY1257: $i] :
~ ( in @ SY1257 @ ( set_intersection2 @ SV376 @ SY1256 ) )
| ~ ( disjoint @ SV376 @ SY1256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2007]) ).
thf(2254,plain,
! [SV377: $i] :
( ( ~ ( empty @ ( singleton @ SV377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2255,plain,
! [SV378: $i] :
( ( finite @ ( singleton @ SV378 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2009]) ).
thf(2256,plain,
! [SV272: $i,SV172: $i] :
( ( ( empty @ SV172 )
= $true )
| ( ( ~ ( relation @ SV272 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK35_D @ SV272 @ SV172 )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1178: $i] :
( ~ ( in @ SY1178 @ ( sK43_SY691 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SY1178 ) @ SV272 ) )
| ~ ~ ( ( ( sK41_SY666 @ SV272 @ SV172 )
!= ( sK43_SY691 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) ) ) ) ) )
| ( ( sK35_D @ SV272 @ SV172 )
!= ( sK37_SY665 @ SV272 @ SV172 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
!= ( sK37_SY665 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1179: $i] :
( ~ ( in @ SY1179 @ ( sK40_SY685 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SY1179 ) @ SV272 ) )
| ~ ~ ( ( ( sK38_SY678 @ SV272 @ SV172 )
!= ( sK40_SY685 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) ) ) ) ) )
| ~ ( ( ( sK36_SY655 @ SV272 @ SV172 )
!= ( sK37_SY665 @ SV272 @ SV172 ) ) ) )
| ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2010]) ).
thf(2257,plain,
! [SV379: $i] :
( ( ( SV379
!= ( union @ SV379 ) )
| ( being_limit_ordinal @ SV379 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2011]) ).
thf(2258,plain,
! [SV380: $i] :
( ( ~ ( being_limit_ordinal @ SV380 )
| ( SV380
= ( union @ SV380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2012]) ).
thf(2259,plain,
! [SV381: $i] :
( ( ~ ( v2_membered @ SV381 )
| ! [SY1258: $i] : ( v1_membered @ ( set_intersection2 @ SY1258 @ SV381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2013]) ).
thf(2260,plain,
! [SV382: $i] :
( ( ~ ( v2_membered @ SV382 )
| ! [SY1259: $i] : ( v2_membered @ ( set_intersection2 @ SY1259 @ SV382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(2261,plain,
! [SV273: $i,SV173: $i] :
( ( ~ ! [SY1188: $i,SY1189: $i] :
( ~ ( in @ SV173 @ SY1188 )
| ~ ( in @ SV273 @ SY1189 )
| ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SY1188 @ SY1189 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2015]) ).
thf(2262,plain,
! [SV273: $i,SV173: $i] :
( ( ~ ~ ( ~ ! [SY1190: $i] :
( ! [SY1191: $i] :
~ ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SY1190 @ SY1191 ) )
| ( in @ SV173 @ SY1190 ) )
| ~ ! [SY1192: $i,SY1193: $i] :
( ~ ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SY1192 @ SY1193 ) )
| ( in @ SV273 @ SY1193 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2015]) ).
thf(2263,plain,
! [SV174: $i,SV274: $i] :
( ( ~ ~ ( ~ ( relation @ ( sK56_C @ SV274 @ SV174 ) )
| ~ ( relation_of2 @ ( sK56_C @ SV274 @ SV174 ) @ SV174 @ SV274 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2016]) ).
thf(2264,plain,
! [SV174: $i,SV274: $i] :
( ( ~ ( function @ ( sK56_C @ SV274 @ SV174 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2016]) ).
thf(2265,plain,
! [SV383: $i] :
( ( ~ ( empty @ SV383 )
| ( empty @ ( relation_dom @ SV383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2017]) ).
thf(2266,plain,
! [SV384: $i] :
( ( ~ ( empty @ SV384 )
| ( relation @ ( relation_dom @ SV384 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2018]) ).
thf(2267,plain,
! [SV385: $i] :
( ( ~ ( v2_membered @ SV385 )
| ! [SY1260: $i] : ( v1_membered @ ( set_difference @ SV385 @ SY1260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2019]) ).
thf(2268,plain,
! [SV386: $i] :
( ( ~ ( v2_membered @ SV386 )
| ! [SY1261: $i] : ( v2_membered @ ( set_difference @ SV386 @ SY1261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2020]) ).
thf(2269,plain,
! [SV175: $i] :
( ( element @ ( sK119_B @ SV175 ) @ ( powerset @ SV175 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2021]) ).
thf(2270,plain,
! [SV175: $i] :
( ( empty @ ( sK119_B @ SV175 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2022]) ).
thf(2271,plain,
( ( ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2023]) ).
thf(2272,plain,
! [SV387: $i] :
( ( ~ ( v3_membered @ SV387 )
| ! [SY1262: $i] : ( v3_membered @ ( set_intersection2 @ SV387 @ SY1262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2024]) ).
thf(2273,plain,
( ( empty @ sK61_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2025]) ).
thf(2274,plain,
! [SV388: $i] :
( ( ~ ( v2_membered @ SV388 )
| ! [SY1263: $i] : ( v1_membered @ ( set_intersection2 @ SV388 @ SY1263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2027]) ).
thf(2275,plain,
! [SV389: $i] :
( ( ~ ( v2_membered @ SV389 )
| ! [SY1264: $i] : ( v2_membered @ ( set_intersection2 @ SV389 @ SY1264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2276,plain,
( ( empty @ sK55_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2029]) ).
thf(2277,plain,
! [SV390: $i] :
( ( ! [SY1265: $i] :
( ( ( set_difference @ SV390 @ SY1265 )
!= empty_set )
| ( subset @ SV390 @ SY1265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2031]) ).
thf(2278,plain,
! [SV391: $i] :
( ( ! [SY1266: $i] :
( ~ ( subset @ SV391 @ SY1266 )
| ( ( set_difference @ SV391 @ SY1266 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2032]) ).
thf(2279,plain,
! [SV275: $i,SV176: $i] :
( ( ~ ! [SY1194: $i] :
( ! [SY1090: $i,SY1091: $i] :
( ( ( ordered_pair @ SY1090 @ SY1091 )
!= SY1194 )
| ~ ( in @ SY1090 @ SV176 )
| ( SY1091
!= ( singleton @ SY1090 ) ) )
| ~ ( in @ SY1194 @ ( cartesian_product2 @ SV176 @ SV275 ) )
| ( in @ SY1194 @ ( sK108_C @ SV275 @ SV176 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2033]) ).
thf(2280,plain,
! [SV176: $i,SV275: $i] :
( ( ~ ~ ( ~ ! [SY1197: $i] :
( ~ ( in @ SY1197 @ ( sK108_C @ SV275 @ SV176 ) )
| ~ ( ~ ~ ( ( ( ordered_pair @ ( sK109_E @ SY1197 @ SV275 @ SV176 ) @ ( sK110_SY756 @ SY1197 @ SV275 @ SV176 ) )
!= SY1197 )
| ~ ( in @ ( sK109_E @ SY1197 @ SV275 @ SV176 ) @ SV176 ) )
| ( ( sK110_SY756 @ SY1197 @ SV275 @ SV176 )
!= ( singleton @ ( sK109_E @ SY1197 @ SV275 @ SV176 ) ) ) ) )
| ~ ! [SY1198: $i] :
( ~ ( in @ SY1198 @ ( sK108_C @ SV275 @ SV176 ) )
| ( in @ SY1198 @ ( cartesian_product2 @ SV176 @ SV275 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2033]) ).
thf(2281,plain,
! [SV177: $i,SV276: $i] :
( ( ( ~ ( in @ ( sK125_C @ SV276 @ SV177 ) @ SV177 )
| ~ ~ ( in @ ( sK125_C @ SV276 @ SV177 ) @ SV276 ) )
= $false )
| ( ( element @ SV177 @ ( powerset @ SV276 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2034]) ).
thf(2282,plain,
! [SV178: $i,SV277: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_C @ SV277 @ SV178 ) @ SV178 )
| ~ ( in @ ( sK6_C @ SV277 @ SV178 ) @ SV277 ) )
| ~ ( ( in @ ( sK6_C @ SV277 @ SV178 ) @ SV178 )
| ( in @ ( sK6_C @ SV277 @ SV178 ) @ SV277 ) ) )
= $false )
| ( ( SV178 = SV277 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2035]) ).
thf(2283,plain,
! [SV179: $i] :
( ( ! [SY1096: $i] :
( ~ ( subset @ SV179 @ SY1096 )
| ! [SY1097: $i] : ( subset @ ( cartesian_product2 @ SV179 @ SY1097 ) @ ( cartesian_product2 @ SY1096 @ SY1097 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2036]) ).
thf(2284,plain,
! [SV179: $i] :
( ( ! [SY1098: $i] :
( ~ ( subset @ SV179 @ SY1098 )
| ! [SY1099: $i] : ( subset @ ( cartesian_product2 @ SY1099 @ SV179 ) @ ( cartesian_product2 @ SY1099 @ SY1098 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2037]) ).
thf(2285,plain,
! [SV180: $i] :
( ( ! [SY1100: $i,SY1101: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK81_D @ SY1101 @ SY1100 @ SV180 ) @ SY1101 )
| ~ ( in @ ( sK81_D @ SY1101 @ SY1100 @ SV180 ) @ SV180 ) )
| ~ ( ~ ( in @ ( sK81_D @ SY1101 @ SY1100 @ SV180 ) @ SY1101 )
| ~ ( in @ ( sK81_D @ SY1101 @ SY1100 @ SV180 ) @ SY1100 ) ) )
| ~ ( ( in @ ( sK81_D @ SY1101 @ SY1100 @ SV180 ) @ SY1101 )
| ( in @ ( sK81_D @ SY1101 @ SY1100 @ SV180 ) @ SV180 )
| ( in @ ( sK81_D @ SY1101 @ SY1100 @ SV180 ) @ SY1100 ) ) )
| ( SY1101
= ( set_union2 @ SV180 @ SY1100 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2038]) ).
thf(2286,plain,
! [SV180: $i] :
( ( ! [SY1102: $i,SY1103: $i] :
( ( SY1103
!= ( set_union2 @ SV180 @ SY1102 ) )
| ~ ( ~ ! [SY1104: $i] :
( ~ ( in @ SY1104 @ SY1103 )
| ( in @ SY1104 @ SV180 )
| ( in @ SY1104 @ SY1102 ) )
| ~ ~ ( ~ ! [SY1105: $i] :
( ~ ( in @ SY1105 @ SV180 )
| ( in @ SY1105 @ SY1103 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1102 )
| ( in @ SX3 @ SY1103 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2039]) ).
thf(2287,plain,
! [SV181: $i] :
( ( ( ~ ( element @ ( sK120_B @ SV181 ) @ ( powerset @ SV181 ) ) )
= $false )
| ( ( empty @ SV181 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2040]) ).
thf(2288,plain,
! [SV181: $i] :
( ( ( ~ ~ ( empty @ ( sK120_B @ SV181 ) ) )
= $false )
| ( ( empty @ SV181 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2040]) ).
thf(2289,plain,
! [SV1: $i,SV182: $i,SV392: $i] :
( ( ( ~ ( in @ SV392 @ SV182 )
| ( in @ SV392 @ SV1 ) )
= $true )
| ( ( element @ SV182 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2041]) ).
thf(2290,plain,
! [SV3: $i,SV308: $i] :
( ( ( ~ ( element @ SV308 @ ( powerset @ ( the_carrier @ SV3 ) ) ) )
= $true )
| ( ( ( subset_intersection2 @ ( the_carrier @ SV3 ) @ SV308 @ ( cast_as_carrier_subset @ SV3 ) )
= SV308 )
= $true )
| ( ( one_sorted_str @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2042]) ).
thf(2291,plain,
! [SV4: $i,SV183: $i] :
( ( ( SV183 = empty_set )
= $true )
| ( ( ( ( complements_of_subsets @ SV4 @ SV183 )
!= empty_set ) )
= $true )
| ( ( element @ SV183 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2043]) ).
thf(2292,plain,
! [SV5: $i,SV278: $i] :
( ( ( element @ SV278 @ ( powerset @ SV5 ) )
= $false )
| ( ( ! [SY1199: $i] :
( ~ ( element @ SY1199 @ SV5 )
| ( in @ SY1199 @ SV278 )
| ( in @ SY1199 @ ( subset_complement @ SV5 @ SV278 ) ) ) )
= $true )
| ( ( SV5 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2044]) ).
thf(2293,plain,
! [SV184: $i,SV6: $i,SV279: $i] :
( ( ( element @ SV279 @ ( powerset @ SV6 ) )
= $false )
| ( ( ~ ( in @ SV184 @ ( subset_complement @ SV6 @ SV279 ) )
| ~ ( in @ SV184 @ SV279 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2045]) ).
thf(2294,plain,
! [SV8: $i,SV309: $i] :
( ( ( ~ ( element @ SV309 @ SV8 ) )
= $true )
| ( ( v1_xcmplx_0 @ SV309 )
= $true )
| ( ( v1_membered @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2046]) ).
thf(2295,plain,
! [SV9: $i,SV310: $i] :
( ( ( ~ ( element @ SV310 @ ( powerset @ SV9 ) ) )
= $true )
| ( ( v1_membered @ SV310 )
= $true )
| ( ( v1_membered @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2047]) ).
thf(2296,plain,
! [SV185: $i,SV10: $i,SV280: $i] :
( ( ( element @ SV280 @ ( powerset @ ( cartesian_product2 @ SV10 @ SV185 ) ) )
= $false )
| ( ( relation @ SV280 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2048]) ).
thf(2297,plain,
! [SV11: $i,SV311: $i] :
( ( ( ~ ( element @ SV311 @ ( powerset @ SV11 ) ) )
= $true )
| ( ( finite @ SV311 )
= $true )
| ( ( finite @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2049]) ).
thf(2298,plain,
! [SV281: $i,SV12: $i,SV186: $i] :
( ( ( ~ ( element @ SV186 @ ( powerset @ SV12 ) ) )
= $true )
| ( ( ~ ( element @ SV281 @ ( powerset @ SV12 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV12 @ SV186 @ SV281 )
= ( subset_intersection2 @ SV12 @ SV281 @ SV186 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2050]) ).
thf(2299,plain,
! [SV189: $i,SV18: $i,SV282: $i] :
( ( ( relation_of2 @ SV282 @ SV18 @ SV189 )
= $false )
| ( ( element @ ( relation_dom_as_subset @ SV18 @ SV189 @ SV282 ) @ ( powerset @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2053]) ).
thf(2300,plain,
! [SV190: $i,SV19: $i,SV283: $i] :
( ( ( relation_of2 @ SV283 @ SV19 @ SV190 )
= $false )
| ( ( element @ ( relation_rng_as_subset @ SV19 @ SV190 @ SV283 ) @ ( powerset @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2054]) ).
thf(2301,plain,
! [SV284: $i,SV21: $i,SV192: $i] :
( ( ( ~ ( element @ SV192 @ ( powerset @ SV21 ) ) )
= $true )
| ( ( ~ ( element @ SV284 @ ( powerset @ SV21 ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV21 @ SV192 @ SV284 ) @ ( powerset @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2056]) ).
thf(2302,plain,
! [SV285: $i,SV23: $i,SV194: $i] :
( ( ( ~ ( element @ SV194 @ ( powerset @ SV23 ) ) )
= $true )
| ( ( ~ ( element @ SV285 @ ( powerset @ SV23 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV23 @ SV194 @ SV285 ) @ ( powerset @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2058]) ).
thf(2303,plain,
! [SV196: $i,SV27: $i,SV286: $i] :
( ( ( relation_of2_as_subset @ SV286 @ SV27 @ SV196 )
= $false )
| ( ( element @ SV286 @ ( powerset @ ( cartesian_product2 @ SV27 @ SV196 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2060]) ).
thf(2304,plain,
! [SV29: $i] :
( ( ( empty @ ( the_carrier @ SV29 ) )
= $false )
| ( ( empty_carrier @ SV29 )
= $true )
| ( ( one_sorted_str @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2061]) ).
thf(2305,plain,
! [SV31: $i,SV197: $i] :
( ( ( element @ SV197 @ ( powerset @ SV31 ) )
= $false )
| ( ( ! [SY805: $i] :
~ ( element @ SY805 @ ( powerset @ SV31 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV31 @ SV197 @ SV197 )
= SV197 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2062]) ).
thf(2306,plain,
! [SV287: $i,SV35: $i,SV201: $i] :
( ( ( ~ ( element @ SV201 @ ( powerset @ SV35 ) ) )
= $true )
| ( ( ~ ( element @ SV287 @ ( powerset @ SV35 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV35 @ SV201 @ SV287 )
= ( set_intersection2 @ SV201 @ SV287 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2066]) ).
thf(2307,plain,
! [SV288: $i,SV37: $i,SV203: $i] :
( ( ( ~ ( element @ SV203 @ ( powerset @ SV37 ) ) )
= $true )
| ( ( ~ ( element @ SV288 @ ( powerset @ SV37 ) ) )
= $true )
| ( ( ( subset_difference @ SV37 @ SV203 @ SV288 )
= ( set_difference @ SV203 @ SV288 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2068]) ).
thf(2308,plain,
! [SV39: $i,SV205: $i] :
( ( ( empty @ SV205 )
= $true )
| ( ( in @ SV39 @ SV205 )
= $true )
| ( ( element @ SV39 @ SV205 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2070]) ).
thf(2309,plain,
! [SV40: $i,SV289: $i,SV206: $i] :
( ( ( ~ ( element @ SV206 @ ( powerset @ SV289 ) ) )
= $true )
| ( ( ~ ( in @ SV40 @ SV206 ) )
= $true )
| ( ( element @ SV40 @ SV289 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2071]) ).
thf(2310,plain,
! [SV41: $i,SV290: $i,SV207: $i] :
( ( ( ~ ( element @ SV207 @ ( powerset @ SV290 ) ) )
= $true )
| ( ( ~ ( in @ SV41 @ SV207 ) )
= $true )
| ( ( ~ ( empty @ SV290 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2072]) ).
thf(2311,plain,
! [SV209: $i,SV44: $i] :
( ( ( in @ SV44 @ SV209 )
= $false )
| ( ( disjoint @ ( singleton @ SV44 ) @ SV209 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2074]) ).
thf(2312,plain,
! [SV211: $i,SV46: $i,SV393: $i] :
( ( ( ( in @ SV393 @ SV46 )
| ( subset @ SV46 @ ( set_difference @ SV211 @ ( singleton @ SV393 ) ) ) )
= $true )
| ( ( subset @ SV46 @ SV211 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2313,plain,
! [SV312: $i,SV291: $i,SV214: $i,SV50: $i] :
( ( ( ~ ( subset @ SV50 @ SV214 )
| ~ ( subset @ SV291 @ SV312 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV50 @ SV291 ) @ ( cartesian_product2 @ SV214 @ SV312 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2078]) ).
thf(2314,plain,
! [SV52: $i,SV292: $i] :
( ( ( finite @ SV292 )
= $false )
| ( ( ~ ( subset @ SV52 @ SV292 ) )
= $true )
| ( ( finite @ SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2080]) ).
thf(2315,plain,
! [SV216: $i,SV53: $i,SV293: $i,SV313: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV313 @ SV293 @ SV53 ) )
= $true )
| ( ( ~ ( subset @ ( relation_rng @ SV313 ) @ SV216 )
| ( relation_of2_as_subset @ SV313 @ SV293 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2081]) ).
thf(2316,plain,
! [SV217: $i,SV55: $i,SV294: $i,SV315: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV315 @ SV294 @ SV55 ) )
= $true )
| ( ( ~ ( subset @ SV55 @ SV217 )
| ( relation_of2_as_subset @ SV315 @ SV294 @ SV217 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2083]) ).
thf(2317,plain,
! [SV218: $i,SV56: $i,SV295: $i] :
( ( ( relation @ SV295 )
= $false )
| ( ( ~ ( subset @ SV56 @ SV218 )
| ( subset @ ( relation_inverse_image @ SV295 @ SV56 ) @ ( relation_inverse_image @ SV295 @ SV218 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2084]) ).
thf(2318,plain,
! [SV296: $i,SV220: $i,SV58: $i] :
( ( ( ~ ( subset @ SV58 @ SV220 ) )
= $true )
| ( ( ~ ( subset @ SV58 @ SV296 ) )
= $true )
| ( ( subset @ SV58 @ ( set_intersection2 @ SV220 @ SV296 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2085]) ).
thf(2319,plain,
! [SV297: $i,SV221: $i,SV59: $i] :
( ( ( ~ ( subset @ SV59 @ SV221 ) )
= $true )
| ( ( ~ ( subset @ SV221 @ SV297 ) )
= $true )
| ( ( subset @ SV59 @ SV297 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2086]) ).
thf(2320,plain,
! [SV222: $i,SV60: $i] :
( ( ( ~ ( in @ SV60 @ SV222 ) )
= $true )
| ( ( ordinal @ SV60 )
= $true )
| ( ( ordinal @ SV222 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2087]) ).
thf(2321,plain,
! [SV61: $i,SV316: $i] :
( ( ( ~ ( ordinal @ SV316 ) )
= $true )
| ( ( ( in @ SV61 @ SV316 )
| ( SV61 = SV316 )
| ( in @ SV316 @ SV61 ) )
= $true )
| ( ( ordinal @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2088]) ).
thf(2322,plain,
! [SV223: $i,SV394: $i,SV62: $i] :
( ( ( subset @ ( set_intersection2 @ SV62 @ SV394 ) @ ( set_intersection2 @ SV223 @ SV394 ) )
= $true )
| ( ( subset @ SV62 @ SV223 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2089]) ).
thf(2323,plain,
! [SV225: $i,SV395: $i,SV65: $i] :
( ( ( subset @ ( set_difference @ SV65 @ SV395 ) @ ( set_difference @ SV225 @ SV395 ) )
= $true )
| ( ( subset @ SV65 @ SV225 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2091]) ).
thf(2324,plain,
! [SV298: $i,SV228: $i,SV68: $i] :
( ( ( ~ ( in @ SV68 @ SV228 ) )
= $true )
| ( ( ~ ( in @ SV228 @ SV298 ) )
= $true )
| ( ( ~ ( in @ SV298 @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2092]) ).
thf(2325,plain,
! [SV73: $i,SV232: $i] :
( ( ( SV232 = empty_set )
= $true )
| ( ( ( subset_difference @ SV73 @ ( cast_to_subset @ SV73 ) @ ( union_of_subsets @ SV73 @ SV232 ) )
= ( meet_of_subsets @ SV73 @ ( complements_of_subsets @ SV73 @ SV232 ) ) )
= $true )
| ( ( element @ SV232 @ ( powerset @ ( powerset @ SV73 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2095]) ).
thf(2326,plain,
! [SV74: $i,SV233: $i] :
( ( ( SV233 = empty_set )
= $true )
| ( ( ( union_of_subsets @ SV74 @ ( complements_of_subsets @ SV74 @ SV233 ) )
= ( subset_difference @ SV74 @ ( cast_to_subset @ SV74 ) @ ( meet_of_subsets @ SV74 @ SV233 ) ) )
= $true )
| ( ( element @ SV233 @ ( powerset @ ( powerset @ SV74 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2096]) ).
thf(2327,plain,
! [SV235: $i,SV77: $i] :
( ( ( subset @ SV77 @ SV235 )
= $false )
| ( ( proper_subset @ SV235 @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2098]) ).
thf(2328,plain,
! [SV78: $i,SV299: $i,SV236: $i] :
( ( ( ~ ( disjoint @ SV236 @ SV299 ) )
= $true )
| ( ( ~ ( subset @ SV78 @ SV236 ) )
= $true )
| ( ( disjoint @ SV78 @ SV299 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2099]) ).
thf(2329,plain,
! [SV300: $i,SV240: $i,SV83: $i] :
( ( ( ~ ( subset @ SV83 @ SV240 ) )
= $true )
| ( ( ~ ( subset @ SV300 @ SV240 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV83 @ SV300 ) @ SV240 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2102]) ).
thf(2330,plain,
! [SV317: $i,SV241: $i,SV84: $i] :
( ( ( ( singleton @ SV84 )
= ( unordered_pair @ SV241 @ SV317 ) )
= $false )
| ( ( SV84 = SV241 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2103]) ).
thf(2331,plain,
! [SV301: $i,SV243: $i,SV86: $i] :
( ( ( ( singleton @ SV86 )
= ( unordered_pair @ SV243 @ SV301 ) )
= $false )
| ( ( SV243 = SV301 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2105]) ).
thf(2332,plain,
! [SV87: $i,SV244: $i] :
( ( ( in @ SV244 @ SV87 )
= $false )
| ( ( in @ SV87 @ SV244 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2106]) ).
thf(2333,plain,
! [SV302: $i,SV246: $i,SV96: $i] :
( ( ( ( empty_carrier @ SV96 )
| ~ ( join_semilatt_str @ SV96 )
| ~ ( element @ SV246 @ ( the_carrier @ SV96 ) ) )
= $true )
| ( ( ~ ( element @ SV302 @ ( the_carrier @ SV96 ) ) )
= $true )
| ( ( element @ ( join @ SV96 @ SV246 @ SV302 ) @ ( the_carrier @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2108]) ).
thf(2334,plain,
! [SV303: $i,SV247: $i,SV98: $i] :
( ( ( ( empty_carrier @ SV98 )
| ~ ( meet_semilatt_str @ SV98 )
| ~ ( element @ SV247 @ ( the_carrier @ SV98 ) ) )
= $true )
| ( ( ~ ( element @ SV303 @ ( the_carrier @ SV98 ) ) )
= $true )
| ( ( element @ ( meet @ SV98 @ SV247 @ SV303 ) @ ( the_carrier @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2109]) ).
thf(2335,plain,
! [SV248: $i,SV101: $i] :
( ( ( relation @ SV101 )
= $false )
| ( ( ~ ( relation @ SV248 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV101 @ SV248 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2111]) ).
thf(2336,plain,
! [SV253: $i,SV111: $i] :
( ( ( relation @ SV111 )
= $false )
| ( ( ~ ( relation @ SV253 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV111 @ SV253 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2117]) ).
thf(2337,plain,
! [SV255: $i,SV115: $i] :
( ( ( relation @ SV115 )
= $false )
| ( ( ~ ( relation @ SV255 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV115 @ SV255 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2120]) ).
thf(2338,plain,
! [SV256: $i,SV119: $i] :
( ( ( relation @ SV119 )
= $false )
| ( ( ~ ( relation @ SV256 ) )
= $true )
| ( ( relation @ ( set_difference @ SV119 @ SV256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2123]) ).
thf(2339,plain,
! [SV258: $i,SV122: $i] :
( ( ( empty @ ( cartesian_product2 @ SV122 @ SV258 ) )
= $false )
| ( ( empty @ SV258 )
= $true )
| ( ( empty @ SV122 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2125]) ).
thf(2340,plain,
! [SV123: $i] :
( ( ( empty @ ( relation_dom @ SV123 ) )
= $false )
| ( ( empty @ SV123 )
= $true )
| ( ( relation @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2126]) ).
thf(2341,plain,
! [SV124: $i] :
( ( ( empty @ ( relation_rng @ SV124 ) )
= $false )
| ( ( empty @ SV124 )
= $true )
| ( ( relation @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2127]) ).
thf(2342,plain,
! [SV259: $i,SV125: $i] :
( ( ( finite @ SV125 )
= $false )
| ( ( ~ ( finite @ SV259 ) )
= $true )
| ( ( finite @ ( set_union2 @ SV125 @ SV259 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2128]) ).
thf(2343,plain,
! [SV260: $i,SV128: $i,SV306: $i] :
( ( ( relation_of2 @ SV306 @ SV128 @ SV260 )
= $false )
| ( ( ( relation_dom_as_subset @ SV128 @ SV260 @ SV306 )
= ( relation_dom @ SV306 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2129]) ).
thf(2344,plain,
! [SV261: $i,SV129: $i,SV307: $i] :
( ( ( relation_of2 @ SV307 @ SV129 @ SV261 )
= $false )
| ( ( ( relation_rng_as_subset @ SV129 @ SV261 @ SV307 )
= ( relation_rng @ SV307 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2130]) ).
thf(2345,plain,
! [SV263: $i,SV137: $i] :
( ( ( in @ SV137 @ SV263 )
= $false )
| ( ( empty @ SV263 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2132]) ).
thf(2346,plain,
! [SV264: $i,SV138: $i] :
( ( ( empty @ SV138 )
= $false )
| ( ( SV138 = SV264 )
= $true )
| ( ( ~ ( empty @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2133]) ).
thf(2347,plain,
! [SV396: $i,SV326: $i] :
( ( ( SV326 = SV396 )
| ~ ( subset @ SV326 @ SV396 )
| ( proper_subset @ SV326 @ SV396 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2134]) ).
thf(2348,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2135]) ).
thf(2349,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2135]) ).
thf(2350,plain,
! [SV397: $i,SV327: $i] :
( ( ( ( set_intersection2 @ SV327 @ SV397 )
!= empty_set )
| ( disjoint @ SV327 @ SV397 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2136]) ).
thf(2351,plain,
! [SV398: $i,SV328: $i] :
( ( ~ ( disjoint @ SV328 @ SV398 )
| ( ( set_intersection2 @ SV328 @ SV398 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2137]) ).
thf(2352,plain,
! [SV139: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ( ( sK17_C @ SV139 )
!= ( sK18_SY613 @ SV139 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
!= ( sK18_SY613 @ SV139 ) )
| ~ ( in @ ( sK22_SY620 @ SV139 ) @ SV139 ) )
| ( ( sK23_SY629 @ SV139 )
!= ( singleton @ ( sK22_SY620 @ SV139 ) ) ) ) )
| ( ( sK17_C @ SV139 )
!= ( sK19_SY619 @ SV139 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
!= ( sK19_SY619 @ SV139 ) )
| ~ ( in @ ( sK20_SY626 @ SV139 ) @ SV139 ) )
| ( ( sK21_SY628 @ SV139 )
!= ( singleton @ ( sK20_SY626 @ SV139 ) ) ) ) ) )
= $true )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2138]) ).
thf(2353,plain,
! [SV139: $i] :
( ( ( ( ( sK18_SY613 @ SV139 )
!= ( sK19_SY619 @ SV139 ) ) )
= $true )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2139]) ).
thf(2354,plain,
! [SV140: $i] :
( ( ( ~ ( element @ ( sK116_B @ SV140 ) @ ( powerset @ ( the_carrier @ SV140 ) ) )
| ~ ~ ( empty @ ( sK116_B @ SV140 ) ) )
= $false )
| ( ( empty_carrier @ SV140 )
= $true )
| ( ( one_sorted_str @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2140]) ).
thf(2355,plain,
( ( ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_intersection2 @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2141]) ).
thf(2356,plain,
( ( ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_intersection2 @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2141]) ).
thf(2357,plain,
! [SV329: $i] :
( ( ( ~ ( v3_membered @ SV329 ) )
= $true )
| ( ( ! [SY1206: $i] : ( v3_membered @ ( set_intersection2 @ SY1206 @ SV329 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2142]) ).
thf(2358,plain,
! [SV141: $i] :
( ( ( in @ ( sK99_B @ SV141 ) @ SV141 )
= $true )
| ( ( ordinal @ SV141 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2143]) ).
thf(2359,plain,
! [SV141: $i] :
( ( ( ~ ( ordinal @ ( sK99_B @ SV141 ) )
| ~ ( subset @ ( sK99_B @ SV141 ) @ SV141 ) )
= $true )
| ( ( ordinal @ SV141 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2144]) ).
thf(2360,plain,
! [SV399: $i,SV142: $i] :
( ( ! [SY1267: $i] :
( ~ ( in @ SV142 @ SY1267 )
| ~ ( in @ SV399 @ SY1267 )
| ( subset @ ( unordered_pair @ SV142 @ SV399 ) @ SY1267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2145]) ).
thf(2361,plain,
! [SV142: $i] :
( ( ~ ! [SY919: $i,SY920: $i] :
( ~ ( subset @ ( unordered_pair @ SV142 @ SY919 ) @ SY920 )
| ( in @ SV142 @ SY920 ) )
| ~ ! [SY921: $i,SY922: $i] :
( ~ ( subset @ ( unordered_pair @ SV142 @ SY921 ) @ SY922 )
| ( in @ SY921 @ SY922 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2146]) ).
thf(2362,plain,
! [SV143: $i,SV400: $i] :
( ( ! [SY1268: $i] :
( ~ ( ~ ( ~ ( in @ ( sK70_D @ SY1268 @ SV400 @ SV143 ) @ SV143 )
| ~ ( in @ ( sK70_D @ SY1268 @ SV400 @ SV143 ) @ SV400 )
| ~ ( in @ ( sK70_D @ SY1268 @ SV400 @ SV143 ) @ SY1268 ) )
| ~ ~ ( ~ ( ( in @ ( sK70_D @ SY1268 @ SV400 @ SV143 ) @ SV143 )
| ( in @ ( sK70_D @ SY1268 @ SV400 @ SV143 ) @ SY1268 ) )
| ~ ( ( in @ ( sK70_D @ SY1268 @ SV400 @ SV143 ) @ SV400 )
| ( in @ ( sK70_D @ SY1268 @ SV400 @ SV143 ) @ SY1268 ) ) ) )
| ( SY1268
= ( set_intersection2 @ SV143 @ SV400 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2147]) ).
thf(2363,plain,
! [SV401: $i,SV143: $i] :
( ( ! [SY1269: $i] :
( ( SY1269
!= ( set_intersection2 @ SV143 @ SV401 ) )
| ~ ( ~ ! [SY1270: $i] :
( ~ ( in @ SY1270 @ SV143 )
| ~ ( in @ SY1270 @ SV401 )
| ( in @ SY1270 @ SY1269 ) )
| ~ ~ ( ~ ! [SY928: $i] :
( ~ ( in @ SY928 @ SY1269 )
| ( in @ SY928 @ SV143 ) )
| ~ ! [SY1272: $i] :
( ~ ( in @ SY1272 @ SY1269 )
| ( in @ SY1272 @ SV401 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2148]) ).
thf(2364,plain,
! [SV144: $i] :
( ( ( ~ ~ ( ~ ! [SY930: $i] :
( ~ ( element @ SY930 @ ( powerset @ SV144 ) )
| ( v1_membered @ SY930 ) )
| ~ ! [SY931: $i] :
( ~ ( element @ SY931 @ ( powerset @ SV144 ) )
| ( v2_membered @ SY931 ) ) ) )
= $false )
| ( ( v3_membered @ SV144 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2149]) ).
thf(2365,plain,
! [SV144: $i] :
( ( ( ~ ! [SY932: $i] :
( ~ ( element @ SY932 @ ( powerset @ SV144 ) )
| ( v3_membered @ SY932 ) ) )
= $false )
| ( ( v3_membered @ SV144 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2149]) ).
thf(2366,plain,
! [SV145: $i,SV265: $i] :
( ( ( relation @ SV265 )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1142: $i] :
( ~ ( in @ SY1142 @ ( sK52_SY712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SY1142 ) @ SV265 ) )
| ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK52_SY712 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) ) ) )
| ~ ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 ) )
| ~ ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 ) )
| ~ ~ ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ ( sK51_SY718 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SY1143 ) @ SV265 ) )
| ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK51_SY718 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) ) ) ) )
| ~ ( ( ( sK49_SY705 @ SV265 @ SV145 )
!= ( sK50_SY711 @ SV265 @ SV145 ) ) ) )
| ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2150]) ).
thf(2367,plain,
! [SV402: $i,SV330: $i] :
( ( ~ ( subset @ SV330 @ SV402 )
| ~ ( subset @ SV402 @ SV330 )
| ( SV330 = SV402 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2151]) ).
thf(2368,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2152]) ).
thf(2369,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2152]) ).
thf(2370,plain,
! [SV146: $i,SV266: $i] :
( ( ( ~ ! [SY1149: $i] :
( ~ ( in @ SY1149 @ SV266 )
| ~ ( in @ SY1149 @ ( sK5_C @ SV266 @ SV146 ) ) ) )
= $false )
| ( ( ~ ( in @ SV146 @ SV266 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2153]) ).
thf(2371,plain,
! [SV146: $i,SV266: $i] :
( ( ( ~ ( in @ ( sK5_C @ SV266 @ SV146 ) @ SV266 ) )
= $false )
| ( ( ~ ( in @ SV146 @ SV266 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2153]) ).
thf(2372,plain,
! [SV331: $i] :
( ( ( ~ ( ~ ( in @ ( sK85_B @ SV331 ) @ SV331 )
| ~ ~ ( subset @ ( sK85_B @ SV331 ) @ SV331 ) ) )
= $true )
| ( ( epsilon_transitive @ SV331 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2154]) ).
thf(2373,plain,
! [SV332: $i] :
( ( ( ~ ( epsilon_transitive @ SV332 ) )
= $true )
| ( ( ! [SY1208: $i] :
( ~ ( in @ SY1208 @ SV332 )
| ( subset @ SY1208 @ SV332 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2155]) ).
thf(2374,plain,
! [SV147: $i,SV403: $i] :
( ( ! [SY1273: $i] :
( ~ ( ~ ( ~ ( in @ ( sK66_D @ SY1273 @ SV403 @ SV147 ) @ SV147 )
| ( in @ ( sK66_D @ SY1273 @ SV403 @ SV147 ) @ SV403 )
| ~ ( in @ ( sK66_D @ SY1273 @ SV403 @ SV147 ) @ SY1273 ) )
| ~ ~ ( ~ ( ( in @ ( sK66_D @ SY1273 @ SV403 @ SV147 ) @ SV147 )
| ( in @ ( sK66_D @ SY1273 @ SV403 @ SV147 ) @ SY1273 ) )
| ~ ( ~ ( in @ ( sK66_D @ SY1273 @ SV403 @ SV147 ) @ SV403 )
| ( in @ ( sK66_D @ SY1273 @ SV403 @ SV147 ) @ SY1273 ) ) ) )
| ( SY1273
= ( set_difference @ SV147 @ SV403 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2156]) ).
thf(2375,plain,
! [SV404: $i,SV147: $i] :
( ( ! [SY1274: $i] :
( ( SY1274
!= ( set_difference @ SV147 @ SV404 ) )
| ~ ( ~ ! [SY1275: $i] :
( ~ ( in @ SY1275 @ SV147 )
| ( in @ SY1275 @ SV404 )
| ( in @ SY1275 @ SY1274 ) )
| ~ ~ ( ~ ! [SY948: $i] :
( ~ ( in @ SY948 @ SY1274 )
| ( in @ SY948 @ SV147 ) )
| ~ ! [SY1277: $i] :
( ~ ( in @ SY1277 @ SY1274 )
| ~ ( in @ SY1277 @ SV404 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2157]) ).
thf(2376,plain,
! [SV333: $i] :
( ( ( in @ ( sK86_B @ SV333 ) @ SV333 )
= $true )
| ( ( SV333 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2158]) ).
thf(2377,plain,
! [SV334: $i] :
( ( ( ( SV334 != empty_set ) )
= $true )
| ( ( ! [SY1209: $i] :
~ ( in @ SY1209 @ SV334 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2159]) ).
thf(2378,plain,
! [SV148: $i,SV335: $i] :
( ( ( ~ ( element @ SV335 @ ( powerset @ ( powerset @ SV148 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1210: $i] :
( ~ ( in @ SY1210 @ SV335 )
| ~ ( subset @ ( sK105_C @ SV335 @ SV148 ) @ SY1210 )
| ( SY1210
= ( sK105_C @ SV335 @ SV148 ) ) )
| ~ ( in @ ( sK105_C @ SV335 @ SV148 ) @ SV335 ) )
| ( SV335 = empty_set ) )
= $true )
| ( ( finite @ SV148 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2160]) ).
thf(2379,plain,
! [SV405: $i,SV336: $i] :
( ( ( ( set_difference @ SV336 @ SV405 )
!= SV336 )
| ( disjoint @ SV336 @ SV405 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2161]) ).
thf(2380,plain,
! [SV406: $i,SV337: $i] :
( ( ~ ( disjoint @ SV337 @ SV406 )
| ( ( set_difference @ SV337 @ SV406 )
= SV337 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2162]) ).
thf(2381,plain,
! [SV407: $i,SV338: $i] :
( ( ( ( set_difference @ SV338 @ ( singleton @ SV407 ) )
!= SV338 )
| ~ ( in @ SV407 @ SV338 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2163]) ).
thf(2382,plain,
! [SV339: $i,SV408: $i] :
( ( ( in @ SV408 @ SV339 )
| ( ( set_difference @ SV339 @ ( singleton @ SV408 ) )
= SV339 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2164]) ).
thf(2383,plain,
! [SV340: $i,SV409: $i] :
( ( ~ ( ~ ( ! [SY1278: $i] :
( ~ ( in @ ( sK68_C @ SV409 @ SV340 ) @ SY1278 )
| ~ ( in @ SY1278 @ SV340 ) )
| ~ ( in @ ( sK68_C @ SV409 @ SV340 ) @ SV409 ) )
| ~ ( ~ ( ~ ( in @ ( sK68_C @ SV409 @ SV340 ) @ ( sK69_SY723 @ SV409 @ SV340 ) )
| ~ ( in @ ( sK69_SY723 @ SV409 @ SV340 ) @ SV340 ) )
| ( in @ ( sK68_C @ SV409 @ SV340 ) @ SV409 ) ) )
| ( SV409
= ( union @ SV340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2165]) ).
thf(2384,plain,
! [SV341: $i,SV410: $i] :
( ( ( SV410
!= ( union @ SV341 ) )
| ~ ( ~ ! [SY1279: $i] :
( ! [SY1219: $i] :
( ~ ( in @ SY1279 @ SY1219 )
| ~ ( in @ SY1219 @ SV341 ) )
| ( in @ SY1279 @ SV410 ) )
| ~ ! [SY1281: $i] :
( ~ ( in @ SY1281 @ SV410 )
| ~ ( ~ ( in @ SY1281 @ ( sK67_D @ SY1281 @ SV410 @ SV341 ) )
| ~ ( in @ ( sK67_D @ SY1281 @ SV410 @ SV341 ) @ SV341 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2166]) ).
thf(2385,plain,
! [SV411: $i,SV342: $i] :
( ( ~ ( element @ SV342 @ ( powerset @ SV411 ) )
| ( subset @ SV342 @ SV411 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2167]) ).
thf(2386,plain,
! [SV412: $i,SV343: $i] :
( ( ~ ( subset @ SV343 @ SV412 )
| ( element @ SV343 @ ( powerset @ SV412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2168]) ).
thf(2387,plain,
! [SV344: $i] :
( ( ( ~ ( empty @ SV344 ) )
= $true )
| ( ( empty @ ( relation_inverse @ SV344 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2169]) ).
thf(2388,plain,
! [SV345: $i] :
( ( ( ~ ( empty @ SV345 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV345 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2170]) ).
thf(2389,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2171]) ).
thf(2390,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2171]) ).
thf(2391,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2172]) ).
thf(2392,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2172]) ).
thf(2393,plain,
! [SV346: $i,SV413: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK124_C @ SV413 @ SV346 ) @ SV413 )
| ~ ( subset @ ( sK124_C @ SV413 @ SV346 ) @ SV346 ) )
| ~ ( ( in @ ( sK124_C @ SV413 @ SV346 ) @ SV413 )
| ( subset @ ( sK124_C @ SV413 @ SV346 ) @ SV346 ) ) )
| ( SV413
= ( powerset @ SV346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2173]) ).
thf(2394,plain,
! [SV347: $i,SV414: $i] :
( ( ( SV414
!= ( powerset @ SV347 ) )
| ~ ( ~ ! [SY1282: $i] :
( ~ ( in @ SY1282 @ SV414 )
| ( subset @ SY1282 @ SV347 ) )
| ~ ! [SY1283: $i] :
( ~ ( subset @ SY1283 @ SV347 )
| ( in @ SY1283 @ SV414 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2174]) ).
thf(2395,plain,
! [SV149: $i] :
( ( ( ~ ( ~ ( element @ ( sK118_B @ SV149 ) @ ( powerset @ SV149 ) )
| ~ ~ ( empty @ ( sK118_B @ SV149 ) ) ) )
= $true )
| ( ( empty @ SV149 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2175]) ).
thf(2396,plain,
! [SV149: $i] :
( ( ( finite @ ( sK118_B @ SV149 ) )
= $true )
| ( ( empty @ SV149 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2176]) ).
thf(2397,plain,
! [SV415: $i,SV150: $i] :
( ( ! [SY1284: $i] :
( ~ ( relation_of2_as_subset @ SY1284 @ SV150 @ SV415 )
| ~ ( ~ ! [SY1285: $i] :
~ ( in @ ( ordered_pair @ SY1285 @ ( sK102_D @ SY1284 @ SV415 @ SV150 ) ) @ SY1284 )
| ~ ( in @ ( sK102_D @ SY1284 @ SV415 @ SV150 ) @ SV415 ) )
| ( ( relation_rng_as_subset @ SV150 @ SV415 @ SY1284 )
= SV415 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2177]) ).
thf(2398,plain,
! [SV416: $i,SV150: $i] :
( ( ! [SY1286: $i] :
( ~ ( relation_of2_as_subset @ SY1286 @ SV150 @ SV416 )
| ( ( relation_rng_as_subset @ SV150 @ SV416 @ SY1286 )
!= SV416 )
| ! [SY1287: $i] :
( ( in @ ( ordered_pair @ ( sK101_E @ SY1287 @ SY1286 @ SV416 @ SV150 ) @ SY1287 ) @ SY1286 )
| ~ ( in @ SY1287 @ SV416 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2178]) ).
thf(2399,plain,
! [SV151: $i,SV267: $i] :
( ( ! [SY1150: $i,SY1151: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 ) @ SY1151 )
| ( ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 )
!= SY1150 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 ) @ SY1151 )
| ( ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 )
!= SV151 ) )
| ~ ( ~ ( in @ ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 ) @ SY1151 )
| ( ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 )
!= SV267 ) ) ) )
| ~ ( ( in @ ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 ) @ SY1151 )
| ( ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 )
= SY1150 )
| ( ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 )
= SV151 )
| ( ( sK94_E @ SY1151 @ SY1150 @ SV267 @ SV151 )
= SV267 ) ) )
| ( SY1151
= ( unordered_triple @ SV151 @ SV267 @ SY1150 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2179]) ).
thf(2400,plain,
! [SV267: $i,SV151: $i] :
( ( ! [SY1152: $i,SY1153: $i] :
( ( SY1153
!= ( unordered_triple @ SV151 @ SV267 @ SY1152 ) )
| ~ ( ~ ! [SY1154: $i] :
( ~ ( in @ SY1154 @ SY1153 )
| ( SY1154 = SY1152 )
| ( SY1154 = SV151 )
| ( SY1154 = SV267 ) )
| ~ ~ ( ~ ! [SX4: $i] :
( ( SX4 != SY1152 )
| ( in @ SX4 @ SY1153 ) )
| ~ ~ ( ~ ! [SY965: $i] :
( ( SY965 != SV151 )
| ( in @ SY965 @ SY1153 ) )
| ~ ! [SY1157: $i] :
( ( SY1157 != SV267 )
| ( in @ SY1157 @ SY1153 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2180]) ).
thf(2401,plain,
! [SV152: $i,SV417: $i] :
( ( ~ ( subset @ SV417 @ ( sK106_B @ SV152 ) )
| ( are_equipotent @ SV417 @ ( sK106_B @ SV152 ) )
| ( in @ SV417 @ ( sK106_B @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2181]) ).
thf(2402,plain,
! [SV152: $i] :
( ( ~ ! [SY968: $i] :
( ~ ( in @ SY968 @ ( sK106_B @ SV152 ) )
| ( in @ ( powerset @ SY968 ) @ ( sK106_B @ SV152 ) ) )
| ~ ~ ( ~ ! [SY969: $i,SY970: $i] :
( ~ ( in @ SY969 @ ( sK106_B @ SV152 ) )
| ~ ( subset @ SY970 @ SY969 )
| ( in @ SY970 @ ( sK106_B @ SV152 ) ) )
| ~ ( in @ SV152 @ ( sK106_B @ SV152 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2182]) ).
thf(2403,plain,
! [SV153: $i,SV418: $i] :
( ( ~ ( in @ SV418 @ SV153 )
| ~ ( ordinal @ SV418 )
| ( in @ SV418 @ ( sK107_B @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2183]) ).
thf(2404,plain,
! [SV153: $i] :
( ( ~ ! [SY972: $i] :
( ~ ( in @ SY972 @ ( sK107_B @ SV153 ) )
| ( in @ SY972 @ SV153 ) )
| ~ ! [SY973: $i] :
( ~ ( in @ SY973 @ ( sK107_B @ SV153 ) )
| ( ordinal @ SY973 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2184]) ).
thf(2405,plain,
! [SV154: $i] :
( ( ( ~ ! [SY974: $i] :
( ~ ( relation @ SY974 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK72_C @ SY974 @ SV154 ) @ ( sK73_SY724 @ SY974 @ SV154 ) ) @ SV154 )
| ~ ~ ( in @ ( ordered_pair @ ( sK72_C @ SY974 @ SV154 ) @ ( sK73_SY724 @ SY974 @ SV154 ) ) @ SY974 ) )
| ( subset @ SV154 @ SY974 ) ) )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2185]) ).
thf(2406,plain,
! [SV154: $i] :
( ( ( ~ ! [SY975: $i] :
( ~ ( relation @ SY975 )
| ~ ( subset @ SV154 @ SY975 )
| ! [SY976: $i,SY977: $i] :
( ~ ( in @ ( ordered_pair @ SY976 @ SY977 ) @ SV154 )
| ( in @ ( ordered_pair @ SY976 @ SY977 ) @ SY975 ) ) ) )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2185]) ).
thf(2407,plain,
! [SV268: $i,SV155: $i] :
( ( ( ~ ! [SY1158: $i] :
( ~ ( element @ SY1158 @ ( powerset @ ( powerset @ SV155 ) ) )
| ~ ( ~ ( element @ ( sK123_D @ SY1158 @ SV268 @ SV155 ) @ ( powerset @ SV155 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK123_D @ SY1158 @ SV268 @ SV155 ) @ SY1158 )
| ~ ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SY1158 @ SV268 @ SV155 ) ) @ SV268 ) )
| ~ ( ( in @ ( sK123_D @ SY1158 @ SV268 @ SV155 ) @ SY1158 )
| ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SY1158 @ SV268 @ SV155 ) ) @ SV268 ) ) ) )
| ( SY1158
= ( complements_of_subsets @ SV155 @ SV268 ) ) )
| ~ ! [SY1159: $i] :
( ~ ( element @ SY1159 @ ( powerset @ ( powerset @ SV155 ) ) )
| ( SY1159
!= ( complements_of_subsets @ SV155 @ SV268 ) )
| ~ ( ~ ! [SY1160: $i] :
( ~ ( element @ SY1160 @ ( powerset @ SV155 ) )
| ~ ( in @ SY1160 @ SY1159 )
| ( in @ ( subset_complement @ SV155 @ SY1160 ) @ SV268 ) )
| ~ ! [SY1161: $i] :
( ~ ( element @ SY1161 @ ( powerset @ SV155 ) )
| ~ ( in @ ( subset_complement @ SV155 @ SY1161 ) @ SV268 )
| ( in @ SY1161 @ SY1159 ) ) ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2186]) ).
thf(2408,plain,
! [SV419: $i,SV348: $i] :
( ( ~ ( subset @ SV348 @ ( singleton @ SV419 ) )
| ( SV348 = empty_set )
| ( SV348
= ( singleton @ SV419 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2187]) ).
thf(2409,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2188]) ).
thf(2410,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2188]) ).
thf(2411,plain,
! [SV420: $i,SV349: $i] :
( ( ~ ( subset @ SV349 @ ( singleton @ SV420 ) )
| ( SV349 = empty_set )
| ( SV349
= ( singleton @ SV420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2189]) ).
thf(2412,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2190]) ).
thf(2413,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2190]) ).
thf(2414,plain,
! [SV421: $i,SV350: $i] :
( ( ( ( set_difference @ SV350 @ SV421 )
!= empty_set )
| ( subset @ SV350 @ SV421 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2191]) ).
thf(2415,plain,
! [SV422: $i,SV351: $i] :
( ( ~ ( subset @ SV351 @ SV422 )
| ( ( set_difference @ SV351 @ SV422 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2192]) ).
thf(2416,plain,
! [SV156: $i] :
( ( ( ~ ! [SY983: $i] :
( ~ ( element @ SY983 @ ( powerset @ SV156 ) )
| ( v1_membered @ SY983 ) ) )
= $false )
| ( ( v2_membered @ SV156 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2193]) ).
thf(2417,plain,
! [SV156: $i] :
( ( ( ~ ! [SY984: $i] :
( ~ ( element @ SY984 @ ( powerset @ SV156 ) )
| ( v2_membered @ SY984 ) ) )
= $false )
| ( ( v2_membered @ SV156 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2193]) ).
thf(2418,plain,
! [SV423: $i,SV352: $i] :
( ( ~ ( empty @ SV352 )
| ~ ( relation @ SV423 )
| ( empty @ ( relation_composition @ SV352 @ SV423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2194]) ).
thf(2419,plain,
! [SV424: $i,SV353: $i] :
( ( ~ ( empty @ SV353 )
| ~ ( relation @ SV424 )
| ( relation @ ( relation_composition @ SV353 @ SV424 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2195]) ).
thf(2420,plain,
! [SV425: $i] :
( ( ( ~ ( ~ ! [SY1288: $i] :
( ! [SY1289: $i] :
( ( SY1289 != SY1288 )
| ~ ( in @ SY1289 @ SV425 ) )
| ~ ( ordinal @ SY1288 )
| ( in @ SY1288 @ ( sK7_B @ SV425 ) ) )
| ~ ! [SY1290: $i] :
( ~ ( in @ SY1290 @ ( sK7_B @ SV425 ) )
| ~ ( ~ ~ ( ( ( sK8_D @ SY1290 @ SV425 )
!= SY1290 )
| ~ ( in @ ( sK8_D @ SY1290 @ SV425 ) @ SV425 ) )
| ~ ( ordinal @ SY1290 ) ) ) ) )
= $true )
| ( sK12_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2196]) ).
thf(2421,plain,
( ( sK12_REN = $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK9_B != sK10_SY601 )
| ~ ( ordinal @ sK10_SY601 ) )
| ( sK9_B != sK11_SY603 ) )
| ~ ( ordinal @ sK11_SY603 ) )
| ~ ( ( sK10_SY601 != sK11_SY603 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2197]) ).
thf(2422,plain,
! [SV426: $i,SV157: $i] :
( ( ! [SY1291: $i] :
( ~ ( relation @ SY1291 )
| ~ ( in @ SV157 @ SY1291 )
| ~ ( in @ SV157 @ ( cartesian_product2 @ SV426 @ SV426 ) )
| ( in @ SV157 @ ( relation_restriction @ SY1291 @ SV426 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2199]) ).
thf(2423,plain,
! [SV157: $i] :
( ( ~ ! [SY987: $i,SY988: $i] :
( ~ ( relation @ SY988 )
| ~ ( in @ SV157 @ ( relation_restriction @ SY988 @ SY987 ) )
| ( in @ SV157 @ SY988 ) )
| ~ ! [SY989: $i,SY990: $i] :
( ~ ( relation @ SY990 )
| ~ ( in @ SV157 @ ( relation_restriction @ SY990 @ SY989 ) )
| ( in @ SV157 @ ( cartesian_product2 @ SY989 @ SY989 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2200]) ).
thf(2424,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2201]) ).
thf(2425,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2201]) ).
thf(2426,plain,
! [SV158: $i] :
( ( ~ ~ ( ~ ! [SY991: $i,SY992: $i] :
( ~ ( relation_of2_as_subset @ SY992 @ SV158 @ SY991 )
| ( SY991 = empty_set )
| ( SV158
!= ( relation_dom_as_subset @ SV158 @ SY991 @ SY992 ) )
| ( quasi_total @ SY992 @ SV158 @ SY991 ) )
| ~ ! [SY993: $i,SY994: $i] :
( ~ ( relation_of2_as_subset @ SY994 @ SV158 @ SY993 )
| ( SY993 = empty_set )
| ~ ( quasi_total @ SY994 @ SV158 @ SY993 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SY993 @ SY994 ) ) ) )
| ~ ~ ( ~ ! [SY995: $i,SY996: $i] :
( ~ ( relation_of2_as_subset @ SY996 @ SV158 @ SY995 )
| ( SV158 != empty_set )
| ( SV158
!= ( relation_dom_as_subset @ SV158 @ SY995 @ SY996 ) )
| ( quasi_total @ SY996 @ SV158 @ SY995 ) )
| ~ ! [SY997: $i,SY998: $i] :
( ~ ( relation_of2_as_subset @ SY998 @ SV158 @ SY997 )
| ( SV158 != empty_set )
| ~ ( quasi_total @ SY998 @ SV158 @ SY997 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SY997 @ SY998 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2202]) ).
thf(2427,plain,
! [SV158: $i] :
( ( ~ ! [SY999: $i,SY1000: $i] :
( ~ ( relation_of2_as_subset @ SY1000 @ SV158 @ SY999 )
| ( SY999 != empty_set )
| ( SY1000 != empty_set )
| ( quasi_total @ SY1000 @ SV158 @ SY999 )
| ( SV158 = empty_set ) )
| ~ ! [SY1001: $i,SY1002: $i] :
( ~ ( relation_of2_as_subset @ SY1002 @ SV158 @ SY1001 )
| ( SY1001 != empty_set )
| ~ ( quasi_total @ SY1002 @ SV158 @ SY1001 )
| ( SY1002 = empty_set )
| ( SV158 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2203]) ).
thf(2428,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK90_SY733 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK89_C @ SX1 @ SX0 ) @ ( sK90_SY733 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK89_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK89_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK89_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2204]) ).
thf(2429,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK88_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK88_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2204]) ).
thf(2430,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2205]) ).
thf(2431,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2205]) ).
thf(2432,plain,
! [SV159: $i,SV427: $i] :
( ( ! [SY1292: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK82_D @ SY1292 @ SV427 @ SV159 ) @ SY1292 )
| ( ( sK82_D @ SY1292 @ SV427 @ SV159 )
!= SV159 ) )
| ~ ( ~ ( in @ ( sK82_D @ SY1292 @ SV427 @ SV159 ) @ SY1292 )
| ( ( sK82_D @ SY1292 @ SV427 @ SV159 )
!= SV427 ) ) )
| ~ ( ( in @ ( sK82_D @ SY1292 @ SV427 @ SV159 ) @ SY1292 )
| ( ( sK82_D @ SY1292 @ SV427 @ SV159 )
= SV159 )
| ( ( sK82_D @ SY1292 @ SV427 @ SV159 )
= SV427 ) ) )
| ( SY1292
= ( unordered_pair @ SV159 @ SV427 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2206]) ).
thf(2433,plain,
! [SV428: $i,SV159: $i] :
( ( ! [SY1293: $i] :
( ( SY1293
!= ( unordered_pair @ SV159 @ SV428 ) )
| ~ ( ~ ! [SY1294: $i] :
( ~ ( in @ SY1294 @ SY1293 )
| ( SY1294 = SV159 )
| ( SY1294 = SV428 ) )
| ~ ~ ( ~ ! [SY1008: $i] :
( ( SY1008 != SV159 )
| ( in @ SY1008 @ SY1293 ) )
| ~ ! [SY1296: $i] :
( ( SY1296 != SV428 )
| ( in @ SY1296 @ SY1293 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2207]) ).
thf(2434,plain,
! [SV429: $i,SV354: $i] :
( ( ~ ( empty @ SV354 )
| ~ ( relation @ SV429 )
| ( empty @ ( relation_composition @ SV429 @ SV354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2208]) ).
thf(2435,plain,
! [SV430: $i,SV355: $i] :
( ( ~ ( empty @ SV355 )
| ~ ( relation @ SV430 )
| ( relation @ ( relation_composition @ SV430 @ SV355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2209]) ).
thf(2436,plain,
! [SV160: $i] :
( ( ( ~ ! [SY1010: $i] :
( ~ ( element @ SY1010 @ SV160 )
| ( v1_xcmplx_0 @ SY1010 ) ) )
= $false )
| ( ( v2_membered @ SV160 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2210]) ).
thf(2437,plain,
! [SV160: $i] :
( ( ( ~ ! [SY1011: $i] :
( ~ ( element @ SY1011 @ SV160 )
| ( v1_xreal_0 @ SY1011 ) ) )
= $false )
| ( ( v2_membered @ SV160 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2210]) ).
thf(2438,plain,
! [SV356: $i] :
( ( ( ~ ( latt_str @ SV356 ) )
= $true )
| ( ( join_semilatt_str @ SV356 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2211]) ).
thf(2439,plain,
! [SV357: $i] :
( ( ( ~ ( latt_str @ SV357 ) )
= $true )
| ( ( meet_semilatt_str @ SV357 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2212]) ).
thf(2440,plain,
! [SV358: $i] :
( ( ( ~ ( ~ ! [SY1235: $i,SY1236: $i] :
( ( sK93_B @ SV358 )
!= ( ordered_pair @ SY1235 @ SY1236 ) )
| ~ ( in @ ( sK93_B @ SV358 ) @ SV358 ) ) )
= $true )
| ( ( relation @ SV358 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2213]) ).
thf(2441,plain,
! [SV359: $i] :
( ( ( ~ ( relation @ SV359 ) )
= $true )
| ( ( ! [SY1237: $i] :
( ( SY1237
= ( ordered_pair @ ( sK91_C @ SY1237 @ SV359 ) @ ( sK92_SY735 @ SY1237 @ SV359 ) ) )
| ~ ( in @ SY1237 @ SV359 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2214]) ).
thf(2442,plain,
! [SV360: $i] :
( ( ( ~ ( empty @ SV360 ) )
= $true )
| ( ( empty @ ( relation_rng @ SV360 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2215]) ).
thf(2443,plain,
! [SV361: $i] :
( ( ( ~ ( empty @ SV361 ) )
= $true )
| ( ( relation @ ( relation_rng @ SV361 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2216]) ).
thf(2444,plain,
! [SV269: $i,SV162: $i] :
( ( ( ~ ! [SY1162: $i] :
( ~ ( element @ SY1162 @ ( powerset @ SV162 ) )
| ~ ( disjoint @ SV269 @ SY1162 )
| ( subset @ SV269 @ ( subset_complement @ SV162 @ SY1162 ) ) )
| ~ ! [SY1163: $i] :
( ~ ( element @ SY1163 @ ( powerset @ SV162 ) )
| ~ ( subset @ SV269 @ ( subset_complement @ SV162 @ SY1163 ) )
| ( disjoint @ SV269 @ SY1163 ) ) )
= $false )
| ( ( element @ SV269 @ ( powerset @ SV162 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2219]) ).
thf(2445,plain,
! [SV431: $i,SV362: $i] :
( ( ~ ( in @ SV362 @ SV431 )
| ( subset @ ( singleton @ SV362 ) @ SV431 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2221]) ).
thf(2446,plain,
! [SV432: $i,SV363: $i] :
( ( ~ ( subset @ ( singleton @ SV363 ) @ SV432 )
| ( in @ SV363 @ SV432 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2222]) ).
thf(2447,plain,
! [SV433: $i,SV163: $i] :
( ( ! [SY1297: $i] :
( ~ ( relation_of2 @ SY1297 @ SV163 @ SV433 )
| ( relation_of2_as_subset @ SY1297 @ SV163 @ SV433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2223]) ).
thf(2448,plain,
! [SV434: $i,SV163: $i] :
( ( ! [SY1298: $i] :
( ~ ( relation_of2_as_subset @ SY1298 @ SV163 @ SV434 )
| ( relation_of2 @ SY1298 @ SV163 @ SV434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2224]) ).
thf(2449,plain,
! [SV364: $i,SV435: $i] :
( ( ~ ( ~ ( ( ( sK87_C @ SV435 @ SV364 )
!= SV364 )
| ~ ( in @ ( sK87_C @ SV435 @ SV364 ) @ SV435 ) )
| ~ ( ( ( sK87_C @ SV435 @ SV364 )
= SV364 )
| ( in @ ( sK87_C @ SV435 @ SV364 ) @ SV435 ) ) )
| ( SV435
= ( singleton @ SV364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2225]) ).
thf(2450,plain,
! [SV365: $i,SV436: $i] :
( ( ( SV436
!= ( singleton @ SV365 ) )
| ~ ( ~ ! [SY1299: $i] :
( ( SY1299 != SV365 )
| ( in @ SY1299 @ SV436 ) )
| ~ ! [SY1300: $i] :
( ~ ( in @ SY1300 @ SV436 )
| ( SY1300 = SV365 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2226]) ).
thf(2451,plain,
! [SV437: $i,SV164: $i] :
( ( ! [SY1301: $i] :
( ~ ( ~ ( ! [SY1302: $i,SY1303: $i] :
( ~ ( in @ SY1302 @ SV164 )
| ~ ( in @ SY1303 @ SV437 )
| ( ( sK78_D @ SY1301 @ SV437 @ SV164 )
!= ( ordered_pair @ SY1302 @ SY1303 ) ) )
| ~ ( in @ ( sK78_D @ SY1301 @ SV437 @ SV164 ) @ SY1301 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK79_SY729 @ SY1301 @ SV437 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK80_SY731 @ SY1301 @ SV437 @ SV164 ) @ SV437 ) )
| ( ( sK78_D @ SY1301 @ SV437 @ SV164 )
!= ( ordered_pair @ ( sK79_SY729 @ SY1301 @ SV437 @ SV164 ) @ ( sK80_SY731 @ SY1301 @ SV437 @ SV164 ) ) ) )
| ( in @ ( sK78_D @ SY1301 @ SV437 @ SV164 ) @ SY1301 ) ) )
| ( SY1301
= ( cartesian_product2 @ SV164 @ SV437 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2227]) ).
thf(2452,plain,
! [SV438: $i,SV164: $i] :
( ( ! [SY1304: $i] :
( ( SY1304
!= ( cartesian_product2 @ SV164 @ SV438 ) )
| ~ ( ~ ! [SY1305: $i] :
( ! [SY1306: $i,SY1307: $i] :
( ~ ( in @ SY1306 @ SV164 )
| ~ ( in @ SY1307 @ SV438 )
| ( SY1305
!= ( ordered_pair @ SY1306 @ SY1307 ) ) )
| ( in @ SY1305 @ SY1304 ) )
| ~ ! [SY1308: $i] :
( ~ ( in @ SY1308 @ SY1304 )
| ~ ( ~ ~ ( ~ ( in @ ( sK76_E @ SY1308 @ SY1304 @ SV438 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK77_SY726 @ SY1308 @ SY1304 @ SV438 @ SV164 ) @ SV438 ) )
| ( SY1308
!= ( ordered_pair @ ( sK76_E @ SY1308 @ SY1304 @ SV438 @ SV164 ) @ ( sK77_SY726 @ SY1308 @ SY1304 @ SV438 @ SV164 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2228]) ).
thf(2453,plain,
! [SV366: $i,SV439: $i] :
( ( ~ ( ~ ( in @ ( sK71_C @ SV439 @ SV366 ) @ SV366 )
| ~ ~ ( in @ ( sK71_C @ SV439 @ SV366 ) @ SV439 ) )
| ( subset @ SV366 @ SV439 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2229]) ).
thf(2454,plain,
! [SV440: $i,SV367: $i] :
( ( ~ ( subset @ SV367 @ SV440 )
| ! [SY1309: $i] :
( ~ ( in @ SY1309 @ SV367 )
| ( in @ SY1309 @ SV440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2230]) ).
thf(2455,plain,
! [SV441: $i,SV165: $i] :
( ( ! [SY1310: $i] :
( ~ ( relation_of2 @ SY1310 @ SV165 @ SV441 )
| ( subset @ SY1310 @ ( cartesian_product2 @ SV165 @ SV441 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2231]) ).
thf(2456,plain,
! [SV442: $i,SV165: $i] :
( ( ! [SY1311: $i] :
( ~ ( subset @ SY1311 @ ( cartesian_product2 @ SV165 @ SV442 ) )
| ( relation_of2 @ SY1311 @ SV165 @ SV442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2232]) ).
thf(2457,plain,
! [SV166: $i,SV443: $i] :
( ( ~ ( subset @ SV443 @ ( sK3_B @ SV166 ) )
| ( are_equipotent @ SV443 @ ( sK3_B @ SV166 ) )
| ( in @ SV443 @ ( sK3_B @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2233]) ).
thf(2458,plain,
! [SV166: $i] :
( ( ~ ! [SY1034: $i] :
( ~ ( ~ ! [SY1035: $i] :
( ~ ( subset @ SY1035 @ SY1034 )
| ( in @ SY1035 @ ( sK4_SY591 @ SY1034 @ SV166 ) ) )
| ~ ( in @ ( sK4_SY591 @ SY1034 @ SV166 ) @ ( sK3_B @ SV166 ) ) )
| ~ ( in @ SY1034 @ ( sK3_B @ SV166 ) ) )
| ~ ~ ( ~ ! [SY1036: $i,SY1037: $i] :
( ~ ( in @ SY1036 @ ( sK3_B @ SV166 ) )
| ~ ( subset @ SY1037 @ SY1036 )
| ( in @ SY1037 @ ( sK3_B @ SV166 ) ) )
| ~ ( in @ SV166 @ ( sK3_B @ SV166 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2234]) ).
thf(2459,plain,
! [SV167: $i,SV444: $i] :
( ( ! [SY1312: $i] :
( ~ ( relation_of2_as_subset @ SY1312 @ SV444 @ SV167 )
| ~ ( ~ ! [SY1313: $i] :
~ ( in @ ( ordered_pair @ ( sK104_D @ SY1312 @ SV444 @ SV167 ) @ SY1313 ) @ SY1312 )
| ~ ( in @ ( sK104_D @ SY1312 @ SV444 @ SV167 ) @ SV444 ) )
| ( ( relation_dom_as_subset @ SV444 @ SV167 @ SY1312 )
= SV444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2235]) ).
thf(2460,plain,
! [SV167: $i,SV445: $i] :
( ( ! [SY1314: $i] :
( ~ ( relation_of2_as_subset @ SY1314 @ SV445 @ SV167 )
| ( ( relation_dom_as_subset @ SV445 @ SV167 @ SY1314 )
!= SV445 )
| ! [SY1315: $i] :
( ( in @ ( ordered_pair @ SY1315 @ ( sK103_E @ SY1315 @ SY1314 @ SV445 @ SV167 ) ) @ SY1314 )
| ~ ( in @ SY1315 @ SV445 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2236]) ).
thf(2461,plain,
! [SV168: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ( ( sK27_SY634 @ SV168 )
!= ( singleton @ ( sK26_B @ SV168 ) ) )
| ~ ( in @ ( sK26_B @ SV168 ) @ SV168 ) )
| ~ ( in @ ( sK26_B @ SV168 ) @ SV168 ) )
| ( ( sK28_SY636 @ SV168 )
!= ( singleton @ ( sK26_B @ SV168 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) )
| ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2237]) ).
thf(2462,plain,
! [SV168: $i] :
( ( ( ( ( sK27_SY634 @ SV168 )
!= ( sK28_SY636 @ SV168 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) )
| ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2238]) ).
thf(2463,plain,
( ( ~ ( empty @ sK57_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2239]) ).
thf(2464,plain,
( ( ~ ( relation @ sK57_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2239]) ).
thf(2465,plain,
! [SV270: $i,SV169: $i] :
( ( ! [SY1164: $i,SY1165: $i] :
( ~ ( in @ SV169 @ SY1164 )
| ~ ( in @ SV270 @ SY1165 )
| ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SY1164 @ SY1165 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2240]) ).
thf(2466,plain,
! [SV270: $i,SV169: $i] :
( ( ~ ( ~ ! [SY1166: $i] :
( ! [SY1167: $i] :
~ ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SY1166 @ SY1167 ) )
| ( in @ SV169 @ SY1166 ) )
| ~ ! [SY1168: $i,SY1169: $i] :
( ~ ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SY1168 @ SY1169 ) )
| ( in @ SV270 @ SY1169 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2241]) ).
thf(2467,plain,
! [SV170: $i,SV271: $i] :
( ( ( relation @ SV271 )
= $false )
| ( ( empty @ SV170 )
= $true )
| ( ( ! [SY1170: $i] :
~ ( ~ ! [SY1171: $i] :
( ! [SY1172: $i,SY1173: $i] :
( ( ( ordered_pair @ SY1172 @ SY1173 )
!= SY1171 )
| ~ ( in @ SY1172 @ SV170 )
| ! [SY1174: $i] :
( ~ ( ~ ( in @ ( sK115_I @ SY1174 @ SY1173 @ SY1172 @ SY1171 @ SY1170 @ SV271 @ SV170 ) @ SY1174 )
| ~ ~ ( in @ ( ordered_pair @ SY1173 @ ( sK115_I @ SY1174 @ SY1173 @ SY1172 @ SY1171 @ SY1170 @ SV271 @ SV170 ) ) @ SV271 ) )
| ( SY1172 != SY1174 )
| ~ ( in @ SY1173 @ SY1174 ) ) )
| ~ ( in @ SY1171 @ ( cartesian_product2 @ SV170 @ SY1170 ) )
| ( in @ SY1171 @ ( sK111_D @ SY1170 @ SV271 @ SV170 ) ) )
| ~ ~ ( ~ ! [SY1175: $i] :
( ~ ( in @ SY1175 @ ( sK111_D @ SY1170 @ SV271 @ SV170 ) )
| ~ ( ~ ~ ( ( ( ordered_pair @ ( sK112_F @ SY1175 @ SY1170 @ SV271 @ SV170 ) @ ( sK113_SY768 @ SY1175 @ SY1170 @ SV271 @ SV170 ) )
!= SY1175 )
| ~ ( in @ ( sK112_F @ SY1175 @ SY1170 @ SV271 @ SV170 ) @ SV170 ) )
| ~ ~ ( ~ ! [SY1176: $i] :
( ~ ( in @ SY1176 @ ( sK114_SY771 @ SY1175 @ SY1170 @ SV271 @ SV170 ) )
| ( in @ ( ordered_pair @ ( sK113_SY768 @ SY1175 @ SY1170 @ SV271 @ SV170 ) @ SY1176 ) @ SV271 ) )
| ~ ~ ( ( ( sK112_F @ SY1175 @ SY1170 @ SV271 @ SV170 )
!= ( sK114_SY771 @ SY1175 @ SY1170 @ SV271 @ SV170 ) )
| ~ ( in @ ( sK113_SY768 @ SY1175 @ SY1170 @ SV271 @ SV170 ) @ ( sK114_SY771 @ SY1175 @ SY1170 @ SV271 @ SV170 ) ) ) ) ) )
| ~ ! [SY1177: $i] :
( ~ ( in @ SY1177 @ ( sK111_D @ SY1170 @ SV271 @ SV170 ) )
| ( in @ SY1177 @ ( cartesian_product2 @ SV170 @ SY1170 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2242]) ).
thf(2468,plain,
! [SV368: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK74_B @ SV368 )
!= ( sK75_SY725 @ SV368 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK74_B @ SV368 ) @ SV368 )
| ~ ( in @ ( sK75_SY725 @ SV368 ) @ SV368 ) )
| ~ ~ ( in @ ( sK74_B @ SV368 ) @ ( sK75_SY725 @ SV368 ) ) ) )
| ~ ~ ( in @ ( sK75_SY725 @ SV368 ) @ ( sK74_B @ SV368 ) ) ) )
= $true )
| ( ( epsilon_connected @ SV368 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2243]) ).
thf(2469,plain,
! [SV369: $i] :
( ( ( ~ ( epsilon_connected @ SV369 ) )
= $true )
| ( ( ! [SY1247: $i,SY1248: $i] :
( ( SY1247 = SY1248 )
| ~ ( in @ SY1247 @ SV369 )
| ~ ( in @ SY1248 @ SV369 )
| ( in @ SY1247 @ SY1248 )
| ( in @ SY1248 @ SY1247 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2244]) ).
thf(2470,plain,
( ( ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_difference @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2245]) ).
thf(2471,plain,
( ( ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_difference @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2245]) ).
thf(2472,plain,
! [SV370: $i] :
( ( ( ~ ( v3_membered @ SV370 ) )
= $true )
| ( ( ! [SY1249: $i] : ( v3_membered @ ( set_difference @ SV370 @ SY1249 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2246]) ).
thf(2473,plain,
! [SV171: $i] :
( ( ( ~ ! [SY1063: $i] :
( ~ ( relation @ SY1063 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK83_C @ SY1063 @ SV171 ) @ ( sK84_SY732 @ SY1063 @ SV171 ) ) @ SV171 )
| ~ ( in @ ( ordered_pair @ ( sK83_C @ SY1063 @ SV171 ) @ ( sK84_SY732 @ SY1063 @ SV171 ) ) @ SY1063 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK83_C @ SY1063 @ SV171 ) @ ( sK84_SY732 @ SY1063 @ SV171 ) ) @ SV171 )
| ( in @ ( ordered_pair @ ( sK83_C @ SY1063 @ SV171 ) @ ( sK84_SY732 @ SY1063 @ SV171 ) ) @ SY1063 ) ) )
| ( SV171 = SY1063 ) ) )
= $false )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2247]) ).
thf(2474,plain,
! [SV171: $i] :
( ( ( ~ ! [SY1064: $i] :
( ~ ( relation @ SY1064 )
| ( SV171 != SY1064 )
| ~ ( ~ ! [SY1065: $i,SY1066: $i] :
( ~ ( in @ ( ordered_pair @ SY1065 @ SY1066 ) @ SV171 )
| ( in @ ( ordered_pair @ SY1065 @ SY1066 ) @ SY1064 ) )
| ~ ! [SY1067: $i,SY1068: $i] :
( ~ ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SY1064 )
| ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SV171 ) ) ) ) )
= $false )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2247]) ).
thf(2475,plain,
! [SV446: $i,SV371: $i] :
( ( ( disjoint @ SV371 @ SV446 )
| ~ ( ~ ( in @ ( sK98_C @ SV446 @ SV371 ) @ SV371 )
| ~ ( in @ ( sK98_C @ SV446 @ SV371 ) @ SV446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2248]) ).
thf(2476,plain,
! [SV447: $i,SV372: $i] :
( ( ! [SY1316: $i] :
( ~ ( in @ SY1316 @ SV372 )
| ~ ( in @ SY1316 @ SV447 ) )
| ~ ( disjoint @ SV372 @ SV447 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2249]) ).
thf(2477,plain,
! [SV448: $i,SV373: $i] :
( ( ~ ( in @ SV373 @ SV448 )
| ( subset @ ( singleton @ SV373 ) @ SV448 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2250]) ).
thf(2478,plain,
! [SV449: $i,SV374: $i] :
( ( ~ ( subset @ ( singleton @ SV374 ) @ SV449 )
| ( in @ SV374 @ SV449 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2251]) ).
thf(2479,plain,
! [SV450: $i,SV375: $i] :
( ( ( disjoint @ SV375 @ SV450 )
| ( in @ ( sK97_C @ SV450 @ SV375 ) @ ( set_intersection2 @ SV375 @ SV450 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2252]) ).
thf(2480,plain,
! [SV451: $i,SV376: $i] :
( ( ! [SY1317: $i] :
~ ( in @ SY1317 @ ( set_intersection2 @ SV376 @ SV451 ) )
| ~ ( disjoint @ SV376 @ SV451 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2253]) ).
thf(2481,plain,
! [SV377: $i] :
( ( empty @ ( singleton @ SV377 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2254]) ).
thf(2482,plain,
! [SV172: $i,SV272: $i] :
( ( ( relation @ SV272 )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK35_D @ SV272 @ SV172 )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1178: $i] :
( ~ ( in @ SY1178 @ ( sK43_SY691 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SY1178 ) @ SV272 ) )
| ~ ~ ( ( ( sK41_SY666 @ SV272 @ SV172 )
!= ( sK43_SY691 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) ) ) ) ) )
| ( ( sK35_D @ SV272 @ SV172 )
!= ( sK37_SY665 @ SV272 @ SV172 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
!= ( sK37_SY665 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1179: $i] :
( ~ ( in @ SY1179 @ ( sK40_SY685 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SY1179 ) @ SV272 ) )
| ~ ~ ( ( ( sK38_SY678 @ SV272 @ SV172 )
!= ( sK40_SY685 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) ) ) ) ) )
| ~ ( ( ( sK36_SY655 @ SV272 @ SV172 )
!= ( sK37_SY665 @ SV272 @ SV172 ) ) ) )
| ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2256]) ).
thf(2483,plain,
! [SV379: $i] :
( ( ( ( SV379
!= ( union @ SV379 ) ) )
= $true )
| ( ( being_limit_ordinal @ SV379 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2257]) ).
thf(2484,plain,
! [SV380: $i] :
( ( ( ~ ( being_limit_ordinal @ SV380 ) )
= $true )
| ( ( SV380
= ( union @ SV380 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2258]) ).
thf(2485,plain,
! [SV381: $i] :
( ( ( ~ ( v2_membered @ SV381 ) )
= $true )
| ( ( ! [SY1258: $i] : ( v1_membered @ ( set_intersection2 @ SY1258 @ SV381 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2259]) ).
thf(2486,plain,
! [SV382: $i] :
( ( ( ~ ( v2_membered @ SV382 ) )
= $true )
| ( ( ! [SY1259: $i] : ( v2_membered @ ( set_intersection2 @ SY1259 @ SV382 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2260]) ).
thf(2487,plain,
! [SV273: $i,SV173: $i] :
( ( ! [SY1188: $i,SY1189: $i] :
( ~ ( in @ SV173 @ SY1188 )
| ~ ( in @ SV273 @ SY1189 )
| ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SY1188 @ SY1189 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2261]) ).
thf(2488,plain,
! [SV273: $i,SV173: $i] :
( ( ~ ( ~ ! [SY1190: $i] :
( ! [SY1191: $i] :
~ ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SY1190 @ SY1191 ) )
| ( in @ SV173 @ SY1190 ) )
| ~ ! [SY1192: $i,SY1193: $i] :
( ~ ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SY1192 @ SY1193 ) )
| ( in @ SV273 @ SY1193 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2262]) ).
thf(2489,plain,
! [SV174: $i,SV274: $i] :
( ( ~ ( ~ ( relation @ ( sK56_C @ SV274 @ SV174 ) )
| ~ ( relation_of2 @ ( sK56_C @ SV274 @ SV174 ) @ SV174 @ SV274 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2263]) ).
thf(2490,plain,
! [SV174: $i,SV274: $i] :
( ( function @ ( sK56_C @ SV274 @ SV174 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2264]) ).
thf(2491,plain,
! [SV383: $i] :
( ( ( ~ ( empty @ SV383 ) )
= $true )
| ( ( empty @ ( relation_dom @ SV383 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2265]) ).
thf(2492,plain,
! [SV384: $i] :
( ( ( ~ ( empty @ SV384 ) )
= $true )
| ( ( relation @ ( relation_dom @ SV384 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2266]) ).
thf(2493,plain,
! [SV385: $i] :
( ( ( ~ ( v2_membered @ SV385 ) )
= $true )
| ( ( ! [SY1260: $i] : ( v1_membered @ ( set_difference @ SV385 @ SY1260 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2267]) ).
thf(2494,plain,
! [SV386: $i] :
( ( ( ~ ( v2_membered @ SV386 ) )
= $true )
| ( ( ! [SY1261: $i] : ( v2_membered @ ( set_difference @ SV386 @ SY1261 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2268]) ).
thf(2495,plain,
( ( ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2271]) ).
thf(2496,plain,
( ( ~ ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2271]) ).
thf(2497,plain,
! [SV387: $i] :
( ( ( ~ ( v3_membered @ SV387 ) )
= $true )
| ( ( ! [SY1262: $i] : ( v3_membered @ ( set_intersection2 @ SV387 @ SY1262 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2272]) ).
thf(2498,plain,
! [SV388: $i] :
( ( ( ~ ( v2_membered @ SV388 ) )
= $true )
| ( ( ! [SY1263: $i] : ( v1_membered @ ( set_intersection2 @ SV388 @ SY1263 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2274]) ).
thf(2499,plain,
! [SV389: $i] :
( ( ( ~ ( v2_membered @ SV389 ) )
= $true )
| ( ( ! [SY1264: $i] : ( v2_membered @ ( set_intersection2 @ SV389 @ SY1264 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2275]) ).
thf(2500,plain,
! [SV452: $i,SV390: $i] :
( ( ( ( set_difference @ SV390 @ SV452 )
!= empty_set )
| ( subset @ SV390 @ SV452 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2277]) ).
thf(2501,plain,
! [SV453: $i,SV391: $i] :
( ( ~ ( subset @ SV391 @ SV453 )
| ( ( set_difference @ SV391 @ SV453 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2278]) ).
thf(2502,plain,
! [SV275: $i,SV176: $i] :
( ( ! [SY1194: $i] :
( ! [SY1090: $i,SY1091: $i] :
( ( ( ordered_pair @ SY1090 @ SY1091 )
!= SY1194 )
| ~ ( in @ SY1090 @ SV176 )
| ( SY1091
!= ( singleton @ SY1090 ) ) )
| ~ ( in @ SY1194 @ ( cartesian_product2 @ SV176 @ SV275 ) )
| ( in @ SY1194 @ ( sK108_C @ SV275 @ SV176 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2279]) ).
thf(2503,plain,
! [SV176: $i,SV275: $i] :
( ( ~ ( ~ ! [SY1197: $i] :
( ~ ( in @ SY1197 @ ( sK108_C @ SV275 @ SV176 ) )
| ~ ( ~ ~ ( ( ( ordered_pair @ ( sK109_E @ SY1197 @ SV275 @ SV176 ) @ ( sK110_SY756 @ SY1197 @ SV275 @ SV176 ) )
!= SY1197 )
| ~ ( in @ ( sK109_E @ SY1197 @ SV275 @ SV176 ) @ SV176 ) )
| ( ( sK110_SY756 @ SY1197 @ SV275 @ SV176 )
!= ( singleton @ ( sK109_E @ SY1197 @ SV275 @ SV176 ) ) ) ) )
| ~ ! [SY1198: $i] :
( ~ ( in @ SY1198 @ ( sK108_C @ SV275 @ SV176 ) )
| ( in @ SY1198 @ ( cartesian_product2 @ SV176 @ SV275 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2280]) ).
thf(2504,plain,
! [SV177: $i,SV276: $i] :
( ( ( ~ ( in @ ( sK125_C @ SV276 @ SV177 ) @ SV177 ) )
= $false )
| ( ( element @ SV177 @ ( powerset @ SV276 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2281]) ).
thf(2505,plain,
! [SV177: $i,SV276: $i] :
( ( ( ~ ~ ( in @ ( sK125_C @ SV276 @ SV177 ) @ SV276 ) )
= $false )
| ( ( element @ SV177 @ ( powerset @ SV276 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2281]) ).
thf(2506,plain,
! [SV178: $i,SV277: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_C @ SV277 @ SV178 ) @ SV178 )
| ~ ( in @ ( sK6_C @ SV277 @ SV178 ) @ SV277 ) ) )
= $false )
| ( ( SV178 = SV277 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2282]) ).
thf(2507,plain,
! [SV178: $i,SV277: $i] :
( ( ( ~ ( ( in @ ( sK6_C @ SV277 @ SV178 ) @ SV178 )
| ( in @ ( sK6_C @ SV277 @ SV178 ) @ SV277 ) ) )
= $false )
| ( ( SV178 = SV277 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2282]) ).
thf(2508,plain,
! [SV454: $i,SV179: $i] :
( ( ~ ( subset @ SV179 @ SV454 )
| ! [SY1318: $i] : ( subset @ ( cartesian_product2 @ SV179 @ SY1318 ) @ ( cartesian_product2 @ SV454 @ SY1318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2283]) ).
thf(2509,plain,
! [SV455: $i,SV179: $i] :
( ( ~ ( subset @ SV179 @ SV455 )
| ! [SY1319: $i] : ( subset @ ( cartesian_product2 @ SY1319 @ SV179 ) @ ( cartesian_product2 @ SY1319 @ SV455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2284]) ).
thf(2510,plain,
! [SV180: $i,SV456: $i] :
( ( ! [SY1320: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK81_D @ SY1320 @ SV456 @ SV180 ) @ SY1320 )
| ~ ( in @ ( sK81_D @ SY1320 @ SV456 @ SV180 ) @ SV180 ) )
| ~ ( ~ ( in @ ( sK81_D @ SY1320 @ SV456 @ SV180 ) @ SY1320 )
| ~ ( in @ ( sK81_D @ SY1320 @ SV456 @ SV180 ) @ SV456 ) ) )
| ~ ( ( in @ ( sK81_D @ SY1320 @ SV456 @ SV180 ) @ SY1320 )
| ( in @ ( sK81_D @ SY1320 @ SV456 @ SV180 ) @ SV180 )
| ( in @ ( sK81_D @ SY1320 @ SV456 @ SV180 ) @ SV456 ) ) )
| ( SY1320
= ( set_union2 @ SV180 @ SV456 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2285]) ).
thf(2511,plain,
! [SV457: $i,SV180: $i] :
( ( ! [SY1321: $i] :
( ( SY1321
!= ( set_union2 @ SV180 @ SV457 ) )
| ~ ( ~ ! [SY1322: $i] :
( ~ ( in @ SY1322 @ SY1321 )
| ( in @ SY1322 @ SV180 )
| ( in @ SY1322 @ SV457 ) )
| ~ ~ ( ~ ! [SY1105: $i] :
( ~ ( in @ SY1105 @ SV180 )
| ( in @ SY1105 @ SY1321 ) )
| ~ ! [SY1324: $i] :
( ~ ( in @ SY1324 @ SV457 )
| ( in @ SY1324 @ SY1321 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2286]) ).
thf(2512,plain,
! [SV181: $i] :
( ( ( element @ ( sK120_B @ SV181 ) @ ( powerset @ SV181 ) )
= $true )
| ( ( empty @ SV181 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2287]) ).
thf(2513,plain,
! [SV181: $i] :
( ( ( ~ ( empty @ ( sK120_B @ SV181 ) ) )
= $true )
| ( ( empty @ SV181 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2288]) ).
thf(2514,plain,
! [SV1: $i,SV182: $i,SV392: $i] :
( ( ( ~ ( in @ SV392 @ SV182 ) )
= $true )
| ( ( in @ SV392 @ SV1 )
= $true )
| ( ( element @ SV182 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2289]) ).
thf(2515,plain,
! [SV3: $i,SV308: $i] :
( ( ( element @ SV308 @ ( powerset @ ( the_carrier @ SV3 ) ) )
= $false )
| ( ( ( subset_intersection2 @ ( the_carrier @ SV3 ) @ SV308 @ ( cast_as_carrier_subset @ SV3 ) )
= SV308 )
= $true )
| ( ( one_sorted_str @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2290]) ).
thf(2516,plain,
! [SV183: $i,SV4: $i] :
( ( ( ( complements_of_subsets @ SV4 @ SV183 )
= empty_set )
= $false )
| ( ( SV183 = empty_set )
= $true )
| ( ( element @ SV183 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2291]) ).
thf(2517,plain,
! [SV278: $i,SV5: $i,SV458: $i] :
( ( ( ~ ( element @ SV458 @ SV5 )
| ( in @ SV458 @ SV278 )
| ( in @ SV458 @ ( subset_complement @ SV5 @ SV278 ) ) )
= $true )
| ( ( element @ SV278 @ ( powerset @ SV5 ) )
= $false )
| ( ( SV5 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2292]) ).
thf(2518,plain,
! [SV279: $i,SV6: $i,SV184: $i] :
( ( ( ~ ( in @ SV184 @ ( subset_complement @ SV6 @ SV279 ) ) )
= $true )
| ( ( ~ ( in @ SV184 @ SV279 ) )
= $true )
| ( ( element @ SV279 @ ( powerset @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2293]) ).
thf(2519,plain,
! [SV8: $i,SV309: $i] :
( ( ( element @ SV309 @ SV8 )
= $false )
| ( ( v1_xcmplx_0 @ SV309 )
= $true )
| ( ( v1_membered @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2294]) ).
thf(2520,plain,
! [SV9: $i,SV310: $i] :
( ( ( element @ SV310 @ ( powerset @ SV9 ) )
= $false )
| ( ( v1_membered @ SV310 )
= $true )
| ( ( v1_membered @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2295]) ).
thf(2521,plain,
! [SV11: $i,SV311: $i] :
( ( ( element @ SV311 @ ( powerset @ SV11 ) )
= $false )
| ( ( finite @ SV311 )
= $true )
| ( ( finite @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2297]) ).
thf(2522,plain,
! [SV281: $i,SV12: $i,SV186: $i] :
( ( ( element @ SV186 @ ( powerset @ SV12 ) )
= $false )
| ( ( ~ ( element @ SV281 @ ( powerset @ SV12 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV12 @ SV186 @ SV281 )
= ( subset_intersection2 @ SV12 @ SV281 @ SV186 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2298]) ).
thf(2523,plain,
! [SV284: $i,SV21: $i,SV192: $i] :
( ( ( element @ SV192 @ ( powerset @ SV21 ) )
= $false )
| ( ( ~ ( element @ SV284 @ ( powerset @ SV21 ) ) )
= $true )
| ( ( element @ ( subset_intersection2 @ SV21 @ SV192 @ SV284 ) @ ( powerset @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2301]) ).
thf(2524,plain,
! [SV285: $i,SV23: $i,SV194: $i] :
( ( ( element @ SV194 @ ( powerset @ SV23 ) )
= $false )
| ( ( ~ ( element @ SV285 @ ( powerset @ SV23 ) ) )
= $true )
| ( ( element @ ( subset_difference @ SV23 @ SV194 @ SV285 ) @ ( powerset @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2302]) ).
thf(2525,plain,
! [SV197: $i,SV31: $i,SV459: $i] :
( ( ( ~ ( element @ SV459 @ ( powerset @ SV31 ) ) )
= $true )
| ( ( element @ SV197 @ ( powerset @ SV31 ) )
= $false )
| ( ( ( subset_intersection2 @ SV31 @ SV197 @ SV197 )
= SV197 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2305]) ).
thf(2526,plain,
! [SV287: $i,SV35: $i,SV201: $i] :
( ( ( element @ SV201 @ ( powerset @ SV35 ) )
= $false )
| ( ( ~ ( element @ SV287 @ ( powerset @ SV35 ) ) )
= $true )
| ( ( ( subset_intersection2 @ SV35 @ SV201 @ SV287 )
= ( set_intersection2 @ SV201 @ SV287 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2306]) ).
thf(2527,plain,
! [SV288: $i,SV37: $i,SV203: $i] :
( ( ( element @ SV203 @ ( powerset @ SV37 ) )
= $false )
| ( ( ~ ( element @ SV288 @ ( powerset @ SV37 ) ) )
= $true )
| ( ( ( subset_difference @ SV37 @ SV203 @ SV288 )
= ( set_difference @ SV203 @ SV288 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2307]) ).
thf(2528,plain,
! [SV40: $i,SV289: $i,SV206: $i] :
( ( ( element @ SV206 @ ( powerset @ SV289 ) )
= $false )
| ( ( ~ ( in @ SV40 @ SV206 ) )
= $true )
| ( ( element @ SV40 @ SV289 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2309]) ).
thf(2529,plain,
! [SV41: $i,SV290: $i,SV207: $i] :
( ( ( element @ SV207 @ ( powerset @ SV290 ) )
= $false )
| ( ( ~ ( in @ SV41 @ SV207 ) )
= $true )
| ( ( ~ ( empty @ SV290 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2310]) ).
thf(2530,plain,
! [SV211: $i,SV46: $i,SV393: $i] :
( ( ( in @ SV393 @ SV46 )
= $true )
| ( ( subset @ SV46 @ ( set_difference @ SV211 @ ( singleton @ SV393 ) ) )
= $true )
| ( ( subset @ SV46 @ SV211 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2312]) ).
thf(2531,plain,
! [SV312: $i,SV291: $i,SV214: $i,SV50: $i] :
( ( ( ~ ( subset @ SV50 @ SV214 ) )
= $true )
| ( ( ~ ( subset @ SV291 @ SV312 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV50 @ SV291 ) @ ( cartesian_product2 @ SV214 @ SV312 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2313]) ).
thf(2532,plain,
! [SV292: $i,SV52: $i] :
( ( ( subset @ SV52 @ SV292 )
= $false )
| ( ( finite @ SV292 )
= $false )
| ( ( finite @ SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2314]) ).
thf(2533,plain,
! [SV216: $i,SV53: $i,SV293: $i,SV313: $i] :
( ( ( relation_of2_as_subset @ SV313 @ SV293 @ SV53 )
= $false )
| ( ( ~ ( subset @ ( relation_rng @ SV313 ) @ SV216 )
| ( relation_of2_as_subset @ SV313 @ SV293 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2315]) ).
thf(2534,plain,
! [SV217: $i,SV55: $i,SV294: $i,SV315: $i] :
( ( ( relation_of2_as_subset @ SV315 @ SV294 @ SV55 )
= $false )
| ( ( ~ ( subset @ SV55 @ SV217 )
| ( relation_of2_as_subset @ SV315 @ SV294 @ SV217 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2316]) ).
thf(2535,plain,
! [SV295: $i,SV218: $i,SV56: $i] :
( ( ( ~ ( subset @ SV56 @ SV218 ) )
= $true )
| ( ( subset @ ( relation_inverse_image @ SV295 @ SV56 ) @ ( relation_inverse_image @ SV295 @ SV218 ) )
= $true )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2317]) ).
thf(2536,plain,
! [SV296: $i,SV220: $i,SV58: $i] :
( ( ( subset @ SV58 @ SV220 )
= $false )
| ( ( ~ ( subset @ SV58 @ SV296 ) )
= $true )
| ( ( subset @ SV58 @ ( set_intersection2 @ SV220 @ SV296 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2318]) ).
thf(2537,plain,
! [SV297: $i,SV221: $i,SV59: $i] :
( ( ( subset @ SV59 @ SV221 )
= $false )
| ( ( ~ ( subset @ SV221 @ SV297 ) )
= $true )
| ( ( subset @ SV59 @ SV297 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2319]) ).
thf(2538,plain,
! [SV222: $i,SV60: $i] :
( ( ( in @ SV60 @ SV222 )
= $false )
| ( ( ordinal @ SV60 )
= $true )
| ( ( ordinal @ SV222 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2320]) ).
thf(2539,plain,
! [SV61: $i,SV316: $i] :
( ( ( ordinal @ SV316 )
= $false )
| ( ( ( in @ SV61 @ SV316 )
| ( SV61 = SV316 )
| ( in @ SV316 @ SV61 ) )
= $true )
| ( ( ordinal @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2321]) ).
thf(2540,plain,
! [SV298: $i,SV228: $i,SV68: $i] :
( ( ( in @ SV68 @ SV228 )
= $false )
| ( ( ~ ( in @ SV228 @ SV298 ) )
= $true )
| ( ( ~ ( in @ SV298 @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2324]) ).
thf(2541,plain,
! [SV78: $i,SV299: $i,SV236: $i] :
( ( ( disjoint @ SV236 @ SV299 )
= $false )
| ( ( ~ ( subset @ SV78 @ SV236 ) )
= $true )
| ( ( disjoint @ SV78 @ SV299 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2328]) ).
thf(2542,plain,
! [SV300: $i,SV240: $i,SV83: $i] :
( ( ( subset @ SV83 @ SV240 )
= $false )
| ( ( ~ ( subset @ SV300 @ SV240 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV83 @ SV300 ) @ SV240 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2329]) ).
thf(2543,plain,
! [SV302: $i,SV246: $i,SV96: $i] :
( ( ( ( empty_carrier @ SV96 )
| ~ ( join_semilatt_str @ SV96 ) )
= $true )
| ( ( ~ ( element @ SV246 @ ( the_carrier @ SV96 ) ) )
= $true )
| ( ( ~ ( element @ SV302 @ ( the_carrier @ SV96 ) ) )
= $true )
| ( ( element @ ( join @ SV96 @ SV246 @ SV302 ) @ ( the_carrier @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2333]) ).
thf(2544,plain,
! [SV303: $i,SV247: $i,SV98: $i] :
( ( ( ( empty_carrier @ SV98 )
| ~ ( meet_semilatt_str @ SV98 ) )
= $true )
| ( ( ~ ( element @ SV247 @ ( the_carrier @ SV98 ) ) )
= $true )
| ( ( ~ ( element @ SV303 @ ( the_carrier @ SV98 ) ) )
= $true )
| ( ( element @ ( meet @ SV98 @ SV247 @ SV303 ) @ ( the_carrier @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2334]) ).
thf(2545,plain,
! [SV101: $i,SV248: $i] :
( ( ( relation @ SV248 )
= $false )
| ( ( relation @ SV101 )
= $false )
| ( ( relation @ ( relation_composition @ SV101 @ SV248 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2335]) ).
thf(2546,plain,
! [SV111: $i,SV253: $i] :
( ( ( relation @ SV253 )
= $false )
| ( ( relation @ SV111 )
= $false )
| ( ( relation @ ( set_intersection2 @ SV111 @ SV253 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2336]) ).
thf(2547,plain,
! [SV115: $i,SV255: $i] :
( ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV115 )
= $false )
| ( ( relation @ ( set_union2 @ SV115 @ SV255 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2337]) ).
thf(2548,plain,
! [SV119: $i,SV256: $i] :
( ( ( relation @ SV256 )
= $false )
| ( ( relation @ SV119 )
= $false )
| ( ( relation @ ( set_difference @ SV119 @ SV256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2338]) ).
thf(2549,plain,
! [SV125: $i,SV259: $i] :
( ( ( finite @ SV259 )
= $false )
| ( ( finite @ SV125 )
= $false )
| ( ( finite @ ( set_union2 @ SV125 @ SV259 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2342]) ).
thf(2550,plain,
! [SV138: $i,SV264: $i] :
( ( ( empty @ SV264 )
= $false )
| ( ( SV138 = SV264 )
= $true )
| ( ( empty @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2346]) ).
thf(2551,plain,
! [SV396: $i,SV326: $i] :
( ( ( ( SV326 = SV396 )
| ~ ( subset @ SV326 @ SV396 ) )
= $true )
| ( ( proper_subset @ SV326 @ SV396 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2347]) ).
thf(2552,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2348]) ).
thf(2553,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2349]) ).
thf(2554,plain,
! [SV397: $i,SV327: $i] :
( ( ( ( ( set_intersection2 @ SV327 @ SV397 )
!= empty_set ) )
= $true )
| ( ( disjoint @ SV327 @ SV397 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2350]) ).
thf(2555,plain,
! [SV398: $i,SV328: $i] :
( ( ( ~ ( disjoint @ SV328 @ SV398 ) )
= $true )
| ( ( ( set_intersection2 @ SV328 @ SV398 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2351]) ).
thf(2556,plain,
! [SV139: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( sK17_C @ SV139 )
!= ( sK18_SY613 @ SV139 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
!= ( sK18_SY613 @ SV139 ) )
| ~ ( in @ ( sK22_SY620 @ SV139 ) @ SV139 ) )
| ( ( sK23_SY629 @ SV139 )
!= ( singleton @ ( sK22_SY620 @ SV139 ) ) ) ) )
| ( ( sK17_C @ SV139 )
!= ( sK19_SY619 @ SV139 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
!= ( sK19_SY619 @ SV139 ) )
| ~ ( in @ ( sK20_SY626 @ SV139 ) @ SV139 ) )
| ( ( sK21_SY628 @ SV139 )
!= ( singleton @ ( sK20_SY626 @ SV139 ) ) ) ) )
= $false )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2352]) ).
thf(2557,plain,
! [SV139: $i] :
( ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2353]) ).
thf(2558,plain,
! [SV140: $i] :
( ( ( ~ ( element @ ( sK116_B @ SV140 ) @ ( powerset @ ( the_carrier @ SV140 ) ) ) )
= $false )
| ( ( empty_carrier @ SV140 )
= $true )
| ( ( one_sorted_str @ SV140 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2354]) ).
thf(2559,plain,
! [SV140: $i] :
( ( ( ~ ~ ( empty @ ( sK116_B @ SV140 ) ) )
= $false )
| ( ( empty_carrier @ SV140 )
= $true )
| ( ( one_sorted_str @ SV140 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2354]) ).
thf(2560,plain,
( ( ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_intersection2 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2355]) ).
thf(2561,plain,
( ( ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_intersection2 @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2356]) ).
thf(2562,plain,
! [SV329: $i] :
( ( ( v3_membered @ SV329 )
= $false )
| ( ( ! [SY1206: $i] : ( v3_membered @ ( set_intersection2 @ SY1206 @ SV329 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2357]) ).
thf(2563,plain,
! [SV141: $i] :
( ( ( ~ ( ordinal @ ( sK99_B @ SV141 ) ) )
= $true )
| ( ( ~ ( subset @ ( sK99_B @ SV141 ) @ SV141 ) )
= $true )
| ( ( ordinal @ SV141 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2359]) ).
thf(2564,plain,
! [SV399: $i,SV460: $i,SV142: $i] :
( ( ~ ( in @ SV142 @ SV460 )
| ~ ( in @ SV399 @ SV460 )
| ( subset @ ( unordered_pair @ SV142 @ SV399 ) @ SV460 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2360]) ).
thf(2565,plain,
! [SV142: $i] :
( ( ~ ! [SY919: $i,SY920: $i] :
( ~ ( subset @ ( unordered_pair @ SV142 @ SY919 ) @ SY920 )
| ( in @ SV142 @ SY920 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2361]) ).
thf(2566,plain,
! [SV142: $i] :
( ( ~ ! [SY921: $i,SY922: $i] :
( ~ ( subset @ ( unordered_pair @ SV142 @ SY921 ) @ SY922 )
| ( in @ SY921 @ SY922 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2361]) ).
thf(2567,plain,
! [SV143: $i,SV400: $i,SV461: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV143 )
| ~ ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV400 )
| ~ ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV461 ) )
| ~ ~ ( ~ ( ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV143 )
| ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV461 ) )
| ~ ( ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV400 )
| ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV461 ) ) ) )
| ( SV461
= ( set_intersection2 @ SV143 @ SV400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2362]) ).
thf(2568,plain,
! [SV401: $i,SV143: $i,SV462: $i] :
( ( ( SV462
!= ( set_intersection2 @ SV143 @ SV401 ) )
| ~ ( ~ ! [SY1325: $i] :
( ~ ( in @ SY1325 @ SV143 )
| ~ ( in @ SY1325 @ SV401 )
| ( in @ SY1325 @ SV462 ) )
| ~ ~ ( ~ ! [SY1326: $i] :
( ~ ( in @ SY1326 @ SV462 )
| ( in @ SY1326 @ SV143 ) )
| ~ ! [SY1327: $i] :
( ~ ( in @ SY1327 @ SV462 )
| ( in @ SY1327 @ SV401 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2363]) ).
thf(2569,plain,
! [SV144: $i] :
( ( ( ~ ( ~ ! [SY930: $i] :
( ~ ( element @ SY930 @ ( powerset @ SV144 ) )
| ( v1_membered @ SY930 ) )
| ~ ! [SY931: $i] :
( ~ ( element @ SY931 @ ( powerset @ SV144 ) )
| ( v2_membered @ SY931 ) ) ) )
= $true )
| ( ( v3_membered @ SV144 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2364]) ).
thf(2570,plain,
! [SV144: $i] :
( ( ( ! [SY932: $i] :
( ~ ( element @ SY932 @ ( powerset @ SV144 ) )
| ( v3_membered @ SY932 ) ) )
= $true )
| ( ( v3_membered @ SV144 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2365]) ).
thf(2571,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1142: $i] :
( ~ ( in @ SY1142 @ ( sK52_SY712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SY1142 ) @ SV265 ) )
| ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK52_SY712 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) ) ) )
| ~ ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 ) )
| ~ ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 ) )
| ~ ~ ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ ( sK51_SY718 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SY1143 ) @ SV265 ) )
| ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK51_SY718 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) ) ) ) )
| ~ ( ( ( sK49_SY705 @ SV265 @ SV145 )
!= ( sK50_SY711 @ SV265 @ SV145 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2366]) ).
thf(2572,plain,
! [SV402: $i,SV330: $i] :
( ( ( ~ ( subset @ SV330 @ SV402 )
| ~ ( subset @ SV402 @ SV330 ) )
= $true )
| ( ( SV330 = SV402 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2367]) ).
thf(2573,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2368]) ).
thf(2574,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2369]) ).
thf(2575,plain,
! [SV146: $i,SV266: $i] :
( ( ( ! [SY1149: $i] :
( ~ ( in @ SY1149 @ SV266 )
| ~ ( in @ SY1149 @ ( sK5_C @ SV266 @ SV146 ) ) ) )
= $true )
| ( ( ~ ( in @ SV146 @ SV266 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2370]) ).
thf(2576,plain,
! [SV146: $i,SV266: $i] :
( ( ( in @ ( sK5_C @ SV266 @ SV146 ) @ SV266 )
= $true )
| ( ( ~ ( in @ SV146 @ SV266 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2371]) ).
thf(2577,plain,
! [SV331: $i] :
( ( ( ~ ( in @ ( sK85_B @ SV331 ) @ SV331 )
| ~ ~ ( subset @ ( sK85_B @ SV331 ) @ SV331 ) )
= $false )
| ( ( epsilon_transitive @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2372]) ).
thf(2578,plain,
! [SV332: $i] :
( ( ( epsilon_transitive @ SV332 )
= $false )
| ( ( ! [SY1208: $i] :
( ~ ( in @ SY1208 @ SV332 )
| ( subset @ SY1208 @ SV332 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2373]) ).
thf(2579,plain,
! [SV147: $i,SV403: $i,SV463: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV147 )
| ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV403 )
| ~ ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV463 ) )
| ~ ~ ( ~ ( ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV147 )
| ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV463 ) )
| ~ ( ~ ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV403 )
| ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV463 ) ) ) )
| ( SV463
= ( set_difference @ SV147 @ SV403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2374]) ).
thf(2580,plain,
! [SV404: $i,SV147: $i,SV464: $i] :
( ( ( SV464
!= ( set_difference @ SV147 @ SV404 ) )
| ~ ( ~ ! [SY1328: $i] :
( ~ ( in @ SY1328 @ SV147 )
| ( in @ SY1328 @ SV404 )
| ( in @ SY1328 @ SV464 ) )
| ~ ~ ( ~ ! [SY1329: $i] :
( ~ ( in @ SY1329 @ SV464 )
| ( in @ SY1329 @ SV147 ) )
| ~ ! [SY1330: $i] :
( ~ ( in @ SY1330 @ SV464 )
| ~ ( in @ SY1330 @ SV404 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2375]) ).
thf(2581,plain,
! [SV334: $i] :
( ( ( SV334 = empty_set )
= $false )
| ( ( ! [SY1209: $i] :
~ ( in @ SY1209 @ SV334 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2377]) ).
thf(2582,plain,
! [SV148: $i,SV335: $i] :
( ( ( element @ SV335 @ ( powerset @ ( powerset @ SV148 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1210: $i] :
( ~ ( in @ SY1210 @ SV335 )
| ~ ( subset @ ( sK105_C @ SV335 @ SV148 ) @ SY1210 )
| ( SY1210
= ( sK105_C @ SV335 @ SV148 ) ) )
| ~ ( in @ ( sK105_C @ SV335 @ SV148 ) @ SV335 ) )
| ( SV335 = empty_set ) )
= $true )
| ( ( finite @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2378]) ).
thf(2583,plain,
! [SV405: $i,SV336: $i] :
( ( ( ( ( set_difference @ SV336 @ SV405 )
!= SV336 ) )
= $true )
| ( ( disjoint @ SV336 @ SV405 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2379]) ).
thf(2584,plain,
! [SV406: $i,SV337: $i] :
( ( ( ~ ( disjoint @ SV337 @ SV406 ) )
= $true )
| ( ( ( set_difference @ SV337 @ SV406 )
= SV337 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2380]) ).
thf(2585,plain,
! [SV407: $i,SV338: $i] :
( ( ( ( ( set_difference @ SV338 @ ( singleton @ SV407 ) )
!= SV338 ) )
= $true )
| ( ( ~ ( in @ SV407 @ SV338 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2381]) ).
thf(2586,plain,
! [SV339: $i,SV408: $i] :
( ( ( in @ SV408 @ SV339 )
= $true )
| ( ( ( set_difference @ SV339 @ ( singleton @ SV408 ) )
= SV339 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2382]) ).
thf(2587,plain,
! [SV340: $i,SV409: $i] :
( ( ( ~ ( ~ ( ! [SY1278: $i] :
( ~ ( in @ ( sK68_C @ SV409 @ SV340 ) @ SY1278 )
| ~ ( in @ SY1278 @ SV340 ) )
| ~ ( in @ ( sK68_C @ SV409 @ SV340 ) @ SV409 ) )
| ~ ( ~ ( ~ ( in @ ( sK68_C @ SV409 @ SV340 ) @ ( sK69_SY723 @ SV409 @ SV340 ) )
| ~ ( in @ ( sK69_SY723 @ SV409 @ SV340 ) @ SV340 ) )
| ( in @ ( sK68_C @ SV409 @ SV340 ) @ SV409 ) ) ) )
= $true )
| ( ( SV409
= ( union @ SV340 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2383]) ).
thf(2588,plain,
! [SV341: $i,SV410: $i] :
( ( ( ( SV410
!= ( union @ SV341 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1279: $i] :
( ! [SY1219: $i] :
( ~ ( in @ SY1279 @ SY1219 )
| ~ ( in @ SY1219 @ SV341 ) )
| ( in @ SY1279 @ SV410 ) )
| ~ ! [SY1281: $i] :
( ~ ( in @ SY1281 @ SV410 )
| ~ ( ~ ( in @ SY1281 @ ( sK67_D @ SY1281 @ SV410 @ SV341 ) )
| ~ ( in @ ( sK67_D @ SY1281 @ SV410 @ SV341 ) @ SV341 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2384]) ).
thf(2589,plain,
! [SV411: $i,SV342: $i] :
( ( ( ~ ( element @ SV342 @ ( powerset @ SV411 ) ) )
= $true )
| ( ( subset @ SV342 @ SV411 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2385]) ).
thf(2590,plain,
! [SV412: $i,SV343: $i] :
( ( ( ~ ( subset @ SV343 @ SV412 ) )
= $true )
| ( ( element @ SV343 @ ( powerset @ SV412 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2386]) ).
thf(2591,plain,
! [SV344: $i] :
( ( ( empty @ SV344 )
= $false )
| ( ( empty @ ( relation_inverse @ SV344 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2387]) ).
thf(2592,plain,
! [SV345: $i] :
( ( ( empty @ SV345 )
= $false )
| ( ( relation @ ( relation_inverse @ SV345 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2388]) ).
thf(2593,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2389]) ).
thf(2594,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2390]) ).
thf(2595,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2391]) ).
thf(2596,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2392]) ).
thf(2597,plain,
! [SV346: $i,SV413: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK124_C @ SV413 @ SV346 ) @ SV413 )
| ~ ( subset @ ( sK124_C @ SV413 @ SV346 ) @ SV346 ) )
| ~ ( ( in @ ( sK124_C @ SV413 @ SV346 ) @ SV413 )
| ( subset @ ( sK124_C @ SV413 @ SV346 ) @ SV346 ) ) ) )
= $true )
| ( ( SV413
= ( powerset @ SV346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2393]) ).
thf(2598,plain,
! [SV347: $i,SV414: $i] :
( ( ( ( SV414
!= ( powerset @ SV347 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1282: $i] :
( ~ ( in @ SY1282 @ SV414 )
| ( subset @ SY1282 @ SV347 ) )
| ~ ! [SY1283: $i] :
( ~ ( subset @ SY1283 @ SV347 )
| ( in @ SY1283 @ SV414 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2394]) ).
thf(2599,plain,
! [SV149: $i] :
( ( ( ~ ( element @ ( sK118_B @ SV149 ) @ ( powerset @ SV149 ) )
| ~ ~ ( empty @ ( sK118_B @ SV149 ) ) )
= $false )
| ( ( empty @ SV149 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2395]) ).
thf(2600,plain,
! [SV415: $i,SV150: $i,SV465: $i] :
( ( ~ ( relation_of2_as_subset @ SV465 @ SV150 @ SV415 )
| ~ ( ~ ! [SY1331: $i] :
~ ( in @ ( ordered_pair @ SY1331 @ ( sK102_D @ SV465 @ SV415 @ SV150 ) ) @ SV465 )
| ~ ( in @ ( sK102_D @ SV465 @ SV415 @ SV150 ) @ SV415 ) )
| ( ( relation_rng_as_subset @ SV150 @ SV415 @ SV465 )
= SV415 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2397]) ).
thf(2601,plain,
! [SV416: $i,SV150: $i,SV466: $i] :
( ( ~ ( relation_of2_as_subset @ SV466 @ SV150 @ SV416 )
| ( ( relation_rng_as_subset @ SV150 @ SV416 @ SV466 )
!= SV416 )
| ! [SY1332: $i] :
( ( in @ ( ordered_pair @ ( sK101_E @ SY1332 @ SV466 @ SV416 @ SV150 ) @ SY1332 ) @ SV466 )
| ~ ( in @ SY1332 @ SV416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2398]) ).
thf(2602,plain,
! [SV151: $i,SV267: $i,SV467: $i] :
( ( ! [SY1333: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK94_E @ SY1333 @ SV467 @ SV267 @ SV151 ) @ SY1333 )
| ( ( sK94_E @ SY1333 @ SV467 @ SV267 @ SV151 )
!= SV467 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK94_E @ SY1333 @ SV467 @ SV267 @ SV151 ) @ SY1333 )
| ( ( sK94_E @ SY1333 @ SV467 @ SV267 @ SV151 )
!= SV151 ) )
| ~ ( ~ ( in @ ( sK94_E @ SY1333 @ SV467 @ SV267 @ SV151 ) @ SY1333 )
| ( ( sK94_E @ SY1333 @ SV467 @ SV267 @ SV151 )
!= SV267 ) ) ) )
| ~ ( ( in @ ( sK94_E @ SY1333 @ SV467 @ SV267 @ SV151 ) @ SY1333 )
| ( ( sK94_E @ SY1333 @ SV467 @ SV267 @ SV151 )
= SV467 )
| ( ( sK94_E @ SY1333 @ SV467 @ SV267 @ SV151 )
= SV151 )
| ( ( sK94_E @ SY1333 @ SV467 @ SV267 @ SV151 )
= SV267 ) ) )
| ( SY1333
= ( unordered_triple @ SV151 @ SV267 @ SV467 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2399]) ).
thf(2603,plain,
! [SV468: $i,SV267: $i,SV151: $i] :
( ( ! [SY1334: $i] :
( ( SY1334
!= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
| ~ ( ~ ! [SY1335: $i] :
( ~ ( in @ SY1335 @ SY1334 )
| ( SY1335 = SV468 )
| ( SY1335 = SV151 )
| ( SY1335 = SV267 ) )
| ~ ~ ( ~ ! [SY1336: $i] :
( ( SY1336 != SV468 )
| ( in @ SY1336 @ SY1334 ) )
| ~ ~ ( ~ ! [SY965: $i] :
( ( SY965 != SV151 )
| ( in @ SY965 @ SY1334 ) )
| ~ ! [SY1157: $i] :
( ( SY1157 != SV267 )
| ( in @ SY1157 @ SY1334 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2400]) ).
thf(2604,plain,
! [SV152: $i,SV417: $i] :
( ( ( ~ ( subset @ SV417 @ ( sK106_B @ SV152 ) )
| ( are_equipotent @ SV417 @ ( sK106_B @ SV152 ) ) )
= $true )
| ( ( in @ SV417 @ ( sK106_B @ SV152 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2401]) ).
thf(2605,plain,
! [SV152: $i] :
( ( ~ ! [SY968: $i] :
( ~ ( in @ SY968 @ ( sK106_B @ SV152 ) )
| ( in @ ( powerset @ SY968 ) @ ( sK106_B @ SV152 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2402]) ).
thf(2606,plain,
! [SV152: $i] :
( ( ~ ~ ( ~ ! [SY969: $i,SY970: $i] :
( ~ ( in @ SY969 @ ( sK106_B @ SV152 ) )
| ~ ( subset @ SY970 @ SY969 )
| ( in @ SY970 @ ( sK106_B @ SV152 ) ) )
| ~ ( in @ SV152 @ ( sK106_B @ SV152 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2402]) ).
thf(2607,plain,
! [SV153: $i,SV418: $i] :
( ( ( ~ ( in @ SV418 @ SV153 )
| ~ ( ordinal @ SV418 ) )
= $true )
| ( ( in @ SV418 @ ( sK107_B @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2403]) ).
thf(2608,plain,
! [SV153: $i] :
( ( ~ ! [SY972: $i] :
( ~ ( in @ SY972 @ ( sK107_B @ SV153 ) )
| ( in @ SY972 @ SV153 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2404]) ).
thf(2609,plain,
! [SV153: $i] :
( ( ~ ! [SY973: $i] :
( ~ ( in @ SY973 @ ( sK107_B @ SV153 ) )
| ( ordinal @ SY973 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2404]) ).
thf(2610,plain,
! [SV154: $i] :
( ( ( ! [SY974: $i] :
( ~ ( relation @ SY974 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK72_C @ SY974 @ SV154 ) @ ( sK73_SY724 @ SY974 @ SV154 ) ) @ SV154 )
| ~ ~ ( in @ ( ordered_pair @ ( sK72_C @ SY974 @ SV154 ) @ ( sK73_SY724 @ SY974 @ SV154 ) ) @ SY974 ) )
| ( subset @ SV154 @ SY974 ) ) )
= $true )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2405]) ).
thf(2611,plain,
! [SV154: $i] :
( ( ( ! [SY975: $i] :
( ~ ( relation @ SY975 )
| ~ ( subset @ SV154 @ SY975 )
| ! [SY976: $i,SY977: $i] :
( ~ ( in @ ( ordered_pair @ SY976 @ SY977 ) @ SV154 )
| ( in @ ( ordered_pair @ SY976 @ SY977 ) @ SY975 ) ) ) )
= $true )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2406]) ).
thf(2612,plain,
! [SV268: $i,SV155: $i] :
( ( ( ~ ! [SY1158: $i] :
( ~ ( element @ SY1158 @ ( powerset @ ( powerset @ SV155 ) ) )
| ~ ( ~ ( element @ ( sK123_D @ SY1158 @ SV268 @ SV155 ) @ ( powerset @ SV155 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK123_D @ SY1158 @ SV268 @ SV155 ) @ SY1158 )
| ~ ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SY1158 @ SV268 @ SV155 ) ) @ SV268 ) )
| ~ ( ( in @ ( sK123_D @ SY1158 @ SV268 @ SV155 ) @ SY1158 )
| ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SY1158 @ SV268 @ SV155 ) ) @ SV268 ) ) ) )
| ( SY1158
= ( complements_of_subsets @ SV155 @ SV268 ) ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2407]) ).
thf(2613,plain,
! [SV268: $i,SV155: $i] :
( ( ( ~ ! [SY1159: $i] :
( ~ ( element @ SY1159 @ ( powerset @ ( powerset @ SV155 ) ) )
| ( SY1159
!= ( complements_of_subsets @ SV155 @ SV268 ) )
| ~ ( ~ ! [SY1160: $i] :
( ~ ( element @ SY1160 @ ( powerset @ SV155 ) )
| ~ ( in @ SY1160 @ SY1159 )
| ( in @ ( subset_complement @ SV155 @ SY1160 ) @ SV268 ) )
| ~ ! [SY1161: $i] :
( ~ ( element @ SY1161 @ ( powerset @ SV155 ) )
| ~ ( in @ ( subset_complement @ SV155 @ SY1161 ) @ SV268 )
| ( in @ SY1161 @ SY1159 ) ) ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2407]) ).
thf(2614,plain,
! [SV419: $i,SV348: $i] :
( ( ( ~ ( subset @ SV348 @ ( singleton @ SV419 ) ) )
= $true )
| ( ( ( SV348 = empty_set )
| ( SV348
= ( singleton @ SV419 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2408]) ).
thf(2615,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2409]) ).
thf(2616,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2410]) ).
thf(2617,plain,
! [SV420: $i,SV349: $i] :
( ( ( ~ ( subset @ SV349 @ ( singleton @ SV420 ) ) )
= $true )
| ( ( ( SV349 = empty_set )
| ( SV349
= ( singleton @ SV420 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2411]) ).
thf(2618,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2412]) ).
thf(2619,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2413]) ).
thf(2620,plain,
! [SV421: $i,SV350: $i] :
( ( ( ( ( set_difference @ SV350 @ SV421 )
!= empty_set ) )
= $true )
| ( ( subset @ SV350 @ SV421 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2414]) ).
thf(2621,plain,
! [SV422: $i,SV351: $i] :
( ( ( ~ ( subset @ SV351 @ SV422 ) )
= $true )
| ( ( ( set_difference @ SV351 @ SV422 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2415]) ).
thf(2622,plain,
! [SV156: $i] :
( ( ( ! [SY983: $i] :
( ~ ( element @ SY983 @ ( powerset @ SV156 ) )
| ( v1_membered @ SY983 ) ) )
= $true )
| ( ( v2_membered @ SV156 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2416]) ).
thf(2623,plain,
! [SV156: $i] :
( ( ( ! [SY984: $i] :
( ~ ( element @ SY984 @ ( powerset @ SV156 ) )
| ( v2_membered @ SY984 ) ) )
= $true )
| ( ( v2_membered @ SV156 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2417]) ).
thf(2624,plain,
! [SV423: $i,SV352: $i] :
( ( ( ~ ( empty @ SV352 )
| ~ ( relation @ SV423 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV352 @ SV423 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2418]) ).
thf(2625,plain,
! [SV424: $i,SV353: $i] :
( ( ( ~ ( empty @ SV353 )
| ~ ( relation @ SV424 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV353 @ SV424 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2419]) ).
thf(2626,plain,
! [SV425: $i] :
( ( ( ~ ! [SY1288: $i] :
( ! [SY1289: $i] :
( ( SY1289 != SY1288 )
| ~ ( in @ SY1289 @ SV425 ) )
| ~ ( ordinal @ SY1288 )
| ( in @ SY1288 @ ( sK7_B @ SV425 ) ) )
| ~ ! [SY1290: $i] :
( ~ ( in @ SY1290 @ ( sK7_B @ SV425 ) )
| ~ ( ~ ~ ( ( ( sK8_D @ SY1290 @ SV425 )
!= SY1290 )
| ~ ( in @ ( sK8_D @ SY1290 @ SV425 ) @ SV425 ) )
| ~ ( ordinal @ SY1290 ) ) ) )
= $false )
| ( sK12_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[2420]) ).
thf(2627,plain,
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK9_B != sK10_SY601 )
| ~ ( ordinal @ sK10_SY601 ) )
| ( sK9_B != sK11_SY603 ) )
| ~ ( ordinal @ sK11_SY603 ) )
| ~ ( ( sK10_SY601 != sK11_SY603 ) ) )
= $false )
| ( sK12_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2421]) ).
thf(2628,plain,
! [SV426: $i,SV157: $i,SV469: $i] :
( ( ~ ( relation @ SV469 )
| ~ ( in @ SV157 @ SV469 )
| ~ ( in @ SV157 @ ( cartesian_product2 @ SV426 @ SV426 ) )
| ( in @ SV157 @ ( relation_restriction @ SV469 @ SV426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2422]) ).
thf(2629,plain,
! [SV157: $i] :
( ( ~ ! [SY987: $i,SY988: $i] :
( ~ ( relation @ SY988 )
| ~ ( in @ SV157 @ ( relation_restriction @ SY988 @ SY987 ) )
| ( in @ SV157 @ SY988 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2423]) ).
thf(2630,plain,
! [SV157: $i] :
( ( ~ ! [SY989: $i,SY990: $i] :
( ~ ( relation @ SY990 )
| ~ ( in @ SV157 @ ( relation_restriction @ SY990 @ SY989 ) )
| ( in @ SV157 @ ( cartesian_product2 @ SY989 @ SY989 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2423]) ).
thf(2631,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2424]) ).
thf(2632,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2425]) ).
thf(2633,plain,
! [SV158: $i] :
( ( ~ ~ ( ~ ! [SY991: $i,SY992: $i] :
( ~ ( relation_of2_as_subset @ SY992 @ SV158 @ SY991 )
| ( SY991 = empty_set )
| ( SV158
!= ( relation_dom_as_subset @ SV158 @ SY991 @ SY992 ) )
| ( quasi_total @ SY992 @ SV158 @ SY991 ) )
| ~ ! [SY993: $i,SY994: $i] :
( ~ ( relation_of2_as_subset @ SY994 @ SV158 @ SY993 )
| ( SY993 = empty_set )
| ~ ( quasi_total @ SY994 @ SV158 @ SY993 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SY993 @ SY994 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2426]) ).
thf(2634,plain,
! [SV158: $i] :
( ( ~ ~ ( ~ ! [SY995: $i,SY996: $i] :
( ~ ( relation_of2_as_subset @ SY996 @ SV158 @ SY995 )
| ( SV158 != empty_set )
| ( SV158
!= ( relation_dom_as_subset @ SV158 @ SY995 @ SY996 ) )
| ( quasi_total @ SY996 @ SV158 @ SY995 ) )
| ~ ! [SY997: $i,SY998: $i] :
( ~ ( relation_of2_as_subset @ SY998 @ SV158 @ SY997 )
| ( SV158 != empty_set )
| ~ ( quasi_total @ SY998 @ SV158 @ SY997 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SY997 @ SY998 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2426]) ).
thf(2635,plain,
! [SV158: $i] :
( ( ~ ! [SY999: $i,SY1000: $i] :
( ~ ( relation_of2_as_subset @ SY1000 @ SV158 @ SY999 )
| ( SY999 != empty_set )
| ( SY1000 != empty_set )
| ( quasi_total @ SY1000 @ SV158 @ SY999 )
| ( SV158 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2427]) ).
thf(2636,plain,
! [SV158: $i] :
( ( ~ ! [SY1001: $i,SY1002: $i] :
( ~ ( relation_of2_as_subset @ SY1002 @ SV158 @ SY1001 )
| ( SY1001 != empty_set )
| ~ ( quasi_total @ SY1002 @ SV158 @ SY1001 )
| ( SY1002 = empty_set )
| ( SV158 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2427]) ).
thf(2637,plain,
( ( ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK90_SY733 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK89_C @ SX1 @ SX0 ) @ ( sK90_SY733 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK89_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( sK89_C @ SX1 @ SX0 ) @ SX2 ) )
| ( in @ ( sK89_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2428]) ).
thf(2638,plain,
( ( ! [SX0: $i] :
( ( SX0 = empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( ~ ( in @ ( sK88_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ SX2 @ ( sK88_D @ SX2 @ SX1 @ SX0 ) ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX2 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2429]) ).
thf(2639,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1
!= ( set_meet @ SX0 ) )
| ( SX1 = empty_set ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2430]) ).
thf(2640,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
( ( SX1 != empty_set )
| ( SX1
= ( set_meet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2431]) ).
thf(2641,plain,
! [SV159: $i,SV427: $i,SV470: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK82_D @ SV470 @ SV427 @ SV159 ) @ SV470 )
| ( ( sK82_D @ SV470 @ SV427 @ SV159 )
!= SV159 ) )
| ~ ( ~ ( in @ ( sK82_D @ SV470 @ SV427 @ SV159 ) @ SV470 )
| ( ( sK82_D @ SV470 @ SV427 @ SV159 )
!= SV427 ) ) )
| ~ ( ( in @ ( sK82_D @ SV470 @ SV427 @ SV159 ) @ SV470 )
| ( ( sK82_D @ SV470 @ SV427 @ SV159 )
= SV159 )
| ( ( sK82_D @ SV470 @ SV427 @ SV159 )
= SV427 ) ) )
| ( SV470
= ( unordered_pair @ SV159 @ SV427 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2432]) ).
thf(2642,plain,
! [SV428: $i,SV159: $i,SV471: $i] :
( ( ( SV471
!= ( unordered_pair @ SV159 @ SV428 ) )
| ~ ( ~ ! [SY1339: $i] :
( ~ ( in @ SY1339 @ SV471 )
| ( SY1339 = SV159 )
| ( SY1339 = SV428 ) )
| ~ ~ ( ~ ! [SY1340: $i] :
( ( SY1340 != SV159 )
| ( in @ SY1340 @ SV471 ) )
| ~ ! [SY1341: $i] :
( ( SY1341 != SV428 )
| ( in @ SY1341 @ SV471 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2433]) ).
thf(2643,plain,
! [SV429: $i,SV354: $i] :
( ( ( ~ ( empty @ SV354 )
| ~ ( relation @ SV429 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV429 @ SV354 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2434]) ).
thf(2644,plain,
! [SV430: $i,SV355: $i] :
( ( ( ~ ( empty @ SV355 )
| ~ ( relation @ SV430 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV430 @ SV355 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2435]) ).
thf(2645,plain,
! [SV160: $i] :
( ( ( ! [SY1010: $i] :
( ~ ( element @ SY1010 @ SV160 )
| ( v1_xcmplx_0 @ SY1010 ) ) )
= $true )
| ( ( v2_membered @ SV160 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2436]) ).
thf(2646,plain,
! [SV160: $i] :
( ( ( ! [SY1011: $i] :
( ~ ( element @ SY1011 @ SV160 )
| ( v1_xreal_0 @ SY1011 ) ) )
= $true )
| ( ( v2_membered @ SV160 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2437]) ).
thf(2647,plain,
! [SV356: $i] :
( ( ( latt_str @ SV356 )
= $false )
| ( ( join_semilatt_str @ SV356 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2438]) ).
thf(2648,plain,
! [SV357: $i] :
( ( ( latt_str @ SV357 )
= $false )
| ( ( meet_semilatt_str @ SV357 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2439]) ).
thf(2649,plain,
! [SV358: $i] :
( ( ( ~ ! [SY1235: $i,SY1236: $i] :
( ( sK93_B @ SV358 )
!= ( ordered_pair @ SY1235 @ SY1236 ) )
| ~ ( in @ ( sK93_B @ SV358 ) @ SV358 ) )
= $false )
| ( ( relation @ SV358 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2440]) ).
thf(2650,plain,
! [SV359: $i] :
( ( ( relation @ SV359 )
= $false )
| ( ( ! [SY1237: $i] :
( ( SY1237
= ( ordered_pair @ ( sK91_C @ SY1237 @ SV359 ) @ ( sK92_SY735 @ SY1237 @ SV359 ) ) )
| ~ ( in @ SY1237 @ SV359 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2441]) ).
thf(2651,plain,
! [SV360: $i] :
( ( ( empty @ SV360 )
= $false )
| ( ( empty @ ( relation_rng @ SV360 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2442]) ).
thf(2652,plain,
! [SV361: $i] :
( ( ( empty @ SV361 )
= $false )
| ( ( relation @ ( relation_rng @ SV361 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2443]) ).
thf(2653,plain,
! [SV269: $i,SV162: $i] :
( ( ( ~ ! [SY1162: $i] :
( ~ ( element @ SY1162 @ ( powerset @ SV162 ) )
| ~ ( disjoint @ SV269 @ SY1162 )
| ( subset @ SV269 @ ( subset_complement @ SV162 @ SY1162 ) ) ) )
= $false )
| ( ( element @ SV269 @ ( powerset @ SV162 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2444]) ).
thf(2654,plain,
! [SV269: $i,SV162: $i] :
( ( ( ~ ! [SY1163: $i] :
( ~ ( element @ SY1163 @ ( powerset @ SV162 ) )
| ~ ( subset @ SV269 @ ( subset_complement @ SV162 @ SY1163 ) )
| ( disjoint @ SV269 @ SY1163 ) ) )
= $false )
| ( ( element @ SV269 @ ( powerset @ SV162 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2444]) ).
thf(2655,plain,
! [SV431: $i,SV362: $i] :
( ( ( ~ ( in @ SV362 @ SV431 ) )
= $true )
| ( ( subset @ ( singleton @ SV362 ) @ SV431 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2445]) ).
thf(2656,plain,
! [SV432: $i,SV363: $i] :
( ( ( ~ ( subset @ ( singleton @ SV363 ) @ SV432 ) )
= $true )
| ( ( in @ SV363 @ SV432 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2446]) ).
thf(2657,plain,
! [SV433: $i,SV163: $i,SV472: $i] :
( ( ~ ( relation_of2 @ SV472 @ SV163 @ SV433 )
| ( relation_of2_as_subset @ SV472 @ SV163 @ SV433 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2447]) ).
thf(2658,plain,
! [SV434: $i,SV163: $i,SV473: $i] :
( ( ~ ( relation_of2_as_subset @ SV473 @ SV163 @ SV434 )
| ( relation_of2 @ SV473 @ SV163 @ SV434 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2448]) ).
thf(2659,plain,
! [SV364: $i,SV435: $i] :
( ( ( ~ ( ~ ( ( ( sK87_C @ SV435 @ SV364 )
!= SV364 )
| ~ ( in @ ( sK87_C @ SV435 @ SV364 ) @ SV435 ) )
| ~ ( ( ( sK87_C @ SV435 @ SV364 )
= SV364 )
| ( in @ ( sK87_C @ SV435 @ SV364 ) @ SV435 ) ) ) )
= $true )
| ( ( SV435
= ( singleton @ SV364 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2449]) ).
thf(2660,plain,
! [SV365: $i,SV436: $i] :
( ( ( ( SV436
!= ( singleton @ SV365 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1299: $i] :
( ( SY1299 != SV365 )
| ( in @ SY1299 @ SV436 ) )
| ~ ! [SY1300: $i] :
( ~ ( in @ SY1300 @ SV436 )
| ( SY1300 = SV365 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2450]) ).
thf(2661,plain,
! [SV474: $i,SV437: $i,SV164: $i] :
( ( ~ ( ~ ( ! [SY1342: $i,SY1343: $i] :
( ~ ( in @ SY1342 @ SV164 )
| ~ ( in @ SY1343 @ SV437 )
| ( ( sK78_D @ SV474 @ SV437 @ SV164 )
!= ( ordered_pair @ SY1342 @ SY1343 ) ) )
| ~ ( in @ ( sK78_D @ SV474 @ SV437 @ SV164 ) @ SV474 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK79_SY729 @ SV474 @ SV437 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK80_SY731 @ SV474 @ SV437 @ SV164 ) @ SV437 ) )
| ( ( sK78_D @ SV474 @ SV437 @ SV164 )
!= ( ordered_pair @ ( sK79_SY729 @ SV474 @ SV437 @ SV164 ) @ ( sK80_SY731 @ SV474 @ SV437 @ SV164 ) ) ) )
| ( in @ ( sK78_D @ SV474 @ SV437 @ SV164 ) @ SV474 ) ) )
| ( SV474
= ( cartesian_product2 @ SV164 @ SV437 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2451]) ).
thf(2662,plain,
! [SV438: $i,SV164: $i,SV475: $i] :
( ( ( SV475
!= ( cartesian_product2 @ SV164 @ SV438 ) )
| ~ ( ~ ! [SY1344: $i] :
( ! [SY1306: $i,SY1307: $i] :
( ~ ( in @ SY1306 @ SV164 )
| ~ ( in @ SY1307 @ SV438 )
| ( SY1344
!= ( ordered_pair @ SY1306 @ SY1307 ) ) )
| ( in @ SY1344 @ SV475 ) )
| ~ ! [SY1347: $i] :
( ~ ( in @ SY1347 @ SV475 )
| ~ ( ~ ~ ( ~ ( in @ ( sK76_E @ SY1347 @ SV475 @ SV438 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK77_SY726 @ SY1347 @ SV475 @ SV438 @ SV164 ) @ SV438 ) )
| ( SY1347
!= ( ordered_pair @ ( sK76_E @ SY1347 @ SV475 @ SV438 @ SV164 ) @ ( sK77_SY726 @ SY1347 @ SV475 @ SV438 @ SV164 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2452]) ).
thf(2663,plain,
! [SV366: $i,SV439: $i] :
( ( ( ~ ( ~ ( in @ ( sK71_C @ SV439 @ SV366 ) @ SV366 )
| ~ ~ ( in @ ( sK71_C @ SV439 @ SV366 ) @ SV439 ) ) )
= $true )
| ( ( subset @ SV366 @ SV439 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2453]) ).
thf(2664,plain,
! [SV440: $i,SV367: $i] :
( ( ( ~ ( subset @ SV367 @ SV440 ) )
= $true )
| ( ( ! [SY1309: $i] :
( ~ ( in @ SY1309 @ SV367 )
| ( in @ SY1309 @ SV440 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2454]) ).
thf(2665,plain,
! [SV441: $i,SV165: $i,SV476: $i] :
( ( ~ ( relation_of2 @ SV476 @ SV165 @ SV441 )
| ( subset @ SV476 @ ( cartesian_product2 @ SV165 @ SV441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2455]) ).
thf(2666,plain,
! [SV442: $i,SV165: $i,SV477: $i] :
( ( ~ ( subset @ SV477 @ ( cartesian_product2 @ SV165 @ SV442 ) )
| ( relation_of2 @ SV477 @ SV165 @ SV442 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2456]) ).
thf(2667,plain,
! [SV166: $i,SV443: $i] :
( ( ( ~ ( subset @ SV443 @ ( sK3_B @ SV166 ) )
| ( are_equipotent @ SV443 @ ( sK3_B @ SV166 ) ) )
= $true )
| ( ( in @ SV443 @ ( sK3_B @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2457]) ).
thf(2668,plain,
! [SV166: $i] :
( ( ~ ! [SY1034: $i] :
( ~ ( ~ ! [SY1035: $i] :
( ~ ( subset @ SY1035 @ SY1034 )
| ( in @ SY1035 @ ( sK4_SY591 @ SY1034 @ SV166 ) ) )
| ~ ( in @ ( sK4_SY591 @ SY1034 @ SV166 ) @ ( sK3_B @ SV166 ) ) )
| ~ ( in @ SY1034 @ ( sK3_B @ SV166 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2458]) ).
thf(2669,plain,
! [SV166: $i] :
( ( ~ ~ ( ~ ! [SY1036: $i,SY1037: $i] :
( ~ ( in @ SY1036 @ ( sK3_B @ SV166 ) )
| ~ ( subset @ SY1037 @ SY1036 )
| ( in @ SY1037 @ ( sK3_B @ SV166 ) ) )
| ~ ( in @ SV166 @ ( sK3_B @ SV166 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2458]) ).
thf(2670,plain,
! [SV167: $i,SV444: $i,SV478: $i] :
( ( ~ ( relation_of2_as_subset @ SV478 @ SV444 @ SV167 )
| ~ ( ~ ! [SY1348: $i] :
~ ( in @ ( ordered_pair @ ( sK104_D @ SV478 @ SV444 @ SV167 ) @ SY1348 ) @ SV478 )
| ~ ( in @ ( sK104_D @ SV478 @ SV444 @ SV167 ) @ SV444 ) )
| ( ( relation_dom_as_subset @ SV444 @ SV167 @ SV478 )
= SV444 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2459]) ).
thf(2671,plain,
! [SV167: $i,SV445: $i,SV479: $i] :
( ( ~ ( relation_of2_as_subset @ SV479 @ SV445 @ SV167 )
| ( ( relation_dom_as_subset @ SV445 @ SV167 @ SV479 )
!= SV445 )
| ! [SY1349: $i] :
( ( in @ ( ordered_pair @ SY1349 @ ( sK103_E @ SY1349 @ SV479 @ SV445 @ SV167 ) ) @ SV479 )
| ~ ( in @ SY1349 @ SV445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2460]) ).
thf(2672,plain,
! [SV168: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( sK27_SY634 @ SV168 )
!= ( singleton @ ( sK26_B @ SV168 ) ) )
| ~ ( in @ ( sK26_B @ SV168 ) @ SV168 ) )
| ~ ( in @ ( sK26_B @ SV168 ) @ SV168 ) )
| ( ( sK28_SY636 @ SV168 )
!= ( singleton @ ( sK26_B @ SV168 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) )
| ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2461]) ).
thf(2673,plain,
! [SV168: $i] :
( ( ( ( sK27_SY634 @ SV168 )
= ( sK28_SY636 @ SV168 ) )
= $false )
| ( ( ~ ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) )
| ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2462]) ).
thf(2674,plain,
( ( empty @ sK57_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2463]) ).
thf(2675,plain,
( ( relation @ sK57_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2464]) ).
thf(2676,plain,
! [SV270: $i,SV480: $i,SV169: $i] :
( ( ! [SY1350: $i] :
( ~ ( in @ SV169 @ SV480 )
| ~ ( in @ SV270 @ SY1350 )
| ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SV480 @ SY1350 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2465]) ).
thf(2677,plain,
! [SV270: $i,SV169: $i] :
( ( ~ ! [SY1166: $i] :
( ! [SY1167: $i] :
~ ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SY1166 @ SY1167 ) )
| ( in @ SV169 @ SY1166 ) )
| ~ ! [SY1168: $i,SY1169: $i] :
( ~ ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SY1168 @ SY1169 ) )
| ( in @ SV270 @ SY1169 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2466]) ).
thf(2678,plain,
! [SV271: $i,SV481: $i,SV170: $i] :
( ( ( ~ ( ~ ! [SY1351: $i] :
( ! [SY1352: $i,SY1353: $i] :
( ( ( ordered_pair @ SY1352 @ SY1353 )
!= SY1351 )
| ~ ( in @ SY1352 @ SV170 )
| ! [SY1354: $i] :
( ~ ( ~ ( in @ ( sK115_I @ SY1354 @ SY1353 @ SY1352 @ SY1351 @ SV481 @ SV271 @ SV170 ) @ SY1354 )
| ~ ~ ( in @ ( ordered_pair @ SY1353 @ ( sK115_I @ SY1354 @ SY1353 @ SY1352 @ SY1351 @ SV481 @ SV271 @ SV170 ) ) @ SV271 ) )
| ( SY1352 != SY1354 )
| ~ ( in @ SY1353 @ SY1354 ) ) )
| ~ ( in @ SY1351 @ ( cartesian_product2 @ SV170 @ SV481 ) )
| ( in @ SY1351 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) ) )
| ~ ~ ( ~ ! [SY1355: $i] :
( ~ ( in @ SY1355 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
| ~ ( ~ ~ ( ( ( ordered_pair @ ( sK112_F @ SY1355 @ SV481 @ SV271 @ SV170 ) @ ( sK113_SY768 @ SY1355 @ SV481 @ SV271 @ SV170 ) )
!= SY1355 )
| ~ ( in @ ( sK112_F @ SY1355 @ SV481 @ SV271 @ SV170 ) @ SV170 ) )
| ~ ~ ( ~ ! [SY1356: $i] :
( ~ ( in @ SY1356 @ ( sK114_SY771 @ SY1355 @ SV481 @ SV271 @ SV170 ) )
| ( in @ ( ordered_pair @ ( sK113_SY768 @ SY1355 @ SV481 @ SV271 @ SV170 ) @ SY1356 ) @ SV271 ) )
| ~ ~ ( ( ( sK112_F @ SY1355 @ SV481 @ SV271 @ SV170 )
!= ( sK114_SY771 @ SY1355 @ SV481 @ SV271 @ SV170 ) )
| ~ ( in @ ( sK113_SY768 @ SY1355 @ SV481 @ SV271 @ SV170 ) @ ( sK114_SY771 @ SY1355 @ SV481 @ SV271 @ SV170 ) ) ) ) ) )
| ~ ! [SY1357: $i] :
( ~ ( in @ SY1357 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
| ( in @ SY1357 @ ( cartesian_product2 @ SV170 @ SV481 ) ) ) ) ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2467]) ).
thf(2679,plain,
! [SV368: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK74_B @ SV368 )
!= ( sK75_SY725 @ SV368 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK74_B @ SV368 ) @ SV368 )
| ~ ( in @ ( sK75_SY725 @ SV368 ) @ SV368 ) )
| ~ ~ ( in @ ( sK74_B @ SV368 ) @ ( sK75_SY725 @ SV368 ) ) ) )
| ~ ~ ( in @ ( sK75_SY725 @ SV368 ) @ ( sK74_B @ SV368 ) ) )
= $false )
| ( ( epsilon_connected @ SV368 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2468]) ).
thf(2680,plain,
! [SV369: $i] :
( ( ( epsilon_connected @ SV369 )
= $false )
| ( ( ! [SY1247: $i,SY1248: $i] :
( ( SY1247 = SY1248 )
| ~ ( in @ SY1247 @ SV369 )
| ~ ( in @ SY1248 @ SV369 )
| ( in @ SY1247 @ SY1248 )
| ( in @ SY1248 @ SY1247 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2469]) ).
thf(2681,plain,
( ( ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_difference @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2470]) ).
thf(2682,plain,
( ( ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_difference @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2471]) ).
thf(2683,plain,
! [SV370: $i] :
( ( ( v3_membered @ SV370 )
= $false )
| ( ( ! [SY1249: $i] : ( v3_membered @ ( set_difference @ SV370 @ SY1249 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2472]) ).
thf(2684,plain,
! [SV171: $i] :
( ( ( ! [SY1063: $i] :
( ~ ( relation @ SY1063 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK83_C @ SY1063 @ SV171 ) @ ( sK84_SY732 @ SY1063 @ SV171 ) ) @ SV171 )
| ~ ( in @ ( ordered_pair @ ( sK83_C @ SY1063 @ SV171 ) @ ( sK84_SY732 @ SY1063 @ SV171 ) ) @ SY1063 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK83_C @ SY1063 @ SV171 ) @ ( sK84_SY732 @ SY1063 @ SV171 ) ) @ SV171 )
| ( in @ ( ordered_pair @ ( sK83_C @ SY1063 @ SV171 ) @ ( sK84_SY732 @ SY1063 @ SV171 ) ) @ SY1063 ) ) )
| ( SV171 = SY1063 ) ) )
= $true )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2473]) ).
thf(2685,plain,
! [SV171: $i] :
( ( ( ! [SY1064: $i] :
( ~ ( relation @ SY1064 )
| ( SV171 != SY1064 )
| ~ ( ~ ! [SY1065: $i,SY1066: $i] :
( ~ ( in @ ( ordered_pair @ SY1065 @ SY1066 ) @ SV171 )
| ( in @ ( ordered_pair @ SY1065 @ SY1066 ) @ SY1064 ) )
| ~ ! [SY1067: $i,SY1068: $i] :
( ~ ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SY1064 )
| ( in @ ( ordered_pair @ SY1067 @ SY1068 ) @ SV171 ) ) ) ) )
= $true )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2474]) ).
thf(2686,plain,
! [SV446: $i,SV371: $i] :
( ( ( disjoint @ SV371 @ SV446 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK98_C @ SV446 @ SV371 ) @ SV371 )
| ~ ( in @ ( sK98_C @ SV446 @ SV371 ) @ SV446 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2475]) ).
thf(2687,plain,
! [SV447: $i,SV372: $i] :
( ( ( ! [SY1316: $i] :
( ~ ( in @ SY1316 @ SV372 )
| ~ ( in @ SY1316 @ SV447 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV372 @ SV447 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2476]) ).
thf(2688,plain,
! [SV448: $i,SV373: $i] :
( ( ( ~ ( in @ SV373 @ SV448 ) )
= $true )
| ( ( subset @ ( singleton @ SV373 ) @ SV448 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2477]) ).
thf(2689,plain,
! [SV449: $i,SV374: $i] :
( ( ( ~ ( subset @ ( singleton @ SV374 ) @ SV449 ) )
= $true )
| ( ( in @ SV374 @ SV449 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2478]) ).
thf(2690,plain,
! [SV450: $i,SV375: $i] :
( ( ( disjoint @ SV375 @ SV450 )
= $true )
| ( ( in @ ( sK97_C @ SV450 @ SV375 ) @ ( set_intersection2 @ SV375 @ SV450 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2479]) ).
thf(2691,plain,
! [SV451: $i,SV376: $i] :
( ( ( ! [SY1317: $i] :
~ ( in @ SY1317 @ ( set_intersection2 @ SV376 @ SV451 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV376 @ SV451 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2480]) ).
thf(2692,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK35_D @ SV272 @ SV172 )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1178: $i] :
( ~ ( in @ SY1178 @ ( sK43_SY691 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SY1178 ) @ SV272 ) )
| ~ ~ ( ( ( sK41_SY666 @ SV272 @ SV172 )
!= ( sK43_SY691 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) ) ) ) ) )
| ( ( sK35_D @ SV272 @ SV172 )
!= ( sK37_SY665 @ SV272 @ SV172 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
!= ( sK37_SY665 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1179: $i] :
( ~ ( in @ SY1179 @ ( sK40_SY685 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SY1179 ) @ SV272 ) )
| ~ ~ ( ( ( sK38_SY678 @ SV272 @ SV172 )
!= ( sK40_SY685 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) ) ) ) ) )
| ~ ( ( ( sK36_SY655 @ SV272 @ SV172 )
!= ( sK37_SY665 @ SV272 @ SV172 ) ) ) ) )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2482]) ).
thf(2693,plain,
! [SV379: $i] :
( ( ( SV379
= ( union @ SV379 ) )
= $false )
| ( ( being_limit_ordinal @ SV379 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2483]) ).
thf(2694,plain,
! [SV380: $i] :
( ( ( being_limit_ordinal @ SV380 )
= $false )
| ( ( SV380
= ( union @ SV380 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2484]) ).
thf(2695,plain,
! [SV381: $i] :
( ( ( v2_membered @ SV381 )
= $false )
| ( ( ! [SY1258: $i] : ( v1_membered @ ( set_intersection2 @ SY1258 @ SV381 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2485]) ).
thf(2696,plain,
! [SV382: $i] :
( ( ( v2_membered @ SV382 )
= $false )
| ( ( ! [SY1259: $i] : ( v2_membered @ ( set_intersection2 @ SY1259 @ SV382 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2486]) ).
thf(2697,plain,
! [SV273: $i,SV482: $i,SV173: $i] :
( ( ! [SY1358: $i] :
( ~ ( in @ SV173 @ SV482 )
| ~ ( in @ SV273 @ SY1358 )
| ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SV482 @ SY1358 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2487]) ).
thf(2698,plain,
! [SV273: $i,SV173: $i] :
( ( ~ ! [SY1190: $i] :
( ! [SY1191: $i] :
~ ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SY1190 @ SY1191 ) )
| ( in @ SV173 @ SY1190 ) )
| ~ ! [SY1192: $i,SY1193: $i] :
( ~ ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SY1192 @ SY1193 ) )
| ( in @ SV273 @ SY1193 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2488]) ).
thf(2699,plain,
! [SV174: $i,SV274: $i] :
( ( ~ ( relation @ ( sK56_C @ SV274 @ SV174 ) )
| ~ ( relation_of2 @ ( sK56_C @ SV274 @ SV174 ) @ SV174 @ SV274 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2489]) ).
thf(2700,plain,
! [SV383: $i] :
( ( ( empty @ SV383 )
= $false )
| ( ( empty @ ( relation_dom @ SV383 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2491]) ).
thf(2701,plain,
! [SV384: $i] :
( ( ( empty @ SV384 )
= $false )
| ( ( relation @ ( relation_dom @ SV384 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2492]) ).
thf(2702,plain,
! [SV385: $i] :
( ( ( v2_membered @ SV385 )
= $false )
| ( ( ! [SY1260: $i] : ( v1_membered @ ( set_difference @ SV385 @ SY1260 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2493]) ).
thf(2703,plain,
! [SV386: $i] :
( ( ( v2_membered @ SV386 )
= $false )
| ( ( ! [SY1261: $i] : ( v2_membered @ ( set_difference @ SV386 @ SY1261 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2494]) ).
thf(2704,plain,
( ( ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v1_membered @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2495]) ).
thf(2705,plain,
( ( ! [SX0: $i] :
( ~ ( v3_membered @ SX0 )
| ! [SX1: $i] : ( v2_membered @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2496]) ).
thf(2706,plain,
! [SV387: $i] :
( ( ( v3_membered @ SV387 )
= $false )
| ( ( ! [SY1262: $i] : ( v3_membered @ ( set_intersection2 @ SV387 @ SY1262 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2497]) ).
thf(2707,plain,
! [SV388: $i] :
( ( ( v2_membered @ SV388 )
= $false )
| ( ( ! [SY1263: $i] : ( v1_membered @ ( set_intersection2 @ SV388 @ SY1263 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2498]) ).
thf(2708,plain,
! [SV389: $i] :
( ( ( v2_membered @ SV389 )
= $false )
| ( ( ! [SY1264: $i] : ( v2_membered @ ( set_intersection2 @ SV389 @ SY1264 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2499]) ).
thf(2709,plain,
! [SV452: $i,SV390: $i] :
( ( ( ( ( set_difference @ SV390 @ SV452 )
!= empty_set ) )
= $true )
| ( ( subset @ SV390 @ SV452 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2500]) ).
thf(2710,plain,
! [SV453: $i,SV391: $i] :
( ( ( ~ ( subset @ SV391 @ SV453 ) )
= $true )
| ( ( ( set_difference @ SV391 @ SV453 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2501]) ).
thf(2711,plain,
! [SV275: $i,SV176: $i,SV483: $i] :
( ( ! [SY1359: $i,SY1360: $i] :
( ( ( ordered_pair @ SY1359 @ SY1360 )
!= SV483 )
| ~ ( in @ SY1359 @ SV176 )
| ( SY1360
!= ( singleton @ SY1359 ) ) )
| ~ ( in @ SV483 @ ( cartesian_product2 @ SV176 @ SV275 ) )
| ( in @ SV483 @ ( sK108_C @ SV275 @ SV176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2502]) ).
thf(2712,plain,
! [SV176: $i,SV275: $i] :
( ( ~ ! [SY1197: $i] :
( ~ ( in @ SY1197 @ ( sK108_C @ SV275 @ SV176 ) )
| ~ ( ~ ~ ( ( ( ordered_pair @ ( sK109_E @ SY1197 @ SV275 @ SV176 ) @ ( sK110_SY756 @ SY1197 @ SV275 @ SV176 ) )
!= SY1197 )
| ~ ( in @ ( sK109_E @ SY1197 @ SV275 @ SV176 ) @ SV176 ) )
| ( ( sK110_SY756 @ SY1197 @ SV275 @ SV176 )
!= ( singleton @ ( sK109_E @ SY1197 @ SV275 @ SV176 ) ) ) ) )
| ~ ! [SY1198: $i] :
( ~ ( in @ SY1198 @ ( sK108_C @ SV275 @ SV176 ) )
| ( in @ SY1198 @ ( cartesian_product2 @ SV176 @ SV275 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2503]) ).
thf(2713,plain,
! [SV177: $i,SV276: $i] :
( ( ( in @ ( sK125_C @ SV276 @ SV177 ) @ SV177 )
= $true )
| ( ( element @ SV177 @ ( powerset @ SV276 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2504]) ).
thf(2714,plain,
! [SV177: $i,SV276: $i] :
( ( ( ~ ( in @ ( sK125_C @ SV276 @ SV177 ) @ SV276 ) )
= $true )
| ( ( element @ SV177 @ ( powerset @ SV276 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2505]) ).
thf(2715,plain,
! [SV178: $i,SV277: $i] :
( ( ( ~ ( in @ ( sK6_C @ SV277 @ SV178 ) @ SV178 )
| ~ ( in @ ( sK6_C @ SV277 @ SV178 ) @ SV277 ) )
= $true )
| ( ( SV178 = SV277 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2506]) ).
thf(2716,plain,
! [SV178: $i,SV277: $i] :
( ( ( ( in @ ( sK6_C @ SV277 @ SV178 ) @ SV178 )
| ( in @ ( sK6_C @ SV277 @ SV178 ) @ SV277 ) )
= $true )
| ( ( SV178 = SV277 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2507]) ).
thf(2717,plain,
! [SV454: $i,SV179: $i] :
( ( ( ~ ( subset @ SV179 @ SV454 ) )
= $true )
| ( ( ! [SY1318: $i] : ( subset @ ( cartesian_product2 @ SV179 @ SY1318 ) @ ( cartesian_product2 @ SV454 @ SY1318 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2508]) ).
thf(2718,plain,
! [SV455: $i,SV179: $i] :
( ( ( ~ ( subset @ SV179 @ SV455 ) )
= $true )
| ( ( ! [SY1319: $i] : ( subset @ ( cartesian_product2 @ SY1319 @ SV179 ) @ ( cartesian_product2 @ SY1319 @ SV455 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2509]) ).
thf(2719,plain,
! [SV180: $i,SV456: $i,SV484: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV484 )
| ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV180 ) )
| ~ ( ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV484 )
| ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV456 ) ) )
| ~ ( ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV484 )
| ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV180 )
| ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV456 ) ) )
| ( SV484
= ( set_union2 @ SV180 @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2510]) ).
thf(2720,plain,
! [SV457: $i,SV180: $i,SV485: $i] :
( ( ( SV485
!= ( set_union2 @ SV180 @ SV457 ) )
| ~ ( ~ ! [SY1361: $i] :
( ~ ( in @ SY1361 @ SV485 )
| ( in @ SY1361 @ SV180 )
| ( in @ SY1361 @ SV457 ) )
| ~ ~ ( ~ ! [SY1362: $i] :
( ~ ( in @ SY1362 @ SV180 )
| ( in @ SY1362 @ SV485 ) )
| ~ ! [SY1363: $i] :
( ~ ( in @ SY1363 @ SV457 )
| ( in @ SY1363 @ SV485 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2511]) ).
thf(2721,plain,
! [SV181: $i] :
( ( ( empty @ ( sK120_B @ SV181 ) )
= $false )
| ( ( empty @ SV181 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2513]) ).
thf(2722,plain,
! [SV1: $i,SV182: $i,SV392: $i] :
( ( ( in @ SV392 @ SV182 )
= $false )
| ( ( in @ SV392 @ SV1 )
= $true )
| ( ( element @ SV182 @ ( powerset @ SV1 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2514]) ).
thf(2723,plain,
! [SV278: $i,SV5: $i,SV458: $i] :
( ( ( ~ ( element @ SV458 @ SV5 ) )
= $true )
| ( ( ( in @ SV458 @ SV278 )
| ( in @ SV458 @ ( subset_complement @ SV5 @ SV278 ) ) )
= $true )
| ( ( element @ SV278 @ ( powerset @ SV5 ) )
= $false )
| ( ( SV5 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2517]) ).
thf(2724,plain,
! [SV279: $i,SV6: $i,SV184: $i] :
( ( ( in @ SV184 @ ( subset_complement @ SV6 @ SV279 ) )
= $false )
| ( ( ~ ( in @ SV184 @ SV279 ) )
= $true )
| ( ( element @ SV279 @ ( powerset @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2518]) ).
thf(2725,plain,
! [SV186: $i,SV12: $i,SV281: $i] :
( ( ( element @ SV281 @ ( powerset @ SV12 ) )
= $false )
| ( ( element @ SV186 @ ( powerset @ SV12 ) )
= $false )
| ( ( ( subset_intersection2 @ SV12 @ SV186 @ SV281 )
= ( subset_intersection2 @ SV12 @ SV281 @ SV186 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2522]) ).
thf(2726,plain,
! [SV192: $i,SV21: $i,SV284: $i] :
( ( ( element @ SV284 @ ( powerset @ SV21 ) )
= $false )
| ( ( element @ SV192 @ ( powerset @ SV21 ) )
= $false )
| ( ( element @ ( subset_intersection2 @ SV21 @ SV192 @ SV284 ) @ ( powerset @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2523]) ).
thf(2727,plain,
! [SV194: $i,SV23: $i,SV285: $i] :
( ( ( element @ SV285 @ ( powerset @ SV23 ) )
= $false )
| ( ( element @ SV194 @ ( powerset @ SV23 ) )
= $false )
| ( ( element @ ( subset_difference @ SV23 @ SV194 @ SV285 ) @ ( powerset @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2524]) ).
thf(2728,plain,
! [SV197: $i,SV31: $i,SV459: $i] :
( ( ( element @ SV459 @ ( powerset @ SV31 ) )
= $false )
| ( ( element @ SV197 @ ( powerset @ SV31 ) )
= $false )
| ( ( ( subset_intersection2 @ SV31 @ SV197 @ SV197 )
= SV197 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2525]) ).
thf(2729,plain,
! [SV201: $i,SV35: $i,SV287: $i] :
( ( ( element @ SV287 @ ( powerset @ SV35 ) )
= $false )
| ( ( element @ SV201 @ ( powerset @ SV35 ) )
= $false )
| ( ( ( subset_intersection2 @ SV35 @ SV201 @ SV287 )
= ( set_intersection2 @ SV201 @ SV287 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2526]) ).
thf(2730,plain,
! [SV203: $i,SV37: $i,SV288: $i] :
( ( ( element @ SV288 @ ( powerset @ SV37 ) )
= $false )
| ( ( element @ SV203 @ ( powerset @ SV37 ) )
= $false )
| ( ( ( subset_difference @ SV37 @ SV203 @ SV288 )
= ( set_difference @ SV203 @ SV288 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2527]) ).
thf(2731,plain,
! [SV289: $i,SV206: $i,SV40: $i] :
( ( ( in @ SV40 @ SV206 )
= $false )
| ( ( element @ SV206 @ ( powerset @ SV289 ) )
= $false )
| ( ( element @ SV40 @ SV289 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2528]) ).
thf(2732,plain,
! [SV290: $i,SV207: $i,SV41: $i] :
( ( ( in @ SV41 @ SV207 )
= $false )
| ( ( element @ SV207 @ ( powerset @ SV290 ) )
= $false )
| ( ( ~ ( empty @ SV290 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2529]) ).
thf(2733,plain,
! [SV312: $i,SV291: $i,SV214: $i,SV50: $i] :
( ( ( subset @ SV50 @ SV214 )
= $false )
| ( ( ~ ( subset @ SV291 @ SV312 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV50 @ SV291 ) @ ( cartesian_product2 @ SV214 @ SV312 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2531]) ).
thf(2734,plain,
! [SV53: $i,SV293: $i,SV216: $i,SV313: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV313 ) @ SV216 ) )
= $true )
| ( ( relation_of2_as_subset @ SV313 @ SV293 @ SV216 )
= $true )
| ( ( relation_of2_as_subset @ SV313 @ SV293 @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2533]) ).
thf(2735,plain,
! [SV294: $i,SV315: $i,SV217: $i,SV55: $i] :
( ( ( ~ ( subset @ SV55 @ SV217 ) )
= $true )
| ( ( relation_of2_as_subset @ SV315 @ SV294 @ SV217 )
= $true )
| ( ( relation_of2_as_subset @ SV315 @ SV294 @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2534]) ).
thf(2736,plain,
! [SV295: $i,SV218: $i,SV56: $i] :
( ( ( subset @ SV56 @ SV218 )
= $false )
| ( ( subset @ ( relation_inverse_image @ SV295 @ SV56 ) @ ( relation_inverse_image @ SV295 @ SV218 ) )
= $true )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2535]) ).
thf(2737,plain,
! [SV220: $i,SV296: $i,SV58: $i] :
( ( ( subset @ SV58 @ SV296 )
= $false )
| ( ( subset @ SV58 @ SV220 )
= $false )
| ( ( subset @ SV58 @ ( set_intersection2 @ SV220 @ SV296 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2536]) ).
thf(2738,plain,
! [SV59: $i,SV297: $i,SV221: $i] :
( ( ( subset @ SV221 @ SV297 )
= $false )
| ( ( subset @ SV59 @ SV221 )
= $false )
| ( ( subset @ SV59 @ SV297 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2537]) ).
thf(2739,plain,
! [SV316: $i,SV61: $i] :
( ( ( ( in @ SV61 @ SV316 )
| ( SV61 = SV316 ) )
= $true )
| ( ( in @ SV316 @ SV61 )
= $true )
| ( ( ordinal @ SV316 )
= $false )
| ( ( ordinal @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2539]) ).
thf(2740,plain,
! [SV68: $i,SV298: $i,SV228: $i] :
( ( ( in @ SV228 @ SV298 )
= $false )
| ( ( in @ SV68 @ SV228 )
= $false )
| ( ( ~ ( in @ SV298 @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2540]) ).
thf(2741,plain,
! [SV299: $i,SV236: $i,SV78: $i] :
( ( ( subset @ SV78 @ SV236 )
= $false )
| ( ( disjoint @ SV236 @ SV299 )
= $false )
| ( ( disjoint @ SV78 @ SV299 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2541]) ).
thf(2742,plain,
! [SV83: $i,SV240: $i,SV300: $i] :
( ( ( subset @ SV300 @ SV240 )
= $false )
| ( ( subset @ SV83 @ SV240 )
= $false )
| ( ( subset @ ( set_union2 @ SV83 @ SV300 ) @ SV240 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2542]) ).
thf(2743,plain,
! [SV302: $i,SV246: $i,SV96: $i] :
( ( ( empty_carrier @ SV96 )
= $true )
| ( ( ~ ( join_semilatt_str @ SV96 ) )
= $true )
| ( ( ~ ( element @ SV246 @ ( the_carrier @ SV96 ) ) )
= $true )
| ( ( ~ ( element @ SV302 @ ( the_carrier @ SV96 ) ) )
= $true )
| ( ( element @ ( join @ SV96 @ SV246 @ SV302 ) @ ( the_carrier @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2543]) ).
thf(2744,plain,
! [SV303: $i,SV247: $i,SV98: $i] :
( ( ( empty_carrier @ SV98 )
= $true )
| ( ( ~ ( meet_semilatt_str @ SV98 ) )
= $true )
| ( ( ~ ( element @ SV247 @ ( the_carrier @ SV98 ) ) )
= $true )
| ( ( ~ ( element @ SV303 @ ( the_carrier @ SV98 ) ) )
= $true )
| ( ( element @ ( meet @ SV98 @ SV247 @ SV303 ) @ ( the_carrier @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2544]) ).
thf(2745,plain,
! [SV396: $i,SV326: $i] :
( ( ( SV326 = SV396 )
= $true )
| ( ( ~ ( subset @ SV326 @ SV396 ) )
= $true )
| ( ( proper_subset @ SV326 @ SV396 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2551]) ).
thf(2746,plain,
! [SV486: $i] :
( ( ! [SY1364: $i] :
( ~ ( proper_subset @ SV486 @ SY1364 )
| ( SV486 != SY1364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2552]) ).
thf(2747,plain,
! [SV487: $i] :
( ( ! [SY1365: $i] :
( ~ ( proper_subset @ SV487 @ SY1365 )
| ( subset @ SV487 @ SY1365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2553]) ).
thf(2748,plain,
! [SV397: $i,SV327: $i] :
( ( ( ( set_intersection2 @ SV327 @ SV397 )
= empty_set )
= $false )
| ( ( disjoint @ SV327 @ SV397 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2554]) ).
thf(2749,plain,
! [SV398: $i,SV328: $i] :
( ( ( disjoint @ SV328 @ SV398 )
= $false )
| ( ( ( set_intersection2 @ SV328 @ SV398 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2555]) ).
thf(2750,plain,
! [SV139: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( sK17_C @ SV139 )
!= ( sK18_SY613 @ SV139 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
!= ( sK18_SY613 @ SV139 ) )
| ~ ( in @ ( sK22_SY620 @ SV139 ) @ SV139 ) )
| ( ( sK23_SY629 @ SV139 )
!= ( singleton @ ( sK22_SY620 @ SV139 ) ) ) ) )
| ( ( sK17_C @ SV139 )
!= ( sK19_SY619 @ SV139 ) ) ) )
= $false )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2556]) ).
thf(2751,plain,
! [SV139: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
!= ( sK19_SY619 @ SV139 ) )
| ~ ( in @ ( sK20_SY626 @ SV139 ) @ SV139 ) )
| ( ( sK21_SY628 @ SV139 )
!= ( singleton @ ( sK20_SY626 @ SV139 ) ) ) ) )
= $false )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2556]) ).
thf(2752,plain,
! [SV488: $i,SV139: $i] :
( ( ( ~ ( ~ ! [SY1366: $i] :
( ! [SY1367: $i] :
( ( SY1367 != SY1366 )
| ~ ( in @ SY1367 @ ( cartesian_product2 @ SV139 @ SV488 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1366 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1366 @ ( sK13_C @ SV488 @ SV139 ) ) )
| ~ ! [SY1370: $i] :
( ~ ( in @ SY1370 @ ( sK13_C @ SV488 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1370 @ SV488 @ SV139 )
!= SY1370 )
| ~ ( in @ ( sK16_E @ SY1370 @ SV488 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV488 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1370 @ SV488 @ SV139 ) @ ( sK15_SY612 @ SY1370 @ SV488 @ SV139 ) )
!= SY1370 )
| ~ ( in @ ( sK14_J @ SY1370 @ SV488 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1370 @ SV488 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1370 @ SV488 @ SV139 ) ) ) ) ) ) ) )
= $true )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2557]) ).
thf(2753,plain,
! [SV140: $i] :
( ( ( element @ ( sK116_B @ SV140 ) @ ( powerset @ ( the_carrier @ SV140 ) ) )
= $true )
| ( ( empty_carrier @ SV140 )
= $true )
| ( ( one_sorted_str @ SV140 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2558]) ).
thf(2754,plain,
! [SV140: $i] :
( ( ( ~ ( empty @ ( sK116_B @ SV140 ) ) )
= $true )
| ( ( empty_carrier @ SV140 )
= $true )
| ( ( one_sorted_str @ SV140 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2559]) ).
thf(2755,plain,
! [SV489: $i] :
( ( ~ ( v3_membered @ SV489 )
| ! [SY1371: $i] : ( v1_membered @ ( set_intersection2 @ SY1371 @ SV489 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2560]) ).
thf(2756,plain,
! [SV490: $i] :
( ( ~ ( v3_membered @ SV490 )
| ! [SY1372: $i] : ( v2_membered @ ( set_intersection2 @ SY1372 @ SV490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2561]) ).
thf(2757,plain,
! [SV329: $i,SV491: $i] :
( ( ( v3_membered @ ( set_intersection2 @ SV491 @ SV329 ) )
= $true )
| ( ( v3_membered @ SV329 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2562]) ).
thf(2758,plain,
! [SV141: $i] :
( ( ( ordinal @ ( sK99_B @ SV141 ) )
= $false )
| ( ( ~ ( subset @ ( sK99_B @ SV141 ) @ SV141 ) )
= $true )
| ( ( ordinal @ SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2563]) ).
thf(2759,plain,
! [SV399: $i,SV460: $i,SV142: $i] :
( ( ( ~ ( in @ SV142 @ SV460 )
| ~ ( in @ SV399 @ SV460 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV142 @ SV399 ) @ SV460 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2564]) ).
thf(2760,plain,
! [SV142: $i] :
( ( ! [SY919: $i,SY920: $i] :
( ~ ( subset @ ( unordered_pair @ SV142 @ SY919 ) @ SY920 )
| ( in @ SV142 @ SY920 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2565]) ).
thf(2761,plain,
! [SV142: $i] :
( ( ! [SY921: $i,SY922: $i] :
( ~ ( subset @ ( unordered_pair @ SV142 @ SY921 ) @ SY922 )
| ( in @ SY921 @ SY922 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2566]) ).
thf(2762,plain,
! [SV143: $i,SV400: $i,SV461: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV143 )
| ~ ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV400 )
| ~ ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV461 ) )
| ~ ~ ( ~ ( ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV143 )
| ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV461 ) )
| ~ ( ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV400 )
| ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV461 ) ) ) ) )
= $true )
| ( ( SV461
= ( set_intersection2 @ SV143 @ SV400 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2567]) ).
thf(2763,plain,
! [SV401: $i,SV143: $i,SV462: $i] :
( ( ( ( SV462
!= ( set_intersection2 @ SV143 @ SV401 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1325: $i] :
( ~ ( in @ SY1325 @ SV143 )
| ~ ( in @ SY1325 @ SV401 )
| ( in @ SY1325 @ SV462 ) )
| ~ ~ ( ~ ! [SY1326: $i] :
( ~ ( in @ SY1326 @ SV462 )
| ( in @ SY1326 @ SV143 ) )
| ~ ! [SY1327: $i] :
( ~ ( in @ SY1327 @ SV462 )
| ( in @ SY1327 @ SV401 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2568]) ).
thf(2764,plain,
! [SV144: $i] :
( ( ( ~ ! [SY930: $i] :
( ~ ( element @ SY930 @ ( powerset @ SV144 ) )
| ( v1_membered @ SY930 ) )
| ~ ! [SY931: $i] :
( ~ ( element @ SY931 @ ( powerset @ SV144 ) )
| ( v2_membered @ SY931 ) ) )
= $false )
| ( ( v3_membered @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2569]) ).
thf(2765,plain,
! [SV144: $i,SV492: $i] :
( ( ( ~ ( element @ SV492 @ ( powerset @ SV144 ) )
| ( v3_membered @ SV492 ) )
= $true )
| ( ( v3_membered @ SV144 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2570]) ).
thf(2766,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1142: $i] :
( ~ ( in @ SY1142 @ ( sK52_SY712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SY1142 ) @ SV265 ) )
| ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK52_SY712 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) ) ) )
| ~ ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 ) )
| ~ ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 ) )
| ~ ~ ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ ( sK51_SY718 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SY1143 ) @ SV265 ) )
| ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK51_SY718 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) ) ) ) )
| ~ ( ( ( sK49_SY705 @ SV265 @ SV145 )
!= ( sK50_SY711 @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2571]) ).
thf(2767,plain,
! [SV402: $i,SV330: $i] :
( ( ( ~ ( subset @ SV330 @ SV402 ) )
= $true )
| ( ( ~ ( subset @ SV402 @ SV330 ) )
= $true )
| ( ( SV330 = SV402 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2572]) ).
thf(2768,plain,
! [SV493: $i] :
( ( ! [SY1373: $i] :
( ( SV493 != SY1373 )
| ( subset @ SV493 @ SY1373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2573]) ).
thf(2769,plain,
! [SV494: $i] :
( ( ! [SY1374: $i] :
( ( SV494 != SY1374 )
| ( subset @ SY1374 @ SV494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2574]) ).
thf(2770,plain,
! [SV146: $i,SV266: $i,SV495: $i] :
( ( ( ~ ( in @ SV495 @ SV266 )
| ~ ( in @ SV495 @ ( sK5_C @ SV266 @ SV146 ) ) )
= $true )
| ( ( ~ ( in @ SV146 @ SV266 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2575]) ).
thf(2771,plain,
! [SV266: $i,SV146: $i] :
( ( ( in @ SV146 @ SV266 )
= $false )
| ( ( in @ ( sK5_C @ SV266 @ SV146 ) @ SV266 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2576]) ).
thf(2772,plain,
! [SV331: $i] :
( ( ( ~ ( in @ ( sK85_B @ SV331 ) @ SV331 ) )
= $false )
| ( ( epsilon_transitive @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2577]) ).
thf(2773,plain,
! [SV331: $i] :
( ( ( ~ ~ ( subset @ ( sK85_B @ SV331 ) @ SV331 ) )
= $false )
| ( ( epsilon_transitive @ SV331 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2577]) ).
thf(2774,plain,
! [SV332: $i,SV496: $i] :
( ( ( ~ ( in @ SV496 @ SV332 )
| ( subset @ SV496 @ SV332 ) )
= $true )
| ( ( epsilon_transitive @ SV332 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2578]) ).
thf(2775,plain,
! [SV147: $i,SV403: $i,SV463: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV147 )
| ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV403 )
| ~ ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV463 ) )
| ~ ~ ( ~ ( ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV147 )
| ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV463 ) )
| ~ ( ~ ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV403 )
| ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV463 ) ) ) ) )
= $true )
| ( ( SV463
= ( set_difference @ SV147 @ SV403 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2579]) ).
thf(2776,plain,
! [SV404: $i,SV147: $i,SV464: $i] :
( ( ( ( SV464
!= ( set_difference @ SV147 @ SV404 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1328: $i] :
( ~ ( in @ SY1328 @ SV147 )
| ( in @ SY1328 @ SV404 )
| ( in @ SY1328 @ SV464 ) )
| ~ ~ ( ~ ! [SY1329: $i] :
( ~ ( in @ SY1329 @ SV464 )
| ( in @ SY1329 @ SV147 ) )
| ~ ! [SY1330: $i] :
( ~ ( in @ SY1330 @ SV464 )
| ~ ( in @ SY1330 @ SV404 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2580]) ).
thf(2777,plain,
! [SV334: $i,SV497: $i] :
( ( ( ~ ( in @ SV497 @ SV334 ) )
= $true )
| ( ( SV334 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2581]) ).
thf(2778,plain,
! [SV148: $i,SV335: $i] :
( ( ( ~ ( ~ ! [SY1210: $i] :
( ~ ( in @ SY1210 @ SV335 )
| ~ ( subset @ ( sK105_C @ SV335 @ SV148 ) @ SY1210 )
| ( SY1210
= ( sK105_C @ SV335 @ SV148 ) ) )
| ~ ( in @ ( sK105_C @ SV335 @ SV148 ) @ SV335 ) ) )
= $true )
| ( ( SV335 = empty_set )
= $true )
| ( ( element @ SV335 @ ( powerset @ ( powerset @ SV148 ) ) )
= $false )
| ( ( finite @ SV148 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2582]) ).
thf(2779,plain,
! [SV405: $i,SV336: $i] :
( ( ( ( set_difference @ SV336 @ SV405 )
= SV336 )
= $false )
| ( ( disjoint @ SV336 @ SV405 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2583]) ).
thf(2780,plain,
! [SV406: $i,SV337: $i] :
( ( ( disjoint @ SV337 @ SV406 )
= $false )
| ( ( ( set_difference @ SV337 @ SV406 )
= SV337 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2584]) ).
thf(2781,plain,
! [SV407: $i,SV338: $i] :
( ( ( ( set_difference @ SV338 @ ( singleton @ SV407 ) )
= SV338 )
= $false )
| ( ( ~ ( in @ SV407 @ SV338 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2585]) ).
thf(2782,plain,
! [SV340: $i,SV409: $i] :
( ( ( ~ ( ! [SY1278: $i] :
( ~ ( in @ ( sK68_C @ SV409 @ SV340 ) @ SY1278 )
| ~ ( in @ SY1278 @ SV340 ) )
| ~ ( in @ ( sK68_C @ SV409 @ SV340 ) @ SV409 ) )
| ~ ( ~ ( ~ ( in @ ( sK68_C @ SV409 @ SV340 ) @ ( sK69_SY723 @ SV409 @ SV340 ) )
| ~ ( in @ ( sK69_SY723 @ SV409 @ SV340 ) @ SV340 ) )
| ( in @ ( sK68_C @ SV409 @ SV340 ) @ SV409 ) ) )
= $false )
| ( ( SV409
= ( union @ SV340 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2587]) ).
thf(2783,plain,
! [SV341: $i,SV410: $i] :
( ( ( SV410
= ( union @ SV341 ) )
= $false )
| ( ( ~ ( ~ ! [SY1279: $i] :
( ! [SY1219: $i] :
( ~ ( in @ SY1279 @ SY1219 )
| ~ ( in @ SY1219 @ SV341 ) )
| ( in @ SY1279 @ SV410 ) )
| ~ ! [SY1281: $i] :
( ~ ( in @ SY1281 @ SV410 )
| ~ ( ~ ( in @ SY1281 @ ( sK67_D @ SY1281 @ SV410 @ SV341 ) )
| ~ ( in @ ( sK67_D @ SY1281 @ SV410 @ SV341 ) @ SV341 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2588]) ).
thf(2784,plain,
! [SV411: $i,SV342: $i] :
( ( ( element @ SV342 @ ( powerset @ SV411 ) )
= $false )
| ( ( subset @ SV342 @ SV411 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2589]) ).
thf(2785,plain,
! [SV412: $i,SV343: $i] :
( ( ( subset @ SV343 @ SV412 )
= $false )
| ( ( element @ SV343 @ ( powerset @ SV412 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2590]) ).
thf(2786,plain,
! [SV498: $i] :
( ( ( empty @ SV498 )
| ! [SY1375: $i] :
( ~ ( element @ SY1375 @ SV498 )
| ( in @ SY1375 @ SV498 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2593]) ).
thf(2787,plain,
! [SV499: $i] :
( ( ( empty @ SV499 )
| ! [SY1376: $i] :
( ~ ( in @ SY1376 @ SV499 )
| ( element @ SY1376 @ SV499 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2594]) ).
thf(2788,plain,
! [SV500: $i] :
( ( ~ ( empty @ SV500 )
| ! [SY1377: $i] :
( ~ ( element @ SY1377 @ SV500 )
| ( empty @ SY1377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2595]) ).
thf(2789,plain,
! [SV501: $i] :
( ( ~ ( empty @ SV501 )
| ! [SY1378: $i] :
( ~ ( empty @ SY1378 )
| ( element @ SY1378 @ SV501 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2596]) ).
thf(2790,plain,
! [SV346: $i,SV413: $i] :
( ( ( ~ ( ~ ( in @ ( sK124_C @ SV413 @ SV346 ) @ SV413 )
| ~ ( subset @ ( sK124_C @ SV413 @ SV346 ) @ SV346 ) )
| ~ ( ( in @ ( sK124_C @ SV413 @ SV346 ) @ SV413 )
| ( subset @ ( sK124_C @ SV413 @ SV346 ) @ SV346 ) ) )
= $false )
| ( ( SV413
= ( powerset @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2597]) ).
thf(2791,plain,
! [SV347: $i,SV414: $i] :
( ( ( SV414
= ( powerset @ SV347 ) )
= $false )
| ( ( ~ ( ~ ! [SY1282: $i] :
( ~ ( in @ SY1282 @ SV414 )
| ( subset @ SY1282 @ SV347 ) )
| ~ ! [SY1283: $i] :
( ~ ( subset @ SY1283 @ SV347 )
| ( in @ SY1283 @ SV414 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2598]) ).
thf(2792,plain,
! [SV149: $i] :
( ( ( ~ ( element @ ( sK118_B @ SV149 ) @ ( powerset @ SV149 ) ) )
= $false )
| ( ( empty @ SV149 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2599]) ).
thf(2793,plain,
! [SV149: $i] :
( ( ( ~ ~ ( empty @ ( sK118_B @ SV149 ) ) )
= $false )
| ( ( empty @ SV149 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2599]) ).
thf(2794,plain,
! [SV415: $i,SV150: $i,SV465: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV465 @ SV150 @ SV415 ) )
= $true )
| ( ( ~ ( ~ ! [SY1331: $i] :
~ ( in @ ( ordered_pair @ SY1331 @ ( sK102_D @ SV465 @ SV415 @ SV150 ) ) @ SV465 )
| ~ ( in @ ( sK102_D @ SV465 @ SV415 @ SV150 ) @ SV415 ) )
| ( ( relation_rng_as_subset @ SV150 @ SV415 @ SV465 )
= SV415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2600]) ).
thf(2795,plain,
! [SV416: $i,SV150: $i,SV466: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV466 @ SV150 @ SV416 ) )
= $true )
| ( ( ( ( relation_rng_as_subset @ SV150 @ SV416 @ SV466 )
!= SV416 )
| ! [SY1332: $i] :
( ( in @ ( ordered_pair @ ( sK101_E @ SY1332 @ SV466 @ SV416 @ SV150 ) @ SY1332 ) @ SV466 )
| ~ ( in @ SY1332 @ SV416 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2601]) ).
thf(2796,plain,
! [SV151: $i,SV267: $i,SV467: $i,SV502: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV467 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV151 ) )
| ~ ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV267 ) ) ) )
| ~ ( ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
= SV467 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
= SV151 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
= SV267 ) ) )
| ( SV502
= ( unordered_triple @ SV151 @ SV267 @ SV467 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2602]) ).
thf(2797,plain,
! [SV468: $i,SV267: $i,SV151: $i,SV503: $i] :
( ( ( SV503
!= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
| ~ ( ~ ! [SY1379: $i] :
( ~ ( in @ SY1379 @ SV503 )
| ( SY1379 = SV468 )
| ( SY1379 = SV151 )
| ( SY1379 = SV267 ) )
| ~ ~ ( ~ ! [SY1380: $i] :
( ( SY1380 != SV468 )
| ( in @ SY1380 @ SV503 ) )
| ~ ~ ( ~ ! [SY1381: $i] :
( ( SY1381 != SV151 )
| ( in @ SY1381 @ SV503 ) )
| ~ ! [SY1382: $i] :
( ( SY1382 != SV267 )
| ( in @ SY1382 @ SV503 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2603]) ).
thf(2798,plain,
! [SV152: $i,SV417: $i] :
( ( ( ~ ( subset @ SV417 @ ( sK106_B @ SV152 ) ) )
= $true )
| ( ( are_equipotent @ SV417 @ ( sK106_B @ SV152 ) )
= $true )
| ( ( in @ SV417 @ ( sK106_B @ SV152 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2604]) ).
thf(2799,plain,
! [SV152: $i] :
( ( ! [SY968: $i] :
( ~ ( in @ SY968 @ ( sK106_B @ SV152 ) )
| ( in @ ( powerset @ SY968 ) @ ( sK106_B @ SV152 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2605]) ).
thf(2800,plain,
! [SV152: $i] :
( ( ~ ( ~ ! [SY969: $i,SY970: $i] :
( ~ ( in @ SY969 @ ( sK106_B @ SV152 ) )
| ~ ( subset @ SY970 @ SY969 )
| ( in @ SY970 @ ( sK106_B @ SV152 ) ) )
| ~ ( in @ SV152 @ ( sK106_B @ SV152 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2606]) ).
thf(2801,plain,
! [SV153: $i,SV418: $i] :
( ( ( ~ ( in @ SV418 @ SV153 ) )
= $true )
| ( ( ~ ( ordinal @ SV418 ) )
= $true )
| ( ( in @ SV418 @ ( sK107_B @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2607]) ).
thf(2802,plain,
! [SV153: $i] :
( ( ! [SY972: $i] :
( ~ ( in @ SY972 @ ( sK107_B @ SV153 ) )
| ( in @ SY972 @ SV153 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2608]) ).
thf(2803,plain,
! [SV153: $i] :
( ( ! [SY973: $i] :
( ~ ( in @ SY973 @ ( sK107_B @ SV153 ) )
| ( ordinal @ SY973 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2609]) ).
thf(2804,plain,
! [SV154: $i,SV504: $i] :
( ( ( ~ ( relation @ SV504 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK72_C @ SV504 @ SV154 ) @ ( sK73_SY724 @ SV504 @ SV154 ) ) @ SV154 )
| ~ ~ ( in @ ( ordered_pair @ ( sK72_C @ SV504 @ SV154 ) @ ( sK73_SY724 @ SV504 @ SV154 ) ) @ SV504 ) )
| ( subset @ SV154 @ SV504 ) )
= $true )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2610]) ).
thf(2805,plain,
! [SV154: $i,SV505: $i] :
( ( ( ~ ( relation @ SV505 )
| ~ ( subset @ SV154 @ SV505 )
| ! [SY1383: $i,SY1384: $i] :
( ~ ( in @ ( ordered_pair @ SY1383 @ SY1384 ) @ SV154 )
| ( in @ ( ordered_pair @ SY1383 @ SY1384 ) @ SV505 ) ) )
= $true )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2611]) ).
thf(2806,plain,
! [SV268: $i,SV155: $i] :
( ( ( ! [SY1158: $i] :
( ~ ( element @ SY1158 @ ( powerset @ ( powerset @ SV155 ) ) )
| ~ ( ~ ( element @ ( sK123_D @ SY1158 @ SV268 @ SV155 ) @ ( powerset @ SV155 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK123_D @ SY1158 @ SV268 @ SV155 ) @ SY1158 )
| ~ ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SY1158 @ SV268 @ SV155 ) ) @ SV268 ) )
| ~ ( ( in @ ( sK123_D @ SY1158 @ SV268 @ SV155 ) @ SY1158 )
| ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SY1158 @ SV268 @ SV155 ) ) @ SV268 ) ) ) )
| ( SY1158
= ( complements_of_subsets @ SV155 @ SV268 ) ) ) )
= $true )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2612]) ).
thf(2807,plain,
! [SV268: $i,SV155: $i] :
( ( ( ! [SY1159: $i] :
( ~ ( element @ SY1159 @ ( powerset @ ( powerset @ SV155 ) ) )
| ( SY1159
!= ( complements_of_subsets @ SV155 @ SV268 ) )
| ~ ( ~ ! [SY1160: $i] :
( ~ ( element @ SY1160 @ ( powerset @ SV155 ) )
| ~ ( in @ SY1160 @ SY1159 )
| ( in @ ( subset_complement @ SV155 @ SY1160 ) @ SV268 ) )
| ~ ! [SY1161: $i] :
( ~ ( element @ SY1161 @ ( powerset @ SV155 ) )
| ~ ( in @ ( subset_complement @ SV155 @ SY1161 ) @ SV268 )
| ( in @ SY1161 @ SY1159 ) ) ) ) )
= $true )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2613]) ).
thf(2808,plain,
! [SV419: $i,SV348: $i] :
( ( ( subset @ SV348 @ ( singleton @ SV419 ) )
= $false )
| ( ( ( SV348 = empty_set )
| ( SV348
= ( singleton @ SV419 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2614]) ).
thf(2809,plain,
! [SV506: $i] :
( ( ( SV506 != empty_set )
| ! [SY1385: $i] : ( subset @ SV506 @ ( singleton @ SY1385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2615]) ).
thf(2810,plain,
! [SV507: $i] :
( ( ! [SY1386: $i] :
( ( SV507
!= ( singleton @ SY1386 ) )
| ( subset @ SV507 @ ( singleton @ SY1386 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2616]) ).
thf(2811,plain,
! [SV420: $i,SV349: $i] :
( ( ( subset @ SV349 @ ( singleton @ SV420 ) )
= $false )
| ( ( ( SV349 = empty_set )
| ( SV349
= ( singleton @ SV420 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2617]) ).
thf(2812,plain,
! [SV508: $i] :
( ( ( SV508 != empty_set )
| ! [SY1387: $i] : ( subset @ SV508 @ ( singleton @ SY1387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2618]) ).
thf(2813,plain,
! [SV509: $i] :
( ( ! [SY1388: $i] :
( ( SV509
!= ( singleton @ SY1388 ) )
| ( subset @ SV509 @ ( singleton @ SY1388 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2619]) ).
thf(2814,plain,
! [SV421: $i,SV350: $i] :
( ( ( ( set_difference @ SV350 @ SV421 )
= empty_set )
= $false )
| ( ( subset @ SV350 @ SV421 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2620]) ).
thf(2815,plain,
! [SV422: $i,SV351: $i] :
( ( ( subset @ SV351 @ SV422 )
= $false )
| ( ( ( set_difference @ SV351 @ SV422 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2621]) ).
thf(2816,plain,
! [SV156: $i,SV510: $i] :
( ( ( ~ ( element @ SV510 @ ( powerset @ SV156 ) )
| ( v1_membered @ SV510 ) )
= $true )
| ( ( v2_membered @ SV156 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2622]) ).
thf(2817,plain,
! [SV156: $i,SV511: $i] :
( ( ( ~ ( element @ SV511 @ ( powerset @ SV156 ) )
| ( v2_membered @ SV511 ) )
= $true )
| ( ( v2_membered @ SV156 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2623]) ).
thf(2818,plain,
! [SV423: $i,SV352: $i] :
( ( ( ~ ( empty @ SV352 ) )
= $true )
| ( ( ~ ( relation @ SV423 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV352 @ SV423 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2624]) ).
thf(2819,plain,
! [SV424: $i,SV353: $i] :
( ( ( ~ ( empty @ SV353 ) )
= $true )
| ( ( ~ ( relation @ SV424 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV353 @ SV424 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2625]) ).
thf(2820,plain,
! [SV425: $i] :
( ( ( ~ ! [SY1288: $i] :
( ! [SY1289: $i] :
( ( SY1289 != SY1288 )
| ~ ( in @ SY1289 @ SV425 ) )
| ~ ( ordinal @ SY1288 )
| ( in @ SY1288 @ ( sK7_B @ SV425 ) ) ) )
= $false )
| ( sK12_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[2626]) ).
thf(2821,plain,
! [SV425: $i] :
( ( ( ~ ! [SY1290: $i] :
( ~ ( in @ SY1290 @ ( sK7_B @ SV425 ) )
| ~ ( ~ ~ ( ( ( sK8_D @ SY1290 @ SV425 )
!= SY1290 )
| ~ ( in @ ( sK8_D @ SY1290 @ SV425 ) @ SV425 ) )
| ~ ( ordinal @ SY1290 ) ) ) )
= $false )
| ( sK12_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[2626]) ).
thf(2822,plain,
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK9_B != sK10_SY601 )
| ~ ( ordinal @ sK10_SY601 ) )
| ( sK9_B != sK11_SY603 ) )
| ~ ( ordinal @ sK11_SY603 ) ) )
= $false )
| ( sK12_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2627]) ).
thf(2823,plain,
( ( ( ~ ( ( sK10_SY601 != sK11_SY603 ) ) )
= $false )
| ( sK12_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[2627]) ).
thf(2824,plain,
! [SV426: $i,SV157: $i,SV469: $i] :
( ( ( ~ ( relation @ SV469 ) )
= $true )
| ( ( ~ ( in @ SV157 @ SV469 )
| ~ ( in @ SV157 @ ( cartesian_product2 @ SV426 @ SV426 ) )
| ( in @ SV157 @ ( relation_restriction @ SV469 @ SV426 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2628]) ).
thf(2825,plain,
! [SV157: $i] :
( ( ! [SY987: $i,SY988: $i] :
( ~ ( relation @ SY988 )
| ~ ( in @ SV157 @ ( relation_restriction @ SY988 @ SY987 ) )
| ( in @ SV157 @ SY988 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2629]) ).
thf(2826,plain,
! [SV157: $i] :
( ( ! [SY989: $i,SY990: $i] :
( ~ ( relation @ SY990 )
| ~ ( in @ SV157 @ ( relation_restriction @ SY990 @ SY989 ) )
| ( in @ SV157 @ ( cartesian_product2 @ SY989 @ SY989 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2630]) ).
thf(2827,plain,
! [SV158: $i] :
( ( ~ ( ~ ! [SY991: $i,SY992: $i] :
( ~ ( relation_of2_as_subset @ SY992 @ SV158 @ SY991 )
| ( SY991 = empty_set )
| ( SV158
!= ( relation_dom_as_subset @ SV158 @ SY991 @ SY992 ) )
| ( quasi_total @ SY992 @ SV158 @ SY991 ) )
| ~ ! [SY993: $i,SY994: $i] :
( ~ ( relation_of2_as_subset @ SY994 @ SV158 @ SY993 )
| ( SY993 = empty_set )
| ~ ( quasi_total @ SY994 @ SV158 @ SY993 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SY993 @ SY994 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2633]) ).
thf(2828,plain,
! [SV158: $i] :
( ( ~ ( ~ ! [SY995: $i,SY996: $i] :
( ~ ( relation_of2_as_subset @ SY996 @ SV158 @ SY995 )
| ( SV158 != empty_set )
| ( SV158
!= ( relation_dom_as_subset @ SV158 @ SY995 @ SY996 ) )
| ( quasi_total @ SY996 @ SV158 @ SY995 ) )
| ~ ! [SY997: $i,SY998: $i] :
( ~ ( relation_of2_as_subset @ SY998 @ SV158 @ SY997 )
| ( SV158 != empty_set )
| ~ ( quasi_total @ SY998 @ SV158 @ SY997 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SY997 @ SY998 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2634]) ).
thf(2829,plain,
! [SV158: $i] :
( ( ! [SY999: $i,SY1000: $i] :
( ~ ( relation_of2_as_subset @ SY1000 @ SV158 @ SY999 )
| ( SY999 != empty_set )
| ( SY1000 != empty_set )
| ( quasi_total @ SY1000 @ SV158 @ SY999 )
| ( SV158 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2635]) ).
thf(2830,plain,
! [SV158: $i] :
( ( ! [SY1001: $i,SY1002: $i] :
( ~ ( relation_of2_as_subset @ SY1002 @ SV158 @ SY1001 )
| ( SY1001 != empty_set )
| ~ ( quasi_total @ SY1002 @ SV158 @ SY1001 )
| ( SY1002 = empty_set )
| ( SV158 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2636]) ).
thf(2831,plain,
! [SV512: $i] :
( ( ( SV512 = empty_set )
| ! [SY1389: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK90_SY733 @ SY1389 @ SV512 ) @ SV512 )
| ~ ~ ( in @ ( sK89_C @ SY1389 @ SV512 ) @ ( sK90_SY733 @ SY1389 @ SV512 ) ) )
| ~ ( in @ ( sK89_C @ SY1389 @ SV512 ) @ SY1389 ) )
| ~ ( ! [SY1390: $i] :
( ~ ( in @ SY1390 @ SV512 )
| ( in @ ( sK89_C @ SY1389 @ SV512 ) @ SY1390 ) )
| ( in @ ( sK89_C @ SY1389 @ SV512 ) @ SY1389 ) ) )
| ( SY1389
= ( set_meet @ SV512 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2637]) ).
thf(2832,plain,
! [SV513: $i] :
( ( ( SV513 = empty_set )
| ! [SY1391: $i] :
( ( SY1391
!= ( set_meet @ SV513 ) )
| ~ ( ~ ! [SY1392: $i] :
( ~ ( ~ ( in @ ( sK88_D @ SY1392 @ SY1391 @ SV513 ) @ SV513 )
| ~ ~ ( in @ SY1392 @ ( sK88_D @ SY1392 @ SY1391 @ SV513 ) ) )
| ( in @ SY1392 @ SY1391 ) )
| ~ ! [SY1393: $i] :
( ~ ( in @ SY1393 @ SY1391 )
| ! [SY1394: $i] :
( ~ ( in @ SY1394 @ SV513 )
| ( in @ SY1393 @ SY1394 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2638]) ).
thf(2833,plain,
! [SV514: $i] :
( ( ( SV514 != empty_set )
| ! [SY1395: $i] :
( ( SY1395
!= ( set_meet @ SV514 ) )
| ( SY1395 = empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2639]) ).
thf(2834,plain,
! [SV515: $i] :
( ( ( SV515 != empty_set )
| ! [SY1396: $i] :
( ( SY1396 != empty_set )
| ( SY1396
= ( set_meet @ SV515 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2640]) ).
thf(2835,plain,
! [SV159: $i,SV427: $i,SV470: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK82_D @ SV470 @ SV427 @ SV159 ) @ SV470 )
| ( ( sK82_D @ SV470 @ SV427 @ SV159 )
!= SV159 ) )
| ~ ( ~ ( in @ ( sK82_D @ SV470 @ SV427 @ SV159 ) @ SV470 )
| ( ( sK82_D @ SV470 @ SV427 @ SV159 )
!= SV427 ) ) )
| ~ ( ( in @ ( sK82_D @ SV470 @ SV427 @ SV159 ) @ SV470 )
| ( ( sK82_D @ SV470 @ SV427 @ SV159 )
= SV159 )
| ( ( sK82_D @ SV470 @ SV427 @ SV159 )
= SV427 ) ) ) )
= $true )
| ( ( SV470
= ( unordered_pair @ SV159 @ SV427 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2641]) ).
thf(2836,plain,
! [SV428: $i,SV159: $i,SV471: $i] :
( ( ( ( SV471
!= ( unordered_pair @ SV159 @ SV428 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1339: $i] :
( ~ ( in @ SY1339 @ SV471 )
| ( SY1339 = SV159 )
| ( SY1339 = SV428 ) )
| ~ ~ ( ~ ! [SY1340: $i] :
( ( SY1340 != SV159 )
| ( in @ SY1340 @ SV471 ) )
| ~ ! [SY1341: $i] :
( ( SY1341 != SV428 )
| ( in @ SY1341 @ SV471 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2642]) ).
thf(2837,plain,
! [SV429: $i,SV354: $i] :
( ( ( ~ ( empty @ SV354 ) )
= $true )
| ( ( ~ ( relation @ SV429 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV429 @ SV354 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2643]) ).
thf(2838,plain,
! [SV430: $i,SV355: $i] :
( ( ( ~ ( empty @ SV355 ) )
= $true )
| ( ( ~ ( relation @ SV430 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV430 @ SV355 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2644]) ).
thf(2839,plain,
! [SV160: $i,SV516: $i] :
( ( ( ~ ( element @ SV516 @ SV160 )
| ( v1_xcmplx_0 @ SV516 ) )
= $true )
| ( ( v2_membered @ SV160 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2645]) ).
thf(2840,plain,
! [SV160: $i,SV517: $i] :
( ( ( ~ ( element @ SV517 @ SV160 )
| ( v1_xreal_0 @ SV517 ) )
= $true )
| ( ( v2_membered @ SV160 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2646]) ).
thf(2841,plain,
! [SV358: $i] :
( ( ( ~ ! [SY1235: $i,SY1236: $i] :
( ( sK93_B @ SV358 )
!= ( ordered_pair @ SY1235 @ SY1236 ) ) )
= $false )
| ( ( relation @ SV358 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2649]) ).
thf(2842,plain,
! [SV358: $i] :
( ( ( ~ ( in @ ( sK93_B @ SV358 ) @ SV358 ) )
= $false )
| ( ( relation @ SV358 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2649]) ).
thf(2843,plain,
! [SV359: $i,SV518: $i] :
( ( ( ( SV518
= ( ordered_pair @ ( sK91_C @ SV518 @ SV359 ) @ ( sK92_SY735 @ SV518 @ SV359 ) ) )
| ~ ( in @ SV518 @ SV359 ) )
= $true )
| ( ( relation @ SV359 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2650]) ).
thf(2844,plain,
! [SV269: $i,SV162: $i] :
( ( ( ! [SY1162: $i] :
( ~ ( element @ SY1162 @ ( powerset @ SV162 ) )
| ~ ( disjoint @ SV269 @ SY1162 )
| ( subset @ SV269 @ ( subset_complement @ SV162 @ SY1162 ) ) ) )
= $true )
| ( ( element @ SV269 @ ( powerset @ SV162 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2653]) ).
thf(2845,plain,
! [SV269: $i,SV162: $i] :
( ( ( ! [SY1163: $i] :
( ~ ( element @ SY1163 @ ( powerset @ SV162 ) )
| ~ ( subset @ SV269 @ ( subset_complement @ SV162 @ SY1163 ) )
| ( disjoint @ SV269 @ SY1163 ) ) )
= $true )
| ( ( element @ SV269 @ ( powerset @ SV162 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2654]) ).
thf(2846,plain,
! [SV431: $i,SV362: $i] :
( ( ( in @ SV362 @ SV431 )
= $false )
| ( ( subset @ ( singleton @ SV362 ) @ SV431 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2655]) ).
thf(2847,plain,
! [SV432: $i,SV363: $i] :
( ( ( subset @ ( singleton @ SV363 ) @ SV432 )
= $false )
| ( ( in @ SV363 @ SV432 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2656]) ).
thf(2848,plain,
! [SV433: $i,SV163: $i,SV472: $i] :
( ( ( ~ ( relation_of2 @ SV472 @ SV163 @ SV433 ) )
= $true )
| ( ( relation_of2_as_subset @ SV472 @ SV163 @ SV433 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2657]) ).
thf(2849,plain,
! [SV434: $i,SV163: $i,SV473: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV473 @ SV163 @ SV434 ) )
= $true )
| ( ( relation_of2 @ SV473 @ SV163 @ SV434 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2658]) ).
thf(2850,plain,
! [SV364: $i,SV435: $i] :
( ( ( ~ ( ( ( sK87_C @ SV435 @ SV364 )
!= SV364 )
| ~ ( in @ ( sK87_C @ SV435 @ SV364 ) @ SV435 ) )
| ~ ( ( ( sK87_C @ SV435 @ SV364 )
= SV364 )
| ( in @ ( sK87_C @ SV435 @ SV364 ) @ SV435 ) ) )
= $false )
| ( ( SV435
= ( singleton @ SV364 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2659]) ).
thf(2851,plain,
! [SV365: $i,SV436: $i] :
( ( ( SV436
= ( singleton @ SV365 ) )
= $false )
| ( ( ~ ( ~ ! [SY1299: $i] :
( ( SY1299 != SV365 )
| ( in @ SY1299 @ SV436 ) )
| ~ ! [SY1300: $i] :
( ~ ( in @ SY1300 @ SV436 )
| ( SY1300 = SV365 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2660]) ).
thf(2852,plain,
! [SV474: $i,SV437: $i,SV164: $i] :
( ( ( ~ ( ~ ( ! [SY1342: $i,SY1343: $i] :
( ~ ( in @ SY1342 @ SV164 )
| ~ ( in @ SY1343 @ SV437 )
| ( ( sK78_D @ SV474 @ SV437 @ SV164 )
!= ( ordered_pair @ SY1342 @ SY1343 ) ) )
| ~ ( in @ ( sK78_D @ SV474 @ SV437 @ SV164 ) @ SV474 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK79_SY729 @ SV474 @ SV437 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK80_SY731 @ SV474 @ SV437 @ SV164 ) @ SV437 ) )
| ( ( sK78_D @ SV474 @ SV437 @ SV164 )
!= ( ordered_pair @ ( sK79_SY729 @ SV474 @ SV437 @ SV164 ) @ ( sK80_SY731 @ SV474 @ SV437 @ SV164 ) ) ) )
| ( in @ ( sK78_D @ SV474 @ SV437 @ SV164 ) @ SV474 ) ) ) )
= $true )
| ( ( SV474
= ( cartesian_product2 @ SV164 @ SV437 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2661]) ).
thf(2853,plain,
! [SV438: $i,SV164: $i,SV475: $i] :
( ( ( ( SV475
!= ( cartesian_product2 @ SV164 @ SV438 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1344: $i] :
( ! [SY1306: $i,SY1307: $i] :
( ~ ( in @ SY1306 @ SV164 )
| ~ ( in @ SY1307 @ SV438 )
| ( SY1344
!= ( ordered_pair @ SY1306 @ SY1307 ) ) )
| ( in @ SY1344 @ SV475 ) )
| ~ ! [SY1347: $i] :
( ~ ( in @ SY1347 @ SV475 )
| ~ ( ~ ~ ( ~ ( in @ ( sK76_E @ SY1347 @ SV475 @ SV438 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK77_SY726 @ SY1347 @ SV475 @ SV438 @ SV164 ) @ SV438 ) )
| ( SY1347
!= ( ordered_pair @ ( sK76_E @ SY1347 @ SV475 @ SV438 @ SV164 ) @ ( sK77_SY726 @ SY1347 @ SV475 @ SV438 @ SV164 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2662]) ).
thf(2854,plain,
! [SV366: $i,SV439: $i] :
( ( ( ~ ( in @ ( sK71_C @ SV439 @ SV366 ) @ SV366 )
| ~ ~ ( in @ ( sK71_C @ SV439 @ SV366 ) @ SV439 ) )
= $false )
| ( ( subset @ SV366 @ SV439 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2663]) ).
thf(2855,plain,
! [SV440: $i,SV367: $i] :
( ( ( subset @ SV367 @ SV440 )
= $false )
| ( ( ! [SY1309: $i] :
( ~ ( in @ SY1309 @ SV367 )
| ( in @ SY1309 @ SV440 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2664]) ).
thf(2856,plain,
! [SV441: $i,SV165: $i,SV476: $i] :
( ( ( ~ ( relation_of2 @ SV476 @ SV165 @ SV441 ) )
= $true )
| ( ( subset @ SV476 @ ( cartesian_product2 @ SV165 @ SV441 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2665]) ).
thf(2857,plain,
! [SV442: $i,SV165: $i,SV477: $i] :
( ( ( ~ ( subset @ SV477 @ ( cartesian_product2 @ SV165 @ SV442 ) ) )
= $true )
| ( ( relation_of2 @ SV477 @ SV165 @ SV442 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2666]) ).
thf(2858,plain,
! [SV166: $i,SV443: $i] :
( ( ( ~ ( subset @ SV443 @ ( sK3_B @ SV166 ) ) )
= $true )
| ( ( are_equipotent @ SV443 @ ( sK3_B @ SV166 ) )
= $true )
| ( ( in @ SV443 @ ( sK3_B @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2667]) ).
thf(2859,plain,
! [SV166: $i] :
( ( ! [SY1034: $i] :
( ~ ( ~ ! [SY1035: $i] :
( ~ ( subset @ SY1035 @ SY1034 )
| ( in @ SY1035 @ ( sK4_SY591 @ SY1034 @ SV166 ) ) )
| ~ ( in @ ( sK4_SY591 @ SY1034 @ SV166 ) @ ( sK3_B @ SV166 ) ) )
| ~ ( in @ SY1034 @ ( sK3_B @ SV166 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2668]) ).
thf(2860,plain,
! [SV166: $i] :
( ( ~ ( ~ ! [SY1036: $i,SY1037: $i] :
( ~ ( in @ SY1036 @ ( sK3_B @ SV166 ) )
| ~ ( subset @ SY1037 @ SY1036 )
| ( in @ SY1037 @ ( sK3_B @ SV166 ) ) )
| ~ ( in @ SV166 @ ( sK3_B @ SV166 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2669]) ).
thf(2861,plain,
! [SV167: $i,SV444: $i,SV478: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV478 @ SV444 @ SV167 ) )
= $true )
| ( ( ~ ( ~ ! [SY1348: $i] :
~ ( in @ ( ordered_pair @ ( sK104_D @ SV478 @ SV444 @ SV167 ) @ SY1348 ) @ SV478 )
| ~ ( in @ ( sK104_D @ SV478 @ SV444 @ SV167 ) @ SV444 ) )
| ( ( relation_dom_as_subset @ SV444 @ SV167 @ SV478 )
= SV444 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2670]) ).
thf(2862,plain,
! [SV167: $i,SV445: $i,SV479: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV479 @ SV445 @ SV167 ) )
= $true )
| ( ( ( ( relation_dom_as_subset @ SV445 @ SV167 @ SV479 )
!= SV445 )
| ! [SY1349: $i] :
( ( in @ ( ordered_pair @ SY1349 @ ( sK103_E @ SY1349 @ SV479 @ SV445 @ SV167 ) ) @ SV479 )
| ~ ( in @ SY1349 @ SV445 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2671]) ).
thf(2863,plain,
! [SV168: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( sK27_SY634 @ SV168 )
!= ( singleton @ ( sK26_B @ SV168 ) ) )
| ~ ( in @ ( sK26_B @ SV168 ) @ SV168 ) )
| ~ ( in @ ( sK26_B @ SV168 ) @ SV168 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) )
| ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2672]) ).
thf(2864,plain,
! [SV168: $i] :
( ( ( ( ( sK28_SY636 @ SV168 )
!= ( singleton @ ( sK26_B @ SV168 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) )
| ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2672]) ).
thf(2865,plain,
! [SV168: $i] :
( ( ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) )
| ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) )
= $false )
| ( ( ( sK27_SY634 @ SV168 )
= ( sK28_SY636 @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2673]) ).
thf(2866,plain,
! [SV519: $i,SV270: $i,SV480: $i,SV169: $i] :
( ( ~ ( in @ SV169 @ SV480 )
| ~ ( in @ SV270 @ SV519 )
| ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SV480 @ SV519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2676]) ).
thf(2867,plain,
! [SV270: $i,SV169: $i] :
( ( ~ ! [SY1166: $i] :
( ! [SY1167: $i] :
~ ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SY1166 @ SY1167 ) )
| ( in @ SV169 @ SY1166 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2677]) ).
thf(2868,plain,
! [SV270: $i,SV169: $i] :
( ( ~ ! [SY1168: $i,SY1169: $i] :
( ~ ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SY1168 @ SY1169 ) )
| ( in @ SV270 @ SY1169 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2677]) ).
thf(2869,plain,
! [SV271: $i,SV481: $i,SV170: $i] :
( ( ( ~ ! [SY1351: $i] :
( ! [SY1352: $i,SY1353: $i] :
( ( ( ordered_pair @ SY1352 @ SY1353 )
!= SY1351 )
| ~ ( in @ SY1352 @ SV170 )
| ! [SY1354: $i] :
( ~ ( ~ ( in @ ( sK115_I @ SY1354 @ SY1353 @ SY1352 @ SY1351 @ SV481 @ SV271 @ SV170 ) @ SY1354 )
| ~ ~ ( in @ ( ordered_pair @ SY1353 @ ( sK115_I @ SY1354 @ SY1353 @ SY1352 @ SY1351 @ SV481 @ SV271 @ SV170 ) ) @ SV271 ) )
| ( SY1352 != SY1354 )
| ~ ( in @ SY1353 @ SY1354 ) ) )
| ~ ( in @ SY1351 @ ( cartesian_product2 @ SV170 @ SV481 ) )
| ( in @ SY1351 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) ) )
| ~ ~ ( ~ ! [SY1355: $i] :
( ~ ( in @ SY1355 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
| ~ ( ~ ~ ( ( ( ordered_pair @ ( sK112_F @ SY1355 @ SV481 @ SV271 @ SV170 ) @ ( sK113_SY768 @ SY1355 @ SV481 @ SV271 @ SV170 ) )
!= SY1355 )
| ~ ( in @ ( sK112_F @ SY1355 @ SV481 @ SV271 @ SV170 ) @ SV170 ) )
| ~ ~ ( ~ ! [SY1356: $i] :
( ~ ( in @ SY1356 @ ( sK114_SY771 @ SY1355 @ SV481 @ SV271 @ SV170 ) )
| ( in @ ( ordered_pair @ ( sK113_SY768 @ SY1355 @ SV481 @ SV271 @ SV170 ) @ SY1356 ) @ SV271 ) )
| ~ ~ ( ( ( sK112_F @ SY1355 @ SV481 @ SV271 @ SV170 )
!= ( sK114_SY771 @ SY1355 @ SV481 @ SV271 @ SV170 ) )
| ~ ( in @ ( sK113_SY768 @ SY1355 @ SV481 @ SV271 @ SV170 ) @ ( sK114_SY771 @ SY1355 @ SV481 @ SV271 @ SV170 ) ) ) ) ) )
| ~ ! [SY1357: $i] :
( ~ ( in @ SY1357 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
| ( in @ SY1357 @ ( cartesian_product2 @ SV170 @ SV481 ) ) ) ) )
= $false )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2678]) ).
thf(2870,plain,
! [SV368: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK74_B @ SV368 )
!= ( sK75_SY725 @ SV368 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK74_B @ SV368 ) @ SV368 )
| ~ ( in @ ( sK75_SY725 @ SV368 ) @ SV368 ) )
| ~ ~ ( in @ ( sK74_B @ SV368 ) @ ( sK75_SY725 @ SV368 ) ) ) ) )
= $false )
| ( ( epsilon_connected @ SV368 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2679]) ).
thf(2871,plain,
! [SV368: $i] :
( ( ( ~ ~ ( in @ ( sK75_SY725 @ SV368 ) @ ( sK74_B @ SV368 ) ) )
= $false )
| ( ( epsilon_connected @ SV368 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2679]) ).
thf(2872,plain,
! [SV369: $i,SV520: $i] :
( ( ( ! [SY1397: $i] :
( ( SV520 = SY1397 )
| ~ ( in @ SV520 @ SV369 )
| ~ ( in @ SY1397 @ SV369 )
| ( in @ SV520 @ SY1397 )
| ( in @ SY1397 @ SV520 ) ) )
= $true )
| ( ( epsilon_connected @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2680]) ).
thf(2873,plain,
! [SV521: $i] :
( ( ~ ( v3_membered @ SV521 )
| ! [SY1398: $i] : ( v1_membered @ ( set_difference @ SV521 @ SY1398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2681]) ).
thf(2874,plain,
! [SV522: $i] :
( ( ~ ( v3_membered @ SV522 )
| ! [SY1399: $i] : ( v2_membered @ ( set_difference @ SV522 @ SY1399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2682]) ).
thf(2875,plain,
! [SV523: $i,SV370: $i] :
( ( ( v3_membered @ ( set_difference @ SV370 @ SV523 ) )
= $true )
| ( ( v3_membered @ SV370 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2683]) ).
thf(2876,plain,
! [SV171: $i,SV524: $i] :
( ( ( ~ ( relation @ SV524 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV171 )
| ~ ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV524 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV171 )
| ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV524 ) ) )
| ( SV171 = SV524 ) )
= $true )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2684]) ).
thf(2877,plain,
! [SV171: $i,SV525: $i] :
( ( ( ~ ( relation @ SV525 )
| ( SV171 != SV525 )
| ~ ( ~ ! [SY1400: $i,SY1401: $i] :
( ~ ( in @ ( ordered_pair @ SY1400 @ SY1401 ) @ SV171 )
| ( in @ ( ordered_pair @ SY1400 @ SY1401 ) @ SV525 ) )
| ~ ! [SY1402: $i,SY1403: $i] :
( ~ ( in @ ( ordered_pair @ SY1402 @ SY1403 ) @ SV525 )
| ( in @ ( ordered_pair @ SY1402 @ SY1403 ) @ SV171 ) ) ) )
= $true )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2685]) ).
thf(2878,plain,
! [SV371: $i,SV446: $i] :
( ( ( ~ ( in @ ( sK98_C @ SV446 @ SV371 ) @ SV371 )
| ~ ( in @ ( sK98_C @ SV446 @ SV371 ) @ SV446 ) )
= $false )
| ( ( disjoint @ SV371 @ SV446 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2686]) ).
thf(2879,plain,
! [SV447: $i,SV372: $i,SV526: $i] :
( ( ( ~ ( in @ SV526 @ SV372 )
| ~ ( in @ SV526 @ SV447 ) )
= $true )
| ( ( ~ ( disjoint @ SV372 @ SV447 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2687]) ).
thf(2880,plain,
! [SV448: $i,SV373: $i] :
( ( ( in @ SV373 @ SV448 )
= $false )
| ( ( subset @ ( singleton @ SV373 ) @ SV448 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2688]) ).
thf(2881,plain,
! [SV449: $i,SV374: $i] :
( ( ( subset @ ( singleton @ SV374 ) @ SV449 )
= $false )
| ( ( in @ SV374 @ SV449 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2689]) ).
thf(2882,plain,
! [SV451: $i,SV376: $i,SV527: $i] :
( ( ( ~ ( in @ SV527 @ ( set_intersection2 @ SV376 @ SV451 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV376 @ SV451 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2691]) ).
thf(2883,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK35_D @ SV272 @ SV172 )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1178: $i] :
( ~ ( in @ SY1178 @ ( sK43_SY691 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SY1178 ) @ SV272 ) )
| ~ ~ ( ( ( sK41_SY666 @ SV272 @ SV172 )
!= ( sK43_SY691 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) ) ) ) ) )
| ( ( sK35_D @ SV272 @ SV172 )
!= ( sK37_SY665 @ SV272 @ SV172 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
!= ( sK37_SY665 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1179: $i] :
( ~ ( in @ SY1179 @ ( sK40_SY685 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SY1179 ) @ SV272 ) )
| ~ ~ ( ( ( sK38_SY678 @ SV272 @ SV172 )
!= ( sK40_SY685 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) ) ) ) ) )
| ~ ( ( ( sK36_SY655 @ SV272 @ SV172 )
!= ( sK37_SY665 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2692]) ).
thf(2884,plain,
! [SV381: $i,SV528: $i] :
( ( ( v1_membered @ ( set_intersection2 @ SV528 @ SV381 ) )
= $true )
| ( ( v2_membered @ SV381 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2695]) ).
thf(2885,plain,
! [SV382: $i,SV529: $i] :
( ( ( v2_membered @ ( set_intersection2 @ SV529 @ SV382 ) )
= $true )
| ( ( v2_membered @ SV382 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2696]) ).
thf(2886,plain,
! [SV530: $i,SV273: $i,SV482: $i,SV173: $i] :
( ( ~ ( in @ SV173 @ SV482 )
| ~ ( in @ SV273 @ SV530 )
| ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SV482 @ SV530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2697]) ).
thf(2887,plain,
! [SV273: $i,SV173: $i] :
( ( ~ ! [SY1190: $i] :
( ! [SY1191: $i] :
~ ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SY1190 @ SY1191 ) )
| ( in @ SV173 @ SY1190 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2698]) ).
thf(2888,plain,
! [SV273: $i,SV173: $i] :
( ( ~ ! [SY1192: $i,SY1193: $i] :
( ~ ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SY1192 @ SY1193 ) )
| ( in @ SV273 @ SY1193 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2698]) ).
thf(2889,plain,
! [SV174: $i,SV274: $i] :
( ( ~ ( relation @ ( sK56_C @ SV274 @ SV174 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2699]) ).
thf(2890,plain,
! [SV174: $i,SV274: $i] :
( ( ~ ( relation_of2 @ ( sK56_C @ SV274 @ SV174 ) @ SV174 @ SV274 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2699]) ).
thf(2891,plain,
! [SV531: $i,SV385: $i] :
( ( ( v1_membered @ ( set_difference @ SV385 @ SV531 ) )
= $true )
| ( ( v2_membered @ SV385 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2702]) ).
thf(2892,plain,
! [SV532: $i,SV386: $i] :
( ( ( v2_membered @ ( set_difference @ SV386 @ SV532 ) )
= $true )
| ( ( v2_membered @ SV386 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2703]) ).
thf(2893,plain,
! [SV533: $i] :
( ( ~ ( v3_membered @ SV533 )
| ! [SY1404: $i] : ( v1_membered @ ( set_intersection2 @ SV533 @ SY1404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2704]) ).
thf(2894,plain,
! [SV534: $i] :
( ( ~ ( v3_membered @ SV534 )
| ! [SY1405: $i] : ( v2_membered @ ( set_intersection2 @ SV534 @ SY1405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2705]) ).
thf(2895,plain,
! [SV535: $i,SV387: $i] :
( ( ( v3_membered @ ( set_intersection2 @ SV387 @ SV535 ) )
= $true )
| ( ( v3_membered @ SV387 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2706]) ).
thf(2896,plain,
! [SV536: $i,SV388: $i] :
( ( ( v1_membered @ ( set_intersection2 @ SV388 @ SV536 ) )
= $true )
| ( ( v2_membered @ SV388 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2707]) ).
thf(2897,plain,
! [SV537: $i,SV389: $i] :
( ( ( v2_membered @ ( set_intersection2 @ SV389 @ SV537 ) )
= $true )
| ( ( v2_membered @ SV389 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2708]) ).
thf(2898,plain,
! [SV452: $i,SV390: $i] :
( ( ( ( set_difference @ SV390 @ SV452 )
= empty_set )
= $false )
| ( ( subset @ SV390 @ SV452 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2709]) ).
thf(2899,plain,
! [SV453: $i,SV391: $i] :
( ( ( subset @ SV391 @ SV453 )
= $false )
| ( ( ( set_difference @ SV391 @ SV453 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2710]) ).
thf(2900,plain,
! [SV275: $i,SV176: $i,SV483: $i] :
( ( ( ! [SY1359: $i,SY1360: $i] :
( ( ( ordered_pair @ SY1359 @ SY1360 )
!= SV483 )
| ~ ( in @ SY1359 @ SV176 )
| ( SY1360
!= ( singleton @ SY1359 ) ) )
| ~ ( in @ SV483 @ ( cartesian_product2 @ SV176 @ SV275 ) ) )
= $true )
| ( ( in @ SV483 @ ( sK108_C @ SV275 @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2711]) ).
thf(2901,plain,
! [SV176: $i,SV275: $i] :
( ( ~ ! [SY1197: $i] :
( ~ ( in @ SY1197 @ ( sK108_C @ SV275 @ SV176 ) )
| ~ ( ~ ~ ( ( ( ordered_pair @ ( sK109_E @ SY1197 @ SV275 @ SV176 ) @ ( sK110_SY756 @ SY1197 @ SV275 @ SV176 ) )
!= SY1197 )
| ~ ( in @ ( sK109_E @ SY1197 @ SV275 @ SV176 ) @ SV176 ) )
| ( ( sK110_SY756 @ SY1197 @ SV275 @ SV176 )
!= ( singleton @ ( sK109_E @ SY1197 @ SV275 @ SV176 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2712]) ).
thf(2902,plain,
! [SV176: $i,SV275: $i] :
( ( ~ ! [SY1198: $i] :
( ~ ( in @ SY1198 @ ( sK108_C @ SV275 @ SV176 ) )
| ( in @ SY1198 @ ( cartesian_product2 @ SV176 @ SV275 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2712]) ).
thf(2903,plain,
! [SV177: $i,SV276: $i] :
( ( ( in @ ( sK125_C @ SV276 @ SV177 ) @ SV276 )
= $false )
| ( ( element @ SV177 @ ( powerset @ SV276 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2714]) ).
thf(2904,plain,
! [SV178: $i,SV277: $i] :
( ( ( ~ ( in @ ( sK6_C @ SV277 @ SV178 ) @ SV178 ) )
= $true )
| ( ( ~ ( in @ ( sK6_C @ SV277 @ SV178 ) @ SV277 ) )
= $true )
| ( ( SV178 = SV277 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2715]) ).
thf(2905,plain,
! [SV178: $i,SV277: $i] :
( ( ( in @ ( sK6_C @ SV277 @ SV178 ) @ SV178 )
= $true )
| ( ( in @ ( sK6_C @ SV277 @ SV178 ) @ SV277 )
= $true )
| ( ( SV178 = SV277 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2716]) ).
thf(2906,plain,
! [SV454: $i,SV179: $i] :
( ( ( subset @ SV179 @ SV454 )
= $false )
| ( ( ! [SY1318: $i] : ( subset @ ( cartesian_product2 @ SV179 @ SY1318 ) @ ( cartesian_product2 @ SV454 @ SY1318 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2717]) ).
thf(2907,plain,
! [SV455: $i,SV179: $i] :
( ( ( subset @ SV179 @ SV455 )
= $false )
| ( ( ! [SY1319: $i] : ( subset @ ( cartesian_product2 @ SY1319 @ SV179 ) @ ( cartesian_product2 @ SY1319 @ SV455 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2718]) ).
thf(2908,plain,
! [SV180: $i,SV456: $i,SV484: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV484 )
| ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV180 ) )
| ~ ( ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV484 )
| ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV456 ) ) )
| ~ ( ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV484 )
| ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV180 )
| ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV456 ) ) ) )
= $true )
| ( ( SV484
= ( set_union2 @ SV180 @ SV456 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2719]) ).
thf(2909,plain,
! [SV457: $i,SV180: $i,SV485: $i] :
( ( ( ( SV485
!= ( set_union2 @ SV180 @ SV457 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1361: $i] :
( ~ ( in @ SY1361 @ SV485 )
| ( in @ SY1361 @ SV180 )
| ( in @ SY1361 @ SV457 ) )
| ~ ~ ( ~ ! [SY1362: $i] :
( ~ ( in @ SY1362 @ SV180 )
| ( in @ SY1362 @ SV485 ) )
| ~ ! [SY1363: $i] :
( ~ ( in @ SY1363 @ SV457 )
| ( in @ SY1363 @ SV485 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2720]) ).
thf(2910,plain,
! [SV278: $i,SV5: $i,SV458: $i] :
( ( ( element @ SV458 @ SV5 )
= $false )
| ( ( ( in @ SV458 @ SV278 )
| ( in @ SV458 @ ( subset_complement @ SV5 @ SV278 ) ) )
= $true )
| ( ( element @ SV278 @ ( powerset @ SV5 ) )
= $false )
| ( ( SV5 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2723]) ).
thf(2911,plain,
! [SV6: $i,SV279: $i,SV184: $i] :
( ( ( in @ SV184 @ SV279 )
= $false )
| ( ( in @ SV184 @ ( subset_complement @ SV6 @ SV279 ) )
= $false )
| ( ( element @ SV279 @ ( powerset @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2724]) ).
thf(2912,plain,
! [SV41: $i,SV207: $i,SV290: $i] :
( ( ( empty @ SV290 )
= $false )
| ( ( element @ SV207 @ ( powerset @ SV290 ) )
= $false )
| ( ( in @ SV41 @ SV207 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2732]) ).
thf(2913,plain,
! [SV214: $i,SV50: $i,SV312: $i,SV291: $i] :
( ( ( subset @ SV291 @ SV312 )
= $false )
| ( ( subset @ SV50 @ SV214 )
= $false )
| ( ( subset @ ( cartesian_product2 @ SV50 @ SV291 ) @ ( cartesian_product2 @ SV214 @ SV312 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2733]) ).
thf(2914,plain,
! [SV53: $i,SV293: $i,SV216: $i,SV313: $i] :
( ( ( subset @ ( relation_rng @ SV313 ) @ SV216 )
= $false )
| ( ( relation_of2_as_subset @ SV313 @ SV293 @ SV216 )
= $true )
| ( ( relation_of2_as_subset @ SV313 @ SV293 @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2734]) ).
thf(2915,plain,
! [SV294: $i,SV315: $i,SV217: $i,SV55: $i] :
( ( ( subset @ SV55 @ SV217 )
= $false )
| ( ( relation_of2_as_subset @ SV315 @ SV294 @ SV217 )
= $true )
| ( ( relation_of2_as_subset @ SV315 @ SV294 @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2735]) ).
thf(2916,plain,
! [SV316: $i,SV61: $i] :
( ( ( in @ SV61 @ SV316 )
= $true )
| ( ( SV61 = SV316 )
= $true )
| ( ( in @ SV316 @ SV61 )
= $true )
| ( ( ordinal @ SV316 )
= $false )
| ( ( ordinal @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2739]) ).
thf(2917,plain,
! [SV228: $i,SV68: $i,SV298: $i] :
( ( ( in @ SV298 @ SV68 )
= $false )
| ( ( in @ SV68 @ SV228 )
= $false )
| ( ( in @ SV228 @ SV298 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2740]) ).
thf(2918,plain,
! [SV302: $i,SV246: $i,SV96: $i] :
( ( ( join_semilatt_str @ SV96 )
= $false )
| ( ( empty_carrier @ SV96 )
= $true )
| ( ( ~ ( element @ SV246 @ ( the_carrier @ SV96 ) ) )
= $true )
| ( ( ~ ( element @ SV302 @ ( the_carrier @ SV96 ) ) )
= $true )
| ( ( element @ ( join @ SV96 @ SV246 @ SV302 ) @ ( the_carrier @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2743]) ).
thf(2919,plain,
! [SV303: $i,SV247: $i,SV98: $i] :
( ( ( meet_semilatt_str @ SV98 )
= $false )
| ( ( empty_carrier @ SV98 )
= $true )
| ( ( ~ ( element @ SV247 @ ( the_carrier @ SV98 ) ) )
= $true )
| ( ( ~ ( element @ SV303 @ ( the_carrier @ SV98 ) ) )
= $true )
| ( ( element @ ( meet @ SV98 @ SV247 @ SV303 ) @ ( the_carrier @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2744]) ).
thf(2920,plain,
! [SV396: $i,SV326: $i] :
( ( ( subset @ SV326 @ SV396 )
= $false )
| ( ( SV326 = SV396 )
= $true )
| ( ( proper_subset @ SV326 @ SV396 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2745]) ).
thf(2921,plain,
! [SV538: $i,SV486: $i] :
( ( ~ ( proper_subset @ SV486 @ SV538 )
| ( SV486 != SV538 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2746]) ).
thf(2922,plain,
! [SV539: $i,SV487: $i] :
( ( ~ ( proper_subset @ SV487 @ SV539 )
| ( subset @ SV487 @ SV539 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2747]) ).
thf(2923,plain,
! [SV139: $i] :
( ( ( ~ ( ~ ~ ( ( ( sK17_C @ SV139 )
!= ( sK18_SY613 @ SV139 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
!= ( sK18_SY613 @ SV139 ) )
| ~ ( in @ ( sK22_SY620 @ SV139 ) @ SV139 ) )
| ( ( sK23_SY629 @ SV139 )
!= ( singleton @ ( sK22_SY620 @ SV139 ) ) ) ) )
| ( ( sK17_C @ SV139 )
!= ( sK19_SY619 @ SV139 ) ) ) )
= $true )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2750]) ).
thf(2924,plain,
! [SV139: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
!= ( sK19_SY619 @ SV139 ) )
| ~ ( in @ ( sK20_SY626 @ SV139 ) @ SV139 ) )
| ( ( sK21_SY628 @ SV139 )
!= ( singleton @ ( sK20_SY626 @ SV139 ) ) ) ) )
= $true )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2751]) ).
thf(2925,plain,
! [SV488: $i,SV139: $i] :
( ( ( ~ ! [SY1366: $i] :
( ! [SY1367: $i] :
( ( SY1367 != SY1366 )
| ~ ( in @ SY1367 @ ( cartesian_product2 @ SV139 @ SV488 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1366 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1366 @ ( sK13_C @ SV488 @ SV139 ) ) )
| ~ ! [SY1370: $i] :
( ~ ( in @ SY1370 @ ( sK13_C @ SV488 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1370 @ SV488 @ SV139 )
!= SY1370 )
| ~ ( in @ ( sK16_E @ SY1370 @ SV488 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV488 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1370 @ SV488 @ SV139 ) @ ( sK15_SY612 @ SY1370 @ SV488 @ SV139 ) )
!= SY1370 )
| ~ ( in @ ( sK14_J @ SY1370 @ SV488 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1370 @ SV488 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1370 @ SV488 @ SV139 ) ) ) ) ) ) )
= $false )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2752]) ).
thf(2926,plain,
! [SV140: $i] :
( ( ( empty @ ( sK116_B @ SV140 ) )
= $false )
| ( ( empty_carrier @ SV140 )
= $true )
| ( ( one_sorted_str @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2754]) ).
thf(2927,plain,
! [SV489: $i] :
( ( ( ~ ( v3_membered @ SV489 ) )
= $true )
| ( ( ! [SY1371: $i] : ( v1_membered @ ( set_intersection2 @ SY1371 @ SV489 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2755]) ).
thf(2928,plain,
! [SV490: $i] :
( ( ( ~ ( v3_membered @ SV490 ) )
= $true )
| ( ( ! [SY1372: $i] : ( v2_membered @ ( set_intersection2 @ SY1372 @ SV490 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2756]) ).
thf(2929,plain,
! [SV141: $i] :
( ( ( subset @ ( sK99_B @ SV141 ) @ SV141 )
= $false )
| ( ( ordinal @ ( sK99_B @ SV141 ) )
= $false )
| ( ( ordinal @ SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2758]) ).
thf(2930,plain,
! [SV399: $i,SV460: $i,SV142: $i] :
( ( ( ~ ( in @ SV142 @ SV460 ) )
= $true )
| ( ( ~ ( in @ SV399 @ SV460 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV142 @ SV399 ) @ SV460 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2759]) ).
thf(2931,plain,
! [SV540: $i,SV142: $i] :
( ( ! [SY1406: $i] :
( ~ ( subset @ ( unordered_pair @ SV142 @ SV540 ) @ SY1406 )
| ( in @ SV142 @ SY1406 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2760]) ).
thf(2932,plain,
! [SV541: $i,SV142: $i] :
( ( ! [SY1407: $i] :
( ~ ( subset @ ( unordered_pair @ SV142 @ SV541 ) @ SY1407 )
| ( in @ SV541 @ SY1407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2761]) ).
thf(2933,plain,
! [SV143: $i,SV400: $i,SV461: $i] :
( ( ( ~ ( ~ ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV143 )
| ~ ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV400 )
| ~ ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV461 ) )
| ~ ~ ( ~ ( ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV143 )
| ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV461 ) )
| ~ ( ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV400 )
| ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV461 ) ) ) )
= $false )
| ( ( SV461
= ( set_intersection2 @ SV143 @ SV400 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2762]) ).
thf(2934,plain,
! [SV401: $i,SV143: $i,SV462: $i] :
( ( ( SV462
= ( set_intersection2 @ SV143 @ SV401 ) )
= $false )
| ( ( ~ ( ~ ! [SY1325: $i] :
( ~ ( in @ SY1325 @ SV143 )
| ~ ( in @ SY1325 @ SV401 )
| ( in @ SY1325 @ SV462 ) )
| ~ ~ ( ~ ! [SY1326: $i] :
( ~ ( in @ SY1326 @ SV462 )
| ( in @ SY1326 @ SV143 ) )
| ~ ! [SY1327: $i] :
( ~ ( in @ SY1327 @ SV462 )
| ( in @ SY1327 @ SV401 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2763]) ).
thf(2935,plain,
! [SV144: $i] :
( ( ( ~ ! [SY930: $i] :
( ~ ( element @ SY930 @ ( powerset @ SV144 ) )
| ( v1_membered @ SY930 ) ) )
= $false )
| ( ( v3_membered @ SV144 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2764]) ).
thf(2936,plain,
! [SV144: $i] :
( ( ( ~ ! [SY931: $i] :
( ~ ( element @ SY931 @ ( powerset @ SV144 ) )
| ( v2_membered @ SY931 ) ) )
= $false )
| ( ( v3_membered @ SV144 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2764]) ).
thf(2937,plain,
! [SV144: $i,SV492: $i] :
( ( ( ~ ( element @ SV492 @ ( powerset @ SV144 ) ) )
= $true )
| ( ( v3_membered @ SV492 )
= $true )
| ( ( v3_membered @ SV144 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2765]) ).
thf(2938,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1142: $i] :
( ~ ( in @ SY1142 @ ( sK52_SY712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SY1142 ) @ SV265 ) )
| ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK52_SY712 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) ) ) )
| ~ ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 ) )
| ~ ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 ) )
| ~ ~ ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ ( sK51_SY718 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SY1143 ) @ SV265 ) )
| ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK51_SY718 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2766]) ).
thf(2939,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ( ( ( sK49_SY705 @ SV265 @ SV145 )
!= ( sK50_SY711 @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2766]) ).
thf(2940,plain,
! [SV402: $i,SV330: $i] :
( ( ( subset @ SV330 @ SV402 )
= $false )
| ( ( ~ ( subset @ SV402 @ SV330 ) )
= $true )
| ( ( SV330 = SV402 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2767]) ).
thf(2941,plain,
! [SV542: $i,SV493: $i] :
( ( ( SV493 != SV542 )
| ( subset @ SV493 @ SV542 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2768]) ).
thf(2942,plain,
! [SV543: $i,SV494: $i] :
( ( ( SV494 != SV543 )
| ( subset @ SV543 @ SV494 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2769]) ).
thf(2943,plain,
! [SV146: $i,SV266: $i,SV495: $i] :
( ( ( ~ ( in @ SV495 @ SV266 ) )
= $true )
| ( ( ~ ( in @ SV495 @ ( sK5_C @ SV266 @ SV146 ) ) )
= $true )
| ( ( ~ ( in @ SV146 @ SV266 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2770]) ).
thf(2944,plain,
! [SV331: $i] :
( ( ( in @ ( sK85_B @ SV331 ) @ SV331 )
= $true )
| ( ( epsilon_transitive @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2772]) ).
thf(2945,plain,
! [SV331: $i] :
( ( ( ~ ( subset @ ( sK85_B @ SV331 ) @ SV331 ) )
= $true )
| ( ( epsilon_transitive @ SV331 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2773]) ).
thf(2946,plain,
! [SV332: $i,SV496: $i] :
( ( ( ~ ( in @ SV496 @ SV332 ) )
= $true )
| ( ( subset @ SV496 @ SV332 )
= $true )
| ( ( epsilon_transitive @ SV332 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2774]) ).
thf(2947,plain,
! [SV147: $i,SV403: $i,SV463: $i] :
( ( ( ~ ( ~ ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV147 )
| ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV403 )
| ~ ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV463 ) )
| ~ ~ ( ~ ( ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV147 )
| ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV463 ) )
| ~ ( ~ ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV403 )
| ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV463 ) ) ) )
= $false )
| ( ( SV463
= ( set_difference @ SV147 @ SV403 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2775]) ).
thf(2948,plain,
! [SV404: $i,SV147: $i,SV464: $i] :
( ( ( SV464
= ( set_difference @ SV147 @ SV404 ) )
= $false )
| ( ( ~ ( ~ ! [SY1328: $i] :
( ~ ( in @ SY1328 @ SV147 )
| ( in @ SY1328 @ SV404 )
| ( in @ SY1328 @ SV464 ) )
| ~ ~ ( ~ ! [SY1329: $i] :
( ~ ( in @ SY1329 @ SV464 )
| ( in @ SY1329 @ SV147 ) )
| ~ ! [SY1330: $i] :
( ~ ( in @ SY1330 @ SV464 )
| ~ ( in @ SY1330 @ SV404 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2776]) ).
thf(2949,plain,
! [SV334: $i,SV497: $i] :
( ( ( in @ SV497 @ SV334 )
= $false )
| ( ( SV334 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2777]) ).
thf(2950,plain,
! [SV148: $i,SV335: $i] :
( ( ( ~ ! [SY1210: $i] :
( ~ ( in @ SY1210 @ SV335 )
| ~ ( subset @ ( sK105_C @ SV335 @ SV148 ) @ SY1210 )
| ( SY1210
= ( sK105_C @ SV335 @ SV148 ) ) )
| ~ ( in @ ( sK105_C @ SV335 @ SV148 ) @ SV335 ) )
= $false )
| ( ( SV335 = empty_set )
= $true )
| ( ( element @ SV335 @ ( powerset @ ( powerset @ SV148 ) ) )
= $false )
| ( ( finite @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2778]) ).
thf(2951,plain,
! [SV338: $i,SV407: $i] :
( ( ( in @ SV407 @ SV338 )
= $false )
| ( ( ( set_difference @ SV338 @ ( singleton @ SV407 ) )
= SV338 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2781]) ).
thf(2952,plain,
! [SV340: $i,SV409: $i] :
( ( ( ~ ( ! [SY1278: $i] :
( ~ ( in @ ( sK68_C @ SV409 @ SV340 ) @ SY1278 )
| ~ ( in @ SY1278 @ SV340 ) )
| ~ ( in @ ( sK68_C @ SV409 @ SV340 ) @ SV409 ) ) )
= $false )
| ( ( SV409
= ( union @ SV340 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2782]) ).
thf(2953,plain,
! [SV340: $i,SV409: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK68_C @ SV409 @ SV340 ) @ ( sK69_SY723 @ SV409 @ SV340 ) )
| ~ ( in @ ( sK69_SY723 @ SV409 @ SV340 ) @ SV340 ) )
| ( in @ ( sK68_C @ SV409 @ SV340 ) @ SV409 ) ) )
= $false )
| ( ( SV409
= ( union @ SV340 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2782]) ).
thf(2954,plain,
! [SV410: $i,SV341: $i] :
( ( ( ~ ! [SY1279: $i] :
( ! [SY1219: $i] :
( ~ ( in @ SY1279 @ SY1219 )
| ~ ( in @ SY1219 @ SV341 ) )
| ( in @ SY1279 @ SV410 ) )
| ~ ! [SY1281: $i] :
( ~ ( in @ SY1281 @ SV410 )
| ~ ( ~ ( in @ SY1281 @ ( sK67_D @ SY1281 @ SV410 @ SV341 ) )
| ~ ( in @ ( sK67_D @ SY1281 @ SV410 @ SV341 ) @ SV341 ) ) ) )
= $false )
| ( ( SV410
= ( union @ SV341 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2783]) ).
thf(2955,plain,
! [SV498: $i] :
( ( ( empty @ SV498 )
= $true )
| ( ( ! [SY1375: $i] :
( ~ ( element @ SY1375 @ SV498 )
| ( in @ SY1375 @ SV498 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2786]) ).
thf(2956,plain,
! [SV499: $i] :
( ( ( empty @ SV499 )
= $true )
| ( ( ! [SY1376: $i] :
( ~ ( in @ SY1376 @ SV499 )
| ( element @ SY1376 @ SV499 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2787]) ).
thf(2957,plain,
! [SV500: $i] :
( ( ( ~ ( empty @ SV500 ) )
= $true )
| ( ( ! [SY1377: $i] :
( ~ ( element @ SY1377 @ SV500 )
| ( empty @ SY1377 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2788]) ).
thf(2958,plain,
! [SV501: $i] :
( ( ( ~ ( empty @ SV501 ) )
= $true )
| ( ( ! [SY1378: $i] :
( ~ ( empty @ SY1378 )
| ( element @ SY1378 @ SV501 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2789]) ).
thf(2959,plain,
! [SV346: $i,SV413: $i] :
( ( ( ~ ( ~ ( in @ ( sK124_C @ SV413 @ SV346 ) @ SV413 )
| ~ ( subset @ ( sK124_C @ SV413 @ SV346 ) @ SV346 ) ) )
= $false )
| ( ( SV413
= ( powerset @ SV346 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2790]) ).
thf(2960,plain,
! [SV346: $i,SV413: $i] :
( ( ( ~ ( ( in @ ( sK124_C @ SV413 @ SV346 ) @ SV413 )
| ( subset @ ( sK124_C @ SV413 @ SV346 ) @ SV346 ) ) )
= $false )
| ( ( SV413
= ( powerset @ SV346 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2790]) ).
thf(2961,plain,
! [SV347: $i,SV414: $i] :
( ( ( ~ ! [SY1282: $i] :
( ~ ( in @ SY1282 @ SV414 )
| ( subset @ SY1282 @ SV347 ) )
| ~ ! [SY1283: $i] :
( ~ ( subset @ SY1283 @ SV347 )
| ( in @ SY1283 @ SV414 ) ) )
= $false )
| ( ( SV414
= ( powerset @ SV347 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2791]) ).
thf(2962,plain,
! [SV149: $i] :
( ( ( element @ ( sK118_B @ SV149 ) @ ( powerset @ SV149 ) )
= $true )
| ( ( empty @ SV149 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2792]) ).
thf(2963,plain,
! [SV149: $i] :
( ( ( ~ ( empty @ ( sK118_B @ SV149 ) ) )
= $true )
| ( ( empty @ SV149 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2793]) ).
thf(2964,plain,
! [SV415: $i,SV150: $i,SV465: $i] :
( ( ( relation_of2_as_subset @ SV465 @ SV150 @ SV415 )
= $false )
| ( ( ~ ( ~ ! [SY1331: $i] :
~ ( in @ ( ordered_pair @ SY1331 @ ( sK102_D @ SV465 @ SV415 @ SV150 ) ) @ SV465 )
| ~ ( in @ ( sK102_D @ SV465 @ SV415 @ SV150 ) @ SV415 ) )
| ( ( relation_rng_as_subset @ SV150 @ SV415 @ SV465 )
= SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2794]) ).
thf(2965,plain,
! [SV416: $i,SV150: $i,SV466: $i] :
( ( ( relation_of2_as_subset @ SV466 @ SV150 @ SV416 )
= $false )
| ( ( ( ( relation_rng_as_subset @ SV150 @ SV416 @ SV466 )
!= SV416 )
| ! [SY1332: $i] :
( ( in @ ( ordered_pair @ ( sK101_E @ SY1332 @ SV466 @ SV416 @ SV150 ) @ SY1332 ) @ SV466 )
| ~ ( in @ SY1332 @ SV416 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2795]) ).
thf(2966,plain,
! [SV151: $i,SV267: $i,SV467: $i,SV502: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV467 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV151 ) )
| ~ ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV267 ) ) ) )
| ~ ( ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
= SV467 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
= SV151 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
= SV267 ) ) ) )
= $true )
| ( ( SV502
= ( unordered_triple @ SV151 @ SV267 @ SV467 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2796]) ).
thf(2967,plain,
! [SV468: $i,SV267: $i,SV151: $i,SV503: $i] :
( ( ( ( SV503
!= ( unordered_triple @ SV151 @ SV267 @ SV468 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1379: $i] :
( ~ ( in @ SY1379 @ SV503 )
| ( SY1379 = SV468 )
| ( SY1379 = SV151 )
| ( SY1379 = SV267 ) )
| ~ ~ ( ~ ! [SY1380: $i] :
( ( SY1380 != SV468 )
| ( in @ SY1380 @ SV503 ) )
| ~ ~ ( ~ ! [SY1381: $i] :
( ( SY1381 != SV151 )
| ( in @ SY1381 @ SV503 ) )
| ~ ! [SY1382: $i] :
( ( SY1382 != SV267 )
| ( in @ SY1382 @ SV503 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2797]) ).
thf(2968,plain,
! [SV152: $i,SV417: $i] :
( ( ( subset @ SV417 @ ( sK106_B @ SV152 ) )
= $false )
| ( ( are_equipotent @ SV417 @ ( sK106_B @ SV152 ) )
= $true )
| ( ( in @ SV417 @ ( sK106_B @ SV152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2798]) ).
thf(2969,plain,
! [SV152: $i,SV544: $i] :
( ( ~ ( in @ SV544 @ ( sK106_B @ SV152 ) )
| ( in @ ( powerset @ SV544 ) @ ( sK106_B @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2799]) ).
thf(2970,plain,
! [SV152: $i] :
( ( ~ ! [SY969: $i,SY970: $i] :
( ~ ( in @ SY969 @ ( sK106_B @ SV152 ) )
| ~ ( subset @ SY970 @ SY969 )
| ( in @ SY970 @ ( sK106_B @ SV152 ) ) )
| ~ ( in @ SV152 @ ( sK106_B @ SV152 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2800]) ).
thf(2971,plain,
! [SV153: $i,SV418: $i] :
( ( ( in @ SV418 @ SV153 )
= $false )
| ( ( ~ ( ordinal @ SV418 ) )
= $true )
| ( ( in @ SV418 @ ( sK107_B @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2801]) ).
thf(2972,plain,
! [SV153: $i,SV545: $i] :
( ( ~ ( in @ SV545 @ ( sK107_B @ SV153 ) )
| ( in @ SV545 @ SV153 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2802]) ).
thf(2973,plain,
! [SV153: $i,SV546: $i] :
( ( ~ ( in @ SV546 @ ( sK107_B @ SV153 ) )
| ( ordinal @ SV546 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2803]) ).
thf(2974,plain,
! [SV154: $i,SV504: $i] :
( ( ( ~ ( relation @ SV504 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK72_C @ SV504 @ SV154 ) @ ( sK73_SY724 @ SV504 @ SV154 ) ) @ SV154 )
| ~ ~ ( in @ ( ordered_pair @ ( sK72_C @ SV504 @ SV154 ) @ ( sK73_SY724 @ SV504 @ SV154 ) ) @ SV504 ) )
| ( subset @ SV154 @ SV504 ) )
= $true )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2804]) ).
thf(2975,plain,
! [SV154: $i,SV505: $i] :
( ( ( ~ ( relation @ SV505 ) )
= $true )
| ( ( ~ ( subset @ SV154 @ SV505 )
| ! [SY1383: $i,SY1384: $i] :
( ~ ( in @ ( ordered_pair @ SY1383 @ SY1384 ) @ SV154 )
| ( in @ ( ordered_pair @ SY1383 @ SY1384 ) @ SV505 ) ) )
= $true )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2805]) ).
thf(2976,plain,
! [SV268: $i,SV155: $i,SV547: $i] :
( ( ( ~ ( element @ SV547 @ ( powerset @ ( powerset @ SV155 ) ) )
| ~ ( ~ ( element @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ ( powerset @ SV155 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ SV547 )
| ~ ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SV547 @ SV268 @ SV155 ) ) @ SV268 ) )
| ~ ( ( in @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ SV547 )
| ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SV547 @ SV268 @ SV155 ) ) @ SV268 ) ) ) )
| ( SV547
= ( complements_of_subsets @ SV155 @ SV268 ) ) )
= $true )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2806]) ).
thf(2977,plain,
! [SV268: $i,SV155: $i,SV548: $i] :
( ( ( ~ ( element @ SV548 @ ( powerset @ ( powerset @ SV155 ) ) )
| ( SV548
!= ( complements_of_subsets @ SV155 @ SV268 ) )
| ~ ( ~ ! [SY1408: $i] :
( ~ ( element @ SY1408 @ ( powerset @ SV155 ) )
| ~ ( in @ SY1408 @ SV548 )
| ( in @ ( subset_complement @ SV155 @ SY1408 ) @ SV268 ) )
| ~ ! [SY1409: $i] :
( ~ ( element @ SY1409 @ ( powerset @ SV155 ) )
| ~ ( in @ ( subset_complement @ SV155 @ SY1409 ) @ SV268 )
| ( in @ SY1409 @ SV548 ) ) ) )
= $true )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2807]) ).
thf(2978,plain,
! [SV419: $i,SV348: $i] :
( ( ( SV348 = empty_set )
= $true )
| ( ( SV348
= ( singleton @ SV419 ) )
= $true )
| ( ( subset @ SV348 @ ( singleton @ SV419 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2808]) ).
thf(2979,plain,
! [SV506: $i] :
( ( ( ( SV506 != empty_set ) )
= $true )
| ( ( ! [SY1385: $i] : ( subset @ SV506 @ ( singleton @ SY1385 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2809]) ).
thf(2980,plain,
! [SV549: $i,SV507: $i] :
( ( ( SV507
!= ( singleton @ SV549 ) )
| ( subset @ SV507 @ ( singleton @ SV549 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2810]) ).
thf(2981,plain,
! [SV420: $i,SV349: $i] :
( ( ( SV349 = empty_set )
= $true )
| ( ( SV349
= ( singleton @ SV420 ) )
= $true )
| ( ( subset @ SV349 @ ( singleton @ SV420 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2811]) ).
thf(2982,plain,
! [SV508: $i] :
( ( ( ( SV508 != empty_set ) )
= $true )
| ( ( ! [SY1387: $i] : ( subset @ SV508 @ ( singleton @ SY1387 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2812]) ).
thf(2983,plain,
! [SV550: $i,SV509: $i] :
( ( ( SV509
!= ( singleton @ SV550 ) )
| ( subset @ SV509 @ ( singleton @ SV550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2813]) ).
thf(2984,plain,
! [SV156: $i,SV510: $i] :
( ( ( ~ ( element @ SV510 @ ( powerset @ SV156 ) ) )
= $true )
| ( ( v1_membered @ SV510 )
= $true )
| ( ( v2_membered @ SV156 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2816]) ).
thf(2985,plain,
! [SV156: $i,SV511: $i] :
( ( ( ~ ( element @ SV511 @ ( powerset @ SV156 ) ) )
= $true )
| ( ( v2_membered @ SV511 )
= $true )
| ( ( v2_membered @ SV156 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2817]) ).
thf(2986,plain,
! [SV423: $i,SV352: $i] :
( ( ( empty @ SV352 )
= $false )
| ( ( ~ ( relation @ SV423 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV352 @ SV423 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2818]) ).
thf(2987,plain,
! [SV424: $i,SV353: $i] :
( ( ( empty @ SV353 )
= $false )
| ( ( ~ ( relation @ SV424 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV353 @ SV424 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2819]) ).
thf(2988,plain,
! [SV425: $i] :
( ( ( ! [SY1288: $i] :
( ! [SY1289: $i] :
( ( SY1289 != SY1288 )
| ~ ( in @ SY1289 @ SV425 ) )
| ~ ( ordinal @ SY1288 )
| ( in @ SY1288 @ ( sK7_B @ SV425 ) ) ) )
= $true )
| ( sK12_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2820]) ).
thf(2989,plain,
! [SV425: $i] :
( ( ( ! [SY1290: $i] :
( ~ ( in @ SY1290 @ ( sK7_B @ SV425 ) )
| ~ ( ~ ~ ( ( ( sK8_D @ SY1290 @ SV425 )
!= SY1290 )
| ~ ( in @ ( sK8_D @ SY1290 @ SV425 ) @ SV425 ) )
| ~ ( ordinal @ SY1290 ) ) ) )
= $true )
| ( sK12_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[2821]) ).
thf(2990,plain,
( ( ( ~ ( ~ ~ ( ~ ~ ( ( sK9_B != sK10_SY601 )
| ~ ( ordinal @ sK10_SY601 ) )
| ( sK9_B != sK11_SY603 ) )
| ~ ( ordinal @ sK11_SY603 ) ) )
= $true )
| ( sK12_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2822]) ).
thf(2991,plain,
( ( ( ( sK10_SY601 != sK11_SY603 ) )
= $true )
| ( sK12_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[2823]) ).
thf(2992,plain,
! [SV426: $i,SV157: $i,SV469: $i] :
( ( ( relation @ SV469 )
= $false )
| ( ( ~ ( in @ SV157 @ SV469 )
| ~ ( in @ SV157 @ ( cartesian_product2 @ SV426 @ SV426 ) )
| ( in @ SV157 @ ( relation_restriction @ SV469 @ SV426 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2824]) ).
thf(2993,plain,
! [SV551: $i,SV157: $i] :
( ( ! [SY1410: $i] :
( ~ ( relation @ SY1410 )
| ~ ( in @ SV157 @ ( relation_restriction @ SY1410 @ SV551 ) )
| ( in @ SV157 @ SY1410 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2825]) ).
thf(2994,plain,
! [SV552: $i,SV157: $i] :
( ( ! [SY1411: $i] :
( ~ ( relation @ SY1411 )
| ~ ( in @ SV157 @ ( relation_restriction @ SY1411 @ SV552 ) )
| ( in @ SV157 @ ( cartesian_product2 @ SV552 @ SV552 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2826]) ).
thf(2995,plain,
! [SV158: $i] :
( ( ~ ! [SY991: $i,SY992: $i] :
( ~ ( relation_of2_as_subset @ SY992 @ SV158 @ SY991 )
| ( SY991 = empty_set )
| ( SV158
!= ( relation_dom_as_subset @ SV158 @ SY991 @ SY992 ) )
| ( quasi_total @ SY992 @ SV158 @ SY991 ) )
| ~ ! [SY993: $i,SY994: $i] :
( ~ ( relation_of2_as_subset @ SY994 @ SV158 @ SY993 )
| ( SY993 = empty_set )
| ~ ( quasi_total @ SY994 @ SV158 @ SY993 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SY993 @ SY994 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2827]) ).
thf(2996,plain,
! [SV158: $i] :
( ( ~ ! [SY995: $i,SY996: $i] :
( ~ ( relation_of2_as_subset @ SY996 @ SV158 @ SY995 )
| ( SV158 != empty_set )
| ( SV158
!= ( relation_dom_as_subset @ SV158 @ SY995 @ SY996 ) )
| ( quasi_total @ SY996 @ SV158 @ SY995 ) )
| ~ ! [SY997: $i,SY998: $i] :
( ~ ( relation_of2_as_subset @ SY998 @ SV158 @ SY997 )
| ( SV158 != empty_set )
| ~ ( quasi_total @ SY998 @ SV158 @ SY997 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SY997 @ SY998 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2828]) ).
thf(2997,plain,
! [SV553: $i,SV158: $i] :
( ( ! [SY1412: $i] :
( ~ ( relation_of2_as_subset @ SY1412 @ SV158 @ SV553 )
| ( SV553 != empty_set )
| ( SY1412 != empty_set )
| ( quasi_total @ SY1412 @ SV158 @ SV553 )
| ( SV158 = empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2829]) ).
thf(2998,plain,
! [SV554: $i,SV158: $i] :
( ( ! [SY1413: $i] :
( ~ ( relation_of2_as_subset @ SY1413 @ SV158 @ SV554 )
| ( SV554 != empty_set )
| ~ ( quasi_total @ SY1413 @ SV158 @ SV554 )
| ( SY1413 = empty_set )
| ( SV158 = empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2830]) ).
thf(2999,plain,
! [SV512: $i] :
( ( ( SV512 = empty_set )
= $true )
| ( ( ! [SY1389: $i] :
( ~ ( ~ ( ~ ( ~ ( in @ ( sK90_SY733 @ SY1389 @ SV512 ) @ SV512 )
| ~ ~ ( in @ ( sK89_C @ SY1389 @ SV512 ) @ ( sK90_SY733 @ SY1389 @ SV512 ) ) )
| ~ ( in @ ( sK89_C @ SY1389 @ SV512 ) @ SY1389 ) )
| ~ ( ! [SY1390: $i] :
( ~ ( in @ SY1390 @ SV512 )
| ( in @ ( sK89_C @ SY1389 @ SV512 ) @ SY1390 ) )
| ( in @ ( sK89_C @ SY1389 @ SV512 ) @ SY1389 ) ) )
| ( SY1389
= ( set_meet @ SV512 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2831]) ).
thf(3000,plain,
! [SV513: $i] :
( ( ( SV513 = empty_set )
= $true )
| ( ( ! [SY1391: $i] :
( ( SY1391
!= ( set_meet @ SV513 ) )
| ~ ( ~ ! [SY1392: $i] :
( ~ ( ~ ( in @ ( sK88_D @ SY1392 @ SY1391 @ SV513 ) @ SV513 )
| ~ ~ ( in @ SY1392 @ ( sK88_D @ SY1392 @ SY1391 @ SV513 ) ) )
| ( in @ SY1392 @ SY1391 ) )
| ~ ! [SY1393: $i] :
( ~ ( in @ SY1393 @ SY1391 )
| ! [SY1394: $i] :
( ~ ( in @ SY1394 @ SV513 )
| ( in @ SY1393 @ SY1394 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2832]) ).
thf(3001,plain,
! [SV514: $i] :
( ( ( ( SV514 != empty_set ) )
= $true )
| ( ( ! [SY1395: $i] :
( ( SY1395
!= ( set_meet @ SV514 ) )
| ( SY1395 = empty_set ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2833]) ).
thf(3002,plain,
! [SV515: $i] :
( ( ( ( SV515 != empty_set ) )
= $true )
| ( ( ! [SY1396: $i] :
( ( SY1396 != empty_set )
| ( SY1396
= ( set_meet @ SV515 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2834]) ).
thf(3003,plain,
! [SV159: $i,SV427: $i,SV470: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK82_D @ SV470 @ SV427 @ SV159 ) @ SV470 )
| ( ( sK82_D @ SV470 @ SV427 @ SV159 )
!= SV159 ) )
| ~ ( ~ ( in @ ( sK82_D @ SV470 @ SV427 @ SV159 ) @ SV470 )
| ( ( sK82_D @ SV470 @ SV427 @ SV159 )
!= SV427 ) ) )
| ~ ( ( in @ ( sK82_D @ SV470 @ SV427 @ SV159 ) @ SV470 )
| ( ( sK82_D @ SV470 @ SV427 @ SV159 )
= SV159 )
| ( ( sK82_D @ SV470 @ SV427 @ SV159 )
= SV427 ) ) )
= $false )
| ( ( SV470
= ( unordered_pair @ SV159 @ SV427 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2835]) ).
thf(3004,plain,
! [SV428: $i,SV159: $i,SV471: $i] :
( ( ( SV471
= ( unordered_pair @ SV159 @ SV428 ) )
= $false )
| ( ( ~ ( ~ ! [SY1339: $i] :
( ~ ( in @ SY1339 @ SV471 )
| ( SY1339 = SV159 )
| ( SY1339 = SV428 ) )
| ~ ~ ( ~ ! [SY1340: $i] :
( ( SY1340 != SV159 )
| ( in @ SY1340 @ SV471 ) )
| ~ ! [SY1341: $i] :
( ( SY1341 != SV428 )
| ( in @ SY1341 @ SV471 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2836]) ).
thf(3005,plain,
! [SV429: $i,SV354: $i] :
( ( ( empty @ SV354 )
= $false )
| ( ( ~ ( relation @ SV429 ) )
= $true )
| ( ( empty @ ( relation_composition @ SV429 @ SV354 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2837]) ).
thf(3006,plain,
! [SV430: $i,SV355: $i] :
( ( ( empty @ SV355 )
= $false )
| ( ( ~ ( relation @ SV430 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV430 @ SV355 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2838]) ).
thf(3007,plain,
! [SV160: $i,SV516: $i] :
( ( ( ~ ( element @ SV516 @ SV160 ) )
= $true )
| ( ( v1_xcmplx_0 @ SV516 )
= $true )
| ( ( v2_membered @ SV160 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2839]) ).
thf(3008,plain,
! [SV160: $i,SV517: $i] :
( ( ( ~ ( element @ SV517 @ SV160 ) )
= $true )
| ( ( v1_xreal_0 @ SV517 )
= $true )
| ( ( v2_membered @ SV160 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2840]) ).
thf(3009,plain,
! [SV358: $i] :
( ( ( ! [SY1235: $i,SY1236: $i] :
( ( sK93_B @ SV358 )
!= ( ordered_pair @ SY1235 @ SY1236 ) ) )
= $true )
| ( ( relation @ SV358 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2841]) ).
thf(3010,plain,
! [SV358: $i] :
( ( ( in @ ( sK93_B @ SV358 ) @ SV358 )
= $true )
| ( ( relation @ SV358 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2842]) ).
thf(3011,plain,
! [SV359: $i,SV518: $i] :
( ( ( SV518
= ( ordered_pair @ ( sK91_C @ SV518 @ SV359 ) @ ( sK92_SY735 @ SV518 @ SV359 ) ) )
= $true )
| ( ( ~ ( in @ SV518 @ SV359 ) )
= $true )
| ( ( relation @ SV359 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2843]) ).
thf(3012,plain,
! [SV269: $i,SV162: $i,SV555: $i] :
( ( ( ~ ( element @ SV555 @ ( powerset @ SV162 ) )
| ~ ( disjoint @ SV269 @ SV555 )
| ( subset @ SV269 @ ( subset_complement @ SV162 @ SV555 ) ) )
= $true )
| ( ( element @ SV269 @ ( powerset @ SV162 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2844]) ).
thf(3013,plain,
! [SV269: $i,SV162: $i,SV556: $i] :
( ( ( ~ ( element @ SV556 @ ( powerset @ SV162 ) )
| ~ ( subset @ SV269 @ ( subset_complement @ SV162 @ SV556 ) )
| ( disjoint @ SV269 @ SV556 ) )
= $true )
| ( ( element @ SV269 @ ( powerset @ SV162 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2845]) ).
thf(3014,plain,
! [SV433: $i,SV163: $i,SV472: $i] :
( ( ( relation_of2 @ SV472 @ SV163 @ SV433 )
= $false )
| ( ( relation_of2_as_subset @ SV472 @ SV163 @ SV433 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2848]) ).
thf(3015,plain,
! [SV434: $i,SV163: $i,SV473: $i] :
( ( ( relation_of2_as_subset @ SV473 @ SV163 @ SV434 )
= $false )
| ( ( relation_of2 @ SV473 @ SV163 @ SV434 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2849]) ).
thf(3016,plain,
! [SV364: $i,SV435: $i] :
( ( ( ~ ( ( ( sK87_C @ SV435 @ SV364 )
!= SV364 )
| ~ ( in @ ( sK87_C @ SV435 @ SV364 ) @ SV435 ) ) )
= $false )
| ( ( SV435
= ( singleton @ SV364 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2850]) ).
thf(3017,plain,
! [SV364: $i,SV435: $i] :
( ( ( ~ ( ( ( sK87_C @ SV435 @ SV364 )
= SV364 )
| ( in @ ( sK87_C @ SV435 @ SV364 ) @ SV435 ) ) )
= $false )
| ( ( SV435
= ( singleton @ SV364 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2850]) ).
thf(3018,plain,
! [SV436: $i,SV365: $i] :
( ( ( ~ ! [SY1299: $i] :
( ( SY1299 != SV365 )
| ( in @ SY1299 @ SV436 ) )
| ~ ! [SY1300: $i] :
( ~ ( in @ SY1300 @ SV436 )
| ( SY1300 = SV365 ) ) )
= $false )
| ( ( SV436
= ( singleton @ SV365 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2851]) ).
thf(3019,plain,
! [SV474: $i,SV437: $i,SV164: $i] :
( ( ( ~ ( ! [SY1342: $i,SY1343: $i] :
( ~ ( in @ SY1342 @ SV164 )
| ~ ( in @ SY1343 @ SV437 )
| ( ( sK78_D @ SV474 @ SV437 @ SV164 )
!= ( ordered_pair @ SY1342 @ SY1343 ) ) )
| ~ ( in @ ( sK78_D @ SV474 @ SV437 @ SV164 ) @ SV474 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK79_SY729 @ SV474 @ SV437 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK80_SY731 @ SV474 @ SV437 @ SV164 ) @ SV437 ) )
| ( ( sK78_D @ SV474 @ SV437 @ SV164 )
!= ( ordered_pair @ ( sK79_SY729 @ SV474 @ SV437 @ SV164 ) @ ( sK80_SY731 @ SV474 @ SV437 @ SV164 ) ) ) )
| ( in @ ( sK78_D @ SV474 @ SV437 @ SV164 ) @ SV474 ) ) )
= $false )
| ( ( SV474
= ( cartesian_product2 @ SV164 @ SV437 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2852]) ).
thf(3020,plain,
! [SV438: $i,SV164: $i,SV475: $i] :
( ( ( SV475
= ( cartesian_product2 @ SV164 @ SV438 ) )
= $false )
| ( ( ~ ( ~ ! [SY1344: $i] :
( ! [SY1306: $i,SY1307: $i] :
( ~ ( in @ SY1306 @ SV164 )
| ~ ( in @ SY1307 @ SV438 )
| ( SY1344
!= ( ordered_pair @ SY1306 @ SY1307 ) ) )
| ( in @ SY1344 @ SV475 ) )
| ~ ! [SY1347: $i] :
( ~ ( in @ SY1347 @ SV475 )
| ~ ( ~ ~ ( ~ ( in @ ( sK76_E @ SY1347 @ SV475 @ SV438 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK77_SY726 @ SY1347 @ SV475 @ SV438 @ SV164 ) @ SV438 ) )
| ( SY1347
!= ( ordered_pair @ ( sK76_E @ SY1347 @ SV475 @ SV438 @ SV164 ) @ ( sK77_SY726 @ SY1347 @ SV475 @ SV438 @ SV164 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2853]) ).
thf(3021,plain,
! [SV366: $i,SV439: $i] :
( ( ( ~ ( in @ ( sK71_C @ SV439 @ SV366 ) @ SV366 ) )
= $false )
| ( ( subset @ SV366 @ SV439 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2854]) ).
thf(3022,plain,
! [SV366: $i,SV439: $i] :
( ( ( ~ ~ ( in @ ( sK71_C @ SV439 @ SV366 ) @ SV439 ) )
= $false )
| ( ( subset @ SV366 @ SV439 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2854]) ).
thf(3023,plain,
! [SV440: $i,SV367: $i,SV557: $i] :
( ( ( ~ ( in @ SV557 @ SV367 )
| ( in @ SV557 @ SV440 ) )
= $true )
| ( ( subset @ SV367 @ SV440 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2855]) ).
thf(3024,plain,
! [SV441: $i,SV165: $i,SV476: $i] :
( ( ( relation_of2 @ SV476 @ SV165 @ SV441 )
= $false )
| ( ( subset @ SV476 @ ( cartesian_product2 @ SV165 @ SV441 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2856]) ).
thf(3025,plain,
! [SV442: $i,SV165: $i,SV477: $i] :
( ( ( subset @ SV477 @ ( cartesian_product2 @ SV165 @ SV442 ) )
= $false )
| ( ( relation_of2 @ SV477 @ SV165 @ SV442 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2857]) ).
thf(3026,plain,
! [SV166: $i,SV443: $i] :
( ( ( subset @ SV443 @ ( sK3_B @ SV166 ) )
= $false )
| ( ( are_equipotent @ SV443 @ ( sK3_B @ SV166 ) )
= $true )
| ( ( in @ SV443 @ ( sK3_B @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2858]) ).
thf(3027,plain,
! [SV166: $i,SV558: $i] :
( ( ~ ( ~ ! [SY1414: $i] :
( ~ ( subset @ SY1414 @ SV558 )
| ( in @ SY1414 @ ( sK4_SY591 @ SV558 @ SV166 ) ) )
| ~ ( in @ ( sK4_SY591 @ SV558 @ SV166 ) @ ( sK3_B @ SV166 ) ) )
| ~ ( in @ SV558 @ ( sK3_B @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2859]) ).
thf(3028,plain,
! [SV166: $i] :
( ( ~ ! [SY1036: $i,SY1037: $i] :
( ~ ( in @ SY1036 @ ( sK3_B @ SV166 ) )
| ~ ( subset @ SY1037 @ SY1036 )
| ( in @ SY1037 @ ( sK3_B @ SV166 ) ) )
| ~ ( in @ SV166 @ ( sK3_B @ SV166 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2860]) ).
thf(3029,plain,
! [SV167: $i,SV444: $i,SV478: $i] :
( ( ( relation_of2_as_subset @ SV478 @ SV444 @ SV167 )
= $false )
| ( ( ~ ( ~ ! [SY1348: $i] :
~ ( in @ ( ordered_pair @ ( sK104_D @ SV478 @ SV444 @ SV167 ) @ SY1348 ) @ SV478 )
| ~ ( in @ ( sK104_D @ SV478 @ SV444 @ SV167 ) @ SV444 ) )
| ( ( relation_dom_as_subset @ SV444 @ SV167 @ SV478 )
= SV444 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2861]) ).
thf(3030,plain,
! [SV167: $i,SV445: $i,SV479: $i] :
( ( ( relation_of2_as_subset @ SV479 @ SV445 @ SV167 )
= $false )
| ( ( ( ( relation_dom_as_subset @ SV445 @ SV167 @ SV479 )
!= SV445 )
| ! [SY1349: $i] :
( ( in @ ( ordered_pair @ SY1349 @ ( sK103_E @ SY1349 @ SV479 @ SV445 @ SV167 ) ) @ SV479 )
| ~ ( in @ SY1349 @ SV445 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2862]) ).
thf(3031,plain,
! [SV168: $i] :
( ( ( ~ ( ~ ~ ( ( ( sK27_SY634 @ SV168 )
!= ( singleton @ ( sK26_B @ SV168 ) ) )
| ~ ( in @ ( sK26_B @ SV168 ) @ SV168 ) )
| ~ ( in @ ( sK26_B @ SV168 ) @ SV168 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) )
| ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2863]) ).
thf(3032,plain,
! [SV168: $i] :
( ( ( ( sK28_SY636 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) )
| ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2864]) ).
thf(3033,plain,
! [SV168: $i] :
( ( ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) ) )
= $false )
| ( ( ( sK27_SY634 @ SV168 )
= ( sK28_SY636 @ SV168 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2865]) ).
thf(3034,plain,
! [SV168: $i] :
( ( ( ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) )
= $false )
| ( ( ( sK27_SY634 @ SV168 )
= ( sK28_SY636 @ SV168 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2865]) ).
thf(3035,plain,
! [SV519: $i,SV270: $i,SV480: $i,SV169: $i] :
( ( ( ~ ( in @ SV169 @ SV480 )
| ~ ( in @ SV270 @ SV519 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SV480 @ SV519 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2866]) ).
thf(3036,plain,
! [SV270: $i,SV169: $i] :
( ( ! [SY1166: $i] :
( ! [SY1167: $i] :
~ ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SY1166 @ SY1167 ) )
| ( in @ SV169 @ SY1166 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2867]) ).
thf(3037,plain,
! [SV270: $i,SV169: $i] :
( ( ! [SY1168: $i,SY1169: $i] :
( ~ ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SY1168 @ SY1169 ) )
| ( in @ SV270 @ SY1169 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2868]) ).
thf(3038,plain,
! [SV271: $i,SV481: $i,SV170: $i] :
( ( ( ~ ! [SY1351: $i] :
( ! [SY1352: $i,SY1353: $i] :
( ( ( ordered_pair @ SY1352 @ SY1353 )
!= SY1351 )
| ~ ( in @ SY1352 @ SV170 )
| ! [SY1354: $i] :
( ~ ( ~ ( in @ ( sK115_I @ SY1354 @ SY1353 @ SY1352 @ SY1351 @ SV481 @ SV271 @ SV170 ) @ SY1354 )
| ~ ~ ( in @ ( ordered_pair @ SY1353 @ ( sK115_I @ SY1354 @ SY1353 @ SY1352 @ SY1351 @ SV481 @ SV271 @ SV170 ) ) @ SV271 ) )
| ( SY1352 != SY1354 )
| ~ ( in @ SY1353 @ SY1354 ) ) )
| ~ ( in @ SY1351 @ ( cartesian_product2 @ SV170 @ SV481 ) )
| ( in @ SY1351 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) ) ) )
= $false )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2869]) ).
thf(3039,plain,
! [SV170: $i,SV271: $i,SV481: $i] :
( ( ( ~ ~ ( ~ ! [SY1355: $i] :
( ~ ( in @ SY1355 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
| ~ ( ~ ~ ( ( ( ordered_pair @ ( sK112_F @ SY1355 @ SV481 @ SV271 @ SV170 ) @ ( sK113_SY768 @ SY1355 @ SV481 @ SV271 @ SV170 ) )
!= SY1355 )
| ~ ( in @ ( sK112_F @ SY1355 @ SV481 @ SV271 @ SV170 ) @ SV170 ) )
| ~ ~ ( ~ ! [SY1356: $i] :
( ~ ( in @ SY1356 @ ( sK114_SY771 @ SY1355 @ SV481 @ SV271 @ SV170 ) )
| ( in @ ( ordered_pair @ ( sK113_SY768 @ SY1355 @ SV481 @ SV271 @ SV170 ) @ SY1356 ) @ SV271 ) )
| ~ ~ ( ( ( sK112_F @ SY1355 @ SV481 @ SV271 @ SV170 )
!= ( sK114_SY771 @ SY1355 @ SV481 @ SV271 @ SV170 ) )
| ~ ( in @ ( sK113_SY768 @ SY1355 @ SV481 @ SV271 @ SV170 ) @ ( sK114_SY771 @ SY1355 @ SV481 @ SV271 @ SV170 ) ) ) ) ) )
| ~ ! [SY1357: $i] :
( ~ ( in @ SY1357 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
| ( in @ SY1357 @ ( cartesian_product2 @ SV170 @ SV481 ) ) ) ) )
= $false )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2869]) ).
thf(3040,plain,
! [SV368: $i] :
( ( ( ~ ( ~ ( ( ( sK74_B @ SV368 )
!= ( sK75_SY725 @ SV368 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK74_B @ SV368 ) @ SV368 )
| ~ ( in @ ( sK75_SY725 @ SV368 ) @ SV368 ) )
| ~ ~ ( in @ ( sK74_B @ SV368 ) @ ( sK75_SY725 @ SV368 ) ) ) ) )
= $true )
| ( ( epsilon_connected @ SV368 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2870]) ).
thf(3041,plain,
! [SV368: $i] :
( ( ( ~ ( in @ ( sK75_SY725 @ SV368 ) @ ( sK74_B @ SV368 ) ) )
= $true )
| ( ( epsilon_connected @ SV368 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2871]) ).
thf(3042,plain,
! [SV369: $i,SV559: $i,SV520: $i] :
( ( ( ( SV520 = SV559 )
| ~ ( in @ SV520 @ SV369 )
| ~ ( in @ SV559 @ SV369 )
| ( in @ SV520 @ SV559 )
| ( in @ SV559 @ SV520 ) )
= $true )
| ( ( epsilon_connected @ SV369 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2872]) ).
thf(3043,plain,
! [SV521: $i] :
( ( ( ~ ( v3_membered @ SV521 ) )
= $true )
| ( ( ! [SY1398: $i] : ( v1_membered @ ( set_difference @ SV521 @ SY1398 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2873]) ).
thf(3044,plain,
! [SV522: $i] :
( ( ( ~ ( v3_membered @ SV522 ) )
= $true )
| ( ( ! [SY1399: $i] : ( v2_membered @ ( set_difference @ SV522 @ SY1399 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2874]) ).
thf(3045,plain,
! [SV171: $i,SV524: $i] :
( ( ( ~ ( relation @ SV524 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV171 )
| ~ ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV524 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV171 )
| ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV524 ) ) )
| ( SV171 = SV524 ) )
= $true )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2876]) ).
thf(3046,plain,
! [SV171: $i,SV525: $i] :
( ( ( ~ ( relation @ SV525 ) )
= $true )
| ( ( ( SV171 != SV525 )
| ~ ( ~ ! [SY1400: $i,SY1401: $i] :
( ~ ( in @ ( ordered_pair @ SY1400 @ SY1401 ) @ SV171 )
| ( in @ ( ordered_pair @ SY1400 @ SY1401 ) @ SV525 ) )
| ~ ! [SY1402: $i,SY1403: $i] :
( ~ ( in @ ( ordered_pair @ SY1402 @ SY1403 ) @ SV525 )
| ( in @ ( ordered_pair @ SY1402 @ SY1403 ) @ SV171 ) ) ) )
= $true )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2877]) ).
thf(3047,plain,
! [SV371: $i,SV446: $i] :
( ( ( ~ ( in @ ( sK98_C @ SV446 @ SV371 ) @ SV371 ) )
= $false )
| ( ( disjoint @ SV371 @ SV446 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2878]) ).
thf(3048,plain,
! [SV371: $i,SV446: $i] :
( ( ( ~ ( in @ ( sK98_C @ SV446 @ SV371 ) @ SV446 ) )
= $false )
| ( ( disjoint @ SV371 @ SV446 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2878]) ).
thf(3049,plain,
! [SV447: $i,SV372: $i,SV526: $i] :
( ( ( ~ ( in @ SV526 @ SV372 ) )
= $true )
| ( ( ~ ( in @ SV526 @ SV447 ) )
= $true )
| ( ( ~ ( disjoint @ SV372 @ SV447 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2879]) ).
thf(3050,plain,
! [SV451: $i,SV376: $i,SV527: $i] :
( ( ( in @ SV527 @ ( set_intersection2 @ SV376 @ SV451 ) )
= $false )
| ( ( ~ ( disjoint @ SV376 @ SV451 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2882]) ).
thf(3051,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK35_D @ SV272 @ SV172 )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1178: $i] :
( ~ ( in @ SY1178 @ ( sK43_SY691 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SY1178 ) @ SV272 ) )
| ~ ~ ( ( ( sK41_SY666 @ SV272 @ SV172 )
!= ( sK43_SY691 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) ) ) ) ) )
| ( ( sK35_D @ SV272 @ SV172 )
!= ( sK37_SY665 @ SV272 @ SV172 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
!= ( sK37_SY665 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1179: $i] :
( ~ ( in @ SY1179 @ ( sK40_SY685 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SY1179 ) @ SV272 ) )
| ~ ~ ( ( ( sK38_SY678 @ SV272 @ SV172 )
!= ( sK40_SY685 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) ) ) ) ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2883]) ).
thf(3052,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ( ( ( sK36_SY655 @ SV272 @ SV172 )
!= ( sK37_SY665 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2883]) ).
thf(3053,plain,
! [SV530: $i,SV273: $i,SV482: $i,SV173: $i] :
( ( ( ~ ( in @ SV173 @ SV482 )
| ~ ( in @ SV273 @ SV530 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SV482 @ SV530 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2886]) ).
thf(3054,plain,
! [SV273: $i,SV173: $i] :
( ( ! [SY1190: $i] :
( ! [SY1191: $i] :
~ ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SY1190 @ SY1191 ) )
| ( in @ SV173 @ SY1190 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2887]) ).
thf(3055,plain,
! [SV273: $i,SV173: $i] :
( ( ! [SY1192: $i,SY1193: $i] :
( ~ ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SY1192 @ SY1193 ) )
| ( in @ SV273 @ SY1193 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2888]) ).
thf(3056,plain,
! [SV174: $i,SV274: $i] :
( ( relation @ ( sK56_C @ SV274 @ SV174 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2889]) ).
thf(3057,plain,
! [SV174: $i,SV274: $i] :
( ( relation_of2 @ ( sK56_C @ SV274 @ SV174 ) @ SV174 @ SV274 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2890]) ).
thf(3058,plain,
! [SV533: $i] :
( ( ( ~ ( v3_membered @ SV533 ) )
= $true )
| ( ( ! [SY1404: $i] : ( v1_membered @ ( set_intersection2 @ SV533 @ SY1404 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2893]) ).
thf(3059,plain,
! [SV534: $i] :
( ( ( ~ ( v3_membered @ SV534 ) )
= $true )
| ( ( ! [SY1405: $i] : ( v2_membered @ ( set_intersection2 @ SV534 @ SY1405 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2894]) ).
thf(3060,plain,
! [SV275: $i,SV176: $i,SV483: $i] :
( ( ( ! [SY1359: $i,SY1360: $i] :
( ( ( ordered_pair @ SY1359 @ SY1360 )
!= SV483 )
| ~ ( in @ SY1359 @ SV176 )
| ( SY1360
!= ( singleton @ SY1359 ) ) ) )
= $true )
| ( ( ~ ( in @ SV483 @ ( cartesian_product2 @ SV176 @ SV275 ) ) )
= $true )
| ( ( in @ SV483 @ ( sK108_C @ SV275 @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2900]) ).
thf(3061,plain,
! [SV176: $i,SV275: $i] :
( ( ! [SY1197: $i] :
( ~ ( in @ SY1197 @ ( sK108_C @ SV275 @ SV176 ) )
| ~ ( ~ ~ ( ( ( ordered_pair @ ( sK109_E @ SY1197 @ SV275 @ SV176 ) @ ( sK110_SY756 @ SY1197 @ SV275 @ SV176 ) )
!= SY1197 )
| ~ ( in @ ( sK109_E @ SY1197 @ SV275 @ SV176 ) @ SV176 ) )
| ( ( sK110_SY756 @ SY1197 @ SV275 @ SV176 )
!= ( singleton @ ( sK109_E @ SY1197 @ SV275 @ SV176 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2901]) ).
thf(3062,plain,
! [SV176: $i,SV275: $i] :
( ( ! [SY1198: $i] :
( ~ ( in @ SY1198 @ ( sK108_C @ SV275 @ SV176 ) )
| ( in @ SY1198 @ ( cartesian_product2 @ SV176 @ SV275 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2902]) ).
thf(3063,plain,
! [SV178: $i,SV277: $i] :
( ( ( in @ ( sK6_C @ SV277 @ SV178 ) @ SV178 )
= $false )
| ( ( ~ ( in @ ( sK6_C @ SV277 @ SV178 ) @ SV277 ) )
= $true )
| ( ( SV178 = SV277 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2904]) ).
thf(3064,plain,
! [SV454: $i,SV560: $i,SV179: $i] :
( ( ( subset @ ( cartesian_product2 @ SV179 @ SV560 ) @ ( cartesian_product2 @ SV454 @ SV560 ) )
= $true )
| ( ( subset @ SV179 @ SV454 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2906]) ).
thf(3065,plain,
! [SV455: $i,SV179: $i,SV561: $i] :
( ( ( subset @ ( cartesian_product2 @ SV561 @ SV179 ) @ ( cartesian_product2 @ SV561 @ SV455 ) )
= $true )
| ( ( subset @ SV179 @ SV455 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2907]) ).
thf(3066,plain,
! [SV180: $i,SV456: $i,SV484: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV484 )
| ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV180 ) )
| ~ ( ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV484 )
| ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV456 ) ) )
| ~ ( ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV484 )
| ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV180 )
| ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV456 ) ) )
= $false )
| ( ( SV484
= ( set_union2 @ SV180 @ SV456 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2908]) ).
thf(3067,plain,
! [SV457: $i,SV180: $i,SV485: $i] :
( ( ( SV485
= ( set_union2 @ SV180 @ SV457 ) )
= $false )
| ( ( ~ ( ~ ! [SY1361: $i] :
( ~ ( in @ SY1361 @ SV485 )
| ( in @ SY1361 @ SV180 )
| ( in @ SY1361 @ SV457 ) )
| ~ ~ ( ~ ! [SY1362: $i] :
( ~ ( in @ SY1362 @ SV180 )
| ( in @ SY1362 @ SV485 ) )
| ~ ! [SY1363: $i] :
( ~ ( in @ SY1363 @ SV457 )
| ( in @ SY1363 @ SV485 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2909]) ).
thf(3068,plain,
! [SV5: $i,SV278: $i,SV458: $i] :
( ( ( in @ SV458 @ SV278 )
= $true )
| ( ( in @ SV458 @ ( subset_complement @ SV5 @ SV278 ) )
= $true )
| ( ( element @ SV458 @ SV5 )
= $false )
| ( ( element @ SV278 @ ( powerset @ SV5 ) )
= $false )
| ( ( SV5 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2910]) ).
thf(3069,plain,
! [SV302: $i,SV96: $i,SV246: $i] :
( ( ( element @ SV246 @ ( the_carrier @ SV96 ) )
= $false )
| ( ( empty_carrier @ SV96 )
= $true )
| ( ( join_semilatt_str @ SV96 )
= $false )
| ( ( ~ ( element @ SV302 @ ( the_carrier @ SV96 ) ) )
= $true )
| ( ( element @ ( join @ SV96 @ SV246 @ SV302 ) @ ( the_carrier @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2918]) ).
thf(3070,plain,
! [SV303: $i,SV98: $i,SV247: $i] :
( ( ( element @ SV247 @ ( the_carrier @ SV98 ) )
= $false )
| ( ( empty_carrier @ SV98 )
= $true )
| ( ( meet_semilatt_str @ SV98 )
= $false )
| ( ( ~ ( element @ SV303 @ ( the_carrier @ SV98 ) ) )
= $true )
| ( ( element @ ( meet @ SV98 @ SV247 @ SV303 ) @ ( the_carrier @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2919]) ).
thf(3071,plain,
! [SV538: $i,SV486: $i] :
( ( ( ~ ( proper_subset @ SV486 @ SV538 ) )
= $true )
| ( ( ( SV486 != SV538 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2921]) ).
thf(3072,plain,
! [SV539: $i,SV487: $i] :
( ( ( ~ ( proper_subset @ SV487 @ SV539 ) )
= $true )
| ( ( subset @ SV487 @ SV539 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2922]) ).
thf(3073,plain,
! [SV139: $i] :
( ( ( ~ ~ ( ( ( sK17_C @ SV139 )
!= ( sK18_SY613 @ SV139 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
!= ( sK18_SY613 @ SV139 ) )
| ~ ( in @ ( sK22_SY620 @ SV139 ) @ SV139 ) )
| ( ( sK23_SY629 @ SV139 )
!= ( singleton @ ( sK22_SY620 @ SV139 ) ) ) ) )
| ( ( sK17_C @ SV139 )
!= ( sK19_SY619 @ SV139 ) ) )
= $false )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2923]) ).
thf(3074,plain,
! [SV139: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
!= ( sK19_SY619 @ SV139 ) )
| ~ ( in @ ( sK20_SY626 @ SV139 ) @ SV139 ) )
| ( ( sK21_SY628 @ SV139 )
!= ( singleton @ ( sK20_SY626 @ SV139 ) ) ) )
= $false )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2924]) ).
thf(3075,plain,
! [SV488: $i,SV139: $i] :
( ( ( ~ ! [SY1366: $i] :
( ! [SY1367: $i] :
( ( SY1367 != SY1366 )
| ~ ( in @ SY1367 @ ( cartesian_product2 @ SV139 @ SV488 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1366 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1366 @ ( sK13_C @ SV488 @ SV139 ) ) ) )
= $false )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2925]) ).
thf(3076,plain,
! [SV139: $i,SV488: $i] :
( ( ( ~ ! [SY1370: $i] :
( ~ ( in @ SY1370 @ ( sK13_C @ SV488 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1370 @ SV488 @ SV139 )
!= SY1370 )
| ~ ( in @ ( sK16_E @ SY1370 @ SV488 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV488 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1370 @ SV488 @ SV139 ) @ ( sK15_SY612 @ SY1370 @ SV488 @ SV139 ) )
!= SY1370 )
| ~ ( in @ ( sK14_J @ SY1370 @ SV488 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1370 @ SV488 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1370 @ SV488 @ SV139 ) ) ) ) ) ) )
= $false )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2925]) ).
thf(3077,plain,
! [SV489: $i] :
( ( ( v3_membered @ SV489 )
= $false )
| ( ( ! [SY1371: $i] : ( v1_membered @ ( set_intersection2 @ SY1371 @ SV489 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2927]) ).
thf(3078,plain,
! [SV490: $i] :
( ( ( v3_membered @ SV490 )
= $false )
| ( ( ! [SY1372: $i] : ( v2_membered @ ( set_intersection2 @ SY1372 @ SV490 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2928]) ).
thf(3079,plain,
! [SV399: $i,SV460: $i,SV142: $i] :
( ( ( in @ SV142 @ SV460 )
= $false )
| ( ( ~ ( in @ SV399 @ SV460 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV142 @ SV399 ) @ SV460 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2930]) ).
thf(3080,plain,
! [SV562: $i,SV540: $i,SV142: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV142 @ SV540 ) @ SV562 )
| ( in @ SV142 @ SV562 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2931]) ).
thf(3081,plain,
! [SV563: $i,SV541: $i,SV142: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV142 @ SV541 ) @ SV563 )
| ( in @ SV541 @ SV563 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2932]) ).
thf(3082,plain,
! [SV143: $i,SV400: $i,SV461: $i] :
( ( ( ~ ( ~ ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV143 )
| ~ ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV400 )
| ~ ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV461 ) ) )
= $false )
| ( ( SV461
= ( set_intersection2 @ SV143 @ SV400 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2933]) ).
thf(3083,plain,
! [SV143: $i,SV400: $i,SV461: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV143 )
| ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV461 ) )
| ~ ( ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV400 )
| ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV461 ) ) ) )
= $false )
| ( ( SV461
= ( set_intersection2 @ SV143 @ SV400 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2933]) ).
thf(3084,plain,
! [SV462: $i,SV401: $i,SV143: $i] :
( ( ( ~ ! [SY1325: $i] :
( ~ ( in @ SY1325 @ SV143 )
| ~ ( in @ SY1325 @ SV401 )
| ( in @ SY1325 @ SV462 ) )
| ~ ~ ( ~ ! [SY1326: $i] :
( ~ ( in @ SY1326 @ SV462 )
| ( in @ SY1326 @ SV143 ) )
| ~ ! [SY1327: $i] :
( ~ ( in @ SY1327 @ SV462 )
| ( in @ SY1327 @ SV401 ) ) ) )
= $false )
| ( ( SV462
= ( set_intersection2 @ SV143 @ SV401 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2934]) ).
thf(3085,plain,
! [SV144: $i] :
( ( ( ! [SY930: $i] :
( ~ ( element @ SY930 @ ( powerset @ SV144 ) )
| ( v1_membered @ SY930 ) ) )
= $true )
| ( ( v3_membered @ SV144 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2935]) ).
thf(3086,plain,
! [SV144: $i] :
( ( ( ! [SY931: $i] :
( ~ ( element @ SY931 @ ( powerset @ SV144 ) )
| ( v2_membered @ SY931 ) ) )
= $true )
| ( ( v3_membered @ SV144 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2936]) ).
thf(3087,plain,
! [SV144: $i,SV492: $i] :
( ( ( element @ SV492 @ ( powerset @ SV144 ) )
= $false )
| ( ( v3_membered @ SV492 )
= $true )
| ( ( v3_membered @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2937]) ).
thf(3088,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1142: $i] :
( ~ ( in @ SY1142 @ ( sK52_SY712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SY1142 ) @ SV265 ) )
| ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK52_SY712 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) ) ) )
| ~ ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 ) )
| ~ ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 ) )
| ~ ~ ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ ( sK51_SY718 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SY1143 ) @ SV265 ) )
| ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK51_SY718 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2938]) ).
thf(3089,plain,
! [SV145: $i,SV265: $i] :
( ( ( ( ( sK49_SY705 @ SV265 @ SV145 )
!= ( sK50_SY711 @ SV265 @ SV145 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2939]) ).
thf(3090,plain,
! [SV330: $i,SV402: $i] :
( ( ( subset @ SV402 @ SV330 )
= $false )
| ( ( subset @ SV330 @ SV402 )
= $false )
| ( ( SV330 = SV402 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2940]) ).
thf(3091,plain,
! [SV542: $i,SV493: $i] :
( ( ( ( SV493 != SV542 ) )
= $true )
| ( ( subset @ SV493 @ SV542 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2941]) ).
thf(3092,plain,
! [SV543: $i,SV494: $i] :
( ( ( ( SV494 != SV543 ) )
= $true )
| ( ( subset @ SV543 @ SV494 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2942]) ).
thf(3093,plain,
! [SV146: $i,SV266: $i,SV495: $i] :
( ( ( in @ SV495 @ SV266 )
= $false )
| ( ( ~ ( in @ SV495 @ ( sK5_C @ SV266 @ SV146 ) ) )
= $true )
| ( ( ~ ( in @ SV146 @ SV266 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2943]) ).
thf(3094,plain,
! [SV331: $i] :
( ( ( subset @ ( sK85_B @ SV331 ) @ SV331 )
= $false )
| ( ( epsilon_transitive @ SV331 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2945]) ).
thf(3095,plain,
! [SV332: $i,SV496: $i] :
( ( ( in @ SV496 @ SV332 )
= $false )
| ( ( subset @ SV496 @ SV332 )
= $true )
| ( ( epsilon_transitive @ SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2946]) ).
thf(3096,plain,
! [SV147: $i,SV403: $i,SV463: $i] :
( ( ( ~ ( ~ ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV147 )
| ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV403 )
| ~ ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV463 ) ) )
= $false )
| ( ( SV463
= ( set_difference @ SV147 @ SV403 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2947]) ).
thf(3097,plain,
! [SV147: $i,SV403: $i,SV463: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV147 )
| ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV463 ) )
| ~ ( ~ ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV403 )
| ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV463 ) ) ) )
= $false )
| ( ( SV463
= ( set_difference @ SV147 @ SV403 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2947]) ).
thf(3098,plain,
! [SV464: $i,SV404: $i,SV147: $i] :
( ( ( ~ ! [SY1328: $i] :
( ~ ( in @ SY1328 @ SV147 )
| ( in @ SY1328 @ SV404 )
| ( in @ SY1328 @ SV464 ) )
| ~ ~ ( ~ ! [SY1329: $i] :
( ~ ( in @ SY1329 @ SV464 )
| ( in @ SY1329 @ SV147 ) )
| ~ ! [SY1330: $i] :
( ~ ( in @ SY1330 @ SV464 )
| ~ ( in @ SY1330 @ SV404 ) ) ) )
= $false )
| ( ( SV464
= ( set_difference @ SV147 @ SV404 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2948]) ).
thf(3099,plain,
! [SV148: $i,SV335: $i] :
( ( ( ~ ! [SY1210: $i] :
( ~ ( in @ SY1210 @ SV335 )
| ~ ( subset @ ( sK105_C @ SV335 @ SV148 ) @ SY1210 )
| ( SY1210
= ( sK105_C @ SV335 @ SV148 ) ) ) )
= $false )
| ( ( SV335 = empty_set )
= $true )
| ( ( element @ SV335 @ ( powerset @ ( powerset @ SV148 ) ) )
= $false )
| ( ( finite @ SV148 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2950]) ).
thf(3100,plain,
! [SV148: $i,SV335: $i] :
( ( ( ~ ( in @ ( sK105_C @ SV335 @ SV148 ) @ SV335 ) )
= $false )
| ( ( SV335 = empty_set )
= $true )
| ( ( element @ SV335 @ ( powerset @ ( powerset @ SV148 ) ) )
= $false )
| ( ( finite @ SV148 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2950]) ).
thf(3101,plain,
! [SV340: $i,SV409: $i] :
( ( ( ! [SY1278: $i] :
( ~ ( in @ ( sK68_C @ SV409 @ SV340 ) @ SY1278 )
| ~ ( in @ SY1278 @ SV340 ) )
| ~ ( in @ ( sK68_C @ SV409 @ SV340 ) @ SV409 ) )
= $true )
| ( ( SV409
= ( union @ SV340 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2952]) ).
thf(3102,plain,
! [SV340: $i,SV409: $i] :
( ( ( ~ ( ~ ( in @ ( sK68_C @ SV409 @ SV340 ) @ ( sK69_SY723 @ SV409 @ SV340 ) )
| ~ ( in @ ( sK69_SY723 @ SV409 @ SV340 ) @ SV340 ) )
| ( in @ ( sK68_C @ SV409 @ SV340 ) @ SV409 ) )
= $true )
| ( ( SV409
= ( union @ SV340 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2953]) ).
thf(3103,plain,
! [SV410: $i,SV341: $i] :
( ( ( ~ ! [SY1279: $i] :
( ! [SY1219: $i] :
( ~ ( in @ SY1279 @ SY1219 )
| ~ ( in @ SY1219 @ SV341 ) )
| ( in @ SY1279 @ SV410 ) ) )
= $false )
| ( ( SV410
= ( union @ SV341 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2954]) ).
thf(3104,plain,
! [SV341: $i,SV410: $i] :
( ( ( ~ ! [SY1281: $i] :
( ~ ( in @ SY1281 @ SV410 )
| ~ ( ~ ( in @ SY1281 @ ( sK67_D @ SY1281 @ SV410 @ SV341 ) )
| ~ ( in @ ( sK67_D @ SY1281 @ SV410 @ SV341 ) @ SV341 ) ) ) )
= $false )
| ( ( SV410
= ( union @ SV341 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2954]) ).
thf(3105,plain,
! [SV498: $i,SV564: $i] :
( ( ( ~ ( element @ SV564 @ SV498 )
| ( in @ SV564 @ SV498 ) )
= $true )
| ( ( empty @ SV498 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2955]) ).
thf(3106,plain,
! [SV499: $i,SV565: $i] :
( ( ( ~ ( in @ SV565 @ SV499 )
| ( element @ SV565 @ SV499 ) )
= $true )
| ( ( empty @ SV499 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2956]) ).
thf(3107,plain,
! [SV500: $i] :
( ( ( empty @ SV500 )
= $false )
| ( ( ! [SY1377: $i] :
( ~ ( element @ SY1377 @ SV500 )
| ( empty @ SY1377 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2957]) ).
thf(3108,plain,
! [SV501: $i] :
( ( ( empty @ SV501 )
= $false )
| ( ( ! [SY1378: $i] :
( ~ ( empty @ SY1378 )
| ( element @ SY1378 @ SV501 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2958]) ).
thf(3109,plain,
! [SV346: $i,SV413: $i] :
( ( ( ~ ( in @ ( sK124_C @ SV413 @ SV346 ) @ SV413 )
| ~ ( subset @ ( sK124_C @ SV413 @ SV346 ) @ SV346 ) )
= $true )
| ( ( SV413
= ( powerset @ SV346 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2959]) ).
thf(3110,plain,
! [SV346: $i,SV413: $i] :
( ( ( ( in @ ( sK124_C @ SV413 @ SV346 ) @ SV413 )
| ( subset @ ( sK124_C @ SV413 @ SV346 ) @ SV346 ) )
= $true )
| ( ( SV413
= ( powerset @ SV346 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2960]) ).
thf(3111,plain,
! [SV347: $i,SV414: $i] :
( ( ( ~ ! [SY1282: $i] :
( ~ ( in @ SY1282 @ SV414 )
| ( subset @ SY1282 @ SV347 ) ) )
= $false )
| ( ( SV414
= ( powerset @ SV347 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2961]) ).
thf(3112,plain,
! [SV414: $i,SV347: $i] :
( ( ( ~ ! [SY1283: $i] :
( ~ ( subset @ SY1283 @ SV347 )
| ( in @ SY1283 @ SV414 ) ) )
= $false )
| ( ( SV414
= ( powerset @ SV347 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2961]) ).
thf(3113,plain,
! [SV149: $i] :
( ( ( empty @ ( sK118_B @ SV149 ) )
= $false )
| ( ( empty @ SV149 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2963]) ).
thf(3114,plain,
! [SV150: $i,SV415: $i,SV465: $i] :
( ( ( ~ ( ~ ! [SY1331: $i] :
~ ( in @ ( ordered_pair @ SY1331 @ ( sK102_D @ SV465 @ SV415 @ SV150 ) ) @ SV465 )
| ~ ( in @ ( sK102_D @ SV465 @ SV415 @ SV150 ) @ SV415 ) ) )
= $true )
| ( ( ( relation_rng_as_subset @ SV150 @ SV415 @ SV465 )
= SV415 )
= $true )
| ( ( relation_of2_as_subset @ SV465 @ SV150 @ SV415 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2964]) ).
thf(3115,plain,
! [SV466: $i,SV416: $i,SV150: $i] :
( ( ( ( ( relation_rng_as_subset @ SV150 @ SV416 @ SV466 )
!= SV416 ) )
= $true )
| ( ( ! [SY1332: $i] :
( ( in @ ( ordered_pair @ ( sK101_E @ SY1332 @ SV466 @ SV416 @ SV150 ) @ SY1332 ) @ SV466 )
| ~ ( in @ SY1332 @ SV416 ) ) )
= $true )
| ( ( relation_of2_as_subset @ SV466 @ SV150 @ SV416 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2965]) ).
thf(3116,plain,
! [SV151: $i,SV267: $i,SV467: $i,SV502: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV467 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV151 ) )
| ~ ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV267 ) ) ) )
| ~ ( ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
= SV467 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
= SV151 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
= SV267 ) ) )
= $false )
| ( ( SV502
= ( unordered_triple @ SV151 @ SV267 @ SV467 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2966]) ).
thf(3117,plain,
! [SV468: $i,SV267: $i,SV151: $i,SV503: $i] :
( ( ( SV503
= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
= $false )
| ( ( ~ ( ~ ! [SY1379: $i] :
( ~ ( in @ SY1379 @ SV503 )
| ( SY1379 = SV468 )
| ( SY1379 = SV151 )
| ( SY1379 = SV267 ) )
| ~ ~ ( ~ ! [SY1380: $i] :
( ( SY1380 != SV468 )
| ( in @ SY1380 @ SV503 ) )
| ~ ~ ( ~ ! [SY1381: $i] :
( ( SY1381 != SV151 )
| ( in @ SY1381 @ SV503 ) )
| ~ ! [SY1382: $i] :
( ( SY1382 != SV267 )
| ( in @ SY1382 @ SV503 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2967]) ).
thf(3118,plain,
! [SV152: $i,SV544: $i] :
( ( ( ~ ( in @ SV544 @ ( sK106_B @ SV152 ) ) )
= $true )
| ( ( in @ ( powerset @ SV544 ) @ ( sK106_B @ SV152 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2969]) ).
thf(3119,plain,
! [SV152: $i] :
( ( ~ ! [SY969: $i,SY970: $i] :
( ~ ( in @ SY969 @ ( sK106_B @ SV152 ) )
| ~ ( subset @ SY970 @ SY969 )
| ( in @ SY970 @ ( sK106_B @ SV152 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2970]) ).
thf(3120,plain,
! [SV152: $i] :
( ( ~ ( in @ SV152 @ ( sK106_B @ SV152 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2970]) ).
thf(3121,plain,
! [SV153: $i,SV418: $i] :
( ( ( ordinal @ SV418 )
= $false )
| ( ( in @ SV418 @ SV153 )
= $false )
| ( ( in @ SV418 @ ( sK107_B @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2971]) ).
thf(3122,plain,
! [SV153: $i,SV545: $i] :
( ( ( ~ ( in @ SV545 @ ( sK107_B @ SV153 ) ) )
= $true )
| ( ( in @ SV545 @ SV153 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2972]) ).
thf(3123,plain,
! [SV153: $i,SV546: $i] :
( ( ( ~ ( in @ SV546 @ ( sK107_B @ SV153 ) ) )
= $true )
| ( ( ordinal @ SV546 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2973]) ).
thf(3124,plain,
! [SV154: $i,SV504: $i] :
( ( ( relation @ SV504 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK72_C @ SV504 @ SV154 ) @ ( sK73_SY724 @ SV504 @ SV154 ) ) @ SV154 )
| ~ ~ ( in @ ( ordered_pair @ ( sK72_C @ SV504 @ SV154 ) @ ( sK73_SY724 @ SV504 @ SV154 ) ) @ SV504 ) )
| ( subset @ SV154 @ SV504 ) )
= $true )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2974]) ).
thf(3125,plain,
! [SV154: $i,SV505: $i] :
( ( ( relation @ SV505 )
= $false )
| ( ( ~ ( subset @ SV154 @ SV505 )
| ! [SY1383: $i,SY1384: $i] :
( ~ ( in @ ( ordered_pair @ SY1383 @ SY1384 ) @ SV154 )
| ( in @ ( ordered_pair @ SY1383 @ SY1384 ) @ SV505 ) ) )
= $true )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2975]) ).
thf(3126,plain,
! [SV268: $i,SV155: $i,SV547: $i] :
( ( ( ~ ( element @ SV547 @ ( powerset @ ( powerset @ SV155 ) ) ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ ( powerset @ SV155 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ SV547 )
| ~ ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SV547 @ SV268 @ SV155 ) ) @ SV268 ) )
| ~ ( ( in @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ SV547 )
| ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SV547 @ SV268 @ SV155 ) ) @ SV268 ) ) ) )
| ( SV547
= ( complements_of_subsets @ SV155 @ SV268 ) ) )
= $true )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2976]) ).
thf(3127,plain,
! [SV268: $i,SV155: $i,SV548: $i] :
( ( ( ~ ( element @ SV548 @ ( powerset @ ( powerset @ SV155 ) ) ) )
= $true )
| ( ( ( SV548
!= ( complements_of_subsets @ SV155 @ SV268 ) )
| ~ ( ~ ! [SY1408: $i] :
( ~ ( element @ SY1408 @ ( powerset @ SV155 ) )
| ~ ( in @ SY1408 @ SV548 )
| ( in @ ( subset_complement @ SV155 @ SY1408 ) @ SV268 ) )
| ~ ! [SY1409: $i] :
( ~ ( element @ SY1409 @ ( powerset @ SV155 ) )
| ~ ( in @ ( subset_complement @ SV155 @ SY1409 ) @ SV268 )
| ( in @ SY1409 @ SV548 ) ) ) )
= $true )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2977]) ).
thf(3128,plain,
! [SV506: $i] :
( ( ( SV506 = empty_set )
= $false )
| ( ( ! [SY1385: $i] : ( subset @ SV506 @ ( singleton @ SY1385 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2979]) ).
thf(3129,plain,
! [SV549: $i,SV507: $i] :
( ( ( ( SV507
!= ( singleton @ SV549 ) ) )
= $true )
| ( ( subset @ SV507 @ ( singleton @ SV549 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2980]) ).
thf(3130,plain,
! [SV508: $i] :
( ( ( SV508 = empty_set )
= $false )
| ( ( ! [SY1387: $i] : ( subset @ SV508 @ ( singleton @ SY1387 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2982]) ).
thf(3131,plain,
! [SV550: $i,SV509: $i] :
( ( ( ( SV509
!= ( singleton @ SV550 ) ) )
= $true )
| ( ( subset @ SV509 @ ( singleton @ SV550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2983]) ).
thf(3132,plain,
! [SV156: $i,SV510: $i] :
( ( ( element @ SV510 @ ( powerset @ SV156 ) )
= $false )
| ( ( v1_membered @ SV510 )
= $true )
| ( ( v2_membered @ SV156 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2984]) ).
thf(3133,plain,
! [SV156: $i,SV511: $i] :
( ( ( element @ SV511 @ ( powerset @ SV156 ) )
= $false )
| ( ( v2_membered @ SV511 )
= $true )
| ( ( v2_membered @ SV156 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2985]) ).
thf(3134,plain,
! [SV352: $i,SV423: $i] :
( ( ( relation @ SV423 )
= $false )
| ( ( empty @ SV352 )
= $false )
| ( ( empty @ ( relation_composition @ SV352 @ SV423 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2986]) ).
thf(3135,plain,
! [SV353: $i,SV424: $i] :
( ( ( relation @ SV424 )
= $false )
| ( ( empty @ SV353 )
= $false )
| ( ( relation @ ( relation_composition @ SV353 @ SV424 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2987]) ).
thf(3136,plain,
! [SV425: $i,SV566: $i] :
( ( ( ! [SY1415: $i] :
( ( SY1415 != SV566 )
| ~ ( in @ SY1415 @ SV425 ) )
| ~ ( ordinal @ SV566 )
| ( in @ SV566 @ ( sK7_B @ SV425 ) ) )
= $true )
| ( sK12_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2988]) ).
thf(3137,plain,
! [SV425: $i,SV567: $i] :
( ( ( ~ ( in @ SV567 @ ( sK7_B @ SV425 ) )
| ~ ( ~ ~ ( ( ( sK8_D @ SV567 @ SV425 )
!= SV567 )
| ~ ( in @ ( sK8_D @ SV567 @ SV425 ) @ SV425 ) )
| ~ ( ordinal @ SV567 ) ) )
= $true )
| ( sK12_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2989]) ).
thf(3138,plain,
( ( ( ~ ~ ( ~ ~ ( ( sK9_B != sK10_SY601 )
| ~ ( ordinal @ sK10_SY601 ) )
| ( sK9_B != sK11_SY603 ) )
| ~ ( ordinal @ sK11_SY603 ) )
= $false )
| ( sK12_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2990]) ).
thf(3139,plain,
( ( ( sK10_SY601 = sK11_SY603 )
= $false )
| ( sK12_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[2991]) ).
thf(3140,plain,
! [SV426: $i,SV469: $i,SV157: $i] :
( ( ( ~ ( in @ SV157 @ SV469 )
| ~ ( in @ SV157 @ ( cartesian_product2 @ SV426 @ SV426 ) ) )
= $true )
| ( ( in @ SV157 @ ( relation_restriction @ SV469 @ SV426 ) )
= $true )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2992]) ).
thf(3141,plain,
! [SV551: $i,SV157: $i,SV568: $i] :
( ( ~ ( relation @ SV568 )
| ~ ( in @ SV157 @ ( relation_restriction @ SV568 @ SV551 ) )
| ( in @ SV157 @ SV568 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2993]) ).
thf(3142,plain,
! [SV552: $i,SV157: $i,SV569: $i] :
( ( ~ ( relation @ SV569 )
| ~ ( in @ SV157 @ ( relation_restriction @ SV569 @ SV552 ) )
| ( in @ SV157 @ ( cartesian_product2 @ SV552 @ SV552 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2994]) ).
thf(3143,plain,
! [SV158: $i] :
( ( ~ ! [SY991: $i,SY992: $i] :
( ~ ( relation_of2_as_subset @ SY992 @ SV158 @ SY991 )
| ( SY991 = empty_set )
| ( SV158
!= ( relation_dom_as_subset @ SV158 @ SY991 @ SY992 ) )
| ( quasi_total @ SY992 @ SV158 @ SY991 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2995]) ).
thf(3144,plain,
! [SV158: $i] :
( ( ~ ! [SY993: $i,SY994: $i] :
( ~ ( relation_of2_as_subset @ SY994 @ SV158 @ SY993 )
| ( SY993 = empty_set )
| ~ ( quasi_total @ SY994 @ SV158 @ SY993 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SY993 @ SY994 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2995]) ).
thf(3145,plain,
! [SV158: $i] :
( ( ~ ! [SY995: $i,SY996: $i] :
( ~ ( relation_of2_as_subset @ SY996 @ SV158 @ SY995 )
| ( SV158 != empty_set )
| ( SV158
!= ( relation_dom_as_subset @ SV158 @ SY995 @ SY996 ) )
| ( quasi_total @ SY996 @ SV158 @ SY995 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2996]) ).
thf(3146,plain,
! [SV158: $i] :
( ( ~ ! [SY997: $i,SY998: $i] :
( ~ ( relation_of2_as_subset @ SY998 @ SV158 @ SY997 )
| ( SV158 != empty_set )
| ~ ( quasi_total @ SY998 @ SV158 @ SY997 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SY997 @ SY998 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2996]) ).
thf(3147,plain,
! [SV553: $i,SV158: $i,SV570: $i] :
( ( ~ ( relation_of2_as_subset @ SV570 @ SV158 @ SV553 )
| ( SV553 != empty_set )
| ( SV570 != empty_set )
| ( quasi_total @ SV570 @ SV158 @ SV553 )
| ( SV158 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2997]) ).
thf(3148,plain,
! [SV554: $i,SV158: $i,SV571: $i] :
( ( ~ ( relation_of2_as_subset @ SV571 @ SV158 @ SV554 )
| ( SV554 != empty_set )
| ~ ( quasi_total @ SV571 @ SV158 @ SV554 )
| ( SV571 = empty_set )
| ( SV158 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2998]) ).
thf(3149,plain,
! [SV512: $i,SV572: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( in @ ( sK90_SY733 @ SV572 @ SV512 ) @ SV512 )
| ~ ~ ( in @ ( sK89_C @ SV572 @ SV512 ) @ ( sK90_SY733 @ SV572 @ SV512 ) ) )
| ~ ( in @ ( sK89_C @ SV572 @ SV512 ) @ SV572 ) )
| ~ ( ! [SY1416: $i] :
( ~ ( in @ SY1416 @ SV512 )
| ( in @ ( sK89_C @ SV572 @ SV512 ) @ SY1416 ) )
| ( in @ ( sK89_C @ SV572 @ SV512 ) @ SV572 ) ) )
| ( SV572
= ( set_meet @ SV512 ) ) )
= $true )
| ( ( SV512 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2999]) ).
thf(3150,plain,
! [SV513: $i,SV573: $i] :
( ( ( ( SV573
!= ( set_meet @ SV513 ) )
| ~ ( ~ ! [SY1417: $i] :
( ~ ( ~ ( in @ ( sK88_D @ SY1417 @ SV573 @ SV513 ) @ SV513 )
| ~ ~ ( in @ SY1417 @ ( sK88_D @ SY1417 @ SV573 @ SV513 ) ) )
| ( in @ SY1417 @ SV573 ) )
| ~ ! [SY1418: $i] :
( ~ ( in @ SY1418 @ SV573 )
| ! [SY1394: $i] :
( ~ ( in @ SY1394 @ SV513 )
| ( in @ SY1418 @ SY1394 ) ) ) ) )
= $true )
| ( ( SV513 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3000]) ).
thf(3151,plain,
! [SV514: $i] :
( ( ( SV514 = empty_set )
= $false )
| ( ( ! [SY1395: $i] :
( ( SY1395
!= ( set_meet @ SV514 ) )
| ( SY1395 = empty_set ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3001]) ).
thf(3152,plain,
! [SV515: $i] :
( ( ( SV515 = empty_set )
= $false )
| ( ( ! [SY1396: $i] :
( ( SY1396 != empty_set )
| ( SY1396
= ( set_meet @ SV515 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3002]) ).
thf(3153,plain,
! [SV159: $i,SV427: $i,SV470: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK82_D @ SV470 @ SV427 @ SV159 ) @ SV470 )
| ( ( sK82_D @ SV470 @ SV427 @ SV159 )
!= SV159 ) )
| ~ ( ~ ( in @ ( sK82_D @ SV470 @ SV427 @ SV159 ) @ SV470 )
| ( ( sK82_D @ SV470 @ SV427 @ SV159 )
!= SV427 ) ) ) )
= $false )
| ( ( SV470
= ( unordered_pair @ SV159 @ SV427 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3003]) ).
thf(3154,plain,
! [SV159: $i,SV427: $i,SV470: $i] :
( ( ( ~ ( ( in @ ( sK82_D @ SV470 @ SV427 @ SV159 ) @ SV470 )
| ( ( sK82_D @ SV470 @ SV427 @ SV159 )
= SV159 )
| ( ( sK82_D @ SV470 @ SV427 @ SV159 )
= SV427 ) ) )
= $false )
| ( ( SV470
= ( unordered_pair @ SV159 @ SV427 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3003]) ).
thf(3155,plain,
! [SV428: $i,SV159: $i,SV471: $i] :
( ( ( ~ ! [SY1339: $i] :
( ~ ( in @ SY1339 @ SV471 )
| ( SY1339 = SV159 )
| ( SY1339 = SV428 ) )
| ~ ~ ( ~ ! [SY1340: $i] :
( ( SY1340 != SV159 )
| ( in @ SY1340 @ SV471 ) )
| ~ ! [SY1341: $i] :
( ( SY1341 != SV428 )
| ( in @ SY1341 @ SV471 ) ) ) )
= $false )
| ( ( SV471
= ( unordered_pair @ SV159 @ SV428 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3004]) ).
thf(3156,plain,
! [SV354: $i,SV429: $i] :
( ( ( relation @ SV429 )
= $false )
| ( ( empty @ SV354 )
= $false )
| ( ( empty @ ( relation_composition @ SV429 @ SV354 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3005]) ).
thf(3157,plain,
! [SV355: $i,SV430: $i] :
( ( ( relation @ SV430 )
= $false )
| ( ( empty @ SV355 )
= $false )
| ( ( relation @ ( relation_composition @ SV430 @ SV355 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3006]) ).
thf(3158,plain,
! [SV160: $i,SV516: $i] :
( ( ( element @ SV516 @ SV160 )
= $false )
| ( ( v1_xcmplx_0 @ SV516 )
= $true )
| ( ( v2_membered @ SV160 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3007]) ).
thf(3159,plain,
! [SV160: $i,SV517: $i] :
( ( ( element @ SV517 @ SV160 )
= $false )
| ( ( v1_xreal_0 @ SV517 )
= $true )
| ( ( v2_membered @ SV160 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3008]) ).
thf(3160,plain,
! [SV574: $i,SV358: $i] :
( ( ( ! [SY1420: $i] :
( ( sK93_B @ SV358 )
!= ( ordered_pair @ SV574 @ SY1420 ) ) )
= $true )
| ( ( relation @ SV358 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3009]) ).
thf(3161,plain,
! [SV359: $i,SV518: $i] :
( ( ( in @ SV518 @ SV359 )
= $false )
| ( ( SV518
= ( ordered_pair @ ( sK91_C @ SV518 @ SV359 ) @ ( sK92_SY735 @ SV518 @ SV359 ) ) )
= $true )
| ( ( relation @ SV359 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3011]) ).
thf(3162,plain,
! [SV269: $i,SV162: $i,SV555: $i] :
( ( ( ~ ( element @ SV555 @ ( powerset @ SV162 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV269 @ SV555 )
| ( subset @ SV269 @ ( subset_complement @ SV162 @ SV555 ) ) )
= $true )
| ( ( element @ SV269 @ ( powerset @ SV162 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3012]) ).
thf(3163,plain,
! [SV269: $i,SV162: $i,SV556: $i] :
( ( ( ~ ( element @ SV556 @ ( powerset @ SV162 ) ) )
= $true )
| ( ( ~ ( subset @ SV269 @ ( subset_complement @ SV162 @ SV556 ) )
| ( disjoint @ SV269 @ SV556 ) )
= $true )
| ( ( element @ SV269 @ ( powerset @ SV162 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3013]) ).
thf(3164,plain,
! [SV364: $i,SV435: $i] :
( ( ( ( ( sK87_C @ SV435 @ SV364 )
!= SV364 )
| ~ ( in @ ( sK87_C @ SV435 @ SV364 ) @ SV435 ) )
= $true )
| ( ( SV435
= ( singleton @ SV364 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3016]) ).
thf(3165,plain,
! [SV364: $i,SV435: $i] :
( ( ( ( ( sK87_C @ SV435 @ SV364 )
= SV364 )
| ( in @ ( sK87_C @ SV435 @ SV364 ) @ SV435 ) )
= $true )
| ( ( SV435
= ( singleton @ SV364 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3017]) ).
thf(3166,plain,
! [SV436: $i,SV365: $i] :
( ( ( ~ ! [SY1299: $i] :
( ( SY1299 != SV365 )
| ( in @ SY1299 @ SV436 ) ) )
= $false )
| ( ( SV436
= ( singleton @ SV365 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3018]) ).
thf(3167,plain,
! [SV365: $i,SV436: $i] :
( ( ( ~ ! [SY1300: $i] :
( ~ ( in @ SY1300 @ SV436 )
| ( SY1300 = SV365 ) ) )
= $false )
| ( ( SV436
= ( singleton @ SV365 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3018]) ).
thf(3168,plain,
! [SV474: $i,SV437: $i,SV164: $i] :
( ( ( ~ ( ! [SY1342: $i,SY1343: $i] :
( ~ ( in @ SY1342 @ SV164 )
| ~ ( in @ SY1343 @ SV437 )
| ( ( sK78_D @ SV474 @ SV437 @ SV164 )
!= ( ordered_pair @ SY1342 @ SY1343 ) ) )
| ~ ( in @ ( sK78_D @ SV474 @ SV437 @ SV164 ) @ SV474 ) ) )
= $false )
| ( ( SV474
= ( cartesian_product2 @ SV164 @ SV437 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3019]) ).
thf(3169,plain,
! [SV164: $i,SV437: $i,SV474: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK79_SY729 @ SV474 @ SV437 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK80_SY731 @ SV474 @ SV437 @ SV164 ) @ SV437 ) )
| ( ( sK78_D @ SV474 @ SV437 @ SV164 )
!= ( ordered_pair @ ( sK79_SY729 @ SV474 @ SV437 @ SV164 ) @ ( sK80_SY731 @ SV474 @ SV437 @ SV164 ) ) ) )
| ( in @ ( sK78_D @ SV474 @ SV437 @ SV164 ) @ SV474 ) ) )
= $false )
| ( ( SV474
= ( cartesian_product2 @ SV164 @ SV437 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3019]) ).
thf(3170,plain,
! [SV475: $i,SV438: $i,SV164: $i] :
( ( ( ~ ! [SY1344: $i] :
( ! [SY1306: $i,SY1307: $i] :
( ~ ( in @ SY1306 @ SV164 )
| ~ ( in @ SY1307 @ SV438 )
| ( SY1344
!= ( ordered_pair @ SY1306 @ SY1307 ) ) )
| ( in @ SY1344 @ SV475 ) )
| ~ ! [SY1347: $i] :
( ~ ( in @ SY1347 @ SV475 )
| ~ ( ~ ~ ( ~ ( in @ ( sK76_E @ SY1347 @ SV475 @ SV438 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK77_SY726 @ SY1347 @ SV475 @ SV438 @ SV164 ) @ SV438 ) )
| ( SY1347
!= ( ordered_pair @ ( sK76_E @ SY1347 @ SV475 @ SV438 @ SV164 ) @ ( sK77_SY726 @ SY1347 @ SV475 @ SV438 @ SV164 ) ) ) ) ) )
= $false )
| ( ( SV475
= ( cartesian_product2 @ SV164 @ SV438 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3020]) ).
thf(3171,plain,
! [SV366: $i,SV439: $i] :
( ( ( in @ ( sK71_C @ SV439 @ SV366 ) @ SV366 )
= $true )
| ( ( subset @ SV366 @ SV439 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3021]) ).
thf(3172,plain,
! [SV366: $i,SV439: $i] :
( ( ( ~ ( in @ ( sK71_C @ SV439 @ SV366 ) @ SV439 ) )
= $true )
| ( ( subset @ SV366 @ SV439 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3022]) ).
thf(3173,plain,
! [SV440: $i,SV367: $i,SV557: $i] :
( ( ( ~ ( in @ SV557 @ SV367 ) )
= $true )
| ( ( in @ SV557 @ SV440 )
= $true )
| ( ( subset @ SV367 @ SV440 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3023]) ).
thf(3174,plain,
! [SV166: $i,SV558: $i] :
( ( ( ~ ( ~ ! [SY1414: $i] :
( ~ ( subset @ SY1414 @ SV558 )
| ( in @ SY1414 @ ( sK4_SY591 @ SV558 @ SV166 ) ) )
| ~ ( in @ ( sK4_SY591 @ SV558 @ SV166 ) @ ( sK3_B @ SV166 ) ) ) )
= $true )
| ( ( ~ ( in @ SV558 @ ( sK3_B @ SV166 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3027]) ).
thf(3175,plain,
! [SV166: $i] :
( ( ~ ! [SY1036: $i,SY1037: $i] :
( ~ ( in @ SY1036 @ ( sK3_B @ SV166 ) )
| ~ ( subset @ SY1037 @ SY1036 )
| ( in @ SY1037 @ ( sK3_B @ SV166 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3028]) ).
thf(3176,plain,
! [SV166: $i] :
( ( ~ ( in @ SV166 @ ( sK3_B @ SV166 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3028]) ).
thf(3177,plain,
! [SV167: $i,SV444: $i,SV478: $i] :
( ( ( ~ ( ~ ! [SY1348: $i] :
~ ( in @ ( ordered_pair @ ( sK104_D @ SV478 @ SV444 @ SV167 ) @ SY1348 ) @ SV478 )
| ~ ( in @ ( sK104_D @ SV478 @ SV444 @ SV167 ) @ SV444 ) ) )
= $true )
| ( ( ( relation_dom_as_subset @ SV444 @ SV167 @ SV478 )
= SV444 )
= $true )
| ( ( relation_of2_as_subset @ SV478 @ SV444 @ SV167 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3029]) ).
thf(3178,plain,
! [SV479: $i,SV167: $i,SV445: $i] :
( ( ( ( ( relation_dom_as_subset @ SV445 @ SV167 @ SV479 )
!= SV445 ) )
= $true )
| ( ( ! [SY1349: $i] :
( ( in @ ( ordered_pair @ SY1349 @ ( sK103_E @ SY1349 @ SV479 @ SV445 @ SV167 ) ) @ SV479 )
| ~ ( in @ SY1349 @ SV445 ) ) )
= $true )
| ( ( relation_of2_as_subset @ SV479 @ SV445 @ SV167 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3030]) ).
thf(3179,plain,
! [SV168: $i] :
( ( ( ~ ~ ( ( ( sK27_SY634 @ SV168 )
!= ( singleton @ ( sK26_B @ SV168 ) ) )
| ~ ( in @ ( sK26_B @ SV168 ) @ SV168 ) )
| ~ ( in @ ( sK26_B @ SV168 ) @ SV168 ) )
= $false )
| ( ( ~ ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) )
| ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3031]) ).
thf(3180,plain,
! [SV168: $i] :
( ( ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) )
| ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) )
= $false )
| ( ( ( sK28_SY636 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3032]) ).
thf(3181,plain,
! [SV168: $i] :
( ( ( ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) ) )
= $true )
| ( ( ( sK27_SY634 @ SV168 )
= ( sK28_SY636 @ SV168 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3033]) ).
thf(3182,plain,
! [SV168: $i] :
( ( ( ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) )
= $true )
| ( ( ( sK27_SY634 @ SV168 )
= ( sK28_SY636 @ SV168 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3034]) ).
thf(3183,plain,
! [SV519: $i,SV270: $i,SV480: $i,SV169: $i] :
( ( ( ~ ( in @ SV169 @ SV480 ) )
= $true )
| ( ( ~ ( in @ SV270 @ SV519 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SV480 @ SV519 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3035]) ).
thf(3184,plain,
! [SV575: $i,SV270: $i,SV169: $i] :
( ( ! [SY1421: $i] :
~ ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SV575 @ SY1421 ) )
| ( in @ SV169 @ SV575 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3036]) ).
thf(3185,plain,
! [SV576: $i,SV270: $i,SV169: $i] :
( ( ! [SY1422: $i] :
( ~ ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SV576 @ SY1422 ) )
| ( in @ SV270 @ SY1422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3037]) ).
thf(3186,plain,
! [SV271: $i,SV481: $i,SV170: $i] :
( ( ( ! [SY1351: $i] :
( ! [SY1352: $i,SY1353: $i] :
( ( ( ordered_pair @ SY1352 @ SY1353 )
!= SY1351 )
| ~ ( in @ SY1352 @ SV170 )
| ! [SY1354: $i] :
( ~ ( ~ ( in @ ( sK115_I @ SY1354 @ SY1353 @ SY1352 @ SY1351 @ SV481 @ SV271 @ SV170 ) @ SY1354 )
| ~ ~ ( in @ ( ordered_pair @ SY1353 @ ( sK115_I @ SY1354 @ SY1353 @ SY1352 @ SY1351 @ SV481 @ SV271 @ SV170 ) ) @ SV271 ) )
| ( SY1352 != SY1354 )
| ~ ( in @ SY1353 @ SY1354 ) ) )
| ~ ( in @ SY1351 @ ( cartesian_product2 @ SV170 @ SV481 ) )
| ( in @ SY1351 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) ) ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3038]) ).
thf(3187,plain,
! [SV170: $i,SV271: $i,SV481: $i] :
( ( ( ~ ( ~ ! [SY1355: $i] :
( ~ ( in @ SY1355 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
| ~ ( ~ ~ ( ( ( ordered_pair @ ( sK112_F @ SY1355 @ SV481 @ SV271 @ SV170 ) @ ( sK113_SY768 @ SY1355 @ SV481 @ SV271 @ SV170 ) )
!= SY1355 )
| ~ ( in @ ( sK112_F @ SY1355 @ SV481 @ SV271 @ SV170 ) @ SV170 ) )
| ~ ~ ( ~ ! [SY1356: $i] :
( ~ ( in @ SY1356 @ ( sK114_SY771 @ SY1355 @ SV481 @ SV271 @ SV170 ) )
| ( in @ ( ordered_pair @ ( sK113_SY768 @ SY1355 @ SV481 @ SV271 @ SV170 ) @ SY1356 ) @ SV271 ) )
| ~ ~ ( ( ( sK112_F @ SY1355 @ SV481 @ SV271 @ SV170 )
!= ( sK114_SY771 @ SY1355 @ SV481 @ SV271 @ SV170 ) )
| ~ ( in @ ( sK113_SY768 @ SY1355 @ SV481 @ SV271 @ SV170 ) @ ( sK114_SY771 @ SY1355 @ SV481 @ SV271 @ SV170 ) ) ) ) ) )
| ~ ! [SY1357: $i] :
( ~ ( in @ SY1357 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
| ( in @ SY1357 @ ( cartesian_product2 @ SV170 @ SV481 ) ) ) ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3039]) ).
thf(3188,plain,
! [SV368: $i] :
( ( ( ~ ( ( ( sK74_B @ SV368 )
!= ( sK75_SY725 @ SV368 ) ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK74_B @ SV368 ) @ SV368 )
| ~ ( in @ ( sK75_SY725 @ SV368 ) @ SV368 ) )
| ~ ~ ( in @ ( sK74_B @ SV368 ) @ ( sK75_SY725 @ SV368 ) ) ) )
= $false )
| ( ( epsilon_connected @ SV368 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3040]) ).
thf(3189,plain,
! [SV368: $i] :
( ( ( in @ ( sK75_SY725 @ SV368 ) @ ( sK74_B @ SV368 ) )
= $false )
| ( ( epsilon_connected @ SV368 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3041]) ).
thf(3190,plain,
! [SV369: $i,SV559: $i,SV520: $i] :
( ( ( ( SV520 = SV559 )
| ~ ( in @ SV520 @ SV369 )
| ~ ( in @ SV559 @ SV369 )
| ( in @ SV520 @ SV559 ) )
= $true )
| ( ( in @ SV559 @ SV520 )
= $true )
| ( ( epsilon_connected @ SV369 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3042]) ).
thf(3191,plain,
! [SV521: $i] :
( ( ( v3_membered @ SV521 )
= $false )
| ( ( ! [SY1398: $i] : ( v1_membered @ ( set_difference @ SV521 @ SY1398 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3043]) ).
thf(3192,plain,
! [SV522: $i] :
( ( ( v3_membered @ SV522 )
= $false )
| ( ( ! [SY1399: $i] : ( v2_membered @ ( set_difference @ SV522 @ SY1399 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3044]) ).
thf(3193,plain,
! [SV171: $i,SV524: $i] :
( ( ( relation @ SV524 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV171 )
| ~ ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV524 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV171 )
| ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV524 ) ) )
| ( SV171 = SV524 ) )
= $true )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3045]) ).
thf(3194,plain,
! [SV171: $i,SV525: $i] :
( ( ( relation @ SV525 )
= $false )
| ( ( ( SV171 != SV525 )
| ~ ( ~ ! [SY1400: $i,SY1401: $i] :
( ~ ( in @ ( ordered_pair @ SY1400 @ SY1401 ) @ SV171 )
| ( in @ ( ordered_pair @ SY1400 @ SY1401 ) @ SV525 ) )
| ~ ! [SY1402: $i,SY1403: $i] :
( ~ ( in @ ( ordered_pair @ SY1402 @ SY1403 ) @ SV525 )
| ( in @ ( ordered_pair @ SY1402 @ SY1403 ) @ SV171 ) ) ) )
= $true )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3046]) ).
thf(3195,plain,
! [SV371: $i,SV446: $i] :
( ( ( in @ ( sK98_C @ SV446 @ SV371 ) @ SV371 )
= $true )
| ( ( disjoint @ SV371 @ SV446 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3047]) ).
thf(3196,plain,
! [SV371: $i,SV446: $i] :
( ( ( in @ ( sK98_C @ SV446 @ SV371 ) @ SV446 )
= $true )
| ( ( disjoint @ SV371 @ SV446 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3048]) ).
thf(3197,plain,
! [SV447: $i,SV372: $i,SV526: $i] :
( ( ( in @ SV526 @ SV372 )
= $false )
| ( ( ~ ( in @ SV526 @ SV447 ) )
= $true )
| ( ( ~ ( disjoint @ SV372 @ SV447 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3049]) ).
thf(3198,plain,
! [SV527: $i,SV451: $i,SV376: $i] :
( ( ( disjoint @ SV376 @ SV451 )
= $false )
| ( ( in @ SV527 @ ( set_intersection2 @ SV376 @ SV451 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3050]) ).
thf(3199,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ( ( sK35_D @ SV272 @ SV172 )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1178: $i] :
( ~ ( in @ SY1178 @ ( sK43_SY691 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SY1178 ) @ SV272 ) )
| ~ ~ ( ( ( sK41_SY666 @ SV272 @ SV172 )
!= ( sK43_SY691 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) ) ) ) ) )
| ( ( sK35_D @ SV272 @ SV172 )
!= ( sK37_SY665 @ SV272 @ SV172 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
!= ( sK37_SY665 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1179: $i] :
( ~ ( in @ SY1179 @ ( sK40_SY685 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SY1179 ) @ SV272 ) )
| ~ ~ ( ( ( sK38_SY678 @ SV272 @ SV172 )
!= ( sK40_SY685 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3051]) ).
thf(3200,plain,
! [SV172: $i,SV272: $i] :
( ( ( ( ( sK36_SY655 @ SV272 @ SV172 )
!= ( sK37_SY665 @ SV272 @ SV172 ) ) )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3052]) ).
thf(3201,plain,
! [SV530: $i,SV273: $i,SV482: $i,SV173: $i] :
( ( ( ~ ( in @ SV173 @ SV482 ) )
= $true )
| ( ( ~ ( in @ SV273 @ SV530 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SV482 @ SV530 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3053]) ).
thf(3202,plain,
! [SV577: $i,SV273: $i,SV173: $i] :
( ( ! [SY1423: $i] :
~ ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SV577 @ SY1423 ) )
| ( in @ SV173 @ SV577 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3054]) ).
thf(3203,plain,
! [SV578: $i,SV273: $i,SV173: $i] :
( ( ! [SY1424: $i] :
( ~ ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SV578 @ SY1424 ) )
| ( in @ SV273 @ SY1424 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3055]) ).
thf(3204,plain,
! [SV533: $i] :
( ( ( v3_membered @ SV533 )
= $false )
| ( ( ! [SY1404: $i] : ( v1_membered @ ( set_intersection2 @ SV533 @ SY1404 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3058]) ).
thf(3205,plain,
! [SV534: $i] :
( ( ( v3_membered @ SV534 )
= $false )
| ( ( ! [SY1405: $i] : ( v2_membered @ ( set_intersection2 @ SV534 @ SY1405 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3059]) ).
thf(3206,plain,
! [SV275: $i,SV176: $i,SV483: $i,SV579: $i] :
( ( ( ! [SY1425: $i] :
( ( ( ordered_pair @ SV579 @ SY1425 )
!= SV483 )
| ~ ( in @ SV579 @ SV176 )
| ( SY1425
!= ( singleton @ SV579 ) ) ) )
= $true )
| ( ( ~ ( in @ SV483 @ ( cartesian_product2 @ SV176 @ SV275 ) ) )
= $true )
| ( ( in @ SV483 @ ( sK108_C @ SV275 @ SV176 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3060]) ).
thf(3207,plain,
! [SV176: $i,SV275: $i,SV580: $i] :
( ( ~ ( in @ SV580 @ ( sK108_C @ SV275 @ SV176 ) )
| ~ ( ~ ~ ( ( ( ordered_pair @ ( sK109_E @ SV580 @ SV275 @ SV176 ) @ ( sK110_SY756 @ SV580 @ SV275 @ SV176 ) )
!= SV580 )
| ~ ( in @ ( sK109_E @ SV580 @ SV275 @ SV176 ) @ SV176 ) )
| ( ( sK110_SY756 @ SV580 @ SV275 @ SV176 )
!= ( singleton @ ( sK109_E @ SV580 @ SV275 @ SV176 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3061]) ).
thf(3208,plain,
! [SV176: $i,SV275: $i,SV581: $i] :
( ( ~ ( in @ SV581 @ ( sK108_C @ SV275 @ SV176 ) )
| ( in @ SV581 @ ( cartesian_product2 @ SV176 @ SV275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3062]) ).
thf(3209,plain,
! [SV178: $i,SV277: $i] :
( ( ( in @ ( sK6_C @ SV277 @ SV178 ) @ SV277 )
= $false )
| ( ( in @ ( sK6_C @ SV277 @ SV178 ) @ SV178 )
= $false )
| ( ( SV178 = SV277 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3063]) ).
thf(3210,plain,
! [SV180: $i,SV456: $i,SV484: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV484 )
| ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV180 ) )
| ~ ( ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV484 )
| ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV456 ) ) ) )
= $false )
| ( ( SV484
= ( set_union2 @ SV180 @ SV456 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3066]) ).
thf(3211,plain,
! [SV180: $i,SV456: $i,SV484: $i] :
( ( ( ~ ( ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV484 )
| ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV180 )
| ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV456 ) ) )
= $false )
| ( ( SV484
= ( set_union2 @ SV180 @ SV456 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3066]) ).
thf(3212,plain,
! [SV457: $i,SV180: $i,SV485: $i] :
( ( ( ~ ! [SY1361: $i] :
( ~ ( in @ SY1361 @ SV485 )
| ( in @ SY1361 @ SV180 )
| ( in @ SY1361 @ SV457 ) )
| ~ ~ ( ~ ! [SY1362: $i] :
( ~ ( in @ SY1362 @ SV180 )
| ( in @ SY1362 @ SV485 ) )
| ~ ! [SY1363: $i] :
( ~ ( in @ SY1363 @ SV457 )
| ( in @ SY1363 @ SV485 ) ) ) )
= $false )
| ( ( SV485
= ( set_union2 @ SV180 @ SV457 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3067]) ).
thf(3213,plain,
! [SV246: $i,SV96: $i,SV302: $i] :
( ( ( element @ SV302 @ ( the_carrier @ SV96 ) )
= $false )
| ( ( join_semilatt_str @ SV96 )
= $false )
| ( ( empty_carrier @ SV96 )
= $true )
| ( ( element @ SV246 @ ( the_carrier @ SV96 ) )
= $false )
| ( ( element @ ( join @ SV96 @ SV246 @ SV302 ) @ ( the_carrier @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3069]) ).
thf(3214,plain,
! [SV247: $i,SV98: $i,SV303: $i] :
( ( ( element @ SV303 @ ( the_carrier @ SV98 ) )
= $false )
| ( ( meet_semilatt_str @ SV98 )
= $false )
| ( ( empty_carrier @ SV98 )
= $true )
| ( ( element @ SV247 @ ( the_carrier @ SV98 ) )
= $false )
| ( ( element @ ( meet @ SV98 @ SV247 @ SV303 ) @ ( the_carrier @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3070]) ).
thf(3215,plain,
! [SV538: $i,SV486: $i] :
( ( ( proper_subset @ SV486 @ SV538 )
= $false )
| ( ( ( SV486 != SV538 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3071]) ).
thf(3216,plain,
! [SV539: $i,SV487: $i] :
( ( ( proper_subset @ SV487 @ SV539 )
= $false )
| ( ( subset @ SV487 @ SV539 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3072]) ).
thf(3217,plain,
! [SV139: $i] :
( ( ( ~ ~ ( ( ( sK17_C @ SV139 )
!= ( sK18_SY613 @ SV139 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
!= ( sK18_SY613 @ SV139 ) )
| ~ ( in @ ( sK22_SY620 @ SV139 ) @ SV139 ) )
| ( ( sK23_SY629 @ SV139 )
!= ( singleton @ ( sK22_SY620 @ SV139 ) ) ) ) ) )
= $false )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3073]) ).
thf(3218,plain,
! [SV139: $i] :
( ( ( ( ( sK17_C @ SV139 )
!= ( sK19_SY619 @ SV139 ) ) )
= $false )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3073]) ).
thf(3219,plain,
! [SV139: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
!= ( sK19_SY619 @ SV139 ) )
| ~ ( in @ ( sK20_SY626 @ SV139 ) @ SV139 ) ) )
= $false )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3074]) ).
thf(3220,plain,
! [SV139: $i] :
( ( ( ( ( sK21_SY628 @ SV139 )
!= ( singleton @ ( sK20_SY626 @ SV139 ) ) ) )
= $false )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3074]) ).
thf(3221,plain,
! [SV488: $i,SV139: $i] :
( ( ( ! [SY1366: $i] :
( ! [SY1367: $i] :
( ( SY1367 != SY1366 )
| ~ ( in @ SY1367 @ ( cartesian_product2 @ SV139 @ SV488 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1366 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1366 @ ( sK13_C @ SV488 @ SV139 ) ) ) )
= $true )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3075]) ).
thf(3222,plain,
! [SV139: $i,SV488: $i] :
( ( ( ! [SY1370: $i] :
( ~ ( in @ SY1370 @ ( sK13_C @ SV488 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1370 @ SV488 @ SV139 )
!= SY1370 )
| ~ ( in @ ( sK16_E @ SY1370 @ SV488 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV488 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1370 @ SV488 @ SV139 ) @ ( sK15_SY612 @ SY1370 @ SV488 @ SV139 ) )
!= SY1370 )
| ~ ( in @ ( sK14_J @ SY1370 @ SV488 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1370 @ SV488 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1370 @ SV488 @ SV139 ) ) ) ) ) ) )
= $true )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3076]) ).
thf(3223,plain,
! [SV489: $i,SV582: $i] :
( ( ( v1_membered @ ( set_intersection2 @ SV582 @ SV489 ) )
= $true )
| ( ( v3_membered @ SV489 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3077]) ).
thf(3224,plain,
! [SV490: $i,SV583: $i] :
( ( ( v2_membered @ ( set_intersection2 @ SV583 @ SV490 ) )
= $true )
| ( ( v3_membered @ SV490 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3078]) ).
thf(3225,plain,
! [SV142: $i,SV460: $i,SV399: $i] :
( ( ( in @ SV399 @ SV460 )
= $false )
| ( ( in @ SV142 @ SV460 )
= $false )
| ( ( subset @ ( unordered_pair @ SV142 @ SV399 ) @ SV460 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3079]) ).
thf(3226,plain,
! [SV562: $i,SV540: $i,SV142: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV142 @ SV540 ) @ SV562 ) )
= $true )
| ( ( in @ SV142 @ SV562 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3080]) ).
thf(3227,plain,
! [SV563: $i,SV541: $i,SV142: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV142 @ SV541 ) @ SV563 ) )
= $true )
| ( ( in @ SV541 @ SV563 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3081]) ).
thf(3228,plain,
! [SV143: $i,SV400: $i,SV461: $i] :
( ( ( ~ ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV143 )
| ~ ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV400 )
| ~ ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV461 ) )
= $true )
| ( ( SV461
= ( set_intersection2 @ SV143 @ SV400 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3082]) ).
thf(3229,plain,
! [SV143: $i,SV400: $i,SV461: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV143 )
| ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV461 ) )
| ~ ( ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV400 )
| ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV461 ) ) ) )
= $true )
| ( ( SV461
= ( set_intersection2 @ SV143 @ SV400 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3083]) ).
thf(3230,plain,
! [SV462: $i,SV401: $i,SV143: $i] :
( ( ( ~ ! [SY1325: $i] :
( ~ ( in @ SY1325 @ SV143 )
| ~ ( in @ SY1325 @ SV401 )
| ( in @ SY1325 @ SV462 ) ) )
= $false )
| ( ( SV462
= ( set_intersection2 @ SV143 @ SV401 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3084]) ).
thf(3231,plain,
! [SV401: $i,SV143: $i,SV462: $i] :
( ( ( ~ ~ ( ~ ! [SY1326: $i] :
( ~ ( in @ SY1326 @ SV462 )
| ( in @ SY1326 @ SV143 ) )
| ~ ! [SY1327: $i] :
( ~ ( in @ SY1327 @ SV462 )
| ( in @ SY1327 @ SV401 ) ) ) )
= $false )
| ( ( SV462
= ( set_intersection2 @ SV143 @ SV401 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3084]) ).
thf(3232,plain,
! [SV144: $i,SV584: $i] :
( ( ( ~ ( element @ SV584 @ ( powerset @ SV144 ) )
| ( v1_membered @ SV584 ) )
= $true )
| ( ( v3_membered @ SV144 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3085]) ).
thf(3233,plain,
! [SV144: $i,SV585: $i] :
( ( ( ~ ( element @ SV585 @ ( powerset @ SV144 ) )
| ( v2_membered @ SV585 ) )
= $true )
| ( ( v3_membered @ SV144 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3086]) ).
thf(3234,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1142: $i] :
( ~ ( in @ SY1142 @ ( sK52_SY712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SY1142 ) @ SV265 ) )
| ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK52_SY712 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) ) ) )
| ~ ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 ) )
| ~ ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 ) )
| ~ ~ ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ ( sK51_SY718 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SY1143 ) @ SV265 ) )
| ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK51_SY718 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3088]) ).
thf(3235,plain,
! [SV145: $i,SV265: $i] :
( ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3089]) ).
thf(3236,plain,
! [SV542: $i,SV493: $i] :
( ( ( SV493 = SV542 )
= $false )
| ( ( subset @ SV493 @ SV542 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3091]) ).
thf(3237,plain,
! [SV543: $i,SV494: $i] :
( ( ( SV494 = SV543 )
= $false )
| ( ( subset @ SV543 @ SV494 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3092]) ).
thf(3238,plain,
! [SV146: $i,SV266: $i,SV495: $i] :
( ( ( in @ SV495 @ ( sK5_C @ SV266 @ SV146 ) )
= $false )
| ( ( in @ SV495 @ SV266 )
= $false )
| ( ( ~ ( in @ SV146 @ SV266 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3093]) ).
thf(3239,plain,
! [SV147: $i,SV403: $i,SV463: $i] :
( ( ( ~ ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV147 )
| ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV403 )
| ~ ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV463 ) )
= $true )
| ( ( SV463
= ( set_difference @ SV147 @ SV403 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3096]) ).
thf(3240,plain,
! [SV147: $i,SV403: $i,SV463: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV147 )
| ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV463 ) )
| ~ ( ~ ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV403 )
| ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV463 ) ) ) )
= $true )
| ( ( SV463
= ( set_difference @ SV147 @ SV403 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3097]) ).
thf(3241,plain,
! [SV464: $i,SV404: $i,SV147: $i] :
( ( ( ~ ! [SY1328: $i] :
( ~ ( in @ SY1328 @ SV147 )
| ( in @ SY1328 @ SV404 )
| ( in @ SY1328 @ SV464 ) ) )
= $false )
| ( ( SV464
= ( set_difference @ SV147 @ SV404 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3098]) ).
thf(3242,plain,
! [SV404: $i,SV147: $i,SV464: $i] :
( ( ( ~ ~ ( ~ ! [SY1329: $i] :
( ~ ( in @ SY1329 @ SV464 )
| ( in @ SY1329 @ SV147 ) )
| ~ ! [SY1330: $i] :
( ~ ( in @ SY1330 @ SV464 )
| ~ ( in @ SY1330 @ SV404 ) ) ) )
= $false )
| ( ( SV464
= ( set_difference @ SV147 @ SV404 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3098]) ).
thf(3243,plain,
! [SV148: $i,SV335: $i] :
( ( ( ! [SY1210: $i] :
( ~ ( in @ SY1210 @ SV335 )
| ~ ( subset @ ( sK105_C @ SV335 @ SV148 ) @ SY1210 )
| ( SY1210
= ( sK105_C @ SV335 @ SV148 ) ) ) )
= $true )
| ( ( SV335 = empty_set )
= $true )
| ( ( element @ SV335 @ ( powerset @ ( powerset @ SV148 ) ) )
= $false )
| ( ( finite @ SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3099]) ).
thf(3244,plain,
! [SV148: $i,SV335: $i] :
( ( ( in @ ( sK105_C @ SV335 @ SV148 ) @ SV335 )
= $true )
| ( ( SV335 = empty_set )
= $true )
| ( ( element @ SV335 @ ( powerset @ ( powerset @ SV148 ) ) )
= $false )
| ( ( finite @ SV148 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3100]) ).
thf(3245,plain,
! [SV340: $i,SV409: $i] :
( ( ( ! [SY1278: $i] :
( ~ ( in @ ( sK68_C @ SV409 @ SV340 ) @ SY1278 )
| ~ ( in @ SY1278 @ SV340 ) ) )
= $true )
| ( ( ~ ( in @ ( sK68_C @ SV409 @ SV340 ) @ SV409 ) )
= $true )
| ( ( SV409
= ( union @ SV340 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3101]) ).
thf(3246,plain,
! [SV340: $i,SV409: $i] :
( ( ( ~ ( ~ ( in @ ( sK68_C @ SV409 @ SV340 ) @ ( sK69_SY723 @ SV409 @ SV340 ) )
| ~ ( in @ ( sK69_SY723 @ SV409 @ SV340 ) @ SV340 ) ) )
= $true )
| ( ( in @ ( sK68_C @ SV409 @ SV340 ) @ SV409 )
= $true )
| ( ( SV409
= ( union @ SV340 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3102]) ).
thf(3247,plain,
! [SV410: $i,SV341: $i] :
( ( ( ! [SY1279: $i] :
( ! [SY1219: $i] :
( ~ ( in @ SY1279 @ SY1219 )
| ~ ( in @ SY1219 @ SV341 ) )
| ( in @ SY1279 @ SV410 ) ) )
= $true )
| ( ( SV410
= ( union @ SV341 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3103]) ).
thf(3248,plain,
! [SV341: $i,SV410: $i] :
( ( ( ! [SY1281: $i] :
( ~ ( in @ SY1281 @ SV410 )
| ~ ( ~ ( in @ SY1281 @ ( sK67_D @ SY1281 @ SV410 @ SV341 ) )
| ~ ( in @ ( sK67_D @ SY1281 @ SV410 @ SV341 ) @ SV341 ) ) ) )
= $true )
| ( ( SV410
= ( union @ SV341 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3104]) ).
thf(3249,plain,
! [SV498: $i,SV564: $i] :
( ( ( ~ ( element @ SV564 @ SV498 ) )
= $true )
| ( ( in @ SV564 @ SV498 )
= $true )
| ( ( empty @ SV498 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3105]) ).
thf(3250,plain,
! [SV499: $i,SV565: $i] :
( ( ( ~ ( in @ SV565 @ SV499 ) )
= $true )
| ( ( element @ SV565 @ SV499 )
= $true )
| ( ( empty @ SV499 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3106]) ).
thf(3251,plain,
! [SV500: $i,SV586: $i] :
( ( ( ~ ( element @ SV586 @ SV500 )
| ( empty @ SV586 ) )
= $true )
| ( ( empty @ SV500 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3107]) ).
thf(3252,plain,
! [SV501: $i,SV587: $i] :
( ( ( ~ ( empty @ SV587 )
| ( element @ SV587 @ SV501 ) )
= $true )
| ( ( empty @ SV501 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3108]) ).
thf(3253,plain,
! [SV346: $i,SV413: $i] :
( ( ( ~ ( in @ ( sK124_C @ SV413 @ SV346 ) @ SV413 ) )
= $true )
| ( ( ~ ( subset @ ( sK124_C @ SV413 @ SV346 ) @ SV346 ) )
= $true )
| ( ( SV413
= ( powerset @ SV346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3109]) ).
thf(3254,plain,
! [SV346: $i,SV413: $i] :
( ( ( in @ ( sK124_C @ SV413 @ SV346 ) @ SV413 )
= $true )
| ( ( subset @ ( sK124_C @ SV413 @ SV346 ) @ SV346 )
= $true )
| ( ( SV413
= ( powerset @ SV346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3110]) ).
thf(3255,plain,
! [SV347: $i,SV414: $i] :
( ( ( ! [SY1282: $i] :
( ~ ( in @ SY1282 @ SV414 )
| ( subset @ SY1282 @ SV347 ) ) )
= $true )
| ( ( SV414
= ( powerset @ SV347 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3111]) ).
thf(3256,plain,
! [SV414: $i,SV347: $i] :
( ( ( ! [SY1283: $i] :
( ~ ( subset @ SY1283 @ SV347 )
| ( in @ SY1283 @ SV414 ) ) )
= $true )
| ( ( SV414
= ( powerset @ SV347 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3112]) ).
thf(3257,plain,
! [SV150: $i,SV415: $i,SV465: $i] :
( ( ( ~ ! [SY1331: $i] :
~ ( in @ ( ordered_pair @ SY1331 @ ( sK102_D @ SV465 @ SV415 @ SV150 ) ) @ SV465 )
| ~ ( in @ ( sK102_D @ SV465 @ SV415 @ SV150 ) @ SV415 ) )
= $false )
| ( ( ( relation_rng_as_subset @ SV150 @ SV415 @ SV465 )
= SV415 )
= $true )
| ( ( relation_of2_as_subset @ SV465 @ SV150 @ SV415 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3114]) ).
thf(3258,plain,
! [SV466: $i,SV416: $i,SV150: $i] :
( ( ( ( relation_rng_as_subset @ SV150 @ SV416 @ SV466 )
= SV416 )
= $false )
| ( ( ! [SY1332: $i] :
( ( in @ ( ordered_pair @ ( sK101_E @ SY1332 @ SV466 @ SV416 @ SV150 ) @ SY1332 ) @ SV466 )
| ~ ( in @ SY1332 @ SV416 ) ) )
= $true )
| ( ( relation_of2_as_subset @ SV466 @ SV150 @ SV416 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3115]) ).
thf(3259,plain,
! [SV151: $i,SV267: $i,SV467: $i,SV502: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV467 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV151 ) )
| ~ ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV267 ) ) ) ) )
= $false )
| ( ( SV502
= ( unordered_triple @ SV151 @ SV267 @ SV467 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3116]) ).
thf(3260,plain,
! [SV151: $i,SV267: $i,SV467: $i,SV502: $i] :
( ( ( ~ ( ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
= SV467 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
= SV151 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
= SV267 ) ) )
= $false )
| ( ( SV502
= ( unordered_triple @ SV151 @ SV267 @ SV467 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3116]) ).
thf(3261,plain,
! [SV267: $i,SV151: $i,SV468: $i,SV503: $i] :
( ( ( ~ ! [SY1379: $i] :
( ~ ( in @ SY1379 @ SV503 )
| ( SY1379 = SV468 )
| ( SY1379 = SV151 )
| ( SY1379 = SV267 ) )
| ~ ~ ( ~ ! [SY1380: $i] :
( ( SY1380 != SV468 )
| ( in @ SY1380 @ SV503 ) )
| ~ ~ ( ~ ! [SY1381: $i] :
( ( SY1381 != SV151 )
| ( in @ SY1381 @ SV503 ) )
| ~ ! [SY1382: $i] :
( ( SY1382 != SV267 )
| ( in @ SY1382 @ SV503 ) ) ) ) )
= $false )
| ( ( SV503
= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3117]) ).
thf(3262,plain,
! [SV152: $i,SV544: $i] :
( ( ( in @ SV544 @ ( sK106_B @ SV152 ) )
= $false )
| ( ( in @ ( powerset @ SV544 ) @ ( sK106_B @ SV152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3118]) ).
thf(3263,plain,
! [SV152: $i] :
( ( ! [SY969: $i,SY970: $i] :
( ~ ( in @ SY969 @ ( sK106_B @ SV152 ) )
| ~ ( subset @ SY970 @ SY969 )
| ( in @ SY970 @ ( sK106_B @ SV152 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3119]) ).
thf(3264,plain,
! [SV152: $i] :
( ( in @ SV152 @ ( sK106_B @ SV152 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3120]) ).
thf(3265,plain,
! [SV153: $i,SV545: $i] :
( ( ( in @ SV545 @ ( sK107_B @ SV153 ) )
= $false )
| ( ( in @ SV545 @ SV153 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3122]) ).
thf(3266,plain,
! [SV153: $i,SV546: $i] :
( ( ( in @ SV546 @ ( sK107_B @ SV153 ) )
= $false )
| ( ( ordinal @ SV546 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3123]) ).
thf(3267,plain,
! [SV154: $i,SV504: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK72_C @ SV504 @ SV154 ) @ ( sK73_SY724 @ SV504 @ SV154 ) ) @ SV154 )
| ~ ~ ( in @ ( ordered_pair @ ( sK72_C @ SV504 @ SV154 ) @ ( sK73_SY724 @ SV504 @ SV154 ) ) @ SV504 ) ) )
= $true )
| ( ( subset @ SV154 @ SV504 )
= $true )
| ( ( relation @ SV504 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3124]) ).
thf(3268,plain,
! [SV505: $i,SV154: $i] :
( ( ( ~ ( subset @ SV154 @ SV505 ) )
= $true )
| ( ( ! [SY1383: $i,SY1384: $i] :
( ~ ( in @ ( ordered_pair @ SY1383 @ SY1384 ) @ SV154 )
| ( in @ ( ordered_pair @ SY1383 @ SY1384 ) @ SV505 ) ) )
= $true )
| ( ( relation @ SV505 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3125]) ).
thf(3269,plain,
! [SV268: $i,SV155: $i,SV547: $i] :
( ( ( element @ SV547 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ ( powerset @ SV155 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ SV547 )
| ~ ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SV547 @ SV268 @ SV155 ) ) @ SV268 ) )
| ~ ( ( in @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ SV547 )
| ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SV547 @ SV268 @ SV155 ) ) @ SV268 ) ) ) )
| ( SV547
= ( complements_of_subsets @ SV155 @ SV268 ) ) )
= $true )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3126]) ).
thf(3270,plain,
! [SV268: $i,SV155: $i,SV548: $i] :
( ( ( element @ SV548 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( ( SV548
!= ( complements_of_subsets @ SV155 @ SV268 ) )
| ~ ( ~ ! [SY1408: $i] :
( ~ ( element @ SY1408 @ ( powerset @ SV155 ) )
| ~ ( in @ SY1408 @ SV548 )
| ( in @ ( subset_complement @ SV155 @ SY1408 ) @ SV268 ) )
| ~ ! [SY1409: $i] :
( ~ ( element @ SY1409 @ ( powerset @ SV155 ) )
| ~ ( in @ ( subset_complement @ SV155 @ SY1409 ) @ SV268 )
| ( in @ SY1409 @ SV548 ) ) ) )
= $true )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3127]) ).
thf(3271,plain,
! [SV588: $i,SV506: $i] :
( ( ( subset @ SV506 @ ( singleton @ SV588 ) )
= $true )
| ( ( SV506 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3128]) ).
thf(3272,plain,
! [SV549: $i,SV507: $i] :
( ( ( SV507
= ( singleton @ SV549 ) )
= $false )
| ( ( subset @ SV507 @ ( singleton @ SV549 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3129]) ).
thf(3273,plain,
! [SV589: $i,SV508: $i] :
( ( ( subset @ SV508 @ ( singleton @ SV589 ) )
= $true )
| ( ( SV508 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3130]) ).
thf(3274,plain,
! [SV550: $i,SV509: $i] :
( ( ( SV509
= ( singleton @ SV550 ) )
= $false )
| ( ( subset @ SV509 @ ( singleton @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3131]) ).
thf(3275,plain,
! [SV425: $i,SV566: $i] :
( ( ( ! [SY1415: $i] :
( ( SY1415 != SV566 )
| ~ ( in @ SY1415 @ SV425 ) )
| ~ ( ordinal @ SV566 ) )
= $true )
| ( ( in @ SV566 @ ( sK7_B @ SV425 ) )
= $true )
| ( sK12_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[3136]) ).
thf(3276,plain,
! [SV425: $i,SV567: $i] :
( ( ( ~ ( in @ SV567 @ ( sK7_B @ SV425 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK8_D @ SV567 @ SV425 )
!= SV567 )
| ~ ( in @ ( sK8_D @ SV567 @ SV425 ) @ SV425 ) )
| ~ ( ordinal @ SV567 ) ) )
= $true )
| ( sK12_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[3137]) ).
thf(3277,plain,
( ( ( ~ ~ ( ~ ~ ( ( sK9_B != sK10_SY601 )
| ~ ( ordinal @ sK10_SY601 ) )
| ( sK9_B != sK11_SY603 ) ) )
= $false )
| ( sK12_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[3138]) ).
thf(3278,plain,
( ( ( ~ ( ordinal @ sK11_SY603 ) )
= $false )
| ( sK12_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[3138]) ).
thf(3279,plain,
! [SV426: $i,SV469: $i,SV157: $i] :
( ( ( ~ ( in @ SV157 @ SV469 ) )
= $true )
| ( ( ~ ( in @ SV157 @ ( cartesian_product2 @ SV426 @ SV426 ) ) )
= $true )
| ( ( in @ SV157 @ ( relation_restriction @ SV469 @ SV426 ) )
= $true )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3140]) ).
thf(3280,plain,
! [SV551: $i,SV157: $i,SV568: $i] :
( ( ( ~ ( relation @ SV568 ) )
= $true )
| ( ( ~ ( in @ SV157 @ ( relation_restriction @ SV568 @ SV551 ) )
| ( in @ SV157 @ SV568 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3141]) ).
thf(3281,plain,
! [SV552: $i,SV157: $i,SV569: $i] :
( ( ( ~ ( relation @ SV569 ) )
= $true )
| ( ( ~ ( in @ SV157 @ ( relation_restriction @ SV569 @ SV552 ) )
| ( in @ SV157 @ ( cartesian_product2 @ SV552 @ SV552 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3142]) ).
thf(3282,plain,
! [SV158: $i] :
( ( ! [SY991: $i,SY992: $i] :
( ~ ( relation_of2_as_subset @ SY992 @ SV158 @ SY991 )
| ( SY991 = empty_set )
| ( SV158
!= ( relation_dom_as_subset @ SV158 @ SY991 @ SY992 ) )
| ( quasi_total @ SY992 @ SV158 @ SY991 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3143]) ).
thf(3283,plain,
! [SV158: $i] :
( ( ! [SY993: $i,SY994: $i] :
( ~ ( relation_of2_as_subset @ SY994 @ SV158 @ SY993 )
| ( SY993 = empty_set )
| ~ ( quasi_total @ SY994 @ SV158 @ SY993 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SY993 @ SY994 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3144]) ).
thf(3284,plain,
! [SV158: $i] :
( ( ! [SY995: $i,SY996: $i] :
( ~ ( relation_of2_as_subset @ SY996 @ SV158 @ SY995 )
| ( SV158 != empty_set )
| ( SV158
!= ( relation_dom_as_subset @ SV158 @ SY995 @ SY996 ) )
| ( quasi_total @ SY996 @ SV158 @ SY995 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3145]) ).
thf(3285,plain,
! [SV158: $i] :
( ( ! [SY997: $i,SY998: $i] :
( ~ ( relation_of2_as_subset @ SY998 @ SV158 @ SY997 )
| ( SV158 != empty_set )
| ~ ( quasi_total @ SY998 @ SV158 @ SY997 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SY997 @ SY998 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3146]) ).
thf(3286,plain,
! [SV553: $i,SV158: $i,SV570: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV570 @ SV158 @ SV553 ) )
= $true )
| ( ( ( SV553 != empty_set )
| ( SV570 != empty_set )
| ( quasi_total @ SV570 @ SV158 @ SV553 )
| ( SV158 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3147]) ).
thf(3287,plain,
! [SV554: $i,SV158: $i,SV571: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV571 @ SV158 @ SV554 ) )
= $true )
| ( ( ( SV554 != empty_set )
| ~ ( quasi_total @ SV571 @ SV158 @ SV554 )
| ( SV571 = empty_set )
| ( SV158 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3148]) ).
thf(3288,plain,
! [SV512: $i,SV572: $i] :
( ( ( ~ ( ~ ( ~ ( ~ ( in @ ( sK90_SY733 @ SV572 @ SV512 ) @ SV512 )
| ~ ~ ( in @ ( sK89_C @ SV572 @ SV512 ) @ ( sK90_SY733 @ SV572 @ SV512 ) ) )
| ~ ( in @ ( sK89_C @ SV572 @ SV512 ) @ SV572 ) )
| ~ ( ! [SY1416: $i] :
( ~ ( in @ SY1416 @ SV512 )
| ( in @ ( sK89_C @ SV572 @ SV512 ) @ SY1416 ) )
| ( in @ ( sK89_C @ SV572 @ SV512 ) @ SV572 ) ) ) )
= $true )
| ( ( SV572
= ( set_meet @ SV512 ) )
= $true )
| ( ( SV512 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3149]) ).
thf(3289,plain,
! [SV513: $i,SV573: $i] :
( ( ( ( SV573
!= ( set_meet @ SV513 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1417: $i] :
( ~ ( ~ ( in @ ( sK88_D @ SY1417 @ SV573 @ SV513 ) @ SV513 )
| ~ ~ ( in @ SY1417 @ ( sK88_D @ SY1417 @ SV573 @ SV513 ) ) )
| ( in @ SY1417 @ SV573 ) )
| ~ ! [SY1418: $i] :
( ~ ( in @ SY1418 @ SV573 )
| ! [SY1394: $i] :
( ~ ( in @ SY1394 @ SV513 )
| ( in @ SY1418 @ SY1394 ) ) ) ) )
= $true )
| ( ( SV513 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3150]) ).
thf(3290,plain,
! [SV514: $i,SV590: $i] :
( ( ( ( SV590
!= ( set_meet @ SV514 ) )
| ( SV590 = empty_set ) )
= $true )
| ( ( SV514 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3151]) ).
thf(3291,plain,
! [SV515: $i,SV591: $i] :
( ( ( ( SV591 != empty_set )
| ( SV591
= ( set_meet @ SV515 ) ) )
= $true )
| ( ( SV515 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3152]) ).
thf(3292,plain,
! [SV159: $i,SV427: $i,SV470: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK82_D @ SV470 @ SV427 @ SV159 ) @ SV470 )
| ( ( sK82_D @ SV470 @ SV427 @ SV159 )
!= SV159 ) )
| ~ ( ~ ( in @ ( sK82_D @ SV470 @ SV427 @ SV159 ) @ SV470 )
| ( ( sK82_D @ SV470 @ SV427 @ SV159 )
!= SV427 ) ) ) )
= $true )
| ( ( SV470
= ( unordered_pair @ SV159 @ SV427 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3153]) ).
thf(3293,plain,
! [SV159: $i,SV427: $i,SV470: $i] :
( ( ( ( in @ ( sK82_D @ SV470 @ SV427 @ SV159 ) @ SV470 )
| ( ( sK82_D @ SV470 @ SV427 @ SV159 )
= SV159 )
| ( ( sK82_D @ SV470 @ SV427 @ SV159 )
= SV427 ) )
= $true )
| ( ( SV470
= ( unordered_pair @ SV159 @ SV427 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3154]) ).
thf(3294,plain,
! [SV428: $i,SV159: $i,SV471: $i] :
( ( ( ~ ! [SY1339: $i] :
( ~ ( in @ SY1339 @ SV471 )
| ( SY1339 = SV159 )
| ( SY1339 = SV428 ) ) )
= $false )
| ( ( SV471
= ( unordered_pair @ SV159 @ SV428 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3155]) ).
thf(3295,plain,
! [SV428: $i,SV471: $i,SV159: $i] :
( ( ( ~ ~ ( ~ ! [SY1340: $i] :
( ( SY1340 != SV159 )
| ( in @ SY1340 @ SV471 ) )
| ~ ! [SY1341: $i] :
( ( SY1341 != SV428 )
| ( in @ SY1341 @ SV471 ) ) ) )
= $false )
| ( ( SV471
= ( unordered_pair @ SV159 @ SV428 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3155]) ).
thf(3296,plain,
! [SV592: $i,SV574: $i,SV358: $i] :
( ( ( ( ( sK93_B @ SV358 )
!= ( ordered_pair @ SV574 @ SV592 ) ) )
= $true )
| ( ( relation @ SV358 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3160]) ).
thf(3297,plain,
! [SV269: $i,SV162: $i,SV555: $i] :
( ( ( element @ SV555 @ ( powerset @ SV162 ) )
= $false )
| ( ( ~ ( disjoint @ SV269 @ SV555 )
| ( subset @ SV269 @ ( subset_complement @ SV162 @ SV555 ) ) )
= $true )
| ( ( element @ SV269 @ ( powerset @ SV162 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3162]) ).
thf(3298,plain,
! [SV269: $i,SV162: $i,SV556: $i] :
( ( ( element @ SV556 @ ( powerset @ SV162 ) )
= $false )
| ( ( ~ ( subset @ SV269 @ ( subset_complement @ SV162 @ SV556 ) )
| ( disjoint @ SV269 @ SV556 ) )
= $true )
| ( ( element @ SV269 @ ( powerset @ SV162 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3163]) ).
thf(3299,plain,
! [SV364: $i,SV435: $i] :
( ( ( ( ( sK87_C @ SV435 @ SV364 )
!= SV364 ) )
= $true )
| ( ( ~ ( in @ ( sK87_C @ SV435 @ SV364 ) @ SV435 ) )
= $true )
| ( ( SV435
= ( singleton @ SV364 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3164]) ).
thf(3300,plain,
! [SV364: $i,SV435: $i] :
( ( ( ( sK87_C @ SV435 @ SV364 )
= SV364 )
= $true )
| ( ( in @ ( sK87_C @ SV435 @ SV364 ) @ SV435 )
= $true )
| ( ( SV435
= ( singleton @ SV364 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3165]) ).
thf(3301,plain,
! [SV436: $i,SV365: $i] :
( ( ( ! [SY1299: $i] :
( ( SY1299 != SV365 )
| ( in @ SY1299 @ SV436 ) ) )
= $true )
| ( ( SV436
= ( singleton @ SV365 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3166]) ).
thf(3302,plain,
! [SV365: $i,SV436: $i] :
( ( ( ! [SY1300: $i] :
( ~ ( in @ SY1300 @ SV436 )
| ( SY1300 = SV365 ) ) )
= $true )
| ( ( SV436
= ( singleton @ SV365 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3167]) ).
thf(3303,plain,
! [SV474: $i,SV437: $i,SV164: $i] :
( ( ( ! [SY1342: $i,SY1343: $i] :
( ~ ( in @ SY1342 @ SV164 )
| ~ ( in @ SY1343 @ SV437 )
| ( ( sK78_D @ SV474 @ SV437 @ SV164 )
!= ( ordered_pair @ SY1342 @ SY1343 ) ) )
| ~ ( in @ ( sK78_D @ SV474 @ SV437 @ SV164 ) @ SV474 ) )
= $true )
| ( ( SV474
= ( cartesian_product2 @ SV164 @ SV437 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3168]) ).
thf(3304,plain,
! [SV164: $i,SV437: $i,SV474: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK79_SY729 @ SV474 @ SV437 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK80_SY731 @ SV474 @ SV437 @ SV164 ) @ SV437 ) )
| ( ( sK78_D @ SV474 @ SV437 @ SV164 )
!= ( ordered_pair @ ( sK79_SY729 @ SV474 @ SV437 @ SV164 ) @ ( sK80_SY731 @ SV474 @ SV437 @ SV164 ) ) ) )
| ( in @ ( sK78_D @ SV474 @ SV437 @ SV164 ) @ SV474 ) )
= $true )
| ( ( SV474
= ( cartesian_product2 @ SV164 @ SV437 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3169]) ).
thf(3305,plain,
! [SV475: $i,SV438: $i,SV164: $i] :
( ( ( ~ ! [SY1344: $i] :
( ! [SY1306: $i,SY1307: $i] :
( ~ ( in @ SY1306 @ SV164 )
| ~ ( in @ SY1307 @ SV438 )
| ( SY1344
!= ( ordered_pair @ SY1306 @ SY1307 ) ) )
| ( in @ SY1344 @ SV475 ) ) )
= $false )
| ( ( SV475
= ( cartesian_product2 @ SV164 @ SV438 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3170]) ).
thf(3306,plain,
! [SV164: $i,SV438: $i,SV475: $i] :
( ( ( ~ ! [SY1347: $i] :
( ~ ( in @ SY1347 @ SV475 )
| ~ ( ~ ~ ( ~ ( in @ ( sK76_E @ SY1347 @ SV475 @ SV438 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK77_SY726 @ SY1347 @ SV475 @ SV438 @ SV164 ) @ SV438 ) )
| ( SY1347
!= ( ordered_pair @ ( sK76_E @ SY1347 @ SV475 @ SV438 @ SV164 ) @ ( sK77_SY726 @ SY1347 @ SV475 @ SV438 @ SV164 ) ) ) ) ) )
= $false )
| ( ( SV475
= ( cartesian_product2 @ SV164 @ SV438 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3170]) ).
thf(3307,plain,
! [SV366: $i,SV439: $i] :
( ( ( in @ ( sK71_C @ SV439 @ SV366 ) @ SV439 )
= $false )
| ( ( subset @ SV366 @ SV439 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3172]) ).
thf(3308,plain,
! [SV440: $i,SV367: $i,SV557: $i] :
( ( ( in @ SV557 @ SV367 )
= $false )
| ( ( in @ SV557 @ SV440 )
= $true )
| ( ( subset @ SV367 @ SV440 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3173]) ).
thf(3309,plain,
! [SV166: $i,SV558: $i] :
( ( ( ~ ! [SY1414: $i] :
( ~ ( subset @ SY1414 @ SV558 )
| ( in @ SY1414 @ ( sK4_SY591 @ SV558 @ SV166 ) ) )
| ~ ( in @ ( sK4_SY591 @ SV558 @ SV166 ) @ ( sK3_B @ SV166 ) ) )
= $false )
| ( ( ~ ( in @ SV558 @ ( sK3_B @ SV166 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3174]) ).
thf(3310,plain,
! [SV166: $i] :
( ( ! [SY1036: $i,SY1037: $i] :
( ~ ( in @ SY1036 @ ( sK3_B @ SV166 ) )
| ~ ( subset @ SY1037 @ SY1036 )
| ( in @ SY1037 @ ( sK3_B @ SV166 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3175]) ).
thf(3311,plain,
! [SV166: $i] :
( ( in @ SV166 @ ( sK3_B @ SV166 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3176]) ).
thf(3312,plain,
! [SV167: $i,SV444: $i,SV478: $i] :
( ( ( ~ ! [SY1348: $i] :
~ ( in @ ( ordered_pair @ ( sK104_D @ SV478 @ SV444 @ SV167 ) @ SY1348 ) @ SV478 )
| ~ ( in @ ( sK104_D @ SV478 @ SV444 @ SV167 ) @ SV444 ) )
= $false )
| ( ( ( relation_dom_as_subset @ SV444 @ SV167 @ SV478 )
= SV444 )
= $true )
| ( ( relation_of2_as_subset @ SV478 @ SV444 @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3177]) ).
thf(3313,plain,
! [SV479: $i,SV167: $i,SV445: $i] :
( ( ( ( relation_dom_as_subset @ SV445 @ SV167 @ SV479 )
= SV445 )
= $false )
| ( ( ! [SY1349: $i] :
( ( in @ ( ordered_pair @ SY1349 @ ( sK103_E @ SY1349 @ SV479 @ SV445 @ SV167 ) ) @ SV479 )
| ~ ( in @ SY1349 @ SV445 ) ) )
= $true )
| ( ( relation_of2_as_subset @ SV479 @ SV445 @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3178]) ).
thf(3314,plain,
! [SV168: $i] :
( ( ( ~ ~ ( ( ( sK27_SY634 @ SV168 )
!= ( singleton @ ( sK26_B @ SV168 ) ) )
| ~ ( in @ ( sK26_B @ SV168 ) @ SV168 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) )
| ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3179]) ).
thf(3315,plain,
! [SV168: $i] :
( ( ( ~ ( in @ ( sK26_B @ SV168 ) @ SV168 ) )
= $false )
| ( ( ~ ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) )
| ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3179]) ).
thf(3316,plain,
! [SV168: $i] :
( ( ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) ) )
= $false )
| ( ( ( sK28_SY636 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3180]) ).
thf(3317,plain,
! [SV168: $i] :
( ( ( ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) )
= $false )
| ( ( ( sK28_SY636 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3180]) ).
thf(3318,plain,
! [SV593: $i,SV168: $i] :
( ( ( ! [SY1426: $i] :
( ~ ( in @ SY1426 @ SV168 )
| ( SV593
!= ( singleton @ SY1426 ) ) )
| ( in @ SV593 @ ( sK24_B @ SV168 ) ) )
= $true )
| ( ( ( sK27_SY634 @ SV168 )
= ( sK28_SY636 @ SV168 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3181]) ).
thf(3319,plain,
! [SV168: $i,SV594: $i] :
( ( ( ~ ( in @ SV594 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SV594 @ SV168 ) @ SV168 )
| ( SV594
!= ( singleton @ ( sK25_D @ SV594 @ SV168 ) ) ) ) )
= $true )
| ( ( ( sK27_SY634 @ SV168 )
= ( sK28_SY636 @ SV168 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3182]) ).
thf(3320,plain,
! [SV519: $i,SV270: $i,SV480: $i,SV169: $i] :
( ( ( in @ SV169 @ SV480 )
= $false )
| ( ( ~ ( in @ SV270 @ SV519 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SV480 @ SV519 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3183]) ).
thf(3321,plain,
! [SV575: $i,SV270: $i,SV169: $i] :
( ( ( ! [SY1421: $i] :
~ ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SV575 @ SY1421 ) ) )
= $true )
| ( ( in @ SV169 @ SV575 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3184]) ).
thf(3322,plain,
! [SV595: $i,SV576: $i,SV270: $i,SV169: $i] :
( ( ~ ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SV576 @ SV595 ) )
| ( in @ SV270 @ SV595 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3185]) ).
thf(3323,plain,
! [SV271: $i,SV481: $i,SV170: $i,SV596: $i] :
( ( ( ! [SY1427: $i,SY1428: $i] :
( ( ( ordered_pair @ SY1427 @ SY1428 )
!= SV596 )
| ~ ( in @ SY1427 @ SV170 )
| ! [SY1429: $i] :
( ~ ( ~ ( in @ ( sK115_I @ SY1429 @ SY1428 @ SY1427 @ SV596 @ SV481 @ SV271 @ SV170 ) @ SY1429 )
| ~ ~ ( in @ ( ordered_pair @ SY1428 @ ( sK115_I @ SY1429 @ SY1428 @ SY1427 @ SV596 @ SV481 @ SV271 @ SV170 ) ) @ SV271 ) )
| ( SY1427 != SY1429 )
| ~ ( in @ SY1428 @ SY1429 ) ) )
| ~ ( in @ SV596 @ ( cartesian_product2 @ SV170 @ SV481 ) )
| ( in @ SV596 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3186]) ).
thf(3324,plain,
! [SV170: $i,SV271: $i,SV481: $i] :
( ( ( ~ ! [SY1355: $i] :
( ~ ( in @ SY1355 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
| ~ ( ~ ~ ( ( ( ordered_pair @ ( sK112_F @ SY1355 @ SV481 @ SV271 @ SV170 ) @ ( sK113_SY768 @ SY1355 @ SV481 @ SV271 @ SV170 ) )
!= SY1355 )
| ~ ( in @ ( sK112_F @ SY1355 @ SV481 @ SV271 @ SV170 ) @ SV170 ) )
| ~ ~ ( ~ ! [SY1356: $i] :
( ~ ( in @ SY1356 @ ( sK114_SY771 @ SY1355 @ SV481 @ SV271 @ SV170 ) )
| ( in @ ( ordered_pair @ ( sK113_SY768 @ SY1355 @ SV481 @ SV271 @ SV170 ) @ SY1356 ) @ SV271 ) )
| ~ ~ ( ( ( sK112_F @ SY1355 @ SV481 @ SV271 @ SV170 )
!= ( sK114_SY771 @ SY1355 @ SV481 @ SV271 @ SV170 ) )
| ~ ( in @ ( sK113_SY768 @ SY1355 @ SV481 @ SV271 @ SV170 ) @ ( sK114_SY771 @ SY1355 @ SV481 @ SV271 @ SV170 ) ) ) ) ) )
| ~ ! [SY1357: $i] :
( ~ ( in @ SY1357 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
| ( in @ SY1357 @ ( cartesian_product2 @ SV170 @ SV481 ) ) ) )
= $false )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3187]) ).
thf(3325,plain,
! [SV368: $i] :
( ( ( ~ ( ( ( sK74_B @ SV368 )
!= ( sK75_SY725 @ SV368 ) ) ) )
= $false )
| ( ( epsilon_connected @ SV368 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3188]) ).
thf(3326,plain,
! [SV368: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK74_B @ SV368 ) @ SV368 )
| ~ ( in @ ( sK75_SY725 @ SV368 ) @ SV368 ) )
| ~ ~ ( in @ ( sK74_B @ SV368 ) @ ( sK75_SY725 @ SV368 ) ) ) )
= $false )
| ( ( epsilon_connected @ SV368 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3188]) ).
thf(3327,plain,
! [SV369: $i,SV559: $i,SV520: $i] :
( ( ( SV520 = SV559 )
= $true )
| ( ( ~ ( in @ SV520 @ SV369 )
| ~ ( in @ SV559 @ SV369 )
| ( in @ SV520 @ SV559 ) )
= $true )
| ( ( in @ SV559 @ SV520 )
= $true )
| ( ( epsilon_connected @ SV369 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3190]) ).
thf(3328,plain,
! [SV597: $i,SV521: $i] :
( ( ( v1_membered @ ( set_difference @ SV521 @ SV597 ) )
= $true )
| ( ( v3_membered @ SV521 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3191]) ).
thf(3329,plain,
! [SV598: $i,SV522: $i] :
( ( ( v2_membered @ ( set_difference @ SV522 @ SV598 ) )
= $true )
| ( ( v3_membered @ SV522 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3192]) ).
thf(3330,plain,
! [SV171: $i,SV524: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV171 )
| ~ ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV524 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV171 )
| ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV524 ) ) ) )
= $true )
| ( ( SV171 = SV524 )
= $true )
| ( ( relation @ SV524 )
= $false )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3193]) ).
thf(3331,plain,
! [SV525: $i,SV171: $i] :
( ( ( ( SV171 != SV525 ) )
= $true )
| ( ( ~ ( ~ ! [SY1400: $i,SY1401: $i] :
( ~ ( in @ ( ordered_pair @ SY1400 @ SY1401 ) @ SV171 )
| ( in @ ( ordered_pair @ SY1400 @ SY1401 ) @ SV525 ) )
| ~ ! [SY1402: $i,SY1403: $i] :
( ~ ( in @ ( ordered_pair @ SY1402 @ SY1403 ) @ SV525 )
| ( in @ ( ordered_pair @ SY1402 @ SY1403 ) @ SV171 ) ) ) )
= $true )
| ( ( relation @ SV525 )
= $false )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3194]) ).
thf(3332,plain,
! [SV372: $i,SV447: $i,SV526: $i] :
( ( ( in @ SV526 @ SV447 )
= $false )
| ( ( in @ SV526 @ SV372 )
= $false )
| ( ( ~ ( disjoint @ SV372 @ SV447 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3197]) ).
thf(3333,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( sK35_D @ SV272 @ SV172 )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1178: $i] :
( ~ ( in @ SY1178 @ ( sK43_SY691 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SY1178 ) @ SV272 ) )
| ~ ~ ( ( ( sK41_SY666 @ SV272 @ SV172 )
!= ( sK43_SY691 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) ) ) ) ) )
| ( ( sK35_D @ SV272 @ SV172 )
!= ( sK37_SY665 @ SV272 @ SV172 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
!= ( sK37_SY665 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1179: $i] :
( ~ ( in @ SY1179 @ ( sK40_SY685 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SY1179 ) @ SV272 ) )
| ~ ~ ( ( ( sK38_SY678 @ SV272 @ SV172 )
!= ( sK40_SY685 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) ) ) ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3199]) ).
thf(3334,plain,
! [SV172: $i,SV272: $i] :
( ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3200]) ).
thf(3335,plain,
! [SV530: $i,SV273: $i,SV482: $i,SV173: $i] :
( ( ( in @ SV173 @ SV482 )
= $false )
| ( ( ~ ( in @ SV273 @ SV530 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SV482 @ SV530 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3201]) ).
thf(3336,plain,
! [SV577: $i,SV273: $i,SV173: $i] :
( ( ( ! [SY1423: $i] :
~ ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SV577 @ SY1423 ) ) )
= $true )
| ( ( in @ SV173 @ SV577 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3202]) ).
thf(3337,plain,
! [SV599: $i,SV578: $i,SV273: $i,SV173: $i] :
( ( ~ ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SV578 @ SV599 ) )
| ( in @ SV273 @ SV599 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3203]) ).
thf(3338,plain,
! [SV600: $i,SV533: $i] :
( ( ( v1_membered @ ( set_intersection2 @ SV533 @ SV600 ) )
= $true )
| ( ( v3_membered @ SV533 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3204]) ).
thf(3339,plain,
! [SV601: $i,SV534: $i] :
( ( ( v2_membered @ ( set_intersection2 @ SV534 @ SV601 ) )
= $true )
| ( ( v3_membered @ SV534 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3205]) ).
thf(3340,plain,
! [SV275: $i,SV176: $i,SV483: $i,SV602: $i,SV579: $i] :
( ( ( ( ( ordered_pair @ SV579 @ SV602 )
!= SV483 )
| ~ ( in @ SV579 @ SV176 )
| ( SV602
!= ( singleton @ SV579 ) ) )
= $true )
| ( ( ~ ( in @ SV483 @ ( cartesian_product2 @ SV176 @ SV275 ) ) )
= $true )
| ( ( in @ SV483 @ ( sK108_C @ SV275 @ SV176 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3206]) ).
thf(3341,plain,
! [SV176: $i,SV275: $i,SV580: $i] :
( ( ( ~ ( in @ SV580 @ ( sK108_C @ SV275 @ SV176 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK109_E @ SV580 @ SV275 @ SV176 ) @ ( sK110_SY756 @ SV580 @ SV275 @ SV176 ) )
!= SV580 )
| ~ ( in @ ( sK109_E @ SV580 @ SV275 @ SV176 ) @ SV176 ) )
| ( ( sK110_SY756 @ SV580 @ SV275 @ SV176 )
!= ( singleton @ ( sK109_E @ SV580 @ SV275 @ SV176 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3207]) ).
thf(3342,plain,
! [SV176: $i,SV275: $i,SV581: $i] :
( ( ( ~ ( in @ SV581 @ ( sK108_C @ SV275 @ SV176 ) ) )
= $true )
| ( ( in @ SV581 @ ( cartesian_product2 @ SV176 @ SV275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3208]) ).
thf(3343,plain,
! [SV180: $i,SV456: $i,SV484: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV484 )
| ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV180 ) )
| ~ ( ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV484 )
| ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV456 ) ) ) )
= $true )
| ( ( SV484
= ( set_union2 @ SV180 @ SV456 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3210]) ).
thf(3344,plain,
! [SV180: $i,SV456: $i,SV484: $i] :
( ( ( ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV484 )
| ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV180 )
| ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV456 ) )
= $true )
| ( ( SV484
= ( set_union2 @ SV180 @ SV456 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3211]) ).
thf(3345,plain,
! [SV457: $i,SV180: $i,SV485: $i] :
( ( ( ~ ! [SY1361: $i] :
( ~ ( in @ SY1361 @ SV485 )
| ( in @ SY1361 @ SV180 )
| ( in @ SY1361 @ SV457 ) ) )
= $false )
| ( ( SV485
= ( set_union2 @ SV180 @ SV457 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3212]) ).
thf(3346,plain,
! [SV457: $i,SV485: $i,SV180: $i] :
( ( ( ~ ~ ( ~ ! [SY1362: $i] :
( ~ ( in @ SY1362 @ SV180 )
| ( in @ SY1362 @ SV485 ) )
| ~ ! [SY1363: $i] :
( ~ ( in @ SY1363 @ SV457 )
| ( in @ SY1363 @ SV485 ) ) ) )
= $false )
| ( ( SV485
= ( set_union2 @ SV180 @ SV457 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3212]) ).
thf(3347,plain,
! [SV538: $i,SV486: $i] :
( ( ( SV486 = SV538 )
= $false )
| ( ( proper_subset @ SV486 @ SV538 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3215]) ).
thf(3348,plain,
! [SV139: $i] :
( ( ( ~ ( ( ( sK17_C @ SV139 )
!= ( sK18_SY613 @ SV139 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
!= ( sK18_SY613 @ SV139 ) )
| ~ ( in @ ( sK22_SY620 @ SV139 ) @ SV139 ) )
| ( ( sK23_SY629 @ SV139 )
!= ( singleton @ ( sK22_SY620 @ SV139 ) ) ) ) ) )
= $true )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3217]) ).
thf(3349,plain,
! [SV139: $i] :
( ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3218]) ).
thf(3350,plain,
! [SV139: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
!= ( sK19_SY619 @ SV139 ) )
| ~ ( in @ ( sK20_SY626 @ SV139 ) @ SV139 ) ) )
= $true )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3219]) ).
thf(3351,plain,
! [SV139: $i] :
( ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3220]) ).
thf(3352,plain,
! [SV488: $i,SV139: $i,SV603: $i] :
( ( ( ! [SY1430: $i] :
( ( SY1430 != SV603 )
| ~ ( in @ SY1430 @ ( cartesian_product2 @ SV139 @ SV488 ) ) )
| ! [SY1431: $i,SY1432: $i] :
( ( ( ordered_pair @ SY1431 @ SY1432 )
!= SV603 )
| ~ ( in @ SY1431 @ SV139 )
| ( SY1432
!= ( singleton @ SY1431 ) ) )
| ( in @ SV603 @ ( sK13_C @ SV488 @ SV139 ) ) )
= $true )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3221]) ).
thf(3353,plain,
! [SV139: $i,SV488: $i,SV604: $i] :
( ( ( ~ ( in @ SV604 @ ( sK13_C @ SV488 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SV604 @ SV488 @ SV139 )
!= SV604 )
| ~ ( in @ ( sK16_E @ SV604 @ SV488 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV488 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV604 @ SV488 @ SV139 ) @ ( sK15_SY612 @ SV604 @ SV488 @ SV139 ) )
!= SV604 )
| ~ ( in @ ( sK14_J @ SV604 @ SV488 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV604 @ SV488 @ SV139 )
!= ( singleton @ ( sK14_J @ SV604 @ SV488 @ SV139 ) ) ) ) ) )
= $true )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3222]) ).
thf(3354,plain,
! [SV562: $i,SV540: $i,SV142: $i] :
( ( ( subset @ ( unordered_pair @ SV142 @ SV540 ) @ SV562 )
= $false )
| ( ( in @ SV142 @ SV562 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3226]) ).
thf(3355,plain,
! [SV563: $i,SV541: $i,SV142: $i] :
( ( ( subset @ ( unordered_pair @ SV142 @ SV541 ) @ SV563 )
= $false )
| ( ( in @ SV541 @ SV563 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3227]) ).
thf(3356,plain,
! [SV143: $i,SV400: $i,SV461: $i] :
( ( ( ~ ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV143 )
| ~ ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV400 ) )
= $true )
| ( ( ~ ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV461 ) )
= $true )
| ( ( SV461
= ( set_intersection2 @ SV143 @ SV400 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3228]) ).
thf(3357,plain,
! [SV143: $i,SV400: $i,SV461: $i] :
( ( ( ~ ( ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV143 )
| ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV461 ) )
| ~ ( ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV400 )
| ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV461 ) ) )
= $false )
| ( ( SV461
= ( set_intersection2 @ SV143 @ SV400 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3229]) ).
thf(3358,plain,
! [SV462: $i,SV401: $i,SV143: $i] :
( ( ( ! [SY1325: $i] :
( ~ ( in @ SY1325 @ SV143 )
| ~ ( in @ SY1325 @ SV401 )
| ( in @ SY1325 @ SV462 ) ) )
= $true )
| ( ( SV462
= ( set_intersection2 @ SV143 @ SV401 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3230]) ).
thf(3359,plain,
! [SV401: $i,SV143: $i,SV462: $i] :
( ( ( ~ ( ~ ! [SY1326: $i] :
( ~ ( in @ SY1326 @ SV462 )
| ( in @ SY1326 @ SV143 ) )
| ~ ! [SY1327: $i] :
( ~ ( in @ SY1327 @ SV462 )
| ( in @ SY1327 @ SV401 ) ) ) )
= $true )
| ( ( SV462
= ( set_intersection2 @ SV143 @ SV401 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3231]) ).
thf(3360,plain,
! [SV144: $i,SV584: $i] :
( ( ( ~ ( element @ SV584 @ ( powerset @ SV144 ) ) )
= $true )
| ( ( v1_membered @ SV584 )
= $true )
| ( ( v3_membered @ SV144 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3232]) ).
thf(3361,plain,
! [SV144: $i,SV585: $i] :
( ( ( ~ ( element @ SV585 @ ( powerset @ SV144 ) ) )
= $true )
| ( ( v2_membered @ SV585 )
= $true )
| ( ( v3_membered @ SV144 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3233]) ).
thf(3362,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1142: $i] :
( ~ ( in @ SY1142 @ ( sK52_SY712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SY1142 ) @ SV265 ) )
| ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK52_SY712 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) ) ) )
| ~ ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 ) )
| ~ ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3234]) ).
thf(3363,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ~ ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ ( sK51_SY718 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SY1143 ) @ SV265 ) )
| ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK51_SY718 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3234]) ).
thf(3364,plain,
! [SV265: $i,SV145: $i] :
( ( ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) )
= $false )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3235]) ).
thf(3365,plain,
! [SV495: $i,SV266: $i,SV146: $i] :
( ( ( in @ SV146 @ SV266 )
= $false )
| ( ( in @ SV495 @ SV266 )
= $false )
| ( ( in @ SV495 @ ( sK5_C @ SV266 @ SV146 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3238]) ).
thf(3366,plain,
! [SV147: $i,SV403: $i,SV463: $i] :
( ( ( ~ ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV147 )
| ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV403 ) )
= $true )
| ( ( ~ ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV463 ) )
= $true )
| ( ( SV463
= ( set_difference @ SV147 @ SV403 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3239]) ).
thf(3367,plain,
! [SV147: $i,SV403: $i,SV463: $i] :
( ( ( ~ ( ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV147 )
| ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV463 ) )
| ~ ( ~ ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV403 )
| ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV463 ) ) )
= $false )
| ( ( SV463
= ( set_difference @ SV147 @ SV403 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3240]) ).
thf(3368,plain,
! [SV464: $i,SV404: $i,SV147: $i] :
( ( ( ! [SY1328: $i] :
( ~ ( in @ SY1328 @ SV147 )
| ( in @ SY1328 @ SV404 )
| ( in @ SY1328 @ SV464 ) ) )
= $true )
| ( ( SV464
= ( set_difference @ SV147 @ SV404 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3241]) ).
thf(3369,plain,
! [SV404: $i,SV147: $i,SV464: $i] :
( ( ( ~ ( ~ ! [SY1329: $i] :
( ~ ( in @ SY1329 @ SV464 )
| ( in @ SY1329 @ SV147 ) )
| ~ ! [SY1330: $i] :
( ~ ( in @ SY1330 @ SV464 )
| ~ ( in @ SY1330 @ SV404 ) ) ) )
= $true )
| ( ( SV464
= ( set_difference @ SV147 @ SV404 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3242]) ).
thf(3370,plain,
! [SV148: $i,SV335: $i,SV605: $i] :
( ( ( ~ ( in @ SV605 @ SV335 )
| ~ ( subset @ ( sK105_C @ SV335 @ SV148 ) @ SV605 )
| ( SV605
= ( sK105_C @ SV335 @ SV148 ) ) )
= $true )
| ( ( SV335 = empty_set )
= $true )
| ( ( element @ SV335 @ ( powerset @ ( powerset @ SV148 ) ) )
= $false )
| ( ( finite @ SV148 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3243]) ).
thf(3371,plain,
! [SV606: $i,SV340: $i,SV409: $i] :
( ( ( ~ ( in @ ( sK68_C @ SV409 @ SV340 ) @ SV606 )
| ~ ( in @ SV606 @ SV340 ) )
= $true )
| ( ( ~ ( in @ ( sK68_C @ SV409 @ SV340 ) @ SV409 ) )
= $true )
| ( ( SV409
= ( union @ SV340 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3245]) ).
thf(3372,plain,
! [SV340: $i,SV409: $i] :
( ( ( ~ ( in @ ( sK68_C @ SV409 @ SV340 ) @ ( sK69_SY723 @ SV409 @ SV340 ) )
| ~ ( in @ ( sK69_SY723 @ SV409 @ SV340 ) @ SV340 ) )
= $false )
| ( ( in @ ( sK68_C @ SV409 @ SV340 ) @ SV409 )
= $true )
| ( ( SV409
= ( union @ SV340 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3246]) ).
thf(3373,plain,
! [SV410: $i,SV341: $i,SV607: $i] :
( ( ( ! [SY1433: $i] :
( ~ ( in @ SV607 @ SY1433 )
| ~ ( in @ SY1433 @ SV341 ) )
| ( in @ SV607 @ SV410 ) )
= $true )
| ( ( SV410
= ( union @ SV341 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3247]) ).
thf(3374,plain,
! [SV341: $i,SV410: $i,SV608: $i] :
( ( ( ~ ( in @ SV608 @ SV410 )
| ~ ( ~ ( in @ SV608 @ ( sK67_D @ SV608 @ SV410 @ SV341 ) )
| ~ ( in @ ( sK67_D @ SV608 @ SV410 @ SV341 ) @ SV341 ) ) )
= $true )
| ( ( SV410
= ( union @ SV341 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3248]) ).
thf(3375,plain,
! [SV498: $i,SV564: $i] :
( ( ( element @ SV564 @ SV498 )
= $false )
| ( ( in @ SV564 @ SV498 )
= $true )
| ( ( empty @ SV498 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3249]) ).
thf(3376,plain,
! [SV499: $i,SV565: $i] :
( ( ( in @ SV565 @ SV499 )
= $false )
| ( ( element @ SV565 @ SV499 )
= $true )
| ( ( empty @ SV499 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3250]) ).
thf(3377,plain,
! [SV500: $i,SV586: $i] :
( ( ( ~ ( element @ SV586 @ SV500 ) )
= $true )
| ( ( empty @ SV586 )
= $true )
| ( ( empty @ SV500 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3251]) ).
thf(3378,plain,
! [SV501: $i,SV587: $i] :
( ( ( ~ ( empty @ SV587 ) )
= $true )
| ( ( element @ SV587 @ SV501 )
= $true )
| ( ( empty @ SV501 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3252]) ).
thf(3379,plain,
! [SV346: $i,SV413: $i] :
( ( ( in @ ( sK124_C @ SV413 @ SV346 ) @ SV413 )
= $false )
| ( ( ~ ( subset @ ( sK124_C @ SV413 @ SV346 ) @ SV346 ) )
= $true )
| ( ( SV413
= ( powerset @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3253]) ).
thf(3380,plain,
! [SV347: $i,SV414: $i,SV609: $i] :
( ( ( ~ ( in @ SV609 @ SV414 )
| ( subset @ SV609 @ SV347 ) )
= $true )
| ( ( SV414
= ( powerset @ SV347 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3255]) ).
thf(3381,plain,
! [SV414: $i,SV347: $i,SV610: $i] :
( ( ( ~ ( subset @ SV610 @ SV347 )
| ( in @ SV610 @ SV414 ) )
= $true )
| ( ( SV414
= ( powerset @ SV347 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3256]) ).
thf(3382,plain,
! [SV150: $i,SV415: $i,SV465: $i] :
( ( ( ~ ! [SY1331: $i] :
~ ( in @ ( ordered_pair @ SY1331 @ ( sK102_D @ SV465 @ SV415 @ SV150 ) ) @ SV465 ) )
= $false )
| ( ( ( relation_rng_as_subset @ SV150 @ SV415 @ SV465 )
= SV415 )
= $true )
| ( ( relation_of2_as_subset @ SV465 @ SV150 @ SV415 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3257]) ).
thf(3383,plain,
! [SV150: $i,SV415: $i,SV465: $i] :
( ( ( ~ ( in @ ( sK102_D @ SV465 @ SV415 @ SV150 ) @ SV415 ) )
= $false )
| ( ( ( relation_rng_as_subset @ SV150 @ SV415 @ SV465 )
= SV415 )
= $true )
| ( ( relation_of2_as_subset @ SV465 @ SV150 @ SV415 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3257]) ).
thf(3384,plain,
! [SV150: $i,SV416: $i,SV466: $i,SV611: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK101_E @ SV611 @ SV466 @ SV416 @ SV150 ) @ SV611 ) @ SV466 )
| ~ ( in @ SV611 @ SV416 ) )
= $true )
| ( ( ( relation_rng_as_subset @ SV150 @ SV416 @ SV466 )
= SV416 )
= $false )
| ( ( relation_of2_as_subset @ SV466 @ SV150 @ SV416 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3258]) ).
thf(3385,plain,
! [SV151: $i,SV267: $i,SV467: $i,SV502: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV467 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV151 ) )
| ~ ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV267 ) ) ) ) )
= $true )
| ( ( SV502
= ( unordered_triple @ SV151 @ SV267 @ SV467 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3259]) ).
thf(3386,plain,
! [SV151: $i,SV267: $i,SV467: $i,SV502: $i] :
( ( ( ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
= SV467 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
= SV151 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
= SV267 ) )
= $true )
| ( ( SV502
= ( unordered_triple @ SV151 @ SV267 @ SV467 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3260]) ).
thf(3387,plain,
! [SV267: $i,SV151: $i,SV468: $i,SV503: $i] :
( ( ( ~ ! [SY1379: $i] :
( ~ ( in @ SY1379 @ SV503 )
| ( SY1379 = SV468 )
| ( SY1379 = SV151 )
| ( SY1379 = SV267 ) ) )
= $false )
| ( ( SV503
= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3261]) ).
thf(3388,plain,
! [SV267: $i,SV151: $i,SV503: $i,SV468: $i] :
( ( ( ~ ~ ( ~ ! [SY1380: $i] :
( ( SY1380 != SV468 )
| ( in @ SY1380 @ SV503 ) )
| ~ ~ ( ~ ! [SY1381: $i] :
( ( SY1381 != SV151 )
| ( in @ SY1381 @ SV503 ) )
| ~ ! [SY1382: $i] :
( ( SY1382 != SV267 )
| ( in @ SY1382 @ SV503 ) ) ) ) )
= $false )
| ( ( SV503
= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3261]) ).
thf(3389,plain,
! [SV152: $i,SV612: $i] :
( ( ! [SY1434: $i] :
( ~ ( in @ SV612 @ ( sK106_B @ SV152 ) )
| ~ ( subset @ SY1434 @ SV612 )
| ( in @ SY1434 @ ( sK106_B @ SV152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3263]) ).
thf(3390,plain,
! [SV154: $i,SV504: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK72_C @ SV504 @ SV154 ) @ ( sK73_SY724 @ SV504 @ SV154 ) ) @ SV154 )
| ~ ~ ( in @ ( ordered_pair @ ( sK72_C @ SV504 @ SV154 ) @ ( sK73_SY724 @ SV504 @ SV154 ) ) @ SV504 ) )
= $false )
| ( ( subset @ SV154 @ SV504 )
= $true )
| ( ( relation @ SV504 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3267]) ).
thf(3391,plain,
! [SV505: $i,SV154: $i] :
( ( ( subset @ SV154 @ SV505 )
= $false )
| ( ( ! [SY1383: $i,SY1384: $i] :
( ~ ( in @ ( ordered_pair @ SY1383 @ SY1384 ) @ SV154 )
| ( in @ ( ordered_pair @ SY1383 @ SY1384 ) @ SV505 ) ) )
= $true )
| ( ( relation @ SV505 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3268]) ).
thf(3392,plain,
! [SV155: $i,SV268: $i,SV547: $i] :
( ( ( ~ ( ~ ( element @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ ( powerset @ SV155 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ SV547 )
| ~ ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SV547 @ SV268 @ SV155 ) ) @ SV268 ) )
| ~ ( ( in @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ SV547 )
| ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SV547 @ SV268 @ SV155 ) ) @ SV268 ) ) ) ) )
= $true )
| ( ( SV547
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $true )
| ( ( element @ SV547 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3269]) ).
thf(3393,plain,
! [SV268: $i,SV155: $i,SV548: $i] :
( ( ( ( SV548
!= ( complements_of_subsets @ SV155 @ SV268 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1408: $i] :
( ~ ( element @ SY1408 @ ( powerset @ SV155 ) )
| ~ ( in @ SY1408 @ SV548 )
| ( in @ ( subset_complement @ SV155 @ SY1408 ) @ SV268 ) )
| ~ ! [SY1409: $i] :
( ~ ( element @ SY1409 @ ( powerset @ SV155 ) )
| ~ ( in @ ( subset_complement @ SV155 @ SY1409 ) @ SV268 )
| ( in @ SY1409 @ SV548 ) ) ) )
= $true )
| ( ( element @ SV548 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3270]) ).
thf(3394,plain,
! [SV425: $i,SV566: $i] :
( ( ( ! [SY1415: $i] :
( ( SY1415 != SV566 )
| ~ ( in @ SY1415 @ SV425 ) ) )
= $true )
| ( ( ~ ( ordinal @ SV566 ) )
= $true )
| ( ( in @ SV566 @ ( sK7_B @ SV425 ) )
= $true )
| ( sK12_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[3275]) ).
thf(3395,plain,
! [SV425: $i,SV567: $i] :
( ( ( in @ SV567 @ ( sK7_B @ SV425 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK8_D @ SV567 @ SV425 )
!= SV567 )
| ~ ( in @ ( sK8_D @ SV567 @ SV425 ) @ SV425 ) )
| ~ ( ordinal @ SV567 ) ) )
= $true )
| ( sK12_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[3276]) ).
thf(3396,plain,
( ( ( ~ ( ~ ~ ( ( sK9_B != sK10_SY601 )
| ~ ( ordinal @ sK10_SY601 ) )
| ( sK9_B != sK11_SY603 ) ) )
= $true )
| ( sK12_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[3277]) ).
thf(3397,plain,
( ( ( ordinal @ sK11_SY603 )
= $true )
| ( sK12_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[3278]) ).
thf(3398,plain,
! [SV426: $i,SV469: $i,SV157: $i] :
( ( ( in @ SV157 @ SV469 )
= $false )
| ( ( ~ ( in @ SV157 @ ( cartesian_product2 @ SV426 @ SV426 ) ) )
= $true )
| ( ( in @ SV157 @ ( relation_restriction @ SV469 @ SV426 ) )
= $true )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3279]) ).
thf(3399,plain,
! [SV551: $i,SV157: $i,SV568: $i] :
( ( ( relation @ SV568 )
= $false )
| ( ( ~ ( in @ SV157 @ ( relation_restriction @ SV568 @ SV551 ) )
| ( in @ SV157 @ SV568 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3280]) ).
thf(3400,plain,
! [SV552: $i,SV157: $i,SV569: $i] :
( ( ( relation @ SV569 )
= $false )
| ( ( ~ ( in @ SV157 @ ( relation_restriction @ SV569 @ SV552 ) )
| ( in @ SV157 @ ( cartesian_product2 @ SV552 @ SV552 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3281]) ).
thf(3401,plain,
! [SV613: $i,SV158: $i] :
( ( ! [SY1435: $i] :
( ~ ( relation_of2_as_subset @ SY1435 @ SV158 @ SV613 )
| ( SV613 = empty_set )
| ( SV158
!= ( relation_dom_as_subset @ SV158 @ SV613 @ SY1435 ) )
| ( quasi_total @ SY1435 @ SV158 @ SV613 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3282]) ).
thf(3402,plain,
! [SV614: $i,SV158: $i] :
( ( ! [SY1436: $i] :
( ~ ( relation_of2_as_subset @ SY1436 @ SV158 @ SV614 )
| ( SV614 = empty_set )
| ~ ( quasi_total @ SY1436 @ SV158 @ SV614 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SV614 @ SY1436 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3283]) ).
thf(3403,plain,
! [SV615: $i,SV158: $i] :
( ( ! [SY1437: $i] :
( ~ ( relation_of2_as_subset @ SY1437 @ SV158 @ SV615 )
| ( SV158 != empty_set )
| ( SV158
!= ( relation_dom_as_subset @ SV158 @ SV615 @ SY1437 ) )
| ( quasi_total @ SY1437 @ SV158 @ SV615 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3284]) ).
thf(3404,plain,
! [SV616: $i,SV158: $i] :
( ( ! [SY1438: $i] :
( ~ ( relation_of2_as_subset @ SY1438 @ SV158 @ SV616 )
| ( SV158 != empty_set )
| ~ ( quasi_total @ SY1438 @ SV158 @ SV616 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SV616 @ SY1438 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3285]) ).
thf(3405,plain,
! [SV553: $i,SV158: $i,SV570: $i] :
( ( ( relation_of2_as_subset @ SV570 @ SV158 @ SV553 )
= $false )
| ( ( ( SV553 != empty_set )
| ( SV570 != empty_set )
| ( quasi_total @ SV570 @ SV158 @ SV553 )
| ( SV158 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3286]) ).
thf(3406,plain,
! [SV554: $i,SV158: $i,SV571: $i] :
( ( ( relation_of2_as_subset @ SV571 @ SV158 @ SV554 )
= $false )
| ( ( ( SV554 != empty_set )
| ~ ( quasi_total @ SV571 @ SV158 @ SV554 )
| ( SV571 = empty_set )
| ( SV158 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3287]) ).
thf(3407,plain,
! [SV512: $i,SV572: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK90_SY733 @ SV572 @ SV512 ) @ SV512 )
| ~ ~ ( in @ ( sK89_C @ SV572 @ SV512 ) @ ( sK90_SY733 @ SV572 @ SV512 ) ) )
| ~ ( in @ ( sK89_C @ SV572 @ SV512 ) @ SV572 ) )
| ~ ( ! [SY1416: $i] :
( ~ ( in @ SY1416 @ SV512 )
| ( in @ ( sK89_C @ SV572 @ SV512 ) @ SY1416 ) )
| ( in @ ( sK89_C @ SV572 @ SV512 ) @ SV572 ) ) )
= $false )
| ( ( SV572
= ( set_meet @ SV512 ) )
= $true )
| ( ( SV512 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3288]) ).
thf(3408,plain,
! [SV513: $i,SV573: $i] :
( ( ( SV573
= ( set_meet @ SV513 ) )
= $false )
| ( ( ~ ( ~ ! [SY1417: $i] :
( ~ ( ~ ( in @ ( sK88_D @ SY1417 @ SV573 @ SV513 ) @ SV513 )
| ~ ~ ( in @ SY1417 @ ( sK88_D @ SY1417 @ SV573 @ SV513 ) ) )
| ( in @ SY1417 @ SV573 ) )
| ~ ! [SY1418: $i] :
( ~ ( in @ SY1418 @ SV573 )
| ! [SY1394: $i] :
( ~ ( in @ SY1394 @ SV513 )
| ( in @ SY1418 @ SY1394 ) ) ) ) )
= $true )
| ( ( SV513 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3289]) ).
thf(3409,plain,
! [SV514: $i,SV590: $i] :
( ( ( ( SV590
!= ( set_meet @ SV514 ) ) )
= $true )
| ( ( SV590 = empty_set )
= $true )
| ( ( SV514 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3290]) ).
thf(3410,plain,
! [SV515: $i,SV591: $i] :
( ( ( ( SV591 != empty_set ) )
= $true )
| ( ( SV591
= ( set_meet @ SV515 ) )
= $true )
| ( ( SV515 = empty_set )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3291]) ).
thf(3411,plain,
! [SV159: $i,SV427: $i,SV470: $i] :
( ( ( ~ ( ~ ( in @ ( sK82_D @ SV470 @ SV427 @ SV159 ) @ SV470 )
| ( ( sK82_D @ SV470 @ SV427 @ SV159 )
!= SV159 ) )
| ~ ( ~ ( in @ ( sK82_D @ SV470 @ SV427 @ SV159 ) @ SV470 )
| ( ( sK82_D @ SV470 @ SV427 @ SV159 )
!= SV427 ) ) )
= $false )
| ( ( SV470
= ( unordered_pair @ SV159 @ SV427 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3292]) ).
thf(3412,plain,
! [SV159: $i,SV427: $i,SV470: $i] :
( ( ( in @ ( sK82_D @ SV470 @ SV427 @ SV159 ) @ SV470 )
= $true )
| ( ( ( ( sK82_D @ SV470 @ SV427 @ SV159 )
= SV159 )
| ( ( sK82_D @ SV470 @ SV427 @ SV159 )
= SV427 ) )
= $true )
| ( ( SV470
= ( unordered_pair @ SV159 @ SV427 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3293]) ).
thf(3413,plain,
! [SV428: $i,SV159: $i,SV471: $i] :
( ( ( ! [SY1339: $i] :
( ~ ( in @ SY1339 @ SV471 )
| ( SY1339 = SV159 )
| ( SY1339 = SV428 ) ) )
= $true )
| ( ( SV471
= ( unordered_pair @ SV159 @ SV428 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3294]) ).
thf(3414,plain,
! [SV428: $i,SV471: $i,SV159: $i] :
( ( ( ~ ( ~ ! [SY1340: $i] :
( ( SY1340 != SV159 )
| ( in @ SY1340 @ SV471 ) )
| ~ ! [SY1341: $i] :
( ( SY1341 != SV428 )
| ( in @ SY1341 @ SV471 ) ) ) )
= $true )
| ( ( SV471
= ( unordered_pair @ SV159 @ SV428 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3295]) ).
thf(3415,plain,
! [SV592: $i,SV574: $i,SV358: $i] :
( ( ( ( sK93_B @ SV358 )
= ( ordered_pair @ SV574 @ SV592 ) )
= $false )
| ( ( relation @ SV358 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3296]) ).
thf(3416,plain,
! [SV162: $i,SV555: $i,SV269: $i] :
( ( ( ~ ( disjoint @ SV269 @ SV555 ) )
= $true )
| ( ( subset @ SV269 @ ( subset_complement @ SV162 @ SV555 ) )
= $true )
| ( ( element @ SV555 @ ( powerset @ SV162 ) )
= $false )
| ( ( element @ SV269 @ ( powerset @ SV162 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3297]) ).
thf(3417,plain,
! [SV556: $i,SV162: $i,SV269: $i] :
( ( ( ~ ( subset @ SV269 @ ( subset_complement @ SV162 @ SV556 ) ) )
= $true )
| ( ( disjoint @ SV269 @ SV556 )
= $true )
| ( ( element @ SV556 @ ( powerset @ SV162 ) )
= $false )
| ( ( element @ SV269 @ ( powerset @ SV162 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3298]) ).
thf(3418,plain,
! [SV364: $i,SV435: $i] :
( ( ( ( sK87_C @ SV435 @ SV364 )
= SV364 )
= $false )
| ( ( ~ ( in @ ( sK87_C @ SV435 @ SV364 ) @ SV435 ) )
= $true )
| ( ( SV435
= ( singleton @ SV364 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3299]) ).
thf(3419,plain,
! [SV436: $i,SV365: $i,SV617: $i] :
( ( ( ( SV617 != SV365 )
| ( in @ SV617 @ SV436 ) )
= $true )
| ( ( SV436
= ( singleton @ SV365 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3301]) ).
thf(3420,plain,
! [SV365: $i,SV436: $i,SV618: $i] :
( ( ( ~ ( in @ SV618 @ SV436 )
| ( SV618 = SV365 ) )
= $true )
| ( ( SV436
= ( singleton @ SV365 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3302]) ).
thf(3421,plain,
! [SV474: $i,SV437: $i,SV164: $i] :
( ( ( ! [SY1342: $i,SY1343: $i] :
( ~ ( in @ SY1342 @ SV164 )
| ~ ( in @ SY1343 @ SV437 )
| ( ( sK78_D @ SV474 @ SV437 @ SV164 )
!= ( ordered_pair @ SY1342 @ SY1343 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK78_D @ SV474 @ SV437 @ SV164 ) @ SV474 ) )
= $true )
| ( ( SV474
= ( cartesian_product2 @ SV164 @ SV437 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3303]) ).
thf(3422,plain,
! [SV164: $i,SV437: $i,SV474: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK79_SY729 @ SV474 @ SV437 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK80_SY731 @ SV474 @ SV437 @ SV164 ) @ SV437 ) )
| ( ( sK78_D @ SV474 @ SV437 @ SV164 )
!= ( ordered_pair @ ( sK79_SY729 @ SV474 @ SV437 @ SV164 ) @ ( sK80_SY731 @ SV474 @ SV437 @ SV164 ) ) ) ) )
= $true )
| ( ( in @ ( sK78_D @ SV474 @ SV437 @ SV164 ) @ SV474 )
= $true )
| ( ( SV474
= ( cartesian_product2 @ SV164 @ SV437 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3304]) ).
thf(3423,plain,
! [SV475: $i,SV438: $i,SV164: $i] :
( ( ( ! [SY1344: $i] :
( ! [SY1306: $i,SY1307: $i] :
( ~ ( in @ SY1306 @ SV164 )
| ~ ( in @ SY1307 @ SV438 )
| ( SY1344
!= ( ordered_pair @ SY1306 @ SY1307 ) ) )
| ( in @ SY1344 @ SV475 ) ) )
= $true )
| ( ( SV475
= ( cartesian_product2 @ SV164 @ SV438 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3305]) ).
thf(3424,plain,
! [SV164: $i,SV438: $i,SV475: $i] :
( ( ( ! [SY1347: $i] :
( ~ ( in @ SY1347 @ SV475 )
| ~ ( ~ ~ ( ~ ( in @ ( sK76_E @ SY1347 @ SV475 @ SV438 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK77_SY726 @ SY1347 @ SV475 @ SV438 @ SV164 ) @ SV438 ) )
| ( SY1347
!= ( ordered_pair @ ( sK76_E @ SY1347 @ SV475 @ SV438 @ SV164 ) @ ( sK77_SY726 @ SY1347 @ SV475 @ SV438 @ SV164 ) ) ) ) ) )
= $true )
| ( ( SV475
= ( cartesian_product2 @ SV164 @ SV438 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3306]) ).
thf(3425,plain,
! [SV166: $i,SV558: $i] :
( ( ( ~ ! [SY1414: $i] :
( ~ ( subset @ SY1414 @ SV558 )
| ( in @ SY1414 @ ( sK4_SY591 @ SV558 @ SV166 ) ) ) )
= $false )
| ( ( ~ ( in @ SV558 @ ( sK3_B @ SV166 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3309]) ).
thf(3426,plain,
! [SV166: $i,SV558: $i] :
( ( ( ~ ( in @ ( sK4_SY591 @ SV558 @ SV166 ) @ ( sK3_B @ SV166 ) ) )
= $false )
| ( ( ~ ( in @ SV558 @ ( sK3_B @ SV166 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3309]) ).
thf(3427,plain,
! [SV166: $i,SV619: $i] :
( ( ! [SY1439: $i] :
( ~ ( in @ SV619 @ ( sK3_B @ SV166 ) )
| ~ ( subset @ SY1439 @ SV619 )
| ( in @ SY1439 @ ( sK3_B @ SV166 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3310]) ).
thf(3428,plain,
! [SV167: $i,SV444: $i,SV478: $i] :
( ( ( ~ ! [SY1348: $i] :
~ ( in @ ( ordered_pair @ ( sK104_D @ SV478 @ SV444 @ SV167 ) @ SY1348 ) @ SV478 ) )
= $false )
| ( ( ( relation_dom_as_subset @ SV444 @ SV167 @ SV478 )
= SV444 )
= $true )
| ( ( relation_of2_as_subset @ SV478 @ SV444 @ SV167 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3312]) ).
thf(3429,plain,
! [SV167: $i,SV444: $i,SV478: $i] :
( ( ( ~ ( in @ ( sK104_D @ SV478 @ SV444 @ SV167 ) @ SV444 ) )
= $false )
| ( ( ( relation_dom_as_subset @ SV444 @ SV167 @ SV478 )
= SV444 )
= $true )
| ( ( relation_of2_as_subset @ SV478 @ SV444 @ SV167 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3312]) ).
thf(3430,plain,
! [SV167: $i,SV445: $i,SV479: $i,SV620: $i] :
( ( ( ( in @ ( ordered_pair @ SV620 @ ( sK103_E @ SV620 @ SV479 @ SV445 @ SV167 ) ) @ SV479 )
| ~ ( in @ SV620 @ SV445 ) )
= $true )
| ( ( ( relation_dom_as_subset @ SV445 @ SV167 @ SV479 )
= SV445 )
= $false )
| ( ( relation_of2_as_subset @ SV479 @ SV445 @ SV167 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3313]) ).
thf(3431,plain,
! [SV168: $i] :
( ( ( ~ ( ( ( sK27_SY634 @ SV168 )
!= ( singleton @ ( sK26_B @ SV168 ) ) )
| ~ ( in @ ( sK26_B @ SV168 ) @ SV168 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) )
| ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3314]) ).
thf(3432,plain,
! [SV168: $i] :
( ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true )
| ( ( ~ ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) )
| ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3315]) ).
thf(3433,plain,
! [SV168: $i] :
( ( ( ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) ) )
= $true )
| ( ( ( sK28_SY636 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3316]) ).
thf(3434,plain,
! [SV168: $i] :
( ( ( ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) )
= $true )
| ( ( ( sK28_SY636 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3317]) ).
thf(3435,plain,
! [SV593: $i,SV168: $i] :
( ( ( ! [SY1426: $i] :
( ~ ( in @ SY1426 @ SV168 )
| ( SV593
!= ( singleton @ SY1426 ) ) ) )
= $true )
| ( ( in @ SV593 @ ( sK24_B @ SV168 ) )
= $true )
| ( ( ( sK27_SY634 @ SV168 )
= ( sK28_SY636 @ SV168 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3318]) ).
thf(3436,plain,
! [SV168: $i,SV594: $i] :
( ( ( ~ ( in @ SV594 @ ( sK24_B @ SV168 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK25_D @ SV594 @ SV168 ) @ SV168 )
| ( SV594
!= ( singleton @ ( sK25_D @ SV594 @ SV168 ) ) ) ) )
= $true )
| ( ( ( sK27_SY634 @ SV168 )
= ( sK28_SY636 @ SV168 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3319]) ).
thf(3437,plain,
! [SV480: $i,SV169: $i,SV519: $i,SV270: $i] :
( ( ( in @ SV270 @ SV519 )
= $false )
| ( ( in @ SV169 @ SV480 )
= $false )
| ( ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SV480 @ SV519 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3320]) ).
thf(3438,plain,
! [SV621: $i,SV575: $i,SV270: $i,SV169: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SV575 @ SV621 ) ) )
= $true )
| ( ( in @ SV169 @ SV575 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3321]) ).
thf(3439,plain,
! [SV595: $i,SV576: $i,SV270: $i,SV169: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SV576 @ SV595 ) ) )
= $true )
| ( ( in @ SV270 @ SV595 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3322]) ).
thf(3440,plain,
! [SV271: $i,SV481: $i,SV170: $i,SV596: $i] :
( ( ( ! [SY1427: $i,SY1428: $i] :
( ( ( ordered_pair @ SY1427 @ SY1428 )
!= SV596 )
| ~ ( in @ SY1427 @ SV170 )
| ! [SY1429: $i] :
( ~ ( ~ ( in @ ( sK115_I @ SY1429 @ SY1428 @ SY1427 @ SV596 @ SV481 @ SV271 @ SV170 ) @ SY1429 )
| ~ ~ ( in @ ( ordered_pair @ SY1428 @ ( sK115_I @ SY1429 @ SY1428 @ SY1427 @ SV596 @ SV481 @ SV271 @ SV170 ) ) @ SV271 ) )
| ( SY1427 != SY1429 )
| ~ ( in @ SY1428 @ SY1429 ) ) )
| ~ ( in @ SV596 @ ( cartesian_product2 @ SV170 @ SV481 ) ) )
= $true )
| ( ( in @ SV596 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3323]) ).
thf(3441,plain,
! [SV170: $i,SV271: $i,SV481: $i] :
( ( ( ~ ! [SY1355: $i] :
( ~ ( in @ SY1355 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
| ~ ( ~ ~ ( ( ( ordered_pair @ ( sK112_F @ SY1355 @ SV481 @ SV271 @ SV170 ) @ ( sK113_SY768 @ SY1355 @ SV481 @ SV271 @ SV170 ) )
!= SY1355 )
| ~ ( in @ ( sK112_F @ SY1355 @ SV481 @ SV271 @ SV170 ) @ SV170 ) )
| ~ ~ ( ~ ! [SY1356: $i] :
( ~ ( in @ SY1356 @ ( sK114_SY771 @ SY1355 @ SV481 @ SV271 @ SV170 ) )
| ( in @ ( ordered_pair @ ( sK113_SY768 @ SY1355 @ SV481 @ SV271 @ SV170 ) @ SY1356 ) @ SV271 ) )
| ~ ~ ( ( ( sK112_F @ SY1355 @ SV481 @ SV271 @ SV170 )
!= ( sK114_SY771 @ SY1355 @ SV481 @ SV271 @ SV170 ) )
| ~ ( in @ ( sK113_SY768 @ SY1355 @ SV481 @ SV271 @ SV170 ) @ ( sK114_SY771 @ SY1355 @ SV481 @ SV271 @ SV170 ) ) ) ) ) ) )
= $false )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3324]) ).
thf(3442,plain,
! [SV170: $i,SV271: $i,SV481: $i] :
( ( ( ~ ! [SY1357: $i] :
( ~ ( in @ SY1357 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
| ( in @ SY1357 @ ( cartesian_product2 @ SV170 @ SV481 ) ) ) )
= $false )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3324]) ).
thf(3443,plain,
! [SV368: $i] :
( ( ( ( ( sK74_B @ SV368 )
!= ( sK75_SY725 @ SV368 ) ) )
= $true )
| ( ( epsilon_connected @ SV368 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3325]) ).
thf(3444,plain,
! [SV368: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK74_B @ SV368 ) @ SV368 )
| ~ ( in @ ( sK75_SY725 @ SV368 ) @ SV368 ) )
| ~ ~ ( in @ ( sK74_B @ SV368 ) @ ( sK75_SY725 @ SV368 ) ) ) )
= $true )
| ( ( epsilon_connected @ SV368 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3326]) ).
thf(3445,plain,
! [SV559: $i,SV369: $i,SV520: $i] :
( ( ( ~ ( in @ SV520 @ SV369 )
| ~ ( in @ SV559 @ SV369 ) )
= $true )
| ( ( in @ SV520 @ SV559 )
= $true )
| ( ( SV520 = SV559 )
= $true )
| ( ( in @ SV559 @ SV520 )
= $true )
| ( ( epsilon_connected @ SV369 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3327]) ).
thf(3446,plain,
! [SV171: $i,SV524: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV171 )
| ~ ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV524 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV171 )
| ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV524 ) ) )
= $false )
| ( ( SV171 = SV524 )
= $true )
| ( ( relation @ SV524 )
= $false )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3330]) ).
thf(3447,plain,
! [SV525: $i,SV171: $i] :
( ( ( SV171 = SV525 )
= $false )
| ( ( ~ ( ~ ! [SY1400: $i,SY1401: $i] :
( ~ ( in @ ( ordered_pair @ SY1400 @ SY1401 ) @ SV171 )
| ( in @ ( ordered_pair @ SY1400 @ SY1401 ) @ SV525 ) )
| ~ ! [SY1402: $i,SY1403: $i] :
( ~ ( in @ ( ordered_pair @ SY1402 @ SY1403 ) @ SV525 )
| ( in @ ( ordered_pair @ SY1402 @ SY1403 ) @ SV171 ) ) ) )
= $true )
| ( ( relation @ SV525 )
= $false )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3331]) ).
thf(3448,plain,
! [SV526: $i,SV447: $i,SV372: $i] :
( ( ( disjoint @ SV372 @ SV447 )
= $false )
| ( ( in @ SV526 @ SV372 )
= $false )
| ( ( in @ SV526 @ SV447 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3332]) ).
thf(3449,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( sK35_D @ SV272 @ SV172 )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1178: $i] :
( ~ ( in @ SY1178 @ ( sK43_SY691 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SY1178 ) @ SV272 ) )
| ~ ~ ( ( ( sK41_SY666 @ SV272 @ SV172 )
!= ( sK43_SY691 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) ) ) ) ) )
| ( ( sK35_D @ SV272 @ SV172 )
!= ( sK37_SY665 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3333]) ).
thf(3450,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
!= ( sK37_SY665 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1179: $i] :
( ~ ( in @ SY1179 @ ( sK40_SY685 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SY1179 ) @ SV272 ) )
| ~ ~ ( ( ( sK38_SY678 @ SV272 @ SV172 )
!= ( sK40_SY685 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) ) ) ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3333]) ).
thf(3451,plain,
! [SV272: $i,SV622: $i,SV172: $i] :
( ( ( ~ ( ~ ! [SY1440: $i] :
( ! [SY1441: $i] :
( ( SY1441 != SY1440 )
| ~ ( in @ SY1441 @ ( cartesian_product2 @ SV172 @ SV622 ) ) )
| ! [SY1442: $i,SY1443: $i] :
( ( ( ordered_pair @ SY1442 @ SY1443 )
!= SY1440 )
| ~ ( in @ SY1442 @ SV172 )
| ! [SY1444: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1444 @ SY1443 @ SY1442 @ SY1440 @ SV622 @ SV272 @ SV172 ) @ SY1444 )
| ~ ~ ( in @ ( ordered_pair @ SY1443 @ ( sK34_R @ SY1444 @ SY1443 @ SY1442 @ SY1440 @ SV622 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1442 != SY1444 )
| ~ ( in @ SY1443 @ SY1444 ) ) )
| ( in @ SY1440 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) ) )
| ~ ! [SY1445: $i] :
( ~ ( in @ SY1445 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1445 @ SV622 @ SV272 @ SV172 )
!= SY1445 )
| ~ ( in @ ( sK33_F @ SY1445 @ SV622 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV622 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1445 @ SV622 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1445 @ SV622 @ SV272 @ SV172 ) )
!= SY1445 )
| ~ ( in @ ( sK30_O @ SY1445 @ SV622 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1446: $i] :
( ~ ( in @ SY1446 @ ( sK32_SY652 @ SY1445 @ SV622 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1445 @ SV622 @ SV272 @ SV172 ) @ SY1446 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1445 @ SV622 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1445 @ SV622 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1445 @ SV622 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1445 @ SV622 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3334]) ).
thf(3452,plain,
! [SV482: $i,SV173: $i,SV530: $i,SV273: $i] :
( ( ( in @ SV273 @ SV530 )
= $false )
| ( ( in @ SV173 @ SV482 )
= $false )
| ( ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SV482 @ SV530 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3335]) ).
thf(3453,plain,
! [SV623: $i,SV577: $i,SV273: $i,SV173: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SV577 @ SV623 ) ) )
= $true )
| ( ( in @ SV173 @ SV577 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3336]) ).
thf(3454,plain,
! [SV599: $i,SV578: $i,SV273: $i,SV173: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SV578 @ SV599 ) ) )
= $true )
| ( ( in @ SV273 @ SV599 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3337]) ).
thf(3455,plain,
! [SV275: $i,SV176: $i,SV483: $i,SV602: $i,SV579: $i] :
( ( ( ( ( ordered_pair @ SV579 @ SV602 )
!= SV483 )
| ~ ( in @ SV579 @ SV176 ) )
= $true )
| ( ( ( SV602
!= ( singleton @ SV579 ) ) )
= $true )
| ( ( ~ ( in @ SV483 @ ( cartesian_product2 @ SV176 @ SV275 ) ) )
= $true )
| ( ( in @ SV483 @ ( sK108_C @ SV275 @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3340]) ).
thf(3456,plain,
! [SV176: $i,SV275: $i,SV580: $i] :
( ( ( in @ SV580 @ ( sK108_C @ SV275 @ SV176 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK109_E @ SV580 @ SV275 @ SV176 ) @ ( sK110_SY756 @ SV580 @ SV275 @ SV176 ) )
!= SV580 )
| ~ ( in @ ( sK109_E @ SV580 @ SV275 @ SV176 ) @ SV176 ) )
| ( ( sK110_SY756 @ SV580 @ SV275 @ SV176 )
!= ( singleton @ ( sK109_E @ SV580 @ SV275 @ SV176 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3341]) ).
thf(3457,plain,
! [SV176: $i,SV275: $i,SV581: $i] :
( ( ( in @ SV581 @ ( sK108_C @ SV275 @ SV176 ) )
= $false )
| ( ( in @ SV581 @ ( cartesian_product2 @ SV176 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3342]) ).
thf(3458,plain,
! [SV180: $i,SV456: $i,SV484: $i] :
( ( ( ~ ( ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV484 )
| ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV180 ) )
| ~ ( ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV484 )
| ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV456 ) ) )
= $false )
| ( ( SV484
= ( set_union2 @ SV180 @ SV456 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3343]) ).
thf(3459,plain,
! [SV180: $i,SV456: $i,SV484: $i] :
( ( ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV484 )
= $true )
| ( ( ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV180 )
| ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV456 ) )
= $true )
| ( ( SV484
= ( set_union2 @ SV180 @ SV456 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3344]) ).
thf(3460,plain,
! [SV457: $i,SV180: $i,SV485: $i] :
( ( ( ! [SY1361: $i] :
( ~ ( in @ SY1361 @ SV485 )
| ( in @ SY1361 @ SV180 )
| ( in @ SY1361 @ SV457 ) ) )
= $true )
| ( ( SV485
= ( set_union2 @ SV180 @ SV457 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3345]) ).
thf(3461,plain,
! [SV457: $i,SV485: $i,SV180: $i] :
( ( ( ~ ( ~ ! [SY1362: $i] :
( ~ ( in @ SY1362 @ SV180 )
| ( in @ SY1362 @ SV485 ) )
| ~ ! [SY1363: $i] :
( ~ ( in @ SY1363 @ SV457 )
| ( in @ SY1363 @ SV485 ) ) ) )
= $true )
| ( ( SV485
= ( set_union2 @ SV180 @ SV457 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3346]) ).
thf(3462,plain,
! [SV139: $i] :
( ( ( ( ( sK17_C @ SV139 )
!= ( sK18_SY613 @ SV139 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
!= ( sK18_SY613 @ SV139 ) )
| ~ ( in @ ( sK22_SY620 @ SV139 ) @ SV139 ) )
| ( ( sK23_SY629 @ SV139 )
!= ( singleton @ ( sK22_SY620 @ SV139 ) ) ) ) )
= $false )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3348]) ).
thf(3463,plain,
! [SV624: $i,SV139: $i] :
( ( ( ~ ( ~ ! [SY1447: $i] :
( ! [SY1448: $i] :
( ( SY1448 != SY1447 )
| ~ ( in @ SY1448 @ ( cartesian_product2 @ SV139 @ SV624 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1447 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1447 @ ( sK13_C @ SV624 @ SV139 ) ) )
| ~ ! [SY1451: $i] :
( ~ ( in @ SY1451 @ ( sK13_C @ SV624 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1451 @ SV624 @ SV139 )
!= SY1451 )
| ~ ( in @ ( sK16_E @ SY1451 @ SV624 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV624 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1451 @ SV624 @ SV139 ) @ ( sK15_SY612 @ SY1451 @ SV624 @ SV139 ) )
!= SY1451 )
| ~ ( in @ ( sK14_J @ SY1451 @ SV624 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1451 @ SV624 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1451 @ SV624 @ SV139 ) ) ) ) ) ) ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3349]) ).
thf(3464,plain,
! [SV139: $i] :
( ( ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
!= ( sK19_SY619 @ SV139 ) )
| ~ ( in @ ( sK20_SY626 @ SV139 ) @ SV139 ) )
= $false )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3350]) ).
thf(3465,plain,
! [SV625: $i,SV139: $i] :
( ( ( ~ ( ~ ! [SY1452: $i] :
( ! [SY1453: $i] :
( ( SY1453 != SY1452 )
| ~ ( in @ SY1453 @ ( cartesian_product2 @ SV139 @ SV625 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1452 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1452 @ ( sK13_C @ SV625 @ SV139 ) ) )
| ~ ! [SY1456: $i] :
( ~ ( in @ SY1456 @ ( sK13_C @ SV625 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1456 @ SV625 @ SV139 )
!= SY1456 )
| ~ ( in @ ( sK16_E @ SY1456 @ SV625 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV625 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1456 @ SV625 @ SV139 ) @ ( sK15_SY612 @ SY1456 @ SV625 @ SV139 ) )
!= SY1456 )
| ~ ( in @ ( sK14_J @ SY1456 @ SV625 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1456 @ SV625 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1456 @ SV625 @ SV139 ) ) ) ) ) ) ) )
= $true )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3351]) ).
thf(3466,plain,
! [SV488: $i,SV139: $i,SV603: $i] :
( ( ( ! [SY1430: $i] :
( ( SY1430 != SV603 )
| ~ ( in @ SY1430 @ ( cartesian_product2 @ SV139 @ SV488 ) ) )
| ! [SY1431: $i,SY1432: $i] :
( ( ( ordered_pair @ SY1431 @ SY1432 )
!= SV603 )
| ~ ( in @ SY1431 @ SV139 )
| ( SY1432
!= ( singleton @ SY1431 ) ) ) )
= $true )
| ( ( in @ SV603 @ ( sK13_C @ SV488 @ SV139 ) )
= $true )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3352]) ).
thf(3467,plain,
! [SV139: $i,SV488: $i,SV604: $i] :
( ( ( ~ ( in @ SV604 @ ( sK13_C @ SV488 @ SV139 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK16_E @ SV604 @ SV488 @ SV139 )
!= SV604 )
| ~ ( in @ ( sK16_E @ SV604 @ SV488 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV488 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV604 @ SV488 @ SV139 ) @ ( sK15_SY612 @ SV604 @ SV488 @ SV139 ) )
!= SV604 )
| ~ ( in @ ( sK14_J @ SV604 @ SV488 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV604 @ SV488 @ SV139 )
!= ( singleton @ ( sK14_J @ SV604 @ SV488 @ SV139 ) ) ) ) ) )
= $true )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3353]) ).
thf(3468,plain,
! [SV143: $i,SV400: $i,SV461: $i] :
( ( ( ~ ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV143 ) )
= $true )
| ( ( ~ ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV400 ) )
= $true )
| ( ( ~ ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV461 ) )
= $true )
| ( ( SV461
= ( set_intersection2 @ SV143 @ SV400 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3356]) ).
thf(3469,plain,
! [SV143: $i,SV400: $i,SV461: $i] :
( ( ( ~ ( ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV143 )
| ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV461 ) ) )
= $false )
| ( ( SV461
= ( set_intersection2 @ SV143 @ SV400 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3357]) ).
thf(3470,plain,
! [SV143: $i,SV400: $i,SV461: $i] :
( ( ( ~ ( ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV400 )
| ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV461 ) ) )
= $false )
| ( ( SV461
= ( set_intersection2 @ SV143 @ SV400 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3357]) ).
thf(3471,plain,
! [SV462: $i,SV401: $i,SV143: $i,SV626: $i] :
( ( ( ~ ( in @ SV626 @ SV143 )
| ~ ( in @ SV626 @ SV401 )
| ( in @ SV626 @ SV462 ) )
= $true )
| ( ( SV462
= ( set_intersection2 @ SV143 @ SV401 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3358]) ).
thf(3472,plain,
! [SV401: $i,SV143: $i,SV462: $i] :
( ( ( ~ ! [SY1326: $i] :
( ~ ( in @ SY1326 @ SV462 )
| ( in @ SY1326 @ SV143 ) )
| ~ ! [SY1327: $i] :
( ~ ( in @ SY1327 @ SV462 )
| ( in @ SY1327 @ SV401 ) ) )
= $false )
| ( ( SV462
= ( set_intersection2 @ SV143 @ SV401 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3359]) ).
thf(3473,plain,
! [SV144: $i,SV584: $i] :
( ( ( element @ SV584 @ ( powerset @ SV144 ) )
= $false )
| ( ( v1_membered @ SV584 )
= $true )
| ( ( v3_membered @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3360]) ).
thf(3474,plain,
! [SV144: $i,SV585: $i] :
( ( ( element @ SV585 @ ( powerset @ SV144 ) )
= $false )
| ( ( v2_membered @ SV585 )
= $true )
| ( ( v3_membered @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3361]) ).
thf(3475,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1142: $i] :
( ~ ( in @ SY1142 @ ( sK52_SY712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SY1142 ) @ SV265 ) )
| ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK52_SY712 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) ) ) )
| ~ ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 ) )
| ~ ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3362]) ).
thf(3476,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ ( sK51_SY718 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SY1143 ) @ SV265 ) )
| ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK51_SY718 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3363]) ).
thf(3477,plain,
! [SV265: $i,SV145: $i] :
( ( ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3364]) ).
thf(3478,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) )
= $false )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3364]) ).
thf(3479,plain,
! [SV147: $i,SV403: $i,SV463: $i] :
( ( ( ~ ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV147 ) )
= $true )
| ( ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV403 )
= $true )
| ( ( ~ ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV463 ) )
= $true )
| ( ( SV463
= ( set_difference @ SV147 @ SV403 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3366]) ).
thf(3480,plain,
! [SV147: $i,SV403: $i,SV463: $i] :
( ( ( ~ ( ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV147 )
| ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV463 ) ) )
= $false )
| ( ( SV463
= ( set_difference @ SV147 @ SV403 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3367]) ).
thf(3481,plain,
! [SV147: $i,SV403: $i,SV463: $i] :
( ( ( ~ ( ~ ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV403 )
| ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV463 ) ) )
= $false )
| ( ( SV463
= ( set_difference @ SV147 @ SV403 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3367]) ).
thf(3482,plain,
! [SV464: $i,SV404: $i,SV147: $i,SV627: $i] :
( ( ( ~ ( in @ SV627 @ SV147 )
| ( in @ SV627 @ SV404 )
| ( in @ SV627 @ SV464 ) )
= $true )
| ( ( SV464
= ( set_difference @ SV147 @ SV404 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3368]) ).
thf(3483,plain,
! [SV404: $i,SV147: $i,SV464: $i] :
( ( ( ~ ! [SY1329: $i] :
( ~ ( in @ SY1329 @ SV464 )
| ( in @ SY1329 @ SV147 ) )
| ~ ! [SY1330: $i] :
( ~ ( in @ SY1330 @ SV464 )
| ~ ( in @ SY1330 @ SV404 ) ) )
= $false )
| ( ( SV464
= ( set_difference @ SV147 @ SV404 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3369]) ).
thf(3484,plain,
! [SV148: $i,SV335: $i,SV605: $i] :
( ( ( ~ ( in @ SV605 @ SV335 )
| ~ ( subset @ ( sK105_C @ SV335 @ SV148 ) @ SV605 ) )
= $true )
| ( ( SV605
= ( sK105_C @ SV335 @ SV148 ) )
= $true )
| ( ( SV335 = empty_set )
= $true )
| ( ( element @ SV335 @ ( powerset @ ( powerset @ SV148 ) ) )
= $false )
| ( ( finite @ SV148 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3370]) ).
thf(3485,plain,
! [SV606: $i,SV340: $i,SV409: $i] :
( ( ( ~ ( in @ ( sK68_C @ SV409 @ SV340 ) @ SV606 ) )
= $true )
| ( ( ~ ( in @ SV606 @ SV340 ) )
= $true )
| ( ( ~ ( in @ ( sK68_C @ SV409 @ SV340 ) @ SV409 ) )
= $true )
| ( ( SV409
= ( union @ SV340 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3371]) ).
thf(3486,plain,
! [SV340: $i,SV409: $i] :
( ( ( ~ ( in @ ( sK68_C @ SV409 @ SV340 ) @ ( sK69_SY723 @ SV409 @ SV340 ) ) )
= $false )
| ( ( in @ ( sK68_C @ SV409 @ SV340 ) @ SV409 )
= $true )
| ( ( SV409
= ( union @ SV340 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3372]) ).
thf(3487,plain,
! [SV340: $i,SV409: $i] :
( ( ( ~ ( in @ ( sK69_SY723 @ SV409 @ SV340 ) @ SV340 ) )
= $false )
| ( ( in @ ( sK68_C @ SV409 @ SV340 ) @ SV409 )
= $true )
| ( ( SV409
= ( union @ SV340 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3372]) ).
thf(3488,plain,
! [SV410: $i,SV341: $i,SV607: $i] :
( ( ( ! [SY1433: $i] :
( ~ ( in @ SV607 @ SY1433 )
| ~ ( in @ SY1433 @ SV341 ) ) )
= $true )
| ( ( in @ SV607 @ SV410 )
= $true )
| ( ( SV410
= ( union @ SV341 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3373]) ).
thf(3489,plain,
! [SV341: $i,SV410: $i,SV608: $i] :
( ( ( ~ ( in @ SV608 @ SV410 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV608 @ ( sK67_D @ SV608 @ SV410 @ SV341 ) )
| ~ ( in @ ( sK67_D @ SV608 @ SV410 @ SV341 ) @ SV341 ) ) )
= $true )
| ( ( SV410
= ( union @ SV341 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3374]) ).
thf(3490,plain,
! [SV500: $i,SV586: $i] :
( ( ( element @ SV586 @ SV500 )
= $false )
| ( ( empty @ SV586 )
= $true )
| ( ( empty @ SV500 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3377]) ).
thf(3491,plain,
! [SV501: $i,SV587: $i] :
( ( ( empty @ SV587 )
= $false )
| ( ( element @ SV587 @ SV501 )
= $true )
| ( ( empty @ SV501 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3378]) ).
thf(3492,plain,
! [SV346: $i,SV413: $i] :
( ( ( subset @ ( sK124_C @ SV413 @ SV346 ) @ SV346 )
= $false )
| ( ( in @ ( sK124_C @ SV413 @ SV346 ) @ SV413 )
= $false )
| ( ( SV413
= ( powerset @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3379]) ).
thf(3493,plain,
! [SV347: $i,SV414: $i,SV609: $i] :
( ( ( ~ ( in @ SV609 @ SV414 ) )
= $true )
| ( ( subset @ SV609 @ SV347 )
= $true )
| ( ( SV414
= ( powerset @ SV347 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3380]) ).
thf(3494,plain,
! [SV414: $i,SV347: $i,SV610: $i] :
( ( ( ~ ( subset @ SV610 @ SV347 ) )
= $true )
| ( ( in @ SV610 @ SV414 )
= $true )
| ( ( SV414
= ( powerset @ SV347 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3381]) ).
thf(3495,plain,
! [SV150: $i,SV415: $i,SV465: $i] :
( ( ( ! [SY1331: $i] :
~ ( in @ ( ordered_pair @ SY1331 @ ( sK102_D @ SV465 @ SV415 @ SV150 ) ) @ SV465 ) )
= $true )
| ( ( ( relation_rng_as_subset @ SV150 @ SV415 @ SV465 )
= SV415 )
= $true )
| ( ( relation_of2_as_subset @ SV465 @ SV150 @ SV415 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3382]) ).
thf(3496,plain,
! [SV150: $i,SV415: $i,SV465: $i] :
( ( ( in @ ( sK102_D @ SV465 @ SV415 @ SV150 ) @ SV415 )
= $true )
| ( ( ( relation_rng_as_subset @ SV150 @ SV415 @ SV465 )
= SV415 )
= $true )
| ( ( relation_of2_as_subset @ SV465 @ SV150 @ SV415 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3383]) ).
thf(3497,plain,
! [SV150: $i,SV416: $i,SV466: $i,SV611: $i] :
( ( ( in @ ( ordered_pair @ ( sK101_E @ SV611 @ SV466 @ SV416 @ SV150 ) @ SV611 ) @ SV466 )
= $true )
| ( ( ~ ( in @ SV611 @ SV416 ) )
= $true )
| ( ( ( relation_rng_as_subset @ SV150 @ SV416 @ SV466 )
= SV416 )
= $false )
| ( ( relation_of2_as_subset @ SV466 @ SV150 @ SV416 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3384]) ).
thf(3498,plain,
! [SV151: $i,SV267: $i,SV467: $i,SV502: $i] :
( ( ( ~ ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV467 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV151 ) )
| ~ ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV267 ) ) ) )
= $false )
| ( ( SV502
= ( unordered_triple @ SV151 @ SV267 @ SV467 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3385]) ).
thf(3499,plain,
! [SV151: $i,SV267: $i,SV467: $i,SV502: $i] :
( ( ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
= $true )
| ( ( ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
= SV467 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
= SV151 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
= SV267 ) )
= $true )
| ( ( SV502
= ( unordered_triple @ SV151 @ SV267 @ SV467 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3386]) ).
thf(3500,plain,
! [SV267: $i,SV151: $i,SV468: $i,SV503: $i] :
( ( ( ! [SY1379: $i] :
( ~ ( in @ SY1379 @ SV503 )
| ( SY1379 = SV468 )
| ( SY1379 = SV151 )
| ( SY1379 = SV267 ) ) )
= $true )
| ( ( SV503
= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3387]) ).
thf(3501,plain,
! [SV267: $i,SV151: $i,SV503: $i,SV468: $i] :
( ( ( ~ ( ~ ! [SY1380: $i] :
( ( SY1380 != SV468 )
| ( in @ SY1380 @ SV503 ) )
| ~ ~ ( ~ ! [SY1381: $i] :
( ( SY1381 != SV151 )
| ( in @ SY1381 @ SV503 ) )
| ~ ! [SY1382: $i] :
( ( SY1382 != SV267 )
| ( in @ SY1382 @ SV503 ) ) ) ) )
= $true )
| ( ( SV503
= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3388]) ).
thf(3502,plain,
! [SV628: $i,SV152: $i,SV612: $i] :
( ( ~ ( in @ SV612 @ ( sK106_B @ SV152 ) )
| ~ ( subset @ SV628 @ SV612 )
| ( in @ SV628 @ ( sK106_B @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3389]) ).
thf(3503,plain,
! [SV154: $i,SV504: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK72_C @ SV504 @ SV154 ) @ ( sK73_SY724 @ SV504 @ SV154 ) ) @ SV154 ) )
= $false )
| ( ( subset @ SV154 @ SV504 )
= $true )
| ( ( relation @ SV504 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3390]) ).
thf(3504,plain,
! [SV154: $i,SV504: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK72_C @ SV504 @ SV154 ) @ ( sK73_SY724 @ SV504 @ SV154 ) ) @ SV504 ) )
= $false )
| ( ( subset @ SV154 @ SV504 )
= $true )
| ( ( relation @ SV504 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3390]) ).
thf(3505,plain,
! [SV505: $i,SV154: $i,SV629: $i] :
( ( ( ! [SY1457: $i] :
( ~ ( in @ ( ordered_pair @ SV629 @ SY1457 ) @ SV154 )
| ( in @ ( ordered_pair @ SV629 @ SY1457 ) @ SV505 ) ) )
= $true )
| ( ( subset @ SV154 @ SV505 )
= $false )
| ( ( relation @ SV505 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3391]) ).
thf(3506,plain,
! [SV155: $i,SV268: $i,SV547: $i] :
( ( ( ~ ( element @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ ( powerset @ SV155 ) )
| ~ ~ ( ~ ( ~ ( in @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ SV547 )
| ~ ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SV547 @ SV268 @ SV155 ) ) @ SV268 ) )
| ~ ( ( in @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ SV547 )
| ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SV547 @ SV268 @ SV155 ) ) @ SV268 ) ) ) )
= $false )
| ( ( SV547
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $true )
| ( ( element @ SV547 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3392]) ).
thf(3507,plain,
! [SV268: $i,SV155: $i,SV548: $i] :
( ( ( SV548
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $false )
| ( ( ~ ( ~ ! [SY1408: $i] :
( ~ ( element @ SY1408 @ ( powerset @ SV155 ) )
| ~ ( in @ SY1408 @ SV548 )
| ( in @ ( subset_complement @ SV155 @ SY1408 ) @ SV268 ) )
| ~ ! [SY1409: $i] :
( ~ ( element @ SY1409 @ ( powerset @ SV155 ) )
| ~ ( in @ ( subset_complement @ SV155 @ SY1409 ) @ SV268 )
| ( in @ SY1409 @ SV548 ) ) ) )
= $true )
| ( ( element @ SV548 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3393]) ).
thf(3508,plain,
! [SV425: $i,SV566: $i,SV630: $i] :
( ( ( ( SV630 != SV566 )
| ~ ( in @ SV630 @ SV425 ) )
= $true )
| ( ( ~ ( ordinal @ SV566 ) )
= $true )
| ( ( in @ SV566 @ ( sK7_B @ SV425 ) )
= $true )
| ( sK12_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3394]) ).
thf(3509,plain,
! [SV425: $i,SV567: $i] :
( ( ( ~ ~ ( ( ( sK8_D @ SV567 @ SV425 )
!= SV567 )
| ~ ( in @ ( sK8_D @ SV567 @ SV425 ) @ SV425 ) )
| ~ ( ordinal @ SV567 ) )
= $false )
| ( ( in @ SV567 @ ( sK7_B @ SV425 ) )
= $false )
| ( sK12_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[3395]) ).
thf(3510,plain,
( ( ( ~ ~ ( ( sK9_B != sK10_SY601 )
| ~ ( ordinal @ sK10_SY601 ) )
| ( sK9_B != sK11_SY603 ) )
= $false )
| ( sK12_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[3396]) ).
thf(3511,plain,
! [SV469: $i,SV426: $i,SV157: $i] :
( ( ( in @ SV157 @ ( cartesian_product2 @ SV426 @ SV426 ) )
= $false )
| ( ( in @ SV157 @ SV469 )
= $false )
| ( ( in @ SV157 @ ( relation_restriction @ SV469 @ SV426 ) )
= $true )
| ( ( relation @ SV469 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3398]) ).
thf(3512,plain,
! [SV551: $i,SV568: $i,SV157: $i] :
( ( ( ~ ( in @ SV157 @ ( relation_restriction @ SV568 @ SV551 ) ) )
= $true )
| ( ( in @ SV157 @ SV568 )
= $true )
| ( ( relation @ SV568 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3399]) ).
thf(3513,plain,
! [SV552: $i,SV569: $i,SV157: $i] :
( ( ( ~ ( in @ SV157 @ ( relation_restriction @ SV569 @ SV552 ) ) )
= $true )
| ( ( in @ SV157 @ ( cartesian_product2 @ SV552 @ SV552 ) )
= $true )
| ( ( relation @ SV569 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3400]) ).
thf(3514,plain,
! [SV613: $i,SV158: $i,SV631: $i] :
( ( ~ ( relation_of2_as_subset @ SV631 @ SV158 @ SV613 )
| ( SV613 = empty_set )
| ( SV158
!= ( relation_dom_as_subset @ SV158 @ SV613 @ SV631 ) )
| ( quasi_total @ SV631 @ SV158 @ SV613 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3401]) ).
thf(3515,plain,
! [SV614: $i,SV158: $i,SV632: $i] :
( ( ~ ( relation_of2_as_subset @ SV632 @ SV158 @ SV614 )
| ( SV614 = empty_set )
| ~ ( quasi_total @ SV632 @ SV158 @ SV614 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SV614 @ SV632 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3402]) ).
thf(3516,plain,
! [SV615: $i,SV158: $i,SV633: $i] :
( ( ~ ( relation_of2_as_subset @ SV633 @ SV158 @ SV615 )
| ( SV158 != empty_set )
| ( SV158
!= ( relation_dom_as_subset @ SV158 @ SV615 @ SV633 ) )
| ( quasi_total @ SV633 @ SV158 @ SV615 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3403]) ).
thf(3517,plain,
! [SV616: $i,SV158: $i,SV634: $i] :
( ( ~ ( relation_of2_as_subset @ SV634 @ SV158 @ SV616 )
| ( SV158 != empty_set )
| ~ ( quasi_total @ SV634 @ SV158 @ SV616 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SV616 @ SV634 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3404]) ).
thf(3518,plain,
! [SV158: $i,SV570: $i,SV553: $i] :
( ( ( ( SV553 != empty_set ) )
= $true )
| ( ( ( SV570 != empty_set )
| ( quasi_total @ SV570 @ SV158 @ SV553 )
| ( SV158 = empty_set ) )
= $true )
| ( ( relation_of2_as_subset @ SV570 @ SV158 @ SV553 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3405]) ).
thf(3519,plain,
! [SV158: $i,SV571: $i,SV554: $i] :
( ( ( ( SV554 != empty_set ) )
= $true )
| ( ( ~ ( quasi_total @ SV571 @ SV158 @ SV554 )
| ( SV571 = empty_set )
| ( SV158 = empty_set ) )
= $true )
| ( ( relation_of2_as_subset @ SV571 @ SV158 @ SV554 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3406]) ).
thf(3520,plain,
! [SV512: $i,SV572: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK90_SY733 @ SV572 @ SV512 ) @ SV512 )
| ~ ~ ( in @ ( sK89_C @ SV572 @ SV512 ) @ ( sK90_SY733 @ SV572 @ SV512 ) ) )
| ~ ( in @ ( sK89_C @ SV572 @ SV512 ) @ SV572 ) ) )
= $false )
| ( ( SV572
= ( set_meet @ SV512 ) )
= $true )
| ( ( SV512 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3407]) ).
thf(3521,plain,
! [SV572: $i,SV512: $i] :
( ( ( ~ ( ! [SY1416: $i] :
( ~ ( in @ SY1416 @ SV512 )
| ( in @ ( sK89_C @ SV572 @ SV512 ) @ SY1416 ) )
| ( in @ ( sK89_C @ SV572 @ SV512 ) @ SV572 ) ) )
= $false )
| ( ( SV572
= ( set_meet @ SV512 ) )
= $true )
| ( ( SV512 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3407]) ).
thf(3522,plain,
! [SV513: $i,SV573: $i] :
( ( ( ~ ! [SY1417: $i] :
( ~ ( ~ ( in @ ( sK88_D @ SY1417 @ SV573 @ SV513 ) @ SV513 )
| ~ ~ ( in @ SY1417 @ ( sK88_D @ SY1417 @ SV573 @ SV513 ) ) )
| ( in @ SY1417 @ SV573 ) )
| ~ ! [SY1418: $i] :
( ~ ( in @ SY1418 @ SV573 )
| ! [SY1394: $i] :
( ~ ( in @ SY1394 @ SV513 )
| ( in @ SY1418 @ SY1394 ) ) ) )
= $false )
| ( ( SV573
= ( set_meet @ SV513 ) )
= $false )
| ( ( SV513 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3408]) ).
thf(3523,plain,
! [SV514: $i,SV590: $i] :
( ( ( SV590
= ( set_meet @ SV514 ) )
= $false )
| ( ( SV590 = empty_set )
= $true )
| ( ( SV514 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3409]) ).
thf(3524,plain,
! [SV515: $i,SV591: $i] :
( ( ( SV591 = empty_set )
= $false )
| ( ( SV591
= ( set_meet @ SV515 ) )
= $true )
| ( ( SV515 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3410]) ).
thf(3525,plain,
! [SV159: $i,SV427: $i,SV470: $i] :
( ( ( ~ ( ~ ( in @ ( sK82_D @ SV470 @ SV427 @ SV159 ) @ SV470 )
| ( ( sK82_D @ SV470 @ SV427 @ SV159 )
!= SV159 ) ) )
= $false )
| ( ( SV470
= ( unordered_pair @ SV159 @ SV427 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3411]) ).
thf(3526,plain,
! [SV159: $i,SV427: $i,SV470: $i] :
( ( ( ~ ( ~ ( in @ ( sK82_D @ SV470 @ SV427 @ SV159 ) @ SV470 )
| ( ( sK82_D @ SV470 @ SV427 @ SV159 )
!= SV427 ) ) )
= $false )
| ( ( SV470
= ( unordered_pair @ SV159 @ SV427 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3411]) ).
thf(3527,plain,
! [SV159: $i,SV427: $i,SV470: $i] :
( ( ( ( sK82_D @ SV470 @ SV427 @ SV159 )
= SV159 )
= $true )
| ( ( ( sK82_D @ SV470 @ SV427 @ SV159 )
= SV427 )
= $true )
| ( ( in @ ( sK82_D @ SV470 @ SV427 @ SV159 ) @ SV470 )
= $true )
| ( ( SV470
= ( unordered_pair @ SV159 @ SV427 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3412]) ).
thf(3528,plain,
! [SV428: $i,SV159: $i,SV471: $i,SV635: $i] :
( ( ( ~ ( in @ SV635 @ SV471 )
| ( SV635 = SV159 )
| ( SV635 = SV428 ) )
= $true )
| ( ( SV471
= ( unordered_pair @ SV159 @ SV428 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3413]) ).
thf(3529,plain,
! [SV428: $i,SV471: $i,SV159: $i] :
( ( ( ~ ! [SY1340: $i] :
( ( SY1340 != SV159 )
| ( in @ SY1340 @ SV471 ) )
| ~ ! [SY1341: $i] :
( ( SY1341 != SV428 )
| ( in @ SY1341 @ SV471 ) ) )
= $false )
| ( ( SV471
= ( unordered_pair @ SV159 @ SV428 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3414]) ).
thf(3530,plain,
! [SV162: $i,SV555: $i,SV269: $i] :
( ( ( disjoint @ SV269 @ SV555 )
= $false )
| ( ( subset @ SV269 @ ( subset_complement @ SV162 @ SV555 ) )
= $true )
| ( ( element @ SV555 @ ( powerset @ SV162 ) )
= $false )
| ( ( element @ SV269 @ ( powerset @ SV162 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3416]) ).
thf(3531,plain,
! [SV556: $i,SV162: $i,SV269: $i] :
( ( ( subset @ SV269 @ ( subset_complement @ SV162 @ SV556 ) )
= $false )
| ( ( disjoint @ SV269 @ SV556 )
= $true )
| ( ( element @ SV556 @ ( powerset @ SV162 ) )
= $false )
| ( ( element @ SV269 @ ( powerset @ SV162 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3417]) ).
thf(3532,plain,
! [SV364: $i,SV435: $i] :
( ( ( in @ ( sK87_C @ SV435 @ SV364 ) @ SV435 )
= $false )
| ( ( ( sK87_C @ SV435 @ SV364 )
= SV364 )
= $false )
| ( ( SV435
= ( singleton @ SV364 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3418]) ).
thf(3533,plain,
! [SV436: $i,SV365: $i,SV617: $i] :
( ( ( ( SV617 != SV365 ) )
= $true )
| ( ( in @ SV617 @ SV436 )
= $true )
| ( ( SV436
= ( singleton @ SV365 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3419]) ).
thf(3534,plain,
! [SV365: $i,SV436: $i,SV618: $i] :
( ( ( ~ ( in @ SV618 @ SV436 ) )
= $true )
| ( ( SV618 = SV365 )
= $true )
| ( ( SV436
= ( singleton @ SV365 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3420]) ).
thf(3535,plain,
! [SV474: $i,SV437: $i,SV164: $i,SV636: $i] :
( ( ( ! [SY1458: $i] :
( ~ ( in @ SV636 @ SV164 )
| ~ ( in @ SY1458 @ SV437 )
| ( ( sK78_D @ SV474 @ SV437 @ SV164 )
!= ( ordered_pair @ SV636 @ SY1458 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK78_D @ SV474 @ SV437 @ SV164 ) @ SV474 ) )
= $true )
| ( ( SV474
= ( cartesian_product2 @ SV164 @ SV437 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3421]) ).
thf(3536,plain,
! [SV164: $i,SV437: $i,SV474: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK79_SY729 @ SV474 @ SV437 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK80_SY731 @ SV474 @ SV437 @ SV164 ) @ SV437 ) )
| ( ( sK78_D @ SV474 @ SV437 @ SV164 )
!= ( ordered_pair @ ( sK79_SY729 @ SV474 @ SV437 @ SV164 ) @ ( sK80_SY731 @ SV474 @ SV437 @ SV164 ) ) ) )
= $false )
| ( ( in @ ( sK78_D @ SV474 @ SV437 @ SV164 ) @ SV474 )
= $true )
| ( ( SV474
= ( cartesian_product2 @ SV164 @ SV437 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3422]) ).
thf(3537,plain,
! [SV475: $i,SV637: $i,SV438: $i,SV164: $i] :
( ( ( ! [SY1459: $i,SY1460: $i] :
( ~ ( in @ SY1459 @ SV164 )
| ~ ( in @ SY1460 @ SV438 )
| ( SV637
!= ( ordered_pair @ SY1459 @ SY1460 ) ) )
| ( in @ SV637 @ SV475 ) )
= $true )
| ( ( SV475
= ( cartesian_product2 @ SV164 @ SV438 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3423]) ).
thf(3538,plain,
! [SV164: $i,SV438: $i,SV475: $i,SV638: $i] :
( ( ( ~ ( in @ SV638 @ SV475 )
| ~ ( ~ ~ ( ~ ( in @ ( sK76_E @ SV638 @ SV475 @ SV438 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK77_SY726 @ SV638 @ SV475 @ SV438 @ SV164 ) @ SV438 ) )
| ( SV638
!= ( ordered_pair @ ( sK76_E @ SV638 @ SV475 @ SV438 @ SV164 ) @ ( sK77_SY726 @ SV638 @ SV475 @ SV438 @ SV164 ) ) ) ) )
= $true )
| ( ( SV475
= ( cartesian_product2 @ SV164 @ SV438 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3424]) ).
thf(3539,plain,
! [SV166: $i,SV558: $i] :
( ( ( ! [SY1414: $i] :
( ~ ( subset @ SY1414 @ SV558 )
| ( in @ SY1414 @ ( sK4_SY591 @ SV558 @ SV166 ) ) ) )
= $true )
| ( ( ~ ( in @ SV558 @ ( sK3_B @ SV166 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3425]) ).
thf(3540,plain,
! [SV166: $i,SV558: $i] :
( ( ( in @ ( sK4_SY591 @ SV558 @ SV166 ) @ ( sK3_B @ SV166 ) )
= $true )
| ( ( ~ ( in @ SV558 @ ( sK3_B @ SV166 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3426]) ).
thf(3541,plain,
! [SV639: $i,SV166: $i,SV619: $i] :
( ( ~ ( in @ SV619 @ ( sK3_B @ SV166 ) )
| ~ ( subset @ SV639 @ SV619 )
| ( in @ SV639 @ ( sK3_B @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3427]) ).
thf(3542,plain,
! [SV167: $i,SV444: $i,SV478: $i] :
( ( ( ! [SY1348: $i] :
~ ( in @ ( ordered_pair @ ( sK104_D @ SV478 @ SV444 @ SV167 ) @ SY1348 ) @ SV478 ) )
= $true )
| ( ( ( relation_dom_as_subset @ SV444 @ SV167 @ SV478 )
= SV444 )
= $true )
| ( ( relation_of2_as_subset @ SV478 @ SV444 @ SV167 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3428]) ).
thf(3543,plain,
! [SV167: $i,SV444: $i,SV478: $i] :
( ( ( in @ ( sK104_D @ SV478 @ SV444 @ SV167 ) @ SV444 )
= $true )
| ( ( ( relation_dom_as_subset @ SV444 @ SV167 @ SV478 )
= SV444 )
= $true )
| ( ( relation_of2_as_subset @ SV478 @ SV444 @ SV167 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3429]) ).
thf(3544,plain,
! [SV167: $i,SV445: $i,SV479: $i,SV620: $i] :
( ( ( in @ ( ordered_pair @ SV620 @ ( sK103_E @ SV620 @ SV479 @ SV445 @ SV167 ) ) @ SV479 )
= $true )
| ( ( ~ ( in @ SV620 @ SV445 ) )
= $true )
| ( ( ( relation_dom_as_subset @ SV445 @ SV167 @ SV479 )
= SV445 )
= $false )
| ( ( relation_of2_as_subset @ SV479 @ SV445 @ SV167 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3430]) ).
thf(3545,plain,
! [SV168: $i] :
( ( ( ( ( sK27_SY634 @ SV168 )
!= ( singleton @ ( sK26_B @ SV168 ) ) )
| ~ ( in @ ( sK26_B @ SV168 ) @ SV168 ) )
= $false )
| ( ( ~ ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) )
| ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3431]) ).
thf(3546,plain,
! [SV168: $i] :
( ( ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) )
| ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) )
= $false )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3432]) ).
thf(3547,plain,
! [SV640: $i,SV168: $i] :
( ( ( ! [SY1461: $i] :
( ~ ( in @ SY1461 @ SV168 )
| ( SV640
!= ( singleton @ SY1461 ) ) )
| ( in @ SV640 @ ( sK24_B @ SV168 ) ) )
= $true )
| ( ( ( sK28_SY636 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3433]) ).
thf(3548,plain,
! [SV168: $i,SV641: $i] :
( ( ( ~ ( in @ SV641 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SV641 @ SV168 ) @ SV168 )
| ( SV641
!= ( singleton @ ( sK25_D @ SV641 @ SV168 ) ) ) ) )
= $true )
| ( ( ( sK28_SY636 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3434]) ).
thf(3549,plain,
! [SV593: $i,SV168: $i,SV642: $i] :
( ( ( ~ ( in @ SV642 @ SV168 )
| ( SV593
!= ( singleton @ SV642 ) ) )
= $true )
| ( ( in @ SV593 @ ( sK24_B @ SV168 ) )
= $true )
| ( ( ( sK27_SY634 @ SV168 )
= ( sK28_SY636 @ SV168 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3435]) ).
thf(3550,plain,
! [SV168: $i,SV594: $i] :
( ( ( in @ SV594 @ ( sK24_B @ SV168 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK25_D @ SV594 @ SV168 ) @ SV168 )
| ( SV594
!= ( singleton @ ( sK25_D @ SV594 @ SV168 ) ) ) ) )
= $true )
| ( ( ( sK27_SY634 @ SV168 )
= ( sK28_SY636 @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3436]) ).
thf(3551,plain,
! [SV621: $i,SV575: $i,SV270: $i,SV169: $i] :
( ( ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SV575 @ SV621 ) )
= $false )
| ( ( in @ SV169 @ SV575 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3438]) ).
thf(3552,plain,
! [SV595: $i,SV576: $i,SV270: $i,SV169: $i] :
( ( ( in @ ( ordered_pair @ SV169 @ SV270 ) @ ( cartesian_product2 @ SV576 @ SV595 ) )
= $false )
| ( ( in @ SV270 @ SV595 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3439]) ).
thf(3553,plain,
! [SV271: $i,SV481: $i,SV170: $i,SV596: $i] :
( ( ( ! [SY1427: $i,SY1428: $i] :
( ( ( ordered_pair @ SY1427 @ SY1428 )
!= SV596 )
| ~ ( in @ SY1427 @ SV170 )
| ! [SY1429: $i] :
( ~ ( ~ ( in @ ( sK115_I @ SY1429 @ SY1428 @ SY1427 @ SV596 @ SV481 @ SV271 @ SV170 ) @ SY1429 )
| ~ ~ ( in @ ( ordered_pair @ SY1428 @ ( sK115_I @ SY1429 @ SY1428 @ SY1427 @ SV596 @ SV481 @ SV271 @ SV170 ) ) @ SV271 ) )
| ( SY1427 != SY1429 )
| ~ ( in @ SY1428 @ SY1429 ) ) ) )
= $true )
| ( ( ~ ( in @ SV596 @ ( cartesian_product2 @ SV170 @ SV481 ) ) )
= $true )
| ( ( in @ SV596 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3440]) ).
thf(3554,plain,
! [SV170: $i,SV271: $i,SV481: $i] :
( ( ( ! [SY1355: $i] :
( ~ ( in @ SY1355 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
| ~ ( ~ ~ ( ( ( ordered_pair @ ( sK112_F @ SY1355 @ SV481 @ SV271 @ SV170 ) @ ( sK113_SY768 @ SY1355 @ SV481 @ SV271 @ SV170 ) )
!= SY1355 )
| ~ ( in @ ( sK112_F @ SY1355 @ SV481 @ SV271 @ SV170 ) @ SV170 ) )
| ~ ~ ( ~ ! [SY1356: $i] :
( ~ ( in @ SY1356 @ ( sK114_SY771 @ SY1355 @ SV481 @ SV271 @ SV170 ) )
| ( in @ ( ordered_pair @ ( sK113_SY768 @ SY1355 @ SV481 @ SV271 @ SV170 ) @ SY1356 ) @ SV271 ) )
| ~ ~ ( ( ( sK112_F @ SY1355 @ SV481 @ SV271 @ SV170 )
!= ( sK114_SY771 @ SY1355 @ SV481 @ SV271 @ SV170 ) )
| ~ ( in @ ( sK113_SY768 @ SY1355 @ SV481 @ SV271 @ SV170 ) @ ( sK114_SY771 @ SY1355 @ SV481 @ SV271 @ SV170 ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3441]) ).
thf(3555,plain,
! [SV170: $i,SV271: $i,SV481: $i] :
( ( ( ! [SY1357: $i] :
( ~ ( in @ SY1357 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
| ( in @ SY1357 @ ( cartesian_product2 @ SV170 @ SV481 ) ) ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3442]) ).
thf(3556,plain,
! [SV368: $i] :
( ( ( ( sK74_B @ SV368 )
= ( sK75_SY725 @ SV368 ) )
= $false )
| ( ( epsilon_connected @ SV368 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3443]) ).
thf(3557,plain,
! [SV368: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK74_B @ SV368 ) @ SV368 )
| ~ ( in @ ( sK75_SY725 @ SV368 ) @ SV368 ) )
| ~ ~ ( in @ ( sK74_B @ SV368 ) @ ( sK75_SY725 @ SV368 ) ) )
= $false )
| ( ( epsilon_connected @ SV368 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3444]) ).
thf(3558,plain,
! [SV559: $i,SV369: $i,SV520: $i] :
( ( ( ~ ( in @ SV520 @ SV369 ) )
= $true )
| ( ( ~ ( in @ SV559 @ SV369 ) )
= $true )
| ( ( in @ SV520 @ SV559 )
= $true )
| ( ( SV520 = SV559 )
= $true )
| ( ( in @ SV559 @ SV520 )
= $true )
| ( ( epsilon_connected @ SV369 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3445]) ).
thf(3559,plain,
! [SV171: $i,SV524: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV171 )
| ~ ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV524 ) ) )
= $false )
| ( ( SV171 = SV524 )
= $true )
| ( ( relation @ SV524 )
= $false )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3446]) ).
thf(3560,plain,
! [SV171: $i,SV524: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV171 )
| ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV524 ) ) )
= $false )
| ( ( SV171 = SV524 )
= $true )
| ( ( relation @ SV524 )
= $false )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3446]) ).
thf(3561,plain,
! [SV525: $i,SV171: $i] :
( ( ( ~ ! [SY1400: $i,SY1401: $i] :
( ~ ( in @ ( ordered_pair @ SY1400 @ SY1401 ) @ SV171 )
| ( in @ ( ordered_pair @ SY1400 @ SY1401 ) @ SV525 ) )
| ~ ! [SY1402: $i,SY1403: $i] :
( ~ ( in @ ( ordered_pair @ SY1402 @ SY1403 ) @ SV525 )
| ( in @ ( ordered_pair @ SY1402 @ SY1403 ) @ SV171 ) ) )
= $false )
| ( ( SV171 = SV525 )
= $false )
| ( ( relation @ SV525 )
= $false )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3447]) ).
thf(3562,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ( ~ ~ ( ( ( sK35_D @ SV272 @ SV172 )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1178: $i] :
( ~ ( in @ SY1178 @ ( sK43_SY691 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SY1178 ) @ SV272 ) )
| ~ ~ ( ( ( sK41_SY666 @ SV272 @ SV172 )
!= ( sK43_SY691 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) ) ) ) ) )
| ( ( sK35_D @ SV272 @ SV172 )
!= ( sK37_SY665 @ SV272 @ SV172 ) ) ) )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3449]) ).
thf(3563,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
!= ( sK37_SY665 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1179: $i] :
( ~ ( in @ SY1179 @ ( sK40_SY685 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SY1179 ) @ SV272 ) )
| ~ ~ ( ( ( sK38_SY678 @ SV272 @ SV172 )
!= ( sK40_SY685 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) ) ) ) ) )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3450]) ).
thf(3564,plain,
! [SV272: $i,SV622: $i,SV172: $i] :
( ( ( ~ ! [SY1440: $i] :
( ! [SY1441: $i] :
( ( SY1441 != SY1440 )
| ~ ( in @ SY1441 @ ( cartesian_product2 @ SV172 @ SV622 ) ) )
| ! [SY1442: $i,SY1443: $i] :
( ( ( ordered_pair @ SY1442 @ SY1443 )
!= SY1440 )
| ~ ( in @ SY1442 @ SV172 )
| ! [SY1444: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1444 @ SY1443 @ SY1442 @ SY1440 @ SV622 @ SV272 @ SV172 ) @ SY1444 )
| ~ ~ ( in @ ( ordered_pair @ SY1443 @ ( sK34_R @ SY1444 @ SY1443 @ SY1442 @ SY1440 @ SV622 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1442 != SY1444 )
| ~ ( in @ SY1443 @ SY1444 ) ) )
| ( in @ SY1440 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) ) )
| ~ ! [SY1445: $i] :
( ~ ( in @ SY1445 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1445 @ SV622 @ SV272 @ SV172 )
!= SY1445 )
| ~ ( in @ ( sK33_F @ SY1445 @ SV622 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV622 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1445 @ SV622 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1445 @ SV622 @ SV272 @ SV172 ) )
!= SY1445 )
| ~ ( in @ ( sK30_O @ SY1445 @ SV622 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1446: $i] :
( ~ ( in @ SY1446 @ ( sK32_SY652 @ SY1445 @ SV622 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1445 @ SV622 @ SV272 @ SV172 ) @ SY1446 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1445 @ SV622 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1445 @ SV622 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1445 @ SV622 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1445 @ SV622 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3451]) ).
thf(3565,plain,
! [SV623: $i,SV577: $i,SV273: $i,SV173: $i] :
( ( ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SV577 @ SV623 ) )
= $false )
| ( ( in @ SV173 @ SV577 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3453]) ).
thf(3566,plain,
! [SV599: $i,SV578: $i,SV273: $i,SV173: $i] :
( ( ( in @ ( ordered_pair @ SV173 @ SV273 ) @ ( cartesian_product2 @ SV578 @ SV599 ) )
= $false )
| ( ( in @ SV273 @ SV599 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3454]) ).
thf(3567,plain,
! [SV275: $i,SV176: $i,SV483: $i,SV602: $i,SV579: $i] :
( ( ( ( ( ordered_pair @ SV579 @ SV602 )
!= SV483 ) )
= $true )
| ( ( ~ ( in @ SV579 @ SV176 ) )
= $true )
| ( ( ( SV602
!= ( singleton @ SV579 ) ) )
= $true )
| ( ( ~ ( in @ SV483 @ ( cartesian_product2 @ SV176 @ SV275 ) ) )
= $true )
| ( ( in @ SV483 @ ( sK108_C @ SV275 @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3455]) ).
thf(3568,plain,
! [SV176: $i,SV275: $i,SV580: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK109_E @ SV580 @ SV275 @ SV176 ) @ ( sK110_SY756 @ SV580 @ SV275 @ SV176 ) )
!= SV580 )
| ~ ( in @ ( sK109_E @ SV580 @ SV275 @ SV176 ) @ SV176 ) )
| ( ( sK110_SY756 @ SV580 @ SV275 @ SV176 )
!= ( singleton @ ( sK109_E @ SV580 @ SV275 @ SV176 ) ) ) )
= $false )
| ( ( in @ SV580 @ ( sK108_C @ SV275 @ SV176 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3456]) ).
thf(3569,plain,
! [SV180: $i,SV456: $i,SV484: $i] :
( ( ( ~ ( ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV484 )
| ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV180 ) ) )
= $false )
| ( ( SV484
= ( set_union2 @ SV180 @ SV456 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3458]) ).
thf(3570,plain,
! [SV180: $i,SV456: $i,SV484: $i] :
( ( ( ~ ( ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV484 )
| ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV456 ) ) )
= $false )
| ( ( SV484
= ( set_union2 @ SV180 @ SV456 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3458]) ).
thf(3571,plain,
! [SV180: $i,SV456: $i,SV484: $i] :
( ( ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV180 )
= $true )
| ( ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV456 )
= $true )
| ( ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV484 )
= $true )
| ( ( SV484
= ( set_union2 @ SV180 @ SV456 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3459]) ).
thf(3572,plain,
! [SV457: $i,SV180: $i,SV485: $i,SV643: $i] :
( ( ( ~ ( in @ SV643 @ SV485 )
| ( in @ SV643 @ SV180 )
| ( in @ SV643 @ SV457 ) )
= $true )
| ( ( SV485
= ( set_union2 @ SV180 @ SV457 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3460]) ).
thf(3573,plain,
! [SV457: $i,SV485: $i,SV180: $i] :
( ( ( ~ ! [SY1362: $i] :
( ~ ( in @ SY1362 @ SV180 )
| ( in @ SY1362 @ SV485 ) )
| ~ ! [SY1363: $i] :
( ~ ( in @ SY1363 @ SV457 )
| ( in @ SY1363 @ SV485 ) ) )
= $false )
| ( ( SV485
= ( set_union2 @ SV180 @ SV457 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3461]) ).
thf(3574,plain,
! [SV139: $i] :
( ( ( ( ( sK17_C @ SV139 )
!= ( sK18_SY613 @ SV139 ) ) )
= $false )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3462]) ).
thf(3575,plain,
! [SV139: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
!= ( sK18_SY613 @ SV139 ) )
| ~ ( in @ ( sK22_SY620 @ SV139 ) @ SV139 ) )
| ( ( sK23_SY629 @ SV139 )
!= ( singleton @ ( sK22_SY620 @ SV139 ) ) ) ) )
= $false )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3462]) ).
thf(3576,plain,
! [SV624: $i,SV139: $i] :
( ( ( ~ ! [SY1447: $i] :
( ! [SY1448: $i] :
( ( SY1448 != SY1447 )
| ~ ( in @ SY1448 @ ( cartesian_product2 @ SV139 @ SV624 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1447 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1447 @ ( sK13_C @ SV624 @ SV139 ) ) )
| ~ ! [SY1451: $i] :
( ~ ( in @ SY1451 @ ( sK13_C @ SV624 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1451 @ SV624 @ SV139 )
!= SY1451 )
| ~ ( in @ ( sK16_E @ SY1451 @ SV624 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV624 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1451 @ SV624 @ SV139 ) @ ( sK15_SY612 @ SY1451 @ SV624 @ SV139 ) )
!= SY1451 )
| ~ ( in @ ( sK14_J @ SY1451 @ SV624 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1451 @ SV624 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1451 @ SV624 @ SV139 ) ) ) ) ) ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3463]) ).
thf(3577,plain,
! [SV139: $i] :
( ( ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
!= ( sK19_SY619 @ SV139 ) ) )
= $false )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3464]) ).
thf(3578,plain,
! [SV139: $i] :
( ( ( ~ ( in @ ( sK20_SY626 @ SV139 ) @ SV139 ) )
= $false )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3464]) ).
thf(3579,plain,
! [SV625: $i,SV139: $i] :
( ( ( ~ ! [SY1452: $i] :
( ! [SY1453: $i] :
( ( SY1453 != SY1452 )
| ~ ( in @ SY1453 @ ( cartesian_product2 @ SV139 @ SV625 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1452 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1452 @ ( sK13_C @ SV625 @ SV139 ) ) )
| ~ ! [SY1456: $i] :
( ~ ( in @ SY1456 @ ( sK13_C @ SV625 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1456 @ SV625 @ SV139 )
!= SY1456 )
| ~ ( in @ ( sK16_E @ SY1456 @ SV625 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV625 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1456 @ SV625 @ SV139 ) @ ( sK15_SY612 @ SY1456 @ SV625 @ SV139 ) )
!= SY1456 )
| ~ ( in @ ( sK14_J @ SY1456 @ SV625 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1456 @ SV625 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1456 @ SV625 @ SV139 ) ) ) ) ) ) )
= $false )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3465]) ).
thf(3580,plain,
! [SV488: $i,SV139: $i,SV603: $i] :
( ( ( ! [SY1430: $i] :
( ( SY1430 != SV603 )
| ~ ( in @ SY1430 @ ( cartesian_product2 @ SV139 @ SV488 ) ) ) )
= $true )
| ( ( ! [SY1431: $i,SY1432: $i] :
( ( ( ordered_pair @ SY1431 @ SY1432 )
!= SV603 )
| ~ ( in @ SY1431 @ SV139 )
| ( SY1432
!= ( singleton @ SY1431 ) ) ) )
= $true )
| ( ( in @ SV603 @ ( sK13_C @ SV488 @ SV139 ) )
= $true )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3466]) ).
thf(3581,plain,
! [SV139: $i,SV488: $i,SV604: $i] :
( ( ( in @ SV604 @ ( sK13_C @ SV488 @ SV139 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK16_E @ SV604 @ SV488 @ SV139 )
!= SV604 )
| ~ ( in @ ( sK16_E @ SV604 @ SV488 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV488 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV604 @ SV488 @ SV139 ) @ ( sK15_SY612 @ SV604 @ SV488 @ SV139 ) )
!= SV604 )
| ~ ( in @ ( sK14_J @ SV604 @ SV488 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV604 @ SV488 @ SV139 )
!= ( singleton @ ( sK14_J @ SV604 @ SV488 @ SV139 ) ) ) ) ) )
= $true )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3467]) ).
thf(3582,plain,
! [SV143: $i,SV400: $i,SV461: $i] :
( ( ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV143 )
= $false )
| ( ( ~ ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV400 ) )
= $true )
| ( ( ~ ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV461 ) )
= $true )
| ( ( SV461
= ( set_intersection2 @ SV143 @ SV400 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3468]) ).
thf(3583,plain,
! [SV143: $i,SV400: $i,SV461: $i] :
( ( ( ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV143 )
| ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV461 ) )
= $true )
| ( ( SV461
= ( set_intersection2 @ SV143 @ SV400 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3469]) ).
thf(3584,plain,
! [SV143: $i,SV400: $i,SV461: $i] :
( ( ( ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV400 )
| ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV461 ) )
= $true )
| ( ( SV461
= ( set_intersection2 @ SV143 @ SV400 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3470]) ).
thf(3585,plain,
! [SV462: $i,SV401: $i,SV143: $i,SV626: $i] :
( ( ( ~ ( in @ SV626 @ SV143 )
| ~ ( in @ SV626 @ SV401 ) )
= $true )
| ( ( in @ SV626 @ SV462 )
= $true )
| ( ( SV462
= ( set_intersection2 @ SV143 @ SV401 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3471]) ).
thf(3586,plain,
! [SV401: $i,SV143: $i,SV462: $i] :
( ( ( ~ ! [SY1326: $i] :
( ~ ( in @ SY1326 @ SV462 )
| ( in @ SY1326 @ SV143 ) ) )
= $false )
| ( ( SV462
= ( set_intersection2 @ SV143 @ SV401 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3472]) ).
thf(3587,plain,
! [SV143: $i,SV401: $i,SV462: $i] :
( ( ( ~ ! [SY1327: $i] :
( ~ ( in @ SY1327 @ SV462 )
| ( in @ SY1327 @ SV401 ) ) )
= $false )
| ( ( SV462
= ( set_intersection2 @ SV143 @ SV401 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3472]) ).
thf(3588,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY1142: $i] :
( ~ ( in @ SY1142 @ ( sK52_SY712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SY1142 ) @ SV265 ) )
| ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK52_SY712 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) ) ) )
| ~ ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 ) )
| ~ ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 ) )
= $false )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3475]) ).
thf(3589,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ ( sK51_SY718 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SY1143 ) @ SV265 ) )
| ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK51_SY718 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3476]) ).
thf(3590,plain,
! [SV265: $i,SV145: $i] :
( ( ( ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) ) )
= $true )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3477]) ).
thf(3591,plain,
! [SV145: $i,SV265: $i] :
( ( ( ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) )
= $true )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3478]) ).
thf(3592,plain,
! [SV147: $i,SV403: $i,SV463: $i] :
( ( ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV147 )
= $false )
| ( ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV403 )
= $true )
| ( ( ~ ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV463 ) )
= $true )
| ( ( SV463
= ( set_difference @ SV147 @ SV403 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3479]) ).
thf(3593,plain,
! [SV147: $i,SV403: $i,SV463: $i] :
( ( ( ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV147 )
| ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV463 ) )
= $true )
| ( ( SV463
= ( set_difference @ SV147 @ SV403 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3480]) ).
thf(3594,plain,
! [SV147: $i,SV403: $i,SV463: $i] :
( ( ( ~ ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV403 )
| ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV463 ) )
= $true )
| ( ( SV463
= ( set_difference @ SV147 @ SV403 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3481]) ).
thf(3595,plain,
! [SV464: $i,SV404: $i,SV147: $i,SV627: $i] :
( ( ( ~ ( in @ SV627 @ SV147 )
| ( in @ SV627 @ SV404 ) )
= $true )
| ( ( in @ SV627 @ SV464 )
= $true )
| ( ( SV464
= ( set_difference @ SV147 @ SV404 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3482]) ).
thf(3596,plain,
! [SV404: $i,SV147: $i,SV464: $i] :
( ( ( ~ ! [SY1329: $i] :
( ~ ( in @ SY1329 @ SV464 )
| ( in @ SY1329 @ SV147 ) ) )
= $false )
| ( ( SV464
= ( set_difference @ SV147 @ SV404 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3483]) ).
thf(3597,plain,
! [SV147: $i,SV404: $i,SV464: $i] :
( ( ( ~ ! [SY1330: $i] :
( ~ ( in @ SY1330 @ SV464 )
| ~ ( in @ SY1330 @ SV404 ) ) )
= $false )
| ( ( SV464
= ( set_difference @ SV147 @ SV404 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3483]) ).
thf(3598,plain,
! [SV148: $i,SV335: $i,SV605: $i] :
( ( ( ~ ( in @ SV605 @ SV335 ) )
= $true )
| ( ( ~ ( subset @ ( sK105_C @ SV335 @ SV148 ) @ SV605 ) )
= $true )
| ( ( SV605
= ( sK105_C @ SV335 @ SV148 ) )
= $true )
| ( ( SV335 = empty_set )
= $true )
| ( ( element @ SV335 @ ( powerset @ ( powerset @ SV148 ) ) )
= $false )
| ( ( finite @ SV148 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3484]) ).
thf(3599,plain,
! [SV606: $i,SV340: $i,SV409: $i] :
( ( ( in @ ( sK68_C @ SV409 @ SV340 ) @ SV606 )
= $false )
| ( ( ~ ( in @ SV606 @ SV340 ) )
= $true )
| ( ( ~ ( in @ ( sK68_C @ SV409 @ SV340 ) @ SV409 ) )
= $true )
| ( ( SV409
= ( union @ SV340 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3485]) ).
thf(3600,plain,
! [SV340: $i,SV409: $i] :
( ( ( in @ ( sK68_C @ SV409 @ SV340 ) @ ( sK69_SY723 @ SV409 @ SV340 ) )
= $true )
| ( ( in @ ( sK68_C @ SV409 @ SV340 ) @ SV409 )
= $true )
| ( ( SV409
= ( union @ SV340 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3486]) ).
thf(3601,plain,
! [SV340: $i,SV409: $i] :
( ( ( in @ ( sK69_SY723 @ SV409 @ SV340 ) @ SV340 )
= $true )
| ( ( in @ ( sK68_C @ SV409 @ SV340 ) @ SV409 )
= $true )
| ( ( SV409
= ( union @ SV340 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3487]) ).
thf(3602,plain,
! [SV410: $i,SV341: $i,SV644: $i,SV607: $i] :
( ( ( ~ ( in @ SV607 @ SV644 )
| ~ ( in @ SV644 @ SV341 ) )
= $true )
| ( ( in @ SV607 @ SV410 )
= $true )
| ( ( SV410
= ( union @ SV341 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3488]) ).
thf(3603,plain,
! [SV341: $i,SV410: $i,SV608: $i] :
( ( ( in @ SV608 @ SV410 )
= $false )
| ( ( ~ ( ~ ( in @ SV608 @ ( sK67_D @ SV608 @ SV410 @ SV341 ) )
| ~ ( in @ ( sK67_D @ SV608 @ SV410 @ SV341 ) @ SV341 ) ) )
= $true )
| ( ( SV410
= ( union @ SV341 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3489]) ).
thf(3604,plain,
! [SV347: $i,SV414: $i,SV609: $i] :
( ( ( in @ SV609 @ SV414 )
= $false )
| ( ( subset @ SV609 @ SV347 )
= $true )
| ( ( SV414
= ( powerset @ SV347 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3493]) ).
thf(3605,plain,
! [SV414: $i,SV347: $i,SV610: $i] :
( ( ( subset @ SV610 @ SV347 )
= $false )
| ( ( in @ SV610 @ SV414 )
= $true )
| ( ( SV414
= ( powerset @ SV347 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3494]) ).
thf(3606,plain,
! [SV150: $i,SV415: $i,SV465: $i,SV645: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV645 @ ( sK102_D @ SV465 @ SV415 @ SV150 ) ) @ SV465 ) )
= $true )
| ( ( ( relation_rng_as_subset @ SV150 @ SV415 @ SV465 )
= SV415 )
= $true )
| ( ( relation_of2_as_subset @ SV465 @ SV150 @ SV415 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3495]) ).
thf(3607,plain,
! [SV150: $i,SV466: $i,SV416: $i,SV611: $i] :
( ( ( in @ SV611 @ SV416 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK101_E @ SV611 @ SV466 @ SV416 @ SV150 ) @ SV611 ) @ SV466 )
= $true )
| ( ( ( relation_rng_as_subset @ SV150 @ SV416 @ SV466 )
= SV416 )
= $false )
| ( ( relation_of2_as_subset @ SV466 @ SV150 @ SV416 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3497]) ).
thf(3608,plain,
! [SV151: $i,SV267: $i,SV467: $i,SV502: $i] :
( ( ( ~ ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV467 ) ) )
= $false )
| ( ( SV502
= ( unordered_triple @ SV151 @ SV267 @ SV467 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3498]) ).
thf(3609,plain,
! [SV151: $i,SV267: $i,SV467: $i,SV502: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV151 ) )
| ~ ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV267 ) ) ) )
= $false )
| ( ( SV502
= ( unordered_triple @ SV151 @ SV267 @ SV467 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3498]) ).
thf(3610,plain,
! [SV151: $i,SV267: $i,SV467: $i,SV502: $i] :
( ( ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
= SV467 )
= $true )
| ( ( ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
= SV151 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
= SV267 ) )
= $true )
| ( ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
= $true )
| ( ( SV502
= ( unordered_triple @ SV151 @ SV267 @ SV467 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3499]) ).
thf(3611,plain,
! [SV267: $i,SV151: $i,SV468: $i,SV503: $i,SV646: $i] :
( ( ( ~ ( in @ SV646 @ SV503 )
| ( SV646 = SV468 )
| ( SV646 = SV151 )
| ( SV646 = SV267 ) )
= $true )
| ( ( SV503
= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3500]) ).
thf(3612,plain,
! [SV267: $i,SV151: $i,SV503: $i,SV468: $i] :
( ( ( ~ ! [SY1380: $i] :
( ( SY1380 != SV468 )
| ( in @ SY1380 @ SV503 ) )
| ~ ~ ( ~ ! [SY1381: $i] :
( ( SY1381 != SV151 )
| ( in @ SY1381 @ SV503 ) )
| ~ ! [SY1382: $i] :
( ( SY1382 != SV267 )
| ( in @ SY1382 @ SV503 ) ) ) )
= $false )
| ( ( SV503
= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3501]) ).
thf(3613,plain,
! [SV628: $i,SV152: $i,SV612: $i] :
( ( ( ~ ( in @ SV612 @ ( sK106_B @ SV152 ) )
| ~ ( subset @ SV628 @ SV612 ) )
= $true )
| ( ( in @ SV628 @ ( sK106_B @ SV152 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3502]) ).
thf(3614,plain,
! [SV154: $i,SV504: $i] :
( ( ( in @ ( ordered_pair @ ( sK72_C @ SV504 @ SV154 ) @ ( sK73_SY724 @ SV504 @ SV154 ) ) @ SV154 )
= $true )
| ( ( subset @ SV154 @ SV504 )
= $true )
| ( ( relation @ SV504 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3503]) ).
thf(3615,plain,
! [SV154: $i,SV504: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK72_C @ SV504 @ SV154 ) @ ( sK73_SY724 @ SV504 @ SV154 ) ) @ SV504 ) )
= $true )
| ( ( subset @ SV154 @ SV504 )
= $true )
| ( ( relation @ SV504 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3504]) ).
thf(3616,plain,
! [SV505: $i,SV154: $i,SV647: $i,SV629: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV629 @ SV647 ) @ SV154 )
| ( in @ ( ordered_pair @ SV629 @ SV647 ) @ SV505 ) )
= $true )
| ( ( subset @ SV154 @ SV505 )
= $false )
| ( ( relation @ SV505 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3505]) ).
thf(3617,plain,
! [SV155: $i,SV268: $i,SV547: $i] :
( ( ( ~ ( element @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ ( powerset @ SV155 ) ) )
= $false )
| ( ( SV547
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $true )
| ( ( element @ SV547 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3506]) ).
thf(3618,plain,
! [SV155: $i,SV268: $i,SV547: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ SV547 )
| ~ ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SV547 @ SV268 @ SV155 ) ) @ SV268 ) )
| ~ ( ( in @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ SV547 )
| ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SV547 @ SV268 @ SV155 ) ) @ SV268 ) ) ) )
= $false )
| ( ( SV547
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $true )
| ( ( element @ SV547 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3506]) ).
thf(3619,plain,
! [SV268: $i,SV548: $i,SV155: $i] :
( ( ( ~ ! [SY1408: $i] :
( ~ ( element @ SY1408 @ ( powerset @ SV155 ) )
| ~ ( in @ SY1408 @ SV548 )
| ( in @ ( subset_complement @ SV155 @ SY1408 ) @ SV268 ) )
| ~ ! [SY1409: $i] :
( ~ ( element @ SY1409 @ ( powerset @ SV155 ) )
| ~ ( in @ ( subset_complement @ SV155 @ SY1409 ) @ SV268 )
| ( in @ SY1409 @ SV548 ) ) )
= $false )
| ( ( SV548
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $false )
| ( ( element @ SV548 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3507]) ).
thf(3620,plain,
! [SV425: $i,SV566: $i,SV630: $i] :
( ( ( ( SV630 != SV566 ) )
= $true )
| ( ( ~ ( in @ SV630 @ SV425 ) )
= $true )
| ( ( ~ ( ordinal @ SV566 ) )
= $true )
| ( ( in @ SV566 @ ( sK7_B @ SV425 ) )
= $true )
| ( sK12_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[3508]) ).
thf(3621,plain,
! [SV425: $i,SV567: $i] :
( ( ( ~ ~ ( ( ( sK8_D @ SV567 @ SV425 )
!= SV567 )
| ~ ( in @ ( sK8_D @ SV567 @ SV425 ) @ SV425 ) ) )
= $false )
| ( ( in @ SV567 @ ( sK7_B @ SV425 ) )
= $false )
| ( sK12_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[3509]) ).
thf(3622,plain,
! [SV425: $i,SV567: $i] :
( ( ( ~ ( ordinal @ SV567 ) )
= $false )
| ( ( in @ SV567 @ ( sK7_B @ SV425 ) )
= $false )
| ( sK12_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[3509]) ).
thf(3623,plain,
( ( ( ~ ~ ( ( sK9_B != sK10_SY601 )
| ~ ( ordinal @ sK10_SY601 ) ) )
= $false )
| ( sK12_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[3510]) ).
thf(3624,plain,
( ( ( ( sK9_B != sK11_SY603 ) )
= $false )
| ( sK12_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[3510]) ).
thf(3625,plain,
! [SV551: $i,SV568: $i,SV157: $i] :
( ( ( in @ SV157 @ ( relation_restriction @ SV568 @ SV551 ) )
= $false )
| ( ( in @ SV157 @ SV568 )
= $true )
| ( ( relation @ SV568 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3512]) ).
thf(3626,plain,
! [SV552: $i,SV569: $i,SV157: $i] :
( ( ( in @ SV157 @ ( relation_restriction @ SV569 @ SV552 ) )
= $false )
| ( ( in @ SV157 @ ( cartesian_product2 @ SV552 @ SV552 ) )
= $true )
| ( ( relation @ SV569 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3513]) ).
thf(3627,plain,
! [SV613: $i,SV158: $i,SV631: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV631 @ SV158 @ SV613 ) )
= $true )
| ( ( ( SV613 = empty_set )
| ( SV158
!= ( relation_dom_as_subset @ SV158 @ SV613 @ SV631 ) )
| ( quasi_total @ SV631 @ SV158 @ SV613 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3514]) ).
thf(3628,plain,
! [SV614: $i,SV158: $i,SV632: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV632 @ SV158 @ SV614 ) )
= $true )
| ( ( ( SV614 = empty_set )
| ~ ( quasi_total @ SV632 @ SV158 @ SV614 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SV614 @ SV632 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3515]) ).
thf(3629,plain,
! [SV615: $i,SV158: $i,SV633: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV633 @ SV158 @ SV615 ) )
= $true )
| ( ( ( SV158 != empty_set )
| ( SV158
!= ( relation_dom_as_subset @ SV158 @ SV615 @ SV633 ) )
| ( quasi_total @ SV633 @ SV158 @ SV615 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3516]) ).
thf(3630,plain,
! [SV616: $i,SV158: $i,SV634: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV634 @ SV158 @ SV616 ) )
= $true )
| ( ( ( SV158 != empty_set )
| ~ ( quasi_total @ SV634 @ SV158 @ SV616 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SV616 @ SV634 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3517]) ).
thf(3631,plain,
! [SV158: $i,SV570: $i,SV553: $i] :
( ( ( SV553 = empty_set )
= $false )
| ( ( ( SV570 != empty_set )
| ( quasi_total @ SV570 @ SV158 @ SV553 )
| ( SV158 = empty_set ) )
= $true )
| ( ( relation_of2_as_subset @ SV570 @ SV158 @ SV553 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3518]) ).
thf(3632,plain,
! [SV158: $i,SV571: $i,SV554: $i] :
( ( ( SV554 = empty_set )
= $false )
| ( ( ~ ( quasi_total @ SV571 @ SV158 @ SV554 )
| ( SV571 = empty_set )
| ( SV158 = empty_set ) )
= $true )
| ( ( relation_of2_as_subset @ SV571 @ SV158 @ SV554 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3519]) ).
thf(3633,plain,
! [SV512: $i,SV572: $i] :
( ( ( ~ ( ~ ( in @ ( sK90_SY733 @ SV572 @ SV512 ) @ SV512 )
| ~ ~ ( in @ ( sK89_C @ SV572 @ SV512 ) @ ( sK90_SY733 @ SV572 @ SV512 ) ) )
| ~ ( in @ ( sK89_C @ SV572 @ SV512 ) @ SV572 ) )
= $true )
| ( ( SV572
= ( set_meet @ SV512 ) )
= $true )
| ( ( SV512 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3520]) ).
thf(3634,plain,
! [SV572: $i,SV512: $i] :
( ( ( ! [SY1416: $i] :
( ~ ( in @ SY1416 @ SV512 )
| ( in @ ( sK89_C @ SV572 @ SV512 ) @ SY1416 ) )
| ( in @ ( sK89_C @ SV572 @ SV512 ) @ SV572 ) )
= $true )
| ( ( SV572
= ( set_meet @ SV512 ) )
= $true )
| ( ( SV512 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3521]) ).
thf(3635,plain,
! [SV513: $i,SV573: $i] :
( ( ( ~ ! [SY1417: $i] :
( ~ ( ~ ( in @ ( sK88_D @ SY1417 @ SV573 @ SV513 ) @ SV513 )
| ~ ~ ( in @ SY1417 @ ( sK88_D @ SY1417 @ SV573 @ SV513 ) ) )
| ( in @ SY1417 @ SV573 ) ) )
= $false )
| ( ( SV573
= ( set_meet @ SV513 ) )
= $false )
| ( ( SV513 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3522]) ).
thf(3636,plain,
! [SV513: $i,SV573: $i] :
( ( ( ~ ! [SY1418: $i] :
( ~ ( in @ SY1418 @ SV573 )
| ! [SY1394: $i] :
( ~ ( in @ SY1394 @ SV513 )
| ( in @ SY1418 @ SY1394 ) ) ) )
= $false )
| ( ( SV573
= ( set_meet @ SV513 ) )
= $false )
| ( ( SV513 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3522]) ).
thf(3637,plain,
! [SV159: $i,SV427: $i,SV470: $i] :
( ( ( ~ ( in @ ( sK82_D @ SV470 @ SV427 @ SV159 ) @ SV470 )
| ( ( sK82_D @ SV470 @ SV427 @ SV159 )
!= SV159 ) )
= $true )
| ( ( SV470
= ( unordered_pair @ SV159 @ SV427 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3525]) ).
thf(3638,plain,
! [SV159: $i,SV427: $i,SV470: $i] :
( ( ( ~ ( in @ ( sK82_D @ SV470 @ SV427 @ SV159 ) @ SV470 )
| ( ( sK82_D @ SV470 @ SV427 @ SV159 )
!= SV427 ) )
= $true )
| ( ( SV470
= ( unordered_pair @ SV159 @ SV427 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3526]) ).
thf(3639,plain,
! [SV428: $i,SV159: $i,SV471: $i,SV635: $i] :
( ( ( ~ ( in @ SV635 @ SV471 ) )
= $true )
| ( ( ( SV635 = SV159 )
| ( SV635 = SV428 ) )
= $true )
| ( ( SV471
= ( unordered_pair @ SV159 @ SV428 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3528]) ).
thf(3640,plain,
! [SV428: $i,SV471: $i,SV159: $i] :
( ( ( ~ ! [SY1340: $i] :
( ( SY1340 != SV159 )
| ( in @ SY1340 @ SV471 ) ) )
= $false )
| ( ( SV471
= ( unordered_pair @ SV159 @ SV428 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3529]) ).
thf(3641,plain,
! [SV159: $i,SV471: $i,SV428: $i] :
( ( ( ~ ! [SY1341: $i] :
( ( SY1341 != SV428 )
| ( in @ SY1341 @ SV471 ) ) )
= $false )
| ( ( SV471
= ( unordered_pair @ SV159 @ SV428 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3529]) ).
thf(3642,plain,
! [SV436: $i,SV365: $i,SV617: $i] :
( ( ( SV617 = SV365 )
= $false )
| ( ( in @ SV617 @ SV436 )
= $true )
| ( ( SV436
= ( singleton @ SV365 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3533]) ).
thf(3643,plain,
! [SV365: $i,SV436: $i,SV618: $i] :
( ( ( in @ SV618 @ SV436 )
= $false )
| ( ( SV618 = SV365 )
= $true )
| ( ( SV436
= ( singleton @ SV365 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3534]) ).
thf(3644,plain,
! [SV474: $i,SV437: $i,SV648: $i,SV164: $i,SV636: $i] :
( ( ( ~ ( in @ SV636 @ SV164 )
| ~ ( in @ SV648 @ SV437 )
| ( ( sK78_D @ SV474 @ SV437 @ SV164 )
!= ( ordered_pair @ SV636 @ SV648 ) ) )
= $true )
| ( ( ~ ( in @ ( sK78_D @ SV474 @ SV437 @ SV164 ) @ SV474 ) )
= $true )
| ( ( SV474
= ( cartesian_product2 @ SV164 @ SV437 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3535]) ).
thf(3645,plain,
! [SV164: $i,SV437: $i,SV474: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK79_SY729 @ SV474 @ SV437 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK80_SY731 @ SV474 @ SV437 @ SV164 ) @ SV437 ) ) )
= $false )
| ( ( in @ ( sK78_D @ SV474 @ SV437 @ SV164 ) @ SV474 )
= $true )
| ( ( SV474
= ( cartesian_product2 @ SV164 @ SV437 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3536]) ).
thf(3646,plain,
! [SV164: $i,SV437: $i,SV474: $i] :
( ( ( ( ( sK78_D @ SV474 @ SV437 @ SV164 )
!= ( ordered_pair @ ( sK79_SY729 @ SV474 @ SV437 @ SV164 ) @ ( sK80_SY731 @ SV474 @ SV437 @ SV164 ) ) ) )
= $false )
| ( ( in @ ( sK78_D @ SV474 @ SV437 @ SV164 ) @ SV474 )
= $true )
| ( ( SV474
= ( cartesian_product2 @ SV164 @ SV437 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3536]) ).
thf(3647,plain,
! [SV475: $i,SV637: $i,SV438: $i,SV164: $i] :
( ( ( ! [SY1459: $i,SY1460: $i] :
( ~ ( in @ SY1459 @ SV164 )
| ~ ( in @ SY1460 @ SV438 )
| ( SV637
!= ( ordered_pair @ SY1459 @ SY1460 ) ) ) )
= $true )
| ( ( in @ SV637 @ SV475 )
= $true )
| ( ( SV475
= ( cartesian_product2 @ SV164 @ SV438 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3537]) ).
thf(3648,plain,
! [SV164: $i,SV438: $i,SV475: $i,SV638: $i] :
( ( ( ~ ( in @ SV638 @ SV475 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK76_E @ SV638 @ SV475 @ SV438 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK77_SY726 @ SV638 @ SV475 @ SV438 @ SV164 ) @ SV438 ) )
| ( SV638
!= ( ordered_pair @ ( sK76_E @ SV638 @ SV475 @ SV438 @ SV164 ) @ ( sK77_SY726 @ SV638 @ SV475 @ SV438 @ SV164 ) ) ) ) )
= $true )
| ( ( SV475
= ( cartesian_product2 @ SV164 @ SV438 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3538]) ).
thf(3649,plain,
! [SV166: $i,SV558: $i,SV649: $i] :
( ( ( ~ ( subset @ SV649 @ SV558 )
| ( in @ SV649 @ ( sK4_SY591 @ SV558 @ SV166 ) ) )
= $true )
| ( ( ~ ( in @ SV558 @ ( sK3_B @ SV166 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3539]) ).
thf(3650,plain,
! [SV166: $i,SV558: $i] :
( ( ( in @ SV558 @ ( sK3_B @ SV166 ) )
= $false )
| ( ( in @ ( sK4_SY591 @ SV558 @ SV166 ) @ ( sK3_B @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3540]) ).
thf(3651,plain,
! [SV639: $i,SV166: $i,SV619: $i] :
( ( ( ~ ( in @ SV619 @ ( sK3_B @ SV166 ) )
| ~ ( subset @ SV639 @ SV619 ) )
= $true )
| ( ( in @ SV639 @ ( sK3_B @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3541]) ).
thf(3652,plain,
! [SV650: $i,SV167: $i,SV444: $i,SV478: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK104_D @ SV478 @ SV444 @ SV167 ) @ SV650 ) @ SV478 ) )
= $true )
| ( ( ( relation_dom_as_subset @ SV444 @ SV167 @ SV478 )
= SV444 )
= $true )
| ( ( relation_of2_as_subset @ SV478 @ SV444 @ SV167 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3542]) ).
thf(3653,plain,
! [SV167: $i,SV479: $i,SV445: $i,SV620: $i] :
( ( ( in @ SV620 @ SV445 )
= $false )
| ( ( in @ ( ordered_pair @ SV620 @ ( sK103_E @ SV620 @ SV479 @ SV445 @ SV167 ) ) @ SV479 )
= $true )
| ( ( ( relation_dom_as_subset @ SV445 @ SV167 @ SV479 )
= SV445 )
= $false )
| ( ( relation_of2_as_subset @ SV479 @ SV445 @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3544]) ).
thf(3654,plain,
! [SV168: $i] :
( ( ( ( ( sK27_SY634 @ SV168 )
!= ( singleton @ ( sK26_B @ SV168 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) )
| ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3545]) ).
thf(3655,plain,
! [SV168: $i] :
( ( ( ~ ( in @ ( sK26_B @ SV168 ) @ SV168 ) )
= $false )
| ( ( ~ ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) )
| ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3545]) ).
thf(3656,plain,
! [SV168: $i] :
( ( ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) ) )
= $false )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3546]) ).
thf(3657,plain,
! [SV168: $i] :
( ( ( ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) )
= $false )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3546]) ).
thf(3658,plain,
! [SV640: $i,SV168: $i] :
( ( ( ! [SY1461: $i] :
( ~ ( in @ SY1461 @ SV168 )
| ( SV640
!= ( singleton @ SY1461 ) ) ) )
= $true )
| ( ( in @ SV640 @ ( sK24_B @ SV168 ) )
= $true )
| ( ( ( sK28_SY636 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3547]) ).
thf(3659,plain,
! [SV168: $i,SV641: $i] :
( ( ( ~ ( in @ SV641 @ ( sK24_B @ SV168 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK25_D @ SV641 @ SV168 ) @ SV168 )
| ( SV641
!= ( singleton @ ( sK25_D @ SV641 @ SV168 ) ) ) ) )
= $true )
| ( ( ( sK28_SY636 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3548]) ).
thf(3660,plain,
! [SV593: $i,SV168: $i,SV642: $i] :
( ( ( ~ ( in @ SV642 @ SV168 ) )
= $true )
| ( ( ( SV593
!= ( singleton @ SV642 ) ) )
= $true )
| ( ( in @ SV593 @ ( sK24_B @ SV168 ) )
= $true )
| ( ( ( sK27_SY634 @ SV168 )
= ( sK28_SY636 @ SV168 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3549]) ).
thf(3661,plain,
! [SV168: $i,SV594: $i] :
( ( ( ~ ( in @ ( sK25_D @ SV594 @ SV168 ) @ SV168 )
| ( SV594
!= ( singleton @ ( sK25_D @ SV594 @ SV168 ) ) ) )
= $false )
| ( ( in @ SV594 @ ( sK24_B @ SV168 ) )
= $false )
| ( ( ( sK27_SY634 @ SV168 )
= ( sK28_SY636 @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3550]) ).
thf(3662,plain,
! [SV271: $i,SV481: $i,SV170: $i,SV596: $i,SV651: $i] :
( ( ( ! [SY1462: $i] :
( ( ( ordered_pair @ SV651 @ SY1462 )
!= SV596 )
| ~ ( in @ SV651 @ SV170 )
| ! [SY1463: $i] :
( ~ ( ~ ( in @ ( sK115_I @ SY1463 @ SY1462 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) @ SY1463 )
| ~ ~ ( in @ ( ordered_pair @ SY1462 @ ( sK115_I @ SY1463 @ SY1462 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) ) @ SV271 ) )
| ( SV651 != SY1463 )
| ~ ( in @ SY1462 @ SY1463 ) ) ) )
= $true )
| ( ( ~ ( in @ SV596 @ ( cartesian_product2 @ SV170 @ SV481 ) ) )
= $true )
| ( ( in @ SV596 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3553]) ).
thf(3663,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV652: $i] :
( ( ( ~ ( in @ SV652 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
| ~ ( ~ ~ ( ( ( ordered_pair @ ( sK112_F @ SV652 @ SV481 @ SV271 @ SV170 ) @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) )
!= SV652 )
| ~ ( in @ ( sK112_F @ SV652 @ SV481 @ SV271 @ SV170 ) @ SV170 ) )
| ~ ~ ( ~ ! [SY1464: $i] :
( ~ ( in @ SY1464 @ ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) )
| ( in @ ( ordered_pair @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) @ SY1464 ) @ SV271 ) )
| ~ ~ ( ( ( sK112_F @ SV652 @ SV481 @ SV271 @ SV170 )
!= ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) )
| ~ ( in @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) @ ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) ) ) ) ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3554]) ).
thf(3664,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV653: $i] :
( ( ( ~ ( in @ SV653 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
| ( in @ SV653 @ ( cartesian_product2 @ SV170 @ SV481 ) ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3555]) ).
thf(3665,plain,
! [SV368: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK74_B @ SV368 ) @ SV368 )
| ~ ( in @ ( sK75_SY725 @ SV368 ) @ SV368 ) ) )
= $false )
| ( ( epsilon_connected @ SV368 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3557]) ).
thf(3666,plain,
! [SV368: $i] :
( ( ( ~ ~ ( in @ ( sK74_B @ SV368 ) @ ( sK75_SY725 @ SV368 ) ) )
= $false )
| ( ( epsilon_connected @ SV368 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3557]) ).
thf(3667,plain,
! [SV559: $i,SV369: $i,SV520: $i] :
( ( ( in @ SV520 @ SV369 )
= $false )
| ( ( ~ ( in @ SV559 @ SV369 ) )
= $true )
| ( ( in @ SV520 @ SV559 )
= $true )
| ( ( SV520 = SV559 )
= $true )
| ( ( in @ SV559 @ SV520 )
= $true )
| ( ( epsilon_connected @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3558]) ).
thf(3668,plain,
! [SV171: $i,SV524: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV171 )
| ~ ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV524 ) )
= $true )
| ( ( SV171 = SV524 )
= $true )
| ( ( relation @ SV524 )
= $false )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3559]) ).
thf(3669,plain,
! [SV171: $i,SV524: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV171 )
| ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV524 ) )
= $true )
| ( ( SV171 = SV524 )
= $true )
| ( ( relation @ SV524 )
= $false )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3560]) ).
thf(3670,plain,
! [SV525: $i,SV171: $i] :
( ( ( ~ ! [SY1400: $i,SY1401: $i] :
( ~ ( in @ ( ordered_pair @ SY1400 @ SY1401 ) @ SV171 )
| ( in @ ( ordered_pair @ SY1400 @ SY1401 ) @ SV525 ) ) )
= $false )
| ( ( SV171 = SV525 )
= $false )
| ( ( relation @ SV525 )
= $false )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3561]) ).
thf(3671,plain,
! [SV171: $i,SV525: $i] :
( ( ( ~ ! [SY1402: $i,SY1403: $i] :
( ~ ( in @ ( ordered_pair @ SY1402 @ SY1403 ) @ SV525 )
| ( in @ ( ordered_pair @ SY1402 @ SY1403 ) @ SV171 ) ) )
= $false )
| ( ( SV171 = SV525 )
= $false )
| ( ( relation @ SV525 )
= $false )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3561]) ).
thf(3672,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ~ ( ( ( sK35_D @ SV272 @ SV172 )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1178: $i] :
( ~ ( in @ SY1178 @ ( sK43_SY691 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SY1178 ) @ SV272 ) )
| ~ ~ ( ( ( sK41_SY666 @ SV272 @ SV172 )
!= ( sK43_SY691 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) ) ) ) ) )
| ( ( sK35_D @ SV272 @ SV172 )
!= ( sK37_SY665 @ SV272 @ SV172 ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3562]) ).
thf(3673,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
!= ( sK37_SY665 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1179: $i] :
( ~ ( in @ SY1179 @ ( sK40_SY685 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SY1179 ) @ SV272 ) )
| ~ ~ ( ( ( sK38_SY678 @ SV272 @ SV172 )
!= ( sK40_SY685 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) ) ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3563]) ).
thf(3674,plain,
! [SV272: $i,SV622: $i,SV172: $i] :
( ( ( ~ ! [SY1440: $i] :
( ! [SY1441: $i] :
( ( SY1441 != SY1440 )
| ~ ( in @ SY1441 @ ( cartesian_product2 @ SV172 @ SV622 ) ) )
| ! [SY1442: $i,SY1443: $i] :
( ( ( ordered_pair @ SY1442 @ SY1443 )
!= SY1440 )
| ~ ( in @ SY1442 @ SV172 )
| ! [SY1444: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1444 @ SY1443 @ SY1442 @ SY1440 @ SV622 @ SV272 @ SV172 ) @ SY1444 )
| ~ ~ ( in @ ( ordered_pair @ SY1443 @ ( sK34_R @ SY1444 @ SY1443 @ SY1442 @ SY1440 @ SV622 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1442 != SY1444 )
| ~ ( in @ SY1443 @ SY1444 ) ) )
| ( in @ SY1440 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3564]) ).
thf(3675,plain,
! [SV172: $i,SV272: $i,SV622: $i] :
( ( ( ~ ! [SY1445: $i] :
( ~ ( in @ SY1445 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1445 @ SV622 @ SV272 @ SV172 )
!= SY1445 )
| ~ ( in @ ( sK33_F @ SY1445 @ SV622 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV622 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1445 @ SV622 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1445 @ SV622 @ SV272 @ SV172 ) )
!= SY1445 )
| ~ ( in @ ( sK30_O @ SY1445 @ SV622 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1446: $i] :
( ~ ( in @ SY1446 @ ( sK32_SY652 @ SY1445 @ SV622 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1445 @ SV622 @ SV272 @ SV172 ) @ SY1446 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1445 @ SV622 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1445 @ SV622 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1445 @ SV622 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1445 @ SV622 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3564]) ).
thf(3676,plain,
! [SV275: $i,SV176: $i,SV483: $i,SV602: $i,SV579: $i] :
( ( ( ( ordered_pair @ SV579 @ SV602 )
= SV483 )
= $false )
| ( ( ~ ( in @ SV579 @ SV176 ) )
= $true )
| ( ( ( SV602
!= ( singleton @ SV579 ) ) )
= $true )
| ( ( ~ ( in @ SV483 @ ( cartesian_product2 @ SV176 @ SV275 ) ) )
= $true )
| ( ( in @ SV483 @ ( sK108_C @ SV275 @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3567]) ).
thf(3677,plain,
! [SV176: $i,SV275: $i,SV580: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK109_E @ SV580 @ SV275 @ SV176 ) @ ( sK110_SY756 @ SV580 @ SV275 @ SV176 ) )
!= SV580 )
| ~ ( in @ ( sK109_E @ SV580 @ SV275 @ SV176 ) @ SV176 ) ) )
= $false )
| ( ( in @ SV580 @ ( sK108_C @ SV275 @ SV176 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3568]) ).
thf(3678,plain,
! [SV176: $i,SV275: $i,SV580: $i] :
( ( ( ( ( sK110_SY756 @ SV580 @ SV275 @ SV176 )
!= ( singleton @ ( sK109_E @ SV580 @ SV275 @ SV176 ) ) ) )
= $false )
| ( ( in @ SV580 @ ( sK108_C @ SV275 @ SV176 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3568]) ).
thf(3679,plain,
! [SV180: $i,SV456: $i,SV484: $i] :
( ( ( ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV484 )
| ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV180 ) )
= $true )
| ( ( SV484
= ( set_union2 @ SV180 @ SV456 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3569]) ).
thf(3680,plain,
! [SV180: $i,SV456: $i,SV484: $i] :
( ( ( ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV484 )
| ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV456 ) )
= $true )
| ( ( SV484
= ( set_union2 @ SV180 @ SV456 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3570]) ).
thf(3681,plain,
! [SV457: $i,SV180: $i,SV485: $i,SV643: $i] :
( ( ( ~ ( in @ SV643 @ SV485 ) )
= $true )
| ( ( ( in @ SV643 @ SV180 )
| ( in @ SV643 @ SV457 ) )
= $true )
| ( ( SV485
= ( set_union2 @ SV180 @ SV457 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3572]) ).
thf(3682,plain,
! [SV457: $i,SV485: $i,SV180: $i] :
( ( ( ~ ! [SY1362: $i] :
( ~ ( in @ SY1362 @ SV180 )
| ( in @ SY1362 @ SV485 ) ) )
= $false )
| ( ( SV485
= ( set_union2 @ SV180 @ SV457 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3573]) ).
thf(3683,plain,
! [SV180: $i,SV485: $i,SV457: $i] :
( ( ( ~ ! [SY1363: $i] :
( ~ ( in @ SY1363 @ SV457 )
| ( in @ SY1363 @ SV485 ) ) )
= $false )
| ( ( SV485
= ( set_union2 @ SV180 @ SV457 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3573]) ).
thf(3684,plain,
! [SV139: $i] :
( ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3574]) ).
thf(3685,plain,
! [SV139: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
!= ( sK18_SY613 @ SV139 ) )
| ~ ( in @ ( sK22_SY620 @ SV139 ) @ SV139 ) )
| ( ( sK23_SY629 @ SV139 )
!= ( singleton @ ( sK22_SY620 @ SV139 ) ) ) ) )
= $true )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3575]) ).
thf(3686,plain,
! [SV624: $i,SV139: $i] :
( ( ( ~ ! [SY1447: $i] :
( ! [SY1448: $i] :
( ( SY1448 != SY1447 )
| ~ ( in @ SY1448 @ ( cartesian_product2 @ SV139 @ SV624 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1447 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1447 @ ( sK13_C @ SV624 @ SV139 ) ) ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3576]) ).
thf(3687,plain,
! [SV139: $i,SV624: $i] :
( ( ( ~ ! [SY1451: $i] :
( ~ ( in @ SY1451 @ ( sK13_C @ SV624 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1451 @ SV624 @ SV139 )
!= SY1451 )
| ~ ( in @ ( sK16_E @ SY1451 @ SV624 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV624 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1451 @ SV624 @ SV139 ) @ ( sK15_SY612 @ SY1451 @ SV624 @ SV139 ) )
!= SY1451 )
| ~ ( in @ ( sK14_J @ SY1451 @ SV624 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1451 @ SV624 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1451 @ SV624 @ SV139 ) ) ) ) ) ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3576]) ).
thf(3688,plain,
! [SV139: $i] :
( ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3577]) ).
thf(3689,plain,
! [SV139: $i] :
( ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3578]) ).
thf(3690,plain,
! [SV625: $i,SV139: $i] :
( ( ( ~ ! [SY1452: $i] :
( ! [SY1453: $i] :
( ( SY1453 != SY1452 )
| ~ ( in @ SY1453 @ ( cartesian_product2 @ SV139 @ SV625 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1452 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1452 @ ( sK13_C @ SV625 @ SV139 ) ) ) )
= $false )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3579]) ).
thf(3691,plain,
! [SV139: $i,SV625: $i] :
( ( ( ~ ! [SY1456: $i] :
( ~ ( in @ SY1456 @ ( sK13_C @ SV625 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1456 @ SV625 @ SV139 )
!= SY1456 )
| ~ ( in @ ( sK16_E @ SY1456 @ SV625 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV625 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1456 @ SV625 @ SV139 ) @ ( sK15_SY612 @ SY1456 @ SV625 @ SV139 ) )
!= SY1456 )
| ~ ( in @ ( sK14_J @ SY1456 @ SV625 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1456 @ SV625 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1456 @ SV625 @ SV139 ) ) ) ) ) ) )
= $false )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3579]) ).
thf(3692,plain,
! [SV488: $i,SV139: $i,SV603: $i,SV654: $i] :
( ( ( ( SV654 != SV603 )
| ~ ( in @ SV654 @ ( cartesian_product2 @ SV139 @ SV488 ) ) )
= $true )
| ( ( ! [SY1431: $i,SY1432: $i] :
( ( ( ordered_pair @ SY1431 @ SY1432 )
!= SV603 )
| ~ ( in @ SY1431 @ SV139 )
| ( SY1432
!= ( singleton @ SY1431 ) ) ) )
= $true )
| ( ( in @ SV603 @ ( sK13_C @ SV488 @ SV139 ) )
= $true )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3580]) ).
thf(3693,plain,
! [SV139: $i,SV488: $i,SV604: $i] :
( ( ( ~ ~ ( ( ( sK16_E @ SV604 @ SV488 @ SV139 )
!= SV604 )
| ~ ( in @ ( sK16_E @ SV604 @ SV488 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV488 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV604 @ SV488 @ SV139 ) @ ( sK15_SY612 @ SV604 @ SV488 @ SV139 ) )
!= SV604 )
| ~ ( in @ ( sK14_J @ SV604 @ SV488 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV604 @ SV488 @ SV139 )
!= ( singleton @ ( sK14_J @ SV604 @ SV488 @ SV139 ) ) ) ) )
= $false )
| ( ( in @ SV604 @ ( sK13_C @ SV488 @ SV139 ) )
= $false )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3581]) ).
thf(3694,plain,
! [SV143: $i,SV400: $i,SV461: $i] :
( ( ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV400 )
= $false )
| ( ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV143 )
= $false )
| ( ( ~ ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV461 ) )
= $true )
| ( ( SV461
= ( set_intersection2 @ SV143 @ SV400 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3582]) ).
thf(3695,plain,
! [SV143: $i,SV400: $i,SV461: $i] :
( ( ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV143 )
= $true )
| ( ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV461 )
= $true )
| ( ( SV461
= ( set_intersection2 @ SV143 @ SV400 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3583]) ).
thf(3696,plain,
! [SV143: $i,SV400: $i,SV461: $i] :
( ( ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV400 )
= $true )
| ( ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV461 )
= $true )
| ( ( SV461
= ( set_intersection2 @ SV143 @ SV400 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3584]) ).
thf(3697,plain,
! [SV462: $i,SV401: $i,SV143: $i,SV626: $i] :
( ( ( ~ ( in @ SV626 @ SV143 ) )
= $true )
| ( ( ~ ( in @ SV626 @ SV401 ) )
= $true )
| ( ( in @ SV626 @ SV462 )
= $true )
| ( ( SV462
= ( set_intersection2 @ SV143 @ SV401 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3585]) ).
thf(3698,plain,
! [SV401: $i,SV143: $i,SV462: $i] :
( ( ( ! [SY1326: $i] :
( ~ ( in @ SY1326 @ SV462 )
| ( in @ SY1326 @ SV143 ) ) )
= $true )
| ( ( SV462
= ( set_intersection2 @ SV143 @ SV401 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3586]) ).
thf(3699,plain,
! [SV143: $i,SV401: $i,SV462: $i] :
( ( ( ! [SY1327: $i] :
( ~ ( in @ SY1327 @ SV462 )
| ( in @ SY1327 @ SV401 ) ) )
= $true )
| ( ( SV462
= ( set_intersection2 @ SV143 @ SV401 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3587]) ).
thf(3700,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY1142: $i] :
( ~ ( in @ SY1142 @ ( sK52_SY712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SY1142 ) @ SV265 ) )
| ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK52_SY712 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) ) ) )
| ~ ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3588]) ).
thf(3701,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 ) )
= $false )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3588]) ).
thf(3702,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ! [SY1143: $i] :
( ~ ( in @ SY1143 @ ( sK51_SY718 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SY1143 ) @ SV265 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3589]) ).
thf(3703,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK51_SY718 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3589]) ).
thf(3704,plain,
! [SV265: $i,SV655: $i,SV145: $i] :
( ( ( ! [SY1465: $i] :
( ~ ( in @ SY1465 @ SV145 )
| ! [SY1466: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1466 @ SY1465 @ SV655 @ SV265 @ SV145 ) @ SY1466 )
| ~ ~ ( in @ ( ordered_pair @ SV655 @ ( sK47_K @ SY1466 @ SY1465 @ SV655 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1465 != SY1466 )
| ~ ( in @ SV655 @ SY1466 ) ) )
| ( in @ SV655 @ ( sK44_C @ SV265 @ SV145 ) ) )
= $true )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3590]) ).
thf(3705,plain,
! [SV145: $i,SV265: $i,SV656: $i] :
( ( ( ~ ( in @ SV656 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SV656 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1467: $i] :
( ~ ( in @ SY1467 @ ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV656 @ SY1467 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV656 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) )
| ~ ( in @ SV656 @ ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) ) ) ) ) )
= $true )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3591]) ).
thf(3706,plain,
! [SV147: $i,SV403: $i,SV463: $i] :
( ( ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV463 )
= $false )
| ( ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV403 )
= $true )
| ( ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV147 )
= $false )
| ( ( SV463
= ( set_difference @ SV147 @ SV403 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3592]) ).
thf(3707,plain,
! [SV147: $i,SV403: $i,SV463: $i] :
( ( ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV147 )
= $true )
| ( ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV463 )
= $true )
| ( ( SV463
= ( set_difference @ SV147 @ SV403 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3593]) ).
thf(3708,plain,
! [SV147: $i,SV403: $i,SV463: $i] :
( ( ( ~ ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV403 ) )
= $true )
| ( ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV463 )
= $true )
| ( ( SV463
= ( set_difference @ SV147 @ SV403 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3594]) ).
thf(3709,plain,
! [SV464: $i,SV404: $i,SV147: $i,SV627: $i] :
( ( ( ~ ( in @ SV627 @ SV147 ) )
= $true )
| ( ( in @ SV627 @ SV404 )
= $true )
| ( ( in @ SV627 @ SV464 )
= $true )
| ( ( SV464
= ( set_difference @ SV147 @ SV404 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3595]) ).
thf(3710,plain,
! [SV404: $i,SV147: $i,SV464: $i] :
( ( ( ! [SY1329: $i] :
( ~ ( in @ SY1329 @ SV464 )
| ( in @ SY1329 @ SV147 ) ) )
= $true )
| ( ( SV464
= ( set_difference @ SV147 @ SV404 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3596]) ).
thf(3711,plain,
! [SV147: $i,SV404: $i,SV464: $i] :
( ( ( ! [SY1330: $i] :
( ~ ( in @ SY1330 @ SV464 )
| ~ ( in @ SY1330 @ SV404 ) ) )
= $true )
| ( ( SV464
= ( set_difference @ SV147 @ SV404 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3597]) ).
thf(3712,plain,
! [SV148: $i,SV335: $i,SV605: $i] :
( ( ( in @ SV605 @ SV335 )
= $false )
| ( ( ~ ( subset @ ( sK105_C @ SV335 @ SV148 ) @ SV605 ) )
= $true )
| ( ( SV605
= ( sK105_C @ SV335 @ SV148 ) )
= $true )
| ( ( SV335 = empty_set )
= $true )
| ( ( element @ SV335 @ ( powerset @ ( powerset @ SV148 ) ) )
= $false )
| ( ( finite @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3598]) ).
thf(3713,plain,
! [SV409: $i,SV340: $i,SV606: $i] :
( ( ( in @ SV606 @ SV340 )
= $false )
| ( ( in @ ( sK68_C @ SV409 @ SV340 ) @ SV606 )
= $false )
| ( ( ~ ( in @ ( sK68_C @ SV409 @ SV340 ) @ SV409 ) )
= $true )
| ( ( SV409
= ( union @ SV340 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3599]) ).
thf(3714,plain,
! [SV410: $i,SV341: $i,SV644: $i,SV607: $i] :
( ( ( ~ ( in @ SV607 @ SV644 ) )
= $true )
| ( ( ~ ( in @ SV644 @ SV341 ) )
= $true )
| ( ( in @ SV607 @ SV410 )
= $true )
| ( ( SV410
= ( union @ SV341 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3602]) ).
thf(3715,plain,
! [SV341: $i,SV410: $i,SV608: $i] :
( ( ( ~ ( in @ SV608 @ ( sK67_D @ SV608 @ SV410 @ SV341 ) )
| ~ ( in @ ( sK67_D @ SV608 @ SV410 @ SV341 ) @ SV341 ) )
= $false )
| ( ( in @ SV608 @ SV410 )
= $false )
| ( ( SV410
= ( union @ SV341 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3603]) ).
thf(3716,plain,
! [SV150: $i,SV415: $i,SV465: $i,SV645: $i] :
( ( ( in @ ( ordered_pair @ SV645 @ ( sK102_D @ SV465 @ SV415 @ SV150 ) ) @ SV465 )
= $false )
| ( ( ( relation_rng_as_subset @ SV150 @ SV415 @ SV465 )
= SV415 )
= $true )
| ( ( relation_of2_as_subset @ SV465 @ SV150 @ SV415 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3606]) ).
thf(3717,plain,
! [SV151: $i,SV267: $i,SV467: $i,SV502: $i] :
( ( ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV467 ) )
= $true )
| ( ( SV502
= ( unordered_triple @ SV151 @ SV267 @ SV467 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3608]) ).
thf(3718,plain,
! [SV151: $i,SV267: $i,SV467: $i,SV502: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV151 ) )
| ~ ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV267 ) ) ) )
= $true )
| ( ( SV502
= ( unordered_triple @ SV151 @ SV267 @ SV467 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3609]) ).
thf(3719,plain,
! [SV151: $i,SV267: $i,SV467: $i,SV502: $i] :
( ( ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
= SV151 )
= $true )
| ( ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
= SV267 )
= $true )
| ( ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
= SV467 )
= $true )
| ( ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
= $true )
| ( ( SV502
= ( unordered_triple @ SV151 @ SV267 @ SV467 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3610]) ).
thf(3720,plain,
! [SV267: $i,SV151: $i,SV468: $i,SV503: $i,SV646: $i] :
( ( ( ~ ( in @ SV646 @ SV503 ) )
= $true )
| ( ( ( SV646 = SV468 )
| ( SV646 = SV151 )
| ( SV646 = SV267 ) )
= $true )
| ( ( SV503
= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3611]) ).
thf(3721,plain,
! [SV267: $i,SV151: $i,SV503: $i,SV468: $i] :
( ( ( ~ ! [SY1380: $i] :
( ( SY1380 != SV468 )
| ( in @ SY1380 @ SV503 ) ) )
= $false )
| ( ( SV503
= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3612]) ).
thf(3722,plain,
! [SV468: $i,SV267: $i,SV503: $i,SV151: $i] :
( ( ( ~ ~ ( ~ ! [SY1381: $i] :
( ( SY1381 != SV151 )
| ( in @ SY1381 @ SV503 ) )
| ~ ! [SY1382: $i] :
( ( SY1382 != SV267 )
| ( in @ SY1382 @ SV503 ) ) ) )
= $false )
| ( ( SV503
= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3612]) ).
thf(3723,plain,
! [SV628: $i,SV152: $i,SV612: $i] :
( ( ( ~ ( in @ SV612 @ ( sK106_B @ SV152 ) ) )
= $true )
| ( ( ~ ( subset @ SV628 @ SV612 ) )
= $true )
| ( ( in @ SV628 @ ( sK106_B @ SV152 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3613]) ).
thf(3724,plain,
! [SV154: $i,SV504: $i] :
( ( ( in @ ( ordered_pair @ ( sK72_C @ SV504 @ SV154 ) @ ( sK73_SY724 @ SV504 @ SV154 ) ) @ SV504 )
= $false )
| ( ( subset @ SV154 @ SV504 )
= $true )
| ( ( relation @ SV504 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3615]) ).
thf(3725,plain,
! [SV505: $i,SV154: $i,SV647: $i,SV629: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV629 @ SV647 ) @ SV154 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV629 @ SV647 ) @ SV505 )
= $true )
| ( ( subset @ SV154 @ SV505 )
= $false )
| ( ( relation @ SV505 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3616]) ).
thf(3726,plain,
! [SV155: $i,SV268: $i,SV547: $i] :
( ( ( element @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ ( powerset @ SV155 ) )
= $true )
| ( ( SV547
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $true )
| ( ( element @ SV547 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3617]) ).
thf(3727,plain,
! [SV155: $i,SV268: $i,SV547: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ SV547 )
| ~ ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SV547 @ SV268 @ SV155 ) ) @ SV268 ) )
| ~ ( ( in @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ SV547 )
| ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SV547 @ SV268 @ SV155 ) ) @ SV268 ) ) ) )
= $true )
| ( ( SV547
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $true )
| ( ( element @ SV547 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3618]) ).
thf(3728,plain,
! [SV268: $i,SV548: $i,SV155: $i] :
( ( ( ~ ! [SY1408: $i] :
( ~ ( element @ SY1408 @ ( powerset @ SV155 ) )
| ~ ( in @ SY1408 @ SV548 )
| ( in @ ( subset_complement @ SV155 @ SY1408 ) @ SV268 ) ) )
= $false )
| ( ( SV548
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $false )
| ( ( element @ SV548 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3619]) ).
thf(3729,plain,
! [SV548: $i,SV268: $i,SV155: $i] :
( ( ( ~ ! [SY1409: $i] :
( ~ ( element @ SY1409 @ ( powerset @ SV155 ) )
| ~ ( in @ ( subset_complement @ SV155 @ SY1409 ) @ SV268 )
| ( in @ SY1409 @ SV548 ) ) )
= $false )
| ( ( SV548
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $false )
| ( ( element @ SV548 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3619]) ).
thf(3730,plain,
! [SV425: $i,SV566: $i,SV630: $i] :
( ( ( SV630 = SV566 )
= $false )
| ( ( ~ ( in @ SV630 @ SV425 ) )
= $true )
| ( ( ~ ( ordinal @ SV566 ) )
= $true )
| ( ( in @ SV566 @ ( sK7_B @ SV425 ) )
= $true )
| ( sK12_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[3620]) ).
thf(3731,plain,
! [SV425: $i,SV567: $i] :
( ( ( ~ ( ( ( sK8_D @ SV567 @ SV425 )
!= SV567 )
| ~ ( in @ ( sK8_D @ SV567 @ SV425 ) @ SV425 ) ) )
= $true )
| ( ( in @ SV567 @ ( sK7_B @ SV425 ) )
= $false )
| ( sK12_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[3621]) ).
thf(3732,plain,
! [SV425: $i,SV567: $i] :
( ( ( ordinal @ SV567 )
= $true )
| ( ( in @ SV567 @ ( sK7_B @ SV425 ) )
= $false )
| ( sK12_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[3622]) ).
thf(3733,plain,
( ( ( ~ ( ( sK9_B != sK10_SY601 )
| ~ ( ordinal @ sK10_SY601 ) ) )
= $true )
| ( sK12_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[3623]) ).
thf(3734,plain,
( ( ( sK9_B = sK11_SY603 )
= $true )
| ( sK12_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[3624]) ).
thf(3735,plain,
! [SV613: $i,SV158: $i,SV631: $i] :
( ( ( relation_of2_as_subset @ SV631 @ SV158 @ SV613 )
= $false )
| ( ( ( SV613 = empty_set )
| ( SV158
!= ( relation_dom_as_subset @ SV158 @ SV613 @ SV631 ) )
| ( quasi_total @ SV631 @ SV158 @ SV613 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3627]) ).
thf(3736,plain,
! [SV614: $i,SV158: $i,SV632: $i] :
( ( ( relation_of2_as_subset @ SV632 @ SV158 @ SV614 )
= $false )
| ( ( ( SV614 = empty_set )
| ~ ( quasi_total @ SV632 @ SV158 @ SV614 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SV614 @ SV632 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3628]) ).
thf(3737,plain,
! [SV615: $i,SV158: $i,SV633: $i] :
( ( ( relation_of2_as_subset @ SV633 @ SV158 @ SV615 )
= $false )
| ( ( ( SV158 != empty_set )
| ( SV158
!= ( relation_dom_as_subset @ SV158 @ SV615 @ SV633 ) )
| ( quasi_total @ SV633 @ SV158 @ SV615 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3629]) ).
thf(3738,plain,
! [SV616: $i,SV158: $i,SV634: $i] :
( ( ( relation_of2_as_subset @ SV634 @ SV158 @ SV616 )
= $false )
| ( ( ( SV158 != empty_set )
| ~ ( quasi_total @ SV634 @ SV158 @ SV616 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SV616 @ SV634 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3630]) ).
thf(3739,plain,
! [SV553: $i,SV158: $i,SV570: $i] :
( ( ( ( SV570 != empty_set )
| ( quasi_total @ SV570 @ SV158 @ SV553 ) )
= $true )
| ( ( SV158 = empty_set )
= $true )
| ( ( SV553 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV570 @ SV158 @ SV553 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3631]) ).
thf(3740,plain,
! [SV554: $i,SV158: $i,SV571: $i] :
( ( ( ~ ( quasi_total @ SV571 @ SV158 @ SV554 )
| ( SV571 = empty_set ) )
= $true )
| ( ( SV158 = empty_set )
= $true )
| ( ( SV554 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV571 @ SV158 @ SV554 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3632]) ).
thf(3741,plain,
! [SV512: $i,SV572: $i] :
( ( ( ~ ( ~ ( in @ ( sK90_SY733 @ SV572 @ SV512 ) @ SV512 )
| ~ ~ ( in @ ( sK89_C @ SV572 @ SV512 ) @ ( sK90_SY733 @ SV572 @ SV512 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK89_C @ SV572 @ SV512 ) @ SV572 ) )
= $true )
| ( ( SV572
= ( set_meet @ SV512 ) )
= $true )
| ( ( SV512 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3633]) ).
thf(3742,plain,
! [SV572: $i,SV512: $i] :
( ( ( ! [SY1416: $i] :
( ~ ( in @ SY1416 @ SV512 )
| ( in @ ( sK89_C @ SV572 @ SV512 ) @ SY1416 ) ) )
= $true )
| ( ( in @ ( sK89_C @ SV572 @ SV512 ) @ SV572 )
= $true )
| ( ( SV572
= ( set_meet @ SV512 ) )
= $true )
| ( ( SV512 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3634]) ).
thf(3743,plain,
! [SV513: $i,SV573: $i] :
( ( ( ! [SY1417: $i] :
( ~ ( ~ ( in @ ( sK88_D @ SY1417 @ SV573 @ SV513 ) @ SV513 )
| ~ ~ ( in @ SY1417 @ ( sK88_D @ SY1417 @ SV573 @ SV513 ) ) )
| ( in @ SY1417 @ SV573 ) ) )
= $true )
| ( ( SV573
= ( set_meet @ SV513 ) )
= $false )
| ( ( SV513 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3635]) ).
thf(3744,plain,
! [SV513: $i,SV573: $i] :
( ( ( ! [SY1418: $i] :
( ~ ( in @ SY1418 @ SV573 )
| ! [SY1394: $i] :
( ~ ( in @ SY1394 @ SV513 )
| ( in @ SY1418 @ SY1394 ) ) ) )
= $true )
| ( ( SV573
= ( set_meet @ SV513 ) )
= $false )
| ( ( SV513 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3636]) ).
thf(3745,plain,
! [SV159: $i,SV427: $i,SV470: $i] :
( ( ( ~ ( in @ ( sK82_D @ SV470 @ SV427 @ SV159 ) @ SV470 ) )
= $true )
| ( ( ( ( sK82_D @ SV470 @ SV427 @ SV159 )
!= SV159 ) )
= $true )
| ( ( SV470
= ( unordered_pair @ SV159 @ SV427 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3637]) ).
thf(3746,plain,
! [SV159: $i,SV427: $i,SV470: $i] :
( ( ( ~ ( in @ ( sK82_D @ SV470 @ SV427 @ SV159 ) @ SV470 ) )
= $true )
| ( ( ( ( sK82_D @ SV470 @ SV427 @ SV159 )
!= SV427 ) )
= $true )
| ( ( SV470
= ( unordered_pair @ SV159 @ SV427 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3638]) ).
thf(3747,plain,
! [SV428: $i,SV159: $i,SV471: $i,SV635: $i] :
( ( ( in @ SV635 @ SV471 )
= $false )
| ( ( ( SV635 = SV159 )
| ( SV635 = SV428 ) )
= $true )
| ( ( SV471
= ( unordered_pair @ SV159 @ SV428 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3639]) ).
thf(3748,plain,
! [SV428: $i,SV471: $i,SV159: $i] :
( ( ( ! [SY1340: $i] :
( ( SY1340 != SV159 )
| ( in @ SY1340 @ SV471 ) ) )
= $true )
| ( ( SV471
= ( unordered_pair @ SV159 @ SV428 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3640]) ).
thf(3749,plain,
! [SV159: $i,SV471: $i,SV428: $i] :
( ( ( ! [SY1341: $i] :
( ( SY1341 != SV428 )
| ( in @ SY1341 @ SV471 ) ) )
= $true )
| ( ( SV471
= ( unordered_pair @ SV159 @ SV428 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3641]) ).
thf(3750,plain,
! [SV474: $i,SV437: $i,SV648: $i,SV164: $i,SV636: $i] :
( ( ( ~ ( in @ SV636 @ SV164 )
| ~ ( in @ SV648 @ SV437 ) )
= $true )
| ( ( ( ( sK78_D @ SV474 @ SV437 @ SV164 )
!= ( ordered_pair @ SV636 @ SV648 ) ) )
= $true )
| ( ( ~ ( in @ ( sK78_D @ SV474 @ SV437 @ SV164 ) @ SV474 ) )
= $true )
| ( ( SV474
= ( cartesian_product2 @ SV164 @ SV437 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3644]) ).
thf(3751,plain,
! [SV164: $i,SV437: $i,SV474: $i] :
( ( ( ~ ( ~ ( in @ ( sK79_SY729 @ SV474 @ SV437 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK80_SY731 @ SV474 @ SV437 @ SV164 ) @ SV437 ) ) )
= $true )
| ( ( in @ ( sK78_D @ SV474 @ SV437 @ SV164 ) @ SV474 )
= $true )
| ( ( SV474
= ( cartesian_product2 @ SV164 @ SV437 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3645]) ).
thf(3752,plain,
! [SV164: $i,SV437: $i,SV474: $i] :
( ( ( ( sK78_D @ SV474 @ SV437 @ SV164 )
= ( ordered_pair @ ( sK79_SY729 @ SV474 @ SV437 @ SV164 ) @ ( sK80_SY731 @ SV474 @ SV437 @ SV164 ) ) )
= $true )
| ( ( in @ ( sK78_D @ SV474 @ SV437 @ SV164 ) @ SV474 )
= $true )
| ( ( SV474
= ( cartesian_product2 @ SV164 @ SV437 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3646]) ).
thf(3753,plain,
! [SV475: $i,SV637: $i,SV438: $i,SV164: $i,SV657: $i] :
( ( ( ! [SY1468: $i] :
( ~ ( in @ SV657 @ SV164 )
| ~ ( in @ SY1468 @ SV438 )
| ( SV637
!= ( ordered_pair @ SV657 @ SY1468 ) ) ) )
= $true )
| ( ( in @ SV637 @ SV475 )
= $true )
| ( ( SV475
= ( cartesian_product2 @ SV164 @ SV438 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3647]) ).
thf(3754,plain,
! [SV164: $i,SV438: $i,SV475: $i,SV638: $i] :
( ( ( in @ SV638 @ SV475 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK76_E @ SV638 @ SV475 @ SV438 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK77_SY726 @ SV638 @ SV475 @ SV438 @ SV164 ) @ SV438 ) )
| ( SV638
!= ( ordered_pair @ ( sK76_E @ SV638 @ SV475 @ SV438 @ SV164 ) @ ( sK77_SY726 @ SV638 @ SV475 @ SV438 @ SV164 ) ) ) ) )
= $true )
| ( ( SV475
= ( cartesian_product2 @ SV164 @ SV438 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3648]) ).
thf(3755,plain,
! [SV166: $i,SV558: $i,SV649: $i] :
( ( ( ~ ( subset @ SV649 @ SV558 ) )
= $true )
| ( ( in @ SV649 @ ( sK4_SY591 @ SV558 @ SV166 ) )
= $true )
| ( ( ~ ( in @ SV558 @ ( sK3_B @ SV166 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3649]) ).
thf(3756,plain,
! [SV639: $i,SV166: $i,SV619: $i] :
( ( ( ~ ( in @ SV619 @ ( sK3_B @ SV166 ) ) )
= $true )
| ( ( ~ ( subset @ SV639 @ SV619 ) )
= $true )
| ( ( in @ SV639 @ ( sK3_B @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3651]) ).
thf(3757,plain,
! [SV650: $i,SV167: $i,SV444: $i,SV478: $i] :
( ( ( in @ ( ordered_pair @ ( sK104_D @ SV478 @ SV444 @ SV167 ) @ SV650 ) @ SV478 )
= $false )
| ( ( ( relation_dom_as_subset @ SV444 @ SV167 @ SV478 )
= SV444 )
= $true )
| ( ( relation_of2_as_subset @ SV478 @ SV444 @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3652]) ).
thf(3758,plain,
! [SV168: $i] :
( ( ( ( sK27_SY634 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) )
| ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3654]) ).
thf(3759,plain,
! [SV168: $i] :
( ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true )
| ( ( ~ ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) )
| ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3655]) ).
thf(3760,plain,
! [SV168: $i] :
( ( ( ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) ) )
= $true )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3656]) ).
thf(3761,plain,
! [SV168: $i] :
( ( ( ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3657]) ).
thf(3762,plain,
! [SV640: $i,SV168: $i,SV658: $i] :
( ( ( ~ ( in @ SV658 @ SV168 )
| ( SV640
!= ( singleton @ SV658 ) ) )
= $true )
| ( ( in @ SV640 @ ( sK24_B @ SV168 ) )
= $true )
| ( ( ( sK28_SY636 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3658]) ).
thf(3763,plain,
! [SV168: $i,SV641: $i] :
( ( ( in @ SV641 @ ( sK24_B @ SV168 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK25_D @ SV641 @ SV168 ) @ SV168 )
| ( SV641
!= ( singleton @ ( sK25_D @ SV641 @ SV168 ) ) ) ) )
= $true )
| ( ( ( sK28_SY636 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3659]) ).
thf(3764,plain,
! [SV593: $i,SV168: $i,SV642: $i] :
( ( ( in @ SV642 @ SV168 )
= $false )
| ( ( ( SV593
!= ( singleton @ SV642 ) ) )
= $true )
| ( ( in @ SV593 @ ( sK24_B @ SV168 ) )
= $true )
| ( ( ( sK27_SY634 @ SV168 )
= ( sK28_SY636 @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3660]) ).
thf(3765,plain,
! [SV168: $i,SV594: $i] :
( ( ( ~ ( in @ ( sK25_D @ SV594 @ SV168 ) @ SV168 ) )
= $false )
| ( ( in @ SV594 @ ( sK24_B @ SV168 ) )
= $false )
| ( ( ( sK27_SY634 @ SV168 )
= ( sK28_SY636 @ SV168 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3661]) ).
thf(3766,plain,
! [SV168: $i,SV594: $i] :
( ( ( ( SV594
!= ( singleton @ ( sK25_D @ SV594 @ SV168 ) ) ) )
= $false )
| ( ( in @ SV594 @ ( sK24_B @ SV168 ) )
= $false )
| ( ( ( sK27_SY634 @ SV168 )
= ( sK28_SY636 @ SV168 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3661]) ).
thf(3767,plain,
! [SV271: $i,SV481: $i,SV170: $i,SV596: $i,SV659: $i,SV651: $i] :
( ( ( ( ( ordered_pair @ SV651 @ SV659 )
!= SV596 )
| ~ ( in @ SV651 @ SV170 )
| ! [SY1469: $i] :
( ~ ( ~ ( in @ ( sK115_I @ SY1469 @ SV659 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) @ SY1469 )
| ~ ~ ( in @ ( ordered_pair @ SV659 @ ( sK115_I @ SY1469 @ SV659 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) ) @ SV271 ) )
| ( SV651 != SY1469 )
| ~ ( in @ SV659 @ SY1469 ) ) )
= $true )
| ( ( ~ ( in @ SV596 @ ( cartesian_product2 @ SV170 @ SV481 ) ) )
= $true )
| ( ( in @ SV596 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3662]) ).
thf(3768,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV652: $i] :
( ( ( ~ ( in @ SV652 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK112_F @ SV652 @ SV481 @ SV271 @ SV170 ) @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) )
!= SV652 )
| ~ ( in @ ( sK112_F @ SV652 @ SV481 @ SV271 @ SV170 ) @ SV170 ) )
| ~ ~ ( ~ ! [SY1464: $i] :
( ~ ( in @ SY1464 @ ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) )
| ( in @ ( ordered_pair @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) @ SY1464 ) @ SV271 ) )
| ~ ~ ( ( ( sK112_F @ SV652 @ SV481 @ SV271 @ SV170 )
!= ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) )
| ~ ( in @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) @ ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) ) ) ) ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3663]) ).
thf(3769,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV653: $i] :
( ( ( ~ ( in @ SV653 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) ) )
= $true )
| ( ( in @ SV653 @ ( cartesian_product2 @ SV170 @ SV481 ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3664]) ).
thf(3770,plain,
! [SV368: $i] :
( ( ( ~ ( ~ ( in @ ( sK74_B @ SV368 ) @ SV368 )
| ~ ( in @ ( sK75_SY725 @ SV368 ) @ SV368 ) ) )
= $true )
| ( ( epsilon_connected @ SV368 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3665]) ).
thf(3771,plain,
! [SV368: $i] :
( ( ( ~ ( in @ ( sK74_B @ SV368 ) @ ( sK75_SY725 @ SV368 ) ) )
= $true )
| ( ( epsilon_connected @ SV368 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3666]) ).
thf(3772,plain,
! [SV520: $i,SV369: $i,SV559: $i] :
( ( ( in @ SV559 @ SV369 )
= $false )
| ( ( in @ SV520 @ SV369 )
= $false )
| ( ( in @ SV520 @ SV559 )
= $true )
| ( ( SV520 = SV559 )
= $true )
| ( ( in @ SV559 @ SV520 )
= $true )
| ( ( epsilon_connected @ SV369 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3667]) ).
thf(3773,plain,
! [SV171: $i,SV524: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV171 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV524 ) )
= $true )
| ( ( SV171 = SV524 )
= $true )
| ( ( relation @ SV524 )
= $false )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3668]) ).
thf(3774,plain,
! [SV171: $i,SV524: $i] :
( ( ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV171 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV524 )
= $true )
| ( ( SV171 = SV524 )
= $true )
| ( ( relation @ SV524 )
= $false )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3669]) ).
thf(3775,plain,
! [SV525: $i,SV171: $i] :
( ( ( ! [SY1400: $i,SY1401: $i] :
( ~ ( in @ ( ordered_pair @ SY1400 @ SY1401 ) @ SV171 )
| ( in @ ( ordered_pair @ SY1400 @ SY1401 ) @ SV525 ) ) )
= $true )
| ( ( SV171 = SV525 )
= $false )
| ( ( relation @ SV525 )
= $false )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3670]) ).
thf(3776,plain,
! [SV171: $i,SV525: $i] :
( ( ( ! [SY1402: $i,SY1403: $i] :
( ~ ( in @ ( ordered_pair @ SY1402 @ SY1403 ) @ SV525 )
| ( in @ ( ordered_pair @ SY1402 @ SY1403 ) @ SV171 ) ) )
= $true )
| ( ( SV171 = SV525 )
= $false )
| ( ( relation @ SV525 )
= $false )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3671]) ).
thf(3777,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ~ ( ( ( sK35_D @ SV272 @ SV172 )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1178: $i] :
( ~ ( in @ SY1178 @ ( sK43_SY691 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SY1178 ) @ SV272 ) )
| ~ ~ ( ( ( sK41_SY666 @ SV272 @ SV172 )
!= ( sK43_SY691 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) ) ) ) ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3672]) ).
thf(3778,plain,
! [SV172: $i,SV272: $i] :
( ( ( ( ( sK35_D @ SV272 @ SV172 )
!= ( sK37_SY665 @ SV272 @ SV172 ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3672]) ).
thf(3779,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
!= ( sK37_SY665 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3673]) ).
thf(3780,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ~ ( ~ ! [SY1179: $i] :
( ~ ( in @ SY1179 @ ( sK40_SY685 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SY1179 ) @ SV272 ) )
| ~ ~ ( ( ( sK38_SY678 @ SV272 @ SV172 )
!= ( sK40_SY685 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) ) ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3673]) ).
thf(3781,plain,
! [SV272: $i,SV622: $i,SV172: $i] :
( ( ( ! [SY1440: $i] :
( ! [SY1441: $i] :
( ( SY1441 != SY1440 )
| ~ ( in @ SY1441 @ ( cartesian_product2 @ SV172 @ SV622 ) ) )
| ! [SY1442: $i,SY1443: $i] :
( ( ( ordered_pair @ SY1442 @ SY1443 )
!= SY1440 )
| ~ ( in @ SY1442 @ SV172 )
| ! [SY1444: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1444 @ SY1443 @ SY1442 @ SY1440 @ SV622 @ SV272 @ SV172 ) @ SY1444 )
| ~ ~ ( in @ ( ordered_pair @ SY1443 @ ( sK34_R @ SY1444 @ SY1443 @ SY1442 @ SY1440 @ SV622 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1442 != SY1444 )
| ~ ( in @ SY1443 @ SY1444 ) ) )
| ( in @ SY1440 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) ) ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3674]) ).
thf(3782,plain,
! [SV172: $i,SV272: $i,SV622: $i] :
( ( ( ! [SY1445: $i] :
( ~ ( in @ SY1445 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1445 @ SV622 @ SV272 @ SV172 )
!= SY1445 )
| ~ ( in @ ( sK33_F @ SY1445 @ SV622 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV622 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1445 @ SV622 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1445 @ SV622 @ SV272 @ SV172 ) )
!= SY1445 )
| ~ ( in @ ( sK30_O @ SY1445 @ SV622 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1446: $i] :
( ~ ( in @ SY1446 @ ( sK32_SY652 @ SY1445 @ SV622 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1445 @ SV622 @ SV272 @ SV172 ) @ SY1446 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1445 @ SV622 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1445 @ SV622 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1445 @ SV622 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1445 @ SV622 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3675]) ).
thf(3783,plain,
! [SV275: $i,SV483: $i,SV602: $i,SV176: $i,SV579: $i] :
( ( ( in @ SV579 @ SV176 )
= $false )
| ( ( ( ordered_pair @ SV579 @ SV602 )
= SV483 )
= $false )
| ( ( ( SV602
!= ( singleton @ SV579 ) ) )
= $true )
| ( ( ~ ( in @ SV483 @ ( cartesian_product2 @ SV176 @ SV275 ) ) )
= $true )
| ( ( in @ SV483 @ ( sK108_C @ SV275 @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3676]) ).
thf(3784,plain,
! [SV176: $i,SV275: $i,SV580: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK109_E @ SV580 @ SV275 @ SV176 ) @ ( sK110_SY756 @ SV580 @ SV275 @ SV176 ) )
!= SV580 )
| ~ ( in @ ( sK109_E @ SV580 @ SV275 @ SV176 ) @ SV176 ) ) )
= $true )
| ( ( in @ SV580 @ ( sK108_C @ SV275 @ SV176 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3677]) ).
thf(3785,plain,
! [SV176: $i,SV275: $i,SV580: $i] :
( ( ( ( sK110_SY756 @ SV580 @ SV275 @ SV176 )
= ( singleton @ ( sK109_E @ SV580 @ SV275 @ SV176 ) ) )
= $true )
| ( ( in @ SV580 @ ( sK108_C @ SV275 @ SV176 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3678]) ).
thf(3786,plain,
! [SV180: $i,SV456: $i,SV484: $i] :
( ( ( ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV484 ) )
= $true )
| ( ( ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV180 ) )
= $true )
| ( ( SV484
= ( set_union2 @ SV180 @ SV456 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3679]) ).
thf(3787,plain,
! [SV180: $i,SV456: $i,SV484: $i] :
( ( ( ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV484 ) )
= $true )
| ( ( ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV456 ) )
= $true )
| ( ( SV484
= ( set_union2 @ SV180 @ SV456 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3680]) ).
thf(3788,plain,
! [SV457: $i,SV180: $i,SV485: $i,SV643: $i] :
( ( ( in @ SV643 @ SV485 )
= $false )
| ( ( ( in @ SV643 @ SV180 )
| ( in @ SV643 @ SV457 ) )
= $true )
| ( ( SV485
= ( set_union2 @ SV180 @ SV457 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3681]) ).
thf(3789,plain,
! [SV457: $i,SV485: $i,SV180: $i] :
( ( ( ! [SY1362: $i] :
( ~ ( in @ SY1362 @ SV180 )
| ( in @ SY1362 @ SV485 ) ) )
= $true )
| ( ( SV485
= ( set_union2 @ SV180 @ SV457 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3682]) ).
thf(3790,plain,
! [SV180: $i,SV485: $i,SV457: $i] :
( ( ( ! [SY1363: $i] :
( ~ ( in @ SY1363 @ SV457 )
| ( in @ SY1363 @ SV485 ) ) )
= $true )
| ( ( SV485
= ( set_union2 @ SV180 @ SV457 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3683]) ).
thf(3791,plain,
! [SV660: $i,SV139: $i] :
( ( ( ~ ( ~ ! [SY1470: $i] :
( ! [SY1471: $i] :
( ( SY1471 != SY1470 )
| ~ ( in @ SY1471 @ ( cartesian_product2 @ SV139 @ SV660 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1470 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1470 @ ( sK13_C @ SV660 @ SV139 ) ) )
| ~ ! [SY1474: $i] :
( ~ ( in @ SY1474 @ ( sK13_C @ SV660 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1474 @ SV660 @ SV139 )
!= SY1474 )
| ~ ( in @ ( sK16_E @ SY1474 @ SV660 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV660 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1474 @ SV660 @ SV139 ) @ ( sK15_SY612 @ SY1474 @ SV660 @ SV139 ) )
!= SY1474 )
| ~ ( in @ ( sK14_J @ SY1474 @ SV660 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1474 @ SV660 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1474 @ SV660 @ SV139 ) ) ) ) ) ) ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3684]) ).
thf(3792,plain,
! [SV139: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
!= ( sK18_SY613 @ SV139 ) )
| ~ ( in @ ( sK22_SY620 @ SV139 ) @ SV139 ) )
| ( ( sK23_SY629 @ SV139 )
!= ( singleton @ ( sK22_SY620 @ SV139 ) ) ) )
= $false )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3685]) ).
thf(3793,plain,
! [SV624: $i,SV139: $i] :
( ( ( ! [SY1447: $i] :
( ! [SY1448: $i] :
( ( SY1448 != SY1447 )
| ~ ( in @ SY1448 @ ( cartesian_product2 @ SV139 @ SV624 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1447 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1447 @ ( sK13_C @ SV624 @ SV139 ) ) ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3686]) ).
thf(3794,plain,
! [SV139: $i,SV624: $i] :
( ( ( ! [SY1451: $i] :
( ~ ( in @ SY1451 @ ( sK13_C @ SV624 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1451 @ SV624 @ SV139 )
!= SY1451 )
| ~ ( in @ ( sK16_E @ SY1451 @ SV624 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV624 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1451 @ SV624 @ SV139 ) @ ( sK15_SY612 @ SY1451 @ SV624 @ SV139 ) )
!= SY1451 )
| ~ ( in @ ( sK14_J @ SY1451 @ SV624 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1451 @ SV624 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1451 @ SV624 @ SV139 ) ) ) ) ) ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3687]) ).
thf(3795,plain,
! [SV661: $i,SV139: $i] :
( ( ( ~ ( ~ ! [SY1475: $i] :
( ! [SY1476: $i] :
( ( SY1476 != SY1475 )
| ~ ( in @ SY1476 @ ( cartesian_product2 @ SV139 @ SV661 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1475 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1475 @ ( sK13_C @ SV661 @ SV139 ) ) )
| ~ ! [SY1479: $i] :
( ~ ( in @ SY1479 @ ( sK13_C @ SV661 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1479 @ SV661 @ SV139 )
!= SY1479 )
| ~ ( in @ ( sK16_E @ SY1479 @ SV661 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV661 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1479 @ SV661 @ SV139 ) @ ( sK15_SY612 @ SY1479 @ SV661 @ SV139 ) )
!= SY1479 )
| ~ ( in @ ( sK14_J @ SY1479 @ SV661 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1479 @ SV661 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1479 @ SV661 @ SV139 ) ) ) ) ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3688]) ).
thf(3796,plain,
! [SV662: $i,SV139: $i] :
( ( ( ~ ( ~ ! [SY1480: $i] :
( ! [SY1481: $i] :
( ( SY1481 != SY1480 )
| ~ ( in @ SY1481 @ ( cartesian_product2 @ SV139 @ SV662 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1480 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1480 @ ( sK13_C @ SV662 @ SV139 ) ) )
| ~ ! [SY1484: $i] :
( ~ ( in @ SY1484 @ ( sK13_C @ SV662 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1484 @ SV662 @ SV139 )
!= SY1484 )
| ~ ( in @ ( sK16_E @ SY1484 @ SV662 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV662 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1484 @ SV662 @ SV139 ) @ ( sK15_SY612 @ SY1484 @ SV662 @ SV139 ) )
!= SY1484 )
| ~ ( in @ ( sK14_J @ SY1484 @ SV662 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1484 @ SV662 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1484 @ SV662 @ SV139 ) ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3689]) ).
thf(3797,plain,
! [SV625: $i,SV139: $i] :
( ( ( ! [SY1452: $i] :
( ! [SY1453: $i] :
( ( SY1453 != SY1452 )
| ~ ( in @ SY1453 @ ( cartesian_product2 @ SV139 @ SV625 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1452 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1452 @ ( sK13_C @ SV625 @ SV139 ) ) ) )
= $true )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3690]) ).
thf(3798,plain,
! [SV139: $i,SV625: $i] :
( ( ( ! [SY1456: $i] :
( ~ ( in @ SY1456 @ ( sK13_C @ SV625 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1456 @ SV625 @ SV139 )
!= SY1456 )
| ~ ( in @ ( sK16_E @ SY1456 @ SV625 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV625 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1456 @ SV625 @ SV139 ) @ ( sK15_SY612 @ SY1456 @ SV625 @ SV139 ) )
!= SY1456 )
| ~ ( in @ ( sK14_J @ SY1456 @ SV625 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1456 @ SV625 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1456 @ SV625 @ SV139 ) ) ) ) ) ) )
= $true )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3691]) ).
thf(3799,plain,
! [SV488: $i,SV139: $i,SV603: $i,SV654: $i] :
( ( ( ( SV654 != SV603 ) )
= $true )
| ( ( ~ ( in @ SV654 @ ( cartesian_product2 @ SV139 @ SV488 ) ) )
= $true )
| ( ( ! [SY1431: $i,SY1432: $i] :
( ( ( ordered_pair @ SY1431 @ SY1432 )
!= SV603 )
| ~ ( in @ SY1431 @ SV139 )
| ( SY1432
!= ( singleton @ SY1431 ) ) ) )
= $true )
| ( ( in @ SV603 @ ( sK13_C @ SV488 @ SV139 ) )
= $true )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3692]) ).
thf(3800,plain,
! [SV139: $i,SV488: $i,SV604: $i] :
( ( ( ~ ~ ( ( ( sK16_E @ SV604 @ SV488 @ SV139 )
!= SV604 )
| ~ ( in @ ( sK16_E @ SV604 @ SV488 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV488 ) ) ) )
= $false )
| ( ( in @ SV604 @ ( sK13_C @ SV488 @ SV139 ) )
= $false )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3693]) ).
thf(3801,plain,
! [SV139: $i,SV488: $i,SV604: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV604 @ SV488 @ SV139 ) @ ( sK15_SY612 @ SV604 @ SV488 @ SV139 ) )
!= SV604 )
| ~ ( in @ ( sK14_J @ SV604 @ SV488 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV604 @ SV488 @ SV139 )
!= ( singleton @ ( sK14_J @ SV604 @ SV488 @ SV139 ) ) ) ) )
= $false )
| ( ( in @ SV604 @ ( sK13_C @ SV488 @ SV139 ) )
= $false )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3693]) ).
thf(3802,plain,
! [SV143: $i,SV400: $i,SV461: $i] :
( ( ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV461 )
= $false )
| ( ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV143 )
= $false )
| ( ( in @ ( sK70_D @ SV461 @ SV400 @ SV143 ) @ SV400 )
= $false )
| ( ( SV461
= ( set_intersection2 @ SV143 @ SV400 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3694]) ).
thf(3803,plain,
! [SV462: $i,SV401: $i,SV143: $i,SV626: $i] :
( ( ( in @ SV626 @ SV143 )
= $false )
| ( ( ~ ( in @ SV626 @ SV401 ) )
= $true )
| ( ( in @ SV626 @ SV462 )
= $true )
| ( ( SV462
= ( set_intersection2 @ SV143 @ SV401 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3697]) ).
thf(3804,plain,
! [SV401: $i,SV143: $i,SV462: $i,SV663: $i] :
( ( ( ~ ( in @ SV663 @ SV462 )
| ( in @ SV663 @ SV143 ) )
= $true )
| ( ( SV462
= ( set_intersection2 @ SV143 @ SV401 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3698]) ).
thf(3805,plain,
! [SV143: $i,SV401: $i,SV462: $i,SV664: $i] :
( ( ( ~ ( in @ SV664 @ SV462 )
| ( in @ SV664 @ SV401 ) )
= $true )
| ( ( SV462
= ( set_intersection2 @ SV143 @ SV401 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3699]) ).
thf(3806,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ( ~ ~ ( ~ ! [SY1142: $i] :
( ~ ( in @ SY1142 @ ( sK52_SY712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SY1142 ) @ SV265 ) )
| ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK52_SY712 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) ) ) )
| ~ ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3700]) ).
thf(3807,plain,
! [SV145: $i,SV265: $i] :
( ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3701]) ).
thf(3808,plain,
! [SV145: $i,SV265: $i] :
( ( ( ! [SY1143: $i] :
( ~ ( in @ SY1143 @ ( sK51_SY718 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SY1143 ) @ SV265 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3702]) ).
thf(3809,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK51_SY718 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3703]) ).
thf(3810,plain,
! [SV265: $i,SV655: $i,SV145: $i] :
( ( ( ! [SY1465: $i] :
( ~ ( in @ SY1465 @ SV145 )
| ! [SY1466: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1466 @ SY1465 @ SV655 @ SV265 @ SV145 ) @ SY1466 )
| ~ ~ ( in @ ( ordered_pair @ SV655 @ ( sK47_K @ SY1466 @ SY1465 @ SV655 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1465 != SY1466 )
| ~ ( in @ SV655 @ SY1466 ) ) ) )
= $true )
| ( ( in @ SV655 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3704]) ).
thf(3811,plain,
! [SV145: $i,SV265: $i,SV656: $i] :
( ( ( ~ ( in @ SV656 @ ( sK44_C @ SV265 @ SV145 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK45_E @ SV656 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1467: $i] :
( ~ ( in @ SY1467 @ ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV656 @ SY1467 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV656 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) )
| ~ ( in @ SV656 @ ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) ) ) ) ) )
= $true )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3705]) ).
thf(3812,plain,
! [SV147: $i,SV403: $i,SV463: $i] :
( ( ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV403 )
= $false )
| ( ( in @ ( sK66_D @ SV463 @ SV403 @ SV147 ) @ SV463 )
= $true )
| ( ( SV463
= ( set_difference @ SV147 @ SV403 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3708]) ).
thf(3813,plain,
! [SV464: $i,SV404: $i,SV147: $i,SV627: $i] :
( ( ( in @ SV627 @ SV147 )
= $false )
| ( ( in @ SV627 @ SV404 )
= $true )
| ( ( in @ SV627 @ SV464 )
= $true )
| ( ( SV464
= ( set_difference @ SV147 @ SV404 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3709]) ).
thf(3814,plain,
! [SV404: $i,SV147: $i,SV464: $i,SV665: $i] :
( ( ( ~ ( in @ SV665 @ SV464 )
| ( in @ SV665 @ SV147 ) )
= $true )
| ( ( SV464
= ( set_difference @ SV147 @ SV404 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3710]) ).
thf(3815,plain,
! [SV147: $i,SV404: $i,SV464: $i,SV666: $i] :
( ( ( ~ ( in @ SV666 @ SV464 )
| ~ ( in @ SV666 @ SV404 ) )
= $true )
| ( ( SV464
= ( set_difference @ SV147 @ SV404 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3711]) ).
thf(3816,plain,
! [SV605: $i,SV148: $i,SV335: $i] :
( ( ( subset @ ( sK105_C @ SV335 @ SV148 ) @ SV605 )
= $false )
| ( ( in @ SV605 @ SV335 )
= $false )
| ( ( SV605
= ( sK105_C @ SV335 @ SV148 ) )
= $true )
| ( ( SV335 = empty_set )
= $true )
| ( ( element @ SV335 @ ( powerset @ ( powerset @ SV148 ) ) )
= $false )
| ( ( finite @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3712]) ).
thf(3817,plain,
! [SV606: $i,SV340: $i,SV409: $i] :
( ( ( in @ ( sK68_C @ SV409 @ SV340 ) @ SV409 )
= $false )
| ( ( in @ ( sK68_C @ SV409 @ SV340 ) @ SV606 )
= $false )
| ( ( in @ SV606 @ SV340 )
= $false )
| ( ( SV409
= ( union @ SV340 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3713]) ).
thf(3818,plain,
! [SV410: $i,SV341: $i,SV644: $i,SV607: $i] :
( ( ( in @ SV607 @ SV644 )
= $false )
| ( ( ~ ( in @ SV644 @ SV341 ) )
= $true )
| ( ( in @ SV607 @ SV410 )
= $true )
| ( ( SV410
= ( union @ SV341 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3714]) ).
thf(3819,plain,
! [SV341: $i,SV410: $i,SV608: $i] :
( ( ( ~ ( in @ SV608 @ ( sK67_D @ SV608 @ SV410 @ SV341 ) ) )
= $false )
| ( ( in @ SV608 @ SV410 )
= $false )
| ( ( SV410
= ( union @ SV341 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3715]) ).
thf(3820,plain,
! [SV341: $i,SV410: $i,SV608: $i] :
( ( ( ~ ( in @ ( sK67_D @ SV608 @ SV410 @ SV341 ) @ SV341 ) )
= $false )
| ( ( in @ SV608 @ SV410 )
= $false )
| ( ( SV410
= ( union @ SV341 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3715]) ).
thf(3821,plain,
! [SV151: $i,SV267: $i,SV467: $i,SV502: $i] :
( ( ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 ) )
= $true )
| ( ( ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV467 ) )
= $true )
| ( ( SV502
= ( unordered_triple @ SV151 @ SV267 @ SV467 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3717]) ).
thf(3822,plain,
! [SV151: $i,SV267: $i,SV467: $i,SV502: $i] :
( ( ( ~ ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV151 ) )
| ~ ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV267 ) ) )
= $false )
| ( ( SV502
= ( unordered_triple @ SV151 @ SV267 @ SV467 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3718]) ).
thf(3823,plain,
! [SV267: $i,SV151: $i,SV468: $i,SV503: $i,SV646: $i] :
( ( ( in @ SV646 @ SV503 )
= $false )
| ( ( ( SV646 = SV468 )
| ( SV646 = SV151 )
| ( SV646 = SV267 ) )
= $true )
| ( ( SV503
= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3720]) ).
thf(3824,plain,
! [SV267: $i,SV151: $i,SV503: $i,SV468: $i] :
( ( ( ! [SY1380: $i] :
( ( SY1380 != SV468 )
| ( in @ SY1380 @ SV503 ) ) )
= $true )
| ( ( SV503
= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3721]) ).
thf(3825,plain,
! [SV468: $i,SV267: $i,SV503: $i,SV151: $i] :
( ( ( ~ ( ~ ! [SY1381: $i] :
( ( SY1381 != SV151 )
| ( in @ SY1381 @ SV503 ) )
| ~ ! [SY1382: $i] :
( ( SY1382 != SV267 )
| ( in @ SY1382 @ SV503 ) ) ) )
= $true )
| ( ( SV503
= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3722]) ).
thf(3826,plain,
! [SV628: $i,SV152: $i,SV612: $i] :
( ( ( in @ SV612 @ ( sK106_B @ SV152 ) )
= $false )
| ( ( ~ ( subset @ SV628 @ SV612 ) )
= $true )
| ( ( in @ SV628 @ ( sK106_B @ SV152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3723]) ).
thf(3827,plain,
! [SV505: $i,SV154: $i,SV647: $i,SV629: $i] :
( ( ( in @ ( ordered_pair @ SV629 @ SV647 ) @ SV154 )
= $false )
| ( ( in @ ( ordered_pair @ SV629 @ SV647 ) @ SV505 )
= $true )
| ( ( subset @ SV154 @ SV505 )
= $false )
| ( ( relation @ SV505 )
= $false )
| ( ( relation @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3725]) ).
thf(3828,plain,
! [SV155: $i,SV268: $i,SV547: $i] :
( ( ( ~ ( ~ ( in @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ SV547 )
| ~ ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SV547 @ SV268 @ SV155 ) ) @ SV268 ) )
| ~ ( ( in @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ SV547 )
| ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SV547 @ SV268 @ SV155 ) ) @ SV268 ) ) )
= $false )
| ( ( SV547
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $true )
| ( ( element @ SV547 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3727]) ).
thf(3829,plain,
! [SV268: $i,SV548: $i,SV155: $i] :
( ( ( ! [SY1408: $i] :
( ~ ( element @ SY1408 @ ( powerset @ SV155 ) )
| ~ ( in @ SY1408 @ SV548 )
| ( in @ ( subset_complement @ SV155 @ SY1408 ) @ SV268 ) ) )
= $true )
| ( ( SV548
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $false )
| ( ( element @ SV548 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3728]) ).
thf(3830,plain,
! [SV548: $i,SV268: $i,SV155: $i] :
( ( ( ! [SY1409: $i] :
( ~ ( element @ SY1409 @ ( powerset @ SV155 ) )
| ~ ( in @ ( subset_complement @ SV155 @ SY1409 ) @ SV268 )
| ( in @ SY1409 @ SV548 ) ) )
= $true )
| ( ( SV548
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $false )
| ( ( element @ SV548 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3729]) ).
thf(3831,plain,
! [SV566: $i,SV425: $i,SV630: $i] :
( ( ( in @ SV630 @ SV425 )
= $false )
| ( ( SV630 = SV566 )
= $false )
| ( ( ~ ( ordinal @ SV566 ) )
= $true )
| ( ( in @ SV566 @ ( sK7_B @ SV425 ) )
= $true )
| ( sK12_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[3730]) ).
thf(3832,plain,
! [SV425: $i,SV567: $i] :
( ( ( ( ( sK8_D @ SV567 @ SV425 )
!= SV567 )
| ~ ( in @ ( sK8_D @ SV567 @ SV425 ) @ SV425 ) )
= $false )
| ( ( in @ SV567 @ ( sK7_B @ SV425 ) )
= $false )
| ( sK12_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[3731]) ).
thf(3833,plain,
( ( ( ( sK9_B != sK10_SY601 )
| ~ ( ordinal @ sK10_SY601 ) )
= $false )
| ( sK12_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[3733]) ).
thf(3834,plain,
! [SV631: $i,SV158: $i,SV613: $i] :
( ( ( SV613 = empty_set )
= $true )
| ( ( ( SV158
!= ( relation_dom_as_subset @ SV158 @ SV613 @ SV631 ) )
| ( quasi_total @ SV631 @ SV158 @ SV613 ) )
= $true )
| ( ( relation_of2_as_subset @ SV631 @ SV158 @ SV613 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3735]) ).
thf(3835,plain,
! [SV158: $i,SV632: $i,SV614: $i] :
( ( ( SV614 = empty_set )
= $true )
| ( ( ~ ( quasi_total @ SV632 @ SV158 @ SV614 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SV614 @ SV632 ) ) )
= $true )
| ( ( relation_of2_as_subset @ SV632 @ SV158 @ SV614 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3736]) ).
thf(3836,plain,
! [SV633: $i,SV615: $i,SV158: $i] :
( ( ( ( SV158 != empty_set ) )
= $true )
| ( ( ( SV158
!= ( relation_dom_as_subset @ SV158 @ SV615 @ SV633 ) )
| ( quasi_total @ SV633 @ SV158 @ SV615 ) )
= $true )
| ( ( relation_of2_as_subset @ SV633 @ SV158 @ SV615 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3737]) ).
thf(3837,plain,
! [SV616: $i,SV634: $i,SV158: $i] :
( ( ( ( SV158 != empty_set ) )
= $true )
| ( ( ~ ( quasi_total @ SV634 @ SV158 @ SV616 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SV616 @ SV634 ) ) )
= $true )
| ( ( relation_of2_as_subset @ SV634 @ SV158 @ SV616 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3738]) ).
thf(3838,plain,
! [SV553: $i,SV158: $i,SV570: $i] :
( ( ( ( SV570 != empty_set ) )
= $true )
| ( ( quasi_total @ SV570 @ SV158 @ SV553 )
= $true )
| ( ( SV158 = empty_set )
= $true )
| ( ( SV553 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV570 @ SV158 @ SV553 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3739]) ).
thf(3839,plain,
! [SV554: $i,SV158: $i,SV571: $i] :
( ( ( ~ ( quasi_total @ SV571 @ SV158 @ SV554 ) )
= $true )
| ( ( SV571 = empty_set )
= $true )
| ( ( SV158 = empty_set )
= $true )
| ( ( SV554 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV571 @ SV158 @ SV554 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3740]) ).
thf(3840,plain,
! [SV512: $i,SV572: $i] :
( ( ( ~ ( in @ ( sK90_SY733 @ SV572 @ SV512 ) @ SV512 )
| ~ ~ ( in @ ( sK89_C @ SV572 @ SV512 ) @ ( sK90_SY733 @ SV572 @ SV512 ) ) )
= $false )
| ( ( ~ ( in @ ( sK89_C @ SV572 @ SV512 ) @ SV572 ) )
= $true )
| ( ( SV572
= ( set_meet @ SV512 ) )
= $true )
| ( ( SV512 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3741]) ).
thf(3841,plain,
! [SV572: $i,SV512: $i,SV667: $i] :
( ( ( ~ ( in @ SV667 @ SV512 )
| ( in @ ( sK89_C @ SV572 @ SV512 ) @ SV667 ) )
= $true )
| ( ( in @ ( sK89_C @ SV572 @ SV512 ) @ SV572 )
= $true )
| ( ( SV572
= ( set_meet @ SV512 ) )
= $true )
| ( ( SV512 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3742]) ).
thf(3842,plain,
! [SV513: $i,SV573: $i,SV668: $i] :
( ( ( ~ ( ~ ( in @ ( sK88_D @ SV668 @ SV573 @ SV513 ) @ SV513 )
| ~ ~ ( in @ SV668 @ ( sK88_D @ SV668 @ SV573 @ SV513 ) ) )
| ( in @ SV668 @ SV573 ) )
= $true )
| ( ( SV573
= ( set_meet @ SV513 ) )
= $false )
| ( ( SV513 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3743]) ).
thf(3843,plain,
! [SV513: $i,SV573: $i,SV669: $i] :
( ( ( ~ ( in @ SV669 @ SV573 )
| ! [SY1485: $i] :
( ~ ( in @ SY1485 @ SV513 )
| ( in @ SV669 @ SY1485 ) ) )
= $true )
| ( ( SV573
= ( set_meet @ SV513 ) )
= $false )
| ( ( SV513 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3744]) ).
thf(3844,plain,
! [SV159: $i,SV427: $i,SV470: $i] :
( ( ( in @ ( sK82_D @ SV470 @ SV427 @ SV159 ) @ SV470 )
= $false )
| ( ( ( ( sK82_D @ SV470 @ SV427 @ SV159 )
!= SV159 ) )
= $true )
| ( ( SV470
= ( unordered_pair @ SV159 @ SV427 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3745]) ).
thf(3845,plain,
! [SV159: $i,SV427: $i,SV470: $i] :
( ( ( in @ ( sK82_D @ SV470 @ SV427 @ SV159 ) @ SV470 )
= $false )
| ( ( ( ( sK82_D @ SV470 @ SV427 @ SV159 )
!= SV427 ) )
= $true )
| ( ( SV470
= ( unordered_pair @ SV159 @ SV427 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3746]) ).
thf(3846,plain,
! [SV471: $i,SV428: $i,SV159: $i,SV635: $i] :
( ( ( SV635 = SV159 )
= $true )
| ( ( SV635 = SV428 )
= $true )
| ( ( in @ SV635 @ SV471 )
= $false )
| ( ( SV471
= ( unordered_pair @ SV159 @ SV428 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3747]) ).
thf(3847,plain,
! [SV428: $i,SV471: $i,SV159: $i,SV670: $i] :
( ( ( ( SV670 != SV159 )
| ( in @ SV670 @ SV471 ) )
= $true )
| ( ( SV471
= ( unordered_pair @ SV159 @ SV428 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3748]) ).
thf(3848,plain,
! [SV159: $i,SV471: $i,SV428: $i,SV671: $i] :
( ( ( ( SV671 != SV428 )
| ( in @ SV671 @ SV471 ) )
= $true )
| ( ( SV471
= ( unordered_pair @ SV159 @ SV428 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3749]) ).
thf(3849,plain,
! [SV474: $i,SV437: $i,SV648: $i,SV164: $i,SV636: $i] :
( ( ( ~ ( in @ SV636 @ SV164 ) )
= $true )
| ( ( ~ ( in @ SV648 @ SV437 ) )
= $true )
| ( ( ( ( sK78_D @ SV474 @ SV437 @ SV164 )
!= ( ordered_pair @ SV636 @ SV648 ) ) )
= $true )
| ( ( ~ ( in @ ( sK78_D @ SV474 @ SV437 @ SV164 ) @ SV474 ) )
= $true )
| ( ( SV474
= ( cartesian_product2 @ SV164 @ SV437 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3750]) ).
thf(3850,plain,
! [SV164: $i,SV437: $i,SV474: $i] :
( ( ( ~ ( in @ ( sK79_SY729 @ SV474 @ SV437 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK80_SY731 @ SV474 @ SV437 @ SV164 ) @ SV437 ) )
= $false )
| ( ( in @ ( sK78_D @ SV474 @ SV437 @ SV164 ) @ SV474 )
= $true )
| ( ( SV474
= ( cartesian_product2 @ SV164 @ SV437 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3751]) ).
thf(3851,plain,
! [SV475: $i,SV637: $i,SV438: $i,SV672: $i,SV164: $i,SV657: $i] :
( ( ( ~ ( in @ SV657 @ SV164 )
| ~ ( in @ SV672 @ SV438 )
| ( SV637
!= ( ordered_pair @ SV657 @ SV672 ) ) )
= $true )
| ( ( in @ SV637 @ SV475 )
= $true )
| ( ( SV475
= ( cartesian_product2 @ SV164 @ SV438 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3753]) ).
thf(3852,plain,
! [SV164: $i,SV438: $i,SV475: $i,SV638: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK76_E @ SV638 @ SV475 @ SV438 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK77_SY726 @ SV638 @ SV475 @ SV438 @ SV164 ) @ SV438 ) )
| ( SV638
!= ( ordered_pair @ ( sK76_E @ SV638 @ SV475 @ SV438 @ SV164 ) @ ( sK77_SY726 @ SV638 @ SV475 @ SV438 @ SV164 ) ) ) )
= $false )
| ( ( in @ SV638 @ SV475 )
= $false )
| ( ( SV475
= ( cartesian_product2 @ SV164 @ SV438 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3754]) ).
thf(3853,plain,
! [SV166: $i,SV558: $i,SV649: $i] :
( ( ( subset @ SV649 @ SV558 )
= $false )
| ( ( in @ SV649 @ ( sK4_SY591 @ SV558 @ SV166 ) )
= $true )
| ( ( ~ ( in @ SV558 @ ( sK3_B @ SV166 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3755]) ).
thf(3854,plain,
! [SV639: $i,SV166: $i,SV619: $i] :
( ( ( in @ SV619 @ ( sK3_B @ SV166 ) )
= $false )
| ( ( ~ ( subset @ SV639 @ SV619 ) )
= $true )
| ( ( in @ SV639 @ ( sK3_B @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3756]) ).
thf(3855,plain,
! [SV168: $i] :
( ( ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) )
| ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) )
= $false )
| ( ( ( sK27_SY634 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3758]) ).
thf(3856,plain,
! [SV168: $i] :
( ( ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) )
| ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) )
= $false )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3759]) ).
thf(3857,plain,
! [SV673: $i,SV168: $i] :
( ( ( ! [SY1486: $i] :
( ~ ( in @ SY1486 @ SV168 )
| ( SV673
!= ( singleton @ SY1486 ) ) )
| ( in @ SV673 @ ( sK24_B @ SV168 ) ) )
= $true )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3760]) ).
thf(3858,plain,
! [SV168: $i,SV674: $i] :
( ( ( ~ ( in @ SV674 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SV674 @ SV168 ) @ SV168 )
| ( SV674
!= ( singleton @ ( sK25_D @ SV674 @ SV168 ) ) ) ) )
= $true )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3761]) ).
thf(3859,plain,
! [SV640: $i,SV168: $i,SV658: $i] :
( ( ( ~ ( in @ SV658 @ SV168 ) )
= $true )
| ( ( ( SV640
!= ( singleton @ SV658 ) ) )
= $true )
| ( ( in @ SV640 @ ( sK24_B @ SV168 ) )
= $true )
| ( ( ( sK28_SY636 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3762]) ).
thf(3860,plain,
! [SV168: $i,SV641: $i] :
( ( ( ~ ( in @ ( sK25_D @ SV641 @ SV168 ) @ SV168 )
| ( SV641
!= ( singleton @ ( sK25_D @ SV641 @ SV168 ) ) ) )
= $false )
| ( ( in @ SV641 @ ( sK24_B @ SV168 ) )
= $false )
| ( ( ( sK28_SY636 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3763]) ).
thf(3861,plain,
! [SV168: $i,SV642: $i,SV593: $i] :
( ( ( SV593
= ( singleton @ SV642 ) )
= $false )
| ( ( in @ SV642 @ SV168 )
= $false )
| ( ( in @ SV593 @ ( sK24_B @ SV168 ) )
= $true )
| ( ( ( sK27_SY634 @ SV168 )
= ( sK28_SY636 @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3764]) ).
thf(3862,plain,
! [SV168: $i,SV594: $i] :
( ( ( in @ ( sK25_D @ SV594 @ SV168 ) @ SV168 )
= $true )
| ( ( in @ SV594 @ ( sK24_B @ SV168 ) )
= $false )
| ( ( ( sK27_SY634 @ SV168 )
= ( sK28_SY636 @ SV168 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3765]) ).
thf(3863,plain,
! [SV168: $i,SV594: $i] :
( ( ( SV594
= ( singleton @ ( sK25_D @ SV594 @ SV168 ) ) )
= $true )
| ( ( in @ SV594 @ ( sK24_B @ SV168 ) )
= $false )
| ( ( ( sK27_SY634 @ SV168 )
= ( sK28_SY636 @ SV168 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3766]) ).
thf(3864,plain,
! [SV271: $i,SV481: $i,SV170: $i,SV596: $i,SV659: $i,SV651: $i] :
( ( ( ( ( ordered_pair @ SV651 @ SV659 )
!= SV596 )
| ~ ( in @ SV651 @ SV170 ) )
= $true )
| ( ( ! [SY1469: $i] :
( ~ ( ~ ( in @ ( sK115_I @ SY1469 @ SV659 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) @ SY1469 )
| ~ ~ ( in @ ( ordered_pair @ SV659 @ ( sK115_I @ SY1469 @ SV659 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) ) @ SV271 ) )
| ( SV651 != SY1469 )
| ~ ( in @ SV659 @ SY1469 ) ) )
= $true )
| ( ( ~ ( in @ SV596 @ ( cartesian_product2 @ SV170 @ SV481 ) ) )
= $true )
| ( ( in @ SV596 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3767]) ).
thf(3865,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV652: $i] :
( ( ( in @ SV652 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK112_F @ SV652 @ SV481 @ SV271 @ SV170 ) @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) )
!= SV652 )
| ~ ( in @ ( sK112_F @ SV652 @ SV481 @ SV271 @ SV170 ) @ SV170 ) )
| ~ ~ ( ~ ! [SY1464: $i] :
( ~ ( in @ SY1464 @ ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) )
| ( in @ ( ordered_pair @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) @ SY1464 ) @ SV271 ) )
| ~ ~ ( ( ( sK112_F @ SV652 @ SV481 @ SV271 @ SV170 )
!= ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) )
| ~ ( in @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) @ ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) ) ) ) ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3768]) ).
thf(3866,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV653: $i] :
( ( ( in @ SV653 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $false )
| ( ( in @ SV653 @ ( cartesian_product2 @ SV170 @ SV481 ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3769]) ).
thf(3867,plain,
! [SV368: $i] :
( ( ( ~ ( in @ ( sK74_B @ SV368 ) @ SV368 )
| ~ ( in @ ( sK75_SY725 @ SV368 ) @ SV368 ) )
= $false )
| ( ( epsilon_connected @ SV368 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3770]) ).
thf(3868,plain,
! [SV368: $i] :
( ( ( in @ ( sK74_B @ SV368 ) @ ( sK75_SY725 @ SV368 ) )
= $false )
| ( ( epsilon_connected @ SV368 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3771]) ).
thf(3869,plain,
! [SV171: $i,SV524: $i] :
( ( ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV171 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV524 ) )
= $true )
| ( ( SV171 = SV524 )
= $true )
| ( ( relation @ SV524 )
= $false )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3773]) ).
thf(3870,plain,
! [SV525: $i,SV171: $i,SV675: $i] :
( ( ( ! [SY1487: $i] :
( ~ ( in @ ( ordered_pair @ SV675 @ SY1487 ) @ SV171 )
| ( in @ ( ordered_pair @ SV675 @ SY1487 ) @ SV525 ) ) )
= $true )
| ( ( SV171 = SV525 )
= $false )
| ( ( relation @ SV525 )
= $false )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3775]) ).
thf(3871,plain,
! [SV171: $i,SV525: $i,SV676: $i] :
( ( ( ! [SY1488: $i] :
( ~ ( in @ ( ordered_pair @ SV676 @ SY1488 ) @ SV525 )
| ( in @ ( ordered_pair @ SV676 @ SY1488 ) @ SV171 ) ) )
= $true )
| ( ( SV171 = SV525 )
= $false )
| ( ( relation @ SV525 )
= $false )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3776]) ).
thf(3872,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ( ( ( sK35_D @ SV272 @ SV172 )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1178: $i] :
( ~ ( in @ SY1178 @ ( sK43_SY691 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SY1178 ) @ SV272 ) )
| ~ ~ ( ( ( sK41_SY666 @ SV272 @ SV172 )
!= ( sK43_SY691 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3777]) ).
thf(3873,plain,
! [SV172: $i,SV272: $i] :
( ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3778]) ).
thf(3874,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
!= ( sK37_SY665 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 ) ) )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3779]) ).
thf(3875,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ( ~ ! [SY1179: $i] :
( ~ ( in @ SY1179 @ ( sK40_SY685 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SY1179 ) @ SV272 ) )
| ~ ~ ( ( ( sK38_SY678 @ SV272 @ SV172 )
!= ( sK40_SY685 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) ) ) ) )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3780]) ).
thf(3876,plain,
! [SV272: $i,SV622: $i,SV172: $i,SV677: $i] :
( ( ( ! [SY1489: $i] :
( ( SY1489 != SV677 )
| ~ ( in @ SY1489 @ ( cartesian_product2 @ SV172 @ SV622 ) ) )
| ! [SY1490: $i,SY1491: $i] :
( ( ( ordered_pair @ SY1490 @ SY1491 )
!= SV677 )
| ~ ( in @ SY1490 @ SV172 )
| ! [SY1492: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1492 @ SY1491 @ SY1490 @ SV677 @ SV622 @ SV272 @ SV172 ) @ SY1492 )
| ~ ~ ( in @ ( ordered_pair @ SY1491 @ ( sK34_R @ SY1492 @ SY1491 @ SY1490 @ SV677 @ SV622 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1490 != SY1492 )
| ~ ( in @ SY1491 @ SY1492 ) ) )
| ( in @ SV677 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3781]) ).
thf(3877,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( ~ ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SV678 @ SV622 @ SV272 @ SV172 )
!= SV678 )
| ~ ( in @ ( sK33_F @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV622 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) )
!= SV678 )
| ~ ( in @ ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1493: $i] :
( ~ ( in @ SY1493 @ ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) @ SY1493 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3782]) ).
thf(3878,plain,
! [SV275: $i,SV176: $i,SV483: $i,SV579: $i,SV602: $i] :
( ( ( SV602
= ( singleton @ SV579 ) )
= $false )
| ( ( ( ordered_pair @ SV579 @ SV602 )
= SV483 )
= $false )
| ( ( in @ SV579 @ SV176 )
= $false )
| ( ( ~ ( in @ SV483 @ ( cartesian_product2 @ SV176 @ SV275 ) ) )
= $true )
| ( ( in @ SV483 @ ( sK108_C @ SV275 @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3783]) ).
thf(3879,plain,
! [SV176: $i,SV275: $i,SV580: $i] :
( ( ( ( ( ordered_pair @ ( sK109_E @ SV580 @ SV275 @ SV176 ) @ ( sK110_SY756 @ SV580 @ SV275 @ SV176 ) )
!= SV580 )
| ~ ( in @ ( sK109_E @ SV580 @ SV275 @ SV176 ) @ SV176 ) )
= $false )
| ( ( in @ SV580 @ ( sK108_C @ SV275 @ SV176 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3784]) ).
thf(3880,plain,
! [SV180: $i,SV456: $i,SV484: $i] :
( ( ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV484 )
= $false )
| ( ( ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV180 ) )
= $true )
| ( ( SV484
= ( set_union2 @ SV180 @ SV456 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3786]) ).
thf(3881,plain,
! [SV180: $i,SV456: $i,SV484: $i] :
( ( ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV484 )
= $false )
| ( ( ~ ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV456 ) )
= $true )
| ( ( SV484
= ( set_union2 @ SV180 @ SV456 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3787]) ).
thf(3882,plain,
! [SV485: $i,SV457: $i,SV180: $i,SV643: $i] :
( ( ( in @ SV643 @ SV180 )
= $true )
| ( ( in @ SV643 @ SV457 )
= $true )
| ( ( in @ SV643 @ SV485 )
= $false )
| ( ( SV485
= ( set_union2 @ SV180 @ SV457 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3788]) ).
thf(3883,plain,
! [SV457: $i,SV485: $i,SV180: $i,SV679: $i] :
( ( ( ~ ( in @ SV679 @ SV180 )
| ( in @ SV679 @ SV485 ) )
= $true )
| ( ( SV485
= ( set_union2 @ SV180 @ SV457 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3789]) ).
thf(3884,plain,
! [SV180: $i,SV485: $i,SV457: $i,SV680: $i] :
( ( ( ~ ( in @ SV680 @ SV457 )
| ( in @ SV680 @ SV485 ) )
= $true )
| ( ( SV485
= ( set_union2 @ SV180 @ SV457 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3790]) ).
thf(3885,plain,
! [SV660: $i,SV139: $i] :
( ( ( ~ ! [SY1470: $i] :
( ! [SY1471: $i] :
( ( SY1471 != SY1470 )
| ~ ( in @ SY1471 @ ( cartesian_product2 @ SV139 @ SV660 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1470 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1470 @ ( sK13_C @ SV660 @ SV139 ) ) )
| ~ ! [SY1474: $i] :
( ~ ( in @ SY1474 @ ( sK13_C @ SV660 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1474 @ SV660 @ SV139 )
!= SY1474 )
| ~ ( in @ ( sK16_E @ SY1474 @ SV660 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV660 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1474 @ SV660 @ SV139 ) @ ( sK15_SY612 @ SY1474 @ SV660 @ SV139 ) )
!= SY1474 )
| ~ ( in @ ( sK14_J @ SY1474 @ SV660 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1474 @ SV660 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1474 @ SV660 @ SV139 ) ) ) ) ) ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3791]) ).
thf(3886,plain,
! [SV139: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
!= ( sK18_SY613 @ SV139 ) )
| ~ ( in @ ( sK22_SY620 @ SV139 ) @ SV139 ) ) )
= $false )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3792]) ).
thf(3887,plain,
! [SV139: $i] :
( ( ( ( ( sK23_SY629 @ SV139 )
!= ( singleton @ ( sK22_SY620 @ SV139 ) ) ) )
= $false )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3792]) ).
thf(3888,plain,
! [SV624: $i,SV139: $i,SV681: $i] :
( ( ( ! [SY1494: $i] :
( ( SY1494 != SV681 )
| ~ ( in @ SY1494 @ ( cartesian_product2 @ SV139 @ SV624 ) ) )
| ! [SY1495: $i,SY1496: $i] :
( ( ( ordered_pair @ SY1495 @ SY1496 )
!= SV681 )
| ~ ( in @ SY1495 @ SV139 )
| ( SY1496
!= ( singleton @ SY1495 ) ) )
| ( in @ SV681 @ ( sK13_C @ SV624 @ SV139 ) ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3793]) ).
thf(3889,plain,
! [SV139: $i,SV624: $i,SV682: $i] :
( ( ( ~ ( in @ SV682 @ ( sK13_C @ SV624 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SV682 @ SV624 @ SV139 )
!= SV682 )
| ~ ( in @ ( sK16_E @ SV682 @ SV624 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV624 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV682 @ SV624 @ SV139 ) @ ( sK15_SY612 @ SV682 @ SV624 @ SV139 ) )
!= SV682 )
| ~ ( in @ ( sK14_J @ SV682 @ SV624 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV682 @ SV624 @ SV139 )
!= ( singleton @ ( sK14_J @ SV682 @ SV624 @ SV139 ) ) ) ) ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3794]) ).
thf(3890,plain,
! [SV661: $i,SV139: $i] :
( ( ( ~ ! [SY1475: $i] :
( ! [SY1476: $i] :
( ( SY1476 != SY1475 )
| ~ ( in @ SY1476 @ ( cartesian_product2 @ SV139 @ SV661 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1475 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1475 @ ( sK13_C @ SV661 @ SV139 ) ) )
| ~ ! [SY1479: $i] :
( ~ ( in @ SY1479 @ ( sK13_C @ SV661 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1479 @ SV661 @ SV139 )
!= SY1479 )
| ~ ( in @ ( sK16_E @ SY1479 @ SV661 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV661 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1479 @ SV661 @ SV139 ) @ ( sK15_SY612 @ SY1479 @ SV661 @ SV139 ) )
!= SY1479 )
| ~ ( in @ ( sK14_J @ SY1479 @ SV661 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1479 @ SV661 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1479 @ SV661 @ SV139 ) ) ) ) ) ) )
= $false )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3795]) ).
thf(3891,plain,
! [SV662: $i,SV139: $i] :
( ( ( ~ ! [SY1480: $i] :
( ! [SY1481: $i] :
( ( SY1481 != SY1480 )
| ~ ( in @ SY1481 @ ( cartesian_product2 @ SV139 @ SV662 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1480 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1480 @ ( sK13_C @ SV662 @ SV139 ) ) )
| ~ ! [SY1484: $i] :
( ~ ( in @ SY1484 @ ( sK13_C @ SV662 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1484 @ SV662 @ SV139 )
!= SY1484 )
| ~ ( in @ ( sK16_E @ SY1484 @ SV662 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV662 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1484 @ SV662 @ SV139 ) @ ( sK15_SY612 @ SY1484 @ SV662 @ SV139 ) )
!= SY1484 )
| ~ ( in @ ( sK14_J @ SY1484 @ SV662 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1484 @ SV662 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1484 @ SV662 @ SV139 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3796]) ).
thf(3892,plain,
! [SV625: $i,SV139: $i,SV683: $i] :
( ( ( ! [SY1497: $i] :
( ( SY1497 != SV683 )
| ~ ( in @ SY1497 @ ( cartesian_product2 @ SV139 @ SV625 ) ) )
| ! [SY1498: $i,SY1499: $i] :
( ( ( ordered_pair @ SY1498 @ SY1499 )
!= SV683 )
| ~ ( in @ SY1498 @ SV139 )
| ( SY1499
!= ( singleton @ SY1498 ) ) )
| ( in @ SV683 @ ( sK13_C @ SV625 @ SV139 ) ) )
= $true )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3797]) ).
thf(3893,plain,
! [SV139: $i,SV625: $i,SV684: $i] :
( ( ( ~ ( in @ SV684 @ ( sK13_C @ SV625 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SV684 @ SV625 @ SV139 )
!= SV684 )
| ~ ( in @ ( sK16_E @ SV684 @ SV625 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV625 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV684 @ SV625 @ SV139 ) @ ( sK15_SY612 @ SV684 @ SV625 @ SV139 ) )
!= SV684 )
| ~ ( in @ ( sK14_J @ SV684 @ SV625 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV684 @ SV625 @ SV139 )
!= ( singleton @ ( sK14_J @ SV684 @ SV625 @ SV139 ) ) ) ) ) )
= $true )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3798]) ).
thf(3894,plain,
! [SV488: $i,SV139: $i,SV603: $i,SV654: $i] :
( ( ( SV654 = SV603 )
= $false )
| ( ( ~ ( in @ SV654 @ ( cartesian_product2 @ SV139 @ SV488 ) ) )
= $true )
| ( ( ! [SY1431: $i,SY1432: $i] :
( ( ( ordered_pair @ SY1431 @ SY1432 )
!= SV603 )
| ~ ( in @ SY1431 @ SV139 )
| ( SY1432
!= ( singleton @ SY1431 ) ) ) )
= $true )
| ( ( in @ SV603 @ ( sK13_C @ SV488 @ SV139 ) )
= $true )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3799]) ).
thf(3895,plain,
! [SV139: $i,SV488: $i,SV604: $i] :
( ( ( ~ ( ( ( sK16_E @ SV604 @ SV488 @ SV139 )
!= SV604 )
| ~ ( in @ ( sK16_E @ SV604 @ SV488 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV488 ) ) ) )
= $true )
| ( ( in @ SV604 @ ( sK13_C @ SV488 @ SV139 ) )
= $false )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3800]) ).
thf(3896,plain,
! [SV139: $i,SV488: $i,SV604: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV604 @ SV488 @ SV139 ) @ ( sK15_SY612 @ SV604 @ SV488 @ SV139 ) )
!= SV604 )
| ~ ( in @ ( sK14_J @ SV604 @ SV488 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV604 @ SV488 @ SV139 )
!= ( singleton @ ( sK14_J @ SV604 @ SV488 @ SV139 ) ) ) ) )
= $true )
| ( ( in @ SV604 @ ( sK13_C @ SV488 @ SV139 ) )
= $false )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3801]) ).
thf(3897,plain,
! [SV462: $i,SV143: $i,SV401: $i,SV626: $i] :
( ( ( in @ SV626 @ SV401 )
= $false )
| ( ( in @ SV626 @ SV143 )
= $false )
| ( ( in @ SV626 @ SV462 )
= $true )
| ( ( SV462
= ( set_intersection2 @ SV143 @ SV401 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3803]) ).
thf(3898,plain,
! [SV401: $i,SV143: $i,SV462: $i,SV663: $i] :
( ( ( ~ ( in @ SV663 @ SV462 ) )
= $true )
| ( ( in @ SV663 @ SV143 )
= $true )
| ( ( SV462
= ( set_intersection2 @ SV143 @ SV401 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3804]) ).
thf(3899,plain,
! [SV143: $i,SV401: $i,SV462: $i,SV664: $i] :
( ( ( ~ ( in @ SV664 @ SV462 ) )
= $true )
| ( ( in @ SV664 @ SV401 )
= $true )
| ( ( SV462
= ( set_intersection2 @ SV143 @ SV401 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3805]) ).
thf(3900,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ~ ( ~ ! [SY1142: $i] :
( ~ ( in @ SY1142 @ ( sK52_SY712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SY1142 ) @ SV265 ) )
| ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK52_SY712 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) ) ) )
| ~ ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 ) )
= $false )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3806]) ).
thf(3901,plain,
! [SV265: $i,SV145: $i] :
( ( ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3807]) ).
thf(3902,plain,
! [SV145: $i,SV265: $i,SV685: $i] :
( ( ( ~ ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 ) )
= $true )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3808]) ).
thf(3903,plain,
! [SV145: $i,SV265: $i] :
( ( ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK51_SY718 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3809]) ).
thf(3904,plain,
! [SV265: $i,SV655: $i,SV145: $i,SV686: $i] :
( ( ( ~ ( in @ SV686 @ SV145 )
| ! [SY1500: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1500 @ SV686 @ SV655 @ SV265 @ SV145 ) @ SY1500 )
| ~ ~ ( in @ ( ordered_pair @ SV655 @ ( sK47_K @ SY1500 @ SV686 @ SV655 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV686 != SY1500 )
| ~ ( in @ SV655 @ SY1500 ) ) )
= $true )
| ( ( in @ SV655 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3810]) ).
thf(3905,plain,
! [SV145: $i,SV265: $i,SV656: $i] :
( ( ( in @ SV656 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK45_E @ SV656 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1467: $i] :
( ~ ( in @ SY1467 @ ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV656 @ SY1467 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV656 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) )
| ~ ( in @ SV656 @ ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) ) ) ) ) )
= $true )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3811]) ).
thf(3906,plain,
! [SV404: $i,SV147: $i,SV464: $i,SV665: $i] :
( ( ( ~ ( in @ SV665 @ SV464 ) )
= $true )
| ( ( in @ SV665 @ SV147 )
= $true )
| ( ( SV464
= ( set_difference @ SV147 @ SV404 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3814]) ).
thf(3907,plain,
! [SV147: $i,SV404: $i,SV464: $i,SV666: $i] :
( ( ( ~ ( in @ SV666 @ SV464 ) )
= $true )
| ( ( ~ ( in @ SV666 @ SV404 ) )
= $true )
| ( ( SV464
= ( set_difference @ SV147 @ SV404 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3815]) ).
thf(3908,plain,
! [SV410: $i,SV607: $i,SV341: $i,SV644: $i] :
( ( ( in @ SV644 @ SV341 )
= $false )
| ( ( in @ SV607 @ SV644 )
= $false )
| ( ( in @ SV607 @ SV410 )
= $true )
| ( ( SV410
= ( union @ SV341 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3818]) ).
thf(3909,plain,
! [SV341: $i,SV410: $i,SV608: $i] :
( ( ( in @ SV608 @ ( sK67_D @ SV608 @ SV410 @ SV341 ) )
= $true )
| ( ( in @ SV608 @ SV410 )
= $false )
| ( ( SV410
= ( union @ SV341 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3819]) ).
thf(3910,plain,
! [SV341: $i,SV410: $i,SV608: $i] :
( ( ( in @ ( sK67_D @ SV608 @ SV410 @ SV341 ) @ SV341 )
= $true )
| ( ( in @ SV608 @ SV410 )
= $false )
| ( ( SV410
= ( union @ SV341 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3820]) ).
thf(3911,plain,
! [SV151: $i,SV267: $i,SV467: $i,SV502: $i] :
( ( ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
= $false )
| ( ( ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV467 ) )
= $true )
| ( ( SV502
= ( unordered_triple @ SV151 @ SV267 @ SV467 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3821]) ).
thf(3912,plain,
! [SV151: $i,SV267: $i,SV467: $i,SV502: $i] :
( ( ( ~ ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV151 ) ) )
= $false )
| ( ( SV502
= ( unordered_triple @ SV151 @ SV267 @ SV467 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3822]) ).
thf(3913,plain,
! [SV151: $i,SV267: $i,SV467: $i,SV502: $i] :
( ( ( ~ ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV267 ) ) )
= $false )
| ( ( SV502
= ( unordered_triple @ SV151 @ SV267 @ SV467 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3822]) ).
thf(3914,plain,
! [SV503: $i,SV267: $i,SV151: $i,SV468: $i,SV646: $i] :
( ( ( SV646 = SV468 )
= $true )
| ( ( ( SV646 = SV151 )
| ( SV646 = SV267 ) )
= $true )
| ( ( in @ SV646 @ SV503 )
= $false )
| ( ( SV503
= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3823]) ).
thf(3915,plain,
! [SV267: $i,SV151: $i,SV503: $i,SV468: $i,SV687: $i] :
( ( ( ( SV687 != SV468 )
| ( in @ SV687 @ SV503 ) )
= $true )
| ( ( SV503
= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3824]) ).
thf(3916,plain,
! [SV468: $i,SV267: $i,SV503: $i,SV151: $i] :
( ( ( ~ ! [SY1381: $i] :
( ( SY1381 != SV151 )
| ( in @ SY1381 @ SV503 ) )
| ~ ! [SY1382: $i] :
( ( SY1382 != SV267 )
| ( in @ SY1382 @ SV503 ) ) )
= $false )
| ( ( SV503
= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3825]) ).
thf(3917,plain,
! [SV152: $i,SV612: $i,SV628: $i] :
( ( ( subset @ SV628 @ SV612 )
= $false )
| ( ( in @ SV612 @ ( sK106_B @ SV152 ) )
= $false )
| ( ( in @ SV628 @ ( sK106_B @ SV152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3826]) ).
thf(3918,plain,
! [SV155: $i,SV268: $i,SV547: $i] :
( ( ( ~ ( ~ ( in @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ SV547 )
| ~ ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SV547 @ SV268 @ SV155 ) ) @ SV268 ) ) )
= $false )
| ( ( SV547
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $true )
| ( ( element @ SV547 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3828]) ).
thf(3919,plain,
! [SV155: $i,SV268: $i,SV547: $i] :
( ( ( ~ ( ( in @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ SV547 )
| ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SV547 @ SV268 @ SV155 ) ) @ SV268 ) ) )
= $false )
| ( ( SV547
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $true )
| ( ( element @ SV547 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3828]) ).
thf(3920,plain,
! [SV268: $i,SV548: $i,SV155: $i,SV688: $i] :
( ( ( ~ ( element @ SV688 @ ( powerset @ SV155 ) )
| ~ ( in @ SV688 @ SV548 )
| ( in @ ( subset_complement @ SV155 @ SV688 ) @ SV268 ) )
= $true )
| ( ( SV548
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $false )
| ( ( element @ SV548 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3829]) ).
thf(3921,plain,
! [SV548: $i,SV268: $i,SV155: $i,SV689: $i] :
( ( ( ~ ( element @ SV689 @ ( powerset @ SV155 ) )
| ~ ( in @ ( subset_complement @ SV155 @ SV689 ) @ SV268 )
| ( in @ SV689 @ SV548 ) )
= $true )
| ( ( SV548
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $false )
| ( ( element @ SV548 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3830]) ).
thf(3922,plain,
! [SV425: $i,SV630: $i,SV566: $i] :
( ( ( ordinal @ SV566 )
= $false )
| ( ( SV630 = SV566 )
= $false )
| ( ( in @ SV630 @ SV425 )
= $false )
| ( ( in @ SV566 @ ( sK7_B @ SV425 ) )
= $true )
| ( sK12_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[3831]) ).
thf(3923,plain,
! [SV425: $i,SV567: $i] :
( ( ( ( ( sK8_D @ SV567 @ SV425 )
!= SV567 ) )
= $false )
| ( ( in @ SV567 @ ( sK7_B @ SV425 ) )
= $false )
| ( sK12_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[3832]) ).
thf(3924,plain,
! [SV425: $i,SV567: $i] :
( ( ( ~ ( in @ ( sK8_D @ SV567 @ SV425 ) @ SV425 ) )
= $false )
| ( ( in @ SV567 @ ( sK7_B @ SV425 ) )
= $false )
| ( sK12_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[3832]) ).
thf(3925,plain,
( ( ( ( sK9_B != sK10_SY601 ) )
= $false )
| ( sK12_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[3833]) ).
thf(3926,plain,
( ( ( ~ ( ordinal @ sK10_SY601 ) )
= $false )
| ( sK12_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[3833]) ).
thf(3927,plain,
! [SV631: $i,SV613: $i,SV158: $i] :
( ( ( ( SV158
!= ( relation_dom_as_subset @ SV158 @ SV613 @ SV631 ) ) )
= $true )
| ( ( quasi_total @ SV631 @ SV158 @ SV613 )
= $true )
| ( ( SV613 = empty_set )
= $true )
| ( ( relation_of2_as_subset @ SV631 @ SV158 @ SV613 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3834]) ).
thf(3928,plain,
! [SV614: $i,SV158: $i,SV632: $i] :
( ( ( ~ ( quasi_total @ SV632 @ SV158 @ SV614 ) )
= $true )
| ( ( SV158
= ( relation_dom_as_subset @ SV158 @ SV614 @ SV632 ) )
= $true )
| ( ( SV614 = empty_set )
= $true )
| ( ( relation_of2_as_subset @ SV632 @ SV158 @ SV614 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3835]) ).
thf(3929,plain,
! [SV633: $i,SV615: $i,SV158: $i] :
( ( ( SV158 = empty_set )
= $false )
| ( ( ( SV158
!= ( relation_dom_as_subset @ SV158 @ SV615 @ SV633 ) )
| ( quasi_total @ SV633 @ SV158 @ SV615 ) )
= $true )
| ( ( relation_of2_as_subset @ SV633 @ SV158 @ SV615 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3836]) ).
thf(3930,plain,
! [SV616: $i,SV634: $i,SV158: $i] :
( ( ( SV158 = empty_set )
= $false )
| ( ( ~ ( quasi_total @ SV634 @ SV158 @ SV616 )
| ( SV158
= ( relation_dom_as_subset @ SV158 @ SV616 @ SV634 ) ) )
= $true )
| ( ( relation_of2_as_subset @ SV634 @ SV158 @ SV616 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3837]) ).
thf(3931,plain,
! [SV553: $i,SV158: $i,SV570: $i] :
( ( ( SV570 = empty_set )
= $false )
| ( ( quasi_total @ SV570 @ SV158 @ SV553 )
= $true )
| ( ( SV158 = empty_set )
= $true )
| ( ( SV553 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV570 @ SV158 @ SV553 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3838]) ).
thf(3932,plain,
! [SV554: $i,SV158: $i,SV571: $i] :
( ( ( quasi_total @ SV571 @ SV158 @ SV554 )
= $false )
| ( ( SV571 = empty_set )
= $true )
| ( ( SV158 = empty_set )
= $true )
| ( ( SV554 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV571 @ SV158 @ SV554 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3839]) ).
thf(3933,plain,
! [SV512: $i,SV572: $i] :
( ( ( ~ ( in @ ( sK90_SY733 @ SV572 @ SV512 ) @ SV512 ) )
= $false )
| ( ( ~ ( in @ ( sK89_C @ SV572 @ SV512 ) @ SV572 ) )
= $true )
| ( ( SV572
= ( set_meet @ SV512 ) )
= $true )
| ( ( SV512 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3840]) ).
thf(3934,plain,
! [SV512: $i,SV572: $i] :
( ( ( ~ ~ ( in @ ( sK89_C @ SV572 @ SV512 ) @ ( sK90_SY733 @ SV572 @ SV512 ) ) )
= $false )
| ( ( ~ ( in @ ( sK89_C @ SV572 @ SV512 ) @ SV572 ) )
= $true )
| ( ( SV572
= ( set_meet @ SV512 ) )
= $true )
| ( ( SV512 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3840]) ).
thf(3935,plain,
! [SV572: $i,SV512: $i,SV667: $i] :
( ( ( ~ ( in @ SV667 @ SV512 ) )
= $true )
| ( ( in @ ( sK89_C @ SV572 @ SV512 ) @ SV667 )
= $true )
| ( ( in @ ( sK89_C @ SV572 @ SV512 ) @ SV572 )
= $true )
| ( ( SV572
= ( set_meet @ SV512 ) )
= $true )
| ( ( SV512 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3841]) ).
thf(3936,plain,
! [SV513: $i,SV573: $i,SV668: $i] :
( ( ( ~ ( ~ ( in @ ( sK88_D @ SV668 @ SV573 @ SV513 ) @ SV513 )
| ~ ~ ( in @ SV668 @ ( sK88_D @ SV668 @ SV573 @ SV513 ) ) ) )
= $true )
| ( ( in @ SV668 @ SV573 )
= $true )
| ( ( SV573
= ( set_meet @ SV513 ) )
= $false )
| ( ( SV513 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3842]) ).
thf(3937,plain,
! [SV513: $i,SV573: $i,SV669: $i] :
( ( ( ~ ( in @ SV669 @ SV573 ) )
= $true )
| ( ( ! [SY1485: $i] :
( ~ ( in @ SY1485 @ SV513 )
| ( in @ SV669 @ SY1485 ) ) )
= $true )
| ( ( SV573
= ( set_meet @ SV513 ) )
= $false )
| ( ( SV513 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3843]) ).
thf(3938,plain,
! [SV159: $i,SV427: $i,SV470: $i] :
( ( ( ( sK82_D @ SV470 @ SV427 @ SV159 )
= SV159 )
= $false )
| ( ( in @ ( sK82_D @ SV470 @ SV427 @ SV159 ) @ SV470 )
= $false )
| ( ( SV470
= ( unordered_pair @ SV159 @ SV427 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3844]) ).
thf(3939,plain,
! [SV159: $i,SV427: $i,SV470: $i] :
( ( ( ( sK82_D @ SV470 @ SV427 @ SV159 )
= SV427 )
= $false )
| ( ( in @ ( sK82_D @ SV470 @ SV427 @ SV159 ) @ SV470 )
= $false )
| ( ( SV470
= ( unordered_pair @ SV159 @ SV427 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3845]) ).
thf(3940,plain,
! [SV428: $i,SV471: $i,SV159: $i,SV670: $i] :
( ( ( ( SV670 != SV159 ) )
= $true )
| ( ( in @ SV670 @ SV471 )
= $true )
| ( ( SV471
= ( unordered_pair @ SV159 @ SV428 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3847]) ).
thf(3941,plain,
! [SV159: $i,SV471: $i,SV428: $i,SV671: $i] :
( ( ( ( SV671 != SV428 ) )
= $true )
| ( ( in @ SV671 @ SV471 )
= $true )
| ( ( SV471
= ( unordered_pair @ SV159 @ SV428 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3848]) ).
thf(3942,plain,
! [SV474: $i,SV437: $i,SV648: $i,SV164: $i,SV636: $i] :
( ( ( in @ SV636 @ SV164 )
= $false )
| ( ( ~ ( in @ SV648 @ SV437 ) )
= $true )
| ( ( ( ( sK78_D @ SV474 @ SV437 @ SV164 )
!= ( ordered_pair @ SV636 @ SV648 ) ) )
= $true )
| ( ( ~ ( in @ ( sK78_D @ SV474 @ SV437 @ SV164 ) @ SV474 ) )
= $true )
| ( ( SV474
= ( cartesian_product2 @ SV164 @ SV437 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3849]) ).
thf(3943,plain,
! [SV164: $i,SV437: $i,SV474: $i] :
( ( ( ~ ( in @ ( sK79_SY729 @ SV474 @ SV437 @ SV164 ) @ SV164 ) )
= $false )
| ( ( in @ ( sK78_D @ SV474 @ SV437 @ SV164 ) @ SV474 )
= $true )
| ( ( SV474
= ( cartesian_product2 @ SV164 @ SV437 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3850]) ).
thf(3944,plain,
! [SV164: $i,SV437: $i,SV474: $i] :
( ( ( ~ ( in @ ( sK80_SY731 @ SV474 @ SV437 @ SV164 ) @ SV437 ) )
= $false )
| ( ( in @ ( sK78_D @ SV474 @ SV437 @ SV164 ) @ SV474 )
= $true )
| ( ( SV474
= ( cartesian_product2 @ SV164 @ SV437 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3850]) ).
thf(3945,plain,
! [SV475: $i,SV637: $i,SV438: $i,SV672: $i,SV164: $i,SV657: $i] :
( ( ( ~ ( in @ SV657 @ SV164 )
| ~ ( in @ SV672 @ SV438 ) )
= $true )
| ( ( ( SV637
!= ( ordered_pair @ SV657 @ SV672 ) ) )
= $true )
| ( ( in @ SV637 @ SV475 )
= $true )
| ( ( SV475
= ( cartesian_product2 @ SV164 @ SV438 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3851]) ).
thf(3946,plain,
! [SV164: $i,SV438: $i,SV475: $i,SV638: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK76_E @ SV638 @ SV475 @ SV438 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK77_SY726 @ SV638 @ SV475 @ SV438 @ SV164 ) @ SV438 ) ) )
= $false )
| ( ( in @ SV638 @ SV475 )
= $false )
| ( ( SV475
= ( cartesian_product2 @ SV164 @ SV438 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3852]) ).
thf(3947,plain,
! [SV164: $i,SV438: $i,SV475: $i,SV638: $i] :
( ( ( ( SV638
!= ( ordered_pair @ ( sK76_E @ SV638 @ SV475 @ SV438 @ SV164 ) @ ( sK77_SY726 @ SV638 @ SV475 @ SV438 @ SV164 ) ) ) )
= $false )
| ( ( in @ SV638 @ SV475 )
= $false )
| ( ( SV475
= ( cartesian_product2 @ SV164 @ SV438 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3852]) ).
thf(3948,plain,
! [SV649: $i,SV166: $i,SV558: $i] :
( ( ( in @ SV558 @ ( sK3_B @ SV166 ) )
= $false )
| ( ( in @ SV649 @ ( sK4_SY591 @ SV558 @ SV166 ) )
= $true )
| ( ( subset @ SV649 @ SV558 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3853]) ).
thf(3949,plain,
! [SV166: $i,SV619: $i,SV639: $i] :
( ( ( subset @ SV639 @ SV619 )
= $false )
| ( ( in @ SV619 @ ( sK3_B @ SV166 ) )
= $false )
| ( ( in @ SV639 @ ( sK3_B @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3854]) ).
thf(3950,plain,
! [SV168: $i] :
( ( ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) ) )
= $false )
| ( ( ( sK27_SY634 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3855]) ).
thf(3951,plain,
! [SV168: $i] :
( ( ( ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) )
= $false )
| ( ( ( sK27_SY634 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3855]) ).
thf(3952,plain,
! [SV168: $i] :
( ( ( ~ ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) ) )
= $false )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3856]) ).
thf(3953,plain,
! [SV168: $i] :
( ( ( ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) )
= $false )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3856]) ).
thf(3954,plain,
! [SV673: $i,SV168: $i] :
( ( ( ! [SY1486: $i] :
( ~ ( in @ SY1486 @ SV168 )
| ( SV673
!= ( singleton @ SY1486 ) ) ) )
= $true )
| ( ( in @ SV673 @ ( sK24_B @ SV168 ) )
= $true )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3857]) ).
thf(3955,plain,
! [SV168: $i,SV674: $i] :
( ( ( ~ ( in @ SV674 @ ( sK24_B @ SV168 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK25_D @ SV674 @ SV168 ) @ SV168 )
| ( SV674
!= ( singleton @ ( sK25_D @ SV674 @ SV168 ) ) ) ) )
= $true )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3858]) ).
thf(3956,plain,
! [SV640: $i,SV168: $i,SV658: $i] :
( ( ( in @ SV658 @ SV168 )
= $false )
| ( ( ( SV640
!= ( singleton @ SV658 ) ) )
= $true )
| ( ( in @ SV640 @ ( sK24_B @ SV168 ) )
= $true )
| ( ( ( sK28_SY636 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3859]) ).
thf(3957,plain,
! [SV168: $i,SV641: $i] :
( ( ( ~ ( in @ ( sK25_D @ SV641 @ SV168 ) @ SV168 ) )
= $false )
| ( ( in @ SV641 @ ( sK24_B @ SV168 ) )
= $false )
| ( ( ( sK28_SY636 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3860]) ).
thf(3958,plain,
! [SV168: $i,SV641: $i] :
( ( ( ( SV641
!= ( singleton @ ( sK25_D @ SV641 @ SV168 ) ) ) )
= $false )
| ( ( in @ SV641 @ ( sK24_B @ SV168 ) )
= $false )
| ( ( ( sK28_SY636 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3860]) ).
thf(3959,plain,
! [SV271: $i,SV481: $i,SV170: $i,SV596: $i,SV659: $i,SV651: $i] :
( ( ( ( ( ordered_pair @ SV651 @ SV659 )
!= SV596 ) )
= $true )
| ( ( ~ ( in @ SV651 @ SV170 ) )
= $true )
| ( ( ! [SY1469: $i] :
( ~ ( ~ ( in @ ( sK115_I @ SY1469 @ SV659 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) @ SY1469 )
| ~ ~ ( in @ ( ordered_pair @ SV659 @ ( sK115_I @ SY1469 @ SV659 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) ) @ SV271 ) )
| ( SV651 != SY1469 )
| ~ ( in @ SV659 @ SY1469 ) ) )
= $true )
| ( ( ~ ( in @ SV596 @ ( cartesian_product2 @ SV170 @ SV481 ) ) )
= $true )
| ( ( in @ SV596 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3864]) ).
thf(3960,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV652: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK112_F @ SV652 @ SV481 @ SV271 @ SV170 ) @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) )
!= SV652 )
| ~ ( in @ ( sK112_F @ SV652 @ SV481 @ SV271 @ SV170 ) @ SV170 ) )
| ~ ~ ( ~ ! [SY1464: $i] :
( ~ ( in @ SY1464 @ ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) )
| ( in @ ( ordered_pair @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) @ SY1464 ) @ SV271 ) )
| ~ ~ ( ( ( sK112_F @ SV652 @ SV481 @ SV271 @ SV170 )
!= ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) )
| ~ ( in @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) @ ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) ) ) ) )
= $false )
| ( ( in @ SV652 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $false )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3865]) ).
thf(3961,plain,
! [SV368: $i] :
( ( ( ~ ( in @ ( sK74_B @ SV368 ) @ SV368 ) )
= $false )
| ( ( epsilon_connected @ SV368 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3867]) ).
thf(3962,plain,
! [SV368: $i] :
( ( ( ~ ( in @ ( sK75_SY725 @ SV368 ) @ SV368 ) )
= $false )
| ( ( epsilon_connected @ SV368 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3867]) ).
thf(3963,plain,
! [SV171: $i,SV524: $i] :
( ( ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV524 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK83_C @ SV524 @ SV171 ) @ ( sK84_SY732 @ SV524 @ SV171 ) ) @ SV171 )
= $false )
| ( ( SV171 = SV524 )
= $true )
| ( ( relation @ SV524 )
= $false )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3869]) ).
thf(3964,plain,
! [SV525: $i,SV171: $i,SV690: $i,SV675: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV675 @ SV690 ) @ SV171 )
| ( in @ ( ordered_pair @ SV675 @ SV690 ) @ SV525 ) )
= $true )
| ( ( SV171 = SV525 )
= $false )
| ( ( relation @ SV525 )
= $false )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3870]) ).
thf(3965,plain,
! [SV171: $i,SV525: $i,SV691: $i,SV676: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV676 @ SV691 ) @ SV525 )
| ( in @ ( ordered_pair @ SV676 @ SV691 ) @ SV171 ) )
= $true )
| ( ( SV171 = SV525 )
= $false )
| ( ( relation @ SV525 )
= $false )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3871]) ).
thf(3966,plain,
! [SV172: $i,SV272: $i] :
( ( ( ( ( sK35_D @ SV272 @ SV172 )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1178: $i] :
( ~ ( in @ SY1178 @ ( sK43_SY691 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SY1178 ) @ SV272 ) )
| ~ ~ ( ( ( sK41_SY666 @ SV272 @ SV172 )
!= ( sK43_SY691 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) ) ) ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3872]) ).
thf(3967,plain,
! [SV272: $i,SV692: $i,SV172: $i] :
( ( ( ~ ( ~ ! [SY1501: $i] :
( ! [SY1502: $i] :
( ( SY1502 != SY1501 )
| ~ ( in @ SY1502 @ ( cartesian_product2 @ SV172 @ SV692 ) ) )
| ! [SY1503: $i,SY1504: $i] :
( ( ( ordered_pair @ SY1503 @ SY1504 )
!= SY1501 )
| ~ ( in @ SY1503 @ SV172 )
| ! [SY1505: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1505 @ SY1504 @ SY1503 @ SY1501 @ SV692 @ SV272 @ SV172 ) @ SY1505 )
| ~ ~ ( in @ ( ordered_pair @ SY1504 @ ( sK34_R @ SY1505 @ SY1504 @ SY1503 @ SY1501 @ SV692 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1503 != SY1505 )
| ~ ( in @ SY1504 @ SY1505 ) ) )
| ( in @ SY1501 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) ) )
| ~ ! [SY1506: $i] :
( ~ ( in @ SY1506 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1506 @ SV692 @ SV272 @ SV172 )
!= SY1506 )
| ~ ( in @ ( sK33_F @ SY1506 @ SV692 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV692 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1506 @ SV692 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1506 @ SV692 @ SV272 @ SV172 ) )
!= SY1506 )
| ~ ( in @ ( sK30_O @ SY1506 @ SV692 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1507: $i] :
( ~ ( in @ SY1507 @ ( sK32_SY652 @ SY1506 @ SV692 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1506 @ SV692 @ SV272 @ SV172 ) @ SY1507 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1506 @ SV692 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1506 @ SV692 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1506 @ SV692 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1506 @ SV692 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3873]) ).
thf(3968,plain,
! [SV172: $i,SV272: $i] :
( ( ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
!= ( sK37_SY665 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3874]) ).
thf(3969,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ! [SY1179: $i] :
( ~ ( in @ SY1179 @ ( sK40_SY685 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SY1179 ) @ SV272 ) )
| ~ ~ ( ( ( sK38_SY678 @ SV272 @ SV172 )
!= ( sK40_SY685 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3875]) ).
thf(3970,plain,
! [SV272: $i,SV622: $i,SV172: $i,SV677: $i] :
( ( ( ! [SY1489: $i] :
( ( SY1489 != SV677 )
| ~ ( in @ SY1489 @ ( cartesian_product2 @ SV172 @ SV622 ) ) )
| ! [SY1490: $i,SY1491: $i] :
( ( ( ordered_pair @ SY1490 @ SY1491 )
!= SV677 )
| ~ ( in @ SY1490 @ SV172 )
| ! [SY1492: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1492 @ SY1491 @ SY1490 @ SV677 @ SV622 @ SV272 @ SV172 ) @ SY1492 )
| ~ ~ ( in @ ( ordered_pair @ SY1491 @ ( sK34_R @ SY1492 @ SY1491 @ SY1490 @ SV677 @ SV622 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1490 != SY1492 )
| ~ ( in @ SY1491 @ SY1492 ) ) ) )
= $true )
| ( ( in @ SV677 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3876]) ).
thf(3971,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( ~ ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK33_F @ SV678 @ SV622 @ SV272 @ SV172 )
!= SV678 )
| ~ ( in @ ( sK33_F @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV622 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) )
!= SV678 )
| ~ ( in @ ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1493: $i] :
( ~ ( in @ SY1493 @ ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) @ SY1493 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3877]) ).
thf(3972,plain,
! [SV602: $i,SV579: $i,SV275: $i,SV176: $i,SV483: $i] :
( ( ( in @ SV483 @ ( cartesian_product2 @ SV176 @ SV275 ) )
= $false )
| ( ( in @ SV579 @ SV176 )
= $false )
| ( ( ( ordered_pair @ SV579 @ SV602 )
= SV483 )
= $false )
| ( ( SV602
= ( singleton @ SV579 ) )
= $false )
| ( ( in @ SV483 @ ( sK108_C @ SV275 @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3878]) ).
thf(3973,plain,
! [SV176: $i,SV275: $i,SV580: $i] :
( ( ( ( ( ordered_pair @ ( sK109_E @ SV580 @ SV275 @ SV176 ) @ ( sK110_SY756 @ SV580 @ SV275 @ SV176 ) )
!= SV580 ) )
= $false )
| ( ( in @ SV580 @ ( sK108_C @ SV275 @ SV176 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3879]) ).
thf(3974,plain,
! [SV176: $i,SV275: $i,SV580: $i] :
( ( ( ~ ( in @ ( sK109_E @ SV580 @ SV275 @ SV176 ) @ SV176 ) )
= $false )
| ( ( in @ SV580 @ ( sK108_C @ SV275 @ SV176 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3879]) ).
thf(3975,plain,
! [SV180: $i,SV456: $i,SV484: $i] :
( ( ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV180 )
= $false )
| ( ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV484 )
= $false )
| ( ( SV484
= ( set_union2 @ SV180 @ SV456 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3880]) ).
thf(3976,plain,
! [SV180: $i,SV456: $i,SV484: $i] :
( ( ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV456 )
= $false )
| ( ( in @ ( sK81_D @ SV484 @ SV456 @ SV180 ) @ SV484 )
= $false )
| ( ( SV484
= ( set_union2 @ SV180 @ SV456 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3881]) ).
thf(3977,plain,
! [SV457: $i,SV485: $i,SV180: $i,SV679: $i] :
( ( ( ~ ( in @ SV679 @ SV180 ) )
= $true )
| ( ( in @ SV679 @ SV485 )
= $true )
| ( ( SV485
= ( set_union2 @ SV180 @ SV457 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3883]) ).
thf(3978,plain,
! [SV180: $i,SV485: $i,SV457: $i,SV680: $i] :
( ( ( ~ ( in @ SV680 @ SV457 ) )
= $true )
| ( ( in @ SV680 @ SV485 )
= $true )
| ( ( SV485
= ( set_union2 @ SV180 @ SV457 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3884]) ).
thf(3979,plain,
! [SV660: $i,SV139: $i] :
( ( ( ~ ! [SY1470: $i] :
( ! [SY1471: $i] :
( ( SY1471 != SY1470 )
| ~ ( in @ SY1471 @ ( cartesian_product2 @ SV139 @ SV660 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1470 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1470 @ ( sK13_C @ SV660 @ SV139 ) ) ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3885]) ).
thf(3980,plain,
! [SV139: $i,SV660: $i] :
( ( ( ~ ! [SY1474: $i] :
( ~ ( in @ SY1474 @ ( sK13_C @ SV660 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1474 @ SV660 @ SV139 )
!= SY1474 )
| ~ ( in @ ( sK16_E @ SY1474 @ SV660 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV660 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1474 @ SV660 @ SV139 ) @ ( sK15_SY612 @ SY1474 @ SV660 @ SV139 ) )
!= SY1474 )
| ~ ( in @ ( sK14_J @ SY1474 @ SV660 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1474 @ SV660 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1474 @ SV660 @ SV139 ) ) ) ) ) ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3885]) ).
thf(3981,plain,
! [SV139: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
!= ( sK18_SY613 @ SV139 ) )
| ~ ( in @ ( sK22_SY620 @ SV139 ) @ SV139 ) ) )
= $true )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3886]) ).
thf(3982,plain,
! [SV139: $i] :
( ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3887]) ).
thf(3983,plain,
! [SV624: $i,SV139: $i,SV681: $i] :
( ( ( ! [SY1494: $i] :
( ( SY1494 != SV681 )
| ~ ( in @ SY1494 @ ( cartesian_product2 @ SV139 @ SV624 ) ) )
| ! [SY1495: $i,SY1496: $i] :
( ( ( ordered_pair @ SY1495 @ SY1496 )
!= SV681 )
| ~ ( in @ SY1495 @ SV139 )
| ( SY1496
!= ( singleton @ SY1495 ) ) ) )
= $true )
| ( ( in @ SV681 @ ( sK13_C @ SV624 @ SV139 ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3888]) ).
thf(3984,plain,
! [SV139: $i,SV624: $i,SV682: $i] :
( ( ( ~ ( in @ SV682 @ ( sK13_C @ SV624 @ SV139 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK16_E @ SV682 @ SV624 @ SV139 )
!= SV682 )
| ~ ( in @ ( sK16_E @ SV682 @ SV624 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV624 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV682 @ SV624 @ SV139 ) @ ( sK15_SY612 @ SV682 @ SV624 @ SV139 ) )
!= SV682 )
| ~ ( in @ ( sK14_J @ SV682 @ SV624 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV682 @ SV624 @ SV139 )
!= ( singleton @ ( sK14_J @ SV682 @ SV624 @ SV139 ) ) ) ) ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3889]) ).
thf(3985,plain,
! [SV661: $i,SV139: $i] :
( ( ( ~ ! [SY1475: $i] :
( ! [SY1476: $i] :
( ( SY1476 != SY1475 )
| ~ ( in @ SY1476 @ ( cartesian_product2 @ SV139 @ SV661 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1475 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1475 @ ( sK13_C @ SV661 @ SV139 ) ) ) )
= $false )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3890]) ).
thf(3986,plain,
! [SV139: $i,SV661: $i] :
( ( ( ~ ! [SY1479: $i] :
( ~ ( in @ SY1479 @ ( sK13_C @ SV661 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1479 @ SV661 @ SV139 )
!= SY1479 )
| ~ ( in @ ( sK16_E @ SY1479 @ SV661 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV661 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1479 @ SV661 @ SV139 ) @ ( sK15_SY612 @ SY1479 @ SV661 @ SV139 ) )
!= SY1479 )
| ~ ( in @ ( sK14_J @ SY1479 @ SV661 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1479 @ SV661 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1479 @ SV661 @ SV139 ) ) ) ) ) ) )
= $false )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3890]) ).
thf(3987,plain,
! [SV662: $i,SV139: $i] :
( ( ( ~ ! [SY1480: $i] :
( ! [SY1481: $i] :
( ( SY1481 != SY1480 )
| ~ ( in @ SY1481 @ ( cartesian_product2 @ SV139 @ SV662 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1480 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1480 @ ( sK13_C @ SV662 @ SV139 ) ) ) )
= $false )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3891]) ).
thf(3988,plain,
! [SV139: $i,SV662: $i] :
( ( ( ~ ! [SY1484: $i] :
( ~ ( in @ SY1484 @ ( sK13_C @ SV662 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1484 @ SV662 @ SV139 )
!= SY1484 )
| ~ ( in @ ( sK16_E @ SY1484 @ SV662 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV662 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1484 @ SV662 @ SV139 ) @ ( sK15_SY612 @ SY1484 @ SV662 @ SV139 ) )
!= SY1484 )
| ~ ( in @ ( sK14_J @ SY1484 @ SV662 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1484 @ SV662 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1484 @ SV662 @ SV139 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3891]) ).
thf(3989,plain,
! [SV625: $i,SV139: $i,SV683: $i] :
( ( ( ! [SY1497: $i] :
( ( SY1497 != SV683 )
| ~ ( in @ SY1497 @ ( cartesian_product2 @ SV139 @ SV625 ) ) )
| ! [SY1498: $i,SY1499: $i] :
( ( ( ordered_pair @ SY1498 @ SY1499 )
!= SV683 )
| ~ ( in @ SY1498 @ SV139 )
| ( SY1499
!= ( singleton @ SY1498 ) ) ) )
= $true )
| ( ( in @ SV683 @ ( sK13_C @ SV625 @ SV139 ) )
= $true )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3892]) ).
thf(3990,plain,
! [SV139: $i,SV625: $i,SV684: $i] :
( ( ( ~ ( in @ SV684 @ ( sK13_C @ SV625 @ SV139 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK16_E @ SV684 @ SV625 @ SV139 )
!= SV684 )
| ~ ( in @ ( sK16_E @ SV684 @ SV625 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV625 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV684 @ SV625 @ SV139 ) @ ( sK15_SY612 @ SV684 @ SV625 @ SV139 ) )
!= SV684 )
| ~ ( in @ ( sK14_J @ SV684 @ SV625 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV684 @ SV625 @ SV139 )
!= ( singleton @ ( sK14_J @ SV684 @ SV625 @ SV139 ) ) ) ) ) )
= $true )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3893]) ).
thf(3991,plain,
! [SV603: $i,SV488: $i,SV139: $i,SV654: $i] :
( ( ( in @ SV654 @ ( cartesian_product2 @ SV139 @ SV488 ) )
= $false )
| ( ( SV654 = SV603 )
= $false )
| ( ( ! [SY1431: $i,SY1432: $i] :
( ( ( ordered_pair @ SY1431 @ SY1432 )
!= SV603 )
| ~ ( in @ SY1431 @ SV139 )
| ( SY1432
!= ( singleton @ SY1431 ) ) ) )
= $true )
| ( ( in @ SV603 @ ( sK13_C @ SV488 @ SV139 ) )
= $true )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3894]) ).
thf(3992,plain,
! [SV139: $i,SV488: $i,SV604: $i] :
( ( ( ( ( sK16_E @ SV604 @ SV488 @ SV139 )
!= SV604 )
| ~ ( in @ ( sK16_E @ SV604 @ SV488 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV488 ) ) )
= $false )
| ( ( in @ SV604 @ ( sK13_C @ SV488 @ SV139 ) )
= $false )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3895]) ).
thf(3993,plain,
! [SV139: $i,SV488: $i,SV604: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV604 @ SV488 @ SV139 ) @ ( sK15_SY612 @ SV604 @ SV488 @ SV139 ) )
!= SV604 )
| ~ ( in @ ( sK14_J @ SV604 @ SV488 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV604 @ SV488 @ SV139 )
!= ( singleton @ ( sK14_J @ SV604 @ SV488 @ SV139 ) ) ) )
= $false )
| ( ( in @ SV604 @ ( sK13_C @ SV488 @ SV139 ) )
= $false )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3896]) ).
thf(3994,plain,
! [SV401: $i,SV143: $i,SV462: $i,SV663: $i] :
( ( ( in @ SV663 @ SV462 )
= $false )
| ( ( in @ SV663 @ SV143 )
= $true )
| ( ( SV462
= ( set_intersection2 @ SV143 @ SV401 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3898]) ).
thf(3995,plain,
! [SV143: $i,SV401: $i,SV462: $i,SV664: $i] :
( ( ( in @ SV664 @ SV462 )
= $false )
| ( ( in @ SV664 @ SV401 )
= $true )
| ( ( SV462
= ( set_intersection2 @ SV143 @ SV401 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3899]) ).
thf(3996,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ~ ( ~ ! [SY1142: $i] :
( ~ ( in @ SY1142 @ ( sK52_SY712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SY1142 ) @ SV265 ) )
| ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK52_SY712 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3900]) ).
thf(3997,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 ) )
= $false )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3900]) ).
thf(3998,plain,
! [SV265: $i,SV145: $i] :
( ( ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3901]) ).
thf(3999,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3901]) ).
thf(4000,plain,
! [SV145: $i,SV265: $i,SV685: $i] :
( ( ( ~ ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3902]) ).
thf(4001,plain,
! [SV145: $i,SV265: $i] :
( ( ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK51_SY718 @ SV265 @ SV145 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3903]) ).
thf(4002,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3903]) ).
thf(4003,plain,
! [SV265: $i,SV655: $i,SV145: $i,SV686: $i] :
( ( ( ~ ( in @ SV686 @ SV145 ) )
= $true )
| ( ( ! [SY1500: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1500 @ SV686 @ SV655 @ SV265 @ SV145 ) @ SY1500 )
| ~ ~ ( in @ ( ordered_pair @ SV655 @ ( sK47_K @ SY1500 @ SV686 @ SV655 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV686 != SY1500 )
| ~ ( in @ SV655 @ SY1500 ) ) )
= $true )
| ( ( in @ SV655 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3904]) ).
thf(4004,plain,
! [SV145: $i,SV265: $i,SV656: $i] :
( ( ( ~ ( in @ ( sK45_E @ SV656 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1467: $i] :
( ~ ( in @ SY1467 @ ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV656 @ SY1467 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV656 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) )
| ~ ( in @ SV656 @ ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) ) ) ) )
= $false )
| ( ( in @ SV656 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3905]) ).
thf(4005,plain,
! [SV404: $i,SV147: $i,SV464: $i,SV665: $i] :
( ( ( in @ SV665 @ SV464 )
= $false )
| ( ( in @ SV665 @ SV147 )
= $true )
| ( ( SV464
= ( set_difference @ SV147 @ SV404 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3906]) ).
thf(4006,plain,
! [SV147: $i,SV404: $i,SV464: $i,SV666: $i] :
( ( ( in @ SV666 @ SV464 )
= $false )
| ( ( ~ ( in @ SV666 @ SV404 ) )
= $true )
| ( ( SV464
= ( set_difference @ SV147 @ SV404 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3907]) ).
thf(4007,plain,
! [SV151: $i,SV267: $i,SV467: $i,SV502: $i] :
( ( ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
= SV467 )
= $false )
| ( ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
= $false )
| ( ( SV502
= ( unordered_triple @ SV151 @ SV267 @ SV467 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3911]) ).
thf(4008,plain,
! [SV151: $i,SV267: $i,SV467: $i,SV502: $i] :
( ( ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV151 ) )
= $true )
| ( ( SV502
= ( unordered_triple @ SV151 @ SV267 @ SV467 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3912]) ).
thf(4009,plain,
! [SV151: $i,SV267: $i,SV467: $i,SV502: $i] :
( ( ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
| ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV267 ) )
= $true )
| ( ( SV502
= ( unordered_triple @ SV151 @ SV267 @ SV467 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3913]) ).
thf(4010,plain,
! [SV503: $i,SV468: $i,SV267: $i,SV151: $i,SV646: $i] :
( ( ( SV646 = SV151 )
= $true )
| ( ( SV646 = SV267 )
= $true )
| ( ( SV646 = SV468 )
= $true )
| ( ( in @ SV646 @ SV503 )
= $false )
| ( ( SV503
= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3914]) ).
thf(4011,plain,
! [SV267: $i,SV151: $i,SV503: $i,SV468: $i,SV687: $i] :
( ( ( ( SV687 != SV468 ) )
= $true )
| ( ( in @ SV687 @ SV503 )
= $true )
| ( ( SV503
= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3915]) ).
thf(4012,plain,
! [SV468: $i,SV267: $i,SV503: $i,SV151: $i] :
( ( ( ~ ! [SY1381: $i] :
( ( SY1381 != SV151 )
| ( in @ SY1381 @ SV503 ) ) )
= $false )
| ( ( SV503
= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3916]) ).
thf(4013,plain,
! [SV468: $i,SV151: $i,SV503: $i,SV267: $i] :
( ( ( ~ ! [SY1382: $i] :
( ( SY1382 != SV267 )
| ( in @ SY1382 @ SV503 ) ) )
= $false )
| ( ( SV503
= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3916]) ).
thf(4014,plain,
! [SV155: $i,SV268: $i,SV547: $i] :
( ( ( ~ ( in @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ SV547 )
| ~ ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SV547 @ SV268 @ SV155 ) ) @ SV268 ) )
= $true )
| ( ( SV547
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $true )
| ( ( element @ SV547 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3918]) ).
thf(4015,plain,
! [SV155: $i,SV268: $i,SV547: $i] :
( ( ( ( in @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ SV547 )
| ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SV547 @ SV268 @ SV155 ) ) @ SV268 ) )
= $true )
| ( ( SV547
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $true )
| ( ( element @ SV547 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3919]) ).
thf(4016,plain,
! [SV268: $i,SV548: $i,SV155: $i,SV688: $i] :
( ( ( ~ ( element @ SV688 @ ( powerset @ SV155 ) ) )
= $true )
| ( ( ~ ( in @ SV688 @ SV548 )
| ( in @ ( subset_complement @ SV155 @ SV688 ) @ SV268 ) )
= $true )
| ( ( SV548
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $false )
| ( ( element @ SV548 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3920]) ).
thf(4017,plain,
! [SV548: $i,SV268: $i,SV155: $i,SV689: $i] :
( ( ( ~ ( element @ SV689 @ ( powerset @ SV155 ) ) )
= $true )
| ( ( ~ ( in @ ( subset_complement @ SV155 @ SV689 ) @ SV268 )
| ( in @ SV689 @ SV548 ) )
= $true )
| ( ( SV548
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $false )
| ( ( element @ SV548 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3921]) ).
thf(4018,plain,
! [SV425: $i,SV567: $i] :
( ( ( ( sK8_D @ SV567 @ SV425 )
= SV567 )
= $true )
| ( ( in @ SV567 @ ( sK7_B @ SV425 ) )
= $false )
| ( sK12_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[3923]) ).
thf(4019,plain,
! [SV425: $i,SV567: $i] :
( ( ( in @ ( sK8_D @ SV567 @ SV425 ) @ SV425 )
= $true )
| ( ( in @ SV567 @ ( sK7_B @ SV425 ) )
= $false )
| ( sK12_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[3924]) ).
thf(4020,plain,
( ( ( sK9_B = sK10_SY601 )
= $true )
| ( sK12_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[3925]) ).
thf(4021,plain,
( ( ( ordinal @ sK10_SY601 )
= $true )
| ( sK12_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[3926]) ).
thf(4022,plain,
! [SV631: $i,SV613: $i,SV158: $i] :
( ( ( SV158
= ( relation_dom_as_subset @ SV158 @ SV613 @ SV631 ) )
= $false )
| ( ( quasi_total @ SV631 @ SV158 @ SV613 )
= $true )
| ( ( SV613 = empty_set )
= $true )
| ( ( relation_of2_as_subset @ SV631 @ SV158 @ SV613 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3927]) ).
thf(4023,plain,
! [SV614: $i,SV158: $i,SV632: $i] :
( ( ( quasi_total @ SV632 @ SV158 @ SV614 )
= $false )
| ( ( SV158
= ( relation_dom_as_subset @ SV158 @ SV614 @ SV632 ) )
= $true )
| ( ( SV614 = empty_set )
= $true )
| ( ( relation_of2_as_subset @ SV632 @ SV158 @ SV614 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3928]) ).
thf(4024,plain,
! [SV633: $i,SV615: $i,SV158: $i] :
( ( ( ( SV158
!= ( relation_dom_as_subset @ SV158 @ SV615 @ SV633 ) ) )
= $true )
| ( ( quasi_total @ SV633 @ SV158 @ SV615 )
= $true )
| ( ( SV158 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV633 @ SV158 @ SV615 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3929]) ).
thf(4025,plain,
! [SV616: $i,SV158: $i,SV634: $i] :
( ( ( ~ ( quasi_total @ SV634 @ SV158 @ SV616 ) )
= $true )
| ( ( SV158
= ( relation_dom_as_subset @ SV158 @ SV616 @ SV634 ) )
= $true )
| ( ( SV158 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV634 @ SV158 @ SV616 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3930]) ).
thf(4026,plain,
! [SV512: $i,SV572: $i] :
( ( ( in @ ( sK90_SY733 @ SV572 @ SV512 ) @ SV512 )
= $true )
| ( ( ~ ( in @ ( sK89_C @ SV572 @ SV512 ) @ SV572 ) )
= $true )
| ( ( SV572
= ( set_meet @ SV512 ) )
= $true )
| ( ( SV512 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3933]) ).
thf(4027,plain,
! [SV512: $i,SV572: $i] :
( ( ( ~ ( in @ ( sK89_C @ SV572 @ SV512 ) @ ( sK90_SY733 @ SV572 @ SV512 ) ) )
= $true )
| ( ( ~ ( in @ ( sK89_C @ SV572 @ SV512 ) @ SV572 ) )
= $true )
| ( ( SV572
= ( set_meet @ SV512 ) )
= $true )
| ( ( SV512 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3934]) ).
thf(4028,plain,
! [SV572: $i,SV512: $i,SV667: $i] :
( ( ( in @ SV667 @ SV512 )
= $false )
| ( ( in @ ( sK89_C @ SV572 @ SV512 ) @ SV667 )
= $true )
| ( ( in @ ( sK89_C @ SV572 @ SV512 ) @ SV572 )
= $true )
| ( ( SV572
= ( set_meet @ SV512 ) )
= $true )
| ( ( SV512 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3935]) ).
thf(4029,plain,
! [SV513: $i,SV573: $i,SV668: $i] :
( ( ( ~ ( in @ ( sK88_D @ SV668 @ SV573 @ SV513 ) @ SV513 )
| ~ ~ ( in @ SV668 @ ( sK88_D @ SV668 @ SV573 @ SV513 ) ) )
= $false )
| ( ( in @ SV668 @ SV573 )
= $true )
| ( ( SV573
= ( set_meet @ SV513 ) )
= $false )
| ( ( SV513 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3936]) ).
thf(4030,plain,
! [SV513: $i,SV573: $i,SV669: $i] :
( ( ( in @ SV669 @ SV573 )
= $false )
| ( ( ! [SY1485: $i] :
( ~ ( in @ SY1485 @ SV513 )
| ( in @ SV669 @ SY1485 ) ) )
= $true )
| ( ( SV573
= ( set_meet @ SV513 ) )
= $false )
| ( ( SV513 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3937]) ).
thf(4031,plain,
! [SV428: $i,SV471: $i,SV159: $i,SV670: $i] :
( ( ( SV670 = SV159 )
= $false )
| ( ( in @ SV670 @ SV471 )
= $true )
| ( ( SV471
= ( unordered_pair @ SV159 @ SV428 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3940]) ).
thf(4032,plain,
! [SV159: $i,SV471: $i,SV428: $i,SV671: $i] :
( ( ( SV671 = SV428 )
= $false )
| ( ( in @ SV671 @ SV471 )
= $true )
| ( ( SV471
= ( unordered_pair @ SV159 @ SV428 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3941]) ).
thf(4033,plain,
! [SV474: $i,SV164: $i,SV636: $i,SV437: $i,SV648: $i] :
( ( ( in @ SV648 @ SV437 )
= $false )
| ( ( in @ SV636 @ SV164 )
= $false )
| ( ( ( ( sK78_D @ SV474 @ SV437 @ SV164 )
!= ( ordered_pair @ SV636 @ SV648 ) ) )
= $true )
| ( ( ~ ( in @ ( sK78_D @ SV474 @ SV437 @ SV164 ) @ SV474 ) )
= $true )
| ( ( SV474
= ( cartesian_product2 @ SV164 @ SV437 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3942]) ).
thf(4034,plain,
! [SV164: $i,SV437: $i,SV474: $i] :
( ( ( in @ ( sK79_SY729 @ SV474 @ SV437 @ SV164 ) @ SV164 )
= $true )
| ( ( in @ ( sK78_D @ SV474 @ SV437 @ SV164 ) @ SV474 )
= $true )
| ( ( SV474
= ( cartesian_product2 @ SV164 @ SV437 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3943]) ).
thf(4035,plain,
! [SV164: $i,SV437: $i,SV474: $i] :
( ( ( in @ ( sK80_SY731 @ SV474 @ SV437 @ SV164 ) @ SV437 )
= $true )
| ( ( in @ ( sK78_D @ SV474 @ SV437 @ SV164 ) @ SV474 )
= $true )
| ( ( SV474
= ( cartesian_product2 @ SV164 @ SV437 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3944]) ).
thf(4036,plain,
! [SV475: $i,SV637: $i,SV438: $i,SV672: $i,SV164: $i,SV657: $i] :
( ( ( ~ ( in @ SV657 @ SV164 ) )
= $true )
| ( ( ~ ( in @ SV672 @ SV438 ) )
= $true )
| ( ( ( SV637
!= ( ordered_pair @ SV657 @ SV672 ) ) )
= $true )
| ( ( in @ SV637 @ SV475 )
= $true )
| ( ( SV475
= ( cartesian_product2 @ SV164 @ SV438 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3945]) ).
thf(4037,plain,
! [SV164: $i,SV438: $i,SV475: $i,SV638: $i] :
( ( ( ~ ( ~ ( in @ ( sK76_E @ SV638 @ SV475 @ SV438 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK77_SY726 @ SV638 @ SV475 @ SV438 @ SV164 ) @ SV438 ) ) )
= $true )
| ( ( in @ SV638 @ SV475 )
= $false )
| ( ( SV475
= ( cartesian_product2 @ SV164 @ SV438 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3946]) ).
thf(4038,plain,
! [SV164: $i,SV438: $i,SV475: $i,SV638: $i] :
( ( ( SV638
= ( ordered_pair @ ( sK76_E @ SV638 @ SV475 @ SV438 @ SV164 ) @ ( sK77_SY726 @ SV638 @ SV475 @ SV438 @ SV164 ) ) )
= $true )
| ( ( in @ SV638 @ SV475 )
= $false )
| ( ( SV475
= ( cartesian_product2 @ SV164 @ SV438 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3947]) ).
thf(4039,plain,
! [SV168: $i] :
( ( ( ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) ) )
= $true )
| ( ( ( sK27_SY634 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3950]) ).
thf(4040,plain,
! [SV168: $i] :
( ( ( ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) )
= $true )
| ( ( ( sK27_SY634 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3951]) ).
thf(4041,plain,
! [SV168: $i] :
( ( ( ! [SY1044: $i] :
( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV168 )
| ( SY1044
!= ( singleton @ SY1045 ) ) )
| ( in @ SY1044 @ ( sK24_B @ SV168 ) ) ) )
= $true )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3952]) ).
thf(4042,plain,
! [SV168: $i] :
( ( ( ! [SY1046: $i] :
( ~ ( in @ SY1046 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SY1046 @ SV168 ) @ SV168 )
| ( SY1046
!= ( singleton @ ( sK25_D @ SY1046 @ SV168 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3953]) ).
thf(4043,plain,
! [SV673: $i,SV168: $i,SV693: $i] :
( ( ( ~ ( in @ SV693 @ SV168 )
| ( SV673
!= ( singleton @ SV693 ) ) )
= $true )
| ( ( in @ SV673 @ ( sK24_B @ SV168 ) )
= $true )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3954]) ).
thf(4044,plain,
! [SV168: $i,SV674: $i] :
( ( ( in @ SV674 @ ( sK24_B @ SV168 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK25_D @ SV674 @ SV168 ) @ SV168 )
| ( SV674
!= ( singleton @ ( sK25_D @ SV674 @ SV168 ) ) ) ) )
= $true )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3955]) ).
thf(4045,plain,
! [SV168: $i,SV658: $i,SV640: $i] :
( ( ( SV640
= ( singleton @ SV658 ) )
= $false )
| ( ( in @ SV658 @ SV168 )
= $false )
| ( ( in @ SV640 @ ( sK24_B @ SV168 ) )
= $true )
| ( ( ( sK28_SY636 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3956]) ).
thf(4046,plain,
! [SV168: $i,SV641: $i] :
( ( ( in @ ( sK25_D @ SV641 @ SV168 ) @ SV168 )
= $true )
| ( ( in @ SV641 @ ( sK24_B @ SV168 ) )
= $false )
| ( ( ( sK28_SY636 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3957]) ).
thf(4047,plain,
! [SV168: $i,SV641: $i] :
( ( ( SV641
= ( singleton @ ( sK25_D @ SV641 @ SV168 ) ) )
= $true )
| ( ( in @ SV641 @ ( sK24_B @ SV168 ) )
= $false )
| ( ( ( sK28_SY636 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3958]) ).
thf(4048,plain,
! [SV271: $i,SV481: $i,SV170: $i,SV596: $i,SV659: $i,SV651: $i] :
( ( ( ( ordered_pair @ SV651 @ SV659 )
= SV596 )
= $false )
| ( ( ~ ( in @ SV651 @ SV170 ) )
= $true )
| ( ( ! [SY1469: $i] :
( ~ ( ~ ( in @ ( sK115_I @ SY1469 @ SV659 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) @ SY1469 )
| ~ ~ ( in @ ( ordered_pair @ SV659 @ ( sK115_I @ SY1469 @ SV659 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) ) @ SV271 ) )
| ( SV651 != SY1469 )
| ~ ( in @ SV659 @ SY1469 ) ) )
= $true )
| ( ( ~ ( in @ SV596 @ ( cartesian_product2 @ SV170 @ SV481 ) ) )
= $true )
| ( ( in @ SV596 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3959]) ).
thf(4049,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV652: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK112_F @ SV652 @ SV481 @ SV271 @ SV170 ) @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) )
!= SV652 )
| ~ ( in @ ( sK112_F @ SV652 @ SV481 @ SV271 @ SV170 ) @ SV170 ) ) )
= $false )
| ( ( in @ SV652 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $false )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3960]) ).
thf(4050,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV652: $i] :
( ( ( ~ ~ ( ~ ! [SY1464: $i] :
( ~ ( in @ SY1464 @ ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) )
| ( in @ ( ordered_pair @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) @ SY1464 ) @ SV271 ) )
| ~ ~ ( ( ( sK112_F @ SV652 @ SV481 @ SV271 @ SV170 )
!= ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) )
| ~ ( in @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) @ ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) ) ) ) )
= $false )
| ( ( in @ SV652 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $false )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3960]) ).
thf(4051,plain,
! [SV368: $i] :
( ( ( in @ ( sK74_B @ SV368 ) @ SV368 )
= $true )
| ( ( epsilon_connected @ SV368 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3961]) ).
thf(4052,plain,
! [SV368: $i] :
( ( ( in @ ( sK75_SY725 @ SV368 ) @ SV368 )
= $true )
| ( ( epsilon_connected @ SV368 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3962]) ).
thf(4053,plain,
! [SV525: $i,SV171: $i,SV690: $i,SV675: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV675 @ SV690 ) @ SV171 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV675 @ SV690 ) @ SV525 )
= $true )
| ( ( SV171 = SV525 )
= $false )
| ( ( relation @ SV525 )
= $false )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3964]) ).
thf(4054,plain,
! [SV171: $i,SV525: $i,SV691: $i,SV676: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV676 @ SV691 ) @ SV525 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV676 @ SV691 ) @ SV171 )
= $true )
| ( ( SV171 = SV525 )
= $false )
| ( ( relation @ SV525 )
= $false )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3965]) ).
thf(4055,plain,
! [SV172: $i,SV272: $i] :
( ( ( ( ( sK35_D @ SV272 @ SV172 )
!= ( sK36_SY655 @ SV272 @ SV172 ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3966]) ).
thf(4056,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1178: $i] :
( ~ ( in @ SY1178 @ ( sK43_SY691 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SY1178 ) @ SV272 ) )
| ~ ~ ( ( ( sK41_SY666 @ SV272 @ SV172 )
!= ( sK43_SY691 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) ) ) ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3966]) ).
thf(4057,plain,
! [SV272: $i,SV692: $i,SV172: $i] :
( ( ( ~ ! [SY1501: $i] :
( ! [SY1502: $i] :
( ( SY1502 != SY1501 )
| ~ ( in @ SY1502 @ ( cartesian_product2 @ SV172 @ SV692 ) ) )
| ! [SY1503: $i,SY1504: $i] :
( ( ( ordered_pair @ SY1503 @ SY1504 )
!= SY1501 )
| ~ ( in @ SY1503 @ SV172 )
| ! [SY1505: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1505 @ SY1504 @ SY1503 @ SY1501 @ SV692 @ SV272 @ SV172 ) @ SY1505 )
| ~ ~ ( in @ ( ordered_pair @ SY1504 @ ( sK34_R @ SY1505 @ SY1504 @ SY1503 @ SY1501 @ SV692 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1503 != SY1505 )
| ~ ( in @ SY1504 @ SY1505 ) ) )
| ( in @ SY1501 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) ) )
| ~ ! [SY1506: $i] :
( ~ ( in @ SY1506 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1506 @ SV692 @ SV272 @ SV172 )
!= SY1506 )
| ~ ( in @ ( sK33_F @ SY1506 @ SV692 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV692 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1506 @ SV692 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1506 @ SV692 @ SV272 @ SV172 ) )
!= SY1506 )
| ~ ( in @ ( sK30_O @ SY1506 @ SV692 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1507: $i] :
( ~ ( in @ SY1507 @ ( sK32_SY652 @ SY1506 @ SV692 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1506 @ SV692 @ SV272 @ SV172 ) @ SY1507 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1506 @ SV692 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1506 @ SV692 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1506 @ SV692 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1506 @ SV692 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3967]) ).
thf(4058,plain,
! [SV172: $i,SV272: $i] :
( ( ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
!= ( sK37_SY665 @ SV272 @ SV172 ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3968]) ).
thf(4059,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3968]) ).
thf(4060,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ! [SY1179: $i] :
( ~ ( in @ SY1179 @ ( sK40_SY685 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SY1179 ) @ SV272 ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3969]) ).
thf(4061,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ~ ( ( ( sK38_SY678 @ SV272 @ SV172 )
!= ( sK40_SY685 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3969]) ).
thf(4062,plain,
! [SV272: $i,SV622: $i,SV172: $i,SV677: $i] :
( ( ( ! [SY1489: $i] :
( ( SY1489 != SV677 )
| ~ ( in @ SY1489 @ ( cartesian_product2 @ SV172 @ SV622 ) ) ) )
= $true )
| ( ( ! [SY1490: $i,SY1491: $i] :
( ( ( ordered_pair @ SY1490 @ SY1491 )
!= SV677 )
| ~ ( in @ SY1490 @ SV172 )
| ! [SY1492: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1492 @ SY1491 @ SY1490 @ SV677 @ SV622 @ SV272 @ SV172 ) @ SY1492 )
| ~ ~ ( in @ ( ordered_pair @ SY1491 @ ( sK34_R @ SY1492 @ SY1491 @ SY1490 @ SV677 @ SV622 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1490 != SY1492 )
| ~ ( in @ SY1491 @ SY1492 ) ) ) )
= $true )
| ( ( in @ SV677 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3970]) ).
thf(4063,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK33_F @ SV678 @ SV622 @ SV272 @ SV172 )
!= SV678 )
| ~ ( in @ ( sK33_F @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV622 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) )
!= SV678 )
| ~ ( in @ ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1493: $i] :
( ~ ( in @ SY1493 @ ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) @ SY1493 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3971]) ).
thf(4064,plain,
! [SV176: $i,SV275: $i,SV580: $i] :
( ( ( ( ordered_pair @ ( sK109_E @ SV580 @ SV275 @ SV176 ) @ ( sK110_SY756 @ SV580 @ SV275 @ SV176 ) )
= SV580 )
= $true )
| ( ( in @ SV580 @ ( sK108_C @ SV275 @ SV176 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3973]) ).
thf(4065,plain,
! [SV176: $i,SV275: $i,SV580: $i] :
( ( ( in @ ( sK109_E @ SV580 @ SV275 @ SV176 ) @ SV176 )
= $true )
| ( ( in @ SV580 @ ( sK108_C @ SV275 @ SV176 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3974]) ).
thf(4066,plain,
! [SV457: $i,SV485: $i,SV180: $i,SV679: $i] :
( ( ( in @ SV679 @ SV180 )
= $false )
| ( ( in @ SV679 @ SV485 )
= $true )
| ( ( SV485
= ( set_union2 @ SV180 @ SV457 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3977]) ).
thf(4067,plain,
! [SV180: $i,SV485: $i,SV457: $i,SV680: $i] :
( ( ( in @ SV680 @ SV457 )
= $false )
| ( ( in @ SV680 @ SV485 )
= $true )
| ( ( SV485
= ( set_union2 @ SV180 @ SV457 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3978]) ).
thf(4068,plain,
! [SV660: $i,SV139: $i] :
( ( ( ! [SY1470: $i] :
( ! [SY1471: $i] :
( ( SY1471 != SY1470 )
| ~ ( in @ SY1471 @ ( cartesian_product2 @ SV139 @ SV660 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1470 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1470 @ ( sK13_C @ SV660 @ SV139 ) ) ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3979]) ).
thf(4069,plain,
! [SV139: $i,SV660: $i] :
( ( ( ! [SY1474: $i] :
( ~ ( in @ SY1474 @ ( sK13_C @ SV660 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1474 @ SV660 @ SV139 )
!= SY1474 )
| ~ ( in @ ( sK16_E @ SY1474 @ SV660 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV660 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1474 @ SV660 @ SV139 ) @ ( sK15_SY612 @ SY1474 @ SV660 @ SV139 ) )
!= SY1474 )
| ~ ( in @ ( sK14_J @ SY1474 @ SV660 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1474 @ SV660 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1474 @ SV660 @ SV139 ) ) ) ) ) ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3980]) ).
thf(4070,plain,
! [SV139: $i] :
( ( ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
!= ( sK18_SY613 @ SV139 ) )
| ~ ( in @ ( sK22_SY620 @ SV139 ) @ SV139 ) )
= $false )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3981]) ).
thf(4071,plain,
! [SV694: $i,SV139: $i] :
( ( ( ~ ( ~ ! [SY1508: $i] :
( ! [SY1509: $i] :
( ( SY1509 != SY1508 )
| ~ ( in @ SY1509 @ ( cartesian_product2 @ SV139 @ SV694 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1508 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1508 @ ( sK13_C @ SV694 @ SV139 ) ) )
| ~ ! [SY1512: $i] :
( ~ ( in @ SY1512 @ ( sK13_C @ SV694 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1512 @ SV694 @ SV139 )
!= SY1512 )
| ~ ( in @ ( sK16_E @ SY1512 @ SV694 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV694 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1512 @ SV694 @ SV139 ) @ ( sK15_SY612 @ SY1512 @ SV694 @ SV139 ) )
!= SY1512 )
| ~ ( in @ ( sK14_J @ SY1512 @ SV694 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1512 @ SV694 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1512 @ SV694 @ SV139 ) ) ) ) ) ) ) )
= $true )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3982]) ).
thf(4072,plain,
! [SV624: $i,SV139: $i,SV681: $i] :
( ( ( ! [SY1494: $i] :
( ( SY1494 != SV681 )
| ~ ( in @ SY1494 @ ( cartesian_product2 @ SV139 @ SV624 ) ) ) )
= $true )
| ( ( ! [SY1495: $i,SY1496: $i] :
( ( ( ordered_pair @ SY1495 @ SY1496 )
!= SV681 )
| ~ ( in @ SY1495 @ SV139 )
| ( SY1496
!= ( singleton @ SY1495 ) ) ) )
= $true )
| ( ( in @ SV681 @ ( sK13_C @ SV624 @ SV139 ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3983]) ).
thf(4073,plain,
! [SV139: $i,SV624: $i,SV682: $i] :
( ( ( in @ SV682 @ ( sK13_C @ SV624 @ SV139 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK16_E @ SV682 @ SV624 @ SV139 )
!= SV682 )
| ~ ( in @ ( sK16_E @ SV682 @ SV624 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV624 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV682 @ SV624 @ SV139 ) @ ( sK15_SY612 @ SV682 @ SV624 @ SV139 ) )
!= SV682 )
| ~ ( in @ ( sK14_J @ SV682 @ SV624 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV682 @ SV624 @ SV139 )
!= ( singleton @ ( sK14_J @ SV682 @ SV624 @ SV139 ) ) ) ) ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3984]) ).
thf(4074,plain,
! [SV661: $i,SV139: $i] :
( ( ( ! [SY1475: $i] :
( ! [SY1476: $i] :
( ( SY1476 != SY1475 )
| ~ ( in @ SY1476 @ ( cartesian_product2 @ SV139 @ SV661 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1475 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1475 @ ( sK13_C @ SV661 @ SV139 ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3985]) ).
thf(4075,plain,
! [SV139: $i,SV661: $i] :
( ( ( ! [SY1479: $i] :
( ~ ( in @ SY1479 @ ( sK13_C @ SV661 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1479 @ SV661 @ SV139 )
!= SY1479 )
| ~ ( in @ ( sK16_E @ SY1479 @ SV661 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV661 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1479 @ SV661 @ SV139 ) @ ( sK15_SY612 @ SY1479 @ SV661 @ SV139 ) )
!= SY1479 )
| ~ ( in @ ( sK14_J @ SY1479 @ SV661 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1479 @ SV661 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1479 @ SV661 @ SV139 ) ) ) ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3986]) ).
thf(4076,plain,
! [SV662: $i,SV139: $i] :
( ( ( ! [SY1480: $i] :
( ! [SY1481: $i] :
( ( SY1481 != SY1480 )
| ~ ( in @ SY1481 @ ( cartesian_product2 @ SV139 @ SV662 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1480 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1480 @ ( sK13_C @ SV662 @ SV139 ) ) ) )
= $true )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3987]) ).
thf(4077,plain,
! [SV139: $i,SV662: $i] :
( ( ( ! [SY1484: $i] :
( ~ ( in @ SY1484 @ ( sK13_C @ SV662 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1484 @ SV662 @ SV139 )
!= SY1484 )
| ~ ( in @ ( sK16_E @ SY1484 @ SV662 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV662 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1484 @ SV662 @ SV139 ) @ ( sK15_SY612 @ SY1484 @ SV662 @ SV139 ) )
!= SY1484 )
| ~ ( in @ ( sK14_J @ SY1484 @ SV662 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1484 @ SV662 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1484 @ SV662 @ SV139 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3988]) ).
thf(4078,plain,
! [SV625: $i,SV139: $i,SV683: $i] :
( ( ( ! [SY1497: $i] :
( ( SY1497 != SV683 )
| ~ ( in @ SY1497 @ ( cartesian_product2 @ SV139 @ SV625 ) ) ) )
= $true )
| ( ( ! [SY1498: $i,SY1499: $i] :
( ( ( ordered_pair @ SY1498 @ SY1499 )
!= SV683 )
| ~ ( in @ SY1498 @ SV139 )
| ( SY1499
!= ( singleton @ SY1498 ) ) ) )
= $true )
| ( ( in @ SV683 @ ( sK13_C @ SV625 @ SV139 ) )
= $true )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3989]) ).
thf(4079,plain,
! [SV139: $i,SV625: $i,SV684: $i] :
( ( ( in @ SV684 @ ( sK13_C @ SV625 @ SV139 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK16_E @ SV684 @ SV625 @ SV139 )
!= SV684 )
| ~ ( in @ ( sK16_E @ SV684 @ SV625 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV625 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV684 @ SV625 @ SV139 ) @ ( sK15_SY612 @ SV684 @ SV625 @ SV139 ) )
!= SV684 )
| ~ ( in @ ( sK14_J @ SV684 @ SV625 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV684 @ SV625 @ SV139 )
!= ( singleton @ ( sK14_J @ SV684 @ SV625 @ SV139 ) ) ) ) ) )
= $true )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3990]) ).
thf(4080,plain,
! [SV488: $i,SV654: $i,SV139: $i,SV603: $i,SV695: $i] :
( ( ( ! [SY1513: $i] :
( ( ( ordered_pair @ SV695 @ SY1513 )
!= SV603 )
| ~ ( in @ SV695 @ SV139 )
| ( SY1513
!= ( singleton @ SV695 ) ) ) )
= $true )
| ( ( SV654 = SV603 )
= $false )
| ( ( in @ SV654 @ ( cartesian_product2 @ SV139 @ SV488 ) )
= $false )
| ( ( in @ SV603 @ ( sK13_C @ SV488 @ SV139 ) )
= $true )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3991]) ).
thf(4081,plain,
! [SV139: $i,SV488: $i,SV604: $i] :
( ( ( ( ( sK16_E @ SV604 @ SV488 @ SV139 )
!= SV604 ) )
= $false )
| ( ( in @ SV604 @ ( sK13_C @ SV488 @ SV139 ) )
= $false )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3992]) ).
thf(4082,plain,
! [SV139: $i,SV488: $i,SV604: $i] :
( ( ( ~ ( in @ ( sK16_E @ SV604 @ SV488 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV488 ) ) )
= $false )
| ( ( in @ SV604 @ ( sK13_C @ SV488 @ SV139 ) )
= $false )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3992]) ).
thf(4083,plain,
! [SV139: $i,SV488: $i,SV604: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV604 @ SV488 @ SV139 ) @ ( sK15_SY612 @ SV604 @ SV488 @ SV139 ) )
!= SV604 )
| ~ ( in @ ( sK14_J @ SV604 @ SV488 @ SV139 ) @ SV139 ) ) )
= $false )
| ( ( in @ SV604 @ ( sK13_C @ SV488 @ SV139 ) )
= $false )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3993]) ).
thf(4084,plain,
! [SV139: $i,SV488: $i,SV604: $i] :
( ( ( ( ( sK15_SY612 @ SV604 @ SV488 @ SV139 )
!= ( singleton @ ( sK14_J @ SV604 @ SV488 @ SV139 ) ) ) )
= $false )
| ( ( in @ SV604 @ ( sK13_C @ SV488 @ SV139 ) )
= $false )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3993]) ).
thf(4085,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ( ~ ! [SY1142: $i] :
( ~ ( in @ SY1142 @ ( sK52_SY712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SY1142 ) @ SV265 ) )
| ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK52_SY712 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3996]) ).
thf(4086,plain,
! [SV145: $i,SV265: $i] :
( ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3997]) ).
thf(4087,plain,
! [SV265: $i,SV145: $i] :
( ( ( ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3998]) ).
thf(4088,plain,
! [SV145: $i,SV265: $i] :
( ( ( ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3999]) ).
thf(4089,plain,
! [SV145: $i,SV265: $i,SV685: $i] :
( ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4000]) ).
thf(4090,plain,
! [SV145: $i,SV265: $i] :
( ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4001]) ).
thf(4091,plain,
! [SV145: $i,SV265: $i] :
( ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4002]) ).
thf(4092,plain,
! [SV265: $i,SV655: $i,SV145: $i,SV686: $i] :
( ( ( in @ SV686 @ SV145 )
= $false )
| ( ( ! [SY1500: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1500 @ SV686 @ SV655 @ SV265 @ SV145 ) @ SY1500 )
| ~ ~ ( in @ ( ordered_pair @ SV655 @ ( sK47_K @ SY1500 @ SV686 @ SV655 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV686 != SY1500 )
| ~ ( in @ SV655 @ SY1500 ) ) )
= $true )
| ( ( in @ SV655 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4003]) ).
thf(4093,plain,
! [SV145: $i,SV265: $i,SV656: $i] :
( ( ( ~ ( in @ ( sK45_E @ SV656 @ SV265 @ SV145 ) @ SV145 ) )
= $false )
| ( ( in @ SV656 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4004]) ).
thf(4094,plain,
! [SV145: $i,SV265: $i,SV656: $i] :
( ( ( ~ ~ ( ~ ! [SY1467: $i] :
( ~ ( in @ SY1467 @ ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV656 @ SY1467 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV656 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) )
| ~ ( in @ SV656 @ ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) ) ) ) )
= $false )
| ( ( in @ SV656 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4004]) ).
thf(4095,plain,
! [SV147: $i,SV464: $i,SV404: $i,SV666: $i] :
( ( ( in @ SV666 @ SV404 )
= $false )
| ( ( in @ SV666 @ SV464 )
= $false )
| ( ( SV464
= ( set_difference @ SV147 @ SV404 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4006]) ).
thf(4096,plain,
! [SV151: $i,SV267: $i,SV467: $i,SV502: $i] :
( ( ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 ) )
= $true )
| ( ( ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV151 ) )
= $true )
| ( ( SV502
= ( unordered_triple @ SV151 @ SV267 @ SV467 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4008]) ).
thf(4097,plain,
! [SV151: $i,SV267: $i,SV467: $i,SV502: $i] :
( ( ( ~ ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 ) )
= $true )
| ( ( ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV267 ) )
= $true )
| ( ( SV502
= ( unordered_triple @ SV151 @ SV267 @ SV467 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4009]) ).
thf(4098,plain,
! [SV267: $i,SV151: $i,SV503: $i,SV468: $i,SV687: $i] :
( ( ( SV687 = SV468 )
= $false )
| ( ( in @ SV687 @ SV503 )
= $true )
| ( ( SV503
= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4011]) ).
thf(4099,plain,
! [SV468: $i,SV267: $i,SV503: $i,SV151: $i] :
( ( ( ! [SY1381: $i] :
( ( SY1381 != SV151 )
| ( in @ SY1381 @ SV503 ) ) )
= $true )
| ( ( SV503
= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4012]) ).
thf(4100,plain,
! [SV468: $i,SV151: $i,SV503: $i,SV267: $i] :
( ( ( ! [SY1382: $i] :
( ( SY1382 != SV267 )
| ( in @ SY1382 @ SV503 ) ) )
= $true )
| ( ( SV503
= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4013]) ).
thf(4101,plain,
! [SV155: $i,SV268: $i,SV547: $i] :
( ( ( ~ ( in @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ SV547 ) )
= $true )
| ( ( ~ ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SV547 @ SV268 @ SV155 ) ) @ SV268 ) )
= $true )
| ( ( SV547
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $true )
| ( ( element @ SV547 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4014]) ).
thf(4102,plain,
! [SV155: $i,SV268: $i,SV547: $i] :
( ( ( in @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ SV547 )
= $true )
| ( ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SV547 @ SV268 @ SV155 ) ) @ SV268 )
= $true )
| ( ( SV547
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $true )
| ( ( element @ SV547 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4015]) ).
thf(4103,plain,
! [SV268: $i,SV548: $i,SV155: $i,SV688: $i] :
( ( ( element @ SV688 @ ( powerset @ SV155 ) )
= $false )
| ( ( ~ ( in @ SV688 @ SV548 )
| ( in @ ( subset_complement @ SV155 @ SV688 ) @ SV268 ) )
= $true )
| ( ( SV548
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $false )
| ( ( element @ SV548 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4016]) ).
thf(4104,plain,
! [SV548: $i,SV268: $i,SV155: $i,SV689: $i] :
( ( ( element @ SV689 @ ( powerset @ SV155 ) )
= $false )
| ( ( ~ ( in @ ( subset_complement @ SV155 @ SV689 ) @ SV268 )
| ( in @ SV689 @ SV548 ) )
= $true )
| ( ( SV548
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $false )
| ( ( element @ SV548 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4017]) ).
thf(4105,plain,
! [SV633: $i,SV615: $i,SV158: $i] :
( ( ( SV158
= ( relation_dom_as_subset @ SV158 @ SV615 @ SV633 ) )
= $false )
| ( ( quasi_total @ SV633 @ SV158 @ SV615 )
= $true )
| ( ( SV158 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV633 @ SV158 @ SV615 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4024]) ).
thf(4106,plain,
! [SV616: $i,SV158: $i,SV634: $i] :
( ( ( quasi_total @ SV634 @ SV158 @ SV616 )
= $false )
| ( ( SV158
= ( relation_dom_as_subset @ SV158 @ SV616 @ SV634 ) )
= $true )
| ( ( SV158 = empty_set )
= $false )
| ( ( relation_of2_as_subset @ SV634 @ SV158 @ SV616 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4025]) ).
thf(4107,plain,
! [SV512: $i,SV572: $i] :
( ( ( in @ ( sK89_C @ SV572 @ SV512 ) @ SV572 )
= $false )
| ( ( in @ ( sK90_SY733 @ SV572 @ SV512 ) @ SV512 )
= $true )
| ( ( SV572
= ( set_meet @ SV512 ) )
= $true )
| ( ( SV512 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4026]) ).
thf(4108,plain,
! [SV512: $i,SV572: $i] :
( ( ( in @ ( sK89_C @ SV572 @ SV512 ) @ ( sK90_SY733 @ SV572 @ SV512 ) )
= $false )
| ( ( ~ ( in @ ( sK89_C @ SV572 @ SV512 ) @ SV572 ) )
= $true )
| ( ( SV572
= ( set_meet @ SV512 ) )
= $true )
| ( ( SV512 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4027]) ).
thf(4109,plain,
! [SV513: $i,SV573: $i,SV668: $i] :
( ( ( ~ ( in @ ( sK88_D @ SV668 @ SV573 @ SV513 ) @ SV513 ) )
= $false )
| ( ( in @ SV668 @ SV573 )
= $true )
| ( ( SV573
= ( set_meet @ SV513 ) )
= $false )
| ( ( SV513 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4029]) ).
thf(4110,plain,
! [SV513: $i,SV573: $i,SV668: $i] :
( ( ( ~ ~ ( in @ SV668 @ ( sK88_D @ SV668 @ SV573 @ SV513 ) ) )
= $false )
| ( ( in @ SV668 @ SV573 )
= $true )
| ( ( SV573
= ( set_meet @ SV513 ) )
= $false )
| ( ( SV513 = empty_set )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4029]) ).
thf(4111,plain,
! [SV573: $i,SV669: $i,SV513: $i,SV696: $i] :
( ( ( ~ ( in @ SV696 @ SV513 )
| ( in @ SV669 @ SV696 ) )
= $true )
| ( ( in @ SV669 @ SV573 )
= $false )
| ( ( SV573
= ( set_meet @ SV513 ) )
= $false )
| ( ( SV513 = empty_set )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4030]) ).
thf(4112,plain,
! [SV648: $i,SV636: $i,SV164: $i,SV437: $i,SV474: $i] :
( ( ( ( sK78_D @ SV474 @ SV437 @ SV164 )
= ( ordered_pair @ SV636 @ SV648 ) )
= $false )
| ( ( in @ SV636 @ SV164 )
= $false )
| ( ( in @ SV648 @ SV437 )
= $false )
| ( ( ~ ( in @ ( sK78_D @ SV474 @ SV437 @ SV164 ) @ SV474 ) )
= $true )
| ( ( SV474
= ( cartesian_product2 @ SV164 @ SV437 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4033]) ).
thf(4113,plain,
! [SV475: $i,SV637: $i,SV438: $i,SV672: $i,SV164: $i,SV657: $i] :
( ( ( in @ SV657 @ SV164 )
= $false )
| ( ( ~ ( in @ SV672 @ SV438 ) )
= $true )
| ( ( ( SV637
!= ( ordered_pair @ SV657 @ SV672 ) ) )
= $true )
| ( ( in @ SV637 @ SV475 )
= $true )
| ( ( SV475
= ( cartesian_product2 @ SV164 @ SV438 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4036]) ).
thf(4114,plain,
! [SV164: $i,SV438: $i,SV475: $i,SV638: $i] :
( ( ( ~ ( in @ ( sK76_E @ SV638 @ SV475 @ SV438 @ SV164 ) @ SV164 )
| ~ ( in @ ( sK77_SY726 @ SV638 @ SV475 @ SV438 @ SV164 ) @ SV438 ) )
= $false )
| ( ( in @ SV638 @ SV475 )
= $false )
| ( ( SV475
= ( cartesian_product2 @ SV164 @ SV438 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4037]) ).
thf(4115,plain,
! [SV697: $i,SV168: $i] :
( ( ( ! [SY1514: $i] :
( ~ ( in @ SY1514 @ SV168 )
| ( SV697
!= ( singleton @ SY1514 ) ) )
| ( in @ SV697 @ ( sK24_B @ SV168 ) ) )
= $true )
| ( ( ( sK27_SY634 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4039]) ).
thf(4116,plain,
! [SV168: $i,SV698: $i] :
( ( ( ~ ( in @ SV698 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SV698 @ SV168 ) @ SV168 )
| ( SV698
!= ( singleton @ ( sK25_D @ SV698 @ SV168 ) ) ) ) )
= $true )
| ( ( ( sK27_SY634 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4040]) ).
thf(4117,plain,
! [SV699: $i,SV168: $i] :
( ( ( ! [SY1515: $i] :
( ~ ( in @ SY1515 @ SV168 )
| ( SV699
!= ( singleton @ SY1515 ) ) )
| ( in @ SV699 @ ( sK24_B @ SV168 ) ) )
= $true )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4041]) ).
thf(4118,plain,
! [SV168: $i,SV700: $i] :
( ( ( ~ ( in @ SV700 @ ( sK24_B @ SV168 ) )
| ~ ( ~ ( in @ ( sK25_D @ SV700 @ SV168 ) @ SV168 )
| ( SV700
!= ( singleton @ ( sK25_D @ SV700 @ SV168 ) ) ) ) )
= $true )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4042]) ).
thf(4119,plain,
! [SV673: $i,SV168: $i,SV693: $i] :
( ( ( ~ ( in @ SV693 @ SV168 ) )
= $true )
| ( ( ( SV673
!= ( singleton @ SV693 ) ) )
= $true )
| ( ( in @ SV673 @ ( sK24_B @ SV168 ) )
= $true )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4043]) ).
thf(4120,plain,
! [SV168: $i,SV674: $i] :
( ( ( ~ ( in @ ( sK25_D @ SV674 @ SV168 ) @ SV168 )
| ( SV674
!= ( singleton @ ( sK25_D @ SV674 @ SV168 ) ) ) )
= $false )
| ( ( in @ SV674 @ ( sK24_B @ SV168 ) )
= $false )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4044]) ).
thf(4121,plain,
! [SV271: $i,SV481: $i,SV596: $i,SV659: $i,SV170: $i,SV651: $i] :
( ( ( in @ SV651 @ SV170 )
= $false )
| ( ( ( ordered_pair @ SV651 @ SV659 )
= SV596 )
= $false )
| ( ( ! [SY1469: $i] :
( ~ ( ~ ( in @ ( sK115_I @ SY1469 @ SV659 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) @ SY1469 )
| ~ ~ ( in @ ( ordered_pair @ SV659 @ ( sK115_I @ SY1469 @ SV659 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) ) @ SV271 ) )
| ( SV651 != SY1469 )
| ~ ( in @ SV659 @ SY1469 ) ) )
= $true )
| ( ( ~ ( in @ SV596 @ ( cartesian_product2 @ SV170 @ SV481 ) ) )
= $true )
| ( ( in @ SV596 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4048]) ).
thf(4122,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV652: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK112_F @ SV652 @ SV481 @ SV271 @ SV170 ) @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) )
!= SV652 )
| ~ ( in @ ( sK112_F @ SV652 @ SV481 @ SV271 @ SV170 ) @ SV170 ) ) )
= $true )
| ( ( in @ SV652 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $false )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4049]) ).
thf(4123,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV652: $i] :
( ( ( ~ ( ~ ! [SY1464: $i] :
( ~ ( in @ SY1464 @ ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) )
| ( in @ ( ordered_pair @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) @ SY1464 ) @ SV271 ) )
| ~ ~ ( ( ( sK112_F @ SV652 @ SV481 @ SV271 @ SV170 )
!= ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) )
| ~ ( in @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) @ ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) ) ) ) )
= $true )
| ( ( in @ SV652 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $false )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4050]) ).
thf(4124,plain,
! [SV525: $i,SV171: $i,SV690: $i,SV675: $i] :
( ( ( in @ ( ordered_pair @ SV675 @ SV690 ) @ SV171 )
= $false )
| ( ( in @ ( ordered_pair @ SV675 @ SV690 ) @ SV525 )
= $true )
| ( ( SV171 = SV525 )
= $false )
| ( ( relation @ SV525 )
= $false )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4053]) ).
thf(4125,plain,
! [SV171: $i,SV525: $i,SV691: $i,SV676: $i] :
( ( ( in @ ( ordered_pair @ SV676 @ SV691 ) @ SV525 )
= $false )
| ( ( in @ ( ordered_pair @ SV676 @ SV691 ) @ SV171 )
= $true )
| ( ( SV171 = SV525 )
= $false )
| ( ( relation @ SV525 )
= $false )
| ( ( relation @ SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4054]) ).
thf(4126,plain,
! [SV172: $i,SV272: $i] :
( ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4055]) ).
thf(4127,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1178: $i] :
( ~ ( in @ SY1178 @ ( sK43_SY691 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SY1178 ) @ SV272 ) )
| ~ ~ ( ( ( sK41_SY666 @ SV272 @ SV172 )
!= ( sK43_SY691 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) ) ) ) ) )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4056]) ).
thf(4128,plain,
! [SV272: $i,SV692: $i,SV172: $i] :
( ( ( ~ ! [SY1501: $i] :
( ! [SY1502: $i] :
( ( SY1502 != SY1501 )
| ~ ( in @ SY1502 @ ( cartesian_product2 @ SV172 @ SV692 ) ) )
| ! [SY1503: $i,SY1504: $i] :
( ( ( ordered_pair @ SY1503 @ SY1504 )
!= SY1501 )
| ~ ( in @ SY1503 @ SV172 )
| ! [SY1505: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1505 @ SY1504 @ SY1503 @ SY1501 @ SV692 @ SV272 @ SV172 ) @ SY1505 )
| ~ ~ ( in @ ( ordered_pair @ SY1504 @ ( sK34_R @ SY1505 @ SY1504 @ SY1503 @ SY1501 @ SV692 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1503 != SY1505 )
| ~ ( in @ SY1504 @ SY1505 ) ) )
| ( in @ SY1501 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4057]) ).
thf(4129,plain,
! [SV172: $i,SV272: $i,SV692: $i] :
( ( ( ~ ! [SY1506: $i] :
( ~ ( in @ SY1506 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1506 @ SV692 @ SV272 @ SV172 )
!= SY1506 )
| ~ ( in @ ( sK33_F @ SY1506 @ SV692 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV692 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1506 @ SV692 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1506 @ SV692 @ SV272 @ SV172 ) )
!= SY1506 )
| ~ ( in @ ( sK30_O @ SY1506 @ SV692 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1507: $i] :
( ~ ( in @ SY1507 @ ( sK32_SY652 @ SY1506 @ SV692 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1506 @ SV692 @ SV272 @ SV172 ) @ SY1507 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1506 @ SV692 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1506 @ SV692 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1506 @ SV692 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1506 @ SV692 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4057]) ).
thf(4130,plain,
! [SV172: $i,SV272: $i] :
( ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4058]) ).
thf(4131,plain,
! [SV172: $i,SV272: $i] :
( ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4059]) ).
thf(4132,plain,
! [SV172: $i,SV272: $i] :
( ( ( ! [SY1179: $i] :
( ~ ( in @ SY1179 @ ( sK40_SY685 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SY1179 ) @ SV272 ) ) )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4060]) ).
thf(4133,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ( ( ( sK38_SY678 @ SV272 @ SV172 )
!= ( sK40_SY685 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) ) ) )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4061]) ).
thf(4134,plain,
! [SV272: $i,SV622: $i,SV172: $i,SV677: $i,SV701: $i] :
( ( ( ( SV701 != SV677 )
| ~ ( in @ SV701 @ ( cartesian_product2 @ SV172 @ SV622 ) ) )
= $true )
| ( ( ! [SY1490: $i,SY1491: $i] :
( ( ( ordered_pair @ SY1490 @ SY1491 )
!= SV677 )
| ~ ( in @ SY1490 @ SV172 )
| ! [SY1492: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1492 @ SY1491 @ SY1490 @ SV677 @ SV622 @ SV272 @ SV172 ) @ SY1492 )
| ~ ~ ( in @ ( ordered_pair @ SY1491 @ ( sK34_R @ SY1492 @ SY1491 @ SY1490 @ SV677 @ SV622 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1490 != SY1492 )
| ~ ( in @ SY1491 @ SY1492 ) ) ) )
= $true )
| ( ( in @ SV677 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4062]) ).
thf(4135,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( ~ ~ ( ( ( sK33_F @ SV678 @ SV622 @ SV272 @ SV172 )
!= SV678 )
| ~ ( in @ ( sK33_F @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV622 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) )
!= SV678 )
| ~ ( in @ ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1493: $i] :
( ~ ( in @ SY1493 @ ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) @ SY1493 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) ) ) ) ) )
= $false )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4063]) ).
thf(4136,plain,
! [SV660: $i,SV139: $i,SV702: $i] :
( ( ( ! [SY1516: $i] :
( ( SY1516 != SV702 )
| ~ ( in @ SY1516 @ ( cartesian_product2 @ SV139 @ SV660 ) ) )
| ! [SY1517: $i,SY1518: $i] :
( ( ( ordered_pair @ SY1517 @ SY1518 )
!= SV702 )
| ~ ( in @ SY1517 @ SV139 )
| ( SY1518
!= ( singleton @ SY1517 ) ) )
| ( in @ SV702 @ ( sK13_C @ SV660 @ SV139 ) ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4068]) ).
thf(4137,plain,
! [SV139: $i,SV660: $i,SV703: $i] :
( ( ( ~ ( in @ SV703 @ ( sK13_C @ SV660 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SV703 @ SV660 @ SV139 )
!= SV703 )
| ~ ( in @ ( sK16_E @ SV703 @ SV660 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV660 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV703 @ SV660 @ SV139 ) @ ( sK15_SY612 @ SV703 @ SV660 @ SV139 ) )
!= SV703 )
| ~ ( in @ ( sK14_J @ SV703 @ SV660 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV703 @ SV660 @ SV139 )
!= ( singleton @ ( sK14_J @ SV703 @ SV660 @ SV139 ) ) ) ) ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4069]) ).
thf(4138,plain,
! [SV139: $i] :
( ( ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
!= ( sK18_SY613 @ SV139 ) ) )
= $false )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4070]) ).
thf(4139,plain,
! [SV139: $i] :
( ( ( ~ ( in @ ( sK22_SY620 @ SV139 ) @ SV139 ) )
= $false )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4070]) ).
thf(4140,plain,
! [SV694: $i,SV139: $i] :
( ( ( ~ ! [SY1508: $i] :
( ! [SY1509: $i] :
( ( SY1509 != SY1508 )
| ~ ( in @ SY1509 @ ( cartesian_product2 @ SV139 @ SV694 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1508 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1508 @ ( sK13_C @ SV694 @ SV139 ) ) )
| ~ ! [SY1512: $i] :
( ~ ( in @ SY1512 @ ( sK13_C @ SV694 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1512 @ SV694 @ SV139 )
!= SY1512 )
| ~ ( in @ ( sK16_E @ SY1512 @ SV694 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV694 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1512 @ SV694 @ SV139 ) @ ( sK15_SY612 @ SY1512 @ SV694 @ SV139 ) )
!= SY1512 )
| ~ ( in @ ( sK14_J @ SY1512 @ SV694 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1512 @ SV694 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1512 @ SV694 @ SV139 ) ) ) ) ) ) )
= $false )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4071]) ).
thf(4141,plain,
! [SV624: $i,SV139: $i,SV681: $i,SV704: $i] :
( ( ( ( SV704 != SV681 )
| ~ ( in @ SV704 @ ( cartesian_product2 @ SV139 @ SV624 ) ) )
= $true )
| ( ( ! [SY1495: $i,SY1496: $i] :
( ( ( ordered_pair @ SY1495 @ SY1496 )
!= SV681 )
| ~ ( in @ SY1495 @ SV139 )
| ( SY1496
!= ( singleton @ SY1495 ) ) ) )
= $true )
| ( ( in @ SV681 @ ( sK13_C @ SV624 @ SV139 ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4072]) ).
thf(4142,plain,
! [SV139: $i,SV624: $i,SV682: $i] :
( ( ( ~ ~ ( ( ( sK16_E @ SV682 @ SV624 @ SV139 )
!= SV682 )
| ~ ( in @ ( sK16_E @ SV682 @ SV624 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV624 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV682 @ SV624 @ SV139 ) @ ( sK15_SY612 @ SV682 @ SV624 @ SV139 ) )
!= SV682 )
| ~ ( in @ ( sK14_J @ SV682 @ SV624 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV682 @ SV624 @ SV139 )
!= ( singleton @ ( sK14_J @ SV682 @ SV624 @ SV139 ) ) ) ) )
= $false )
| ( ( in @ SV682 @ ( sK13_C @ SV624 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4073]) ).
thf(4143,plain,
! [SV661: $i,SV139: $i,SV705: $i] :
( ( ( ! [SY1519: $i] :
( ( SY1519 != SV705 )
| ~ ( in @ SY1519 @ ( cartesian_product2 @ SV139 @ SV661 ) ) )
| ! [SY1520: $i,SY1521: $i] :
( ( ( ordered_pair @ SY1520 @ SY1521 )
!= SV705 )
| ~ ( in @ SY1520 @ SV139 )
| ( SY1521
!= ( singleton @ SY1520 ) ) )
| ( in @ SV705 @ ( sK13_C @ SV661 @ SV139 ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4074]) ).
thf(4144,plain,
! [SV139: $i,SV661: $i,SV706: $i] :
( ( ( ~ ( in @ SV706 @ ( sK13_C @ SV661 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SV706 @ SV661 @ SV139 )
!= SV706 )
| ~ ( in @ ( sK16_E @ SV706 @ SV661 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV661 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV706 @ SV661 @ SV139 ) @ ( sK15_SY612 @ SV706 @ SV661 @ SV139 ) )
!= SV706 )
| ~ ( in @ ( sK14_J @ SV706 @ SV661 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV706 @ SV661 @ SV139 )
!= ( singleton @ ( sK14_J @ SV706 @ SV661 @ SV139 ) ) ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4075]) ).
thf(4145,plain,
! [SV662: $i,SV139: $i,SV707: $i] :
( ( ( ! [SY1522: $i] :
( ( SY1522 != SV707 )
| ~ ( in @ SY1522 @ ( cartesian_product2 @ SV139 @ SV662 ) ) )
| ! [SY1523: $i,SY1524: $i] :
( ( ( ordered_pair @ SY1523 @ SY1524 )
!= SV707 )
| ~ ( in @ SY1523 @ SV139 )
| ( SY1524
!= ( singleton @ SY1523 ) ) )
| ( in @ SV707 @ ( sK13_C @ SV662 @ SV139 ) ) )
= $true )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4076]) ).
thf(4146,plain,
! [SV139: $i,SV662: $i,SV708: $i] :
( ( ( ~ ( in @ SV708 @ ( sK13_C @ SV662 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SV708 @ SV662 @ SV139 )
!= SV708 )
| ~ ( in @ ( sK16_E @ SV708 @ SV662 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV662 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV708 @ SV662 @ SV139 ) @ ( sK15_SY612 @ SV708 @ SV662 @ SV139 ) )
!= SV708 )
| ~ ( in @ ( sK14_J @ SV708 @ SV662 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV708 @ SV662 @ SV139 )
!= ( singleton @ ( sK14_J @ SV708 @ SV662 @ SV139 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4077]) ).
thf(4147,plain,
! [SV625: $i,SV139: $i,SV683: $i,SV709: $i] :
( ( ( ( SV709 != SV683 )
| ~ ( in @ SV709 @ ( cartesian_product2 @ SV139 @ SV625 ) ) )
= $true )
| ( ( ! [SY1498: $i,SY1499: $i] :
( ( ( ordered_pair @ SY1498 @ SY1499 )
!= SV683 )
| ~ ( in @ SY1498 @ SV139 )
| ( SY1499
!= ( singleton @ SY1498 ) ) ) )
= $true )
| ( ( in @ SV683 @ ( sK13_C @ SV625 @ SV139 ) )
= $true )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4078]) ).
thf(4148,plain,
! [SV139: $i,SV625: $i,SV684: $i] :
( ( ( ~ ~ ( ( ( sK16_E @ SV684 @ SV625 @ SV139 )
!= SV684 )
| ~ ( in @ ( sK16_E @ SV684 @ SV625 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV625 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV684 @ SV625 @ SV139 ) @ ( sK15_SY612 @ SV684 @ SV625 @ SV139 ) )
!= SV684 )
| ~ ( in @ ( sK14_J @ SV684 @ SV625 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV684 @ SV625 @ SV139 )
!= ( singleton @ ( sK14_J @ SV684 @ SV625 @ SV139 ) ) ) ) )
= $false )
| ( ( in @ SV684 @ ( sK13_C @ SV625 @ SV139 ) )
= $false )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4079]) ).
thf(4149,plain,
! [SV488: $i,SV654: $i,SV139: $i,SV603: $i,SV710: $i,SV695: $i] :
( ( ( ( ( ordered_pair @ SV695 @ SV710 )
!= SV603 )
| ~ ( in @ SV695 @ SV139 )
| ( SV710
!= ( singleton @ SV695 ) ) )
= $true )
| ( ( SV654 = SV603 )
= $false )
| ( ( in @ SV654 @ ( cartesian_product2 @ SV139 @ SV488 ) )
= $false )
| ( ( in @ SV603 @ ( sK13_C @ SV488 @ SV139 ) )
= $true )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4080]) ).
thf(4150,plain,
! [SV139: $i,SV488: $i,SV604: $i] :
( ( ( ( sK16_E @ SV604 @ SV488 @ SV139 )
= SV604 )
= $true )
| ( ( in @ SV604 @ ( sK13_C @ SV488 @ SV139 ) )
= $false )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4081]) ).
thf(4151,plain,
! [SV139: $i,SV488: $i,SV604: $i] :
( ( ( in @ ( sK16_E @ SV604 @ SV488 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV488 ) )
= $true )
| ( ( in @ SV604 @ ( sK13_C @ SV488 @ SV139 ) )
= $false )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4082]) ).
thf(4152,plain,
! [SV139: $i,SV488: $i,SV604: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK14_J @ SV604 @ SV488 @ SV139 ) @ ( sK15_SY612 @ SV604 @ SV488 @ SV139 ) )
!= SV604 )
| ~ ( in @ ( sK14_J @ SV604 @ SV488 @ SV139 ) @ SV139 ) ) )
= $true )
| ( ( in @ SV604 @ ( sK13_C @ SV488 @ SV139 ) )
= $false )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4083]) ).
thf(4153,plain,
! [SV139: $i,SV488: $i,SV604: $i] :
( ( ( ( sK15_SY612 @ SV604 @ SV488 @ SV139 )
= ( singleton @ ( sK14_J @ SV604 @ SV488 @ SV139 ) ) )
= $true )
| ( ( in @ SV604 @ ( sK13_C @ SV488 @ SV139 ) )
= $false )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4084]) ).
thf(4154,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ! [SY1142: $i] :
( ~ ( in @ SY1142 @ ( sK52_SY712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SY1142 ) @ SV265 ) )
| ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK52_SY712 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4085]) ).
thf(4155,plain,
! [SV265: $i,SV145: $i] :
( ( ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4086]) ).
thf(4156,plain,
! [SV265: $i,SV711: $i,SV145: $i] :
( ( ( ! [SY1525: $i] :
( ~ ( in @ SY1525 @ SV145 )
| ! [SY1526: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1526 @ SY1525 @ SV711 @ SV265 @ SV145 ) @ SY1526 )
| ~ ~ ( in @ ( ordered_pair @ SV711 @ ( sK47_K @ SY1526 @ SY1525 @ SV711 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1525 != SY1526 )
| ~ ( in @ SV711 @ SY1526 ) ) )
| ( in @ SV711 @ ( sK44_C @ SV265 @ SV145 ) ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4087]) ).
thf(4157,plain,
! [SV145: $i,SV265: $i,SV712: $i] :
( ( ( ~ ( in @ SV712 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SV712 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1527: $i] :
( ~ ( in @ SY1527 @ ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV712 @ SY1527 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV712 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) )
| ~ ( in @ SV712 @ ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4088]) ).
thf(4158,plain,
! [SV685: $i,SV265: $i,SV145: $i] :
( ( ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4089]) ).
thf(4159,plain,
! [SV265: $i,SV145: $i] :
( ( ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4090]) ).
thf(4160,plain,
! [SV265: $i,SV145: $i] :
( ( ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4091]) ).
thf(4161,plain,
! [SV145: $i,SV265: $i,SV655: $i,SV686: $i,SV713: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_K @ SV713 @ SV686 @ SV655 @ SV265 @ SV145 ) @ SV713 )
| ~ ~ ( in @ ( ordered_pair @ SV655 @ ( sK47_K @ SV713 @ SV686 @ SV655 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV686 != SV713 )
| ~ ( in @ SV655 @ SV713 ) )
= $true )
| ( ( in @ SV686 @ SV145 )
= $false )
| ( ( in @ SV655 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4092]) ).
thf(4162,plain,
! [SV145: $i,SV265: $i,SV656: $i] :
( ( ( in @ ( sK45_E @ SV656 @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( in @ SV656 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4093]) ).
thf(4163,plain,
! [SV145: $i,SV265: $i,SV656: $i] :
( ( ( ~ ( ~ ! [SY1467: $i] :
( ~ ( in @ SY1467 @ ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV656 @ SY1467 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV656 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) )
| ~ ( in @ SV656 @ ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) ) ) ) )
= $true )
| ( ( in @ SV656 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4094]) ).
thf(4164,plain,
! [SV151: $i,SV267: $i,SV467: $i,SV502: $i] :
( ( ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
= $false )
| ( ( ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV151 ) )
= $true )
| ( ( SV502
= ( unordered_triple @ SV151 @ SV267 @ SV467 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4096]) ).
thf(4165,plain,
! [SV151: $i,SV267: $i,SV467: $i,SV502: $i] :
( ( ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
= $false )
| ( ( ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
!= SV267 ) )
= $true )
| ( ( SV502
= ( unordered_triple @ SV151 @ SV267 @ SV467 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4097]) ).
thf(4166,plain,
! [SV468: $i,SV267: $i,SV503: $i,SV151: $i,SV714: $i] :
( ( ( ( SV714 != SV151 )
| ( in @ SV714 @ SV503 ) )
= $true )
| ( ( SV503
= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4099]) ).
thf(4167,plain,
! [SV468: $i,SV151: $i,SV503: $i,SV267: $i,SV715: $i] :
( ( ( ( SV715 != SV267 )
| ( in @ SV715 @ SV503 ) )
= $true )
| ( ( SV503
= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4100]) ).
thf(4168,plain,
! [SV155: $i,SV268: $i,SV547: $i] :
( ( ( in @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ SV547 )
= $false )
| ( ( ~ ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SV547 @ SV268 @ SV155 ) ) @ SV268 ) )
= $true )
| ( ( SV547
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $true )
| ( ( element @ SV547 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4101]) ).
thf(4169,plain,
! [SV268: $i,SV155: $i,SV548: $i,SV688: $i] :
( ( ( ~ ( in @ SV688 @ SV548 ) )
= $true )
| ( ( in @ ( subset_complement @ SV155 @ SV688 ) @ SV268 )
= $true )
| ( ( element @ SV688 @ ( powerset @ SV155 ) )
= $false )
| ( ( SV548
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $false )
| ( ( element @ SV548 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4103]) ).
thf(4170,plain,
! [SV548: $i,SV268: $i,SV689: $i,SV155: $i] :
( ( ( ~ ( in @ ( subset_complement @ SV155 @ SV689 ) @ SV268 ) )
= $true )
| ( ( in @ SV689 @ SV548 )
= $true )
| ( ( element @ SV689 @ ( powerset @ SV155 ) )
= $false )
| ( ( SV548
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $false )
| ( ( element @ SV548 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4104]) ).
thf(4171,plain,
! [SV512: $i,SV572: $i] :
( ( ( in @ ( sK89_C @ SV572 @ SV512 ) @ SV572 )
= $false )
| ( ( in @ ( sK89_C @ SV572 @ SV512 ) @ ( sK90_SY733 @ SV572 @ SV512 ) )
= $false )
| ( ( SV572
= ( set_meet @ SV512 ) )
= $true )
| ( ( SV512 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4108]) ).
thf(4172,plain,
! [SV513: $i,SV573: $i,SV668: $i] :
( ( ( in @ ( sK88_D @ SV668 @ SV573 @ SV513 ) @ SV513 )
= $true )
| ( ( in @ SV668 @ SV573 )
= $true )
| ( ( SV573
= ( set_meet @ SV513 ) )
= $false )
| ( ( SV513 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4109]) ).
thf(4173,plain,
! [SV513: $i,SV573: $i,SV668: $i] :
( ( ( ~ ( in @ SV668 @ ( sK88_D @ SV668 @ SV573 @ SV513 ) ) )
= $true )
| ( ( in @ SV668 @ SV573 )
= $true )
| ( ( SV573
= ( set_meet @ SV513 ) )
= $false )
| ( ( SV513 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4110]) ).
thf(4174,plain,
! [SV573: $i,SV669: $i,SV513: $i,SV696: $i] :
( ( ( ~ ( in @ SV696 @ SV513 ) )
= $true )
| ( ( in @ SV669 @ SV696 )
= $true )
| ( ( in @ SV669 @ SV573 )
= $false )
| ( ( SV573
= ( set_meet @ SV513 ) )
= $false )
| ( ( SV513 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4111]) ).
thf(4175,plain,
! [SV636: $i,SV648: $i,SV164: $i,SV437: $i,SV474: $i] :
( ( ( in @ ( sK78_D @ SV474 @ SV437 @ SV164 ) @ SV474 )
= $false )
| ( ( in @ SV648 @ SV437 )
= $false )
| ( ( in @ SV636 @ SV164 )
= $false )
| ( ( ( sK78_D @ SV474 @ SV437 @ SV164 )
= ( ordered_pair @ SV636 @ SV648 ) )
= $false )
| ( ( SV474
= ( cartesian_product2 @ SV164 @ SV437 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4112]) ).
thf(4176,plain,
! [SV475: $i,SV637: $i,SV164: $i,SV657: $i,SV438: $i,SV672: $i] :
( ( ( in @ SV672 @ SV438 )
= $false )
| ( ( in @ SV657 @ SV164 )
= $false )
| ( ( ( SV637
!= ( ordered_pair @ SV657 @ SV672 ) ) )
= $true )
| ( ( in @ SV637 @ SV475 )
= $true )
| ( ( SV475
= ( cartesian_product2 @ SV164 @ SV438 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4113]) ).
thf(4177,plain,
! [SV164: $i,SV438: $i,SV475: $i,SV638: $i] :
( ( ( ~ ( in @ ( sK76_E @ SV638 @ SV475 @ SV438 @ SV164 ) @ SV164 ) )
= $false )
| ( ( in @ SV638 @ SV475 )
= $false )
| ( ( SV475
= ( cartesian_product2 @ SV164 @ SV438 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4114]) ).
thf(4178,plain,
! [SV164: $i,SV438: $i,SV475: $i,SV638: $i] :
( ( ( ~ ( in @ ( sK77_SY726 @ SV638 @ SV475 @ SV438 @ SV164 ) @ SV438 ) )
= $false )
| ( ( in @ SV638 @ SV475 )
= $false )
| ( ( SV475
= ( cartesian_product2 @ SV164 @ SV438 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4114]) ).
thf(4179,plain,
! [SV697: $i,SV168: $i] :
( ( ( ! [SY1514: $i] :
( ~ ( in @ SY1514 @ SV168 )
| ( SV697
!= ( singleton @ SY1514 ) ) ) )
= $true )
| ( ( in @ SV697 @ ( sK24_B @ SV168 ) )
= $true )
| ( ( ( sK27_SY634 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4115]) ).
thf(4180,plain,
! [SV168: $i,SV698: $i] :
( ( ( ~ ( in @ SV698 @ ( sK24_B @ SV168 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK25_D @ SV698 @ SV168 ) @ SV168 )
| ( SV698
!= ( singleton @ ( sK25_D @ SV698 @ SV168 ) ) ) ) )
= $true )
| ( ( ( sK27_SY634 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4116]) ).
thf(4181,plain,
! [SV699: $i,SV168: $i] :
( ( ( ! [SY1515: $i] :
( ~ ( in @ SY1515 @ SV168 )
| ( SV699
!= ( singleton @ SY1515 ) ) ) )
= $true )
| ( ( in @ SV699 @ ( sK24_B @ SV168 ) )
= $true )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4117]) ).
thf(4182,plain,
! [SV168: $i,SV700: $i] :
( ( ( ~ ( in @ SV700 @ ( sK24_B @ SV168 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK25_D @ SV700 @ SV168 ) @ SV168 )
| ( SV700
!= ( singleton @ ( sK25_D @ SV700 @ SV168 ) ) ) ) )
= $true )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4118]) ).
thf(4183,plain,
! [SV673: $i,SV168: $i,SV693: $i] :
( ( ( in @ SV693 @ SV168 )
= $false )
| ( ( ( SV673
!= ( singleton @ SV693 ) ) )
= $true )
| ( ( in @ SV673 @ ( sK24_B @ SV168 ) )
= $true )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4119]) ).
thf(4184,plain,
! [SV168: $i,SV674: $i] :
( ( ( ~ ( in @ ( sK25_D @ SV674 @ SV168 ) @ SV168 ) )
= $false )
| ( ( in @ SV674 @ ( sK24_B @ SV168 ) )
= $false )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4120]) ).
thf(4185,plain,
! [SV168: $i,SV674: $i] :
( ( ( ( SV674
!= ( singleton @ ( sK25_D @ SV674 @ SV168 ) ) ) )
= $false )
| ( ( in @ SV674 @ ( sK24_B @ SV168 ) )
= $false )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4120]) ).
thf(4186,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV596: $i,SV651: $i,SV659: $i,SV716: $i] :
( ( ( ~ ( ~ ( in @ ( sK115_I @ SV716 @ SV659 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) @ SV716 )
| ~ ~ ( in @ ( ordered_pair @ SV659 @ ( sK115_I @ SV716 @ SV659 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) ) @ SV271 ) )
| ( SV651 != SV716 )
| ~ ( in @ SV659 @ SV716 ) )
= $true )
| ( ( ( ordered_pair @ SV651 @ SV659 )
= SV596 )
= $false )
| ( ( in @ SV651 @ SV170 )
= $false )
| ( ( ~ ( in @ SV596 @ ( cartesian_product2 @ SV170 @ SV481 ) ) )
= $true )
| ( ( in @ SV596 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4121]) ).
thf(4187,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV652: $i] :
( ( ( ( ( ordered_pair @ ( sK112_F @ SV652 @ SV481 @ SV271 @ SV170 ) @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) )
!= SV652 )
| ~ ( in @ ( sK112_F @ SV652 @ SV481 @ SV271 @ SV170 ) @ SV170 ) )
= $false )
| ( ( in @ SV652 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $false )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4122]) ).
thf(4188,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV652: $i] :
( ( ( ~ ! [SY1464: $i] :
( ~ ( in @ SY1464 @ ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) )
| ( in @ ( ordered_pair @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) @ SY1464 ) @ SV271 ) )
| ~ ~ ( ( ( sK112_F @ SV652 @ SV481 @ SV271 @ SV170 )
!= ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) )
| ~ ( in @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) @ ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) ) ) )
= $false )
| ( ( in @ SV652 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $false )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4123]) ).
thf(4189,plain,
! [SV272: $i,SV717: $i,SV172: $i] :
( ( ( ~ ( ~ ! [SY1528: $i] :
( ! [SY1529: $i] :
( ( SY1529 != SY1528 )
| ~ ( in @ SY1529 @ ( cartesian_product2 @ SV172 @ SV717 ) ) )
| ! [SY1530: $i,SY1531: $i] :
( ( ( ordered_pair @ SY1530 @ SY1531 )
!= SY1528 )
| ~ ( in @ SY1530 @ SV172 )
| ! [SY1532: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1532 @ SY1531 @ SY1530 @ SY1528 @ SV717 @ SV272 @ SV172 ) @ SY1532 )
| ~ ~ ( in @ ( ordered_pair @ SY1531 @ ( sK34_R @ SY1532 @ SY1531 @ SY1530 @ SY1528 @ SV717 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1530 != SY1532 )
| ~ ( in @ SY1531 @ SY1532 ) ) )
| ( in @ SY1528 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) ) )
| ~ ! [SY1533: $i] :
( ~ ( in @ SY1533 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1533 @ SV717 @ SV272 @ SV172 )
!= SY1533 )
| ~ ( in @ ( sK33_F @ SY1533 @ SV717 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV717 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1533 @ SV717 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1533 @ SV717 @ SV272 @ SV172 ) )
!= SY1533 )
| ~ ( in @ ( sK30_O @ SY1533 @ SV717 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1534: $i] :
( ~ ( in @ SY1534 @ ( sK32_SY652 @ SY1533 @ SV717 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1533 @ SV717 @ SV272 @ SV172 ) @ SY1534 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1533 @ SV717 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1533 @ SV717 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1533 @ SV717 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1533 @ SV717 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4126]) ).
thf(4190,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1178: $i] :
( ~ ( in @ SY1178 @ ( sK43_SY691 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SY1178 ) @ SV272 ) )
| ~ ~ ( ( ( sK41_SY666 @ SV272 @ SV172 )
!= ( sK43_SY691 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) ) ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4127]) ).
thf(4191,plain,
! [SV272: $i,SV692: $i,SV172: $i] :
( ( ( ! [SY1501: $i] :
( ! [SY1502: $i] :
( ( SY1502 != SY1501 )
| ~ ( in @ SY1502 @ ( cartesian_product2 @ SV172 @ SV692 ) ) )
| ! [SY1503: $i,SY1504: $i] :
( ( ( ordered_pair @ SY1503 @ SY1504 )
!= SY1501 )
| ~ ( in @ SY1503 @ SV172 )
| ! [SY1505: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1505 @ SY1504 @ SY1503 @ SY1501 @ SV692 @ SV272 @ SV172 ) @ SY1505 )
| ~ ~ ( in @ ( ordered_pair @ SY1504 @ ( sK34_R @ SY1505 @ SY1504 @ SY1503 @ SY1501 @ SV692 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1503 != SY1505 )
| ~ ( in @ SY1504 @ SY1505 ) ) )
| ( in @ SY1501 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) ) ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4128]) ).
thf(4192,plain,
! [SV172: $i,SV272: $i,SV692: $i] :
( ( ( ! [SY1506: $i] :
( ~ ( in @ SY1506 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1506 @ SV692 @ SV272 @ SV172 )
!= SY1506 )
| ~ ( in @ ( sK33_F @ SY1506 @ SV692 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV692 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1506 @ SV692 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1506 @ SV692 @ SV272 @ SV172 ) )
!= SY1506 )
| ~ ( in @ ( sK30_O @ SY1506 @ SV692 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1507: $i] :
( ~ ( in @ SY1507 @ ( sK32_SY652 @ SY1506 @ SV692 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1506 @ SV692 @ SV272 @ SV172 ) @ SY1507 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1506 @ SV692 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1506 @ SV692 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1506 @ SV692 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1506 @ SV692 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4129]) ).
thf(4193,plain,
! [SV272: $i,SV718: $i,SV172: $i] :
( ( ( ~ ( ~ ! [SY1535: $i] :
( ! [SY1536: $i] :
( ( SY1536 != SY1535 )
| ~ ( in @ SY1536 @ ( cartesian_product2 @ SV172 @ SV718 ) ) )
| ! [SY1537: $i,SY1538: $i] :
( ( ( ordered_pair @ SY1537 @ SY1538 )
!= SY1535 )
| ~ ( in @ SY1537 @ SV172 )
| ! [SY1539: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1539 @ SY1538 @ SY1537 @ SY1535 @ SV718 @ SV272 @ SV172 ) @ SY1539 )
| ~ ~ ( in @ ( ordered_pair @ SY1538 @ ( sK34_R @ SY1539 @ SY1538 @ SY1537 @ SY1535 @ SV718 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1537 != SY1539 )
| ~ ( in @ SY1538 @ SY1539 ) ) )
| ( in @ SY1535 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) ) )
| ~ ! [SY1540: $i] :
( ~ ( in @ SY1540 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1540 @ SV718 @ SV272 @ SV172 )
!= SY1540 )
| ~ ( in @ ( sK33_F @ SY1540 @ SV718 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV718 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1540 @ SV718 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1540 @ SV718 @ SV272 @ SV172 ) )
!= SY1540 )
| ~ ( in @ ( sK30_O @ SY1540 @ SV718 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1541: $i] :
( ~ ( in @ SY1541 @ ( sK32_SY652 @ SY1540 @ SV718 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1540 @ SV718 @ SV272 @ SV172 ) @ SY1541 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1540 @ SV718 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1540 @ SV718 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1540 @ SV718 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1540 @ SV718 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4130]) ).
thf(4194,plain,
! [SV272: $i,SV719: $i,SV172: $i] :
( ( ( ~ ( ~ ! [SY1542: $i] :
( ! [SY1543: $i] :
( ( SY1543 != SY1542 )
| ~ ( in @ SY1543 @ ( cartesian_product2 @ SV172 @ SV719 ) ) )
| ! [SY1544: $i,SY1545: $i] :
( ( ( ordered_pair @ SY1544 @ SY1545 )
!= SY1542 )
| ~ ( in @ SY1544 @ SV172 )
| ! [SY1546: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1546 @ SY1545 @ SY1544 @ SY1542 @ SV719 @ SV272 @ SV172 ) @ SY1546 )
| ~ ~ ( in @ ( ordered_pair @ SY1545 @ ( sK34_R @ SY1546 @ SY1545 @ SY1544 @ SY1542 @ SV719 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1544 != SY1546 )
| ~ ( in @ SY1545 @ SY1546 ) ) )
| ( in @ SY1542 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) ) )
| ~ ! [SY1547: $i] :
( ~ ( in @ SY1547 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1547 @ SV719 @ SV272 @ SV172 )
!= SY1547 )
| ~ ( in @ ( sK33_F @ SY1547 @ SV719 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV719 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1547 @ SV719 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1547 @ SV719 @ SV272 @ SV172 ) )
!= SY1547 )
| ~ ( in @ ( sK30_O @ SY1547 @ SV719 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1548: $i] :
( ~ ( in @ SY1548 @ ( sK32_SY652 @ SY1547 @ SV719 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1547 @ SV719 @ SV272 @ SV172 ) @ SY1548 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1547 @ SV719 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1547 @ SV719 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1547 @ SV719 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1547 @ SV719 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4131]) ).
thf(4195,plain,
! [SV172: $i,SV272: $i,SV720: $i] :
( ( ( ~ ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 ) )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4132]) ).
thf(4196,plain,
! [SV172: $i,SV272: $i] :
( ( ( ( ( sK38_SY678 @ SV272 @ SV172 )
!= ( sK40_SY685 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4133]) ).
thf(4197,plain,
! [SV272: $i,SV622: $i,SV172: $i,SV677: $i,SV701: $i] :
( ( ( ( SV701 != SV677 ) )
= $true )
| ( ( ~ ( in @ SV701 @ ( cartesian_product2 @ SV172 @ SV622 ) ) )
= $true )
| ( ( ! [SY1490: $i,SY1491: $i] :
( ( ( ordered_pair @ SY1490 @ SY1491 )
!= SV677 )
| ~ ( in @ SY1490 @ SV172 )
| ! [SY1492: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1492 @ SY1491 @ SY1490 @ SV677 @ SV622 @ SV272 @ SV172 ) @ SY1492 )
| ~ ~ ( in @ ( ordered_pair @ SY1491 @ ( sK34_R @ SY1492 @ SY1491 @ SY1490 @ SV677 @ SV622 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1490 != SY1492 )
| ~ ( in @ SY1491 @ SY1492 ) ) ) )
= $true )
| ( ( in @ SV677 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4134]) ).
thf(4198,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( ~ ~ ( ( ( sK33_F @ SV678 @ SV622 @ SV272 @ SV172 )
!= SV678 )
| ~ ( in @ ( sK33_F @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV622 ) ) ) )
= $false )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4135]) ).
thf(4199,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) )
!= SV678 )
| ~ ( in @ ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1493: $i] :
( ~ ( in @ SY1493 @ ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) @ SY1493 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) ) ) ) ) )
= $false )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4135]) ).
thf(4200,plain,
! [SV660: $i,SV139: $i,SV702: $i] :
( ( ( ! [SY1516: $i] :
( ( SY1516 != SV702 )
| ~ ( in @ SY1516 @ ( cartesian_product2 @ SV139 @ SV660 ) ) )
| ! [SY1517: $i,SY1518: $i] :
( ( ( ordered_pair @ SY1517 @ SY1518 )
!= SV702 )
| ~ ( in @ SY1517 @ SV139 )
| ( SY1518
!= ( singleton @ SY1517 ) ) ) )
= $true )
| ( ( in @ SV702 @ ( sK13_C @ SV660 @ SV139 ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4136]) ).
thf(4201,plain,
! [SV139: $i,SV660: $i,SV703: $i] :
( ( ( ~ ( in @ SV703 @ ( sK13_C @ SV660 @ SV139 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK16_E @ SV703 @ SV660 @ SV139 )
!= SV703 )
| ~ ( in @ ( sK16_E @ SV703 @ SV660 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV660 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV703 @ SV660 @ SV139 ) @ ( sK15_SY612 @ SV703 @ SV660 @ SV139 ) )
!= SV703 )
| ~ ( in @ ( sK14_J @ SV703 @ SV660 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV703 @ SV660 @ SV139 )
!= ( singleton @ ( sK14_J @ SV703 @ SV660 @ SV139 ) ) ) ) ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4137]) ).
thf(4202,plain,
! [SV139: $i] :
( ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4138]) ).
thf(4203,plain,
! [SV139: $i] :
( ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true )
| ( ( ! [SY911: $i] :
~ ( ~ ! [SY912: $i] :
( ! [SY913: $i] :
( ( SY913 != SY912 )
| ~ ( in @ SY913 @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY912 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY912 @ ( sK13_C @ SY911 @ SV139 ) ) )
| ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ ( sK13_C @ SY911 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY916 @ SY911 @ SV139 )
!= SY916 )
| ~ ( in @ ( sK16_E @ SY916 @ SY911 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SY911 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ ( sK15_SY612 @ SY916 @ SY911 @ SV139 ) )
!= SY916 )
| ~ ( in @ ( sK14_J @ SY916 @ SY911 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY916 @ SY911 @ SV139 )
!= ( singleton @ ( sK14_J @ SY916 @ SY911 @ SV139 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4139]) ).
thf(4204,plain,
! [SV694: $i,SV139: $i] :
( ( ( ~ ! [SY1508: $i] :
( ! [SY1509: $i] :
( ( SY1509 != SY1508 )
| ~ ( in @ SY1509 @ ( cartesian_product2 @ SV139 @ SV694 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1508 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1508 @ ( sK13_C @ SV694 @ SV139 ) ) ) )
= $false )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4140]) ).
thf(4205,plain,
! [SV139: $i,SV694: $i] :
( ( ( ~ ! [SY1512: $i] :
( ~ ( in @ SY1512 @ ( sK13_C @ SV694 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1512 @ SV694 @ SV139 )
!= SY1512 )
| ~ ( in @ ( sK16_E @ SY1512 @ SV694 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV694 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1512 @ SV694 @ SV139 ) @ ( sK15_SY612 @ SY1512 @ SV694 @ SV139 ) )
!= SY1512 )
| ~ ( in @ ( sK14_J @ SY1512 @ SV694 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1512 @ SV694 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1512 @ SV694 @ SV139 ) ) ) ) ) ) )
= $false )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4140]) ).
thf(4206,plain,
! [SV624: $i,SV139: $i,SV681: $i,SV704: $i] :
( ( ( ( SV704 != SV681 ) )
= $true )
| ( ( ~ ( in @ SV704 @ ( cartesian_product2 @ SV139 @ SV624 ) ) )
= $true )
| ( ( ! [SY1495: $i,SY1496: $i] :
( ( ( ordered_pair @ SY1495 @ SY1496 )
!= SV681 )
| ~ ( in @ SY1495 @ SV139 )
| ( SY1496
!= ( singleton @ SY1495 ) ) ) )
= $true )
| ( ( in @ SV681 @ ( sK13_C @ SV624 @ SV139 ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4141]) ).
thf(4207,plain,
! [SV139: $i,SV624: $i,SV682: $i] :
( ( ( ~ ~ ( ( ( sK16_E @ SV682 @ SV624 @ SV139 )
!= SV682 )
| ~ ( in @ ( sK16_E @ SV682 @ SV624 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV624 ) ) ) )
= $false )
| ( ( in @ SV682 @ ( sK13_C @ SV624 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4142]) ).
thf(4208,plain,
! [SV139: $i,SV624: $i,SV682: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV682 @ SV624 @ SV139 ) @ ( sK15_SY612 @ SV682 @ SV624 @ SV139 ) )
!= SV682 )
| ~ ( in @ ( sK14_J @ SV682 @ SV624 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV682 @ SV624 @ SV139 )
!= ( singleton @ ( sK14_J @ SV682 @ SV624 @ SV139 ) ) ) ) )
= $false )
| ( ( in @ SV682 @ ( sK13_C @ SV624 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4142]) ).
thf(4209,plain,
! [SV661: $i,SV139: $i,SV705: $i] :
( ( ( ! [SY1519: $i] :
( ( SY1519 != SV705 )
| ~ ( in @ SY1519 @ ( cartesian_product2 @ SV139 @ SV661 ) ) )
| ! [SY1520: $i,SY1521: $i] :
( ( ( ordered_pair @ SY1520 @ SY1521 )
!= SV705 )
| ~ ( in @ SY1520 @ SV139 )
| ( SY1521
!= ( singleton @ SY1520 ) ) ) )
= $true )
| ( ( in @ SV705 @ ( sK13_C @ SV661 @ SV139 ) )
= $true )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4143]) ).
thf(4210,plain,
! [SV139: $i,SV661: $i,SV706: $i] :
( ( ( ~ ( in @ SV706 @ ( sK13_C @ SV661 @ SV139 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK16_E @ SV706 @ SV661 @ SV139 )
!= SV706 )
| ~ ( in @ ( sK16_E @ SV706 @ SV661 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV661 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV706 @ SV661 @ SV139 ) @ ( sK15_SY612 @ SV706 @ SV661 @ SV139 ) )
!= SV706 )
| ~ ( in @ ( sK14_J @ SV706 @ SV661 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV706 @ SV661 @ SV139 )
!= ( singleton @ ( sK14_J @ SV706 @ SV661 @ SV139 ) ) ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4144]) ).
thf(4211,plain,
! [SV662: $i,SV139: $i,SV707: $i] :
( ( ( ! [SY1522: $i] :
( ( SY1522 != SV707 )
| ~ ( in @ SY1522 @ ( cartesian_product2 @ SV139 @ SV662 ) ) )
| ! [SY1523: $i,SY1524: $i] :
( ( ( ordered_pair @ SY1523 @ SY1524 )
!= SV707 )
| ~ ( in @ SY1523 @ SV139 )
| ( SY1524
!= ( singleton @ SY1523 ) ) ) )
= $true )
| ( ( in @ SV707 @ ( sK13_C @ SV662 @ SV139 ) )
= $true )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4145]) ).
thf(4212,plain,
! [SV139: $i,SV662: $i,SV708: $i] :
( ( ( ~ ( in @ SV708 @ ( sK13_C @ SV662 @ SV139 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK16_E @ SV708 @ SV662 @ SV139 )
!= SV708 )
| ~ ( in @ ( sK16_E @ SV708 @ SV662 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV662 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV708 @ SV662 @ SV139 ) @ ( sK15_SY612 @ SV708 @ SV662 @ SV139 ) )
!= SV708 )
| ~ ( in @ ( sK14_J @ SV708 @ SV662 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV708 @ SV662 @ SV139 )
!= ( singleton @ ( sK14_J @ SV708 @ SV662 @ SV139 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4146]) ).
thf(4213,plain,
! [SV625: $i,SV139: $i,SV683: $i,SV709: $i] :
( ( ( ( SV709 != SV683 ) )
= $true )
| ( ( ~ ( in @ SV709 @ ( cartesian_product2 @ SV139 @ SV625 ) ) )
= $true )
| ( ( ! [SY1498: $i,SY1499: $i] :
( ( ( ordered_pair @ SY1498 @ SY1499 )
!= SV683 )
| ~ ( in @ SY1498 @ SV139 )
| ( SY1499
!= ( singleton @ SY1498 ) ) ) )
= $true )
| ( ( in @ SV683 @ ( sK13_C @ SV625 @ SV139 ) )
= $true )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4147]) ).
thf(4214,plain,
! [SV139: $i,SV625: $i,SV684: $i] :
( ( ( ~ ~ ( ( ( sK16_E @ SV684 @ SV625 @ SV139 )
!= SV684 )
| ~ ( in @ ( sK16_E @ SV684 @ SV625 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV625 ) ) ) )
= $false )
| ( ( in @ SV684 @ ( sK13_C @ SV625 @ SV139 ) )
= $false )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4148]) ).
thf(4215,plain,
! [SV139: $i,SV625: $i,SV684: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV684 @ SV625 @ SV139 ) @ ( sK15_SY612 @ SV684 @ SV625 @ SV139 ) )
!= SV684 )
| ~ ( in @ ( sK14_J @ SV684 @ SV625 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV684 @ SV625 @ SV139 )
!= ( singleton @ ( sK14_J @ SV684 @ SV625 @ SV139 ) ) ) ) )
= $false )
| ( ( in @ SV684 @ ( sK13_C @ SV625 @ SV139 ) )
= $false )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4148]) ).
thf(4216,plain,
! [SV488: $i,SV654: $i,SV139: $i,SV603: $i,SV710: $i,SV695: $i] :
( ( ( ( ( ordered_pair @ SV695 @ SV710 )
!= SV603 )
| ~ ( in @ SV695 @ SV139 ) )
= $true )
| ( ( ( SV710
!= ( singleton @ SV695 ) ) )
= $true )
| ( ( SV654 = SV603 )
= $false )
| ( ( in @ SV654 @ ( cartesian_product2 @ SV139 @ SV488 ) )
= $false )
| ( ( in @ SV603 @ ( sK13_C @ SV488 @ SV139 ) )
= $true )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4149]) ).
thf(4217,plain,
! [SV139: $i,SV488: $i,SV604: $i] :
( ( ( ( ( ordered_pair @ ( sK14_J @ SV604 @ SV488 @ SV139 ) @ ( sK15_SY612 @ SV604 @ SV488 @ SV139 ) )
!= SV604 )
| ~ ( in @ ( sK14_J @ SV604 @ SV488 @ SV139 ) @ SV139 ) )
= $false )
| ( ( in @ SV604 @ ( sK13_C @ SV488 @ SV139 ) )
= $false )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4152]) ).
thf(4218,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ! [SY1142: $i] :
( ~ ( in @ SY1142 @ ( sK52_SY712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SY1142 ) @ SV265 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4154]) ).
thf(4219,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK52_SY712 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4154]) ).
thf(4220,plain,
! [SV265: $i,SV145: $i] :
( ( ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4155]) ).
thf(4221,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4155]) ).
thf(4222,plain,
! [SV265: $i,SV711: $i,SV145: $i] :
( ( ( ! [SY1525: $i] :
( ~ ( in @ SY1525 @ SV145 )
| ! [SY1526: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1526 @ SY1525 @ SV711 @ SV265 @ SV145 ) @ SY1526 )
| ~ ~ ( in @ ( ordered_pair @ SV711 @ ( sK47_K @ SY1526 @ SY1525 @ SV711 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1525 != SY1526 )
| ~ ( in @ SV711 @ SY1526 ) ) ) )
= $true )
| ( ( in @ SV711 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4156]) ).
thf(4223,plain,
! [SV145: $i,SV265: $i,SV712: $i] :
( ( ( ~ ( in @ SV712 @ ( sK44_C @ SV265 @ SV145 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK45_E @ SV712 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1527: $i] :
( ~ ( in @ SY1527 @ ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV712 @ SY1527 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV712 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) )
| ~ ( in @ SV712 @ ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4157]) ).
thf(4224,plain,
! [SV685: $i,SV265: $i,SV145: $i] :
( ( ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4158]) ).
thf(4225,plain,
! [SV685: $i,SV145: $i,SV265: $i] :
( ( ( ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4158]) ).
thf(4226,plain,
! [SV265: $i,SV145: $i] :
( ( ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4159]) ).
thf(4227,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4159]) ).
thf(4228,plain,
! [SV265: $i,SV145: $i] :
( ( ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4160]) ).
thf(4229,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4160]) ).
thf(4230,plain,
! [SV145: $i,SV265: $i,SV655: $i,SV686: $i,SV713: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_K @ SV713 @ SV686 @ SV655 @ SV265 @ SV145 ) @ SV713 )
| ~ ~ ( in @ ( ordered_pair @ SV655 @ ( sK47_K @ SV713 @ SV686 @ SV655 @ SV265 @ SV145 ) ) @ SV265 ) ) )
= $true )
| ( ( ( SV686 != SV713 )
| ~ ( in @ SV655 @ SV713 ) )
= $true )
| ( ( in @ SV686 @ SV145 )
= $false )
| ( ( in @ SV655 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4161]) ).
thf(4231,plain,
! [SV145: $i,SV265: $i,SV656: $i] :
( ( ( ~ ! [SY1467: $i] :
( ~ ( in @ SY1467 @ ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV656 @ SY1467 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV656 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) )
| ~ ( in @ SV656 @ ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( in @ SV656 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4163]) ).
thf(4232,plain,
! [SV151: $i,SV267: $i,SV467: $i,SV502: $i] :
( ( ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
= SV151 )
= $false )
| ( ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
= $false )
| ( ( SV502
= ( unordered_triple @ SV151 @ SV267 @ SV467 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4164]) ).
thf(4233,plain,
! [SV151: $i,SV267: $i,SV467: $i,SV502: $i] :
( ( ( ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 )
= SV267 )
= $false )
| ( ( in @ ( sK94_E @ SV502 @ SV467 @ SV267 @ SV151 ) @ SV502 )
= $false )
| ( ( SV502
= ( unordered_triple @ SV151 @ SV267 @ SV467 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4165]) ).
thf(4234,plain,
! [SV468: $i,SV267: $i,SV503: $i,SV151: $i,SV714: $i] :
( ( ( ( SV714 != SV151 ) )
= $true )
| ( ( in @ SV714 @ SV503 )
= $true )
| ( ( SV503
= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4166]) ).
thf(4235,plain,
! [SV468: $i,SV151: $i,SV503: $i,SV267: $i,SV715: $i] :
( ( ( ( SV715 != SV267 ) )
= $true )
| ( ( in @ SV715 @ SV503 )
= $true )
| ( ( SV503
= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4167]) ).
thf(4236,plain,
! [SV268: $i,SV547: $i,SV155: $i] :
( ( ( in @ ( subset_complement @ SV155 @ ( sK123_D @ SV547 @ SV268 @ SV155 ) ) @ SV268 )
= $false )
| ( ( in @ ( sK123_D @ SV547 @ SV268 @ SV155 ) @ SV547 )
= $false )
| ( ( SV547
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $true )
| ( ( element @ SV547 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4168]) ).
thf(4237,plain,
! [SV268: $i,SV155: $i,SV548: $i,SV688: $i] :
( ( ( in @ SV688 @ SV548 )
= $false )
| ( ( in @ ( subset_complement @ SV155 @ SV688 ) @ SV268 )
= $true )
| ( ( element @ SV688 @ ( powerset @ SV155 ) )
= $false )
| ( ( SV548
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $false )
| ( ( element @ SV548 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4169]) ).
thf(4238,plain,
! [SV548: $i,SV268: $i,SV689: $i,SV155: $i] :
( ( ( in @ ( subset_complement @ SV155 @ SV689 ) @ SV268 )
= $false )
| ( ( in @ SV689 @ SV548 )
= $true )
| ( ( element @ SV689 @ ( powerset @ SV155 ) )
= $false )
| ( ( SV548
= ( complements_of_subsets @ SV155 @ SV268 ) )
= $false )
| ( ( element @ SV548 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false )
| ( ( element @ SV268 @ ( powerset @ ( powerset @ SV155 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4170]) ).
thf(4239,plain,
! [SV513: $i,SV573: $i,SV668: $i] :
( ( ( in @ SV668 @ ( sK88_D @ SV668 @ SV573 @ SV513 ) )
= $false )
| ( ( in @ SV668 @ SV573 )
= $true )
| ( ( SV573
= ( set_meet @ SV513 ) )
= $false )
| ( ( SV513 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4173]) ).
thf(4240,plain,
! [SV573: $i,SV669: $i,SV513: $i,SV696: $i] :
( ( ( in @ SV696 @ SV513 )
= $false )
| ( ( in @ SV669 @ SV696 )
= $true )
| ( ( in @ SV669 @ SV573 )
= $false )
| ( ( SV573
= ( set_meet @ SV513 ) )
= $false )
| ( ( SV513 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4174]) ).
thf(4241,plain,
! [SV475: $i,SV438: $i,SV164: $i,SV672: $i,SV657: $i,SV637: $i] :
( ( ( SV637
= ( ordered_pair @ SV657 @ SV672 ) )
= $false )
| ( ( in @ SV657 @ SV164 )
= $false )
| ( ( in @ SV672 @ SV438 )
= $false )
| ( ( in @ SV637 @ SV475 )
= $true )
| ( ( SV475
= ( cartesian_product2 @ SV164 @ SV438 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4176]) ).
thf(4242,plain,
! [SV164: $i,SV438: $i,SV475: $i,SV638: $i] :
( ( ( in @ ( sK76_E @ SV638 @ SV475 @ SV438 @ SV164 ) @ SV164 )
= $true )
| ( ( in @ SV638 @ SV475 )
= $false )
| ( ( SV475
= ( cartesian_product2 @ SV164 @ SV438 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4177]) ).
thf(4243,plain,
! [SV164: $i,SV438: $i,SV475: $i,SV638: $i] :
( ( ( in @ ( sK77_SY726 @ SV638 @ SV475 @ SV438 @ SV164 ) @ SV438 )
= $true )
| ( ( in @ SV638 @ SV475 )
= $false )
| ( ( SV475
= ( cartesian_product2 @ SV164 @ SV438 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4178]) ).
thf(4244,plain,
! [SV697: $i,SV168: $i,SV721: $i] :
( ( ( ~ ( in @ SV721 @ SV168 )
| ( SV697
!= ( singleton @ SV721 ) ) )
= $true )
| ( ( in @ SV697 @ ( sK24_B @ SV168 ) )
= $true )
| ( ( ( sK27_SY634 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4179]) ).
thf(4245,plain,
! [SV168: $i,SV698: $i] :
( ( ( in @ SV698 @ ( sK24_B @ SV168 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK25_D @ SV698 @ SV168 ) @ SV168 )
| ( SV698
!= ( singleton @ ( sK25_D @ SV698 @ SV168 ) ) ) ) )
= $true )
| ( ( ( sK27_SY634 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4180]) ).
thf(4246,plain,
! [SV699: $i,SV168: $i,SV722: $i] :
( ( ( ~ ( in @ SV722 @ SV168 )
| ( SV699
!= ( singleton @ SV722 ) ) )
= $true )
| ( ( in @ SV699 @ ( sK24_B @ SV168 ) )
= $true )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4181]) ).
thf(4247,plain,
! [SV168: $i,SV700: $i] :
( ( ( in @ SV700 @ ( sK24_B @ SV168 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK25_D @ SV700 @ SV168 ) @ SV168 )
| ( SV700
!= ( singleton @ ( sK25_D @ SV700 @ SV168 ) ) ) ) )
= $true )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4182]) ).
thf(4248,plain,
! [SV168: $i,SV693: $i,SV673: $i] :
( ( ( SV673
= ( singleton @ SV693 ) )
= $false )
| ( ( in @ SV693 @ SV168 )
= $false )
| ( ( in @ SV673 @ ( sK24_B @ SV168 ) )
= $true )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4183]) ).
thf(4249,plain,
! [SV168: $i,SV674: $i] :
( ( ( in @ ( sK25_D @ SV674 @ SV168 ) @ SV168 )
= $true )
| ( ( in @ SV674 @ ( sK24_B @ SV168 ) )
= $false )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4184]) ).
thf(4250,plain,
! [SV168: $i,SV674: $i] :
( ( ( SV674
= ( singleton @ ( sK25_D @ SV674 @ SV168 ) ) )
= $true )
| ( ( in @ SV674 @ ( sK24_B @ SV168 ) )
= $false )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4185]) ).
thf(4251,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV596: $i,SV651: $i,SV659: $i,SV716: $i] :
( ( ( ~ ( ~ ( in @ ( sK115_I @ SV716 @ SV659 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) @ SV716 )
| ~ ~ ( in @ ( ordered_pair @ SV659 @ ( sK115_I @ SV716 @ SV659 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) ) @ SV271 ) ) )
= $true )
| ( ( ( SV651 != SV716 )
| ~ ( in @ SV659 @ SV716 ) )
= $true )
| ( ( ( ordered_pair @ SV651 @ SV659 )
= SV596 )
= $false )
| ( ( in @ SV651 @ SV170 )
= $false )
| ( ( ~ ( in @ SV596 @ ( cartesian_product2 @ SV170 @ SV481 ) ) )
= $true )
| ( ( in @ SV596 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4186]) ).
thf(4252,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV652: $i] :
( ( ( ( ( ordered_pair @ ( sK112_F @ SV652 @ SV481 @ SV271 @ SV170 ) @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) )
!= SV652 ) )
= $false )
| ( ( in @ SV652 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $false )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4187]) ).
thf(4253,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV652: $i] :
( ( ( ~ ( in @ ( sK112_F @ SV652 @ SV481 @ SV271 @ SV170 ) @ SV170 ) )
= $false )
| ( ( in @ SV652 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $false )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4187]) ).
thf(4254,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV652: $i] :
( ( ( ~ ! [SY1464: $i] :
( ~ ( in @ SY1464 @ ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) )
| ( in @ ( ordered_pair @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) @ SY1464 ) @ SV271 ) ) )
= $false )
| ( ( in @ SV652 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $false )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4188]) ).
thf(4255,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV652: $i] :
( ( ( ~ ~ ( ( ( sK112_F @ SV652 @ SV481 @ SV271 @ SV170 )
!= ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) )
| ~ ( in @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) @ ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) ) ) )
= $false )
| ( ( in @ SV652 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $false )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4188]) ).
thf(4256,plain,
! [SV272: $i,SV717: $i,SV172: $i] :
( ( ( ~ ! [SY1528: $i] :
( ! [SY1529: $i] :
( ( SY1529 != SY1528 )
| ~ ( in @ SY1529 @ ( cartesian_product2 @ SV172 @ SV717 ) ) )
| ! [SY1530: $i,SY1531: $i] :
( ( ( ordered_pair @ SY1530 @ SY1531 )
!= SY1528 )
| ~ ( in @ SY1530 @ SV172 )
| ! [SY1532: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1532 @ SY1531 @ SY1530 @ SY1528 @ SV717 @ SV272 @ SV172 ) @ SY1532 )
| ~ ~ ( in @ ( ordered_pair @ SY1531 @ ( sK34_R @ SY1532 @ SY1531 @ SY1530 @ SY1528 @ SV717 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1530 != SY1532 )
| ~ ( in @ SY1531 @ SY1532 ) ) )
| ( in @ SY1528 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) ) )
| ~ ! [SY1533: $i] :
( ~ ( in @ SY1533 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1533 @ SV717 @ SV272 @ SV172 )
!= SY1533 )
| ~ ( in @ ( sK33_F @ SY1533 @ SV717 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV717 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1533 @ SV717 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1533 @ SV717 @ SV272 @ SV172 ) )
!= SY1533 )
| ~ ( in @ ( sK30_O @ SY1533 @ SV717 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1534: $i] :
( ~ ( in @ SY1534 @ ( sK32_SY652 @ SY1533 @ SV717 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1533 @ SV717 @ SV272 @ SV172 ) @ SY1534 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1533 @ SV717 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1533 @ SV717 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1533 @ SV717 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1533 @ SV717 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4189]) ).
thf(4257,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4190]) ).
thf(4258,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ~ ( ~ ! [SY1178: $i] :
( ~ ( in @ SY1178 @ ( sK43_SY691 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SY1178 ) @ SV272 ) )
| ~ ~ ( ( ( sK41_SY666 @ SV272 @ SV172 )
!= ( sK43_SY691 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) ) ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4190]) ).
thf(4259,plain,
! [SV272: $i,SV692: $i,SV172: $i,SV723: $i] :
( ( ( ! [SY1549: $i] :
( ( SY1549 != SV723 )
| ~ ( in @ SY1549 @ ( cartesian_product2 @ SV172 @ SV692 ) ) )
| ! [SY1550: $i,SY1551: $i] :
( ( ( ordered_pair @ SY1550 @ SY1551 )
!= SV723 )
| ~ ( in @ SY1550 @ SV172 )
| ! [SY1552: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1552 @ SY1551 @ SY1550 @ SV723 @ SV692 @ SV272 @ SV172 ) @ SY1552 )
| ~ ~ ( in @ ( ordered_pair @ SY1551 @ ( sK34_R @ SY1552 @ SY1551 @ SY1550 @ SV723 @ SV692 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1550 != SY1552 )
| ~ ( in @ SY1551 @ SY1552 ) ) )
| ( in @ SV723 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4191]) ).
thf(4260,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( ~ ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SV724 @ SV692 @ SV272 @ SV172 )
!= SV724 )
| ~ ( in @ ( sK33_F @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV692 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) )
!= SV724 )
| ~ ( in @ ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1553: $i] :
( ~ ( in @ SY1553 @ ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) @ SY1553 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4192]) ).
thf(4261,plain,
! [SV272: $i,SV718: $i,SV172: $i] :
( ( ( ~ ! [SY1535: $i] :
( ! [SY1536: $i] :
( ( SY1536 != SY1535 )
| ~ ( in @ SY1536 @ ( cartesian_product2 @ SV172 @ SV718 ) ) )
| ! [SY1537: $i,SY1538: $i] :
( ( ( ordered_pair @ SY1537 @ SY1538 )
!= SY1535 )
| ~ ( in @ SY1537 @ SV172 )
| ! [SY1539: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1539 @ SY1538 @ SY1537 @ SY1535 @ SV718 @ SV272 @ SV172 ) @ SY1539 )
| ~ ~ ( in @ ( ordered_pair @ SY1538 @ ( sK34_R @ SY1539 @ SY1538 @ SY1537 @ SY1535 @ SV718 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1537 != SY1539 )
| ~ ( in @ SY1538 @ SY1539 ) ) )
| ( in @ SY1535 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) ) )
| ~ ! [SY1540: $i] :
( ~ ( in @ SY1540 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1540 @ SV718 @ SV272 @ SV172 )
!= SY1540 )
| ~ ( in @ ( sK33_F @ SY1540 @ SV718 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV718 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1540 @ SV718 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1540 @ SV718 @ SV272 @ SV172 ) )
!= SY1540 )
| ~ ( in @ ( sK30_O @ SY1540 @ SV718 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1541: $i] :
( ~ ( in @ SY1541 @ ( sK32_SY652 @ SY1540 @ SV718 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1540 @ SV718 @ SV272 @ SV172 ) @ SY1541 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1540 @ SV718 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1540 @ SV718 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1540 @ SV718 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1540 @ SV718 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4193]) ).
thf(4262,plain,
! [SV272: $i,SV719: $i,SV172: $i] :
( ( ( ~ ! [SY1542: $i] :
( ! [SY1543: $i] :
( ( SY1543 != SY1542 )
| ~ ( in @ SY1543 @ ( cartesian_product2 @ SV172 @ SV719 ) ) )
| ! [SY1544: $i,SY1545: $i] :
( ( ( ordered_pair @ SY1544 @ SY1545 )
!= SY1542 )
| ~ ( in @ SY1544 @ SV172 )
| ! [SY1546: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1546 @ SY1545 @ SY1544 @ SY1542 @ SV719 @ SV272 @ SV172 ) @ SY1546 )
| ~ ~ ( in @ ( ordered_pair @ SY1545 @ ( sK34_R @ SY1546 @ SY1545 @ SY1544 @ SY1542 @ SV719 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1544 != SY1546 )
| ~ ( in @ SY1545 @ SY1546 ) ) )
| ( in @ SY1542 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) ) )
| ~ ! [SY1547: $i] :
( ~ ( in @ SY1547 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1547 @ SV719 @ SV272 @ SV172 )
!= SY1547 )
| ~ ( in @ ( sK33_F @ SY1547 @ SV719 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV719 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1547 @ SV719 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1547 @ SV719 @ SV272 @ SV172 ) )
!= SY1547 )
| ~ ( in @ ( sK30_O @ SY1547 @ SV719 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1548: $i] :
( ~ ( in @ SY1548 @ ( sK32_SY652 @ SY1547 @ SV719 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1547 @ SV719 @ SV272 @ SV172 ) @ SY1548 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1547 @ SV719 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1547 @ SV719 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1547 @ SV719 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1547 @ SV719 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4194]) ).
thf(4263,plain,
! [SV172: $i,SV272: $i,SV720: $i] :
( ( ( ~ ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4195]) ).
thf(4264,plain,
! [SV172: $i,SV272: $i] :
( ( ( ( ( sK38_SY678 @ SV272 @ SV172 )
!= ( sK40_SY685 @ SV272 @ SV172 ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4196]) ).
thf(4265,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4196]) ).
thf(4266,plain,
! [SV272: $i,SV622: $i,SV172: $i,SV677: $i,SV701: $i] :
( ( ( SV701 = SV677 )
= $false )
| ( ( ~ ( in @ SV701 @ ( cartesian_product2 @ SV172 @ SV622 ) ) )
= $true )
| ( ( ! [SY1490: $i,SY1491: $i] :
( ( ( ordered_pair @ SY1490 @ SY1491 )
!= SV677 )
| ~ ( in @ SY1490 @ SV172 )
| ! [SY1492: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1492 @ SY1491 @ SY1490 @ SV677 @ SV622 @ SV272 @ SV172 ) @ SY1492 )
| ~ ~ ( in @ ( ordered_pair @ SY1491 @ ( sK34_R @ SY1492 @ SY1491 @ SY1490 @ SV677 @ SV622 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1490 != SY1492 )
| ~ ( in @ SY1491 @ SY1492 ) ) ) )
= $true )
| ( ( in @ SV677 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4197]) ).
thf(4267,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( ~ ( ( ( sK33_F @ SV678 @ SV622 @ SV272 @ SV172 )
!= SV678 )
| ~ ( in @ ( sK33_F @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV622 ) ) ) )
= $true )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4198]) ).
thf(4268,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) )
!= SV678 )
| ~ ( in @ ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1493: $i] :
( ~ ( in @ SY1493 @ ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) @ SY1493 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) ) ) ) ) )
= $true )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4199]) ).
thf(4269,plain,
! [SV660: $i,SV139: $i,SV702: $i] :
( ( ( ! [SY1516: $i] :
( ( SY1516 != SV702 )
| ~ ( in @ SY1516 @ ( cartesian_product2 @ SV139 @ SV660 ) ) ) )
= $true )
| ( ( ! [SY1517: $i,SY1518: $i] :
( ( ( ordered_pair @ SY1517 @ SY1518 )
!= SV702 )
| ~ ( in @ SY1517 @ SV139 )
| ( SY1518
!= ( singleton @ SY1517 ) ) ) )
= $true )
| ( ( in @ SV702 @ ( sK13_C @ SV660 @ SV139 ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4200]) ).
thf(4270,plain,
! [SV139: $i,SV660: $i,SV703: $i] :
( ( ( in @ SV703 @ ( sK13_C @ SV660 @ SV139 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK16_E @ SV703 @ SV660 @ SV139 )
!= SV703 )
| ~ ( in @ ( sK16_E @ SV703 @ SV660 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV660 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV703 @ SV660 @ SV139 ) @ ( sK15_SY612 @ SV703 @ SV660 @ SV139 ) )
!= SV703 )
| ~ ( in @ ( sK14_J @ SV703 @ SV660 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV703 @ SV660 @ SV139 )
!= ( singleton @ ( sK14_J @ SV703 @ SV660 @ SV139 ) ) ) ) ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4201]) ).
thf(4271,plain,
! [SV725: $i,SV139: $i] :
( ( ( ~ ( ~ ! [SY1554: $i] :
( ! [SY1555: $i] :
( ( SY1555 != SY1554 )
| ~ ( in @ SY1555 @ ( cartesian_product2 @ SV139 @ SV725 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1554 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1554 @ ( sK13_C @ SV725 @ SV139 ) ) )
| ~ ! [SY1558: $i] :
( ~ ( in @ SY1558 @ ( sK13_C @ SV725 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1558 @ SV725 @ SV139 )
!= SY1558 )
| ~ ( in @ ( sK16_E @ SY1558 @ SV725 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV725 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1558 @ SV725 @ SV139 ) @ ( sK15_SY612 @ SY1558 @ SV725 @ SV139 ) )
!= SY1558 )
| ~ ( in @ ( sK14_J @ SY1558 @ SV725 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1558 @ SV725 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1558 @ SV725 @ SV139 ) ) ) ) ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4202]) ).
thf(4272,plain,
! [SV726: $i,SV139: $i] :
( ( ( ~ ( ~ ! [SY1559: $i] :
( ! [SY1560: $i] :
( ( SY1560 != SY1559 )
| ~ ( in @ SY1560 @ ( cartesian_product2 @ SV139 @ SV726 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1559 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1559 @ ( sK13_C @ SV726 @ SV139 ) ) )
| ~ ! [SY1563: $i] :
( ~ ( in @ SY1563 @ ( sK13_C @ SV726 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1563 @ SV726 @ SV139 )
!= SY1563 )
| ~ ( in @ ( sK16_E @ SY1563 @ SV726 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV726 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1563 @ SV726 @ SV139 ) @ ( sK15_SY612 @ SY1563 @ SV726 @ SV139 ) )
!= SY1563 )
| ~ ( in @ ( sK14_J @ SY1563 @ SV726 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1563 @ SV726 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1563 @ SV726 @ SV139 ) ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4203]) ).
thf(4273,plain,
! [SV694: $i,SV139: $i] :
( ( ( ! [SY1508: $i] :
( ! [SY1509: $i] :
( ( SY1509 != SY1508 )
| ~ ( in @ SY1509 @ ( cartesian_product2 @ SV139 @ SV694 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1508 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1508 @ ( sK13_C @ SV694 @ SV139 ) ) ) )
= $true )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4204]) ).
thf(4274,plain,
! [SV139: $i,SV694: $i] :
( ( ( ! [SY1512: $i] :
( ~ ( in @ SY1512 @ ( sK13_C @ SV694 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1512 @ SV694 @ SV139 )
!= SY1512 )
| ~ ( in @ ( sK16_E @ SY1512 @ SV694 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV694 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1512 @ SV694 @ SV139 ) @ ( sK15_SY612 @ SY1512 @ SV694 @ SV139 ) )
!= SY1512 )
| ~ ( in @ ( sK14_J @ SY1512 @ SV694 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1512 @ SV694 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1512 @ SV694 @ SV139 ) ) ) ) ) ) )
= $true )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4205]) ).
thf(4275,plain,
! [SV624: $i,SV139: $i,SV681: $i,SV704: $i] :
( ( ( SV704 = SV681 )
= $false )
| ( ( ~ ( in @ SV704 @ ( cartesian_product2 @ SV139 @ SV624 ) ) )
= $true )
| ( ( ! [SY1495: $i,SY1496: $i] :
( ( ( ordered_pair @ SY1495 @ SY1496 )
!= SV681 )
| ~ ( in @ SY1495 @ SV139 )
| ( SY1496
!= ( singleton @ SY1495 ) ) ) )
= $true )
| ( ( in @ SV681 @ ( sK13_C @ SV624 @ SV139 ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4206]) ).
thf(4276,plain,
! [SV139: $i,SV624: $i,SV682: $i] :
( ( ( ~ ( ( ( sK16_E @ SV682 @ SV624 @ SV139 )
!= SV682 )
| ~ ( in @ ( sK16_E @ SV682 @ SV624 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV624 ) ) ) )
= $true )
| ( ( in @ SV682 @ ( sK13_C @ SV624 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4207]) ).
thf(4277,plain,
! [SV139: $i,SV624: $i,SV682: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV682 @ SV624 @ SV139 ) @ ( sK15_SY612 @ SV682 @ SV624 @ SV139 ) )
!= SV682 )
| ~ ( in @ ( sK14_J @ SV682 @ SV624 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV682 @ SV624 @ SV139 )
!= ( singleton @ ( sK14_J @ SV682 @ SV624 @ SV139 ) ) ) ) )
= $true )
| ( ( in @ SV682 @ ( sK13_C @ SV624 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4208]) ).
thf(4278,plain,
! [SV661: $i,SV139: $i,SV705: $i] :
( ( ( ! [SY1519: $i] :
( ( SY1519 != SV705 )
| ~ ( in @ SY1519 @ ( cartesian_product2 @ SV139 @ SV661 ) ) ) )
= $true )
| ( ( ! [SY1520: $i,SY1521: $i] :
( ( ( ordered_pair @ SY1520 @ SY1521 )
!= SV705 )
| ~ ( in @ SY1520 @ SV139 )
| ( SY1521
!= ( singleton @ SY1520 ) ) ) )
= $true )
| ( ( in @ SV705 @ ( sK13_C @ SV661 @ SV139 ) )
= $true )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4209]) ).
thf(4279,plain,
! [SV139: $i,SV661: $i,SV706: $i] :
( ( ( in @ SV706 @ ( sK13_C @ SV661 @ SV139 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK16_E @ SV706 @ SV661 @ SV139 )
!= SV706 )
| ~ ( in @ ( sK16_E @ SV706 @ SV661 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV661 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV706 @ SV661 @ SV139 ) @ ( sK15_SY612 @ SV706 @ SV661 @ SV139 ) )
!= SV706 )
| ~ ( in @ ( sK14_J @ SV706 @ SV661 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV706 @ SV661 @ SV139 )
!= ( singleton @ ( sK14_J @ SV706 @ SV661 @ SV139 ) ) ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4210]) ).
thf(4280,plain,
! [SV662: $i,SV139: $i,SV707: $i] :
( ( ( ! [SY1522: $i] :
( ( SY1522 != SV707 )
| ~ ( in @ SY1522 @ ( cartesian_product2 @ SV139 @ SV662 ) ) ) )
= $true )
| ( ( ! [SY1523: $i,SY1524: $i] :
( ( ( ordered_pair @ SY1523 @ SY1524 )
!= SV707 )
| ~ ( in @ SY1523 @ SV139 )
| ( SY1524
!= ( singleton @ SY1523 ) ) ) )
= $true )
| ( ( in @ SV707 @ ( sK13_C @ SV662 @ SV139 ) )
= $true )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4211]) ).
thf(4281,plain,
! [SV139: $i,SV662: $i,SV708: $i] :
( ( ( in @ SV708 @ ( sK13_C @ SV662 @ SV139 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK16_E @ SV708 @ SV662 @ SV139 )
!= SV708 )
| ~ ( in @ ( sK16_E @ SV708 @ SV662 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV662 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV708 @ SV662 @ SV139 ) @ ( sK15_SY612 @ SV708 @ SV662 @ SV139 ) )
!= SV708 )
| ~ ( in @ ( sK14_J @ SV708 @ SV662 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV708 @ SV662 @ SV139 )
!= ( singleton @ ( sK14_J @ SV708 @ SV662 @ SV139 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4212]) ).
thf(4282,plain,
! [SV625: $i,SV139: $i,SV683: $i,SV709: $i] :
( ( ( SV709 = SV683 )
= $false )
| ( ( ~ ( in @ SV709 @ ( cartesian_product2 @ SV139 @ SV625 ) ) )
= $true )
| ( ( ! [SY1498: $i,SY1499: $i] :
( ( ( ordered_pair @ SY1498 @ SY1499 )
!= SV683 )
| ~ ( in @ SY1498 @ SV139 )
| ( SY1499
!= ( singleton @ SY1498 ) ) ) )
= $true )
| ( ( in @ SV683 @ ( sK13_C @ SV625 @ SV139 ) )
= $true )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4213]) ).
thf(4283,plain,
! [SV139: $i,SV625: $i,SV684: $i] :
( ( ( ~ ( ( ( sK16_E @ SV684 @ SV625 @ SV139 )
!= SV684 )
| ~ ( in @ ( sK16_E @ SV684 @ SV625 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV625 ) ) ) )
= $true )
| ( ( in @ SV684 @ ( sK13_C @ SV625 @ SV139 ) )
= $false )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4214]) ).
thf(4284,plain,
! [SV139: $i,SV625: $i,SV684: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV684 @ SV625 @ SV139 ) @ ( sK15_SY612 @ SV684 @ SV625 @ SV139 ) )
!= SV684 )
| ~ ( in @ ( sK14_J @ SV684 @ SV625 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV684 @ SV625 @ SV139 )
!= ( singleton @ ( sK14_J @ SV684 @ SV625 @ SV139 ) ) ) ) )
= $true )
| ( ( in @ SV684 @ ( sK13_C @ SV625 @ SV139 ) )
= $false )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4215]) ).
thf(4285,plain,
! [SV488: $i,SV654: $i,SV139: $i,SV603: $i,SV710: $i,SV695: $i] :
( ( ( ( ( ordered_pair @ SV695 @ SV710 )
!= SV603 ) )
= $true )
| ( ( ~ ( in @ SV695 @ SV139 ) )
= $true )
| ( ( ( SV710
!= ( singleton @ SV695 ) ) )
= $true )
| ( ( SV654 = SV603 )
= $false )
| ( ( in @ SV654 @ ( cartesian_product2 @ SV139 @ SV488 ) )
= $false )
| ( ( in @ SV603 @ ( sK13_C @ SV488 @ SV139 ) )
= $true )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4216]) ).
thf(4286,plain,
! [SV139: $i,SV488: $i,SV604: $i] :
( ( ( ( ( ordered_pair @ ( sK14_J @ SV604 @ SV488 @ SV139 ) @ ( sK15_SY612 @ SV604 @ SV488 @ SV139 ) )
!= SV604 ) )
= $false )
| ( ( in @ SV604 @ ( sK13_C @ SV488 @ SV139 ) )
= $false )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4217]) ).
thf(4287,plain,
! [SV139: $i,SV488: $i,SV604: $i] :
( ( ( ~ ( in @ ( sK14_J @ SV604 @ SV488 @ SV139 ) @ SV139 ) )
= $false )
| ( ( in @ SV604 @ ( sK13_C @ SV488 @ SV139 ) )
= $false )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4217]) ).
thf(4288,plain,
! [SV145: $i,SV265: $i] :
( ( ( ! [SY1142: $i] :
( ~ ( in @ SY1142 @ ( sK52_SY712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SY1142 ) @ SV265 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4218]) ).
thf(4289,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK52_SY712 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4219]) ).
thf(4290,plain,
! [SV265: $i,SV145: $i] :
( ( ( ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4220]) ).
thf(4291,plain,
! [SV145: $i,SV265: $i] :
( ( ( ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4221]) ).
thf(4292,plain,
! [SV265: $i,SV711: $i,SV145: $i,SV727: $i] :
( ( ( ~ ( in @ SV727 @ SV145 )
| ! [SY1564: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1564 @ SV727 @ SV711 @ SV265 @ SV145 ) @ SY1564 )
| ~ ~ ( in @ ( ordered_pair @ SV711 @ ( sK47_K @ SY1564 @ SV727 @ SV711 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV727 != SY1564 )
| ~ ( in @ SV711 @ SY1564 ) ) )
= $true )
| ( ( in @ SV711 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4222]) ).
thf(4293,plain,
! [SV145: $i,SV265: $i,SV712: $i] :
( ( ( in @ SV712 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK45_E @ SV712 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1527: $i] :
( ~ ( in @ SY1527 @ ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV712 @ SY1527 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV712 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) )
| ~ ( in @ SV712 @ ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4223]) ).
thf(4294,plain,
! [SV685: $i,SV265: $i,SV145: $i] :
( ( ( ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4224]) ).
thf(4295,plain,
! [SV685: $i,SV145: $i,SV265: $i] :
( ( ( ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4225]) ).
thf(4296,plain,
! [SV265: $i,SV145: $i] :
( ( ( ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4226]) ).
thf(4297,plain,
! [SV145: $i,SV265: $i] :
( ( ( ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4227]) ).
thf(4298,plain,
! [SV265: $i,SV145: $i] :
( ( ( ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) ) )
= $true )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4228]) ).
thf(4299,plain,
! [SV145: $i,SV265: $i] :
( ( ( ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4229]) ).
thf(4300,plain,
! [SV145: $i,SV265: $i,SV655: $i,SV686: $i,SV713: $i] :
( ( ( ~ ( in @ ( sK47_K @ SV713 @ SV686 @ SV655 @ SV265 @ SV145 ) @ SV713 )
| ~ ~ ( in @ ( ordered_pair @ SV655 @ ( sK47_K @ SV713 @ SV686 @ SV655 @ SV265 @ SV145 ) ) @ SV265 ) )
= $false )
| ( ( ( SV686 != SV713 )
| ~ ( in @ SV655 @ SV713 ) )
= $true )
| ( ( in @ SV686 @ SV145 )
= $false )
| ( ( in @ SV655 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4230]) ).
thf(4301,plain,
! [SV145: $i,SV265: $i,SV656: $i] :
( ( ( ~ ! [SY1467: $i] :
( ~ ( in @ SY1467 @ ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV656 @ SY1467 ) @ SV265 ) ) )
= $false )
| ( ( in @ SV656 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4231]) ).
thf(4302,plain,
! [SV145: $i,SV265: $i,SV656: $i] :
( ( ( ~ ~ ( ( ( sK45_E @ SV656 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) )
| ~ ( in @ SV656 @ ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( in @ SV656 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4231]) ).
thf(4303,plain,
! [SV468: $i,SV267: $i,SV503: $i,SV151: $i,SV714: $i] :
( ( ( SV714 = SV151 )
= $false )
| ( ( in @ SV714 @ SV503 )
= $true )
| ( ( SV503
= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4234]) ).
thf(4304,plain,
! [SV468: $i,SV151: $i,SV503: $i,SV267: $i,SV715: $i] :
( ( ( SV715 = SV267 )
= $false )
| ( ( in @ SV715 @ SV503 )
= $true )
| ( ( SV503
= ( unordered_triple @ SV151 @ SV267 @ SV468 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4235]) ).
thf(4305,plain,
! [SV697: $i,SV168: $i,SV721: $i] :
( ( ( ~ ( in @ SV721 @ SV168 ) )
= $true )
| ( ( ( SV697
!= ( singleton @ SV721 ) ) )
= $true )
| ( ( in @ SV697 @ ( sK24_B @ SV168 ) )
= $true )
| ( ( ( sK27_SY634 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4244]) ).
thf(4306,plain,
! [SV168: $i,SV698: $i] :
( ( ( ~ ( in @ ( sK25_D @ SV698 @ SV168 ) @ SV168 )
| ( SV698
!= ( singleton @ ( sK25_D @ SV698 @ SV168 ) ) ) )
= $false )
| ( ( in @ SV698 @ ( sK24_B @ SV168 ) )
= $false )
| ( ( ( sK27_SY634 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4245]) ).
thf(4307,plain,
! [SV699: $i,SV168: $i,SV722: $i] :
( ( ( ~ ( in @ SV722 @ SV168 ) )
= $true )
| ( ( ( SV699
!= ( singleton @ SV722 ) ) )
= $true )
| ( ( in @ SV699 @ ( sK24_B @ SV168 ) )
= $true )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4246]) ).
thf(4308,plain,
! [SV168: $i,SV700: $i] :
( ( ( ~ ( in @ ( sK25_D @ SV700 @ SV168 ) @ SV168 )
| ( SV700
!= ( singleton @ ( sK25_D @ SV700 @ SV168 ) ) ) )
= $false )
| ( ( in @ SV700 @ ( sK24_B @ SV168 ) )
= $false )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4247]) ).
thf(4309,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV596: $i,SV651: $i,SV659: $i,SV716: $i] :
( ( ( ~ ( in @ ( sK115_I @ SV716 @ SV659 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) @ SV716 )
| ~ ~ ( in @ ( ordered_pair @ SV659 @ ( sK115_I @ SV716 @ SV659 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) ) @ SV271 ) )
= $false )
| ( ( ( SV651 != SV716 )
| ~ ( in @ SV659 @ SV716 ) )
= $true )
| ( ( ( ordered_pair @ SV651 @ SV659 )
= SV596 )
= $false )
| ( ( in @ SV651 @ SV170 )
= $false )
| ( ( ~ ( in @ SV596 @ ( cartesian_product2 @ SV170 @ SV481 ) ) )
= $true )
| ( ( in @ SV596 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4251]) ).
thf(4310,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV652: $i] :
( ( ( ( ordered_pair @ ( sK112_F @ SV652 @ SV481 @ SV271 @ SV170 ) @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) )
= SV652 )
= $true )
| ( ( in @ SV652 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $false )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4252]) ).
thf(4311,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV652: $i] :
( ( ( in @ ( sK112_F @ SV652 @ SV481 @ SV271 @ SV170 ) @ SV170 )
= $true )
| ( ( in @ SV652 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $false )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4253]) ).
thf(4312,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV652: $i] :
( ( ( ! [SY1464: $i] :
( ~ ( in @ SY1464 @ ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) )
| ( in @ ( ordered_pair @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) @ SY1464 ) @ SV271 ) ) )
= $true )
| ( ( in @ SV652 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $false )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4254]) ).
thf(4313,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV652: $i] :
( ( ( ~ ( ( ( sK112_F @ SV652 @ SV481 @ SV271 @ SV170 )
!= ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) )
| ~ ( in @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) @ ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) ) ) )
= $true )
| ( ( in @ SV652 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $false )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4255]) ).
thf(4314,plain,
! [SV272: $i,SV717: $i,SV172: $i] :
( ( ( ~ ! [SY1528: $i] :
( ! [SY1529: $i] :
( ( SY1529 != SY1528 )
| ~ ( in @ SY1529 @ ( cartesian_product2 @ SV172 @ SV717 ) ) )
| ! [SY1530: $i,SY1531: $i] :
( ( ( ordered_pair @ SY1530 @ SY1531 )
!= SY1528 )
| ~ ( in @ SY1530 @ SV172 )
| ! [SY1532: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1532 @ SY1531 @ SY1530 @ SY1528 @ SV717 @ SV272 @ SV172 ) @ SY1532 )
| ~ ~ ( in @ ( ordered_pair @ SY1531 @ ( sK34_R @ SY1532 @ SY1531 @ SY1530 @ SY1528 @ SV717 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1530 != SY1532 )
| ~ ( in @ SY1531 @ SY1532 ) ) )
| ( in @ SY1528 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4256]) ).
thf(4315,plain,
! [SV172: $i,SV272: $i,SV717: $i] :
( ( ( ~ ! [SY1533: $i] :
( ~ ( in @ SY1533 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1533 @ SV717 @ SV272 @ SV172 )
!= SY1533 )
| ~ ( in @ ( sK33_F @ SY1533 @ SV717 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV717 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1533 @ SV717 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1533 @ SV717 @ SV272 @ SV172 ) )
!= SY1533 )
| ~ ( in @ ( sK30_O @ SY1533 @ SV717 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1534: $i] :
( ~ ( in @ SY1534 @ ( sK32_SY652 @ SY1533 @ SV717 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1533 @ SV717 @ SV272 @ SV172 ) @ SY1534 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1533 @ SV717 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1533 @ SV717 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1533 @ SV717 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1533 @ SV717 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4256]) ).
thf(4316,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 ) ) )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4257]) ).
thf(4317,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ( ~ ! [SY1178: $i] :
( ~ ( in @ SY1178 @ ( sK43_SY691 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SY1178 ) @ SV272 ) )
| ~ ~ ( ( ( sK41_SY666 @ SV272 @ SV172 )
!= ( sK43_SY691 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) ) ) ) )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4258]) ).
thf(4318,plain,
! [SV272: $i,SV692: $i,SV172: $i,SV723: $i] :
( ( ( ! [SY1549: $i] :
( ( SY1549 != SV723 )
| ~ ( in @ SY1549 @ ( cartesian_product2 @ SV172 @ SV692 ) ) )
| ! [SY1550: $i,SY1551: $i] :
( ( ( ordered_pair @ SY1550 @ SY1551 )
!= SV723 )
| ~ ( in @ SY1550 @ SV172 )
| ! [SY1552: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1552 @ SY1551 @ SY1550 @ SV723 @ SV692 @ SV272 @ SV172 ) @ SY1552 )
| ~ ~ ( in @ ( ordered_pair @ SY1551 @ ( sK34_R @ SY1552 @ SY1551 @ SY1550 @ SV723 @ SV692 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1550 != SY1552 )
| ~ ( in @ SY1551 @ SY1552 ) ) ) )
= $true )
| ( ( in @ SV723 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4259]) ).
thf(4319,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( ~ ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK33_F @ SV724 @ SV692 @ SV272 @ SV172 )
!= SV724 )
| ~ ( in @ ( sK33_F @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV692 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) )
!= SV724 )
| ~ ( in @ ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1553: $i] :
( ~ ( in @ SY1553 @ ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) @ SY1553 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4260]) ).
thf(4320,plain,
! [SV272: $i,SV718: $i,SV172: $i] :
( ( ( ~ ! [SY1535: $i] :
( ! [SY1536: $i] :
( ( SY1536 != SY1535 )
| ~ ( in @ SY1536 @ ( cartesian_product2 @ SV172 @ SV718 ) ) )
| ! [SY1537: $i,SY1538: $i] :
( ( ( ordered_pair @ SY1537 @ SY1538 )
!= SY1535 )
| ~ ( in @ SY1537 @ SV172 )
| ! [SY1539: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1539 @ SY1538 @ SY1537 @ SY1535 @ SV718 @ SV272 @ SV172 ) @ SY1539 )
| ~ ~ ( in @ ( ordered_pair @ SY1538 @ ( sK34_R @ SY1539 @ SY1538 @ SY1537 @ SY1535 @ SV718 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1537 != SY1539 )
| ~ ( in @ SY1538 @ SY1539 ) ) )
| ( in @ SY1535 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4261]) ).
thf(4321,plain,
! [SV172: $i,SV272: $i,SV718: $i] :
( ( ( ~ ! [SY1540: $i] :
( ~ ( in @ SY1540 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1540 @ SV718 @ SV272 @ SV172 )
!= SY1540 )
| ~ ( in @ ( sK33_F @ SY1540 @ SV718 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV718 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1540 @ SV718 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1540 @ SV718 @ SV272 @ SV172 ) )
!= SY1540 )
| ~ ( in @ ( sK30_O @ SY1540 @ SV718 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1541: $i] :
( ~ ( in @ SY1541 @ ( sK32_SY652 @ SY1540 @ SV718 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1540 @ SV718 @ SV272 @ SV172 ) @ SY1541 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1540 @ SV718 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1540 @ SV718 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1540 @ SV718 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1540 @ SV718 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4261]) ).
thf(4322,plain,
! [SV272: $i,SV719: $i,SV172: $i] :
( ( ( ~ ! [SY1542: $i] :
( ! [SY1543: $i] :
( ( SY1543 != SY1542 )
| ~ ( in @ SY1543 @ ( cartesian_product2 @ SV172 @ SV719 ) ) )
| ! [SY1544: $i,SY1545: $i] :
( ( ( ordered_pair @ SY1544 @ SY1545 )
!= SY1542 )
| ~ ( in @ SY1544 @ SV172 )
| ! [SY1546: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1546 @ SY1545 @ SY1544 @ SY1542 @ SV719 @ SV272 @ SV172 ) @ SY1546 )
| ~ ~ ( in @ ( ordered_pair @ SY1545 @ ( sK34_R @ SY1546 @ SY1545 @ SY1544 @ SY1542 @ SV719 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1544 != SY1546 )
| ~ ( in @ SY1545 @ SY1546 ) ) )
| ( in @ SY1542 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4262]) ).
thf(4323,plain,
! [SV172: $i,SV272: $i,SV719: $i] :
( ( ( ~ ! [SY1547: $i] :
( ~ ( in @ SY1547 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1547 @ SV719 @ SV272 @ SV172 )
!= SY1547 )
| ~ ( in @ ( sK33_F @ SY1547 @ SV719 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV719 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1547 @ SV719 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1547 @ SV719 @ SV272 @ SV172 ) )
!= SY1547 )
| ~ ( in @ ( sK30_O @ SY1547 @ SV719 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1548: $i] :
( ~ ( in @ SY1548 @ ( sK32_SY652 @ SY1547 @ SV719 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1547 @ SV719 @ SV272 @ SV172 ) @ SY1548 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1547 @ SV719 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1547 @ SV719 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1547 @ SV719 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1547 @ SV719 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4262]) ).
thf(4324,plain,
! [SV172: $i,SV272: $i,SV720: $i] :
( ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4263]) ).
thf(4325,plain,
! [SV172: $i,SV272: $i] :
( ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4264]) ).
thf(4326,plain,
! [SV172: $i,SV272: $i] :
( ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4265]) ).
thf(4327,plain,
! [SV272: $i,SV677: $i,SV622: $i,SV172: $i,SV701: $i] :
( ( ( in @ SV701 @ ( cartesian_product2 @ SV172 @ SV622 ) )
= $false )
| ( ( SV701 = SV677 )
= $false )
| ( ( ! [SY1490: $i,SY1491: $i] :
( ( ( ordered_pair @ SY1490 @ SY1491 )
!= SV677 )
| ~ ( in @ SY1490 @ SV172 )
| ! [SY1492: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1492 @ SY1491 @ SY1490 @ SV677 @ SV622 @ SV272 @ SV172 ) @ SY1492 )
| ~ ~ ( in @ ( ordered_pair @ SY1491 @ ( sK34_R @ SY1492 @ SY1491 @ SY1490 @ SV677 @ SV622 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1490 != SY1492 )
| ~ ( in @ SY1491 @ SY1492 ) ) ) )
= $true )
| ( ( in @ SV677 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4266]) ).
thf(4328,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( ( ( sK33_F @ SV678 @ SV622 @ SV272 @ SV172 )
!= SV678 )
| ~ ( in @ ( sK33_F @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV622 ) ) )
= $false )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4267]) ).
thf(4329,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) )
!= SV678 )
| ~ ( in @ ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1493: $i] :
( ~ ( in @ SY1493 @ ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) @ SY1493 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) ) ) ) )
= $false )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4268]) ).
thf(4330,plain,
! [SV660: $i,SV139: $i,SV702: $i,SV728: $i] :
( ( ( ( SV728 != SV702 )
| ~ ( in @ SV728 @ ( cartesian_product2 @ SV139 @ SV660 ) ) )
= $true )
| ( ( ! [SY1517: $i,SY1518: $i] :
( ( ( ordered_pair @ SY1517 @ SY1518 )
!= SV702 )
| ~ ( in @ SY1517 @ SV139 )
| ( SY1518
!= ( singleton @ SY1517 ) ) ) )
= $true )
| ( ( in @ SV702 @ ( sK13_C @ SV660 @ SV139 ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4269]) ).
thf(4331,plain,
! [SV139: $i,SV660: $i,SV703: $i] :
( ( ( ~ ~ ( ( ( sK16_E @ SV703 @ SV660 @ SV139 )
!= SV703 )
| ~ ( in @ ( sK16_E @ SV703 @ SV660 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV660 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV703 @ SV660 @ SV139 ) @ ( sK15_SY612 @ SV703 @ SV660 @ SV139 ) )
!= SV703 )
| ~ ( in @ ( sK14_J @ SV703 @ SV660 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV703 @ SV660 @ SV139 )
!= ( singleton @ ( sK14_J @ SV703 @ SV660 @ SV139 ) ) ) ) )
= $false )
| ( ( in @ SV703 @ ( sK13_C @ SV660 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4270]) ).
thf(4332,plain,
! [SV725: $i,SV139: $i] :
( ( ( ~ ! [SY1554: $i] :
( ! [SY1555: $i] :
( ( SY1555 != SY1554 )
| ~ ( in @ SY1555 @ ( cartesian_product2 @ SV139 @ SV725 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1554 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1554 @ ( sK13_C @ SV725 @ SV139 ) ) )
| ~ ! [SY1558: $i] :
( ~ ( in @ SY1558 @ ( sK13_C @ SV725 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1558 @ SV725 @ SV139 )
!= SY1558 )
| ~ ( in @ ( sK16_E @ SY1558 @ SV725 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV725 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1558 @ SV725 @ SV139 ) @ ( sK15_SY612 @ SY1558 @ SV725 @ SV139 ) )
!= SY1558 )
| ~ ( in @ ( sK14_J @ SY1558 @ SV725 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1558 @ SV725 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1558 @ SV725 @ SV139 ) ) ) ) ) ) )
= $false )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4271]) ).
thf(4333,plain,
! [SV726: $i,SV139: $i] :
( ( ( ~ ! [SY1559: $i] :
( ! [SY1560: $i] :
( ( SY1560 != SY1559 )
| ~ ( in @ SY1560 @ ( cartesian_product2 @ SV139 @ SV726 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1559 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1559 @ ( sK13_C @ SV726 @ SV139 ) ) )
| ~ ! [SY1563: $i] :
( ~ ( in @ SY1563 @ ( sK13_C @ SV726 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1563 @ SV726 @ SV139 )
!= SY1563 )
| ~ ( in @ ( sK16_E @ SY1563 @ SV726 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV726 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1563 @ SV726 @ SV139 ) @ ( sK15_SY612 @ SY1563 @ SV726 @ SV139 ) )
!= SY1563 )
| ~ ( in @ ( sK14_J @ SY1563 @ SV726 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1563 @ SV726 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1563 @ SV726 @ SV139 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4272]) ).
thf(4334,plain,
! [SV694: $i,SV139: $i,SV729: $i] :
( ( ( ! [SY1565: $i] :
( ( SY1565 != SV729 )
| ~ ( in @ SY1565 @ ( cartesian_product2 @ SV139 @ SV694 ) ) )
| ! [SY1566: $i,SY1567: $i] :
( ( ( ordered_pair @ SY1566 @ SY1567 )
!= SV729 )
| ~ ( in @ SY1566 @ SV139 )
| ( SY1567
!= ( singleton @ SY1566 ) ) )
| ( in @ SV729 @ ( sK13_C @ SV694 @ SV139 ) ) )
= $true )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4273]) ).
thf(4335,plain,
! [SV139: $i,SV694: $i,SV730: $i] :
( ( ( ~ ( in @ SV730 @ ( sK13_C @ SV694 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SV730 @ SV694 @ SV139 )
!= SV730 )
| ~ ( in @ ( sK16_E @ SV730 @ SV694 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV694 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV730 @ SV694 @ SV139 ) @ ( sK15_SY612 @ SV730 @ SV694 @ SV139 ) )
!= SV730 )
| ~ ( in @ ( sK14_J @ SV730 @ SV694 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV730 @ SV694 @ SV139 )
!= ( singleton @ ( sK14_J @ SV730 @ SV694 @ SV139 ) ) ) ) ) )
= $true )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4274]) ).
thf(4336,plain,
! [SV681: $i,SV624: $i,SV139: $i,SV704: $i] :
( ( ( in @ SV704 @ ( cartesian_product2 @ SV139 @ SV624 ) )
= $false )
| ( ( SV704 = SV681 )
= $false )
| ( ( ! [SY1495: $i,SY1496: $i] :
( ( ( ordered_pair @ SY1495 @ SY1496 )
!= SV681 )
| ~ ( in @ SY1495 @ SV139 )
| ( SY1496
!= ( singleton @ SY1495 ) ) ) )
= $true )
| ( ( in @ SV681 @ ( sK13_C @ SV624 @ SV139 ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4275]) ).
thf(4337,plain,
! [SV139: $i,SV624: $i,SV682: $i] :
( ( ( ( ( sK16_E @ SV682 @ SV624 @ SV139 )
!= SV682 )
| ~ ( in @ ( sK16_E @ SV682 @ SV624 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV624 ) ) )
= $false )
| ( ( in @ SV682 @ ( sK13_C @ SV624 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4276]) ).
thf(4338,plain,
! [SV139: $i,SV624: $i,SV682: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV682 @ SV624 @ SV139 ) @ ( sK15_SY612 @ SV682 @ SV624 @ SV139 ) )
!= SV682 )
| ~ ( in @ ( sK14_J @ SV682 @ SV624 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV682 @ SV624 @ SV139 )
!= ( singleton @ ( sK14_J @ SV682 @ SV624 @ SV139 ) ) ) )
= $false )
| ( ( in @ SV682 @ ( sK13_C @ SV624 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4277]) ).
thf(4339,plain,
! [SV661: $i,SV139: $i,SV705: $i,SV731: $i] :
( ( ( ( SV731 != SV705 )
| ~ ( in @ SV731 @ ( cartesian_product2 @ SV139 @ SV661 ) ) )
= $true )
| ( ( ! [SY1520: $i,SY1521: $i] :
( ( ( ordered_pair @ SY1520 @ SY1521 )
!= SV705 )
| ~ ( in @ SY1520 @ SV139 )
| ( SY1521
!= ( singleton @ SY1520 ) ) ) )
= $true )
| ( ( in @ SV705 @ ( sK13_C @ SV661 @ SV139 ) )
= $true )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4278]) ).
thf(4340,plain,
! [SV139: $i,SV661: $i,SV706: $i] :
( ( ( ~ ~ ( ( ( sK16_E @ SV706 @ SV661 @ SV139 )
!= SV706 )
| ~ ( in @ ( sK16_E @ SV706 @ SV661 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV661 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV706 @ SV661 @ SV139 ) @ ( sK15_SY612 @ SV706 @ SV661 @ SV139 ) )
!= SV706 )
| ~ ( in @ ( sK14_J @ SV706 @ SV661 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV706 @ SV661 @ SV139 )
!= ( singleton @ ( sK14_J @ SV706 @ SV661 @ SV139 ) ) ) ) )
= $false )
| ( ( in @ SV706 @ ( sK13_C @ SV661 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4279]) ).
thf(4341,plain,
! [SV662: $i,SV139: $i,SV707: $i,SV732: $i] :
( ( ( ( SV732 != SV707 )
| ~ ( in @ SV732 @ ( cartesian_product2 @ SV139 @ SV662 ) ) )
= $true )
| ( ( ! [SY1523: $i,SY1524: $i] :
( ( ( ordered_pair @ SY1523 @ SY1524 )
!= SV707 )
| ~ ( in @ SY1523 @ SV139 )
| ( SY1524
!= ( singleton @ SY1523 ) ) ) )
= $true )
| ( ( in @ SV707 @ ( sK13_C @ SV662 @ SV139 ) )
= $true )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4280]) ).
thf(4342,plain,
! [SV139: $i,SV662: $i,SV708: $i] :
( ( ( ~ ~ ( ( ( sK16_E @ SV708 @ SV662 @ SV139 )
!= SV708 )
| ~ ( in @ ( sK16_E @ SV708 @ SV662 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV662 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV708 @ SV662 @ SV139 ) @ ( sK15_SY612 @ SV708 @ SV662 @ SV139 ) )
!= SV708 )
| ~ ( in @ ( sK14_J @ SV708 @ SV662 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV708 @ SV662 @ SV139 )
!= ( singleton @ ( sK14_J @ SV708 @ SV662 @ SV139 ) ) ) ) )
= $false )
| ( ( in @ SV708 @ ( sK13_C @ SV662 @ SV139 ) )
= $false )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4281]) ).
thf(4343,plain,
! [SV683: $i,SV625: $i,SV139: $i,SV709: $i] :
( ( ( in @ SV709 @ ( cartesian_product2 @ SV139 @ SV625 ) )
= $false )
| ( ( SV709 = SV683 )
= $false )
| ( ( ! [SY1498: $i,SY1499: $i] :
( ( ( ordered_pair @ SY1498 @ SY1499 )
!= SV683 )
| ~ ( in @ SY1498 @ SV139 )
| ( SY1499
!= ( singleton @ SY1498 ) ) ) )
= $true )
| ( ( in @ SV683 @ ( sK13_C @ SV625 @ SV139 ) )
= $true )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4282]) ).
thf(4344,plain,
! [SV139: $i,SV625: $i,SV684: $i] :
( ( ( ( ( sK16_E @ SV684 @ SV625 @ SV139 )
!= SV684 )
| ~ ( in @ ( sK16_E @ SV684 @ SV625 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV625 ) ) )
= $false )
| ( ( in @ SV684 @ ( sK13_C @ SV625 @ SV139 ) )
= $false )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4283]) ).
thf(4345,plain,
! [SV139: $i,SV625: $i,SV684: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV684 @ SV625 @ SV139 ) @ ( sK15_SY612 @ SV684 @ SV625 @ SV139 ) )
!= SV684 )
| ~ ( in @ ( sK14_J @ SV684 @ SV625 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV684 @ SV625 @ SV139 )
!= ( singleton @ ( sK14_J @ SV684 @ SV625 @ SV139 ) ) ) )
= $false )
| ( ( in @ SV684 @ ( sK13_C @ SV625 @ SV139 ) )
= $false )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4284]) ).
thf(4346,plain,
! [SV488: $i,SV654: $i,SV139: $i,SV603: $i,SV710: $i,SV695: $i] :
( ( ( ( ordered_pair @ SV695 @ SV710 )
= SV603 )
= $false )
| ( ( ~ ( in @ SV695 @ SV139 ) )
= $true )
| ( ( ( SV710
!= ( singleton @ SV695 ) ) )
= $true )
| ( ( SV654 = SV603 )
= $false )
| ( ( in @ SV654 @ ( cartesian_product2 @ SV139 @ SV488 ) )
= $false )
| ( ( in @ SV603 @ ( sK13_C @ SV488 @ SV139 ) )
= $true )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4285]) ).
thf(4347,plain,
! [SV139: $i,SV488: $i,SV604: $i] :
( ( ( ( ordered_pair @ ( sK14_J @ SV604 @ SV488 @ SV139 ) @ ( sK15_SY612 @ SV604 @ SV488 @ SV139 ) )
= SV604 )
= $true )
| ( ( in @ SV604 @ ( sK13_C @ SV488 @ SV139 ) )
= $false )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4286]) ).
thf(4348,plain,
! [SV139: $i,SV488: $i,SV604: $i] :
( ( ( in @ ( sK14_J @ SV604 @ SV488 @ SV139 ) @ SV139 )
= $true )
| ( ( in @ SV604 @ ( sK13_C @ SV488 @ SV139 ) )
= $false )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4287]) ).
thf(4349,plain,
! [SV145: $i,SV265: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 ) )
= $true )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4288]) ).
thf(4350,plain,
! [SV145: $i,SV265: $i] :
( ( ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK52_SY712 @ SV265 @ SV145 ) )
| ~ ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4289]) ).
thf(4351,plain,
! [SV265: $i,SV734: $i,SV145: $i] :
( ( ( ! [SY1568: $i] :
( ~ ( in @ SY1568 @ SV145 )
| ! [SY1569: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1569 @ SY1568 @ SV734 @ SV265 @ SV145 ) @ SY1569 )
| ~ ~ ( in @ ( ordered_pair @ SV734 @ ( sK47_K @ SY1569 @ SY1568 @ SV734 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1568 != SY1569 )
| ~ ( in @ SV734 @ SY1569 ) ) )
| ( in @ SV734 @ ( sK44_C @ SV265 @ SV145 ) ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4290]) ).
thf(4352,plain,
! [SV145: $i,SV265: $i,SV735: $i] :
( ( ( ~ ( in @ SV735 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SV735 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1570: $i] :
( ~ ( in @ SY1570 @ ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV735 @ SY1570 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV735 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) )
| ~ ( in @ SV735 @ ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4291]) ).
thf(4353,plain,
! [SV265: $i,SV711: $i,SV145: $i,SV727: $i] :
( ( ( ~ ( in @ SV727 @ SV145 ) )
= $true )
| ( ( ! [SY1564: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1564 @ SV727 @ SV711 @ SV265 @ SV145 ) @ SY1564 )
| ~ ~ ( in @ ( ordered_pair @ SV711 @ ( sK47_K @ SY1564 @ SV727 @ SV711 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV727 != SY1564 )
| ~ ( in @ SV711 @ SY1564 ) ) )
= $true )
| ( ( in @ SV711 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4292]) ).
thf(4354,plain,
! [SV145: $i,SV265: $i,SV712: $i] :
( ( ( ~ ( in @ ( sK45_E @ SV712 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1527: $i] :
( ~ ( in @ SY1527 @ ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV712 @ SY1527 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV712 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) )
| ~ ( in @ SV712 @ ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) ) ) ) )
= $false )
| ( ( in @ SV712 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4293]) ).
thf(4355,plain,
! [SV685: $i,SV265: $i,SV736: $i,SV145: $i] :
( ( ( ! [SY1571: $i] :
( ~ ( in @ SY1571 @ SV145 )
| ! [SY1572: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1572 @ SY1571 @ SV736 @ SV265 @ SV145 ) @ SY1572 )
| ~ ~ ( in @ ( ordered_pair @ SV736 @ ( sK47_K @ SY1572 @ SY1571 @ SV736 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1571 != SY1572 )
| ~ ( in @ SV736 @ SY1572 ) ) )
| ( in @ SV736 @ ( sK44_C @ SV265 @ SV145 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4294]) ).
thf(4356,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV737: $i] :
( ( ( ~ ( in @ SV737 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SV737 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1573: $i] :
( ~ ( in @ SY1573 @ ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV737 @ SY1573 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV737 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) )
| ~ ( in @ SV737 @ ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) ) ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4295]) ).
thf(4357,plain,
! [SV265: $i,SV738: $i,SV145: $i] :
( ( ( ! [SY1574: $i] :
( ~ ( in @ SY1574 @ SV145 )
| ! [SY1575: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1575 @ SY1574 @ SV738 @ SV265 @ SV145 ) @ SY1575 )
| ~ ~ ( in @ ( ordered_pair @ SV738 @ ( sK47_K @ SY1575 @ SY1574 @ SV738 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1574 != SY1575 )
| ~ ( in @ SV738 @ SY1575 ) ) )
| ( in @ SV738 @ ( sK44_C @ SV265 @ SV145 ) ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4296]) ).
thf(4358,plain,
! [SV145: $i,SV265: $i,SV739: $i] :
( ( ( ~ ( in @ SV739 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SV739 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1576: $i] :
( ~ ( in @ SY1576 @ ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV739 @ SY1576 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV739 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) )
| ~ ( in @ SV739 @ ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) ) ) ) ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4297]) ).
thf(4359,plain,
! [SV265: $i,SV740: $i,SV145: $i] :
( ( ( ! [SY1577: $i] :
( ~ ( in @ SY1577 @ SV145 )
| ! [SY1578: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1578 @ SY1577 @ SV740 @ SV265 @ SV145 ) @ SY1578 )
| ~ ~ ( in @ ( ordered_pair @ SV740 @ ( sK47_K @ SY1578 @ SY1577 @ SV740 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1577 != SY1578 )
| ~ ( in @ SV740 @ SY1578 ) ) )
| ( in @ SV740 @ ( sK44_C @ SV265 @ SV145 ) ) )
= $true )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4298]) ).
thf(4360,plain,
! [SV145: $i,SV265: $i,SV741: $i] :
( ( ( ~ ( in @ SV741 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SV741 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1579: $i] :
( ~ ( in @ SY1579 @ ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV741 @ SY1579 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV741 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) )
| ~ ( in @ SV741 @ ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4299]) ).
thf(4361,plain,
! [SV145: $i,SV265: $i,SV655: $i,SV686: $i,SV713: $i] :
( ( ( ~ ( in @ ( sK47_K @ SV713 @ SV686 @ SV655 @ SV265 @ SV145 ) @ SV713 ) )
= $false )
| ( ( ( SV686 != SV713 )
| ~ ( in @ SV655 @ SV713 ) )
= $true )
| ( ( in @ SV686 @ SV145 )
= $false )
| ( ( in @ SV655 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4300]) ).
thf(4362,plain,
! [SV145: $i,SV265: $i,SV686: $i,SV713: $i,SV655: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV655 @ ( sK47_K @ SV713 @ SV686 @ SV655 @ SV265 @ SV145 ) ) @ SV265 ) )
= $false )
| ( ( ( SV686 != SV713 )
| ~ ( in @ SV655 @ SV713 ) )
= $true )
| ( ( in @ SV686 @ SV145 )
= $false )
| ( ( in @ SV655 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4300]) ).
thf(4363,plain,
! [SV145: $i,SV265: $i,SV656: $i] :
( ( ( ! [SY1467: $i] :
( ~ ( in @ SY1467 @ ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV656 @ SY1467 ) @ SV265 ) ) )
= $true )
| ( ( in @ SV656 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4301]) ).
thf(4364,plain,
! [SV145: $i,SV265: $i,SV656: $i] :
( ( ( ~ ( ( ( sK45_E @ SV656 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) )
| ~ ( in @ SV656 @ ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) ) ) )
= $true )
| ( ( in @ SV656 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4302]) ).
thf(4365,plain,
! [SV697: $i,SV168: $i,SV721: $i] :
( ( ( in @ SV721 @ SV168 )
= $false )
| ( ( ( SV697
!= ( singleton @ SV721 ) ) )
= $true )
| ( ( in @ SV697 @ ( sK24_B @ SV168 ) )
= $true )
| ( ( ( sK27_SY634 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4305]) ).
thf(4366,plain,
! [SV168: $i,SV698: $i] :
( ( ( ~ ( in @ ( sK25_D @ SV698 @ SV168 ) @ SV168 ) )
= $false )
| ( ( in @ SV698 @ ( sK24_B @ SV168 ) )
= $false )
| ( ( ( sK27_SY634 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4306]) ).
thf(4367,plain,
! [SV168: $i,SV698: $i] :
( ( ( ( SV698
!= ( singleton @ ( sK25_D @ SV698 @ SV168 ) ) ) )
= $false )
| ( ( in @ SV698 @ ( sK24_B @ SV168 ) )
= $false )
| ( ( ( sK27_SY634 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4306]) ).
thf(4368,plain,
! [SV699: $i,SV168: $i,SV722: $i] :
( ( ( in @ SV722 @ SV168 )
= $false )
| ( ( ( SV699
!= ( singleton @ SV722 ) ) )
= $true )
| ( ( in @ SV699 @ ( sK24_B @ SV168 ) )
= $true )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4307]) ).
thf(4369,plain,
! [SV168: $i,SV700: $i] :
( ( ( ~ ( in @ ( sK25_D @ SV700 @ SV168 ) @ SV168 ) )
= $false )
| ( ( in @ SV700 @ ( sK24_B @ SV168 ) )
= $false )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4308]) ).
thf(4370,plain,
! [SV168: $i,SV700: $i] :
( ( ( ( SV700
!= ( singleton @ ( sK25_D @ SV700 @ SV168 ) ) ) )
= $false )
| ( ( in @ SV700 @ ( sK24_B @ SV168 ) )
= $false )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4308]) ).
thf(4371,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV596: $i,SV651: $i,SV659: $i,SV716: $i] :
( ( ( ~ ( in @ ( sK115_I @ SV716 @ SV659 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) @ SV716 ) )
= $false )
| ( ( ( SV651 != SV716 )
| ~ ( in @ SV659 @ SV716 ) )
= $true )
| ( ( ( ordered_pair @ SV651 @ SV659 )
= SV596 )
= $false )
| ( ( in @ SV651 @ SV170 )
= $false )
| ( ( ~ ( in @ SV596 @ ( cartesian_product2 @ SV170 @ SV481 ) ) )
= $true )
| ( ( in @ SV596 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4309]) ).
thf(4372,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV596: $i,SV651: $i,SV716: $i,SV659: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV659 @ ( sK115_I @ SV716 @ SV659 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) ) @ SV271 ) )
= $false )
| ( ( ( SV651 != SV716 )
| ~ ( in @ SV659 @ SV716 ) )
= $true )
| ( ( ( ordered_pair @ SV651 @ SV659 )
= SV596 )
= $false )
| ( ( in @ SV651 @ SV170 )
= $false )
| ( ( ~ ( in @ SV596 @ ( cartesian_product2 @ SV170 @ SV481 ) ) )
= $true )
| ( ( in @ SV596 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4309]) ).
thf(4373,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV652: $i,SV742: $i] :
( ( ( ~ ( in @ SV742 @ ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) )
| ( in @ ( ordered_pair @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) @ SV742 ) @ SV271 ) )
= $true )
| ( ( in @ SV652 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $false )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4312]) ).
thf(4374,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV652: $i] :
( ( ( ( ( sK112_F @ SV652 @ SV481 @ SV271 @ SV170 )
!= ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) )
| ~ ( in @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) @ ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) ) )
= $false )
| ( ( in @ SV652 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $false )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4313]) ).
thf(4375,plain,
! [SV272: $i,SV717: $i,SV172: $i] :
( ( ( ! [SY1528: $i] :
( ! [SY1529: $i] :
( ( SY1529 != SY1528 )
| ~ ( in @ SY1529 @ ( cartesian_product2 @ SV172 @ SV717 ) ) )
| ! [SY1530: $i,SY1531: $i] :
( ( ( ordered_pair @ SY1530 @ SY1531 )
!= SY1528 )
| ~ ( in @ SY1530 @ SV172 )
| ! [SY1532: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1532 @ SY1531 @ SY1530 @ SY1528 @ SV717 @ SV272 @ SV172 ) @ SY1532 )
| ~ ~ ( in @ ( ordered_pair @ SY1531 @ ( sK34_R @ SY1532 @ SY1531 @ SY1530 @ SY1528 @ SV717 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1530 != SY1532 )
| ~ ( in @ SY1531 @ SY1532 ) ) )
| ( in @ SY1528 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) ) ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4314]) ).
thf(4376,plain,
! [SV172: $i,SV272: $i,SV717: $i] :
( ( ( ! [SY1533: $i] :
( ~ ( in @ SY1533 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1533 @ SV717 @ SV272 @ SV172 )
!= SY1533 )
| ~ ( in @ ( sK33_F @ SY1533 @ SV717 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV717 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1533 @ SV717 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1533 @ SV717 @ SV272 @ SV172 ) )
!= SY1533 )
| ~ ( in @ ( sK30_O @ SY1533 @ SV717 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1534: $i] :
( ~ ( in @ SY1534 @ ( sK32_SY652 @ SY1533 @ SV717 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1533 @ SV717 @ SV272 @ SV172 ) @ SY1534 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1533 @ SV717 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1533 @ SV717 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1533 @ SV717 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1533 @ SV717 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4315]) ).
thf(4377,plain,
! [SV172: $i,SV272: $i] :
( ( ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
!= ( sK36_SY655 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4316]) ).
thf(4378,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ! [SY1178: $i] :
( ~ ( in @ SY1178 @ ( sK43_SY691 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SY1178 ) @ SV272 ) )
| ~ ~ ( ( ( sK41_SY666 @ SV272 @ SV172 )
!= ( sK43_SY691 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4317]) ).
thf(4379,plain,
! [SV272: $i,SV692: $i,SV172: $i,SV723: $i] :
( ( ( ! [SY1549: $i] :
( ( SY1549 != SV723 )
| ~ ( in @ SY1549 @ ( cartesian_product2 @ SV172 @ SV692 ) ) ) )
= $true )
| ( ( ! [SY1550: $i,SY1551: $i] :
( ( ( ordered_pair @ SY1550 @ SY1551 )
!= SV723 )
| ~ ( in @ SY1550 @ SV172 )
| ! [SY1552: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1552 @ SY1551 @ SY1550 @ SV723 @ SV692 @ SV272 @ SV172 ) @ SY1552 )
| ~ ~ ( in @ ( ordered_pair @ SY1551 @ ( sK34_R @ SY1552 @ SY1551 @ SY1550 @ SV723 @ SV692 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1550 != SY1552 )
| ~ ( in @ SY1551 @ SY1552 ) ) ) )
= $true )
| ( ( in @ SV723 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4318]) ).
thf(4380,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK33_F @ SV724 @ SV692 @ SV272 @ SV172 )
!= SV724 )
| ~ ( in @ ( sK33_F @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV692 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) )
!= SV724 )
| ~ ( in @ ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1553: $i] :
( ~ ( in @ SY1553 @ ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) @ SY1553 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4319]) ).
thf(4381,plain,
! [SV272: $i,SV718: $i,SV172: $i] :
( ( ( ! [SY1535: $i] :
( ! [SY1536: $i] :
( ( SY1536 != SY1535 )
| ~ ( in @ SY1536 @ ( cartesian_product2 @ SV172 @ SV718 ) ) )
| ! [SY1537: $i,SY1538: $i] :
( ( ( ordered_pair @ SY1537 @ SY1538 )
!= SY1535 )
| ~ ( in @ SY1537 @ SV172 )
| ! [SY1539: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1539 @ SY1538 @ SY1537 @ SY1535 @ SV718 @ SV272 @ SV172 ) @ SY1539 )
| ~ ~ ( in @ ( ordered_pair @ SY1538 @ ( sK34_R @ SY1539 @ SY1538 @ SY1537 @ SY1535 @ SV718 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1537 != SY1539 )
| ~ ( in @ SY1538 @ SY1539 ) ) )
| ( in @ SY1535 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4320]) ).
thf(4382,plain,
! [SV172: $i,SV272: $i,SV718: $i] :
( ( ( ! [SY1540: $i] :
( ~ ( in @ SY1540 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1540 @ SV718 @ SV272 @ SV172 )
!= SY1540 )
| ~ ( in @ ( sK33_F @ SY1540 @ SV718 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV718 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1540 @ SV718 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1540 @ SV718 @ SV272 @ SV172 ) )
!= SY1540 )
| ~ ( in @ ( sK30_O @ SY1540 @ SV718 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1541: $i] :
( ~ ( in @ SY1541 @ ( sK32_SY652 @ SY1540 @ SV718 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1540 @ SV718 @ SV272 @ SV172 ) @ SY1541 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1540 @ SV718 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1540 @ SV718 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1540 @ SV718 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1540 @ SV718 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4321]) ).
thf(4383,plain,
! [SV272: $i,SV719: $i,SV172: $i] :
( ( ( ! [SY1542: $i] :
( ! [SY1543: $i] :
( ( SY1543 != SY1542 )
| ~ ( in @ SY1543 @ ( cartesian_product2 @ SV172 @ SV719 ) ) )
| ! [SY1544: $i,SY1545: $i] :
( ( ( ordered_pair @ SY1544 @ SY1545 )
!= SY1542 )
| ~ ( in @ SY1544 @ SV172 )
| ! [SY1546: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1546 @ SY1545 @ SY1544 @ SY1542 @ SV719 @ SV272 @ SV172 ) @ SY1546 )
| ~ ~ ( in @ ( ordered_pair @ SY1545 @ ( sK34_R @ SY1546 @ SY1545 @ SY1544 @ SY1542 @ SV719 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1544 != SY1546 )
| ~ ( in @ SY1545 @ SY1546 ) ) )
| ( in @ SY1542 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) ) ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4322]) ).
thf(4384,plain,
! [SV172: $i,SV272: $i,SV719: $i] :
( ( ( ! [SY1547: $i] :
( ~ ( in @ SY1547 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1547 @ SV719 @ SV272 @ SV172 )
!= SY1547 )
| ~ ( in @ ( sK33_F @ SY1547 @ SV719 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV719 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1547 @ SV719 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1547 @ SV719 @ SV272 @ SV172 ) )
!= SY1547 )
| ~ ( in @ ( sK30_O @ SY1547 @ SV719 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1548: $i] :
( ~ ( in @ SY1548 @ ( sK32_SY652 @ SY1547 @ SV719 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1547 @ SV719 @ SV272 @ SV172 ) @ SY1548 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1547 @ SV719 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1547 @ SV719 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1547 @ SV719 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1547 @ SV719 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4323]) ).
thf(4385,plain,
! [SV720: $i,SV272: $i,SV743: $i,SV172: $i] :
( ( ( ~ ( ~ ! [SY1580: $i] :
( ! [SY1581: $i] :
( ( SY1581 != SY1580 )
| ~ ( in @ SY1581 @ ( cartesian_product2 @ SV172 @ SV743 ) ) )
| ! [SY1582: $i,SY1583: $i] :
( ( ( ordered_pair @ SY1582 @ SY1583 )
!= SY1580 )
| ~ ( in @ SY1582 @ SV172 )
| ! [SY1584: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1584 @ SY1583 @ SY1582 @ SY1580 @ SV743 @ SV272 @ SV172 ) @ SY1584 )
| ~ ~ ( in @ ( ordered_pair @ SY1583 @ ( sK34_R @ SY1584 @ SY1583 @ SY1582 @ SY1580 @ SV743 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1582 != SY1584 )
| ~ ( in @ SY1583 @ SY1584 ) ) )
| ( in @ SY1580 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) ) )
| ~ ! [SY1585: $i] :
( ~ ( in @ SY1585 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1585 @ SV743 @ SV272 @ SV172 )
!= SY1585 )
| ~ ( in @ ( sK33_F @ SY1585 @ SV743 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV743 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1585 @ SV743 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1585 @ SV743 @ SV272 @ SV172 ) )
!= SY1585 )
| ~ ( in @ ( sK30_O @ SY1585 @ SV743 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1586: $i] :
( ~ ( in @ SY1586 @ ( sK32_SY652 @ SY1585 @ SV743 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1585 @ SV743 @ SV272 @ SV172 ) @ SY1586 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1585 @ SV743 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1585 @ SV743 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1585 @ SV743 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1585 @ SV743 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4324]) ).
thf(4386,plain,
! [SV272: $i,SV744: $i,SV172: $i] :
( ( ( ~ ( ~ ! [SY1587: $i] :
( ! [SY1588: $i] :
( ( SY1588 != SY1587 )
| ~ ( in @ SY1588 @ ( cartesian_product2 @ SV172 @ SV744 ) ) )
| ! [SY1589: $i,SY1590: $i] :
( ( ( ordered_pair @ SY1589 @ SY1590 )
!= SY1587 )
| ~ ( in @ SY1589 @ SV172 )
| ! [SY1591: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1591 @ SY1590 @ SY1589 @ SY1587 @ SV744 @ SV272 @ SV172 ) @ SY1591 )
| ~ ~ ( in @ ( ordered_pair @ SY1590 @ ( sK34_R @ SY1591 @ SY1590 @ SY1589 @ SY1587 @ SV744 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1589 != SY1591 )
| ~ ( in @ SY1590 @ SY1591 ) ) )
| ( in @ SY1587 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) ) )
| ~ ! [SY1592: $i] :
( ~ ( in @ SY1592 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1592 @ SV744 @ SV272 @ SV172 )
!= SY1592 )
| ~ ( in @ ( sK33_F @ SY1592 @ SV744 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV744 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1592 @ SV744 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1592 @ SV744 @ SV272 @ SV172 ) )
!= SY1592 )
| ~ ( in @ ( sK30_O @ SY1592 @ SV744 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1593: $i] :
( ~ ( in @ SY1593 @ ( sK32_SY652 @ SY1592 @ SV744 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1592 @ SV744 @ SV272 @ SV172 ) @ SY1593 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1592 @ SV744 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1592 @ SV744 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1592 @ SV744 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1592 @ SV744 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4325]) ).
thf(4387,plain,
! [SV272: $i,SV745: $i,SV172: $i] :
( ( ( ~ ( ~ ! [SY1594: $i] :
( ! [SY1595: $i] :
( ( SY1595 != SY1594 )
| ~ ( in @ SY1595 @ ( cartesian_product2 @ SV172 @ SV745 ) ) )
| ! [SY1596: $i,SY1597: $i] :
( ( ( ordered_pair @ SY1596 @ SY1597 )
!= SY1594 )
| ~ ( in @ SY1596 @ SV172 )
| ! [SY1598: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1598 @ SY1597 @ SY1596 @ SY1594 @ SV745 @ SV272 @ SV172 ) @ SY1598 )
| ~ ~ ( in @ ( ordered_pair @ SY1597 @ ( sK34_R @ SY1598 @ SY1597 @ SY1596 @ SY1594 @ SV745 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1596 != SY1598 )
| ~ ( in @ SY1597 @ SY1598 ) ) )
| ( in @ SY1594 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) ) )
| ~ ! [SY1599: $i] :
( ~ ( in @ SY1599 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1599 @ SV745 @ SV272 @ SV172 )
!= SY1599 )
| ~ ( in @ ( sK33_F @ SY1599 @ SV745 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV745 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1599 @ SV745 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1599 @ SV745 @ SV272 @ SV172 ) )
!= SY1599 )
| ~ ( in @ ( sK30_O @ SY1599 @ SV745 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1600: $i] :
( ~ ( in @ SY1600 @ ( sK32_SY652 @ SY1599 @ SV745 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1599 @ SV745 @ SV272 @ SV172 ) @ SY1600 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1599 @ SV745 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1599 @ SV745 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1599 @ SV745 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1599 @ SV745 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4326]) ).
thf(4388,plain,
! [SV701: $i,SV272: $i,SV622: $i,SV172: $i,SV677: $i,SV746: $i] :
( ( ( ! [SY1601: $i] :
( ( ( ordered_pair @ SV746 @ SY1601 )
!= SV677 )
| ~ ( in @ SV746 @ SV172 )
| ! [SY1602: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1602 @ SY1601 @ SV746 @ SV677 @ SV622 @ SV272 @ SV172 ) @ SY1602 )
| ~ ~ ( in @ ( ordered_pair @ SY1601 @ ( sK34_R @ SY1602 @ SY1601 @ SV746 @ SV677 @ SV622 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV746 != SY1602 )
| ~ ( in @ SY1601 @ SY1602 ) ) ) )
= $true )
| ( ( SV701 = SV677 )
= $false )
| ( ( in @ SV701 @ ( cartesian_product2 @ SV172 @ SV622 ) )
= $false )
| ( ( in @ SV677 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4327]) ).
thf(4389,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( ( ( sK33_F @ SV678 @ SV622 @ SV272 @ SV172 )
!= SV678 ) )
= $false )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4328]) ).
thf(4390,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( ~ ( in @ ( sK33_F @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV622 ) ) )
= $false )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4328]) ).
thf(4391,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) )
!= SV678 )
| ~ ( in @ ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 ) @ SV172 ) ) )
= $false )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4329]) ).
thf(4392,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( ~ ~ ( ~ ! [SY1493: $i] :
( ~ ( in @ SY1493 @ ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) @ SY1493 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) ) ) ) )
= $false )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4329]) ).
thf(4393,plain,
! [SV660: $i,SV139: $i,SV702: $i,SV728: $i] :
( ( ( ( SV728 != SV702 ) )
= $true )
| ( ( ~ ( in @ SV728 @ ( cartesian_product2 @ SV139 @ SV660 ) ) )
= $true )
| ( ( ! [SY1517: $i,SY1518: $i] :
( ( ( ordered_pair @ SY1517 @ SY1518 )
!= SV702 )
| ~ ( in @ SY1517 @ SV139 )
| ( SY1518
!= ( singleton @ SY1517 ) ) ) )
= $true )
| ( ( in @ SV702 @ ( sK13_C @ SV660 @ SV139 ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4330]) ).
thf(4394,plain,
! [SV139: $i,SV660: $i,SV703: $i] :
( ( ( ~ ~ ( ( ( sK16_E @ SV703 @ SV660 @ SV139 )
!= SV703 )
| ~ ( in @ ( sK16_E @ SV703 @ SV660 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV660 ) ) ) )
= $false )
| ( ( in @ SV703 @ ( sK13_C @ SV660 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4331]) ).
thf(4395,plain,
! [SV139: $i,SV660: $i,SV703: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV703 @ SV660 @ SV139 ) @ ( sK15_SY612 @ SV703 @ SV660 @ SV139 ) )
!= SV703 )
| ~ ( in @ ( sK14_J @ SV703 @ SV660 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV703 @ SV660 @ SV139 )
!= ( singleton @ ( sK14_J @ SV703 @ SV660 @ SV139 ) ) ) ) )
= $false )
| ( ( in @ SV703 @ ( sK13_C @ SV660 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4331]) ).
thf(4396,plain,
! [SV725: $i,SV139: $i] :
( ( ( ~ ! [SY1554: $i] :
( ! [SY1555: $i] :
( ( SY1555 != SY1554 )
| ~ ( in @ SY1555 @ ( cartesian_product2 @ SV139 @ SV725 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1554 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1554 @ ( sK13_C @ SV725 @ SV139 ) ) ) )
= $false )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4332]) ).
thf(4397,plain,
! [SV139: $i,SV725: $i] :
( ( ( ~ ! [SY1558: $i] :
( ~ ( in @ SY1558 @ ( sK13_C @ SV725 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1558 @ SV725 @ SV139 )
!= SY1558 )
| ~ ( in @ ( sK16_E @ SY1558 @ SV725 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV725 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1558 @ SV725 @ SV139 ) @ ( sK15_SY612 @ SY1558 @ SV725 @ SV139 ) )
!= SY1558 )
| ~ ( in @ ( sK14_J @ SY1558 @ SV725 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1558 @ SV725 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1558 @ SV725 @ SV139 ) ) ) ) ) ) )
= $false )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4332]) ).
thf(4398,plain,
! [SV726: $i,SV139: $i] :
( ( ( ~ ! [SY1559: $i] :
( ! [SY1560: $i] :
( ( SY1560 != SY1559 )
| ~ ( in @ SY1560 @ ( cartesian_product2 @ SV139 @ SV726 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1559 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1559 @ ( sK13_C @ SV726 @ SV139 ) ) ) )
= $false )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4333]) ).
thf(4399,plain,
! [SV139: $i,SV726: $i] :
( ( ( ~ ! [SY1563: $i] :
( ~ ( in @ SY1563 @ ( sK13_C @ SV726 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1563 @ SV726 @ SV139 )
!= SY1563 )
| ~ ( in @ ( sK16_E @ SY1563 @ SV726 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV726 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1563 @ SV726 @ SV139 ) @ ( sK15_SY612 @ SY1563 @ SV726 @ SV139 ) )
!= SY1563 )
| ~ ( in @ ( sK14_J @ SY1563 @ SV726 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1563 @ SV726 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1563 @ SV726 @ SV139 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4333]) ).
thf(4400,plain,
! [SV694: $i,SV139: $i,SV729: $i] :
( ( ( ! [SY1565: $i] :
( ( SY1565 != SV729 )
| ~ ( in @ SY1565 @ ( cartesian_product2 @ SV139 @ SV694 ) ) )
| ! [SY1566: $i,SY1567: $i] :
( ( ( ordered_pair @ SY1566 @ SY1567 )
!= SV729 )
| ~ ( in @ SY1566 @ SV139 )
| ( SY1567
!= ( singleton @ SY1566 ) ) ) )
= $true )
| ( ( in @ SV729 @ ( sK13_C @ SV694 @ SV139 ) )
= $true )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4334]) ).
thf(4401,plain,
! [SV139: $i,SV694: $i,SV730: $i] :
( ( ( ~ ( in @ SV730 @ ( sK13_C @ SV694 @ SV139 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK16_E @ SV730 @ SV694 @ SV139 )
!= SV730 )
| ~ ( in @ ( sK16_E @ SV730 @ SV694 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV694 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV730 @ SV694 @ SV139 ) @ ( sK15_SY612 @ SV730 @ SV694 @ SV139 ) )
!= SV730 )
| ~ ( in @ ( sK14_J @ SV730 @ SV694 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV730 @ SV694 @ SV139 )
!= ( singleton @ ( sK14_J @ SV730 @ SV694 @ SV139 ) ) ) ) ) )
= $true )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4335]) ).
thf(4402,plain,
! [SV624: $i,SV704: $i,SV139: $i,SV681: $i,SV747: $i] :
( ( ( ! [SY1603: $i] :
( ( ( ordered_pair @ SV747 @ SY1603 )
!= SV681 )
| ~ ( in @ SV747 @ SV139 )
| ( SY1603
!= ( singleton @ SV747 ) ) ) )
= $true )
| ( ( SV704 = SV681 )
= $false )
| ( ( in @ SV704 @ ( cartesian_product2 @ SV139 @ SV624 ) )
= $false )
| ( ( in @ SV681 @ ( sK13_C @ SV624 @ SV139 ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4336]) ).
thf(4403,plain,
! [SV139: $i,SV624: $i,SV682: $i] :
( ( ( ( ( sK16_E @ SV682 @ SV624 @ SV139 )
!= SV682 ) )
= $false )
| ( ( in @ SV682 @ ( sK13_C @ SV624 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4337]) ).
thf(4404,plain,
! [SV139: $i,SV624: $i,SV682: $i] :
( ( ( ~ ( in @ ( sK16_E @ SV682 @ SV624 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV624 ) ) )
= $false )
| ( ( in @ SV682 @ ( sK13_C @ SV624 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4337]) ).
thf(4405,plain,
! [SV139: $i,SV624: $i,SV682: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV682 @ SV624 @ SV139 ) @ ( sK15_SY612 @ SV682 @ SV624 @ SV139 ) )
!= SV682 )
| ~ ( in @ ( sK14_J @ SV682 @ SV624 @ SV139 ) @ SV139 ) ) )
= $false )
| ( ( in @ SV682 @ ( sK13_C @ SV624 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4338]) ).
thf(4406,plain,
! [SV139: $i,SV624: $i,SV682: $i] :
( ( ( ( ( sK15_SY612 @ SV682 @ SV624 @ SV139 )
!= ( singleton @ ( sK14_J @ SV682 @ SV624 @ SV139 ) ) ) )
= $false )
| ( ( in @ SV682 @ ( sK13_C @ SV624 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4338]) ).
thf(4407,plain,
! [SV661: $i,SV139: $i,SV705: $i,SV731: $i] :
( ( ( ( SV731 != SV705 ) )
= $true )
| ( ( ~ ( in @ SV731 @ ( cartesian_product2 @ SV139 @ SV661 ) ) )
= $true )
| ( ( ! [SY1520: $i,SY1521: $i] :
( ( ( ordered_pair @ SY1520 @ SY1521 )
!= SV705 )
| ~ ( in @ SY1520 @ SV139 )
| ( SY1521
!= ( singleton @ SY1520 ) ) ) )
= $true )
| ( ( in @ SV705 @ ( sK13_C @ SV661 @ SV139 ) )
= $true )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4339]) ).
thf(4408,plain,
! [SV139: $i,SV661: $i,SV706: $i] :
( ( ( ~ ~ ( ( ( sK16_E @ SV706 @ SV661 @ SV139 )
!= SV706 )
| ~ ( in @ ( sK16_E @ SV706 @ SV661 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV661 ) ) ) )
= $false )
| ( ( in @ SV706 @ ( sK13_C @ SV661 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4340]) ).
thf(4409,plain,
! [SV139: $i,SV661: $i,SV706: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV706 @ SV661 @ SV139 ) @ ( sK15_SY612 @ SV706 @ SV661 @ SV139 ) )
!= SV706 )
| ~ ( in @ ( sK14_J @ SV706 @ SV661 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV706 @ SV661 @ SV139 )
!= ( singleton @ ( sK14_J @ SV706 @ SV661 @ SV139 ) ) ) ) )
= $false )
| ( ( in @ SV706 @ ( sK13_C @ SV661 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4340]) ).
thf(4410,plain,
! [SV662: $i,SV139: $i,SV707: $i,SV732: $i] :
( ( ( ( SV732 != SV707 ) )
= $true )
| ( ( ~ ( in @ SV732 @ ( cartesian_product2 @ SV139 @ SV662 ) ) )
= $true )
| ( ( ! [SY1523: $i,SY1524: $i] :
( ( ( ordered_pair @ SY1523 @ SY1524 )
!= SV707 )
| ~ ( in @ SY1523 @ SV139 )
| ( SY1524
!= ( singleton @ SY1523 ) ) ) )
= $true )
| ( ( in @ SV707 @ ( sK13_C @ SV662 @ SV139 ) )
= $true )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4341]) ).
thf(4411,plain,
! [SV139: $i,SV662: $i,SV708: $i] :
( ( ( ~ ~ ( ( ( sK16_E @ SV708 @ SV662 @ SV139 )
!= SV708 )
| ~ ( in @ ( sK16_E @ SV708 @ SV662 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV662 ) ) ) )
= $false )
| ( ( in @ SV708 @ ( sK13_C @ SV662 @ SV139 ) )
= $false )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4342]) ).
thf(4412,plain,
! [SV139: $i,SV662: $i,SV708: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV708 @ SV662 @ SV139 ) @ ( sK15_SY612 @ SV708 @ SV662 @ SV139 ) )
!= SV708 )
| ~ ( in @ ( sK14_J @ SV708 @ SV662 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV708 @ SV662 @ SV139 )
!= ( singleton @ ( sK14_J @ SV708 @ SV662 @ SV139 ) ) ) ) )
= $false )
| ( ( in @ SV708 @ ( sK13_C @ SV662 @ SV139 ) )
= $false )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4342]) ).
thf(4413,plain,
! [SV625: $i,SV709: $i,SV139: $i,SV683: $i,SV748: $i] :
( ( ( ! [SY1604: $i] :
( ( ( ordered_pair @ SV748 @ SY1604 )
!= SV683 )
| ~ ( in @ SV748 @ SV139 )
| ( SY1604
!= ( singleton @ SV748 ) ) ) )
= $true )
| ( ( SV709 = SV683 )
= $false )
| ( ( in @ SV709 @ ( cartesian_product2 @ SV139 @ SV625 ) )
= $false )
| ( ( in @ SV683 @ ( sK13_C @ SV625 @ SV139 ) )
= $true )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4343]) ).
thf(4414,plain,
! [SV139: $i,SV625: $i,SV684: $i] :
( ( ( ( ( sK16_E @ SV684 @ SV625 @ SV139 )
!= SV684 ) )
= $false )
| ( ( in @ SV684 @ ( sK13_C @ SV625 @ SV139 ) )
= $false )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4344]) ).
thf(4415,plain,
! [SV139: $i,SV625: $i,SV684: $i] :
( ( ( ~ ( in @ ( sK16_E @ SV684 @ SV625 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV625 ) ) )
= $false )
| ( ( in @ SV684 @ ( sK13_C @ SV625 @ SV139 ) )
= $false )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4344]) ).
thf(4416,plain,
! [SV139: $i,SV625: $i,SV684: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV684 @ SV625 @ SV139 ) @ ( sK15_SY612 @ SV684 @ SV625 @ SV139 ) )
!= SV684 )
| ~ ( in @ ( sK14_J @ SV684 @ SV625 @ SV139 ) @ SV139 ) ) )
= $false )
| ( ( in @ SV684 @ ( sK13_C @ SV625 @ SV139 ) )
= $false )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4345]) ).
thf(4417,plain,
! [SV139: $i,SV625: $i,SV684: $i] :
( ( ( ( ( sK15_SY612 @ SV684 @ SV625 @ SV139 )
!= ( singleton @ ( sK14_J @ SV684 @ SV625 @ SV139 ) ) ) )
= $false )
| ( ( in @ SV684 @ ( sK13_C @ SV625 @ SV139 ) )
= $false )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4345]) ).
thf(4418,plain,
! [SV488: $i,SV654: $i,SV603: $i,SV710: $i,SV139: $i,SV695: $i] :
( ( ( in @ SV695 @ SV139 )
= $false )
| ( ( ( ordered_pair @ SV695 @ SV710 )
= SV603 )
= $false )
| ( ( ( SV710
!= ( singleton @ SV695 ) ) )
= $true )
| ( ( SV654 = SV603 )
= $false )
| ( ( in @ SV654 @ ( cartesian_product2 @ SV139 @ SV488 ) )
= $false )
| ( ( in @ SV603 @ ( sK13_C @ SV488 @ SV139 ) )
= $true )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4346]) ).
thf(4419,plain,
! [SV145: $i,SV265: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4349]) ).
thf(4420,plain,
! [SV145: $i,SV265: $i] :
( ( ( ( ( sK48_C @ SV265 @ SV145 )
!= ( sK52_SY712 @ SV265 @ SV145 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4350]) ).
thf(4421,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4350]) ).
thf(4422,plain,
! [SV265: $i,SV734: $i,SV145: $i] :
( ( ( ! [SY1568: $i] :
( ~ ( in @ SY1568 @ SV145 )
| ! [SY1569: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1569 @ SY1568 @ SV734 @ SV265 @ SV145 ) @ SY1569 )
| ~ ~ ( in @ ( ordered_pair @ SV734 @ ( sK47_K @ SY1569 @ SY1568 @ SV734 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1568 != SY1569 )
| ~ ( in @ SV734 @ SY1569 ) ) ) )
= $true )
| ( ( in @ SV734 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4351]) ).
thf(4423,plain,
! [SV145: $i,SV265: $i,SV735: $i] :
( ( ( ~ ( in @ SV735 @ ( sK44_C @ SV265 @ SV145 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK45_E @ SV735 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1570: $i] :
( ~ ( in @ SY1570 @ ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV735 @ SY1570 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV735 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) )
| ~ ( in @ SV735 @ ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4352]) ).
thf(4424,plain,
! [SV265: $i,SV711: $i,SV145: $i,SV727: $i] :
( ( ( in @ SV727 @ SV145 )
= $false )
| ( ( ! [SY1564: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1564 @ SV727 @ SV711 @ SV265 @ SV145 ) @ SY1564 )
| ~ ~ ( in @ ( ordered_pair @ SV711 @ ( sK47_K @ SY1564 @ SV727 @ SV711 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV727 != SY1564 )
| ~ ( in @ SV711 @ SY1564 ) ) )
= $true )
| ( ( in @ SV711 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4353]) ).
thf(4425,plain,
! [SV145: $i,SV265: $i,SV712: $i] :
( ( ( ~ ( in @ ( sK45_E @ SV712 @ SV265 @ SV145 ) @ SV145 ) )
= $false )
| ( ( in @ SV712 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4354]) ).
thf(4426,plain,
! [SV145: $i,SV265: $i,SV712: $i] :
( ( ( ~ ~ ( ~ ! [SY1527: $i] :
( ~ ( in @ SY1527 @ ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV712 @ SY1527 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV712 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) )
| ~ ( in @ SV712 @ ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) ) ) ) )
= $false )
| ( ( in @ SV712 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4354]) ).
thf(4427,plain,
! [SV685: $i,SV265: $i,SV736: $i,SV145: $i] :
( ( ( ! [SY1571: $i] :
( ~ ( in @ SY1571 @ SV145 )
| ! [SY1572: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1572 @ SY1571 @ SV736 @ SV265 @ SV145 ) @ SY1572 )
| ~ ~ ( in @ ( ordered_pair @ SV736 @ ( sK47_K @ SY1572 @ SY1571 @ SV736 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1571 != SY1572 )
| ~ ( in @ SV736 @ SY1572 ) ) ) )
= $true )
| ( ( in @ SV736 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4355]) ).
thf(4428,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV737: $i] :
( ( ( ~ ( in @ SV737 @ ( sK44_C @ SV265 @ SV145 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK45_E @ SV737 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1573: $i] :
( ~ ( in @ SY1573 @ ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV737 @ SY1573 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV737 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) )
| ~ ( in @ SV737 @ ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) ) ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4356]) ).
thf(4429,plain,
! [SV265: $i,SV738: $i,SV145: $i] :
( ( ( ! [SY1574: $i] :
( ~ ( in @ SY1574 @ SV145 )
| ! [SY1575: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1575 @ SY1574 @ SV738 @ SV265 @ SV145 ) @ SY1575 )
| ~ ~ ( in @ ( ordered_pair @ SV738 @ ( sK47_K @ SY1575 @ SY1574 @ SV738 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1574 != SY1575 )
| ~ ( in @ SV738 @ SY1575 ) ) ) )
= $true )
| ( ( in @ SV738 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4357]) ).
thf(4430,plain,
! [SV145: $i,SV265: $i,SV739: $i] :
( ( ( ~ ( in @ SV739 @ ( sK44_C @ SV265 @ SV145 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK45_E @ SV739 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1576: $i] :
( ~ ( in @ SY1576 @ ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV739 @ SY1576 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV739 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) )
| ~ ( in @ SV739 @ ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) ) ) ) ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4358]) ).
thf(4431,plain,
! [SV265: $i,SV740: $i,SV145: $i] :
( ( ( ! [SY1577: $i] :
( ~ ( in @ SY1577 @ SV145 )
| ! [SY1578: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1578 @ SY1577 @ SV740 @ SV265 @ SV145 ) @ SY1578 )
| ~ ~ ( in @ ( ordered_pair @ SV740 @ ( sK47_K @ SY1578 @ SY1577 @ SV740 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1577 != SY1578 )
| ~ ( in @ SV740 @ SY1578 ) ) ) )
= $true )
| ( ( in @ SV740 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4359]) ).
thf(4432,plain,
! [SV145: $i,SV265: $i,SV741: $i] :
( ( ( ~ ( in @ SV741 @ ( sK44_C @ SV265 @ SV145 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK45_E @ SV741 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1579: $i] :
( ~ ( in @ SY1579 @ ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV741 @ SY1579 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV741 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) )
| ~ ( in @ SV741 @ ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4360]) ).
thf(4433,plain,
! [SV145: $i,SV265: $i,SV655: $i,SV686: $i,SV713: $i] :
( ( ( in @ ( sK47_K @ SV713 @ SV686 @ SV655 @ SV265 @ SV145 ) @ SV713 )
= $true )
| ( ( ( SV686 != SV713 )
| ~ ( in @ SV655 @ SV713 ) )
= $true )
| ( ( in @ SV686 @ SV145 )
= $false )
| ( ( in @ SV655 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4361]) ).
thf(4434,plain,
! [SV145: $i,SV265: $i,SV686: $i,SV713: $i,SV655: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV655 @ ( sK47_K @ SV713 @ SV686 @ SV655 @ SV265 @ SV145 ) ) @ SV265 ) )
= $true )
| ( ( ( SV686 != SV713 )
| ~ ( in @ SV655 @ SV713 ) )
= $true )
| ( ( in @ SV686 @ SV145 )
= $false )
| ( ( in @ SV655 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4362]) ).
thf(4435,plain,
! [SV145: $i,SV265: $i,SV656: $i,SV749: $i] :
( ( ( ~ ( in @ SV749 @ ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV656 @ SV749 ) @ SV265 ) )
= $true )
| ( ( in @ SV656 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4363]) ).
thf(4436,plain,
! [SV145: $i,SV265: $i,SV656: $i] :
( ( ( ( ( sK45_E @ SV656 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) )
| ~ ( in @ SV656 @ ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) ) )
= $false )
| ( ( in @ SV656 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4364]) ).
thf(4437,plain,
! [SV168: $i,SV721: $i,SV697: $i] :
( ( ( SV697
= ( singleton @ SV721 ) )
= $false )
| ( ( in @ SV721 @ SV168 )
= $false )
| ( ( in @ SV697 @ ( sK24_B @ SV168 ) )
= $true )
| ( ( ( sK27_SY634 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4365]) ).
thf(4438,plain,
! [SV168: $i,SV698: $i] :
( ( ( in @ ( sK25_D @ SV698 @ SV168 ) @ SV168 )
= $true )
| ( ( in @ SV698 @ ( sK24_B @ SV168 ) )
= $false )
| ( ( ( sK27_SY634 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4366]) ).
thf(4439,plain,
! [SV168: $i,SV698: $i] :
( ( ( SV698
= ( singleton @ ( sK25_D @ SV698 @ SV168 ) ) )
= $true )
| ( ( in @ SV698 @ ( sK24_B @ SV168 ) )
= $false )
| ( ( ( sK27_SY634 @ SV168 )
= ( singleton @ ( sK26_B @ SV168 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4367]) ).
thf(4440,plain,
! [SV168: $i,SV722: $i,SV699: $i] :
( ( ( SV699
= ( singleton @ SV722 ) )
= $false )
| ( ( in @ SV722 @ SV168 )
= $false )
| ( ( in @ SV699 @ ( sK24_B @ SV168 ) )
= $true )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4368]) ).
thf(4441,plain,
! [SV168: $i,SV700: $i] :
( ( ( in @ ( sK25_D @ SV700 @ SV168 ) @ SV168 )
= $true )
| ( ( in @ SV700 @ ( sK24_B @ SV168 ) )
= $false )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4369]) ).
thf(4442,plain,
! [SV168: $i,SV700: $i] :
( ( ( SV700
= ( singleton @ ( sK25_D @ SV700 @ SV168 ) ) )
= $true )
| ( ( in @ SV700 @ ( sK24_B @ SV168 ) )
= $false )
| ( ( in @ ( sK26_B @ SV168 ) @ SV168 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4370]) ).
thf(4443,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV596: $i,SV651: $i,SV659: $i,SV716: $i] :
( ( ( in @ ( sK115_I @ SV716 @ SV659 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) @ SV716 )
= $true )
| ( ( ( SV651 != SV716 )
| ~ ( in @ SV659 @ SV716 ) )
= $true )
| ( ( ( ordered_pair @ SV651 @ SV659 )
= SV596 )
= $false )
| ( ( in @ SV651 @ SV170 )
= $false )
| ( ( ~ ( in @ SV596 @ ( cartesian_product2 @ SV170 @ SV481 ) ) )
= $true )
| ( ( in @ SV596 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4371]) ).
thf(4444,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV596: $i,SV651: $i,SV716: $i,SV659: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV659 @ ( sK115_I @ SV716 @ SV659 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) ) @ SV271 ) )
= $true )
| ( ( ( SV651 != SV716 )
| ~ ( in @ SV659 @ SV716 ) )
= $true )
| ( ( ( ordered_pair @ SV651 @ SV659 )
= SV596 )
= $false )
| ( ( in @ SV651 @ SV170 )
= $false )
| ( ( ~ ( in @ SV596 @ ( cartesian_product2 @ SV170 @ SV481 ) ) )
= $true )
| ( ( in @ SV596 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4372]) ).
thf(4445,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV652: $i,SV742: $i] :
( ( ( ~ ( in @ SV742 @ ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) @ SV742 ) @ SV271 )
= $true )
| ( ( in @ SV652 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $false )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4373]) ).
thf(4446,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV652: $i] :
( ( ( ( ( sK112_F @ SV652 @ SV481 @ SV271 @ SV170 )
!= ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) ) )
= $false )
| ( ( in @ SV652 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $false )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4374]) ).
thf(4447,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV652: $i] :
( ( ( ~ ( in @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) @ ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) ) )
= $false )
| ( ( in @ SV652 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $false )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4374]) ).
thf(4448,plain,
! [SV272: $i,SV717: $i,SV172: $i,SV750: $i] :
( ( ( ! [SY1605: $i] :
( ( SY1605 != SV750 )
| ~ ( in @ SY1605 @ ( cartesian_product2 @ SV172 @ SV717 ) ) )
| ! [SY1606: $i,SY1607: $i] :
( ( ( ordered_pair @ SY1606 @ SY1607 )
!= SV750 )
| ~ ( in @ SY1606 @ SV172 )
| ! [SY1608: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1608 @ SY1607 @ SY1606 @ SV750 @ SV717 @ SV272 @ SV172 ) @ SY1608 )
| ~ ~ ( in @ ( ordered_pair @ SY1607 @ ( sK34_R @ SY1608 @ SY1607 @ SY1606 @ SV750 @ SV717 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1606 != SY1608 )
| ~ ( in @ SY1607 @ SY1608 ) ) )
| ( in @ SV750 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4375]) ).
thf(4449,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( ~ ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SV751 @ SV717 @ SV272 @ SV172 )
!= SV751 )
| ~ ( in @ ( sK33_F @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV717 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) )
!= SV751 )
| ~ ( in @ ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1609: $i] :
( ~ ( in @ SY1609 @ ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) @ SY1609 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4376]) ).
thf(4450,plain,
! [SV172: $i,SV272: $i] :
( ( ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
!= ( sK36_SY655 @ SV272 @ SV172 ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4377]) ).
thf(4451,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4377]) ).
thf(4452,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ! [SY1178: $i] :
( ~ ( in @ SY1178 @ ( sK43_SY691 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SY1178 ) @ SV272 ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4378]) ).
thf(4453,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ~ ( ( ( sK41_SY666 @ SV272 @ SV172 )
!= ( sK43_SY691 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4378]) ).
thf(4454,plain,
! [SV272: $i,SV692: $i,SV172: $i,SV723: $i,SV752: $i] :
( ( ( ( SV752 != SV723 )
| ~ ( in @ SV752 @ ( cartesian_product2 @ SV172 @ SV692 ) ) )
= $true )
| ( ( ! [SY1550: $i,SY1551: $i] :
( ( ( ordered_pair @ SY1550 @ SY1551 )
!= SV723 )
| ~ ( in @ SY1550 @ SV172 )
| ! [SY1552: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1552 @ SY1551 @ SY1550 @ SV723 @ SV692 @ SV272 @ SV172 ) @ SY1552 )
| ~ ~ ( in @ ( ordered_pair @ SY1551 @ ( sK34_R @ SY1552 @ SY1551 @ SY1550 @ SV723 @ SV692 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1550 != SY1552 )
| ~ ( in @ SY1551 @ SY1552 ) ) ) )
= $true )
| ( ( in @ SV723 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4379]) ).
thf(4455,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( ~ ~ ( ( ( sK33_F @ SV724 @ SV692 @ SV272 @ SV172 )
!= SV724 )
| ~ ( in @ ( sK33_F @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV692 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) )
!= SV724 )
| ~ ( in @ ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1553: $i] :
( ~ ( in @ SY1553 @ ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) @ SY1553 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) ) ) ) ) )
= $false )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4380]) ).
thf(4456,plain,
! [SV272: $i,SV718: $i,SV172: $i,SV753: $i] :
( ( ( ! [SY1610: $i] :
( ( SY1610 != SV753 )
| ~ ( in @ SY1610 @ ( cartesian_product2 @ SV172 @ SV718 ) ) )
| ! [SY1611: $i,SY1612: $i] :
( ( ( ordered_pair @ SY1611 @ SY1612 )
!= SV753 )
| ~ ( in @ SY1611 @ SV172 )
| ! [SY1613: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1613 @ SY1612 @ SY1611 @ SV753 @ SV718 @ SV272 @ SV172 ) @ SY1613 )
| ~ ~ ( in @ ( ordered_pair @ SY1612 @ ( sK34_R @ SY1613 @ SY1612 @ SY1611 @ SV753 @ SV718 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1611 != SY1613 )
| ~ ( in @ SY1612 @ SY1613 ) ) )
| ( in @ SV753 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4381]) ).
thf(4457,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( ~ ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SV754 @ SV718 @ SV272 @ SV172 )
!= SV754 )
| ~ ( in @ ( sK33_F @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV718 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) )
!= SV754 )
| ~ ( in @ ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1614: $i] :
( ~ ( in @ SY1614 @ ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) @ SY1614 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4382]) ).
thf(4458,plain,
! [SV272: $i,SV719: $i,SV172: $i,SV755: $i] :
( ( ( ! [SY1615: $i] :
( ( SY1615 != SV755 )
| ~ ( in @ SY1615 @ ( cartesian_product2 @ SV172 @ SV719 ) ) )
| ! [SY1616: $i,SY1617: $i] :
( ( ( ordered_pair @ SY1616 @ SY1617 )
!= SV755 )
| ~ ( in @ SY1616 @ SV172 )
| ! [SY1618: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1618 @ SY1617 @ SY1616 @ SV755 @ SV719 @ SV272 @ SV172 ) @ SY1618 )
| ~ ~ ( in @ ( ordered_pair @ SY1617 @ ( sK34_R @ SY1618 @ SY1617 @ SY1616 @ SV755 @ SV719 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1616 != SY1618 )
| ~ ( in @ SY1617 @ SY1618 ) ) )
| ( in @ SV755 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4383]) ).
thf(4459,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( ~ ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SV756 @ SV719 @ SV272 @ SV172 )
!= SV756 )
| ~ ( in @ ( sK33_F @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV719 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) )
!= SV756 )
| ~ ( in @ ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1619: $i] :
( ~ ( in @ SY1619 @ ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) @ SY1619 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4384]) ).
thf(4460,plain,
! [SV720: $i,SV272: $i,SV743: $i,SV172: $i] :
( ( ( ~ ! [SY1580: $i] :
( ! [SY1581: $i] :
( ( SY1581 != SY1580 )
| ~ ( in @ SY1581 @ ( cartesian_product2 @ SV172 @ SV743 ) ) )
| ! [SY1582: $i,SY1583: $i] :
( ( ( ordered_pair @ SY1582 @ SY1583 )
!= SY1580 )
| ~ ( in @ SY1582 @ SV172 )
| ! [SY1584: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1584 @ SY1583 @ SY1582 @ SY1580 @ SV743 @ SV272 @ SV172 ) @ SY1584 )
| ~ ~ ( in @ ( ordered_pair @ SY1583 @ ( sK34_R @ SY1584 @ SY1583 @ SY1582 @ SY1580 @ SV743 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1582 != SY1584 )
| ~ ( in @ SY1583 @ SY1584 ) ) )
| ( in @ SY1580 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) ) )
| ~ ! [SY1585: $i] :
( ~ ( in @ SY1585 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1585 @ SV743 @ SV272 @ SV172 )
!= SY1585 )
| ~ ( in @ ( sK33_F @ SY1585 @ SV743 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV743 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1585 @ SV743 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1585 @ SV743 @ SV272 @ SV172 ) )
!= SY1585 )
| ~ ( in @ ( sK30_O @ SY1585 @ SV743 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1586: $i] :
( ~ ( in @ SY1586 @ ( sK32_SY652 @ SY1585 @ SV743 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1585 @ SV743 @ SV272 @ SV172 ) @ SY1586 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1585 @ SV743 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1585 @ SV743 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1585 @ SV743 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1585 @ SV743 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4385]) ).
thf(4461,plain,
! [SV272: $i,SV744: $i,SV172: $i] :
( ( ( ~ ! [SY1587: $i] :
( ! [SY1588: $i] :
( ( SY1588 != SY1587 )
| ~ ( in @ SY1588 @ ( cartesian_product2 @ SV172 @ SV744 ) ) )
| ! [SY1589: $i,SY1590: $i] :
( ( ( ordered_pair @ SY1589 @ SY1590 )
!= SY1587 )
| ~ ( in @ SY1589 @ SV172 )
| ! [SY1591: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1591 @ SY1590 @ SY1589 @ SY1587 @ SV744 @ SV272 @ SV172 ) @ SY1591 )
| ~ ~ ( in @ ( ordered_pair @ SY1590 @ ( sK34_R @ SY1591 @ SY1590 @ SY1589 @ SY1587 @ SV744 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1589 != SY1591 )
| ~ ( in @ SY1590 @ SY1591 ) ) )
| ( in @ SY1587 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) ) )
| ~ ! [SY1592: $i] :
( ~ ( in @ SY1592 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1592 @ SV744 @ SV272 @ SV172 )
!= SY1592 )
| ~ ( in @ ( sK33_F @ SY1592 @ SV744 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV744 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1592 @ SV744 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1592 @ SV744 @ SV272 @ SV172 ) )
!= SY1592 )
| ~ ( in @ ( sK30_O @ SY1592 @ SV744 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1593: $i] :
( ~ ( in @ SY1593 @ ( sK32_SY652 @ SY1592 @ SV744 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1592 @ SV744 @ SV272 @ SV172 ) @ SY1593 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1592 @ SV744 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1592 @ SV744 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1592 @ SV744 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1592 @ SV744 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4386]) ).
thf(4462,plain,
! [SV272: $i,SV745: $i,SV172: $i] :
( ( ( ~ ! [SY1594: $i] :
( ! [SY1595: $i] :
( ( SY1595 != SY1594 )
| ~ ( in @ SY1595 @ ( cartesian_product2 @ SV172 @ SV745 ) ) )
| ! [SY1596: $i,SY1597: $i] :
( ( ( ordered_pair @ SY1596 @ SY1597 )
!= SY1594 )
| ~ ( in @ SY1596 @ SV172 )
| ! [SY1598: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1598 @ SY1597 @ SY1596 @ SY1594 @ SV745 @ SV272 @ SV172 ) @ SY1598 )
| ~ ~ ( in @ ( ordered_pair @ SY1597 @ ( sK34_R @ SY1598 @ SY1597 @ SY1596 @ SY1594 @ SV745 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1596 != SY1598 )
| ~ ( in @ SY1597 @ SY1598 ) ) )
| ( in @ SY1594 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) ) )
| ~ ! [SY1599: $i] :
( ~ ( in @ SY1599 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1599 @ SV745 @ SV272 @ SV172 )
!= SY1599 )
| ~ ( in @ ( sK33_F @ SY1599 @ SV745 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV745 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1599 @ SV745 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1599 @ SV745 @ SV272 @ SV172 ) )
!= SY1599 )
| ~ ( in @ ( sK30_O @ SY1599 @ SV745 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1600: $i] :
( ~ ( in @ SY1600 @ ( sK32_SY652 @ SY1599 @ SV745 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1599 @ SV745 @ SV272 @ SV172 ) @ SY1600 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1599 @ SV745 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1599 @ SV745 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1599 @ SV745 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1599 @ SV745 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4387]) ).
thf(4463,plain,
! [SV701: $i,SV272: $i,SV622: $i,SV172: $i,SV677: $i,SV757: $i,SV746: $i] :
( ( ( ( ( ordered_pair @ SV746 @ SV757 )
!= SV677 )
| ~ ( in @ SV746 @ SV172 )
| ! [SY1620: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1620 @ SV757 @ SV746 @ SV677 @ SV622 @ SV272 @ SV172 ) @ SY1620 )
| ~ ~ ( in @ ( ordered_pair @ SV757 @ ( sK34_R @ SY1620 @ SV757 @ SV746 @ SV677 @ SV622 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV746 != SY1620 )
| ~ ( in @ SV757 @ SY1620 ) ) )
= $true )
| ( ( SV701 = SV677 )
= $false )
| ( ( in @ SV701 @ ( cartesian_product2 @ SV172 @ SV622 ) )
= $false )
| ( ( in @ SV677 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4388]) ).
thf(4464,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( ( sK33_F @ SV678 @ SV622 @ SV272 @ SV172 )
= SV678 )
= $true )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4389]) ).
thf(4465,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( in @ ( sK33_F @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV622 ) )
= $true )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4390]) ).
thf(4466,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) )
!= SV678 )
| ~ ( in @ ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 ) @ SV172 ) ) )
= $true )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4391]) ).
thf(4467,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( ~ ( ~ ! [SY1493: $i] :
( ~ ( in @ SY1493 @ ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) @ SY1493 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) ) ) ) )
= $true )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4392]) ).
thf(4468,plain,
! [SV660: $i,SV139: $i,SV702: $i,SV728: $i] :
( ( ( SV728 = SV702 )
= $false )
| ( ( ~ ( in @ SV728 @ ( cartesian_product2 @ SV139 @ SV660 ) ) )
= $true )
| ( ( ! [SY1517: $i,SY1518: $i] :
( ( ( ordered_pair @ SY1517 @ SY1518 )
!= SV702 )
| ~ ( in @ SY1517 @ SV139 )
| ( SY1518
!= ( singleton @ SY1517 ) ) ) )
= $true )
| ( ( in @ SV702 @ ( sK13_C @ SV660 @ SV139 ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4393]) ).
thf(4469,plain,
! [SV139: $i,SV660: $i,SV703: $i] :
( ( ( ~ ( ( ( sK16_E @ SV703 @ SV660 @ SV139 )
!= SV703 )
| ~ ( in @ ( sK16_E @ SV703 @ SV660 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV660 ) ) ) )
= $true )
| ( ( in @ SV703 @ ( sK13_C @ SV660 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4394]) ).
thf(4470,plain,
! [SV139: $i,SV660: $i,SV703: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV703 @ SV660 @ SV139 ) @ ( sK15_SY612 @ SV703 @ SV660 @ SV139 ) )
!= SV703 )
| ~ ( in @ ( sK14_J @ SV703 @ SV660 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV703 @ SV660 @ SV139 )
!= ( singleton @ ( sK14_J @ SV703 @ SV660 @ SV139 ) ) ) ) )
= $true )
| ( ( in @ SV703 @ ( sK13_C @ SV660 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4395]) ).
thf(4471,plain,
! [SV725: $i,SV139: $i] :
( ( ( ! [SY1554: $i] :
( ! [SY1555: $i] :
( ( SY1555 != SY1554 )
| ~ ( in @ SY1555 @ ( cartesian_product2 @ SV139 @ SV725 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1554 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1554 @ ( sK13_C @ SV725 @ SV139 ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4396]) ).
thf(4472,plain,
! [SV139: $i,SV725: $i] :
( ( ( ! [SY1558: $i] :
( ~ ( in @ SY1558 @ ( sK13_C @ SV725 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1558 @ SV725 @ SV139 )
!= SY1558 )
| ~ ( in @ ( sK16_E @ SY1558 @ SV725 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV725 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1558 @ SV725 @ SV139 ) @ ( sK15_SY612 @ SY1558 @ SV725 @ SV139 ) )
!= SY1558 )
| ~ ( in @ ( sK14_J @ SY1558 @ SV725 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1558 @ SV725 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1558 @ SV725 @ SV139 ) ) ) ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4397]) ).
thf(4473,plain,
! [SV726: $i,SV139: $i] :
( ( ( ! [SY1559: $i] :
( ! [SY1560: $i] :
( ( SY1560 != SY1559 )
| ~ ( in @ SY1560 @ ( cartesian_product2 @ SV139 @ SV726 ) ) )
| ! [SY914: $i,SY915: $i] :
( ( ( ordered_pair @ SY914 @ SY915 )
!= SY1559 )
| ~ ( in @ SY914 @ SV139 )
| ( SY915
!= ( singleton @ SY914 ) ) )
| ( in @ SY1559 @ ( sK13_C @ SV726 @ SV139 ) ) ) )
= $true )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4398]) ).
thf(4474,plain,
! [SV139: $i,SV726: $i] :
( ( ( ! [SY1563: $i] :
( ~ ( in @ SY1563 @ ( sK13_C @ SV726 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SY1563 @ SV726 @ SV139 )
!= SY1563 )
| ~ ( in @ ( sK16_E @ SY1563 @ SV726 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV726 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SY1563 @ SV726 @ SV139 ) @ ( sK15_SY612 @ SY1563 @ SV726 @ SV139 ) )
!= SY1563 )
| ~ ( in @ ( sK14_J @ SY1563 @ SV726 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SY1563 @ SV726 @ SV139 )
!= ( singleton @ ( sK14_J @ SY1563 @ SV726 @ SV139 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4399]) ).
thf(4475,plain,
! [SV694: $i,SV139: $i,SV729: $i] :
( ( ( ! [SY1565: $i] :
( ( SY1565 != SV729 )
| ~ ( in @ SY1565 @ ( cartesian_product2 @ SV139 @ SV694 ) ) ) )
= $true )
| ( ( ! [SY1566: $i,SY1567: $i] :
( ( ( ordered_pair @ SY1566 @ SY1567 )
!= SV729 )
| ~ ( in @ SY1566 @ SV139 )
| ( SY1567
!= ( singleton @ SY1566 ) ) ) )
= $true )
| ( ( in @ SV729 @ ( sK13_C @ SV694 @ SV139 ) )
= $true )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4400]) ).
thf(4476,plain,
! [SV139: $i,SV694: $i,SV730: $i] :
( ( ( in @ SV730 @ ( sK13_C @ SV694 @ SV139 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK16_E @ SV730 @ SV694 @ SV139 )
!= SV730 )
| ~ ( in @ ( sK16_E @ SV730 @ SV694 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV694 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV730 @ SV694 @ SV139 ) @ ( sK15_SY612 @ SV730 @ SV694 @ SV139 ) )
!= SV730 )
| ~ ( in @ ( sK14_J @ SV730 @ SV694 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV730 @ SV694 @ SV139 )
!= ( singleton @ ( sK14_J @ SV730 @ SV694 @ SV139 ) ) ) ) ) )
= $true )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4401]) ).
thf(4477,plain,
! [SV624: $i,SV704: $i,SV139: $i,SV681: $i,SV758: $i,SV747: $i] :
( ( ( ( ( ordered_pair @ SV747 @ SV758 )
!= SV681 )
| ~ ( in @ SV747 @ SV139 )
| ( SV758
!= ( singleton @ SV747 ) ) )
= $true )
| ( ( SV704 = SV681 )
= $false )
| ( ( in @ SV704 @ ( cartesian_product2 @ SV139 @ SV624 ) )
= $false )
| ( ( in @ SV681 @ ( sK13_C @ SV624 @ SV139 ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4402]) ).
thf(4478,plain,
! [SV139: $i,SV624: $i,SV682: $i] :
( ( ( ( sK16_E @ SV682 @ SV624 @ SV139 )
= SV682 )
= $true )
| ( ( in @ SV682 @ ( sK13_C @ SV624 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4403]) ).
thf(4479,plain,
! [SV139: $i,SV624: $i,SV682: $i] :
( ( ( in @ ( sK16_E @ SV682 @ SV624 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV624 ) )
= $true )
| ( ( in @ SV682 @ ( sK13_C @ SV624 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4404]) ).
thf(4480,plain,
! [SV139: $i,SV624: $i,SV682: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK14_J @ SV682 @ SV624 @ SV139 ) @ ( sK15_SY612 @ SV682 @ SV624 @ SV139 ) )
!= SV682 )
| ~ ( in @ ( sK14_J @ SV682 @ SV624 @ SV139 ) @ SV139 ) ) )
= $true )
| ( ( in @ SV682 @ ( sK13_C @ SV624 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4405]) ).
thf(4481,plain,
! [SV139: $i,SV624: $i,SV682: $i] :
( ( ( ( sK15_SY612 @ SV682 @ SV624 @ SV139 )
= ( singleton @ ( sK14_J @ SV682 @ SV624 @ SV139 ) ) )
= $true )
| ( ( in @ SV682 @ ( sK13_C @ SV624 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4406]) ).
thf(4482,plain,
! [SV661: $i,SV139: $i,SV705: $i,SV731: $i] :
( ( ( SV731 = SV705 )
= $false )
| ( ( ~ ( in @ SV731 @ ( cartesian_product2 @ SV139 @ SV661 ) ) )
= $true )
| ( ( ! [SY1520: $i,SY1521: $i] :
( ( ( ordered_pair @ SY1520 @ SY1521 )
!= SV705 )
| ~ ( in @ SY1520 @ SV139 )
| ( SY1521
!= ( singleton @ SY1520 ) ) ) )
= $true )
| ( ( in @ SV705 @ ( sK13_C @ SV661 @ SV139 ) )
= $true )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4407]) ).
thf(4483,plain,
! [SV139: $i,SV661: $i,SV706: $i] :
( ( ( ~ ( ( ( sK16_E @ SV706 @ SV661 @ SV139 )
!= SV706 )
| ~ ( in @ ( sK16_E @ SV706 @ SV661 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV661 ) ) ) )
= $true )
| ( ( in @ SV706 @ ( sK13_C @ SV661 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4408]) ).
thf(4484,plain,
! [SV139: $i,SV661: $i,SV706: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV706 @ SV661 @ SV139 ) @ ( sK15_SY612 @ SV706 @ SV661 @ SV139 ) )
!= SV706 )
| ~ ( in @ ( sK14_J @ SV706 @ SV661 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV706 @ SV661 @ SV139 )
!= ( singleton @ ( sK14_J @ SV706 @ SV661 @ SV139 ) ) ) ) )
= $true )
| ( ( in @ SV706 @ ( sK13_C @ SV661 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4409]) ).
thf(4485,plain,
! [SV662: $i,SV139: $i,SV707: $i,SV732: $i] :
( ( ( SV732 = SV707 )
= $false )
| ( ( ~ ( in @ SV732 @ ( cartesian_product2 @ SV139 @ SV662 ) ) )
= $true )
| ( ( ! [SY1523: $i,SY1524: $i] :
( ( ( ordered_pair @ SY1523 @ SY1524 )
!= SV707 )
| ~ ( in @ SY1523 @ SV139 )
| ( SY1524
!= ( singleton @ SY1523 ) ) ) )
= $true )
| ( ( in @ SV707 @ ( sK13_C @ SV662 @ SV139 ) )
= $true )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4410]) ).
thf(4486,plain,
! [SV139: $i,SV662: $i,SV708: $i] :
( ( ( ~ ( ( ( sK16_E @ SV708 @ SV662 @ SV139 )
!= SV708 )
| ~ ( in @ ( sK16_E @ SV708 @ SV662 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV662 ) ) ) )
= $true )
| ( ( in @ SV708 @ ( sK13_C @ SV662 @ SV139 ) )
= $false )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4411]) ).
thf(4487,plain,
! [SV139: $i,SV662: $i,SV708: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV708 @ SV662 @ SV139 ) @ ( sK15_SY612 @ SV708 @ SV662 @ SV139 ) )
!= SV708 )
| ~ ( in @ ( sK14_J @ SV708 @ SV662 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV708 @ SV662 @ SV139 )
!= ( singleton @ ( sK14_J @ SV708 @ SV662 @ SV139 ) ) ) ) )
= $true )
| ( ( in @ SV708 @ ( sK13_C @ SV662 @ SV139 ) )
= $false )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4412]) ).
thf(4488,plain,
! [SV625: $i,SV709: $i,SV139: $i,SV683: $i,SV759: $i,SV748: $i] :
( ( ( ( ( ordered_pair @ SV748 @ SV759 )
!= SV683 )
| ~ ( in @ SV748 @ SV139 )
| ( SV759
!= ( singleton @ SV748 ) ) )
= $true )
| ( ( SV709 = SV683 )
= $false )
| ( ( in @ SV709 @ ( cartesian_product2 @ SV139 @ SV625 ) )
= $false )
| ( ( in @ SV683 @ ( sK13_C @ SV625 @ SV139 ) )
= $true )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4413]) ).
thf(4489,plain,
! [SV139: $i,SV625: $i,SV684: $i] :
( ( ( ( sK16_E @ SV684 @ SV625 @ SV139 )
= SV684 )
= $true )
| ( ( in @ SV684 @ ( sK13_C @ SV625 @ SV139 ) )
= $false )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4414]) ).
thf(4490,plain,
! [SV139: $i,SV625: $i,SV684: $i] :
( ( ( in @ ( sK16_E @ SV684 @ SV625 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV625 ) )
= $true )
| ( ( in @ SV684 @ ( sK13_C @ SV625 @ SV139 ) )
= $false )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4415]) ).
thf(4491,plain,
! [SV139: $i,SV625: $i,SV684: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK14_J @ SV684 @ SV625 @ SV139 ) @ ( sK15_SY612 @ SV684 @ SV625 @ SV139 ) )
!= SV684 )
| ~ ( in @ ( sK14_J @ SV684 @ SV625 @ SV139 ) @ SV139 ) ) )
= $true )
| ( ( in @ SV684 @ ( sK13_C @ SV625 @ SV139 ) )
= $false )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4416]) ).
thf(4492,plain,
! [SV139: $i,SV625: $i,SV684: $i] :
( ( ( ( sK15_SY612 @ SV684 @ SV625 @ SV139 )
= ( singleton @ ( sK14_J @ SV684 @ SV625 @ SV139 ) ) )
= $true )
| ( ( in @ SV684 @ ( sK13_C @ SV625 @ SV139 ) )
= $false )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4417]) ).
thf(4493,plain,
! [SV488: $i,SV654: $i,SV139: $i,SV603: $i,SV695: $i,SV710: $i] :
( ( ( SV710
= ( singleton @ SV695 ) )
= $false )
| ( ( ( ordered_pair @ SV695 @ SV710 )
= SV603 )
= $false )
| ( ( in @ SV695 @ SV139 )
= $false )
| ( ( SV654 = SV603 )
= $false )
| ( ( in @ SV654 @ ( cartesian_product2 @ SV139 @ SV488 ) )
= $false )
| ( ( in @ SV603 @ ( sK13_C @ SV488 @ SV139 ) )
= $true )
| ( ( ( sK18_SY613 @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4418]) ).
thf(4494,plain,
! [SV145: $i,SV265: $i,SV733: $i] :
( ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4419]) ).
thf(4495,plain,
! [SV145: $i,SV265: $i] :
( ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4420]) ).
thf(4496,plain,
! [SV145: $i,SV265: $i] :
( ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( ~ ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4421]) ).
thf(4497,plain,
! [SV265: $i,SV734: $i,SV145: $i,SV760: $i] :
( ( ( ~ ( in @ SV760 @ SV145 )
| ! [SY1621: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1621 @ SV760 @ SV734 @ SV265 @ SV145 ) @ SY1621 )
| ~ ~ ( in @ ( ordered_pair @ SV734 @ ( sK47_K @ SY1621 @ SV760 @ SV734 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV760 != SY1621 )
| ~ ( in @ SV734 @ SY1621 ) ) )
= $true )
| ( ( in @ SV734 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4422]) ).
thf(4498,plain,
! [SV145: $i,SV265: $i,SV735: $i] :
( ( ( in @ SV735 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK45_E @ SV735 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1570: $i] :
( ~ ( in @ SY1570 @ ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV735 @ SY1570 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV735 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) )
| ~ ( in @ SV735 @ ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4423]) ).
thf(4499,plain,
! [SV145: $i,SV265: $i,SV711: $i,SV727: $i,SV761: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_K @ SV761 @ SV727 @ SV711 @ SV265 @ SV145 ) @ SV761 )
| ~ ~ ( in @ ( ordered_pair @ SV711 @ ( sK47_K @ SV761 @ SV727 @ SV711 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV727 != SV761 )
| ~ ( in @ SV711 @ SV761 ) )
= $true )
| ( ( in @ SV727 @ SV145 )
= $false )
| ( ( in @ SV711 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4424]) ).
thf(4500,plain,
! [SV145: $i,SV265: $i,SV712: $i] :
( ( ( in @ ( sK45_E @ SV712 @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( in @ SV712 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4425]) ).
thf(4501,plain,
! [SV145: $i,SV265: $i,SV712: $i] :
( ( ( ~ ( ~ ! [SY1527: $i] :
( ~ ( in @ SY1527 @ ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV712 @ SY1527 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV712 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) )
| ~ ( in @ SV712 @ ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) ) ) ) )
= $true )
| ( ( in @ SV712 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4426]) ).
thf(4502,plain,
! [SV685: $i,SV265: $i,SV736: $i,SV145: $i,SV762: $i] :
( ( ( ~ ( in @ SV762 @ SV145 )
| ! [SY1622: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1622 @ SV762 @ SV736 @ SV265 @ SV145 ) @ SY1622 )
| ~ ~ ( in @ ( ordered_pair @ SV736 @ ( sK47_K @ SY1622 @ SV762 @ SV736 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV762 != SY1622 )
| ~ ( in @ SV736 @ SY1622 ) ) )
= $true )
| ( ( in @ SV736 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4427]) ).
thf(4503,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV737: $i] :
( ( ( in @ SV737 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK45_E @ SV737 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1573: $i] :
( ~ ( in @ SY1573 @ ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV737 @ SY1573 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV737 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) )
| ~ ( in @ SV737 @ ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) ) ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4428]) ).
thf(4504,plain,
! [SV265: $i,SV738: $i,SV145: $i,SV763: $i] :
( ( ( ~ ( in @ SV763 @ SV145 )
| ! [SY1623: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1623 @ SV763 @ SV738 @ SV265 @ SV145 ) @ SY1623 )
| ~ ~ ( in @ ( ordered_pair @ SV738 @ ( sK47_K @ SY1623 @ SV763 @ SV738 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV763 != SY1623 )
| ~ ( in @ SV738 @ SY1623 ) ) )
= $true )
| ( ( in @ SV738 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4429]) ).
thf(4505,plain,
! [SV145: $i,SV265: $i,SV739: $i] :
( ( ( in @ SV739 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK45_E @ SV739 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1576: $i] :
( ~ ( in @ SY1576 @ ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV739 @ SY1576 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV739 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) )
| ~ ( in @ SV739 @ ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) ) ) ) ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4430]) ).
thf(4506,plain,
! [SV265: $i,SV740: $i,SV145: $i,SV764: $i] :
( ( ( ~ ( in @ SV764 @ SV145 )
| ! [SY1624: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1624 @ SV764 @ SV740 @ SV265 @ SV145 ) @ SY1624 )
| ~ ~ ( in @ ( ordered_pair @ SV740 @ ( sK47_K @ SY1624 @ SV764 @ SV740 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV764 != SY1624 )
| ~ ( in @ SV740 @ SY1624 ) ) )
= $true )
| ( ( in @ SV740 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4431]) ).
thf(4507,plain,
! [SV145: $i,SV265: $i,SV741: $i] :
( ( ( in @ SV741 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK45_E @ SV741 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1579: $i] :
( ~ ( in @ SY1579 @ ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV741 @ SY1579 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV741 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) )
| ~ ( in @ SV741 @ ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4432]) ).
thf(4508,plain,
! [SV145: $i,SV265: $i,SV655: $i,SV713: $i,SV686: $i] :
( ( ( ( SV686 != SV713 ) )
= $true )
| ( ( ~ ( in @ SV655 @ SV713 ) )
= $true )
| ( ( in @ ( sK47_K @ SV713 @ SV686 @ SV655 @ SV265 @ SV145 ) @ SV713 )
= $true )
| ( ( in @ SV686 @ SV145 )
= $false )
| ( ( in @ SV655 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4433]) ).
thf(4509,plain,
! [SV145: $i,SV265: $i,SV686: $i,SV713: $i,SV655: $i] :
( ( ( in @ ( ordered_pair @ SV655 @ ( sK47_K @ SV713 @ SV686 @ SV655 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( ( SV686 != SV713 )
| ~ ( in @ SV655 @ SV713 ) )
= $true )
| ( ( in @ SV686 @ SV145 )
= $false )
| ( ( in @ SV655 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4434]) ).
thf(4510,plain,
! [SV145: $i,SV265: $i,SV656: $i,SV749: $i] :
( ( ( ~ ( in @ SV749 @ ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV656 @ SV749 ) @ SV265 )
= $true )
| ( ( in @ SV656 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4435]) ).
thf(4511,plain,
! [SV145: $i,SV265: $i,SV656: $i] :
( ( ( ( ( sK45_E @ SV656 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) ) )
= $false )
| ( ( in @ SV656 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4436]) ).
thf(4512,plain,
! [SV145: $i,SV265: $i,SV656: $i] :
( ( ( ~ ( in @ SV656 @ ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) ) )
= $false )
| ( ( in @ SV656 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4436]) ).
thf(4513,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV596: $i,SV659: $i,SV716: $i,SV651: $i] :
( ( ( ( SV651 != SV716 ) )
= $true )
| ( ( ~ ( in @ SV659 @ SV716 ) )
= $true )
| ( ( in @ ( sK115_I @ SV716 @ SV659 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) @ SV716 )
= $true )
| ( ( ( ordered_pair @ SV651 @ SV659 )
= SV596 )
= $false )
| ( ( in @ SV651 @ SV170 )
= $false )
| ( ( ~ ( in @ SV596 @ ( cartesian_product2 @ SV170 @ SV481 ) ) )
= $true )
| ( ( in @ SV596 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4443]) ).
thf(4514,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV596: $i,SV651: $i,SV716: $i,SV659: $i] :
( ( ( in @ ( ordered_pair @ SV659 @ ( sK115_I @ SV716 @ SV659 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) ) @ SV271 )
= $false )
| ( ( ( SV651 != SV716 )
| ~ ( in @ SV659 @ SV716 ) )
= $true )
| ( ( ( ordered_pair @ SV651 @ SV659 )
= SV596 )
= $false )
| ( ( in @ SV651 @ SV170 )
= $false )
| ( ( ~ ( in @ SV596 @ ( cartesian_product2 @ SV170 @ SV481 ) ) )
= $true )
| ( ( in @ SV596 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4444]) ).
thf(4515,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV652: $i,SV742: $i] :
( ( ( in @ SV742 @ ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) @ SV742 ) @ SV271 )
= $true )
| ( ( in @ SV652 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $false )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4445]) ).
thf(4516,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV652: $i] :
( ( ( ( sK112_F @ SV652 @ SV481 @ SV271 @ SV170 )
= ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) )
= $true )
| ( ( in @ SV652 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $false )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4446]) ).
thf(4517,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV652: $i] :
( ( ( in @ ( sK113_SY768 @ SV652 @ SV481 @ SV271 @ SV170 ) @ ( sK114_SY771 @ SV652 @ SV481 @ SV271 @ SV170 ) )
= $true )
| ( ( in @ SV652 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $false )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4447]) ).
thf(4518,plain,
! [SV272: $i,SV717: $i,SV172: $i,SV750: $i] :
( ( ( ! [SY1605: $i] :
( ( SY1605 != SV750 )
| ~ ( in @ SY1605 @ ( cartesian_product2 @ SV172 @ SV717 ) ) )
| ! [SY1606: $i,SY1607: $i] :
( ( ( ordered_pair @ SY1606 @ SY1607 )
!= SV750 )
| ~ ( in @ SY1606 @ SV172 )
| ! [SY1608: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1608 @ SY1607 @ SY1606 @ SV750 @ SV717 @ SV272 @ SV172 ) @ SY1608 )
| ~ ~ ( in @ ( ordered_pair @ SY1607 @ ( sK34_R @ SY1608 @ SY1607 @ SY1606 @ SV750 @ SV717 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1606 != SY1608 )
| ~ ( in @ SY1607 @ SY1608 ) ) ) )
= $true )
| ( ( in @ SV750 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4448]) ).
thf(4519,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( ~ ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK33_F @ SV751 @ SV717 @ SV272 @ SV172 )
!= SV751 )
| ~ ( in @ ( sK33_F @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV717 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) )
!= SV751 )
| ~ ( in @ ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1609: $i] :
( ~ ( in @ SY1609 @ ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) @ SY1609 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4449]) ).
thf(4520,plain,
! [SV172: $i,SV272: $i] :
( ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4450]) ).
thf(4521,plain,
! [SV172: $i,SV272: $i] :
( ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4451]) ).
thf(4522,plain,
! [SV172: $i,SV272: $i] :
( ( ( ! [SY1178: $i] :
( ~ ( in @ SY1178 @ ( sK43_SY691 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SY1178 ) @ SV272 ) ) )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4452]) ).
thf(4523,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ( ( ( sK41_SY666 @ SV272 @ SV172 )
!= ( sK43_SY691 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) ) ) )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4453]) ).
thf(4524,plain,
! [SV272: $i,SV692: $i,SV172: $i,SV723: $i,SV752: $i] :
( ( ( ( SV752 != SV723 ) )
= $true )
| ( ( ~ ( in @ SV752 @ ( cartesian_product2 @ SV172 @ SV692 ) ) )
= $true )
| ( ( ! [SY1550: $i,SY1551: $i] :
( ( ( ordered_pair @ SY1550 @ SY1551 )
!= SV723 )
| ~ ( in @ SY1550 @ SV172 )
| ! [SY1552: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1552 @ SY1551 @ SY1550 @ SV723 @ SV692 @ SV272 @ SV172 ) @ SY1552 )
| ~ ~ ( in @ ( ordered_pair @ SY1551 @ ( sK34_R @ SY1552 @ SY1551 @ SY1550 @ SV723 @ SV692 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1550 != SY1552 )
| ~ ( in @ SY1551 @ SY1552 ) ) ) )
= $true )
| ( ( in @ SV723 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4454]) ).
thf(4525,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( ~ ~ ( ( ( sK33_F @ SV724 @ SV692 @ SV272 @ SV172 )
!= SV724 )
| ~ ( in @ ( sK33_F @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV692 ) ) ) )
= $false )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4455]) ).
thf(4526,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) )
!= SV724 )
| ~ ( in @ ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1553: $i] :
( ~ ( in @ SY1553 @ ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) @ SY1553 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) ) ) ) ) )
= $false )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4455]) ).
thf(4527,plain,
! [SV272: $i,SV718: $i,SV172: $i,SV753: $i] :
( ( ( ! [SY1610: $i] :
( ( SY1610 != SV753 )
| ~ ( in @ SY1610 @ ( cartesian_product2 @ SV172 @ SV718 ) ) )
| ! [SY1611: $i,SY1612: $i] :
( ( ( ordered_pair @ SY1611 @ SY1612 )
!= SV753 )
| ~ ( in @ SY1611 @ SV172 )
| ! [SY1613: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1613 @ SY1612 @ SY1611 @ SV753 @ SV718 @ SV272 @ SV172 ) @ SY1613 )
| ~ ~ ( in @ ( ordered_pair @ SY1612 @ ( sK34_R @ SY1613 @ SY1612 @ SY1611 @ SV753 @ SV718 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1611 != SY1613 )
| ~ ( in @ SY1612 @ SY1613 ) ) ) )
= $true )
| ( ( in @ SV753 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4456]) ).
thf(4528,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( ~ ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK33_F @ SV754 @ SV718 @ SV272 @ SV172 )
!= SV754 )
| ~ ( in @ ( sK33_F @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV718 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) )
!= SV754 )
| ~ ( in @ ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1614: $i] :
( ~ ( in @ SY1614 @ ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) @ SY1614 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4457]) ).
thf(4529,plain,
! [SV272: $i,SV719: $i,SV172: $i,SV755: $i] :
( ( ( ! [SY1615: $i] :
( ( SY1615 != SV755 )
| ~ ( in @ SY1615 @ ( cartesian_product2 @ SV172 @ SV719 ) ) )
| ! [SY1616: $i,SY1617: $i] :
( ( ( ordered_pair @ SY1616 @ SY1617 )
!= SV755 )
| ~ ( in @ SY1616 @ SV172 )
| ! [SY1618: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1618 @ SY1617 @ SY1616 @ SV755 @ SV719 @ SV272 @ SV172 ) @ SY1618 )
| ~ ~ ( in @ ( ordered_pair @ SY1617 @ ( sK34_R @ SY1618 @ SY1617 @ SY1616 @ SV755 @ SV719 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1616 != SY1618 )
| ~ ( in @ SY1617 @ SY1618 ) ) ) )
= $true )
| ( ( in @ SV755 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4458]) ).
thf(4530,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( ~ ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK33_F @ SV756 @ SV719 @ SV272 @ SV172 )
!= SV756 )
| ~ ( in @ ( sK33_F @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV719 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) )
!= SV756 )
| ~ ( in @ ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1619: $i] :
( ~ ( in @ SY1619 @ ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) @ SY1619 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4459]) ).
thf(4531,plain,
! [SV720: $i,SV272: $i,SV743: $i,SV172: $i] :
( ( ( ~ ! [SY1580: $i] :
( ! [SY1581: $i] :
( ( SY1581 != SY1580 )
| ~ ( in @ SY1581 @ ( cartesian_product2 @ SV172 @ SV743 ) ) )
| ! [SY1582: $i,SY1583: $i] :
( ( ( ordered_pair @ SY1582 @ SY1583 )
!= SY1580 )
| ~ ( in @ SY1582 @ SV172 )
| ! [SY1584: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1584 @ SY1583 @ SY1582 @ SY1580 @ SV743 @ SV272 @ SV172 ) @ SY1584 )
| ~ ~ ( in @ ( ordered_pair @ SY1583 @ ( sK34_R @ SY1584 @ SY1583 @ SY1582 @ SY1580 @ SV743 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1582 != SY1584 )
| ~ ( in @ SY1583 @ SY1584 ) ) )
| ( in @ SY1580 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4460]) ).
thf(4532,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i] :
( ( ( ~ ! [SY1585: $i] :
( ~ ( in @ SY1585 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1585 @ SV743 @ SV272 @ SV172 )
!= SY1585 )
| ~ ( in @ ( sK33_F @ SY1585 @ SV743 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV743 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1585 @ SV743 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1585 @ SV743 @ SV272 @ SV172 ) )
!= SY1585 )
| ~ ( in @ ( sK30_O @ SY1585 @ SV743 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1586: $i] :
( ~ ( in @ SY1586 @ ( sK32_SY652 @ SY1585 @ SV743 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1585 @ SV743 @ SV272 @ SV172 ) @ SY1586 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1585 @ SV743 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1585 @ SV743 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1585 @ SV743 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1585 @ SV743 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4460]) ).
thf(4533,plain,
! [SV272: $i,SV744: $i,SV172: $i] :
( ( ( ~ ! [SY1587: $i] :
( ! [SY1588: $i] :
( ( SY1588 != SY1587 )
| ~ ( in @ SY1588 @ ( cartesian_product2 @ SV172 @ SV744 ) ) )
| ! [SY1589: $i,SY1590: $i] :
( ( ( ordered_pair @ SY1589 @ SY1590 )
!= SY1587 )
| ~ ( in @ SY1589 @ SV172 )
| ! [SY1591: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1591 @ SY1590 @ SY1589 @ SY1587 @ SV744 @ SV272 @ SV172 ) @ SY1591 )
| ~ ~ ( in @ ( ordered_pair @ SY1590 @ ( sK34_R @ SY1591 @ SY1590 @ SY1589 @ SY1587 @ SV744 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1589 != SY1591 )
| ~ ( in @ SY1590 @ SY1591 ) ) )
| ( in @ SY1587 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4461]) ).
thf(4534,plain,
! [SV172: $i,SV272: $i,SV744: $i] :
( ( ( ~ ! [SY1592: $i] :
( ~ ( in @ SY1592 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1592 @ SV744 @ SV272 @ SV172 )
!= SY1592 )
| ~ ( in @ ( sK33_F @ SY1592 @ SV744 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV744 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1592 @ SV744 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1592 @ SV744 @ SV272 @ SV172 ) )
!= SY1592 )
| ~ ( in @ ( sK30_O @ SY1592 @ SV744 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1593: $i] :
( ~ ( in @ SY1593 @ ( sK32_SY652 @ SY1592 @ SV744 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1592 @ SV744 @ SV272 @ SV172 ) @ SY1593 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1592 @ SV744 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1592 @ SV744 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1592 @ SV744 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1592 @ SV744 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4461]) ).
thf(4535,plain,
! [SV272: $i,SV745: $i,SV172: $i] :
( ( ( ~ ! [SY1594: $i] :
( ! [SY1595: $i] :
( ( SY1595 != SY1594 )
| ~ ( in @ SY1595 @ ( cartesian_product2 @ SV172 @ SV745 ) ) )
| ! [SY1596: $i,SY1597: $i] :
( ( ( ordered_pair @ SY1596 @ SY1597 )
!= SY1594 )
| ~ ( in @ SY1596 @ SV172 )
| ! [SY1598: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1598 @ SY1597 @ SY1596 @ SY1594 @ SV745 @ SV272 @ SV172 ) @ SY1598 )
| ~ ~ ( in @ ( ordered_pair @ SY1597 @ ( sK34_R @ SY1598 @ SY1597 @ SY1596 @ SY1594 @ SV745 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1596 != SY1598 )
| ~ ( in @ SY1597 @ SY1598 ) ) )
| ( in @ SY1594 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4462]) ).
thf(4536,plain,
! [SV172: $i,SV272: $i,SV745: $i] :
( ( ( ~ ! [SY1599: $i] :
( ~ ( in @ SY1599 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1599 @ SV745 @ SV272 @ SV172 )
!= SY1599 )
| ~ ( in @ ( sK33_F @ SY1599 @ SV745 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV745 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1599 @ SV745 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1599 @ SV745 @ SV272 @ SV172 ) )
!= SY1599 )
| ~ ( in @ ( sK30_O @ SY1599 @ SV745 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1600: $i] :
( ~ ( in @ SY1600 @ ( sK32_SY652 @ SY1599 @ SV745 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1599 @ SV745 @ SV272 @ SV172 ) @ SY1600 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1599 @ SV745 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1599 @ SV745 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1599 @ SV745 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1599 @ SV745 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4462]) ).
thf(4537,plain,
! [SV701: $i,SV272: $i,SV622: $i,SV172: $i,SV677: $i,SV757: $i,SV746: $i] :
( ( ( ( ( ordered_pair @ SV746 @ SV757 )
!= SV677 )
| ~ ( in @ SV746 @ SV172 ) )
= $true )
| ( ( ! [SY1620: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1620 @ SV757 @ SV746 @ SV677 @ SV622 @ SV272 @ SV172 ) @ SY1620 )
| ~ ~ ( in @ ( ordered_pair @ SV757 @ ( sK34_R @ SY1620 @ SV757 @ SV746 @ SV677 @ SV622 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV746 != SY1620 )
| ~ ( in @ SV757 @ SY1620 ) ) )
= $true )
| ( ( SV701 = SV677 )
= $false )
| ( ( in @ SV701 @ ( cartesian_product2 @ SV172 @ SV622 ) )
= $false )
| ( ( in @ SV677 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4463]) ).
thf(4538,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( ( ( ordered_pair @ ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) )
!= SV678 )
| ~ ( in @ ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 ) @ SV172 ) )
= $false )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4466]) ).
thf(4539,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( ~ ! [SY1493: $i] :
( ~ ( in @ SY1493 @ ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) @ SY1493 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4467]) ).
thf(4540,plain,
! [SV702: $i,SV660: $i,SV139: $i,SV728: $i] :
( ( ( in @ SV728 @ ( cartesian_product2 @ SV139 @ SV660 ) )
= $false )
| ( ( SV728 = SV702 )
= $false )
| ( ( ! [SY1517: $i,SY1518: $i] :
( ( ( ordered_pair @ SY1517 @ SY1518 )
!= SV702 )
| ~ ( in @ SY1517 @ SV139 )
| ( SY1518
!= ( singleton @ SY1517 ) ) ) )
= $true )
| ( ( in @ SV702 @ ( sK13_C @ SV660 @ SV139 ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4468]) ).
thf(4541,plain,
! [SV139: $i,SV660: $i,SV703: $i] :
( ( ( ( ( sK16_E @ SV703 @ SV660 @ SV139 )
!= SV703 )
| ~ ( in @ ( sK16_E @ SV703 @ SV660 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV660 ) ) )
= $false )
| ( ( in @ SV703 @ ( sK13_C @ SV660 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4469]) ).
thf(4542,plain,
! [SV139: $i,SV660: $i,SV703: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV703 @ SV660 @ SV139 ) @ ( sK15_SY612 @ SV703 @ SV660 @ SV139 ) )
!= SV703 )
| ~ ( in @ ( sK14_J @ SV703 @ SV660 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV703 @ SV660 @ SV139 )
!= ( singleton @ ( sK14_J @ SV703 @ SV660 @ SV139 ) ) ) )
= $false )
| ( ( in @ SV703 @ ( sK13_C @ SV660 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4470]) ).
thf(4543,plain,
! [SV725: $i,SV139: $i,SV765: $i] :
( ( ( ! [SY1625: $i] :
( ( SY1625 != SV765 )
| ~ ( in @ SY1625 @ ( cartesian_product2 @ SV139 @ SV725 ) ) )
| ! [SY1626: $i,SY1627: $i] :
( ( ( ordered_pair @ SY1626 @ SY1627 )
!= SV765 )
| ~ ( in @ SY1626 @ SV139 )
| ( SY1627
!= ( singleton @ SY1626 ) ) )
| ( in @ SV765 @ ( sK13_C @ SV725 @ SV139 ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4471]) ).
thf(4544,plain,
! [SV139: $i,SV725: $i,SV766: $i] :
( ( ( ~ ( in @ SV766 @ ( sK13_C @ SV725 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SV766 @ SV725 @ SV139 )
!= SV766 )
| ~ ( in @ ( sK16_E @ SV766 @ SV725 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV725 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV766 @ SV725 @ SV139 ) @ ( sK15_SY612 @ SV766 @ SV725 @ SV139 ) )
!= SV766 )
| ~ ( in @ ( sK14_J @ SV766 @ SV725 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV766 @ SV725 @ SV139 )
!= ( singleton @ ( sK14_J @ SV766 @ SV725 @ SV139 ) ) ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4472]) ).
thf(4545,plain,
! [SV726: $i,SV139: $i,SV767: $i] :
( ( ( ! [SY1628: $i] :
( ( SY1628 != SV767 )
| ~ ( in @ SY1628 @ ( cartesian_product2 @ SV139 @ SV726 ) ) )
| ! [SY1629: $i,SY1630: $i] :
( ( ( ordered_pair @ SY1629 @ SY1630 )
!= SV767 )
| ~ ( in @ SY1629 @ SV139 )
| ( SY1630
!= ( singleton @ SY1629 ) ) )
| ( in @ SV767 @ ( sK13_C @ SV726 @ SV139 ) ) )
= $true )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4473]) ).
thf(4546,plain,
! [SV139: $i,SV726: $i,SV768: $i] :
( ( ( ~ ( in @ SV768 @ ( sK13_C @ SV726 @ SV139 ) )
| ~ ( ~ ~ ( ( ( sK16_E @ SV768 @ SV726 @ SV139 )
!= SV768 )
| ~ ( in @ ( sK16_E @ SV768 @ SV726 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV726 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV768 @ SV726 @ SV139 ) @ ( sK15_SY612 @ SV768 @ SV726 @ SV139 ) )
!= SV768 )
| ~ ( in @ ( sK14_J @ SV768 @ SV726 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV768 @ SV726 @ SV139 )
!= ( singleton @ ( sK14_J @ SV768 @ SV726 @ SV139 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4474]) ).
thf(4547,plain,
! [SV694: $i,SV139: $i,SV729: $i,SV769: $i] :
( ( ( ( SV769 != SV729 )
| ~ ( in @ SV769 @ ( cartesian_product2 @ SV139 @ SV694 ) ) )
= $true )
| ( ( ! [SY1566: $i,SY1567: $i] :
( ( ( ordered_pair @ SY1566 @ SY1567 )
!= SV729 )
| ~ ( in @ SY1566 @ SV139 )
| ( SY1567
!= ( singleton @ SY1566 ) ) ) )
= $true )
| ( ( in @ SV729 @ ( sK13_C @ SV694 @ SV139 ) )
= $true )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4475]) ).
thf(4548,plain,
! [SV139: $i,SV694: $i,SV730: $i] :
( ( ( ~ ~ ( ( ( sK16_E @ SV730 @ SV694 @ SV139 )
!= SV730 )
| ~ ( in @ ( sK16_E @ SV730 @ SV694 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV694 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV730 @ SV694 @ SV139 ) @ ( sK15_SY612 @ SV730 @ SV694 @ SV139 ) )
!= SV730 )
| ~ ( in @ ( sK14_J @ SV730 @ SV694 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV730 @ SV694 @ SV139 )
!= ( singleton @ ( sK14_J @ SV730 @ SV694 @ SV139 ) ) ) ) )
= $false )
| ( ( in @ SV730 @ ( sK13_C @ SV694 @ SV139 ) )
= $false )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4476]) ).
thf(4549,plain,
! [SV624: $i,SV704: $i,SV139: $i,SV681: $i,SV758: $i,SV747: $i] :
( ( ( ( ( ordered_pair @ SV747 @ SV758 )
!= SV681 )
| ~ ( in @ SV747 @ SV139 ) )
= $true )
| ( ( ( SV758
!= ( singleton @ SV747 ) ) )
= $true )
| ( ( SV704 = SV681 )
= $false )
| ( ( in @ SV704 @ ( cartesian_product2 @ SV139 @ SV624 ) )
= $false )
| ( ( in @ SV681 @ ( sK13_C @ SV624 @ SV139 ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4477]) ).
thf(4550,plain,
! [SV139: $i,SV624: $i,SV682: $i] :
( ( ( ( ( ordered_pair @ ( sK14_J @ SV682 @ SV624 @ SV139 ) @ ( sK15_SY612 @ SV682 @ SV624 @ SV139 ) )
!= SV682 )
| ~ ( in @ ( sK14_J @ SV682 @ SV624 @ SV139 ) @ SV139 ) )
= $false )
| ( ( in @ SV682 @ ( sK13_C @ SV624 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4480]) ).
thf(4551,plain,
! [SV705: $i,SV661: $i,SV139: $i,SV731: $i] :
( ( ( in @ SV731 @ ( cartesian_product2 @ SV139 @ SV661 ) )
= $false )
| ( ( SV731 = SV705 )
= $false )
| ( ( ! [SY1520: $i,SY1521: $i] :
( ( ( ordered_pair @ SY1520 @ SY1521 )
!= SV705 )
| ~ ( in @ SY1520 @ SV139 )
| ( SY1521
!= ( singleton @ SY1520 ) ) ) )
= $true )
| ( ( in @ SV705 @ ( sK13_C @ SV661 @ SV139 ) )
= $true )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4482]) ).
thf(4552,plain,
! [SV139: $i,SV661: $i,SV706: $i] :
( ( ( ( ( sK16_E @ SV706 @ SV661 @ SV139 )
!= SV706 )
| ~ ( in @ ( sK16_E @ SV706 @ SV661 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV661 ) ) )
= $false )
| ( ( in @ SV706 @ ( sK13_C @ SV661 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4483]) ).
thf(4553,plain,
! [SV139: $i,SV661: $i,SV706: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV706 @ SV661 @ SV139 ) @ ( sK15_SY612 @ SV706 @ SV661 @ SV139 ) )
!= SV706 )
| ~ ( in @ ( sK14_J @ SV706 @ SV661 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV706 @ SV661 @ SV139 )
!= ( singleton @ ( sK14_J @ SV706 @ SV661 @ SV139 ) ) ) )
= $false )
| ( ( in @ SV706 @ ( sK13_C @ SV661 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4484]) ).
thf(4554,plain,
! [SV707: $i,SV662: $i,SV139: $i,SV732: $i] :
( ( ( in @ SV732 @ ( cartesian_product2 @ SV139 @ SV662 ) )
= $false )
| ( ( SV732 = SV707 )
= $false )
| ( ( ! [SY1523: $i,SY1524: $i] :
( ( ( ordered_pair @ SY1523 @ SY1524 )
!= SV707 )
| ~ ( in @ SY1523 @ SV139 )
| ( SY1524
!= ( singleton @ SY1523 ) ) ) )
= $true )
| ( ( in @ SV707 @ ( sK13_C @ SV662 @ SV139 ) )
= $true )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4485]) ).
thf(4555,plain,
! [SV139: $i,SV662: $i,SV708: $i] :
( ( ( ( ( sK16_E @ SV708 @ SV662 @ SV139 )
!= SV708 )
| ~ ( in @ ( sK16_E @ SV708 @ SV662 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV662 ) ) )
= $false )
| ( ( in @ SV708 @ ( sK13_C @ SV662 @ SV139 ) )
= $false )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4486]) ).
thf(4556,plain,
! [SV139: $i,SV662: $i,SV708: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV708 @ SV662 @ SV139 ) @ ( sK15_SY612 @ SV708 @ SV662 @ SV139 ) )
!= SV708 )
| ~ ( in @ ( sK14_J @ SV708 @ SV662 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV708 @ SV662 @ SV139 )
!= ( singleton @ ( sK14_J @ SV708 @ SV662 @ SV139 ) ) ) )
= $false )
| ( ( in @ SV708 @ ( sK13_C @ SV662 @ SV139 ) )
= $false )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4487]) ).
thf(4557,plain,
! [SV625: $i,SV709: $i,SV139: $i,SV683: $i,SV759: $i,SV748: $i] :
( ( ( ( ( ordered_pair @ SV748 @ SV759 )
!= SV683 )
| ~ ( in @ SV748 @ SV139 ) )
= $true )
| ( ( ( SV759
!= ( singleton @ SV748 ) ) )
= $true )
| ( ( SV709 = SV683 )
= $false )
| ( ( in @ SV709 @ ( cartesian_product2 @ SV139 @ SV625 ) )
= $false )
| ( ( in @ SV683 @ ( sK13_C @ SV625 @ SV139 ) )
= $true )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4488]) ).
thf(4558,plain,
! [SV139: $i,SV625: $i,SV684: $i] :
( ( ( ( ( ordered_pair @ ( sK14_J @ SV684 @ SV625 @ SV139 ) @ ( sK15_SY612 @ SV684 @ SV625 @ SV139 ) )
!= SV684 )
| ~ ( in @ ( sK14_J @ SV684 @ SV625 @ SV139 ) @ SV139 ) )
= $false )
| ( ( in @ SV684 @ ( sK13_C @ SV625 @ SV139 ) )
= $false )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4491]) ).
thf(4559,plain,
! [SV733: $i,SV265: $i,SV145: $i] :
( ( ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4494]) ).
thf(4560,plain,
! [SV265: $i,SV145: $i] :
( ( ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4495]) ).
thf(4561,plain,
! [SV265: $i,SV145: $i] :
( ( ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) )
| ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4496]) ).
thf(4562,plain,
! [SV265: $i,SV734: $i,SV145: $i,SV760: $i] :
( ( ( ~ ( in @ SV760 @ SV145 ) )
= $true )
| ( ( ! [SY1621: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1621 @ SV760 @ SV734 @ SV265 @ SV145 ) @ SY1621 )
| ~ ~ ( in @ ( ordered_pair @ SV734 @ ( sK47_K @ SY1621 @ SV760 @ SV734 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV760 != SY1621 )
| ~ ( in @ SV734 @ SY1621 ) ) )
= $true )
| ( ( in @ SV734 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4497]) ).
thf(4563,plain,
! [SV145: $i,SV265: $i,SV735: $i] :
( ( ( ~ ( in @ ( sK45_E @ SV735 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1570: $i] :
( ~ ( in @ SY1570 @ ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV735 @ SY1570 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV735 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) )
| ~ ( in @ SV735 @ ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) ) ) ) )
= $false )
| ( ( in @ SV735 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4498]) ).
thf(4564,plain,
! [SV145: $i,SV265: $i,SV711: $i,SV727: $i,SV761: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_K @ SV761 @ SV727 @ SV711 @ SV265 @ SV145 ) @ SV761 )
| ~ ~ ( in @ ( ordered_pair @ SV711 @ ( sK47_K @ SV761 @ SV727 @ SV711 @ SV265 @ SV145 ) ) @ SV265 ) ) )
= $true )
| ( ( ( SV727 != SV761 )
| ~ ( in @ SV711 @ SV761 ) )
= $true )
| ( ( in @ SV727 @ SV145 )
= $false )
| ( ( in @ SV711 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4499]) ).
thf(4565,plain,
! [SV145: $i,SV265: $i,SV712: $i] :
( ( ( ~ ! [SY1527: $i] :
( ~ ( in @ SY1527 @ ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV712 @ SY1527 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV712 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) )
| ~ ( in @ SV712 @ ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( in @ SV712 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4501]) ).
thf(4566,plain,
! [SV685: $i,SV265: $i,SV736: $i,SV145: $i,SV762: $i] :
( ( ( ~ ( in @ SV762 @ SV145 ) )
= $true )
| ( ( ! [SY1622: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1622 @ SV762 @ SV736 @ SV265 @ SV145 ) @ SY1622 )
| ~ ~ ( in @ ( ordered_pair @ SV736 @ ( sK47_K @ SY1622 @ SV762 @ SV736 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV762 != SY1622 )
| ~ ( in @ SV736 @ SY1622 ) ) )
= $true )
| ( ( in @ SV736 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4502]) ).
thf(4567,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV737: $i] :
( ( ( ~ ( in @ ( sK45_E @ SV737 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1573: $i] :
( ~ ( in @ SY1573 @ ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV737 @ SY1573 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV737 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) )
| ~ ( in @ SV737 @ ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) ) ) ) )
= $false )
| ( ( in @ SV737 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4503]) ).
thf(4568,plain,
! [SV265: $i,SV738: $i,SV145: $i,SV763: $i] :
( ( ( ~ ( in @ SV763 @ SV145 ) )
= $true )
| ( ( ! [SY1623: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1623 @ SV763 @ SV738 @ SV265 @ SV145 ) @ SY1623 )
| ~ ~ ( in @ ( ordered_pair @ SV738 @ ( sK47_K @ SY1623 @ SV763 @ SV738 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV763 != SY1623 )
| ~ ( in @ SV738 @ SY1623 ) ) )
= $true )
| ( ( in @ SV738 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4504]) ).
thf(4569,plain,
! [SV145: $i,SV265: $i,SV739: $i] :
( ( ( ~ ( in @ ( sK45_E @ SV739 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1576: $i] :
( ~ ( in @ SY1576 @ ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV739 @ SY1576 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV739 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) )
| ~ ( in @ SV739 @ ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) ) ) ) )
= $false )
| ( ( in @ SV739 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4505]) ).
thf(4570,plain,
! [SV265: $i,SV740: $i,SV145: $i,SV764: $i] :
( ( ( ~ ( in @ SV764 @ SV145 ) )
= $true )
| ( ( ! [SY1624: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1624 @ SV764 @ SV740 @ SV265 @ SV145 ) @ SY1624 )
| ~ ~ ( in @ ( ordered_pair @ SV740 @ ( sK47_K @ SY1624 @ SV764 @ SV740 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV764 != SY1624 )
| ~ ( in @ SV740 @ SY1624 ) ) )
= $true )
| ( ( in @ SV740 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4506]) ).
thf(4571,plain,
! [SV145: $i,SV265: $i,SV741: $i] :
( ( ( ~ ( in @ ( sK45_E @ SV741 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1579: $i] :
( ~ ( in @ SY1579 @ ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV741 @ SY1579 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV741 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) )
| ~ ( in @ SV741 @ ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) ) ) ) )
= $false )
| ( ( in @ SV741 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4507]) ).
thf(4572,plain,
! [SV145: $i,SV265: $i,SV655: $i,SV713: $i,SV686: $i] :
( ( ( SV686 = SV713 )
= $false )
| ( ( ~ ( in @ SV655 @ SV713 ) )
= $true )
| ( ( in @ ( sK47_K @ SV713 @ SV686 @ SV655 @ SV265 @ SV145 ) @ SV713 )
= $true )
| ( ( in @ SV686 @ SV145 )
= $false )
| ( ( in @ SV655 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4508]) ).
thf(4573,plain,
! [SV145: $i,SV265: $i,SV655: $i,SV713: $i,SV686: $i] :
( ( ( ( SV686 != SV713 ) )
= $true )
| ( ( ~ ( in @ SV655 @ SV713 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV655 @ ( sK47_K @ SV713 @ SV686 @ SV655 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( in @ SV686 @ SV145 )
= $false )
| ( ( in @ SV655 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4509]) ).
thf(4574,plain,
! [SV145: $i,SV265: $i,SV656: $i,SV749: $i] :
( ( ( in @ SV749 @ ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV656 @ SV749 ) @ SV265 )
= $true )
| ( ( in @ SV656 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4510]) ).
thf(4575,plain,
! [SV145: $i,SV265: $i,SV656: $i] :
( ( ( ( sK45_E @ SV656 @ SV265 @ SV145 )
= ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) )
= $true )
| ( ( in @ SV656 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4511]) ).
thf(4576,plain,
! [SV145: $i,SV265: $i,SV656: $i] :
( ( ( in @ SV656 @ ( sK46_SY702 @ SV656 @ SV265 @ SV145 ) )
= $true )
| ( ( in @ SV656 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4512]) ).
thf(4577,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV596: $i,SV659: $i,SV716: $i,SV651: $i] :
( ( ( SV651 = SV716 )
= $false )
| ( ( ~ ( in @ SV659 @ SV716 ) )
= $true )
| ( ( in @ ( sK115_I @ SV716 @ SV659 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) @ SV716 )
= $true )
| ( ( ( ordered_pair @ SV651 @ SV659 )
= SV596 )
= $false )
| ( ( in @ SV651 @ SV170 )
= $false )
| ( ( ~ ( in @ SV596 @ ( cartesian_product2 @ SV170 @ SV481 ) ) )
= $true )
| ( ( in @ SV596 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4513]) ).
thf(4578,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV596: $i,SV659: $i,SV716: $i,SV651: $i] :
( ( ( ( SV651 != SV716 ) )
= $true )
| ( ( ~ ( in @ SV659 @ SV716 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV659 @ ( sK115_I @ SV716 @ SV659 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) ) @ SV271 )
= $false )
| ( ( ( ordered_pair @ SV651 @ SV659 )
= SV596 )
= $false )
| ( ( in @ SV651 @ SV170 )
= $false )
| ( ( ~ ( in @ SV596 @ ( cartesian_product2 @ SV170 @ SV481 ) ) )
= $true )
| ( ( in @ SV596 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4514]) ).
thf(4579,plain,
! [SV272: $i,SV717: $i,SV172: $i,SV750: $i] :
( ( ( ! [SY1605: $i] :
( ( SY1605 != SV750 )
| ~ ( in @ SY1605 @ ( cartesian_product2 @ SV172 @ SV717 ) ) ) )
= $true )
| ( ( ! [SY1606: $i,SY1607: $i] :
( ( ( ordered_pair @ SY1606 @ SY1607 )
!= SV750 )
| ~ ( in @ SY1606 @ SV172 )
| ! [SY1608: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1608 @ SY1607 @ SY1606 @ SV750 @ SV717 @ SV272 @ SV172 ) @ SY1608 )
| ~ ~ ( in @ ( ordered_pair @ SY1607 @ ( sK34_R @ SY1608 @ SY1607 @ SY1606 @ SV750 @ SV717 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1606 != SY1608 )
| ~ ( in @ SY1607 @ SY1608 ) ) ) )
= $true )
| ( ( in @ SV750 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4518]) ).
thf(4580,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK33_F @ SV751 @ SV717 @ SV272 @ SV172 )
!= SV751 )
| ~ ( in @ ( sK33_F @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV717 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) )
!= SV751 )
| ~ ( in @ ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1609: $i] :
( ~ ( in @ SY1609 @ ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) @ SY1609 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4519]) ).
thf(4581,plain,
! [SV272: $i,SV770: $i,SV172: $i] :
( ( ( ~ ( ~ ! [SY1631: $i] :
( ! [SY1632: $i] :
( ( SY1632 != SY1631 )
| ~ ( in @ SY1632 @ ( cartesian_product2 @ SV172 @ SV770 ) ) )
| ! [SY1633: $i,SY1634: $i] :
( ( ( ordered_pair @ SY1633 @ SY1634 )
!= SY1631 )
| ~ ( in @ SY1633 @ SV172 )
| ! [SY1635: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1635 @ SY1634 @ SY1633 @ SY1631 @ SV770 @ SV272 @ SV172 ) @ SY1635 )
| ~ ~ ( in @ ( ordered_pair @ SY1634 @ ( sK34_R @ SY1635 @ SY1634 @ SY1633 @ SY1631 @ SV770 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1633 != SY1635 )
| ~ ( in @ SY1634 @ SY1635 ) ) )
| ( in @ SY1631 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) ) )
| ~ ! [SY1636: $i] :
( ~ ( in @ SY1636 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1636 @ SV770 @ SV272 @ SV172 )
!= SY1636 )
| ~ ( in @ ( sK33_F @ SY1636 @ SV770 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV770 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1636 @ SV770 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1636 @ SV770 @ SV272 @ SV172 ) )
!= SY1636 )
| ~ ( in @ ( sK30_O @ SY1636 @ SV770 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1637: $i] :
( ~ ( in @ SY1637 @ ( sK32_SY652 @ SY1636 @ SV770 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1636 @ SV770 @ SV272 @ SV172 ) @ SY1637 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1636 @ SV770 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1636 @ SV770 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1636 @ SV770 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1636 @ SV770 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4520]) ).
thf(4582,plain,
! [SV272: $i,SV771: $i,SV172: $i] :
( ( ( ~ ( ~ ! [SY1638: $i] :
( ! [SY1639: $i] :
( ( SY1639 != SY1638 )
| ~ ( in @ SY1639 @ ( cartesian_product2 @ SV172 @ SV771 ) ) )
| ! [SY1640: $i,SY1641: $i] :
( ( ( ordered_pair @ SY1640 @ SY1641 )
!= SY1638 )
| ~ ( in @ SY1640 @ SV172 )
| ! [SY1642: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1642 @ SY1641 @ SY1640 @ SY1638 @ SV771 @ SV272 @ SV172 ) @ SY1642 )
| ~ ~ ( in @ ( ordered_pair @ SY1641 @ ( sK34_R @ SY1642 @ SY1641 @ SY1640 @ SY1638 @ SV771 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1640 != SY1642 )
| ~ ( in @ SY1641 @ SY1642 ) ) )
| ( in @ SY1638 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) ) )
| ~ ! [SY1643: $i] :
( ~ ( in @ SY1643 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1643 @ SV771 @ SV272 @ SV172 )
!= SY1643 )
| ~ ( in @ ( sK33_F @ SY1643 @ SV771 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV771 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1643 @ SV771 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1643 @ SV771 @ SV272 @ SV172 ) )
!= SY1643 )
| ~ ( in @ ( sK30_O @ SY1643 @ SV771 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1644: $i] :
( ~ ( in @ SY1644 @ ( sK32_SY652 @ SY1643 @ SV771 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1643 @ SV771 @ SV272 @ SV172 ) @ SY1644 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1643 @ SV771 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1643 @ SV771 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1643 @ SV771 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1643 @ SV771 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4521]) ).
thf(4583,plain,
! [SV172: $i,SV272: $i,SV772: $i] :
( ( ( ~ ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 ) )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4522]) ).
thf(4584,plain,
! [SV172: $i,SV272: $i] :
( ( ( ( ( sK41_SY666 @ SV272 @ SV172 )
!= ( sK43_SY691 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4523]) ).
thf(4585,plain,
! [SV272: $i,SV692: $i,SV172: $i,SV723: $i,SV752: $i] :
( ( ( SV752 = SV723 )
= $false )
| ( ( ~ ( in @ SV752 @ ( cartesian_product2 @ SV172 @ SV692 ) ) )
= $true )
| ( ( ! [SY1550: $i,SY1551: $i] :
( ( ( ordered_pair @ SY1550 @ SY1551 )
!= SV723 )
| ~ ( in @ SY1550 @ SV172 )
| ! [SY1552: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1552 @ SY1551 @ SY1550 @ SV723 @ SV692 @ SV272 @ SV172 ) @ SY1552 )
| ~ ~ ( in @ ( ordered_pair @ SY1551 @ ( sK34_R @ SY1552 @ SY1551 @ SY1550 @ SV723 @ SV692 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1550 != SY1552 )
| ~ ( in @ SY1551 @ SY1552 ) ) ) )
= $true )
| ( ( in @ SV723 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4524]) ).
thf(4586,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( ~ ( ( ( sK33_F @ SV724 @ SV692 @ SV272 @ SV172 )
!= SV724 )
| ~ ( in @ ( sK33_F @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV692 ) ) ) )
= $true )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4525]) ).
thf(4587,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) )
!= SV724 )
| ~ ( in @ ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1553: $i] :
( ~ ( in @ SY1553 @ ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) @ SY1553 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) ) ) ) ) )
= $true )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4526]) ).
thf(4588,plain,
! [SV272: $i,SV718: $i,SV172: $i,SV753: $i] :
( ( ( ! [SY1610: $i] :
( ( SY1610 != SV753 )
| ~ ( in @ SY1610 @ ( cartesian_product2 @ SV172 @ SV718 ) ) ) )
= $true )
| ( ( ! [SY1611: $i,SY1612: $i] :
( ( ( ordered_pair @ SY1611 @ SY1612 )
!= SV753 )
| ~ ( in @ SY1611 @ SV172 )
| ! [SY1613: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1613 @ SY1612 @ SY1611 @ SV753 @ SV718 @ SV272 @ SV172 ) @ SY1613 )
| ~ ~ ( in @ ( ordered_pair @ SY1612 @ ( sK34_R @ SY1613 @ SY1612 @ SY1611 @ SV753 @ SV718 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1611 != SY1613 )
| ~ ( in @ SY1612 @ SY1613 ) ) ) )
= $true )
| ( ( in @ SV753 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4527]) ).
thf(4589,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK33_F @ SV754 @ SV718 @ SV272 @ SV172 )
!= SV754 )
| ~ ( in @ ( sK33_F @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV718 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) )
!= SV754 )
| ~ ( in @ ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1614: $i] :
( ~ ( in @ SY1614 @ ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) @ SY1614 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4528]) ).
thf(4590,plain,
! [SV272: $i,SV719: $i,SV172: $i,SV755: $i] :
( ( ( ! [SY1615: $i] :
( ( SY1615 != SV755 )
| ~ ( in @ SY1615 @ ( cartesian_product2 @ SV172 @ SV719 ) ) ) )
= $true )
| ( ( ! [SY1616: $i,SY1617: $i] :
( ( ( ordered_pair @ SY1616 @ SY1617 )
!= SV755 )
| ~ ( in @ SY1616 @ SV172 )
| ! [SY1618: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1618 @ SY1617 @ SY1616 @ SV755 @ SV719 @ SV272 @ SV172 ) @ SY1618 )
| ~ ~ ( in @ ( ordered_pair @ SY1617 @ ( sK34_R @ SY1618 @ SY1617 @ SY1616 @ SV755 @ SV719 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1616 != SY1618 )
| ~ ( in @ SY1617 @ SY1618 ) ) ) )
= $true )
| ( ( in @ SV755 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4529]) ).
thf(4591,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK33_F @ SV756 @ SV719 @ SV272 @ SV172 )
!= SV756 )
| ~ ( in @ ( sK33_F @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV719 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) )
!= SV756 )
| ~ ( in @ ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1619: $i] :
( ~ ( in @ SY1619 @ ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) @ SY1619 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4530]) ).
thf(4592,plain,
! [SV720: $i,SV272: $i,SV743: $i,SV172: $i] :
( ( ( ! [SY1580: $i] :
( ! [SY1581: $i] :
( ( SY1581 != SY1580 )
| ~ ( in @ SY1581 @ ( cartesian_product2 @ SV172 @ SV743 ) ) )
| ! [SY1582: $i,SY1583: $i] :
( ( ( ordered_pair @ SY1582 @ SY1583 )
!= SY1580 )
| ~ ( in @ SY1582 @ SV172 )
| ! [SY1584: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1584 @ SY1583 @ SY1582 @ SY1580 @ SV743 @ SV272 @ SV172 ) @ SY1584 )
| ~ ~ ( in @ ( ordered_pair @ SY1583 @ ( sK34_R @ SY1584 @ SY1583 @ SY1582 @ SY1580 @ SV743 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1582 != SY1584 )
| ~ ( in @ SY1583 @ SY1584 ) ) )
| ( in @ SY1580 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4531]) ).
thf(4593,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i] :
( ( ( ! [SY1585: $i] :
( ~ ( in @ SY1585 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1585 @ SV743 @ SV272 @ SV172 )
!= SY1585 )
| ~ ( in @ ( sK33_F @ SY1585 @ SV743 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV743 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1585 @ SV743 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1585 @ SV743 @ SV272 @ SV172 ) )
!= SY1585 )
| ~ ( in @ ( sK30_O @ SY1585 @ SV743 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1586: $i] :
( ~ ( in @ SY1586 @ ( sK32_SY652 @ SY1585 @ SV743 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1585 @ SV743 @ SV272 @ SV172 ) @ SY1586 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1585 @ SV743 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1585 @ SV743 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1585 @ SV743 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1585 @ SV743 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4532]) ).
thf(4594,plain,
! [SV272: $i,SV744: $i,SV172: $i] :
( ( ( ! [SY1587: $i] :
( ! [SY1588: $i] :
( ( SY1588 != SY1587 )
| ~ ( in @ SY1588 @ ( cartesian_product2 @ SV172 @ SV744 ) ) )
| ! [SY1589: $i,SY1590: $i] :
( ( ( ordered_pair @ SY1589 @ SY1590 )
!= SY1587 )
| ~ ( in @ SY1589 @ SV172 )
| ! [SY1591: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1591 @ SY1590 @ SY1589 @ SY1587 @ SV744 @ SV272 @ SV172 ) @ SY1591 )
| ~ ~ ( in @ ( ordered_pair @ SY1590 @ ( sK34_R @ SY1591 @ SY1590 @ SY1589 @ SY1587 @ SV744 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1589 != SY1591 )
| ~ ( in @ SY1590 @ SY1591 ) ) )
| ( in @ SY1587 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) ) ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4533]) ).
thf(4595,plain,
! [SV172: $i,SV272: $i,SV744: $i] :
( ( ( ! [SY1592: $i] :
( ~ ( in @ SY1592 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1592 @ SV744 @ SV272 @ SV172 )
!= SY1592 )
| ~ ( in @ ( sK33_F @ SY1592 @ SV744 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV744 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1592 @ SV744 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1592 @ SV744 @ SV272 @ SV172 ) )
!= SY1592 )
| ~ ( in @ ( sK30_O @ SY1592 @ SV744 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1593: $i] :
( ~ ( in @ SY1593 @ ( sK32_SY652 @ SY1592 @ SV744 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1592 @ SV744 @ SV272 @ SV172 ) @ SY1593 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1592 @ SV744 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1592 @ SV744 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1592 @ SV744 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1592 @ SV744 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4534]) ).
thf(4596,plain,
! [SV272: $i,SV745: $i,SV172: $i] :
( ( ( ! [SY1594: $i] :
( ! [SY1595: $i] :
( ( SY1595 != SY1594 )
| ~ ( in @ SY1595 @ ( cartesian_product2 @ SV172 @ SV745 ) ) )
| ! [SY1596: $i,SY1597: $i] :
( ( ( ordered_pair @ SY1596 @ SY1597 )
!= SY1594 )
| ~ ( in @ SY1596 @ SV172 )
| ! [SY1598: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1598 @ SY1597 @ SY1596 @ SY1594 @ SV745 @ SV272 @ SV172 ) @ SY1598 )
| ~ ~ ( in @ ( ordered_pair @ SY1597 @ ( sK34_R @ SY1598 @ SY1597 @ SY1596 @ SY1594 @ SV745 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1596 != SY1598 )
| ~ ( in @ SY1597 @ SY1598 ) ) )
| ( in @ SY1594 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) ) ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4535]) ).
thf(4597,plain,
! [SV172: $i,SV272: $i,SV745: $i] :
( ( ( ! [SY1599: $i] :
( ~ ( in @ SY1599 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1599 @ SV745 @ SV272 @ SV172 )
!= SY1599 )
| ~ ( in @ ( sK33_F @ SY1599 @ SV745 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV745 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1599 @ SV745 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1599 @ SV745 @ SV272 @ SV172 ) )
!= SY1599 )
| ~ ( in @ ( sK30_O @ SY1599 @ SV745 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1600: $i] :
( ~ ( in @ SY1600 @ ( sK32_SY652 @ SY1599 @ SV745 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1599 @ SV745 @ SV272 @ SV172 ) @ SY1600 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1599 @ SV745 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1599 @ SV745 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1599 @ SV745 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1599 @ SV745 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4536]) ).
thf(4598,plain,
! [SV701: $i,SV272: $i,SV622: $i,SV172: $i,SV677: $i,SV757: $i,SV746: $i] :
( ( ( ( ( ordered_pair @ SV746 @ SV757 )
!= SV677 ) )
= $true )
| ( ( ~ ( in @ SV746 @ SV172 ) )
= $true )
| ( ( ! [SY1620: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1620 @ SV757 @ SV746 @ SV677 @ SV622 @ SV272 @ SV172 ) @ SY1620 )
| ~ ~ ( in @ ( ordered_pair @ SV757 @ ( sK34_R @ SY1620 @ SV757 @ SV746 @ SV677 @ SV622 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV746 != SY1620 )
| ~ ( in @ SV757 @ SY1620 ) ) )
= $true )
| ( ( SV701 = SV677 )
= $false )
| ( ( in @ SV701 @ ( cartesian_product2 @ SV172 @ SV622 ) )
= $false )
| ( ( in @ SV677 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4537]) ).
thf(4599,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( ( ( ordered_pair @ ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) )
!= SV678 ) )
= $false )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4538]) ).
thf(4600,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( ~ ( in @ ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 ) @ SV172 ) )
= $false )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4538]) ).
thf(4601,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( ~ ! [SY1493: $i] :
( ~ ( in @ SY1493 @ ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) @ SY1493 ) @ SV272 ) ) )
= $false )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4539]) ).
thf(4602,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( ~ ~ ( ( ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4539]) ).
thf(4603,plain,
! [SV660: $i,SV728: $i,SV139: $i,SV702: $i,SV773: $i] :
( ( ( ! [SY1645: $i] :
( ( ( ordered_pair @ SV773 @ SY1645 )
!= SV702 )
| ~ ( in @ SV773 @ SV139 )
| ( SY1645
!= ( singleton @ SV773 ) ) ) )
= $true )
| ( ( SV728 = SV702 )
= $false )
| ( ( in @ SV728 @ ( cartesian_product2 @ SV139 @ SV660 ) )
= $false )
| ( ( in @ SV702 @ ( sK13_C @ SV660 @ SV139 ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4540]) ).
thf(4604,plain,
! [SV139: $i,SV660: $i,SV703: $i] :
( ( ( ( ( sK16_E @ SV703 @ SV660 @ SV139 )
!= SV703 ) )
= $false )
| ( ( in @ SV703 @ ( sK13_C @ SV660 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4541]) ).
thf(4605,plain,
! [SV139: $i,SV660: $i,SV703: $i] :
( ( ( ~ ( in @ ( sK16_E @ SV703 @ SV660 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV660 ) ) )
= $false )
| ( ( in @ SV703 @ ( sK13_C @ SV660 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4541]) ).
thf(4606,plain,
! [SV139: $i,SV660: $i,SV703: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV703 @ SV660 @ SV139 ) @ ( sK15_SY612 @ SV703 @ SV660 @ SV139 ) )
!= SV703 )
| ~ ( in @ ( sK14_J @ SV703 @ SV660 @ SV139 ) @ SV139 ) ) )
= $false )
| ( ( in @ SV703 @ ( sK13_C @ SV660 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4542]) ).
thf(4607,plain,
! [SV139: $i,SV660: $i,SV703: $i] :
( ( ( ( ( sK15_SY612 @ SV703 @ SV660 @ SV139 )
!= ( singleton @ ( sK14_J @ SV703 @ SV660 @ SV139 ) ) ) )
= $false )
| ( ( in @ SV703 @ ( sK13_C @ SV660 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4542]) ).
thf(4608,plain,
! [SV725: $i,SV139: $i,SV765: $i] :
( ( ( ! [SY1625: $i] :
( ( SY1625 != SV765 )
| ~ ( in @ SY1625 @ ( cartesian_product2 @ SV139 @ SV725 ) ) )
| ! [SY1626: $i,SY1627: $i] :
( ( ( ordered_pair @ SY1626 @ SY1627 )
!= SV765 )
| ~ ( in @ SY1626 @ SV139 )
| ( SY1627
!= ( singleton @ SY1626 ) ) ) )
= $true )
| ( ( in @ SV765 @ ( sK13_C @ SV725 @ SV139 ) )
= $true )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4543]) ).
thf(4609,plain,
! [SV139: $i,SV725: $i,SV766: $i] :
( ( ( ~ ( in @ SV766 @ ( sK13_C @ SV725 @ SV139 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK16_E @ SV766 @ SV725 @ SV139 )
!= SV766 )
| ~ ( in @ ( sK16_E @ SV766 @ SV725 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV725 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV766 @ SV725 @ SV139 ) @ ( sK15_SY612 @ SV766 @ SV725 @ SV139 ) )
!= SV766 )
| ~ ( in @ ( sK14_J @ SV766 @ SV725 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV766 @ SV725 @ SV139 )
!= ( singleton @ ( sK14_J @ SV766 @ SV725 @ SV139 ) ) ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4544]) ).
thf(4610,plain,
! [SV726: $i,SV139: $i,SV767: $i] :
( ( ( ! [SY1628: $i] :
( ( SY1628 != SV767 )
| ~ ( in @ SY1628 @ ( cartesian_product2 @ SV139 @ SV726 ) ) )
| ! [SY1629: $i,SY1630: $i] :
( ( ( ordered_pair @ SY1629 @ SY1630 )
!= SV767 )
| ~ ( in @ SY1629 @ SV139 )
| ( SY1630
!= ( singleton @ SY1629 ) ) ) )
= $true )
| ( ( in @ SV767 @ ( sK13_C @ SV726 @ SV139 ) )
= $true )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4545]) ).
thf(4611,plain,
! [SV139: $i,SV726: $i,SV768: $i] :
( ( ( ~ ( in @ SV768 @ ( sK13_C @ SV726 @ SV139 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK16_E @ SV768 @ SV726 @ SV139 )
!= SV768 )
| ~ ( in @ ( sK16_E @ SV768 @ SV726 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV726 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV768 @ SV726 @ SV139 ) @ ( sK15_SY612 @ SV768 @ SV726 @ SV139 ) )
!= SV768 )
| ~ ( in @ ( sK14_J @ SV768 @ SV726 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV768 @ SV726 @ SV139 )
!= ( singleton @ ( sK14_J @ SV768 @ SV726 @ SV139 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4546]) ).
thf(4612,plain,
! [SV694: $i,SV139: $i,SV729: $i,SV769: $i] :
( ( ( ( SV769 != SV729 ) )
= $true )
| ( ( ~ ( in @ SV769 @ ( cartesian_product2 @ SV139 @ SV694 ) ) )
= $true )
| ( ( ! [SY1566: $i,SY1567: $i] :
( ( ( ordered_pair @ SY1566 @ SY1567 )
!= SV729 )
| ~ ( in @ SY1566 @ SV139 )
| ( SY1567
!= ( singleton @ SY1566 ) ) ) )
= $true )
| ( ( in @ SV729 @ ( sK13_C @ SV694 @ SV139 ) )
= $true )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4547]) ).
thf(4613,plain,
! [SV139: $i,SV694: $i,SV730: $i] :
( ( ( ~ ~ ( ( ( sK16_E @ SV730 @ SV694 @ SV139 )
!= SV730 )
| ~ ( in @ ( sK16_E @ SV730 @ SV694 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV694 ) ) ) )
= $false )
| ( ( in @ SV730 @ ( sK13_C @ SV694 @ SV139 ) )
= $false )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4548]) ).
thf(4614,plain,
! [SV139: $i,SV694: $i,SV730: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV730 @ SV694 @ SV139 ) @ ( sK15_SY612 @ SV730 @ SV694 @ SV139 ) )
!= SV730 )
| ~ ( in @ ( sK14_J @ SV730 @ SV694 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV730 @ SV694 @ SV139 )
!= ( singleton @ ( sK14_J @ SV730 @ SV694 @ SV139 ) ) ) ) )
= $false )
| ( ( in @ SV730 @ ( sK13_C @ SV694 @ SV139 ) )
= $false )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4548]) ).
thf(4615,plain,
! [SV624: $i,SV704: $i,SV139: $i,SV681: $i,SV758: $i,SV747: $i] :
( ( ( ( ( ordered_pair @ SV747 @ SV758 )
!= SV681 ) )
= $true )
| ( ( ~ ( in @ SV747 @ SV139 ) )
= $true )
| ( ( ( SV758
!= ( singleton @ SV747 ) ) )
= $true )
| ( ( SV704 = SV681 )
= $false )
| ( ( in @ SV704 @ ( cartesian_product2 @ SV139 @ SV624 ) )
= $false )
| ( ( in @ SV681 @ ( sK13_C @ SV624 @ SV139 ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4549]) ).
thf(4616,plain,
! [SV139: $i,SV624: $i,SV682: $i] :
( ( ( ( ( ordered_pair @ ( sK14_J @ SV682 @ SV624 @ SV139 ) @ ( sK15_SY612 @ SV682 @ SV624 @ SV139 ) )
!= SV682 ) )
= $false )
| ( ( in @ SV682 @ ( sK13_C @ SV624 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4550]) ).
thf(4617,plain,
! [SV139: $i,SV624: $i,SV682: $i] :
( ( ( ~ ( in @ ( sK14_J @ SV682 @ SV624 @ SV139 ) @ SV139 ) )
= $false )
| ( ( in @ SV682 @ ( sK13_C @ SV624 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4550]) ).
thf(4618,plain,
! [SV661: $i,SV731: $i,SV139: $i,SV705: $i,SV774: $i] :
( ( ( ! [SY1646: $i] :
( ( ( ordered_pair @ SV774 @ SY1646 )
!= SV705 )
| ~ ( in @ SV774 @ SV139 )
| ( SY1646
!= ( singleton @ SV774 ) ) ) )
= $true )
| ( ( SV731 = SV705 )
= $false )
| ( ( in @ SV731 @ ( cartesian_product2 @ SV139 @ SV661 ) )
= $false )
| ( ( in @ SV705 @ ( sK13_C @ SV661 @ SV139 ) )
= $true )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4551]) ).
thf(4619,plain,
! [SV139: $i,SV661: $i,SV706: $i] :
( ( ( ( ( sK16_E @ SV706 @ SV661 @ SV139 )
!= SV706 ) )
= $false )
| ( ( in @ SV706 @ ( sK13_C @ SV661 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4552]) ).
thf(4620,plain,
! [SV139: $i,SV661: $i,SV706: $i] :
( ( ( ~ ( in @ ( sK16_E @ SV706 @ SV661 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV661 ) ) )
= $false )
| ( ( in @ SV706 @ ( sK13_C @ SV661 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4552]) ).
thf(4621,plain,
! [SV139: $i,SV661: $i,SV706: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV706 @ SV661 @ SV139 ) @ ( sK15_SY612 @ SV706 @ SV661 @ SV139 ) )
!= SV706 )
| ~ ( in @ ( sK14_J @ SV706 @ SV661 @ SV139 ) @ SV139 ) ) )
= $false )
| ( ( in @ SV706 @ ( sK13_C @ SV661 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4553]) ).
thf(4622,plain,
! [SV139: $i,SV661: $i,SV706: $i] :
( ( ( ( ( sK15_SY612 @ SV706 @ SV661 @ SV139 )
!= ( singleton @ ( sK14_J @ SV706 @ SV661 @ SV139 ) ) ) )
= $false )
| ( ( in @ SV706 @ ( sK13_C @ SV661 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4553]) ).
thf(4623,plain,
! [SV662: $i,SV732: $i,SV139: $i,SV707: $i,SV775: $i] :
( ( ( ! [SY1647: $i] :
( ( ( ordered_pair @ SV775 @ SY1647 )
!= SV707 )
| ~ ( in @ SV775 @ SV139 )
| ( SY1647
!= ( singleton @ SV775 ) ) ) )
= $true )
| ( ( SV732 = SV707 )
= $false )
| ( ( in @ SV732 @ ( cartesian_product2 @ SV139 @ SV662 ) )
= $false )
| ( ( in @ SV707 @ ( sK13_C @ SV662 @ SV139 ) )
= $true )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4554]) ).
thf(4624,plain,
! [SV139: $i,SV662: $i,SV708: $i] :
( ( ( ( ( sK16_E @ SV708 @ SV662 @ SV139 )
!= SV708 ) )
= $false )
| ( ( in @ SV708 @ ( sK13_C @ SV662 @ SV139 ) )
= $false )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4555]) ).
thf(4625,plain,
! [SV139: $i,SV662: $i,SV708: $i] :
( ( ( ~ ( in @ ( sK16_E @ SV708 @ SV662 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV662 ) ) )
= $false )
| ( ( in @ SV708 @ ( sK13_C @ SV662 @ SV139 ) )
= $false )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4555]) ).
thf(4626,plain,
! [SV139: $i,SV662: $i,SV708: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV708 @ SV662 @ SV139 ) @ ( sK15_SY612 @ SV708 @ SV662 @ SV139 ) )
!= SV708 )
| ~ ( in @ ( sK14_J @ SV708 @ SV662 @ SV139 ) @ SV139 ) ) )
= $false )
| ( ( in @ SV708 @ ( sK13_C @ SV662 @ SV139 ) )
= $false )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4556]) ).
thf(4627,plain,
! [SV139: $i,SV662: $i,SV708: $i] :
( ( ( ( ( sK15_SY612 @ SV708 @ SV662 @ SV139 )
!= ( singleton @ ( sK14_J @ SV708 @ SV662 @ SV139 ) ) ) )
= $false )
| ( ( in @ SV708 @ ( sK13_C @ SV662 @ SV139 ) )
= $false )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4556]) ).
thf(4628,plain,
! [SV625: $i,SV709: $i,SV139: $i,SV683: $i,SV759: $i,SV748: $i] :
( ( ( ( ( ordered_pair @ SV748 @ SV759 )
!= SV683 ) )
= $true )
| ( ( ~ ( in @ SV748 @ SV139 ) )
= $true )
| ( ( ( SV759
!= ( singleton @ SV748 ) ) )
= $true )
| ( ( SV709 = SV683 )
= $false )
| ( ( in @ SV709 @ ( cartesian_product2 @ SV139 @ SV625 ) )
= $false )
| ( ( in @ SV683 @ ( sK13_C @ SV625 @ SV139 ) )
= $true )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4557]) ).
thf(4629,plain,
! [SV139: $i,SV625: $i,SV684: $i] :
( ( ( ( ( ordered_pair @ ( sK14_J @ SV684 @ SV625 @ SV139 ) @ ( sK15_SY612 @ SV684 @ SV625 @ SV139 ) )
!= SV684 ) )
= $false )
| ( ( in @ SV684 @ ( sK13_C @ SV625 @ SV139 ) )
= $false )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4558]) ).
thf(4630,plain,
! [SV139: $i,SV625: $i,SV684: $i] :
( ( ( ~ ( in @ ( sK14_J @ SV684 @ SV625 @ SV139 ) @ SV139 ) )
= $false )
| ( ( in @ SV684 @ ( sK13_C @ SV625 @ SV139 ) )
= $false )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4558]) ).
thf(4631,plain,
! [SV733: $i,SV265: $i,SV145: $i] :
( ( ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4559]) ).
thf(4632,plain,
! [SV733: $i,SV145: $i,SV265: $i] :
( ( ( ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4559]) ).
thf(4633,plain,
! [SV265: $i,SV145: $i] :
( ( ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4560]) ).
thf(4634,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4560]) ).
thf(4635,plain,
! [SV265: $i,SV145: $i] :
( ( ( ~ ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4561]) ).
thf(4636,plain,
! [SV145: $i,SV265: $i] :
( ( ( ~ ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4561]) ).
thf(4637,plain,
! [SV265: $i,SV734: $i,SV145: $i,SV760: $i] :
( ( ( in @ SV760 @ SV145 )
= $false )
| ( ( ! [SY1621: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1621 @ SV760 @ SV734 @ SV265 @ SV145 ) @ SY1621 )
| ~ ~ ( in @ ( ordered_pair @ SV734 @ ( sK47_K @ SY1621 @ SV760 @ SV734 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV760 != SY1621 )
| ~ ( in @ SV734 @ SY1621 ) ) )
= $true )
| ( ( in @ SV734 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4562]) ).
thf(4638,plain,
! [SV145: $i,SV265: $i,SV735: $i] :
( ( ( ~ ( in @ ( sK45_E @ SV735 @ SV265 @ SV145 ) @ SV145 ) )
= $false )
| ( ( in @ SV735 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4563]) ).
thf(4639,plain,
! [SV145: $i,SV265: $i,SV735: $i] :
( ( ( ~ ~ ( ~ ! [SY1570: $i] :
( ~ ( in @ SY1570 @ ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV735 @ SY1570 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV735 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) )
| ~ ( in @ SV735 @ ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) ) ) ) )
= $false )
| ( ( in @ SV735 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4563]) ).
thf(4640,plain,
! [SV145: $i,SV265: $i,SV711: $i,SV727: $i,SV761: $i] :
( ( ( ~ ( in @ ( sK47_K @ SV761 @ SV727 @ SV711 @ SV265 @ SV145 ) @ SV761 )
| ~ ~ ( in @ ( ordered_pair @ SV711 @ ( sK47_K @ SV761 @ SV727 @ SV711 @ SV265 @ SV145 ) ) @ SV265 ) )
= $false )
| ( ( ( SV727 != SV761 )
| ~ ( in @ SV711 @ SV761 ) )
= $true )
| ( ( in @ SV727 @ SV145 )
= $false )
| ( ( in @ SV711 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4564]) ).
thf(4641,plain,
! [SV145: $i,SV265: $i,SV712: $i] :
( ( ( ~ ! [SY1527: $i] :
( ~ ( in @ SY1527 @ ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV712 @ SY1527 ) @ SV265 ) ) )
= $false )
| ( ( in @ SV712 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4565]) ).
thf(4642,plain,
! [SV145: $i,SV265: $i,SV712: $i] :
( ( ( ~ ~ ( ( ( sK45_E @ SV712 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) )
| ~ ( in @ SV712 @ ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( in @ SV712 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4565]) ).
thf(4643,plain,
! [SV685: $i,SV265: $i,SV736: $i,SV145: $i,SV762: $i] :
( ( ( in @ SV762 @ SV145 )
= $false )
| ( ( ! [SY1622: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1622 @ SV762 @ SV736 @ SV265 @ SV145 ) @ SY1622 )
| ~ ~ ( in @ ( ordered_pair @ SV736 @ ( sK47_K @ SY1622 @ SV762 @ SV736 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV762 != SY1622 )
| ~ ( in @ SV736 @ SY1622 ) ) )
= $true )
| ( ( in @ SV736 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4566]) ).
thf(4644,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV737: $i] :
( ( ( ~ ( in @ ( sK45_E @ SV737 @ SV265 @ SV145 ) @ SV145 ) )
= $false )
| ( ( in @ SV737 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4567]) ).
thf(4645,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV737: $i] :
( ( ( ~ ~ ( ~ ! [SY1573: $i] :
( ~ ( in @ SY1573 @ ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV737 @ SY1573 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV737 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) )
| ~ ( in @ SV737 @ ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) ) ) ) )
= $false )
| ( ( in @ SV737 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4567]) ).
thf(4646,plain,
! [SV265: $i,SV738: $i,SV145: $i,SV763: $i] :
( ( ( in @ SV763 @ SV145 )
= $false )
| ( ( ! [SY1623: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1623 @ SV763 @ SV738 @ SV265 @ SV145 ) @ SY1623 )
| ~ ~ ( in @ ( ordered_pair @ SV738 @ ( sK47_K @ SY1623 @ SV763 @ SV738 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV763 != SY1623 )
| ~ ( in @ SV738 @ SY1623 ) ) )
= $true )
| ( ( in @ SV738 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4568]) ).
thf(4647,plain,
! [SV145: $i,SV265: $i,SV739: $i] :
( ( ( ~ ( in @ ( sK45_E @ SV739 @ SV265 @ SV145 ) @ SV145 ) )
= $false )
| ( ( in @ SV739 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4569]) ).
thf(4648,plain,
! [SV145: $i,SV265: $i,SV739: $i] :
( ( ( ~ ~ ( ~ ! [SY1576: $i] :
( ~ ( in @ SY1576 @ ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV739 @ SY1576 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV739 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) )
| ~ ( in @ SV739 @ ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) ) ) ) )
= $false )
| ( ( in @ SV739 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4569]) ).
thf(4649,plain,
! [SV265: $i,SV740: $i,SV145: $i,SV764: $i] :
( ( ( in @ SV764 @ SV145 )
= $false )
| ( ( ! [SY1624: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1624 @ SV764 @ SV740 @ SV265 @ SV145 ) @ SY1624 )
| ~ ~ ( in @ ( ordered_pair @ SV740 @ ( sK47_K @ SY1624 @ SV764 @ SV740 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV764 != SY1624 )
| ~ ( in @ SV740 @ SY1624 ) ) )
= $true )
| ( ( in @ SV740 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4570]) ).
thf(4650,plain,
! [SV145: $i,SV265: $i,SV741: $i] :
( ( ( ~ ( in @ ( sK45_E @ SV741 @ SV265 @ SV145 ) @ SV145 ) )
= $false )
| ( ( in @ SV741 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4571]) ).
thf(4651,plain,
! [SV145: $i,SV265: $i,SV741: $i] :
( ( ( ~ ~ ( ~ ! [SY1579: $i] :
( ~ ( in @ SY1579 @ ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV741 @ SY1579 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV741 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) )
| ~ ( in @ SV741 @ ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) ) ) ) )
= $false )
| ( ( in @ SV741 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4571]) ).
thf(4652,plain,
! [SV145: $i,SV265: $i,SV686: $i,SV713: $i,SV655: $i] :
( ( ( in @ SV655 @ SV713 )
= $false )
| ( ( SV686 = SV713 )
= $false )
| ( ( in @ ( sK47_K @ SV713 @ SV686 @ SV655 @ SV265 @ SV145 ) @ SV713 )
= $true )
| ( ( in @ SV686 @ SV145 )
= $false )
| ( ( in @ SV655 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4572]) ).
thf(4653,plain,
! [SV145: $i,SV265: $i,SV655: $i,SV713: $i,SV686: $i] :
( ( ( SV686 = SV713 )
= $false )
| ( ( ~ ( in @ SV655 @ SV713 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV655 @ ( sK47_K @ SV713 @ SV686 @ SV655 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( in @ SV686 @ SV145 )
= $false )
| ( ( in @ SV655 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4573]) ).
thf(4654,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV596: $i,SV651: $i,SV716: $i,SV659: $i] :
( ( ( in @ SV659 @ SV716 )
= $false )
| ( ( SV651 = SV716 )
= $false )
| ( ( in @ ( sK115_I @ SV716 @ SV659 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) @ SV716 )
= $true )
| ( ( ( ordered_pair @ SV651 @ SV659 )
= SV596 )
= $false )
| ( ( in @ SV651 @ SV170 )
= $false )
| ( ( ~ ( in @ SV596 @ ( cartesian_product2 @ SV170 @ SV481 ) ) )
= $true )
| ( ( in @ SV596 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4577]) ).
thf(4655,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV596: $i,SV659: $i,SV716: $i,SV651: $i] :
( ( ( SV651 = SV716 )
= $false )
| ( ( ~ ( in @ SV659 @ SV716 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV659 @ ( sK115_I @ SV716 @ SV659 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) ) @ SV271 )
= $false )
| ( ( ( ordered_pair @ SV651 @ SV659 )
= SV596 )
= $false )
| ( ( in @ SV651 @ SV170 )
= $false )
| ( ( ~ ( in @ SV596 @ ( cartesian_product2 @ SV170 @ SV481 ) ) )
= $true )
| ( ( in @ SV596 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4578]) ).
thf(4656,plain,
! [SV272: $i,SV717: $i,SV172: $i,SV750: $i,SV776: $i] :
( ( ( ( SV776 != SV750 )
| ~ ( in @ SV776 @ ( cartesian_product2 @ SV172 @ SV717 ) ) )
= $true )
| ( ( ! [SY1606: $i,SY1607: $i] :
( ( ( ordered_pair @ SY1606 @ SY1607 )
!= SV750 )
| ~ ( in @ SY1606 @ SV172 )
| ! [SY1608: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1608 @ SY1607 @ SY1606 @ SV750 @ SV717 @ SV272 @ SV172 ) @ SY1608 )
| ~ ~ ( in @ ( ordered_pair @ SY1607 @ ( sK34_R @ SY1608 @ SY1607 @ SY1606 @ SV750 @ SV717 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1606 != SY1608 )
| ~ ( in @ SY1607 @ SY1608 ) ) ) )
= $true )
| ( ( in @ SV750 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4579]) ).
thf(4657,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( ~ ~ ( ( ( sK33_F @ SV751 @ SV717 @ SV272 @ SV172 )
!= SV751 )
| ~ ( in @ ( sK33_F @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV717 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) )
!= SV751 )
| ~ ( in @ ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1609: $i] :
( ~ ( in @ SY1609 @ ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) @ SY1609 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) ) ) ) ) )
= $false )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4580]) ).
thf(4658,plain,
! [SV272: $i,SV770: $i,SV172: $i] :
( ( ( ~ ! [SY1631: $i] :
( ! [SY1632: $i] :
( ( SY1632 != SY1631 )
| ~ ( in @ SY1632 @ ( cartesian_product2 @ SV172 @ SV770 ) ) )
| ! [SY1633: $i,SY1634: $i] :
( ( ( ordered_pair @ SY1633 @ SY1634 )
!= SY1631 )
| ~ ( in @ SY1633 @ SV172 )
| ! [SY1635: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1635 @ SY1634 @ SY1633 @ SY1631 @ SV770 @ SV272 @ SV172 ) @ SY1635 )
| ~ ~ ( in @ ( ordered_pair @ SY1634 @ ( sK34_R @ SY1635 @ SY1634 @ SY1633 @ SY1631 @ SV770 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1633 != SY1635 )
| ~ ( in @ SY1634 @ SY1635 ) ) )
| ( in @ SY1631 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) ) )
| ~ ! [SY1636: $i] :
( ~ ( in @ SY1636 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1636 @ SV770 @ SV272 @ SV172 )
!= SY1636 )
| ~ ( in @ ( sK33_F @ SY1636 @ SV770 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV770 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1636 @ SV770 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1636 @ SV770 @ SV272 @ SV172 ) )
!= SY1636 )
| ~ ( in @ ( sK30_O @ SY1636 @ SV770 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1637: $i] :
( ~ ( in @ SY1637 @ ( sK32_SY652 @ SY1636 @ SV770 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1636 @ SV770 @ SV272 @ SV172 ) @ SY1637 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1636 @ SV770 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1636 @ SV770 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1636 @ SV770 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1636 @ SV770 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4581]) ).
thf(4659,plain,
! [SV272: $i,SV771: $i,SV172: $i] :
( ( ( ~ ! [SY1638: $i] :
( ! [SY1639: $i] :
( ( SY1639 != SY1638 )
| ~ ( in @ SY1639 @ ( cartesian_product2 @ SV172 @ SV771 ) ) )
| ! [SY1640: $i,SY1641: $i] :
( ( ( ordered_pair @ SY1640 @ SY1641 )
!= SY1638 )
| ~ ( in @ SY1640 @ SV172 )
| ! [SY1642: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1642 @ SY1641 @ SY1640 @ SY1638 @ SV771 @ SV272 @ SV172 ) @ SY1642 )
| ~ ~ ( in @ ( ordered_pair @ SY1641 @ ( sK34_R @ SY1642 @ SY1641 @ SY1640 @ SY1638 @ SV771 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1640 != SY1642 )
| ~ ( in @ SY1641 @ SY1642 ) ) )
| ( in @ SY1638 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) ) )
| ~ ! [SY1643: $i] :
( ~ ( in @ SY1643 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1643 @ SV771 @ SV272 @ SV172 )
!= SY1643 )
| ~ ( in @ ( sK33_F @ SY1643 @ SV771 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV771 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1643 @ SV771 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1643 @ SV771 @ SV272 @ SV172 ) )
!= SY1643 )
| ~ ( in @ ( sK30_O @ SY1643 @ SV771 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1644: $i] :
( ~ ( in @ SY1644 @ ( sK32_SY652 @ SY1643 @ SV771 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1643 @ SV771 @ SV272 @ SV172 ) @ SY1644 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1643 @ SV771 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1643 @ SV771 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1643 @ SV771 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1643 @ SV771 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4582]) ).
thf(4660,plain,
! [SV172: $i,SV272: $i,SV772: $i] :
( ( ( ~ ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4583]) ).
thf(4661,plain,
! [SV172: $i,SV272: $i] :
( ( ( ( ( sK41_SY666 @ SV272 @ SV172 )
!= ( sK43_SY691 @ SV272 @ SV172 ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4584]) ).
thf(4662,plain,
! [SV172: $i,SV272: $i] :
( ( ( ~ ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) ) )
= $false )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4584]) ).
thf(4663,plain,
! [SV272: $i,SV723: $i,SV692: $i,SV172: $i,SV752: $i] :
( ( ( in @ SV752 @ ( cartesian_product2 @ SV172 @ SV692 ) )
= $false )
| ( ( SV752 = SV723 )
= $false )
| ( ( ! [SY1550: $i,SY1551: $i] :
( ( ( ordered_pair @ SY1550 @ SY1551 )
!= SV723 )
| ~ ( in @ SY1550 @ SV172 )
| ! [SY1552: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1552 @ SY1551 @ SY1550 @ SV723 @ SV692 @ SV272 @ SV172 ) @ SY1552 )
| ~ ~ ( in @ ( ordered_pair @ SY1551 @ ( sK34_R @ SY1552 @ SY1551 @ SY1550 @ SV723 @ SV692 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1550 != SY1552 )
| ~ ( in @ SY1551 @ SY1552 ) ) ) )
= $true )
| ( ( in @ SV723 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4585]) ).
thf(4664,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( ( ( sK33_F @ SV724 @ SV692 @ SV272 @ SV172 )
!= SV724 )
| ~ ( in @ ( sK33_F @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV692 ) ) )
= $false )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4586]) ).
thf(4665,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) )
!= SV724 )
| ~ ( in @ ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1553: $i] :
( ~ ( in @ SY1553 @ ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) @ SY1553 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) ) ) ) )
= $false )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4587]) ).
thf(4666,plain,
! [SV272: $i,SV718: $i,SV172: $i,SV753: $i,SV777: $i] :
( ( ( ( SV777 != SV753 )
| ~ ( in @ SV777 @ ( cartesian_product2 @ SV172 @ SV718 ) ) )
= $true )
| ( ( ! [SY1611: $i,SY1612: $i] :
( ( ( ordered_pair @ SY1611 @ SY1612 )
!= SV753 )
| ~ ( in @ SY1611 @ SV172 )
| ! [SY1613: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1613 @ SY1612 @ SY1611 @ SV753 @ SV718 @ SV272 @ SV172 ) @ SY1613 )
| ~ ~ ( in @ ( ordered_pair @ SY1612 @ ( sK34_R @ SY1613 @ SY1612 @ SY1611 @ SV753 @ SV718 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1611 != SY1613 )
| ~ ( in @ SY1612 @ SY1613 ) ) ) )
= $true )
| ( ( in @ SV753 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4588]) ).
thf(4667,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( ~ ~ ( ( ( sK33_F @ SV754 @ SV718 @ SV272 @ SV172 )
!= SV754 )
| ~ ( in @ ( sK33_F @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV718 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) )
!= SV754 )
| ~ ( in @ ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1614: $i] :
( ~ ( in @ SY1614 @ ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) @ SY1614 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) ) ) ) ) )
= $false )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4589]) ).
thf(4668,plain,
! [SV272: $i,SV719: $i,SV172: $i,SV755: $i,SV778: $i] :
( ( ( ( SV778 != SV755 )
| ~ ( in @ SV778 @ ( cartesian_product2 @ SV172 @ SV719 ) ) )
= $true )
| ( ( ! [SY1616: $i,SY1617: $i] :
( ( ( ordered_pair @ SY1616 @ SY1617 )
!= SV755 )
| ~ ( in @ SY1616 @ SV172 )
| ! [SY1618: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1618 @ SY1617 @ SY1616 @ SV755 @ SV719 @ SV272 @ SV172 ) @ SY1618 )
| ~ ~ ( in @ ( ordered_pair @ SY1617 @ ( sK34_R @ SY1618 @ SY1617 @ SY1616 @ SV755 @ SV719 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1616 != SY1618 )
| ~ ( in @ SY1617 @ SY1618 ) ) ) )
= $true )
| ( ( in @ SV755 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4590]) ).
thf(4669,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( ~ ~ ( ( ( sK33_F @ SV756 @ SV719 @ SV272 @ SV172 )
!= SV756 )
| ~ ( in @ ( sK33_F @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV719 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) )
!= SV756 )
| ~ ( in @ ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1619: $i] :
( ~ ( in @ SY1619 @ ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) @ SY1619 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) ) ) ) ) )
= $false )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4591]) ).
thf(4670,plain,
! [SV720: $i,SV272: $i,SV743: $i,SV172: $i,SV779: $i] :
( ( ( ! [SY1648: $i] :
( ( SY1648 != SV779 )
| ~ ( in @ SY1648 @ ( cartesian_product2 @ SV172 @ SV743 ) ) )
| ! [SY1649: $i,SY1650: $i] :
( ( ( ordered_pair @ SY1649 @ SY1650 )
!= SV779 )
| ~ ( in @ SY1649 @ SV172 )
| ! [SY1651: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1651 @ SY1650 @ SY1649 @ SV779 @ SV743 @ SV272 @ SV172 ) @ SY1651 )
| ~ ~ ( in @ ( ordered_pair @ SY1650 @ ( sK34_R @ SY1651 @ SY1650 @ SY1649 @ SV779 @ SV743 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1649 != SY1651 )
| ~ ( in @ SY1650 @ SY1651 ) ) )
| ( in @ SV779 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4592]) ).
thf(4671,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( ~ ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SV780 @ SV743 @ SV272 @ SV172 )
!= SV780 )
| ~ ( in @ ( sK33_F @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV743 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) )
!= SV780 )
| ~ ( in @ ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1652: $i] :
( ~ ( in @ SY1652 @ ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) @ SY1652 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4593]) ).
thf(4672,plain,
! [SV272: $i,SV744: $i,SV172: $i,SV781: $i] :
( ( ( ! [SY1653: $i] :
( ( SY1653 != SV781 )
| ~ ( in @ SY1653 @ ( cartesian_product2 @ SV172 @ SV744 ) ) )
| ! [SY1654: $i,SY1655: $i] :
( ( ( ordered_pair @ SY1654 @ SY1655 )
!= SV781 )
| ~ ( in @ SY1654 @ SV172 )
| ! [SY1656: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1656 @ SY1655 @ SY1654 @ SV781 @ SV744 @ SV272 @ SV172 ) @ SY1656 )
| ~ ~ ( in @ ( ordered_pair @ SY1655 @ ( sK34_R @ SY1656 @ SY1655 @ SY1654 @ SV781 @ SV744 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1654 != SY1656 )
| ~ ( in @ SY1655 @ SY1656 ) ) )
| ( in @ SV781 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4594]) ).
thf(4673,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( ~ ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SV782 @ SV744 @ SV272 @ SV172 )
!= SV782 )
| ~ ( in @ ( sK33_F @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV744 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) )
!= SV782 )
| ~ ( in @ ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1657: $i] :
( ~ ( in @ SY1657 @ ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) @ SY1657 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4595]) ).
thf(4674,plain,
! [SV272: $i,SV745: $i,SV172: $i,SV783: $i] :
( ( ( ! [SY1658: $i] :
( ( SY1658 != SV783 )
| ~ ( in @ SY1658 @ ( cartesian_product2 @ SV172 @ SV745 ) ) )
| ! [SY1659: $i,SY1660: $i] :
( ( ( ordered_pair @ SY1659 @ SY1660 )
!= SV783 )
| ~ ( in @ SY1659 @ SV172 )
| ! [SY1661: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1661 @ SY1660 @ SY1659 @ SV783 @ SV745 @ SV272 @ SV172 ) @ SY1661 )
| ~ ~ ( in @ ( ordered_pair @ SY1660 @ ( sK34_R @ SY1661 @ SY1660 @ SY1659 @ SV783 @ SV745 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1659 != SY1661 )
| ~ ( in @ SY1660 @ SY1661 ) ) )
| ( in @ SV783 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4596]) ).
thf(4675,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( ~ ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SV784 @ SV745 @ SV272 @ SV172 )
!= SV784 )
| ~ ( in @ ( sK33_F @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV745 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) )
!= SV784 )
| ~ ( in @ ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1662: $i] :
( ~ ( in @ SY1662 @ ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) @ SY1662 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4597]) ).
thf(4676,plain,
! [SV701: $i,SV272: $i,SV622: $i,SV172: $i,SV677: $i,SV757: $i,SV746: $i] :
( ( ( ( ordered_pair @ SV746 @ SV757 )
= SV677 )
= $false )
| ( ( ~ ( in @ SV746 @ SV172 ) )
= $true )
| ( ( ! [SY1620: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1620 @ SV757 @ SV746 @ SV677 @ SV622 @ SV272 @ SV172 ) @ SY1620 )
| ~ ~ ( in @ ( ordered_pair @ SV757 @ ( sK34_R @ SY1620 @ SV757 @ SV746 @ SV677 @ SV622 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV746 != SY1620 )
| ~ ( in @ SV757 @ SY1620 ) ) )
= $true )
| ( ( SV701 = SV677 )
= $false )
| ( ( in @ SV701 @ ( cartesian_product2 @ SV172 @ SV622 ) )
= $false )
| ( ( in @ SV677 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4598]) ).
thf(4677,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( ( ordered_pair @ ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) )
= SV678 )
= $true )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4599]) ).
thf(4678,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( in @ ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4600]) ).
thf(4679,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( ! [SY1493: $i] :
( ~ ( in @ SY1493 @ ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) @ SY1493 ) @ SV272 ) ) )
= $true )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4601]) ).
thf(4680,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( ~ ( ( ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) ) ) )
= $true )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4602]) ).
thf(4681,plain,
! [SV660: $i,SV728: $i,SV139: $i,SV702: $i,SV785: $i,SV773: $i] :
( ( ( ( ( ordered_pair @ SV773 @ SV785 )
!= SV702 )
| ~ ( in @ SV773 @ SV139 )
| ( SV785
!= ( singleton @ SV773 ) ) )
= $true )
| ( ( SV728 = SV702 )
= $false )
| ( ( in @ SV728 @ ( cartesian_product2 @ SV139 @ SV660 ) )
= $false )
| ( ( in @ SV702 @ ( sK13_C @ SV660 @ SV139 ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4603]) ).
thf(4682,plain,
! [SV139: $i,SV660: $i,SV703: $i] :
( ( ( ( sK16_E @ SV703 @ SV660 @ SV139 )
= SV703 )
= $true )
| ( ( in @ SV703 @ ( sK13_C @ SV660 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4604]) ).
thf(4683,plain,
! [SV139: $i,SV660: $i,SV703: $i] :
( ( ( in @ ( sK16_E @ SV703 @ SV660 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV660 ) )
= $true )
| ( ( in @ SV703 @ ( sK13_C @ SV660 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4605]) ).
thf(4684,plain,
! [SV139: $i,SV660: $i,SV703: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK14_J @ SV703 @ SV660 @ SV139 ) @ ( sK15_SY612 @ SV703 @ SV660 @ SV139 ) )
!= SV703 )
| ~ ( in @ ( sK14_J @ SV703 @ SV660 @ SV139 ) @ SV139 ) ) )
= $true )
| ( ( in @ SV703 @ ( sK13_C @ SV660 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4606]) ).
thf(4685,plain,
! [SV139: $i,SV660: $i,SV703: $i] :
( ( ( ( sK15_SY612 @ SV703 @ SV660 @ SV139 )
= ( singleton @ ( sK14_J @ SV703 @ SV660 @ SV139 ) ) )
= $true )
| ( ( in @ SV703 @ ( sK13_C @ SV660 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4607]) ).
thf(4686,plain,
! [SV725: $i,SV139: $i,SV765: $i] :
( ( ( ! [SY1625: $i] :
( ( SY1625 != SV765 )
| ~ ( in @ SY1625 @ ( cartesian_product2 @ SV139 @ SV725 ) ) ) )
= $true )
| ( ( ! [SY1626: $i,SY1627: $i] :
( ( ( ordered_pair @ SY1626 @ SY1627 )
!= SV765 )
| ~ ( in @ SY1626 @ SV139 )
| ( SY1627
!= ( singleton @ SY1626 ) ) ) )
= $true )
| ( ( in @ SV765 @ ( sK13_C @ SV725 @ SV139 ) )
= $true )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4608]) ).
thf(4687,plain,
! [SV139: $i,SV725: $i,SV766: $i] :
( ( ( in @ SV766 @ ( sK13_C @ SV725 @ SV139 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK16_E @ SV766 @ SV725 @ SV139 )
!= SV766 )
| ~ ( in @ ( sK16_E @ SV766 @ SV725 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV725 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV766 @ SV725 @ SV139 ) @ ( sK15_SY612 @ SV766 @ SV725 @ SV139 ) )
!= SV766 )
| ~ ( in @ ( sK14_J @ SV766 @ SV725 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV766 @ SV725 @ SV139 )
!= ( singleton @ ( sK14_J @ SV766 @ SV725 @ SV139 ) ) ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4609]) ).
thf(4688,plain,
! [SV726: $i,SV139: $i,SV767: $i] :
( ( ( ! [SY1628: $i] :
( ( SY1628 != SV767 )
| ~ ( in @ SY1628 @ ( cartesian_product2 @ SV139 @ SV726 ) ) ) )
= $true )
| ( ( ! [SY1629: $i,SY1630: $i] :
( ( ( ordered_pair @ SY1629 @ SY1630 )
!= SV767 )
| ~ ( in @ SY1629 @ SV139 )
| ( SY1630
!= ( singleton @ SY1629 ) ) ) )
= $true )
| ( ( in @ SV767 @ ( sK13_C @ SV726 @ SV139 ) )
= $true )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4610]) ).
thf(4689,plain,
! [SV139: $i,SV726: $i,SV768: $i] :
( ( ( in @ SV768 @ ( sK13_C @ SV726 @ SV139 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK16_E @ SV768 @ SV726 @ SV139 )
!= SV768 )
| ~ ( in @ ( sK16_E @ SV768 @ SV726 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV726 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV768 @ SV726 @ SV139 ) @ ( sK15_SY612 @ SV768 @ SV726 @ SV139 ) )
!= SV768 )
| ~ ( in @ ( sK14_J @ SV768 @ SV726 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV768 @ SV726 @ SV139 )
!= ( singleton @ ( sK14_J @ SV768 @ SV726 @ SV139 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4611]) ).
thf(4690,plain,
! [SV694: $i,SV139: $i,SV729: $i,SV769: $i] :
( ( ( SV769 = SV729 )
= $false )
| ( ( ~ ( in @ SV769 @ ( cartesian_product2 @ SV139 @ SV694 ) ) )
= $true )
| ( ( ! [SY1566: $i,SY1567: $i] :
( ( ( ordered_pair @ SY1566 @ SY1567 )
!= SV729 )
| ~ ( in @ SY1566 @ SV139 )
| ( SY1567
!= ( singleton @ SY1566 ) ) ) )
= $true )
| ( ( in @ SV729 @ ( sK13_C @ SV694 @ SV139 ) )
= $true )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4612]) ).
thf(4691,plain,
! [SV139: $i,SV694: $i,SV730: $i] :
( ( ( ~ ( ( ( sK16_E @ SV730 @ SV694 @ SV139 )
!= SV730 )
| ~ ( in @ ( sK16_E @ SV730 @ SV694 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV694 ) ) ) )
= $true )
| ( ( in @ SV730 @ ( sK13_C @ SV694 @ SV139 ) )
= $false )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4613]) ).
thf(4692,plain,
! [SV139: $i,SV694: $i,SV730: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV730 @ SV694 @ SV139 ) @ ( sK15_SY612 @ SV730 @ SV694 @ SV139 ) )
!= SV730 )
| ~ ( in @ ( sK14_J @ SV730 @ SV694 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV730 @ SV694 @ SV139 )
!= ( singleton @ ( sK14_J @ SV730 @ SV694 @ SV139 ) ) ) ) )
= $true )
| ( ( in @ SV730 @ ( sK13_C @ SV694 @ SV139 ) )
= $false )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4614]) ).
thf(4693,plain,
! [SV624: $i,SV704: $i,SV139: $i,SV681: $i,SV758: $i,SV747: $i] :
( ( ( ( ordered_pair @ SV747 @ SV758 )
= SV681 )
= $false )
| ( ( ~ ( in @ SV747 @ SV139 ) )
= $true )
| ( ( ( SV758
!= ( singleton @ SV747 ) ) )
= $true )
| ( ( SV704 = SV681 )
= $false )
| ( ( in @ SV704 @ ( cartesian_product2 @ SV139 @ SV624 ) )
= $false )
| ( ( in @ SV681 @ ( sK13_C @ SV624 @ SV139 ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4615]) ).
thf(4694,plain,
! [SV139: $i,SV624: $i,SV682: $i] :
( ( ( ( ordered_pair @ ( sK14_J @ SV682 @ SV624 @ SV139 ) @ ( sK15_SY612 @ SV682 @ SV624 @ SV139 ) )
= SV682 )
= $true )
| ( ( in @ SV682 @ ( sK13_C @ SV624 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4616]) ).
thf(4695,plain,
! [SV139: $i,SV624: $i,SV682: $i] :
( ( ( in @ ( sK14_J @ SV682 @ SV624 @ SV139 ) @ SV139 )
= $true )
| ( ( in @ SV682 @ ( sK13_C @ SV624 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4617]) ).
thf(4696,plain,
! [SV661: $i,SV731: $i,SV139: $i,SV705: $i,SV786: $i,SV774: $i] :
( ( ( ( ( ordered_pair @ SV774 @ SV786 )
!= SV705 )
| ~ ( in @ SV774 @ SV139 )
| ( SV786
!= ( singleton @ SV774 ) ) )
= $true )
| ( ( SV731 = SV705 )
= $false )
| ( ( in @ SV731 @ ( cartesian_product2 @ SV139 @ SV661 ) )
= $false )
| ( ( in @ SV705 @ ( sK13_C @ SV661 @ SV139 ) )
= $true )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4618]) ).
thf(4697,plain,
! [SV139: $i,SV661: $i,SV706: $i] :
( ( ( ( sK16_E @ SV706 @ SV661 @ SV139 )
= SV706 )
= $true )
| ( ( in @ SV706 @ ( sK13_C @ SV661 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4619]) ).
thf(4698,plain,
! [SV139: $i,SV661: $i,SV706: $i] :
( ( ( in @ ( sK16_E @ SV706 @ SV661 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV661 ) )
= $true )
| ( ( in @ SV706 @ ( sK13_C @ SV661 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4620]) ).
thf(4699,plain,
! [SV139: $i,SV661: $i,SV706: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK14_J @ SV706 @ SV661 @ SV139 ) @ ( sK15_SY612 @ SV706 @ SV661 @ SV139 ) )
!= SV706 )
| ~ ( in @ ( sK14_J @ SV706 @ SV661 @ SV139 ) @ SV139 ) ) )
= $true )
| ( ( in @ SV706 @ ( sK13_C @ SV661 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4621]) ).
thf(4700,plain,
! [SV139: $i,SV661: $i,SV706: $i] :
( ( ( ( sK15_SY612 @ SV706 @ SV661 @ SV139 )
= ( singleton @ ( sK14_J @ SV706 @ SV661 @ SV139 ) ) )
= $true )
| ( ( in @ SV706 @ ( sK13_C @ SV661 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4622]) ).
thf(4701,plain,
! [SV662: $i,SV732: $i,SV139: $i,SV707: $i,SV787: $i,SV775: $i] :
( ( ( ( ( ordered_pair @ SV775 @ SV787 )
!= SV707 )
| ~ ( in @ SV775 @ SV139 )
| ( SV787
!= ( singleton @ SV775 ) ) )
= $true )
| ( ( SV732 = SV707 )
= $false )
| ( ( in @ SV732 @ ( cartesian_product2 @ SV139 @ SV662 ) )
= $false )
| ( ( in @ SV707 @ ( sK13_C @ SV662 @ SV139 ) )
= $true )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4623]) ).
thf(4702,plain,
! [SV139: $i,SV662: $i,SV708: $i] :
( ( ( ( sK16_E @ SV708 @ SV662 @ SV139 )
= SV708 )
= $true )
| ( ( in @ SV708 @ ( sK13_C @ SV662 @ SV139 ) )
= $false )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4624]) ).
thf(4703,plain,
! [SV139: $i,SV662: $i,SV708: $i] :
( ( ( in @ ( sK16_E @ SV708 @ SV662 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV662 ) )
= $true )
| ( ( in @ SV708 @ ( sK13_C @ SV662 @ SV139 ) )
= $false )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4625]) ).
thf(4704,plain,
! [SV139: $i,SV662: $i,SV708: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK14_J @ SV708 @ SV662 @ SV139 ) @ ( sK15_SY612 @ SV708 @ SV662 @ SV139 ) )
!= SV708 )
| ~ ( in @ ( sK14_J @ SV708 @ SV662 @ SV139 ) @ SV139 ) ) )
= $true )
| ( ( in @ SV708 @ ( sK13_C @ SV662 @ SV139 ) )
= $false )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4626]) ).
thf(4705,plain,
! [SV139: $i,SV662: $i,SV708: $i] :
( ( ( ( sK15_SY612 @ SV708 @ SV662 @ SV139 )
= ( singleton @ ( sK14_J @ SV708 @ SV662 @ SV139 ) ) )
= $true )
| ( ( in @ SV708 @ ( sK13_C @ SV662 @ SV139 ) )
= $false )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4627]) ).
thf(4706,plain,
! [SV625: $i,SV709: $i,SV139: $i,SV683: $i,SV759: $i,SV748: $i] :
( ( ( ( ordered_pair @ SV748 @ SV759 )
= SV683 )
= $false )
| ( ( ~ ( in @ SV748 @ SV139 ) )
= $true )
| ( ( ( SV759
!= ( singleton @ SV748 ) ) )
= $true )
| ( ( SV709 = SV683 )
= $false )
| ( ( in @ SV709 @ ( cartesian_product2 @ SV139 @ SV625 ) )
= $false )
| ( ( in @ SV683 @ ( sK13_C @ SV625 @ SV139 ) )
= $true )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4628]) ).
thf(4707,plain,
! [SV139: $i,SV625: $i,SV684: $i] :
( ( ( ( ordered_pair @ ( sK14_J @ SV684 @ SV625 @ SV139 ) @ ( sK15_SY612 @ SV684 @ SV625 @ SV139 ) )
= SV684 )
= $true )
| ( ( in @ SV684 @ ( sK13_C @ SV625 @ SV139 ) )
= $false )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4629]) ).
thf(4708,plain,
! [SV139: $i,SV625: $i,SV684: $i] :
( ( ( in @ ( sK14_J @ SV684 @ SV625 @ SV139 ) @ SV139 )
= $true )
| ( ( in @ SV684 @ ( sK13_C @ SV625 @ SV139 ) )
= $false )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4630]) ).
thf(4709,plain,
! [SV733: $i,SV265: $i,SV145: $i] :
( ( ( ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4631]) ).
thf(4710,plain,
! [SV733: $i,SV145: $i,SV265: $i] :
( ( ( ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4632]) ).
thf(4711,plain,
! [SV265: $i,SV145: $i] :
( ( ( ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4633]) ).
thf(4712,plain,
! [SV145: $i,SV265: $i] :
( ( ( ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4634]) ).
thf(4713,plain,
! [SV265: $i,SV145: $i] :
( ( ( ! [SY1144: $i] :
( ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV145 )
| ! [SY1146: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) @ SY1146 )
| ~ ~ ( in @ ( ordered_pair @ SY1144 @ ( sK47_K @ SY1146 @ SY1145 @ SY1144 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1145 != SY1146 )
| ~ ( in @ SY1144 @ SY1146 ) ) )
| ( in @ SY1144 @ ( sK44_C @ SV265 @ SV145 ) ) ) )
= $true )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4635]) ).
thf(4714,plain,
! [SV145: $i,SV265: $i] :
( ( ( ! [SY1147: $i] :
( ~ ( in @ SY1147 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SY1147 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SY1147 @ SY1148 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SY1147 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) )
| ~ ( in @ SY1147 @ ( sK46_SY702 @ SY1147 @ SV265 @ SV145 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4636]) ).
thf(4715,plain,
! [SV145: $i,SV265: $i,SV734: $i,SV760: $i,SV788: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_K @ SV788 @ SV760 @ SV734 @ SV265 @ SV145 ) @ SV788 )
| ~ ~ ( in @ ( ordered_pair @ SV734 @ ( sK47_K @ SV788 @ SV760 @ SV734 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV760 != SV788 )
| ~ ( in @ SV734 @ SV788 ) )
= $true )
| ( ( in @ SV760 @ SV145 )
= $false )
| ( ( in @ SV734 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4637]) ).
thf(4716,plain,
! [SV145: $i,SV265: $i,SV735: $i] :
( ( ( in @ ( sK45_E @ SV735 @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( in @ SV735 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4638]) ).
thf(4717,plain,
! [SV145: $i,SV265: $i,SV735: $i] :
( ( ( ~ ( ~ ! [SY1570: $i] :
( ~ ( in @ SY1570 @ ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV735 @ SY1570 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV735 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) )
| ~ ( in @ SV735 @ ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) ) ) ) )
= $true )
| ( ( in @ SV735 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4639]) ).
thf(4718,plain,
! [SV145: $i,SV265: $i,SV711: $i,SV727: $i,SV761: $i] :
( ( ( ~ ( in @ ( sK47_K @ SV761 @ SV727 @ SV711 @ SV265 @ SV145 ) @ SV761 ) )
= $false )
| ( ( ( SV727 != SV761 )
| ~ ( in @ SV711 @ SV761 ) )
= $true )
| ( ( in @ SV727 @ SV145 )
= $false )
| ( ( in @ SV711 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4640]) ).
thf(4719,plain,
! [SV145: $i,SV265: $i,SV727: $i,SV761: $i,SV711: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV711 @ ( sK47_K @ SV761 @ SV727 @ SV711 @ SV265 @ SV145 ) ) @ SV265 ) )
= $false )
| ( ( ( SV727 != SV761 )
| ~ ( in @ SV711 @ SV761 ) )
= $true )
| ( ( in @ SV727 @ SV145 )
= $false )
| ( ( in @ SV711 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4640]) ).
thf(4720,plain,
! [SV145: $i,SV265: $i,SV712: $i] :
( ( ( ! [SY1527: $i] :
( ~ ( in @ SY1527 @ ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV712 @ SY1527 ) @ SV265 ) ) )
= $true )
| ( ( in @ SV712 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4641]) ).
thf(4721,plain,
! [SV145: $i,SV265: $i,SV712: $i] :
( ( ( ~ ( ( ( sK45_E @ SV712 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) )
| ~ ( in @ SV712 @ ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) ) ) )
= $true )
| ( ( in @ SV712 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4642]) ).
thf(4722,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV736: $i,SV762: $i,SV789: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_K @ SV789 @ SV762 @ SV736 @ SV265 @ SV145 ) @ SV789 )
| ~ ~ ( in @ ( ordered_pair @ SV736 @ ( sK47_K @ SV789 @ SV762 @ SV736 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV762 != SV789 )
| ~ ( in @ SV736 @ SV789 ) )
= $true )
| ( ( in @ SV762 @ SV145 )
= $false )
| ( ( in @ SV736 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4643]) ).
thf(4723,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV737: $i] :
( ( ( in @ ( sK45_E @ SV737 @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( in @ SV737 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4644]) ).
thf(4724,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV737: $i] :
( ( ( ~ ( ~ ! [SY1573: $i] :
( ~ ( in @ SY1573 @ ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV737 @ SY1573 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV737 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) )
| ~ ( in @ SV737 @ ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) ) ) ) )
= $true )
| ( ( in @ SV737 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4645]) ).
thf(4725,plain,
! [SV145: $i,SV265: $i,SV738: $i,SV763: $i,SV790: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_K @ SV790 @ SV763 @ SV738 @ SV265 @ SV145 ) @ SV790 )
| ~ ~ ( in @ ( ordered_pair @ SV738 @ ( sK47_K @ SV790 @ SV763 @ SV738 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV763 != SV790 )
| ~ ( in @ SV738 @ SV790 ) )
= $true )
| ( ( in @ SV763 @ SV145 )
= $false )
| ( ( in @ SV738 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4646]) ).
thf(4726,plain,
! [SV145: $i,SV265: $i,SV739: $i] :
( ( ( in @ ( sK45_E @ SV739 @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( in @ SV739 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4647]) ).
thf(4727,plain,
! [SV145: $i,SV265: $i,SV739: $i] :
( ( ( ~ ( ~ ! [SY1576: $i] :
( ~ ( in @ SY1576 @ ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV739 @ SY1576 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV739 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) )
| ~ ( in @ SV739 @ ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) ) ) ) )
= $true )
| ( ( in @ SV739 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4648]) ).
thf(4728,plain,
! [SV145: $i,SV265: $i,SV740: $i,SV764: $i,SV791: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_K @ SV791 @ SV764 @ SV740 @ SV265 @ SV145 ) @ SV791 )
| ~ ~ ( in @ ( ordered_pair @ SV740 @ ( sK47_K @ SV791 @ SV764 @ SV740 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV764 != SV791 )
| ~ ( in @ SV740 @ SV791 ) )
= $true )
| ( ( in @ SV764 @ SV145 )
= $false )
| ( ( in @ SV740 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4649]) ).
thf(4729,plain,
! [SV145: $i,SV265: $i,SV741: $i] :
( ( ( in @ ( sK45_E @ SV741 @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( in @ SV741 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4650]) ).
thf(4730,plain,
! [SV145: $i,SV265: $i,SV741: $i] :
( ( ( ~ ( ~ ! [SY1579: $i] :
( ~ ( in @ SY1579 @ ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV741 @ SY1579 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV741 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) )
| ~ ( in @ SV741 @ ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) ) ) ) )
= $true )
| ( ( in @ SV741 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4651]) ).
thf(4731,plain,
! [SV145: $i,SV265: $i,SV686: $i,SV713: $i,SV655: $i] :
( ( ( in @ SV655 @ SV713 )
= $false )
| ( ( SV686 = SV713 )
= $false )
| ( ( in @ ( ordered_pair @ SV655 @ ( sK47_K @ SV713 @ SV686 @ SV655 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( in @ SV686 @ SV145 )
= $false )
| ( ( in @ SV655 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK49_SY705 @ SV265 @ SV145 )
= ( sK50_SY711 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4653]) ).
thf(4732,plain,
! [SV271: $i,SV716: $i,SV659: $i,SV651: $i,SV481: $i,SV170: $i,SV596: $i] :
( ( ( in @ SV596 @ ( cartesian_product2 @ SV170 @ SV481 ) )
= $false )
| ( ( in @ SV651 @ SV170 )
= $false )
| ( ( ( ordered_pair @ SV651 @ SV659 )
= SV596 )
= $false )
| ( ( in @ ( sK115_I @ SV716 @ SV659 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) @ SV716 )
= $true )
| ( ( SV651 = SV716 )
= $false )
| ( ( in @ SV659 @ SV716 )
= $false )
| ( ( in @ SV596 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4654]) ).
thf(4733,plain,
! [SV170: $i,SV271: $i,SV481: $i,SV596: $i,SV651: $i,SV716: $i,SV659: $i] :
( ( ( in @ SV659 @ SV716 )
= $false )
| ( ( SV651 = SV716 )
= $false )
| ( ( in @ ( ordered_pair @ SV659 @ ( sK115_I @ SV716 @ SV659 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) ) @ SV271 )
= $false )
| ( ( ( ordered_pair @ SV651 @ SV659 )
= SV596 )
= $false )
| ( ( in @ SV651 @ SV170 )
= $false )
| ( ( ~ ( in @ SV596 @ ( cartesian_product2 @ SV170 @ SV481 ) ) )
= $true )
| ( ( in @ SV596 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4655]) ).
thf(4734,plain,
! [SV272: $i,SV717: $i,SV172: $i,SV750: $i,SV776: $i] :
( ( ( ( SV776 != SV750 ) )
= $true )
| ( ( ~ ( in @ SV776 @ ( cartesian_product2 @ SV172 @ SV717 ) ) )
= $true )
| ( ( ! [SY1606: $i,SY1607: $i] :
( ( ( ordered_pair @ SY1606 @ SY1607 )
!= SV750 )
| ~ ( in @ SY1606 @ SV172 )
| ! [SY1608: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1608 @ SY1607 @ SY1606 @ SV750 @ SV717 @ SV272 @ SV172 ) @ SY1608 )
| ~ ~ ( in @ ( ordered_pair @ SY1607 @ ( sK34_R @ SY1608 @ SY1607 @ SY1606 @ SV750 @ SV717 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1606 != SY1608 )
| ~ ( in @ SY1607 @ SY1608 ) ) ) )
= $true )
| ( ( in @ SV750 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4656]) ).
thf(4735,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( ~ ~ ( ( ( sK33_F @ SV751 @ SV717 @ SV272 @ SV172 )
!= SV751 )
| ~ ( in @ ( sK33_F @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV717 ) ) ) )
= $false )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4657]) ).
thf(4736,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) )
!= SV751 )
| ~ ( in @ ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1609: $i] :
( ~ ( in @ SY1609 @ ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) @ SY1609 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) ) ) ) ) )
= $false )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4657]) ).
thf(4737,plain,
! [SV272: $i,SV770: $i,SV172: $i] :
( ( ( ~ ! [SY1631: $i] :
( ! [SY1632: $i] :
( ( SY1632 != SY1631 )
| ~ ( in @ SY1632 @ ( cartesian_product2 @ SV172 @ SV770 ) ) )
| ! [SY1633: $i,SY1634: $i] :
( ( ( ordered_pair @ SY1633 @ SY1634 )
!= SY1631 )
| ~ ( in @ SY1633 @ SV172 )
| ! [SY1635: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1635 @ SY1634 @ SY1633 @ SY1631 @ SV770 @ SV272 @ SV172 ) @ SY1635 )
| ~ ~ ( in @ ( ordered_pair @ SY1634 @ ( sK34_R @ SY1635 @ SY1634 @ SY1633 @ SY1631 @ SV770 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1633 != SY1635 )
| ~ ( in @ SY1634 @ SY1635 ) ) )
| ( in @ SY1631 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4658]) ).
thf(4738,plain,
! [SV172: $i,SV272: $i,SV770: $i] :
( ( ( ~ ! [SY1636: $i] :
( ~ ( in @ SY1636 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1636 @ SV770 @ SV272 @ SV172 )
!= SY1636 )
| ~ ( in @ ( sK33_F @ SY1636 @ SV770 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV770 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1636 @ SV770 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1636 @ SV770 @ SV272 @ SV172 ) )
!= SY1636 )
| ~ ( in @ ( sK30_O @ SY1636 @ SV770 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1637: $i] :
( ~ ( in @ SY1637 @ ( sK32_SY652 @ SY1636 @ SV770 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1636 @ SV770 @ SV272 @ SV172 ) @ SY1637 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1636 @ SV770 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1636 @ SV770 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1636 @ SV770 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1636 @ SV770 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4658]) ).
thf(4739,plain,
! [SV272: $i,SV771: $i,SV172: $i] :
( ( ( ~ ! [SY1638: $i] :
( ! [SY1639: $i] :
( ( SY1639 != SY1638 )
| ~ ( in @ SY1639 @ ( cartesian_product2 @ SV172 @ SV771 ) ) )
| ! [SY1640: $i,SY1641: $i] :
( ( ( ordered_pair @ SY1640 @ SY1641 )
!= SY1638 )
| ~ ( in @ SY1640 @ SV172 )
| ! [SY1642: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1642 @ SY1641 @ SY1640 @ SY1638 @ SV771 @ SV272 @ SV172 ) @ SY1642 )
| ~ ~ ( in @ ( ordered_pair @ SY1641 @ ( sK34_R @ SY1642 @ SY1641 @ SY1640 @ SY1638 @ SV771 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1640 != SY1642 )
| ~ ( in @ SY1641 @ SY1642 ) ) )
| ( in @ SY1638 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4659]) ).
thf(4740,plain,
! [SV172: $i,SV272: $i,SV771: $i] :
( ( ( ~ ! [SY1643: $i] :
( ~ ( in @ SY1643 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1643 @ SV771 @ SV272 @ SV172 )
!= SY1643 )
| ~ ( in @ ( sK33_F @ SY1643 @ SV771 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV771 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1643 @ SV771 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1643 @ SV771 @ SV272 @ SV172 ) )
!= SY1643 )
| ~ ( in @ ( sK30_O @ SY1643 @ SV771 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1644: $i] :
( ~ ( in @ SY1644 @ ( sK32_SY652 @ SY1643 @ SV771 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1643 @ SV771 @ SV272 @ SV172 ) @ SY1644 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1643 @ SV771 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1643 @ SV771 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1643 @ SV771 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1643 @ SV771 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4659]) ).
thf(4741,plain,
! [SV172: $i,SV272: $i,SV772: $i] :
( ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4660]) ).
thf(4742,plain,
! [SV172: $i,SV272: $i] :
( ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4661]) ).
thf(4743,plain,
! [SV172: $i,SV272: $i] :
( ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( ! [SY1180: $i] :
~ ( ~ ! [SY1181: $i] :
( ! [SY1074: $i] :
( ( SY1074 != SY1181 )
| ~ ( in @ SY1074 @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ! [SY1183: $i,SY1184: $i] :
( ( ( ordered_pair @ SY1183 @ SY1184 )
!= SY1181 )
| ~ ( in @ SY1183 @ SV172 )
| ! [SY1185: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) @ SY1185 )
| ~ ~ ( in @ ( ordered_pair @ SY1184 @ ( sK34_R @ SY1185 @ SY1184 @ SY1183 @ SY1181 @ SY1180 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1183 != SY1185 )
| ~ ( in @ SY1184 @ SY1185 ) ) )
| ( in @ SY1181 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) ) )
| ~ ! [SY1186: $i] :
( ~ ( in @ SY1186 @ ( sK29_D @ SY1180 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= SY1186 )
| ~ ( in @ ( sK33_F @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SY1180 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
!= SY1186 )
| ~ ( in @ ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1187: $i] :
( ~ ( in @ SY1187 @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ SY1187 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1186 @ SY1180 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1186 @ SY1180 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1186 @ SY1180 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4662]) ).
thf(4744,plain,
! [SV752: $i,SV272: $i,SV692: $i,SV172: $i,SV723: $i,SV792: $i] :
( ( ( ! [SY1663: $i] :
( ( ( ordered_pair @ SV792 @ SY1663 )
!= SV723 )
| ~ ( in @ SV792 @ SV172 )
| ! [SY1664: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1664 @ SY1663 @ SV792 @ SV723 @ SV692 @ SV272 @ SV172 ) @ SY1664 )
| ~ ~ ( in @ ( ordered_pair @ SY1663 @ ( sK34_R @ SY1664 @ SY1663 @ SV792 @ SV723 @ SV692 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV792 != SY1664 )
| ~ ( in @ SY1663 @ SY1664 ) ) ) )
= $true )
| ( ( SV752 = SV723 )
= $false )
| ( ( in @ SV752 @ ( cartesian_product2 @ SV172 @ SV692 ) )
= $false )
| ( ( in @ SV723 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4663]) ).
thf(4745,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( ( ( sK33_F @ SV724 @ SV692 @ SV272 @ SV172 )
!= SV724 ) )
= $false )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4664]) ).
thf(4746,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( ~ ( in @ ( sK33_F @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV692 ) ) )
= $false )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4664]) ).
thf(4747,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) )
!= SV724 )
| ~ ( in @ ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 ) @ SV172 ) ) )
= $false )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4665]) ).
thf(4748,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( ~ ~ ( ~ ! [SY1553: $i] :
( ~ ( in @ SY1553 @ ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) @ SY1553 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) ) ) ) )
= $false )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4665]) ).
thf(4749,plain,
! [SV272: $i,SV718: $i,SV172: $i,SV753: $i,SV777: $i] :
( ( ( ( SV777 != SV753 ) )
= $true )
| ( ( ~ ( in @ SV777 @ ( cartesian_product2 @ SV172 @ SV718 ) ) )
= $true )
| ( ( ! [SY1611: $i,SY1612: $i] :
( ( ( ordered_pair @ SY1611 @ SY1612 )
!= SV753 )
| ~ ( in @ SY1611 @ SV172 )
| ! [SY1613: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1613 @ SY1612 @ SY1611 @ SV753 @ SV718 @ SV272 @ SV172 ) @ SY1613 )
| ~ ~ ( in @ ( ordered_pair @ SY1612 @ ( sK34_R @ SY1613 @ SY1612 @ SY1611 @ SV753 @ SV718 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1611 != SY1613 )
| ~ ( in @ SY1612 @ SY1613 ) ) ) )
= $true )
| ( ( in @ SV753 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4666]) ).
thf(4750,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( ~ ~ ( ( ( sK33_F @ SV754 @ SV718 @ SV272 @ SV172 )
!= SV754 )
| ~ ( in @ ( sK33_F @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV718 ) ) ) )
= $false )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4667]) ).
thf(4751,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) )
!= SV754 )
| ~ ( in @ ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1614: $i] :
( ~ ( in @ SY1614 @ ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) @ SY1614 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) ) ) ) ) )
= $false )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4667]) ).
thf(4752,plain,
! [SV272: $i,SV719: $i,SV172: $i,SV755: $i,SV778: $i] :
( ( ( ( SV778 != SV755 ) )
= $true )
| ( ( ~ ( in @ SV778 @ ( cartesian_product2 @ SV172 @ SV719 ) ) )
= $true )
| ( ( ! [SY1616: $i,SY1617: $i] :
( ( ( ordered_pair @ SY1616 @ SY1617 )
!= SV755 )
| ~ ( in @ SY1616 @ SV172 )
| ! [SY1618: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1618 @ SY1617 @ SY1616 @ SV755 @ SV719 @ SV272 @ SV172 ) @ SY1618 )
| ~ ~ ( in @ ( ordered_pair @ SY1617 @ ( sK34_R @ SY1618 @ SY1617 @ SY1616 @ SV755 @ SV719 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1616 != SY1618 )
| ~ ( in @ SY1617 @ SY1618 ) ) ) )
= $true )
| ( ( in @ SV755 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4668]) ).
thf(4753,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( ~ ~ ( ( ( sK33_F @ SV756 @ SV719 @ SV272 @ SV172 )
!= SV756 )
| ~ ( in @ ( sK33_F @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV719 ) ) ) )
= $false )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4669]) ).
thf(4754,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) )
!= SV756 )
| ~ ( in @ ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1619: $i] :
( ~ ( in @ SY1619 @ ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) @ SY1619 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) ) ) ) ) )
= $false )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4669]) ).
thf(4755,plain,
! [SV720: $i,SV272: $i,SV743: $i,SV172: $i,SV779: $i] :
( ( ( ! [SY1648: $i] :
( ( SY1648 != SV779 )
| ~ ( in @ SY1648 @ ( cartesian_product2 @ SV172 @ SV743 ) ) )
| ! [SY1649: $i,SY1650: $i] :
( ( ( ordered_pair @ SY1649 @ SY1650 )
!= SV779 )
| ~ ( in @ SY1649 @ SV172 )
| ! [SY1651: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1651 @ SY1650 @ SY1649 @ SV779 @ SV743 @ SV272 @ SV172 ) @ SY1651 )
| ~ ~ ( in @ ( ordered_pair @ SY1650 @ ( sK34_R @ SY1651 @ SY1650 @ SY1649 @ SV779 @ SV743 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1649 != SY1651 )
| ~ ( in @ SY1650 @ SY1651 ) ) ) )
= $true )
| ( ( in @ SV779 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4670]) ).
thf(4756,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( ~ ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK33_F @ SV780 @ SV743 @ SV272 @ SV172 )
!= SV780 )
| ~ ( in @ ( sK33_F @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV743 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) )
!= SV780 )
| ~ ( in @ ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1652: $i] :
( ~ ( in @ SY1652 @ ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) @ SY1652 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4671]) ).
thf(4757,plain,
! [SV272: $i,SV744: $i,SV172: $i,SV781: $i] :
( ( ( ! [SY1653: $i] :
( ( SY1653 != SV781 )
| ~ ( in @ SY1653 @ ( cartesian_product2 @ SV172 @ SV744 ) ) )
| ! [SY1654: $i,SY1655: $i] :
( ( ( ordered_pair @ SY1654 @ SY1655 )
!= SV781 )
| ~ ( in @ SY1654 @ SV172 )
| ! [SY1656: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1656 @ SY1655 @ SY1654 @ SV781 @ SV744 @ SV272 @ SV172 ) @ SY1656 )
| ~ ~ ( in @ ( ordered_pair @ SY1655 @ ( sK34_R @ SY1656 @ SY1655 @ SY1654 @ SV781 @ SV744 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1654 != SY1656 )
| ~ ( in @ SY1655 @ SY1656 ) ) ) )
= $true )
| ( ( in @ SV781 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4672]) ).
thf(4758,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( ~ ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK33_F @ SV782 @ SV744 @ SV272 @ SV172 )
!= SV782 )
| ~ ( in @ ( sK33_F @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV744 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) )
!= SV782 )
| ~ ( in @ ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1657: $i] :
( ~ ( in @ SY1657 @ ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) @ SY1657 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4673]) ).
thf(4759,plain,
! [SV272: $i,SV745: $i,SV172: $i,SV783: $i] :
( ( ( ! [SY1658: $i] :
( ( SY1658 != SV783 )
| ~ ( in @ SY1658 @ ( cartesian_product2 @ SV172 @ SV745 ) ) )
| ! [SY1659: $i,SY1660: $i] :
( ( ( ordered_pair @ SY1659 @ SY1660 )
!= SV783 )
| ~ ( in @ SY1659 @ SV172 )
| ! [SY1661: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1661 @ SY1660 @ SY1659 @ SV783 @ SV745 @ SV272 @ SV172 ) @ SY1661 )
| ~ ~ ( in @ ( ordered_pair @ SY1660 @ ( sK34_R @ SY1661 @ SY1660 @ SY1659 @ SV783 @ SV745 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1659 != SY1661 )
| ~ ( in @ SY1660 @ SY1661 ) ) ) )
= $true )
| ( ( in @ SV783 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4674]) ).
thf(4760,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( ~ ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK33_F @ SV784 @ SV745 @ SV272 @ SV172 )
!= SV784 )
| ~ ( in @ ( sK33_F @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV745 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) )
!= SV784 )
| ~ ( in @ ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1662: $i] :
( ~ ( in @ SY1662 @ ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) @ SY1662 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4675]) ).
thf(4761,plain,
! [SV701: $i,SV272: $i,SV622: $i,SV677: $i,SV757: $i,SV172: $i,SV746: $i] :
( ( ( in @ SV746 @ SV172 )
= $false )
| ( ( ( ordered_pair @ SV746 @ SV757 )
= SV677 )
= $false )
| ( ( ! [SY1620: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1620 @ SV757 @ SV746 @ SV677 @ SV622 @ SV272 @ SV172 ) @ SY1620 )
| ~ ~ ( in @ ( ordered_pair @ SV757 @ ( sK34_R @ SY1620 @ SV757 @ SV746 @ SV677 @ SV622 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV746 != SY1620 )
| ~ ( in @ SV757 @ SY1620 ) ) )
= $true )
| ( ( SV701 = SV677 )
= $false )
| ( ( in @ SV701 @ ( cartesian_product2 @ SV172 @ SV622 ) )
= $false )
| ( ( in @ SV677 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4676]) ).
thf(4762,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i,SV793: $i] :
( ( ( ~ ( in @ SV793 @ ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) @ SV793 ) @ SV272 ) )
= $true )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4679]) ).
thf(4763,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( ( ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4680]) ).
thf(4764,plain,
! [SV660: $i,SV728: $i,SV139: $i,SV702: $i,SV785: $i,SV773: $i] :
( ( ( ( ( ordered_pair @ SV773 @ SV785 )
!= SV702 )
| ~ ( in @ SV773 @ SV139 ) )
= $true )
| ( ( ( SV785
!= ( singleton @ SV773 ) ) )
= $true )
| ( ( SV728 = SV702 )
= $false )
| ( ( in @ SV728 @ ( cartesian_product2 @ SV139 @ SV660 ) )
= $false )
| ( ( in @ SV702 @ ( sK13_C @ SV660 @ SV139 ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4681]) ).
thf(4765,plain,
! [SV139: $i,SV660: $i,SV703: $i] :
( ( ( ( ( ordered_pair @ ( sK14_J @ SV703 @ SV660 @ SV139 ) @ ( sK15_SY612 @ SV703 @ SV660 @ SV139 ) )
!= SV703 )
| ~ ( in @ ( sK14_J @ SV703 @ SV660 @ SV139 ) @ SV139 ) )
= $false )
| ( ( in @ SV703 @ ( sK13_C @ SV660 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4684]) ).
thf(4766,plain,
! [SV725: $i,SV139: $i,SV765: $i,SV794: $i] :
( ( ( ( SV794 != SV765 )
| ~ ( in @ SV794 @ ( cartesian_product2 @ SV139 @ SV725 ) ) )
= $true )
| ( ( ! [SY1626: $i,SY1627: $i] :
( ( ( ordered_pair @ SY1626 @ SY1627 )
!= SV765 )
| ~ ( in @ SY1626 @ SV139 )
| ( SY1627
!= ( singleton @ SY1626 ) ) ) )
= $true )
| ( ( in @ SV765 @ ( sK13_C @ SV725 @ SV139 ) )
= $true )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4686]) ).
thf(4767,plain,
! [SV139: $i,SV725: $i,SV766: $i] :
( ( ( ~ ~ ( ( ( sK16_E @ SV766 @ SV725 @ SV139 )
!= SV766 )
| ~ ( in @ ( sK16_E @ SV766 @ SV725 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV725 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV766 @ SV725 @ SV139 ) @ ( sK15_SY612 @ SV766 @ SV725 @ SV139 ) )
!= SV766 )
| ~ ( in @ ( sK14_J @ SV766 @ SV725 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV766 @ SV725 @ SV139 )
!= ( singleton @ ( sK14_J @ SV766 @ SV725 @ SV139 ) ) ) ) )
= $false )
| ( ( in @ SV766 @ ( sK13_C @ SV725 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4687]) ).
thf(4768,plain,
! [SV726: $i,SV139: $i,SV767: $i,SV795: $i] :
( ( ( ( SV795 != SV767 )
| ~ ( in @ SV795 @ ( cartesian_product2 @ SV139 @ SV726 ) ) )
= $true )
| ( ( ! [SY1629: $i,SY1630: $i] :
( ( ( ordered_pair @ SY1629 @ SY1630 )
!= SV767 )
| ~ ( in @ SY1629 @ SV139 )
| ( SY1630
!= ( singleton @ SY1629 ) ) ) )
= $true )
| ( ( in @ SV767 @ ( sK13_C @ SV726 @ SV139 ) )
= $true )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4688]) ).
thf(4769,plain,
! [SV139: $i,SV726: $i,SV768: $i] :
( ( ( ~ ~ ( ( ( sK16_E @ SV768 @ SV726 @ SV139 )
!= SV768 )
| ~ ( in @ ( sK16_E @ SV768 @ SV726 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV726 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV768 @ SV726 @ SV139 ) @ ( sK15_SY612 @ SV768 @ SV726 @ SV139 ) )
!= SV768 )
| ~ ( in @ ( sK14_J @ SV768 @ SV726 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV768 @ SV726 @ SV139 )
!= ( singleton @ ( sK14_J @ SV768 @ SV726 @ SV139 ) ) ) ) )
= $false )
| ( ( in @ SV768 @ ( sK13_C @ SV726 @ SV139 ) )
= $false )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4689]) ).
thf(4770,plain,
! [SV729: $i,SV694: $i,SV139: $i,SV769: $i] :
( ( ( in @ SV769 @ ( cartesian_product2 @ SV139 @ SV694 ) )
= $false )
| ( ( SV769 = SV729 )
= $false )
| ( ( ! [SY1566: $i,SY1567: $i] :
( ( ( ordered_pair @ SY1566 @ SY1567 )
!= SV729 )
| ~ ( in @ SY1566 @ SV139 )
| ( SY1567
!= ( singleton @ SY1566 ) ) ) )
= $true )
| ( ( in @ SV729 @ ( sK13_C @ SV694 @ SV139 ) )
= $true )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4690]) ).
thf(4771,plain,
! [SV139: $i,SV694: $i,SV730: $i] :
( ( ( ( ( sK16_E @ SV730 @ SV694 @ SV139 )
!= SV730 )
| ~ ( in @ ( sK16_E @ SV730 @ SV694 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV694 ) ) )
= $false )
| ( ( in @ SV730 @ ( sK13_C @ SV694 @ SV139 ) )
= $false )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4691]) ).
thf(4772,plain,
! [SV139: $i,SV694: $i,SV730: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV730 @ SV694 @ SV139 ) @ ( sK15_SY612 @ SV730 @ SV694 @ SV139 ) )
!= SV730 )
| ~ ( in @ ( sK14_J @ SV730 @ SV694 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV730 @ SV694 @ SV139 )
!= ( singleton @ ( sK14_J @ SV730 @ SV694 @ SV139 ) ) ) )
= $false )
| ( ( in @ SV730 @ ( sK13_C @ SV694 @ SV139 ) )
= $false )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4692]) ).
thf(4773,plain,
! [SV624: $i,SV704: $i,SV681: $i,SV758: $i,SV139: $i,SV747: $i] :
( ( ( in @ SV747 @ SV139 )
= $false )
| ( ( ( ordered_pair @ SV747 @ SV758 )
= SV681 )
= $false )
| ( ( ( SV758
!= ( singleton @ SV747 ) ) )
= $true )
| ( ( SV704 = SV681 )
= $false )
| ( ( in @ SV704 @ ( cartesian_product2 @ SV139 @ SV624 ) )
= $false )
| ( ( in @ SV681 @ ( sK13_C @ SV624 @ SV139 ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4693]) ).
thf(4774,plain,
! [SV661: $i,SV731: $i,SV139: $i,SV705: $i,SV786: $i,SV774: $i] :
( ( ( ( ( ordered_pair @ SV774 @ SV786 )
!= SV705 )
| ~ ( in @ SV774 @ SV139 ) )
= $true )
| ( ( ( SV786
!= ( singleton @ SV774 ) ) )
= $true )
| ( ( SV731 = SV705 )
= $false )
| ( ( in @ SV731 @ ( cartesian_product2 @ SV139 @ SV661 ) )
= $false )
| ( ( in @ SV705 @ ( sK13_C @ SV661 @ SV139 ) )
= $true )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4696]) ).
thf(4775,plain,
! [SV139: $i,SV661: $i,SV706: $i] :
( ( ( ( ( ordered_pair @ ( sK14_J @ SV706 @ SV661 @ SV139 ) @ ( sK15_SY612 @ SV706 @ SV661 @ SV139 ) )
!= SV706 )
| ~ ( in @ ( sK14_J @ SV706 @ SV661 @ SV139 ) @ SV139 ) )
= $false )
| ( ( in @ SV706 @ ( sK13_C @ SV661 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4699]) ).
thf(4776,plain,
! [SV662: $i,SV732: $i,SV139: $i,SV707: $i,SV787: $i,SV775: $i] :
( ( ( ( ( ordered_pair @ SV775 @ SV787 )
!= SV707 )
| ~ ( in @ SV775 @ SV139 ) )
= $true )
| ( ( ( SV787
!= ( singleton @ SV775 ) ) )
= $true )
| ( ( SV732 = SV707 )
= $false )
| ( ( in @ SV732 @ ( cartesian_product2 @ SV139 @ SV662 ) )
= $false )
| ( ( in @ SV707 @ ( sK13_C @ SV662 @ SV139 ) )
= $true )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4701]) ).
thf(4777,plain,
! [SV139: $i,SV662: $i,SV708: $i] :
( ( ( ( ( ordered_pair @ ( sK14_J @ SV708 @ SV662 @ SV139 ) @ ( sK15_SY612 @ SV708 @ SV662 @ SV139 ) )
!= SV708 )
| ~ ( in @ ( sK14_J @ SV708 @ SV662 @ SV139 ) @ SV139 ) )
= $false )
| ( ( in @ SV708 @ ( sK13_C @ SV662 @ SV139 ) )
= $false )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4704]) ).
thf(4778,plain,
! [SV625: $i,SV709: $i,SV683: $i,SV759: $i,SV139: $i,SV748: $i] :
( ( ( in @ SV748 @ SV139 )
= $false )
| ( ( ( ordered_pair @ SV748 @ SV759 )
= SV683 )
= $false )
| ( ( ( SV759
!= ( singleton @ SV748 ) ) )
= $true )
| ( ( SV709 = SV683 )
= $false )
| ( ( in @ SV709 @ ( cartesian_product2 @ SV139 @ SV625 ) )
= $false )
| ( ( in @ SV683 @ ( sK13_C @ SV625 @ SV139 ) )
= $true )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4706]) ).
thf(4779,plain,
! [SV733: $i,SV265: $i,SV796: $i,SV145: $i] :
( ( ( ! [SY1665: $i] :
( ~ ( in @ SY1665 @ SV145 )
| ! [SY1666: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1666 @ SY1665 @ SV796 @ SV265 @ SV145 ) @ SY1666 )
| ~ ~ ( in @ ( ordered_pair @ SV796 @ ( sK47_K @ SY1666 @ SY1665 @ SV796 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1665 != SY1666 )
| ~ ( in @ SV796 @ SY1666 ) ) )
| ( in @ SV796 @ ( sK44_C @ SV265 @ SV145 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4709]) ).
thf(4780,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV797: $i] :
( ( ( ~ ( in @ SV797 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SV797 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1667: $i] :
( ~ ( in @ SY1667 @ ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV797 @ SY1667 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV797 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) )
| ~ ( in @ SV797 @ ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) ) ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4710]) ).
thf(4781,plain,
! [SV265: $i,SV798: $i,SV145: $i] :
( ( ( ! [SY1668: $i] :
( ~ ( in @ SY1668 @ SV145 )
| ! [SY1669: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1669 @ SY1668 @ SV798 @ SV265 @ SV145 ) @ SY1669 )
| ~ ~ ( in @ ( ordered_pair @ SV798 @ ( sK47_K @ SY1669 @ SY1668 @ SV798 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1668 != SY1669 )
| ~ ( in @ SV798 @ SY1669 ) ) )
| ( in @ SV798 @ ( sK44_C @ SV265 @ SV145 ) ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4711]) ).
thf(4782,plain,
! [SV145: $i,SV265: $i,SV799: $i] :
( ( ( ~ ( in @ SV799 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SV799 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1670: $i] :
( ~ ( in @ SY1670 @ ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV799 @ SY1670 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV799 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) )
| ~ ( in @ SV799 @ ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) ) ) ) ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4712]) ).
thf(4783,plain,
! [SV265: $i,SV800: $i,SV145: $i] :
( ( ( ! [SY1671: $i] :
( ~ ( in @ SY1671 @ SV145 )
| ! [SY1672: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1672 @ SY1671 @ SV800 @ SV265 @ SV145 ) @ SY1672 )
| ~ ~ ( in @ ( ordered_pair @ SV800 @ ( sK47_K @ SY1672 @ SY1671 @ SV800 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1671 != SY1672 )
| ~ ( in @ SV800 @ SY1672 ) ) )
| ( in @ SV800 @ ( sK44_C @ SV265 @ SV145 ) ) )
= $true )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4713]) ).
thf(4784,plain,
! [SV145: $i,SV265: $i,SV801: $i] :
( ( ( ~ ( in @ SV801 @ ( sK44_C @ SV265 @ SV145 ) )
| ~ ( ~ ( in @ ( sK45_E @ SV801 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1673: $i] :
( ~ ( in @ SY1673 @ ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV801 @ SY1673 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV801 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) )
| ~ ( in @ SV801 @ ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4714]) ).
thf(4785,plain,
! [SV145: $i,SV265: $i,SV734: $i,SV760: $i,SV788: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_K @ SV788 @ SV760 @ SV734 @ SV265 @ SV145 ) @ SV788 )
| ~ ~ ( in @ ( ordered_pair @ SV734 @ ( sK47_K @ SV788 @ SV760 @ SV734 @ SV265 @ SV145 ) ) @ SV265 ) ) )
= $true )
| ( ( ( SV760 != SV788 )
| ~ ( in @ SV734 @ SV788 ) )
= $true )
| ( ( in @ SV760 @ SV145 )
= $false )
| ( ( in @ SV734 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4715]) ).
thf(4786,plain,
! [SV145: $i,SV265: $i,SV735: $i] :
( ( ( ~ ! [SY1570: $i] :
( ~ ( in @ SY1570 @ ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV735 @ SY1570 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV735 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) )
| ~ ( in @ SV735 @ ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( in @ SV735 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4717]) ).
thf(4787,plain,
! [SV145: $i,SV265: $i,SV711: $i,SV727: $i,SV761: $i] :
( ( ( in @ ( sK47_K @ SV761 @ SV727 @ SV711 @ SV265 @ SV145 ) @ SV761 )
= $true )
| ( ( ( SV727 != SV761 )
| ~ ( in @ SV711 @ SV761 ) )
= $true )
| ( ( in @ SV727 @ SV145 )
= $false )
| ( ( in @ SV711 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4718]) ).
thf(4788,plain,
! [SV145: $i,SV265: $i,SV727: $i,SV761: $i,SV711: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV711 @ ( sK47_K @ SV761 @ SV727 @ SV711 @ SV265 @ SV145 ) ) @ SV265 ) )
= $true )
| ( ( ( SV727 != SV761 )
| ~ ( in @ SV711 @ SV761 ) )
= $true )
| ( ( in @ SV727 @ SV145 )
= $false )
| ( ( in @ SV711 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4719]) ).
thf(4789,plain,
! [SV145: $i,SV265: $i,SV712: $i,SV802: $i] :
( ( ( ~ ( in @ SV802 @ ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV712 @ SV802 ) @ SV265 ) )
= $true )
| ( ( in @ SV712 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4720]) ).
thf(4790,plain,
! [SV145: $i,SV265: $i,SV712: $i] :
( ( ( ( ( sK45_E @ SV712 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) )
| ~ ( in @ SV712 @ ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) ) )
= $false )
| ( ( in @ SV712 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4721]) ).
thf(4791,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV736: $i,SV762: $i,SV789: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_K @ SV789 @ SV762 @ SV736 @ SV265 @ SV145 ) @ SV789 )
| ~ ~ ( in @ ( ordered_pair @ SV736 @ ( sK47_K @ SV789 @ SV762 @ SV736 @ SV265 @ SV145 ) ) @ SV265 ) ) )
= $true )
| ( ( ( SV762 != SV789 )
| ~ ( in @ SV736 @ SV789 ) )
= $true )
| ( ( in @ SV762 @ SV145 )
= $false )
| ( ( in @ SV736 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4722]) ).
thf(4792,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV737: $i] :
( ( ( ~ ! [SY1573: $i] :
( ~ ( in @ SY1573 @ ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV737 @ SY1573 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV737 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) )
| ~ ( in @ SV737 @ ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( in @ SV737 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4724]) ).
thf(4793,plain,
! [SV145: $i,SV265: $i,SV738: $i,SV763: $i,SV790: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_K @ SV790 @ SV763 @ SV738 @ SV265 @ SV145 ) @ SV790 )
| ~ ~ ( in @ ( ordered_pair @ SV738 @ ( sK47_K @ SV790 @ SV763 @ SV738 @ SV265 @ SV145 ) ) @ SV265 ) ) )
= $true )
| ( ( ( SV763 != SV790 )
| ~ ( in @ SV738 @ SV790 ) )
= $true )
| ( ( in @ SV763 @ SV145 )
= $false )
| ( ( in @ SV738 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4725]) ).
thf(4794,plain,
! [SV145: $i,SV265: $i,SV739: $i] :
( ( ( ~ ! [SY1576: $i] :
( ~ ( in @ SY1576 @ ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV739 @ SY1576 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV739 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) )
| ~ ( in @ SV739 @ ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( in @ SV739 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4727]) ).
thf(4795,plain,
! [SV145: $i,SV265: $i,SV740: $i,SV764: $i,SV791: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_K @ SV791 @ SV764 @ SV740 @ SV265 @ SV145 ) @ SV791 )
| ~ ~ ( in @ ( ordered_pair @ SV740 @ ( sK47_K @ SV791 @ SV764 @ SV740 @ SV265 @ SV145 ) ) @ SV265 ) ) )
= $true )
| ( ( ( SV764 != SV791 )
| ~ ( in @ SV740 @ SV791 ) )
= $true )
| ( ( in @ SV764 @ SV145 )
= $false )
| ( ( in @ SV740 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4728]) ).
thf(4796,plain,
! [SV145: $i,SV265: $i,SV741: $i] :
( ( ( ~ ! [SY1579: $i] :
( ~ ( in @ SY1579 @ ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV741 @ SY1579 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV741 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) )
| ~ ( in @ SV741 @ ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( in @ SV741 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4730]) ).
thf(4797,plain,
! [SV271: $i,SV716: $i,SV659: $i,SV651: $i,SV481: $i,SV170: $i,SV596: $i] :
( ( ( in @ SV596 @ ( cartesian_product2 @ SV170 @ SV481 ) )
= $false )
| ( ( in @ SV651 @ SV170 )
= $false )
| ( ( ( ordered_pair @ SV651 @ SV659 )
= SV596 )
= $false )
| ( ( in @ ( ordered_pair @ SV659 @ ( sK115_I @ SV716 @ SV659 @ SV651 @ SV596 @ SV481 @ SV271 @ SV170 ) ) @ SV271 )
= $false )
| ( ( SV651 = SV716 )
= $false )
| ( ( in @ SV659 @ SV716 )
= $false )
| ( ( in @ SV596 @ ( sK111_D @ SV481 @ SV271 @ SV170 ) )
= $true )
| ( ( empty @ SV170 )
= $true )
| ( ( relation @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4733]) ).
thf(4798,plain,
! [SV272: $i,SV717: $i,SV172: $i,SV750: $i,SV776: $i] :
( ( ( SV776 = SV750 )
= $false )
| ( ( ~ ( in @ SV776 @ ( cartesian_product2 @ SV172 @ SV717 ) ) )
= $true )
| ( ( ! [SY1606: $i,SY1607: $i] :
( ( ( ordered_pair @ SY1606 @ SY1607 )
!= SV750 )
| ~ ( in @ SY1606 @ SV172 )
| ! [SY1608: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1608 @ SY1607 @ SY1606 @ SV750 @ SV717 @ SV272 @ SV172 ) @ SY1608 )
| ~ ~ ( in @ ( ordered_pair @ SY1607 @ ( sK34_R @ SY1608 @ SY1607 @ SY1606 @ SV750 @ SV717 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1606 != SY1608 )
| ~ ( in @ SY1607 @ SY1608 ) ) ) )
= $true )
| ( ( in @ SV750 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4734]) ).
thf(4799,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( ~ ( ( ( sK33_F @ SV751 @ SV717 @ SV272 @ SV172 )
!= SV751 )
| ~ ( in @ ( sK33_F @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV717 ) ) ) )
= $true )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4735]) ).
thf(4800,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) )
!= SV751 )
| ~ ( in @ ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1609: $i] :
( ~ ( in @ SY1609 @ ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) @ SY1609 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) ) ) ) ) )
= $true )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4736]) ).
thf(4801,plain,
! [SV272: $i,SV770: $i,SV172: $i] :
( ( ( ! [SY1631: $i] :
( ! [SY1632: $i] :
( ( SY1632 != SY1631 )
| ~ ( in @ SY1632 @ ( cartesian_product2 @ SV172 @ SV770 ) ) )
| ! [SY1633: $i,SY1634: $i] :
( ( ( ordered_pair @ SY1633 @ SY1634 )
!= SY1631 )
| ~ ( in @ SY1633 @ SV172 )
| ! [SY1635: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1635 @ SY1634 @ SY1633 @ SY1631 @ SV770 @ SV272 @ SV172 ) @ SY1635 )
| ~ ~ ( in @ ( ordered_pair @ SY1634 @ ( sK34_R @ SY1635 @ SY1634 @ SY1633 @ SY1631 @ SV770 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1633 != SY1635 )
| ~ ( in @ SY1634 @ SY1635 ) ) )
| ( in @ SY1631 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4737]) ).
thf(4802,plain,
! [SV172: $i,SV272: $i,SV770: $i] :
( ( ( ! [SY1636: $i] :
( ~ ( in @ SY1636 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1636 @ SV770 @ SV272 @ SV172 )
!= SY1636 )
| ~ ( in @ ( sK33_F @ SY1636 @ SV770 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV770 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1636 @ SV770 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1636 @ SV770 @ SV272 @ SV172 ) )
!= SY1636 )
| ~ ( in @ ( sK30_O @ SY1636 @ SV770 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1637: $i] :
( ~ ( in @ SY1637 @ ( sK32_SY652 @ SY1636 @ SV770 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1636 @ SV770 @ SV272 @ SV172 ) @ SY1637 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1636 @ SV770 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1636 @ SV770 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1636 @ SV770 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1636 @ SV770 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4738]) ).
thf(4803,plain,
! [SV272: $i,SV771: $i,SV172: $i] :
( ( ( ! [SY1638: $i] :
( ! [SY1639: $i] :
( ( SY1639 != SY1638 )
| ~ ( in @ SY1639 @ ( cartesian_product2 @ SV172 @ SV771 ) ) )
| ! [SY1640: $i,SY1641: $i] :
( ( ( ordered_pair @ SY1640 @ SY1641 )
!= SY1638 )
| ~ ( in @ SY1640 @ SV172 )
| ! [SY1642: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1642 @ SY1641 @ SY1640 @ SY1638 @ SV771 @ SV272 @ SV172 ) @ SY1642 )
| ~ ~ ( in @ ( ordered_pair @ SY1641 @ ( sK34_R @ SY1642 @ SY1641 @ SY1640 @ SY1638 @ SV771 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1640 != SY1642 )
| ~ ( in @ SY1641 @ SY1642 ) ) )
| ( in @ SY1638 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) ) ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4739]) ).
thf(4804,plain,
! [SV172: $i,SV272: $i,SV771: $i] :
( ( ( ! [SY1643: $i] :
( ~ ( in @ SY1643 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1643 @ SV771 @ SV272 @ SV172 )
!= SY1643 )
| ~ ( in @ ( sK33_F @ SY1643 @ SV771 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV771 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1643 @ SV771 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1643 @ SV771 @ SV272 @ SV172 ) )
!= SY1643 )
| ~ ( in @ ( sK30_O @ SY1643 @ SV771 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1644: $i] :
( ~ ( in @ SY1644 @ ( sK32_SY652 @ SY1643 @ SV771 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1643 @ SV771 @ SV272 @ SV172 ) @ SY1644 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1643 @ SV771 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1643 @ SV771 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1643 @ SV771 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1643 @ SV771 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4740]) ).
thf(4805,plain,
! [SV772: $i,SV272: $i,SV803: $i,SV172: $i] :
( ( ( ~ ( ~ ! [SY1674: $i] :
( ! [SY1675: $i] :
( ( SY1675 != SY1674 )
| ~ ( in @ SY1675 @ ( cartesian_product2 @ SV172 @ SV803 ) ) )
| ! [SY1676: $i,SY1677: $i] :
( ( ( ordered_pair @ SY1676 @ SY1677 )
!= SY1674 )
| ~ ( in @ SY1676 @ SV172 )
| ! [SY1678: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1678 @ SY1677 @ SY1676 @ SY1674 @ SV803 @ SV272 @ SV172 ) @ SY1678 )
| ~ ~ ( in @ ( ordered_pair @ SY1677 @ ( sK34_R @ SY1678 @ SY1677 @ SY1676 @ SY1674 @ SV803 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1676 != SY1678 )
| ~ ( in @ SY1677 @ SY1678 ) ) )
| ( in @ SY1674 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) ) )
| ~ ! [SY1679: $i] :
( ~ ( in @ SY1679 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1679 @ SV803 @ SV272 @ SV172 )
!= SY1679 )
| ~ ( in @ ( sK33_F @ SY1679 @ SV803 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV803 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1679 @ SV803 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1679 @ SV803 @ SV272 @ SV172 ) )
!= SY1679 )
| ~ ( in @ ( sK30_O @ SY1679 @ SV803 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1680: $i] :
( ~ ( in @ SY1680 @ ( sK32_SY652 @ SY1679 @ SV803 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1679 @ SV803 @ SV272 @ SV172 ) @ SY1680 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1679 @ SV803 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1679 @ SV803 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1679 @ SV803 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1679 @ SV803 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4741]) ).
thf(4806,plain,
! [SV272: $i,SV804: $i,SV172: $i] :
( ( ( ~ ( ~ ! [SY1681: $i] :
( ! [SY1682: $i] :
( ( SY1682 != SY1681 )
| ~ ( in @ SY1682 @ ( cartesian_product2 @ SV172 @ SV804 ) ) )
| ! [SY1683: $i,SY1684: $i] :
( ( ( ordered_pair @ SY1683 @ SY1684 )
!= SY1681 )
| ~ ( in @ SY1683 @ SV172 )
| ! [SY1685: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1685 @ SY1684 @ SY1683 @ SY1681 @ SV804 @ SV272 @ SV172 ) @ SY1685 )
| ~ ~ ( in @ ( ordered_pair @ SY1684 @ ( sK34_R @ SY1685 @ SY1684 @ SY1683 @ SY1681 @ SV804 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1683 != SY1685 )
| ~ ( in @ SY1684 @ SY1685 ) ) )
| ( in @ SY1681 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) ) )
| ~ ! [SY1686: $i] :
( ~ ( in @ SY1686 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1686 @ SV804 @ SV272 @ SV172 )
!= SY1686 )
| ~ ( in @ ( sK33_F @ SY1686 @ SV804 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV804 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1686 @ SV804 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1686 @ SV804 @ SV272 @ SV172 ) )
!= SY1686 )
| ~ ( in @ ( sK30_O @ SY1686 @ SV804 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1687: $i] :
( ~ ( in @ SY1687 @ ( sK32_SY652 @ SY1686 @ SV804 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1686 @ SV804 @ SV272 @ SV172 ) @ SY1687 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1686 @ SV804 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1686 @ SV804 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1686 @ SV804 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1686 @ SV804 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4742]) ).
thf(4807,plain,
! [SV272: $i,SV805: $i,SV172: $i] :
( ( ( ~ ( ~ ! [SY1688: $i] :
( ! [SY1689: $i] :
( ( SY1689 != SY1688 )
| ~ ( in @ SY1689 @ ( cartesian_product2 @ SV172 @ SV805 ) ) )
| ! [SY1690: $i,SY1691: $i] :
( ( ( ordered_pair @ SY1690 @ SY1691 )
!= SY1688 )
| ~ ( in @ SY1690 @ SV172 )
| ! [SY1692: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1692 @ SY1691 @ SY1690 @ SY1688 @ SV805 @ SV272 @ SV172 ) @ SY1692 )
| ~ ~ ( in @ ( ordered_pair @ SY1691 @ ( sK34_R @ SY1692 @ SY1691 @ SY1690 @ SY1688 @ SV805 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1690 != SY1692 )
| ~ ( in @ SY1691 @ SY1692 ) ) )
| ( in @ SY1688 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) ) )
| ~ ! [SY1693: $i] :
( ~ ( in @ SY1693 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1693 @ SV805 @ SV272 @ SV172 )
!= SY1693 )
| ~ ( in @ ( sK33_F @ SY1693 @ SV805 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV805 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1693 @ SV805 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1693 @ SV805 @ SV272 @ SV172 ) )
!= SY1693 )
| ~ ( in @ ( sK30_O @ SY1693 @ SV805 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1694: $i] :
( ~ ( in @ SY1694 @ ( sK32_SY652 @ SY1693 @ SV805 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1693 @ SV805 @ SV272 @ SV172 ) @ SY1694 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1693 @ SV805 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1693 @ SV805 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1693 @ SV805 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1693 @ SV805 @ SV272 @ SV172 ) ) ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4743]) ).
thf(4808,plain,
! [SV752: $i,SV272: $i,SV692: $i,SV172: $i,SV723: $i,SV806: $i,SV792: $i] :
( ( ( ( ( ordered_pair @ SV792 @ SV806 )
!= SV723 )
| ~ ( in @ SV792 @ SV172 )
| ! [SY1695: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1695 @ SV806 @ SV792 @ SV723 @ SV692 @ SV272 @ SV172 ) @ SY1695 )
| ~ ~ ( in @ ( ordered_pair @ SV806 @ ( sK34_R @ SY1695 @ SV806 @ SV792 @ SV723 @ SV692 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV792 != SY1695 )
| ~ ( in @ SV806 @ SY1695 ) ) )
= $true )
| ( ( SV752 = SV723 )
= $false )
| ( ( in @ SV752 @ ( cartesian_product2 @ SV172 @ SV692 ) )
= $false )
| ( ( in @ SV723 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4744]) ).
thf(4809,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( ( sK33_F @ SV724 @ SV692 @ SV272 @ SV172 )
= SV724 )
= $true )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4745]) ).
thf(4810,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( in @ ( sK33_F @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV692 ) )
= $true )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4746]) ).
thf(4811,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) )
!= SV724 )
| ~ ( in @ ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 ) @ SV172 ) ) )
= $true )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4747]) ).
thf(4812,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( ~ ( ~ ! [SY1553: $i] :
( ~ ( in @ SY1553 @ ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) @ SY1553 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) ) ) ) )
= $true )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4748]) ).
thf(4813,plain,
! [SV272: $i,SV718: $i,SV172: $i,SV753: $i,SV777: $i] :
( ( ( SV777 = SV753 )
= $false )
| ( ( ~ ( in @ SV777 @ ( cartesian_product2 @ SV172 @ SV718 ) ) )
= $true )
| ( ( ! [SY1611: $i,SY1612: $i] :
( ( ( ordered_pair @ SY1611 @ SY1612 )
!= SV753 )
| ~ ( in @ SY1611 @ SV172 )
| ! [SY1613: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1613 @ SY1612 @ SY1611 @ SV753 @ SV718 @ SV272 @ SV172 ) @ SY1613 )
| ~ ~ ( in @ ( ordered_pair @ SY1612 @ ( sK34_R @ SY1613 @ SY1612 @ SY1611 @ SV753 @ SV718 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1611 != SY1613 )
| ~ ( in @ SY1612 @ SY1613 ) ) ) )
= $true )
| ( ( in @ SV753 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4749]) ).
thf(4814,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( ~ ( ( ( sK33_F @ SV754 @ SV718 @ SV272 @ SV172 )
!= SV754 )
| ~ ( in @ ( sK33_F @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV718 ) ) ) )
= $true )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4750]) ).
thf(4815,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) )
!= SV754 )
| ~ ( in @ ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1614: $i] :
( ~ ( in @ SY1614 @ ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) @ SY1614 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) ) ) ) ) )
= $true )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4751]) ).
thf(4816,plain,
! [SV272: $i,SV719: $i,SV172: $i,SV755: $i,SV778: $i] :
( ( ( SV778 = SV755 )
= $false )
| ( ( ~ ( in @ SV778 @ ( cartesian_product2 @ SV172 @ SV719 ) ) )
= $true )
| ( ( ! [SY1616: $i,SY1617: $i] :
( ( ( ordered_pair @ SY1616 @ SY1617 )
!= SV755 )
| ~ ( in @ SY1616 @ SV172 )
| ! [SY1618: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1618 @ SY1617 @ SY1616 @ SV755 @ SV719 @ SV272 @ SV172 ) @ SY1618 )
| ~ ~ ( in @ ( ordered_pair @ SY1617 @ ( sK34_R @ SY1618 @ SY1617 @ SY1616 @ SV755 @ SV719 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1616 != SY1618 )
| ~ ( in @ SY1617 @ SY1618 ) ) ) )
= $true )
| ( ( in @ SV755 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4752]) ).
thf(4817,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( ~ ( ( ( sK33_F @ SV756 @ SV719 @ SV272 @ SV172 )
!= SV756 )
| ~ ( in @ ( sK33_F @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV719 ) ) ) )
= $true )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4753]) ).
thf(4818,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) )
!= SV756 )
| ~ ( in @ ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1619: $i] :
( ~ ( in @ SY1619 @ ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) @ SY1619 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) ) ) ) ) )
= $true )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4754]) ).
thf(4819,plain,
! [SV720: $i,SV272: $i,SV743: $i,SV172: $i,SV779: $i] :
( ( ( ! [SY1648: $i] :
( ( SY1648 != SV779 )
| ~ ( in @ SY1648 @ ( cartesian_product2 @ SV172 @ SV743 ) ) ) )
= $true )
| ( ( ! [SY1649: $i,SY1650: $i] :
( ( ( ordered_pair @ SY1649 @ SY1650 )
!= SV779 )
| ~ ( in @ SY1649 @ SV172 )
| ! [SY1651: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1651 @ SY1650 @ SY1649 @ SV779 @ SV743 @ SV272 @ SV172 ) @ SY1651 )
| ~ ~ ( in @ ( ordered_pair @ SY1650 @ ( sK34_R @ SY1651 @ SY1650 @ SY1649 @ SV779 @ SV743 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1649 != SY1651 )
| ~ ( in @ SY1650 @ SY1651 ) ) ) )
= $true )
| ( ( in @ SV779 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4755]) ).
thf(4820,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK33_F @ SV780 @ SV743 @ SV272 @ SV172 )
!= SV780 )
| ~ ( in @ ( sK33_F @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV743 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) )
!= SV780 )
| ~ ( in @ ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1652: $i] :
( ~ ( in @ SY1652 @ ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) @ SY1652 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4756]) ).
thf(4821,plain,
! [SV272: $i,SV744: $i,SV172: $i,SV781: $i] :
( ( ( ! [SY1653: $i] :
( ( SY1653 != SV781 )
| ~ ( in @ SY1653 @ ( cartesian_product2 @ SV172 @ SV744 ) ) ) )
= $true )
| ( ( ! [SY1654: $i,SY1655: $i] :
( ( ( ordered_pair @ SY1654 @ SY1655 )
!= SV781 )
| ~ ( in @ SY1654 @ SV172 )
| ! [SY1656: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1656 @ SY1655 @ SY1654 @ SV781 @ SV744 @ SV272 @ SV172 ) @ SY1656 )
| ~ ~ ( in @ ( ordered_pair @ SY1655 @ ( sK34_R @ SY1656 @ SY1655 @ SY1654 @ SV781 @ SV744 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1654 != SY1656 )
| ~ ( in @ SY1655 @ SY1656 ) ) ) )
= $true )
| ( ( in @ SV781 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4757]) ).
thf(4822,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK33_F @ SV782 @ SV744 @ SV272 @ SV172 )
!= SV782 )
| ~ ( in @ ( sK33_F @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV744 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) )
!= SV782 )
| ~ ( in @ ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1657: $i] :
( ~ ( in @ SY1657 @ ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) @ SY1657 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4758]) ).
thf(4823,plain,
! [SV272: $i,SV745: $i,SV172: $i,SV783: $i] :
( ( ( ! [SY1658: $i] :
( ( SY1658 != SV783 )
| ~ ( in @ SY1658 @ ( cartesian_product2 @ SV172 @ SV745 ) ) ) )
= $true )
| ( ( ! [SY1659: $i,SY1660: $i] :
( ( ( ordered_pair @ SY1659 @ SY1660 )
!= SV783 )
| ~ ( in @ SY1659 @ SV172 )
| ! [SY1661: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1661 @ SY1660 @ SY1659 @ SV783 @ SV745 @ SV272 @ SV172 ) @ SY1661 )
| ~ ~ ( in @ ( ordered_pair @ SY1660 @ ( sK34_R @ SY1661 @ SY1660 @ SY1659 @ SV783 @ SV745 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1659 != SY1661 )
| ~ ( in @ SY1660 @ SY1661 ) ) ) )
= $true )
| ( ( in @ SV783 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4759]) ).
thf(4824,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK33_F @ SV784 @ SV745 @ SV272 @ SV172 )
!= SV784 )
| ~ ( in @ ( sK33_F @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV745 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) )
!= SV784 )
| ~ ( in @ ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1662: $i] :
( ~ ( in @ SY1662 @ ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) @ SY1662 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4760]) ).
thf(4825,plain,
! [SV701: $i,SV172: $i,SV272: $i,SV622: $i,SV677: $i,SV746: $i,SV757: $i,SV807: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_R @ SV807 @ SV757 @ SV746 @ SV677 @ SV622 @ SV272 @ SV172 ) @ SV807 )
| ~ ~ ( in @ ( ordered_pair @ SV757 @ ( sK34_R @ SV807 @ SV757 @ SV746 @ SV677 @ SV622 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV746 != SV807 )
| ~ ( in @ SV757 @ SV807 ) )
= $true )
| ( ( ( ordered_pair @ SV746 @ SV757 )
= SV677 )
= $false )
| ( ( in @ SV746 @ SV172 )
= $false )
| ( ( SV701 = SV677 )
= $false )
| ( ( in @ SV701 @ ( cartesian_product2 @ SV172 @ SV622 ) )
= $false )
| ( ( in @ SV677 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4761]) ).
thf(4826,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i,SV793: $i] :
( ( ( ~ ( in @ SV793 @ ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) @ SV793 ) @ SV272 )
= $true )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4762]) ).
thf(4827,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( ( ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4763]) ).
thf(4828,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( ~ ( in @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4763]) ).
thf(4829,plain,
! [SV660: $i,SV728: $i,SV139: $i,SV702: $i,SV785: $i,SV773: $i] :
( ( ( ( ( ordered_pair @ SV773 @ SV785 )
!= SV702 ) )
= $true )
| ( ( ~ ( in @ SV773 @ SV139 ) )
= $true )
| ( ( ( SV785
!= ( singleton @ SV773 ) ) )
= $true )
| ( ( SV728 = SV702 )
= $false )
| ( ( in @ SV728 @ ( cartesian_product2 @ SV139 @ SV660 ) )
= $false )
| ( ( in @ SV702 @ ( sK13_C @ SV660 @ SV139 ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4764]) ).
thf(4830,plain,
! [SV139: $i,SV660: $i,SV703: $i] :
( ( ( ( ( ordered_pair @ ( sK14_J @ SV703 @ SV660 @ SV139 ) @ ( sK15_SY612 @ SV703 @ SV660 @ SV139 ) )
!= SV703 ) )
= $false )
| ( ( in @ SV703 @ ( sK13_C @ SV660 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4765]) ).
thf(4831,plain,
! [SV139: $i,SV660: $i,SV703: $i] :
( ( ( ~ ( in @ ( sK14_J @ SV703 @ SV660 @ SV139 ) @ SV139 ) )
= $false )
| ( ( in @ SV703 @ ( sK13_C @ SV660 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4765]) ).
thf(4832,plain,
! [SV725: $i,SV139: $i,SV765: $i,SV794: $i] :
( ( ( ( SV794 != SV765 ) )
= $true )
| ( ( ~ ( in @ SV794 @ ( cartesian_product2 @ SV139 @ SV725 ) ) )
= $true )
| ( ( ! [SY1626: $i,SY1627: $i] :
( ( ( ordered_pair @ SY1626 @ SY1627 )
!= SV765 )
| ~ ( in @ SY1626 @ SV139 )
| ( SY1627
!= ( singleton @ SY1626 ) ) ) )
= $true )
| ( ( in @ SV765 @ ( sK13_C @ SV725 @ SV139 ) )
= $true )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4766]) ).
thf(4833,plain,
! [SV139: $i,SV725: $i,SV766: $i] :
( ( ( ~ ~ ( ( ( sK16_E @ SV766 @ SV725 @ SV139 )
!= SV766 )
| ~ ( in @ ( sK16_E @ SV766 @ SV725 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV725 ) ) ) )
= $false )
| ( ( in @ SV766 @ ( sK13_C @ SV725 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4767]) ).
thf(4834,plain,
! [SV139: $i,SV725: $i,SV766: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV766 @ SV725 @ SV139 ) @ ( sK15_SY612 @ SV766 @ SV725 @ SV139 ) )
!= SV766 )
| ~ ( in @ ( sK14_J @ SV766 @ SV725 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV766 @ SV725 @ SV139 )
!= ( singleton @ ( sK14_J @ SV766 @ SV725 @ SV139 ) ) ) ) )
= $false )
| ( ( in @ SV766 @ ( sK13_C @ SV725 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4767]) ).
thf(4835,plain,
! [SV726: $i,SV139: $i,SV767: $i,SV795: $i] :
( ( ( ( SV795 != SV767 ) )
= $true )
| ( ( ~ ( in @ SV795 @ ( cartesian_product2 @ SV139 @ SV726 ) ) )
= $true )
| ( ( ! [SY1629: $i,SY1630: $i] :
( ( ( ordered_pair @ SY1629 @ SY1630 )
!= SV767 )
| ~ ( in @ SY1629 @ SV139 )
| ( SY1630
!= ( singleton @ SY1629 ) ) ) )
= $true )
| ( ( in @ SV767 @ ( sK13_C @ SV726 @ SV139 ) )
= $true )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4768]) ).
thf(4836,plain,
! [SV139: $i,SV726: $i,SV768: $i] :
( ( ( ~ ~ ( ( ( sK16_E @ SV768 @ SV726 @ SV139 )
!= SV768 )
| ~ ( in @ ( sK16_E @ SV768 @ SV726 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV726 ) ) ) )
= $false )
| ( ( in @ SV768 @ ( sK13_C @ SV726 @ SV139 ) )
= $false )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4769]) ).
thf(4837,plain,
! [SV139: $i,SV726: $i,SV768: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV768 @ SV726 @ SV139 ) @ ( sK15_SY612 @ SV768 @ SV726 @ SV139 ) )
!= SV768 )
| ~ ( in @ ( sK14_J @ SV768 @ SV726 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV768 @ SV726 @ SV139 )
!= ( singleton @ ( sK14_J @ SV768 @ SV726 @ SV139 ) ) ) ) )
= $false )
| ( ( in @ SV768 @ ( sK13_C @ SV726 @ SV139 ) )
= $false )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4769]) ).
thf(4838,plain,
! [SV694: $i,SV769: $i,SV139: $i,SV729: $i,SV808: $i] :
( ( ( ! [SY1696: $i] :
( ( ( ordered_pair @ SV808 @ SY1696 )
!= SV729 )
| ~ ( in @ SV808 @ SV139 )
| ( SY1696
!= ( singleton @ SV808 ) ) ) )
= $true )
| ( ( SV769 = SV729 )
= $false )
| ( ( in @ SV769 @ ( cartesian_product2 @ SV139 @ SV694 ) )
= $false )
| ( ( in @ SV729 @ ( sK13_C @ SV694 @ SV139 ) )
= $true )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4770]) ).
thf(4839,plain,
! [SV139: $i,SV694: $i,SV730: $i] :
( ( ( ( ( sK16_E @ SV730 @ SV694 @ SV139 )
!= SV730 ) )
= $false )
| ( ( in @ SV730 @ ( sK13_C @ SV694 @ SV139 ) )
= $false )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4771]) ).
thf(4840,plain,
! [SV139: $i,SV694: $i,SV730: $i] :
( ( ( ~ ( in @ ( sK16_E @ SV730 @ SV694 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV694 ) ) )
= $false )
| ( ( in @ SV730 @ ( sK13_C @ SV694 @ SV139 ) )
= $false )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4771]) ).
thf(4841,plain,
! [SV139: $i,SV694: $i,SV730: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV730 @ SV694 @ SV139 ) @ ( sK15_SY612 @ SV730 @ SV694 @ SV139 ) )
!= SV730 )
| ~ ( in @ ( sK14_J @ SV730 @ SV694 @ SV139 ) @ SV139 ) ) )
= $false )
| ( ( in @ SV730 @ ( sK13_C @ SV694 @ SV139 ) )
= $false )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4772]) ).
thf(4842,plain,
! [SV139: $i,SV694: $i,SV730: $i] :
( ( ( ( ( sK15_SY612 @ SV730 @ SV694 @ SV139 )
!= ( singleton @ ( sK14_J @ SV730 @ SV694 @ SV139 ) ) ) )
= $false )
| ( ( in @ SV730 @ ( sK13_C @ SV694 @ SV139 ) )
= $false )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4772]) ).
thf(4843,plain,
! [SV624: $i,SV704: $i,SV139: $i,SV681: $i,SV747: $i,SV758: $i] :
( ( ( SV758
= ( singleton @ SV747 ) )
= $false )
| ( ( ( ordered_pair @ SV747 @ SV758 )
= SV681 )
= $false )
| ( ( in @ SV747 @ SV139 )
= $false )
| ( ( SV704 = SV681 )
= $false )
| ( ( in @ SV704 @ ( cartesian_product2 @ SV139 @ SV624 ) )
= $false )
| ( ( in @ SV681 @ ( sK13_C @ SV624 @ SV139 ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4773]) ).
thf(4844,plain,
! [SV661: $i,SV731: $i,SV139: $i,SV705: $i,SV786: $i,SV774: $i] :
( ( ( ( ( ordered_pair @ SV774 @ SV786 )
!= SV705 ) )
= $true )
| ( ( ~ ( in @ SV774 @ SV139 ) )
= $true )
| ( ( ( SV786
!= ( singleton @ SV774 ) ) )
= $true )
| ( ( SV731 = SV705 )
= $false )
| ( ( in @ SV731 @ ( cartesian_product2 @ SV139 @ SV661 ) )
= $false )
| ( ( in @ SV705 @ ( sK13_C @ SV661 @ SV139 ) )
= $true )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4774]) ).
thf(4845,plain,
! [SV139: $i,SV661: $i,SV706: $i] :
( ( ( ( ( ordered_pair @ ( sK14_J @ SV706 @ SV661 @ SV139 ) @ ( sK15_SY612 @ SV706 @ SV661 @ SV139 ) )
!= SV706 ) )
= $false )
| ( ( in @ SV706 @ ( sK13_C @ SV661 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4775]) ).
thf(4846,plain,
! [SV139: $i,SV661: $i,SV706: $i] :
( ( ( ~ ( in @ ( sK14_J @ SV706 @ SV661 @ SV139 ) @ SV139 ) )
= $false )
| ( ( in @ SV706 @ ( sK13_C @ SV661 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4775]) ).
thf(4847,plain,
! [SV662: $i,SV732: $i,SV139: $i,SV707: $i,SV787: $i,SV775: $i] :
( ( ( ( ( ordered_pair @ SV775 @ SV787 )
!= SV707 ) )
= $true )
| ( ( ~ ( in @ SV775 @ SV139 ) )
= $true )
| ( ( ( SV787
!= ( singleton @ SV775 ) ) )
= $true )
| ( ( SV732 = SV707 )
= $false )
| ( ( in @ SV732 @ ( cartesian_product2 @ SV139 @ SV662 ) )
= $false )
| ( ( in @ SV707 @ ( sK13_C @ SV662 @ SV139 ) )
= $true )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4776]) ).
thf(4848,plain,
! [SV139: $i,SV662: $i,SV708: $i] :
( ( ( ( ( ordered_pair @ ( sK14_J @ SV708 @ SV662 @ SV139 ) @ ( sK15_SY612 @ SV708 @ SV662 @ SV139 ) )
!= SV708 ) )
= $false )
| ( ( in @ SV708 @ ( sK13_C @ SV662 @ SV139 ) )
= $false )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4777]) ).
thf(4849,plain,
! [SV139: $i,SV662: $i,SV708: $i] :
( ( ( ~ ( in @ ( sK14_J @ SV708 @ SV662 @ SV139 ) @ SV139 ) )
= $false )
| ( ( in @ SV708 @ ( sK13_C @ SV662 @ SV139 ) )
= $false )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4777]) ).
thf(4850,plain,
! [SV625: $i,SV709: $i,SV139: $i,SV683: $i,SV748: $i,SV759: $i] :
( ( ( SV759
= ( singleton @ SV748 ) )
= $false )
| ( ( ( ordered_pair @ SV748 @ SV759 )
= SV683 )
= $false )
| ( ( in @ SV748 @ SV139 )
= $false )
| ( ( SV709 = SV683 )
= $false )
| ( ( in @ SV709 @ ( cartesian_product2 @ SV139 @ SV625 ) )
= $false )
| ( ( in @ SV683 @ ( sK13_C @ SV625 @ SV139 ) )
= $true )
| ( ( ( sK21_SY628 @ SV139 )
= ( singleton @ ( sK20_SY626 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4778]) ).
thf(4851,plain,
! [SV733: $i,SV265: $i,SV796: $i,SV145: $i] :
( ( ( ! [SY1665: $i] :
( ~ ( in @ SY1665 @ SV145 )
| ! [SY1666: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1666 @ SY1665 @ SV796 @ SV265 @ SV145 ) @ SY1666 )
| ~ ~ ( in @ ( ordered_pair @ SV796 @ ( sK47_K @ SY1666 @ SY1665 @ SV796 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1665 != SY1666 )
| ~ ( in @ SV796 @ SY1666 ) ) ) )
= $true )
| ( ( in @ SV796 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4779]) ).
thf(4852,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV797: $i] :
( ( ( ~ ( in @ SV797 @ ( sK44_C @ SV265 @ SV145 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK45_E @ SV797 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1667: $i] :
( ~ ( in @ SY1667 @ ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV797 @ SY1667 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV797 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) )
| ~ ( in @ SV797 @ ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) ) ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4780]) ).
thf(4853,plain,
! [SV265: $i,SV798: $i,SV145: $i] :
( ( ( ! [SY1668: $i] :
( ~ ( in @ SY1668 @ SV145 )
| ! [SY1669: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1669 @ SY1668 @ SV798 @ SV265 @ SV145 ) @ SY1669 )
| ~ ~ ( in @ ( ordered_pair @ SV798 @ ( sK47_K @ SY1669 @ SY1668 @ SV798 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1668 != SY1669 )
| ~ ( in @ SV798 @ SY1669 ) ) ) )
= $true )
| ( ( in @ SV798 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4781]) ).
thf(4854,plain,
! [SV145: $i,SV265: $i,SV799: $i] :
( ( ( ~ ( in @ SV799 @ ( sK44_C @ SV265 @ SV145 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK45_E @ SV799 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1670: $i] :
( ~ ( in @ SY1670 @ ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV799 @ SY1670 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV799 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) )
| ~ ( in @ SV799 @ ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) ) ) ) ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4782]) ).
thf(4855,plain,
! [SV265: $i,SV800: $i,SV145: $i] :
( ( ( ! [SY1671: $i] :
( ~ ( in @ SY1671 @ SV145 )
| ! [SY1672: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1672 @ SY1671 @ SV800 @ SV265 @ SV145 ) @ SY1672 )
| ~ ~ ( in @ ( ordered_pair @ SV800 @ ( sK47_K @ SY1672 @ SY1671 @ SV800 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SY1671 != SY1672 )
| ~ ( in @ SV800 @ SY1672 ) ) ) )
= $true )
| ( ( in @ SV800 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4783]) ).
thf(4856,plain,
! [SV145: $i,SV265: $i,SV801: $i] :
( ( ( ~ ( in @ SV801 @ ( sK44_C @ SV265 @ SV145 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK45_E @ SV801 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1673: $i] :
( ~ ( in @ SY1673 @ ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV801 @ SY1673 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV801 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) )
| ~ ( in @ SV801 @ ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4784]) ).
thf(4857,plain,
! [SV145: $i,SV265: $i,SV734: $i,SV760: $i,SV788: $i] :
( ( ( ~ ( in @ ( sK47_K @ SV788 @ SV760 @ SV734 @ SV265 @ SV145 ) @ SV788 )
| ~ ~ ( in @ ( ordered_pair @ SV734 @ ( sK47_K @ SV788 @ SV760 @ SV734 @ SV265 @ SV145 ) ) @ SV265 ) )
= $false )
| ( ( ( SV760 != SV788 )
| ~ ( in @ SV734 @ SV788 ) )
= $true )
| ( ( in @ SV760 @ SV145 )
= $false )
| ( ( in @ SV734 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4785]) ).
thf(4858,plain,
! [SV145: $i,SV265: $i,SV735: $i] :
( ( ( ~ ! [SY1570: $i] :
( ~ ( in @ SY1570 @ ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV735 @ SY1570 ) @ SV265 ) ) )
= $false )
| ( ( in @ SV735 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4786]) ).
thf(4859,plain,
! [SV145: $i,SV265: $i,SV735: $i] :
( ( ( ~ ~ ( ( ( sK45_E @ SV735 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) )
| ~ ( in @ SV735 @ ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( in @ SV735 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4786]) ).
thf(4860,plain,
! [SV145: $i,SV265: $i,SV711: $i,SV761: $i,SV727: $i] :
( ( ( ( SV727 != SV761 ) )
= $true )
| ( ( ~ ( in @ SV711 @ SV761 ) )
= $true )
| ( ( in @ ( sK47_K @ SV761 @ SV727 @ SV711 @ SV265 @ SV145 ) @ SV761 )
= $true )
| ( ( in @ SV727 @ SV145 )
= $false )
| ( ( in @ SV711 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4787]) ).
thf(4861,plain,
! [SV145: $i,SV265: $i,SV727: $i,SV761: $i,SV711: $i] :
( ( ( in @ ( ordered_pair @ SV711 @ ( sK47_K @ SV761 @ SV727 @ SV711 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( ( SV727 != SV761 )
| ~ ( in @ SV711 @ SV761 ) )
= $true )
| ( ( in @ SV727 @ SV145 )
= $false )
| ( ( in @ SV711 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4788]) ).
thf(4862,plain,
! [SV145: $i,SV265: $i,SV712: $i,SV802: $i] :
( ( ( ~ ( in @ SV802 @ ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV712 @ SV802 ) @ SV265 )
= $true )
| ( ( in @ SV712 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4789]) ).
thf(4863,plain,
! [SV145: $i,SV265: $i,SV712: $i] :
( ( ( ( ( sK45_E @ SV712 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) ) )
= $false )
| ( ( in @ SV712 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4790]) ).
thf(4864,plain,
! [SV145: $i,SV265: $i,SV712: $i] :
( ( ( ~ ( in @ SV712 @ ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) ) )
= $false )
| ( ( in @ SV712 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4790]) ).
thf(4865,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV736: $i,SV762: $i,SV789: $i] :
( ( ( ~ ( in @ ( sK47_K @ SV789 @ SV762 @ SV736 @ SV265 @ SV145 ) @ SV789 )
| ~ ~ ( in @ ( ordered_pair @ SV736 @ ( sK47_K @ SV789 @ SV762 @ SV736 @ SV265 @ SV145 ) ) @ SV265 ) )
= $false )
| ( ( ( SV762 != SV789 )
| ~ ( in @ SV736 @ SV789 ) )
= $true )
| ( ( in @ SV762 @ SV145 )
= $false )
| ( ( in @ SV736 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4791]) ).
thf(4866,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV737: $i] :
( ( ( ~ ! [SY1573: $i] :
( ~ ( in @ SY1573 @ ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV737 @ SY1573 ) @ SV265 ) ) )
= $false )
| ( ( in @ SV737 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4792]) ).
thf(4867,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV737: $i] :
( ( ( ~ ~ ( ( ( sK45_E @ SV737 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) )
| ~ ( in @ SV737 @ ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( in @ SV737 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4792]) ).
thf(4868,plain,
! [SV145: $i,SV265: $i,SV738: $i,SV763: $i,SV790: $i] :
( ( ( ~ ( in @ ( sK47_K @ SV790 @ SV763 @ SV738 @ SV265 @ SV145 ) @ SV790 )
| ~ ~ ( in @ ( ordered_pair @ SV738 @ ( sK47_K @ SV790 @ SV763 @ SV738 @ SV265 @ SV145 ) ) @ SV265 ) )
= $false )
| ( ( ( SV763 != SV790 )
| ~ ( in @ SV738 @ SV790 ) )
= $true )
| ( ( in @ SV763 @ SV145 )
= $false )
| ( ( in @ SV738 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4793]) ).
thf(4869,plain,
! [SV145: $i,SV265: $i,SV739: $i] :
( ( ( ~ ! [SY1576: $i] :
( ~ ( in @ SY1576 @ ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV739 @ SY1576 ) @ SV265 ) ) )
= $false )
| ( ( in @ SV739 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4794]) ).
thf(4870,plain,
! [SV145: $i,SV265: $i,SV739: $i] :
( ( ( ~ ~ ( ( ( sK45_E @ SV739 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) )
| ~ ( in @ SV739 @ ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( in @ SV739 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4794]) ).
thf(4871,plain,
! [SV145: $i,SV265: $i,SV740: $i,SV764: $i,SV791: $i] :
( ( ( ~ ( in @ ( sK47_K @ SV791 @ SV764 @ SV740 @ SV265 @ SV145 ) @ SV791 )
| ~ ~ ( in @ ( ordered_pair @ SV740 @ ( sK47_K @ SV791 @ SV764 @ SV740 @ SV265 @ SV145 ) ) @ SV265 ) )
= $false )
| ( ( ( SV764 != SV791 )
| ~ ( in @ SV740 @ SV791 ) )
= $true )
| ( ( in @ SV764 @ SV145 )
= $false )
| ( ( in @ SV740 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4795]) ).
thf(4872,plain,
! [SV145: $i,SV265: $i,SV741: $i] :
( ( ( ~ ! [SY1579: $i] :
( ~ ( in @ SY1579 @ ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV741 @ SY1579 ) @ SV265 ) ) )
= $false )
| ( ( in @ SV741 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4796]) ).
thf(4873,plain,
! [SV145: $i,SV265: $i,SV741: $i] :
( ( ( ~ ~ ( ( ( sK45_E @ SV741 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) )
| ~ ( in @ SV741 @ ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( in @ SV741 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4796]) ).
thf(4874,plain,
! [SV272: $i,SV750: $i,SV717: $i,SV172: $i,SV776: $i] :
( ( ( in @ SV776 @ ( cartesian_product2 @ SV172 @ SV717 ) )
= $false )
| ( ( SV776 = SV750 )
= $false )
| ( ( ! [SY1606: $i,SY1607: $i] :
( ( ( ordered_pair @ SY1606 @ SY1607 )
!= SV750 )
| ~ ( in @ SY1606 @ SV172 )
| ! [SY1608: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1608 @ SY1607 @ SY1606 @ SV750 @ SV717 @ SV272 @ SV172 ) @ SY1608 )
| ~ ~ ( in @ ( ordered_pair @ SY1607 @ ( sK34_R @ SY1608 @ SY1607 @ SY1606 @ SV750 @ SV717 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1606 != SY1608 )
| ~ ( in @ SY1607 @ SY1608 ) ) ) )
= $true )
| ( ( in @ SV750 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4798]) ).
thf(4875,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( ( ( sK33_F @ SV751 @ SV717 @ SV272 @ SV172 )
!= SV751 )
| ~ ( in @ ( sK33_F @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV717 ) ) )
= $false )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4799]) ).
thf(4876,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) )
!= SV751 )
| ~ ( in @ ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1609: $i] :
( ~ ( in @ SY1609 @ ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) @ SY1609 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) ) ) ) )
= $false )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4800]) ).
thf(4877,plain,
! [SV272: $i,SV770: $i,SV172: $i,SV809: $i] :
( ( ( ! [SY1697: $i] :
( ( SY1697 != SV809 )
| ~ ( in @ SY1697 @ ( cartesian_product2 @ SV172 @ SV770 ) ) )
| ! [SY1698: $i,SY1699: $i] :
( ( ( ordered_pair @ SY1698 @ SY1699 )
!= SV809 )
| ~ ( in @ SY1698 @ SV172 )
| ! [SY1700: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1700 @ SY1699 @ SY1698 @ SV809 @ SV770 @ SV272 @ SV172 ) @ SY1700 )
| ~ ~ ( in @ ( ordered_pair @ SY1699 @ ( sK34_R @ SY1700 @ SY1699 @ SY1698 @ SV809 @ SV770 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1698 != SY1700 )
| ~ ( in @ SY1699 @ SY1700 ) ) )
| ( in @ SV809 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4801]) ).
thf(4878,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( ~ ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SV810 @ SV770 @ SV272 @ SV172 )
!= SV810 )
| ~ ( in @ ( sK33_F @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV770 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) )
!= SV810 )
| ~ ( in @ ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1701: $i] :
( ~ ( in @ SY1701 @ ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) @ SY1701 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4802]) ).
thf(4879,plain,
! [SV272: $i,SV771: $i,SV172: $i,SV811: $i] :
( ( ( ! [SY1702: $i] :
( ( SY1702 != SV811 )
| ~ ( in @ SY1702 @ ( cartesian_product2 @ SV172 @ SV771 ) ) )
| ! [SY1703: $i,SY1704: $i] :
( ( ( ordered_pair @ SY1703 @ SY1704 )
!= SV811 )
| ~ ( in @ SY1703 @ SV172 )
| ! [SY1705: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1705 @ SY1704 @ SY1703 @ SV811 @ SV771 @ SV272 @ SV172 ) @ SY1705 )
| ~ ~ ( in @ ( ordered_pair @ SY1704 @ ( sK34_R @ SY1705 @ SY1704 @ SY1703 @ SV811 @ SV771 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1703 != SY1705 )
| ~ ( in @ SY1704 @ SY1705 ) ) )
| ( in @ SV811 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4803]) ).
thf(4880,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( ~ ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SV812 @ SV771 @ SV272 @ SV172 )
!= SV812 )
| ~ ( in @ ( sK33_F @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV771 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) )
!= SV812 )
| ~ ( in @ ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1706: $i] :
( ~ ( in @ SY1706 @ ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) @ SY1706 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4804]) ).
thf(4881,plain,
! [SV772: $i,SV272: $i,SV803: $i,SV172: $i] :
( ( ( ~ ! [SY1674: $i] :
( ! [SY1675: $i] :
( ( SY1675 != SY1674 )
| ~ ( in @ SY1675 @ ( cartesian_product2 @ SV172 @ SV803 ) ) )
| ! [SY1676: $i,SY1677: $i] :
( ( ( ordered_pair @ SY1676 @ SY1677 )
!= SY1674 )
| ~ ( in @ SY1676 @ SV172 )
| ! [SY1678: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1678 @ SY1677 @ SY1676 @ SY1674 @ SV803 @ SV272 @ SV172 ) @ SY1678 )
| ~ ~ ( in @ ( ordered_pair @ SY1677 @ ( sK34_R @ SY1678 @ SY1677 @ SY1676 @ SY1674 @ SV803 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1676 != SY1678 )
| ~ ( in @ SY1677 @ SY1678 ) ) )
| ( in @ SY1674 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) ) )
| ~ ! [SY1679: $i] :
( ~ ( in @ SY1679 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1679 @ SV803 @ SV272 @ SV172 )
!= SY1679 )
| ~ ( in @ ( sK33_F @ SY1679 @ SV803 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV803 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1679 @ SV803 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1679 @ SV803 @ SV272 @ SV172 ) )
!= SY1679 )
| ~ ( in @ ( sK30_O @ SY1679 @ SV803 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1680: $i] :
( ~ ( in @ SY1680 @ ( sK32_SY652 @ SY1679 @ SV803 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1679 @ SV803 @ SV272 @ SV172 ) @ SY1680 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1679 @ SV803 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1679 @ SV803 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1679 @ SV803 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1679 @ SV803 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4805]) ).
thf(4882,plain,
! [SV272: $i,SV804: $i,SV172: $i] :
( ( ( ~ ! [SY1681: $i] :
( ! [SY1682: $i] :
( ( SY1682 != SY1681 )
| ~ ( in @ SY1682 @ ( cartesian_product2 @ SV172 @ SV804 ) ) )
| ! [SY1683: $i,SY1684: $i] :
( ( ( ordered_pair @ SY1683 @ SY1684 )
!= SY1681 )
| ~ ( in @ SY1683 @ SV172 )
| ! [SY1685: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1685 @ SY1684 @ SY1683 @ SY1681 @ SV804 @ SV272 @ SV172 ) @ SY1685 )
| ~ ~ ( in @ ( ordered_pair @ SY1684 @ ( sK34_R @ SY1685 @ SY1684 @ SY1683 @ SY1681 @ SV804 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1683 != SY1685 )
| ~ ( in @ SY1684 @ SY1685 ) ) )
| ( in @ SY1681 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) ) )
| ~ ! [SY1686: $i] :
( ~ ( in @ SY1686 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1686 @ SV804 @ SV272 @ SV172 )
!= SY1686 )
| ~ ( in @ ( sK33_F @ SY1686 @ SV804 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV804 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1686 @ SV804 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1686 @ SV804 @ SV272 @ SV172 ) )
!= SY1686 )
| ~ ( in @ ( sK30_O @ SY1686 @ SV804 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1687: $i] :
( ~ ( in @ SY1687 @ ( sK32_SY652 @ SY1686 @ SV804 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1686 @ SV804 @ SV272 @ SV172 ) @ SY1687 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1686 @ SV804 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1686 @ SV804 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1686 @ SV804 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1686 @ SV804 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4806]) ).
thf(4883,plain,
! [SV272: $i,SV805: $i,SV172: $i] :
( ( ( ~ ! [SY1688: $i] :
( ! [SY1689: $i] :
( ( SY1689 != SY1688 )
| ~ ( in @ SY1689 @ ( cartesian_product2 @ SV172 @ SV805 ) ) )
| ! [SY1690: $i,SY1691: $i] :
( ( ( ordered_pair @ SY1690 @ SY1691 )
!= SY1688 )
| ~ ( in @ SY1690 @ SV172 )
| ! [SY1692: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1692 @ SY1691 @ SY1690 @ SY1688 @ SV805 @ SV272 @ SV172 ) @ SY1692 )
| ~ ~ ( in @ ( ordered_pair @ SY1691 @ ( sK34_R @ SY1692 @ SY1691 @ SY1690 @ SY1688 @ SV805 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1690 != SY1692 )
| ~ ( in @ SY1691 @ SY1692 ) ) )
| ( in @ SY1688 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) ) )
| ~ ! [SY1693: $i] :
( ~ ( in @ SY1693 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1693 @ SV805 @ SV272 @ SV172 )
!= SY1693 )
| ~ ( in @ ( sK33_F @ SY1693 @ SV805 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV805 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1693 @ SV805 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1693 @ SV805 @ SV272 @ SV172 ) )
!= SY1693 )
| ~ ( in @ ( sK30_O @ SY1693 @ SV805 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1694: $i] :
( ~ ( in @ SY1694 @ ( sK32_SY652 @ SY1693 @ SV805 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1693 @ SV805 @ SV272 @ SV172 ) @ SY1694 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1693 @ SV805 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1693 @ SV805 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1693 @ SV805 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1693 @ SV805 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4807]) ).
thf(4884,plain,
! [SV752: $i,SV272: $i,SV692: $i,SV172: $i,SV723: $i,SV806: $i,SV792: $i] :
( ( ( ( ( ordered_pair @ SV792 @ SV806 )
!= SV723 )
| ~ ( in @ SV792 @ SV172 ) )
= $true )
| ( ( ! [SY1695: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1695 @ SV806 @ SV792 @ SV723 @ SV692 @ SV272 @ SV172 ) @ SY1695 )
| ~ ~ ( in @ ( ordered_pair @ SV806 @ ( sK34_R @ SY1695 @ SV806 @ SV792 @ SV723 @ SV692 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV792 != SY1695 )
| ~ ( in @ SV806 @ SY1695 ) ) )
= $true )
| ( ( SV752 = SV723 )
= $false )
| ( ( in @ SV752 @ ( cartesian_product2 @ SV172 @ SV692 ) )
= $false )
| ( ( in @ SV723 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4808]) ).
thf(4885,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( ( ( ordered_pair @ ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) )
!= SV724 )
| ~ ( in @ ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 ) @ SV172 ) )
= $false )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4811]) ).
thf(4886,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( ~ ! [SY1553: $i] :
( ~ ( in @ SY1553 @ ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) @ SY1553 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4812]) ).
thf(4887,plain,
! [SV272: $i,SV753: $i,SV718: $i,SV172: $i,SV777: $i] :
( ( ( in @ SV777 @ ( cartesian_product2 @ SV172 @ SV718 ) )
= $false )
| ( ( SV777 = SV753 )
= $false )
| ( ( ! [SY1611: $i,SY1612: $i] :
( ( ( ordered_pair @ SY1611 @ SY1612 )
!= SV753 )
| ~ ( in @ SY1611 @ SV172 )
| ! [SY1613: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1613 @ SY1612 @ SY1611 @ SV753 @ SV718 @ SV272 @ SV172 ) @ SY1613 )
| ~ ~ ( in @ ( ordered_pair @ SY1612 @ ( sK34_R @ SY1613 @ SY1612 @ SY1611 @ SV753 @ SV718 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1611 != SY1613 )
| ~ ( in @ SY1612 @ SY1613 ) ) ) )
= $true )
| ( ( in @ SV753 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4813]) ).
thf(4888,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( ( ( sK33_F @ SV754 @ SV718 @ SV272 @ SV172 )
!= SV754 )
| ~ ( in @ ( sK33_F @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV718 ) ) )
= $false )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4814]) ).
thf(4889,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) )
!= SV754 )
| ~ ( in @ ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1614: $i] :
( ~ ( in @ SY1614 @ ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) @ SY1614 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) ) ) ) )
= $false )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4815]) ).
thf(4890,plain,
! [SV272: $i,SV755: $i,SV719: $i,SV172: $i,SV778: $i] :
( ( ( in @ SV778 @ ( cartesian_product2 @ SV172 @ SV719 ) )
= $false )
| ( ( SV778 = SV755 )
= $false )
| ( ( ! [SY1616: $i,SY1617: $i] :
( ( ( ordered_pair @ SY1616 @ SY1617 )
!= SV755 )
| ~ ( in @ SY1616 @ SV172 )
| ! [SY1618: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1618 @ SY1617 @ SY1616 @ SV755 @ SV719 @ SV272 @ SV172 ) @ SY1618 )
| ~ ~ ( in @ ( ordered_pair @ SY1617 @ ( sK34_R @ SY1618 @ SY1617 @ SY1616 @ SV755 @ SV719 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1616 != SY1618 )
| ~ ( in @ SY1617 @ SY1618 ) ) ) )
= $true )
| ( ( in @ SV755 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4816]) ).
thf(4891,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( ( ( sK33_F @ SV756 @ SV719 @ SV272 @ SV172 )
!= SV756 )
| ~ ( in @ ( sK33_F @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV719 ) ) )
= $false )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4817]) ).
thf(4892,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) )
!= SV756 )
| ~ ( in @ ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1619: $i] :
( ~ ( in @ SY1619 @ ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) @ SY1619 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) ) ) ) )
= $false )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4818]) ).
thf(4893,plain,
! [SV720: $i,SV272: $i,SV743: $i,SV172: $i,SV779: $i,SV813: $i] :
( ( ( ( SV813 != SV779 )
| ~ ( in @ SV813 @ ( cartesian_product2 @ SV172 @ SV743 ) ) )
= $true )
| ( ( ! [SY1649: $i,SY1650: $i] :
( ( ( ordered_pair @ SY1649 @ SY1650 )
!= SV779 )
| ~ ( in @ SY1649 @ SV172 )
| ! [SY1651: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1651 @ SY1650 @ SY1649 @ SV779 @ SV743 @ SV272 @ SV172 ) @ SY1651 )
| ~ ~ ( in @ ( ordered_pair @ SY1650 @ ( sK34_R @ SY1651 @ SY1650 @ SY1649 @ SV779 @ SV743 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1649 != SY1651 )
| ~ ( in @ SY1650 @ SY1651 ) ) ) )
= $true )
| ( ( in @ SV779 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4819]) ).
thf(4894,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( ~ ~ ( ( ( sK33_F @ SV780 @ SV743 @ SV272 @ SV172 )
!= SV780 )
| ~ ( in @ ( sK33_F @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV743 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) )
!= SV780 )
| ~ ( in @ ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1652: $i] :
( ~ ( in @ SY1652 @ ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) @ SY1652 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) ) ) ) ) )
= $false )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4820]) ).
thf(4895,plain,
! [SV272: $i,SV744: $i,SV172: $i,SV781: $i,SV814: $i] :
( ( ( ( SV814 != SV781 )
| ~ ( in @ SV814 @ ( cartesian_product2 @ SV172 @ SV744 ) ) )
= $true )
| ( ( ! [SY1654: $i,SY1655: $i] :
( ( ( ordered_pair @ SY1654 @ SY1655 )
!= SV781 )
| ~ ( in @ SY1654 @ SV172 )
| ! [SY1656: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1656 @ SY1655 @ SY1654 @ SV781 @ SV744 @ SV272 @ SV172 ) @ SY1656 )
| ~ ~ ( in @ ( ordered_pair @ SY1655 @ ( sK34_R @ SY1656 @ SY1655 @ SY1654 @ SV781 @ SV744 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1654 != SY1656 )
| ~ ( in @ SY1655 @ SY1656 ) ) ) )
= $true )
| ( ( in @ SV781 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4821]) ).
thf(4896,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( ~ ~ ( ( ( sK33_F @ SV782 @ SV744 @ SV272 @ SV172 )
!= SV782 )
| ~ ( in @ ( sK33_F @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV744 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) )
!= SV782 )
| ~ ( in @ ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1657: $i] :
( ~ ( in @ SY1657 @ ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) @ SY1657 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) ) ) ) ) )
= $false )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4822]) ).
thf(4897,plain,
! [SV272: $i,SV745: $i,SV172: $i,SV783: $i,SV815: $i] :
( ( ( ( SV815 != SV783 )
| ~ ( in @ SV815 @ ( cartesian_product2 @ SV172 @ SV745 ) ) )
= $true )
| ( ( ! [SY1659: $i,SY1660: $i] :
( ( ( ordered_pair @ SY1659 @ SY1660 )
!= SV783 )
| ~ ( in @ SY1659 @ SV172 )
| ! [SY1661: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1661 @ SY1660 @ SY1659 @ SV783 @ SV745 @ SV272 @ SV172 ) @ SY1661 )
| ~ ~ ( in @ ( ordered_pair @ SY1660 @ ( sK34_R @ SY1661 @ SY1660 @ SY1659 @ SV783 @ SV745 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1659 != SY1661 )
| ~ ( in @ SY1660 @ SY1661 ) ) ) )
= $true )
| ( ( in @ SV783 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4823]) ).
thf(4898,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( ~ ~ ( ( ( sK33_F @ SV784 @ SV745 @ SV272 @ SV172 )
!= SV784 )
| ~ ( in @ ( sK33_F @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV745 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) )
!= SV784 )
| ~ ( in @ ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1662: $i] :
( ~ ( in @ SY1662 @ ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) @ SY1662 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) ) ) ) ) )
= $false )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4824]) ).
thf(4899,plain,
! [SV701: $i,SV172: $i,SV272: $i,SV622: $i,SV677: $i,SV746: $i,SV757: $i,SV807: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_R @ SV807 @ SV757 @ SV746 @ SV677 @ SV622 @ SV272 @ SV172 ) @ SV807 )
| ~ ~ ( in @ ( ordered_pair @ SV757 @ ( sK34_R @ SV807 @ SV757 @ SV746 @ SV677 @ SV622 @ SV272 @ SV172 ) ) @ SV272 ) ) )
= $true )
| ( ( ( SV746 != SV807 )
| ~ ( in @ SV757 @ SV807 ) )
= $true )
| ( ( ( ordered_pair @ SV746 @ SV757 )
= SV677 )
= $false )
| ( ( in @ SV746 @ SV172 )
= $false )
| ( ( SV701 = SV677 )
= $false )
| ( ( in @ SV701 @ ( cartesian_product2 @ SV172 @ SV622 ) )
= $false )
| ( ( in @ SV677 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4825]) ).
thf(4900,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i,SV793: $i] :
( ( ( in @ SV793 @ ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) @ SV793 ) @ SV272 )
= $true )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4826]) ).
thf(4901,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( ( sK30_O @ SV678 @ SV622 @ SV272 @ SV172 )
= ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4827]) ).
thf(4902,plain,
! [SV172: $i,SV272: $i,SV622: $i,SV678: $i] :
( ( ( in @ ( sK31_SY649 @ SV678 @ SV622 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV678 @ SV622 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ SV678 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4828]) ).
thf(4903,plain,
! [SV660: $i,SV728: $i,SV139: $i,SV702: $i,SV785: $i,SV773: $i] :
( ( ( ( ordered_pair @ SV773 @ SV785 )
= SV702 )
= $false )
| ( ( ~ ( in @ SV773 @ SV139 ) )
= $true )
| ( ( ( SV785
!= ( singleton @ SV773 ) ) )
= $true )
| ( ( SV728 = SV702 )
= $false )
| ( ( in @ SV728 @ ( cartesian_product2 @ SV139 @ SV660 ) )
= $false )
| ( ( in @ SV702 @ ( sK13_C @ SV660 @ SV139 ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4829]) ).
thf(4904,plain,
! [SV139: $i,SV660: $i,SV703: $i] :
( ( ( ( ordered_pair @ ( sK14_J @ SV703 @ SV660 @ SV139 ) @ ( sK15_SY612 @ SV703 @ SV660 @ SV139 ) )
= SV703 )
= $true )
| ( ( in @ SV703 @ ( sK13_C @ SV660 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4830]) ).
thf(4905,plain,
! [SV139: $i,SV660: $i,SV703: $i] :
( ( ( in @ ( sK14_J @ SV703 @ SV660 @ SV139 ) @ SV139 )
= $true )
| ( ( in @ SV703 @ ( sK13_C @ SV660 @ SV139 ) )
= $false )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4831]) ).
thf(4906,plain,
! [SV725: $i,SV139: $i,SV765: $i,SV794: $i] :
( ( ( SV794 = SV765 )
= $false )
| ( ( ~ ( in @ SV794 @ ( cartesian_product2 @ SV139 @ SV725 ) ) )
= $true )
| ( ( ! [SY1626: $i,SY1627: $i] :
( ( ( ordered_pair @ SY1626 @ SY1627 )
!= SV765 )
| ~ ( in @ SY1626 @ SV139 )
| ( SY1627
!= ( singleton @ SY1626 ) ) ) )
= $true )
| ( ( in @ SV765 @ ( sK13_C @ SV725 @ SV139 ) )
= $true )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4832]) ).
thf(4907,plain,
! [SV139: $i,SV725: $i,SV766: $i] :
( ( ( ~ ( ( ( sK16_E @ SV766 @ SV725 @ SV139 )
!= SV766 )
| ~ ( in @ ( sK16_E @ SV766 @ SV725 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV725 ) ) ) )
= $true )
| ( ( in @ SV766 @ ( sK13_C @ SV725 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4833]) ).
thf(4908,plain,
! [SV139: $i,SV725: $i,SV766: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV766 @ SV725 @ SV139 ) @ ( sK15_SY612 @ SV766 @ SV725 @ SV139 ) )
!= SV766 )
| ~ ( in @ ( sK14_J @ SV766 @ SV725 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV766 @ SV725 @ SV139 )
!= ( singleton @ ( sK14_J @ SV766 @ SV725 @ SV139 ) ) ) ) )
= $true )
| ( ( in @ SV766 @ ( sK13_C @ SV725 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4834]) ).
thf(4909,plain,
! [SV726: $i,SV139: $i,SV767: $i,SV795: $i] :
( ( ( SV795 = SV767 )
= $false )
| ( ( ~ ( in @ SV795 @ ( cartesian_product2 @ SV139 @ SV726 ) ) )
= $true )
| ( ( ! [SY1629: $i,SY1630: $i] :
( ( ( ordered_pair @ SY1629 @ SY1630 )
!= SV767 )
| ~ ( in @ SY1629 @ SV139 )
| ( SY1630
!= ( singleton @ SY1629 ) ) ) )
= $true )
| ( ( in @ SV767 @ ( sK13_C @ SV726 @ SV139 ) )
= $true )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4835]) ).
thf(4910,plain,
! [SV139: $i,SV726: $i,SV768: $i] :
( ( ( ~ ( ( ( sK16_E @ SV768 @ SV726 @ SV139 )
!= SV768 )
| ~ ( in @ ( sK16_E @ SV768 @ SV726 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV726 ) ) ) )
= $true )
| ( ( in @ SV768 @ ( sK13_C @ SV726 @ SV139 ) )
= $false )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4836]) ).
thf(4911,plain,
! [SV139: $i,SV726: $i,SV768: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV768 @ SV726 @ SV139 ) @ ( sK15_SY612 @ SV768 @ SV726 @ SV139 ) )
!= SV768 )
| ~ ( in @ ( sK14_J @ SV768 @ SV726 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV768 @ SV726 @ SV139 )
!= ( singleton @ ( sK14_J @ SV768 @ SV726 @ SV139 ) ) ) ) )
= $true )
| ( ( in @ SV768 @ ( sK13_C @ SV726 @ SV139 ) )
= $false )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4837]) ).
thf(4912,plain,
! [SV694: $i,SV769: $i,SV139: $i,SV729: $i,SV816: $i,SV808: $i] :
( ( ( ( ( ordered_pair @ SV808 @ SV816 )
!= SV729 )
| ~ ( in @ SV808 @ SV139 )
| ( SV816
!= ( singleton @ SV808 ) ) )
= $true )
| ( ( SV769 = SV729 )
= $false )
| ( ( in @ SV769 @ ( cartesian_product2 @ SV139 @ SV694 ) )
= $false )
| ( ( in @ SV729 @ ( sK13_C @ SV694 @ SV139 ) )
= $true )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4838]) ).
thf(4913,plain,
! [SV139: $i,SV694: $i,SV730: $i] :
( ( ( ( sK16_E @ SV730 @ SV694 @ SV139 )
= SV730 )
= $true )
| ( ( in @ SV730 @ ( sK13_C @ SV694 @ SV139 ) )
= $false )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4839]) ).
thf(4914,plain,
! [SV139: $i,SV694: $i,SV730: $i] :
( ( ( in @ ( sK16_E @ SV730 @ SV694 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV694 ) )
= $true )
| ( ( in @ SV730 @ ( sK13_C @ SV694 @ SV139 ) )
= $false )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4840]) ).
thf(4915,plain,
! [SV139: $i,SV694: $i,SV730: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK14_J @ SV730 @ SV694 @ SV139 ) @ ( sK15_SY612 @ SV730 @ SV694 @ SV139 ) )
!= SV730 )
| ~ ( in @ ( sK14_J @ SV730 @ SV694 @ SV139 ) @ SV139 ) ) )
= $true )
| ( ( in @ SV730 @ ( sK13_C @ SV694 @ SV139 ) )
= $false )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4841]) ).
thf(4916,plain,
! [SV139: $i,SV694: $i,SV730: $i] :
( ( ( ( sK15_SY612 @ SV730 @ SV694 @ SV139 )
= ( singleton @ ( sK14_J @ SV730 @ SV694 @ SV139 ) ) )
= $true )
| ( ( in @ SV730 @ ( sK13_C @ SV694 @ SV139 ) )
= $false )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4842]) ).
thf(4917,plain,
! [SV661: $i,SV731: $i,SV139: $i,SV705: $i,SV786: $i,SV774: $i] :
( ( ( ( ordered_pair @ SV774 @ SV786 )
= SV705 )
= $false )
| ( ( ~ ( in @ SV774 @ SV139 ) )
= $true )
| ( ( ( SV786
!= ( singleton @ SV774 ) ) )
= $true )
| ( ( SV731 = SV705 )
= $false )
| ( ( in @ SV731 @ ( cartesian_product2 @ SV139 @ SV661 ) )
= $false )
| ( ( in @ SV705 @ ( sK13_C @ SV661 @ SV139 ) )
= $true )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4844]) ).
thf(4918,plain,
! [SV139: $i,SV661: $i,SV706: $i] :
( ( ( ( ordered_pair @ ( sK14_J @ SV706 @ SV661 @ SV139 ) @ ( sK15_SY612 @ SV706 @ SV661 @ SV139 ) )
= SV706 )
= $true )
| ( ( in @ SV706 @ ( sK13_C @ SV661 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4845]) ).
thf(4919,plain,
! [SV139: $i,SV661: $i,SV706: $i] :
( ( ( in @ ( sK14_J @ SV706 @ SV661 @ SV139 ) @ SV139 )
= $true )
| ( ( in @ SV706 @ ( sK13_C @ SV661 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4846]) ).
thf(4920,plain,
! [SV662: $i,SV732: $i,SV139: $i,SV707: $i,SV787: $i,SV775: $i] :
( ( ( ( ordered_pair @ SV775 @ SV787 )
= SV707 )
= $false )
| ( ( ~ ( in @ SV775 @ SV139 ) )
= $true )
| ( ( ( SV787
!= ( singleton @ SV775 ) ) )
= $true )
| ( ( SV732 = SV707 )
= $false )
| ( ( in @ SV732 @ ( cartesian_product2 @ SV139 @ SV662 ) )
= $false )
| ( ( in @ SV707 @ ( sK13_C @ SV662 @ SV139 ) )
= $true )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4847]) ).
thf(4921,plain,
! [SV139: $i,SV662: $i,SV708: $i] :
( ( ( ( ordered_pair @ ( sK14_J @ SV708 @ SV662 @ SV139 ) @ ( sK15_SY612 @ SV708 @ SV662 @ SV139 ) )
= SV708 )
= $true )
| ( ( in @ SV708 @ ( sK13_C @ SV662 @ SV139 ) )
= $false )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4848]) ).
thf(4922,plain,
! [SV139: $i,SV662: $i,SV708: $i] :
( ( ( in @ ( sK14_J @ SV708 @ SV662 @ SV139 ) @ SV139 )
= $true )
| ( ( in @ SV708 @ ( sK13_C @ SV662 @ SV139 ) )
= $false )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4849]) ).
thf(4923,plain,
! [SV733: $i,SV265: $i,SV796: $i,SV145: $i,SV817: $i] :
( ( ( ~ ( in @ SV817 @ SV145 )
| ! [SY1707: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1707 @ SV817 @ SV796 @ SV265 @ SV145 ) @ SY1707 )
| ~ ~ ( in @ ( ordered_pair @ SV796 @ ( sK47_K @ SY1707 @ SV817 @ SV796 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV817 != SY1707 )
| ~ ( in @ SV796 @ SY1707 ) ) )
= $true )
| ( ( in @ SV796 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4851]) ).
thf(4924,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV797: $i] :
( ( ( in @ SV797 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK45_E @ SV797 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1667: $i] :
( ~ ( in @ SY1667 @ ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV797 @ SY1667 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV797 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) )
| ~ ( in @ SV797 @ ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) ) ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4852]) ).
thf(4925,plain,
! [SV265: $i,SV798: $i,SV145: $i,SV818: $i] :
( ( ( ~ ( in @ SV818 @ SV145 )
| ! [SY1708: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1708 @ SV818 @ SV798 @ SV265 @ SV145 ) @ SY1708 )
| ~ ~ ( in @ ( ordered_pair @ SV798 @ ( sK47_K @ SY1708 @ SV818 @ SV798 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV818 != SY1708 )
| ~ ( in @ SV798 @ SY1708 ) ) )
= $true )
| ( ( in @ SV798 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4853]) ).
thf(4926,plain,
! [SV145: $i,SV265: $i,SV799: $i] :
( ( ( in @ SV799 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK45_E @ SV799 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1670: $i] :
( ~ ( in @ SY1670 @ ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV799 @ SY1670 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV799 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) )
| ~ ( in @ SV799 @ ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) ) ) ) ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4854]) ).
thf(4927,plain,
! [SV265: $i,SV800: $i,SV145: $i,SV819: $i] :
( ( ( ~ ( in @ SV819 @ SV145 )
| ! [SY1709: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1709 @ SV819 @ SV800 @ SV265 @ SV145 ) @ SY1709 )
| ~ ~ ( in @ ( ordered_pair @ SV800 @ ( sK47_K @ SY1709 @ SV819 @ SV800 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV819 != SY1709 )
| ~ ( in @ SV800 @ SY1709 ) ) )
= $true )
| ( ( in @ SV800 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4855]) ).
thf(4928,plain,
! [SV145: $i,SV265: $i,SV801: $i] :
( ( ( in @ SV801 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK45_E @ SV801 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1673: $i] :
( ~ ( in @ SY1673 @ ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV801 @ SY1673 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV801 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) )
| ~ ( in @ SV801 @ ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) ) ) ) ) )
= $true )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4856]) ).
thf(4929,plain,
! [SV145: $i,SV265: $i,SV734: $i,SV760: $i,SV788: $i] :
( ( ( ~ ( in @ ( sK47_K @ SV788 @ SV760 @ SV734 @ SV265 @ SV145 ) @ SV788 ) )
= $false )
| ( ( ( SV760 != SV788 )
| ~ ( in @ SV734 @ SV788 ) )
= $true )
| ( ( in @ SV760 @ SV145 )
= $false )
| ( ( in @ SV734 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4857]) ).
thf(4930,plain,
! [SV145: $i,SV265: $i,SV760: $i,SV788: $i,SV734: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV734 @ ( sK47_K @ SV788 @ SV760 @ SV734 @ SV265 @ SV145 ) ) @ SV265 ) )
= $false )
| ( ( ( SV760 != SV788 )
| ~ ( in @ SV734 @ SV788 ) )
= $true )
| ( ( in @ SV760 @ SV145 )
= $false )
| ( ( in @ SV734 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4857]) ).
thf(4931,plain,
! [SV145: $i,SV265: $i,SV735: $i] :
( ( ( ! [SY1570: $i] :
( ~ ( in @ SY1570 @ ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV735 @ SY1570 ) @ SV265 ) ) )
= $true )
| ( ( in @ SV735 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4858]) ).
thf(4932,plain,
! [SV145: $i,SV265: $i,SV735: $i] :
( ( ( ~ ( ( ( sK45_E @ SV735 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) )
| ~ ( in @ SV735 @ ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) ) ) )
= $true )
| ( ( in @ SV735 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4859]) ).
thf(4933,plain,
! [SV145: $i,SV265: $i,SV711: $i,SV761: $i,SV727: $i] :
( ( ( SV727 = SV761 )
= $false )
| ( ( ~ ( in @ SV711 @ SV761 ) )
= $true )
| ( ( in @ ( sK47_K @ SV761 @ SV727 @ SV711 @ SV265 @ SV145 ) @ SV761 )
= $true )
| ( ( in @ SV727 @ SV145 )
= $false )
| ( ( in @ SV711 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4860]) ).
thf(4934,plain,
! [SV145: $i,SV265: $i,SV711: $i,SV761: $i,SV727: $i] :
( ( ( ( SV727 != SV761 ) )
= $true )
| ( ( ~ ( in @ SV711 @ SV761 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV711 @ ( sK47_K @ SV761 @ SV727 @ SV711 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( in @ SV727 @ SV145 )
= $false )
| ( ( in @ SV711 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4861]) ).
thf(4935,plain,
! [SV145: $i,SV265: $i,SV712: $i,SV802: $i] :
( ( ( in @ SV802 @ ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV712 @ SV802 ) @ SV265 )
= $true )
| ( ( in @ SV712 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4862]) ).
thf(4936,plain,
! [SV145: $i,SV265: $i,SV712: $i] :
( ( ( ( sK45_E @ SV712 @ SV265 @ SV145 )
= ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) )
= $true )
| ( ( in @ SV712 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4863]) ).
thf(4937,plain,
! [SV145: $i,SV265: $i,SV712: $i] :
( ( ( in @ SV712 @ ( sK46_SY702 @ SV712 @ SV265 @ SV145 ) )
= $true )
| ( ( in @ SV712 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4864]) ).
thf(4938,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV736: $i,SV762: $i,SV789: $i] :
( ( ( ~ ( in @ ( sK47_K @ SV789 @ SV762 @ SV736 @ SV265 @ SV145 ) @ SV789 ) )
= $false )
| ( ( ( SV762 != SV789 )
| ~ ( in @ SV736 @ SV789 ) )
= $true )
| ( ( in @ SV762 @ SV145 )
= $false )
| ( ( in @ SV736 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4865]) ).
thf(4939,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV762: $i,SV789: $i,SV736: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV736 @ ( sK47_K @ SV789 @ SV762 @ SV736 @ SV265 @ SV145 ) ) @ SV265 ) )
= $false )
| ( ( ( SV762 != SV789 )
| ~ ( in @ SV736 @ SV789 ) )
= $true )
| ( ( in @ SV762 @ SV145 )
= $false )
| ( ( in @ SV736 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4865]) ).
thf(4940,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV737: $i] :
( ( ( ! [SY1573: $i] :
( ~ ( in @ SY1573 @ ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV737 @ SY1573 ) @ SV265 ) ) )
= $true )
| ( ( in @ SV737 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4866]) ).
thf(4941,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV737: $i] :
( ( ( ~ ( ( ( sK45_E @ SV737 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) )
| ~ ( in @ SV737 @ ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) ) ) )
= $true )
| ( ( in @ SV737 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4867]) ).
thf(4942,plain,
! [SV145: $i,SV265: $i,SV738: $i,SV763: $i,SV790: $i] :
( ( ( ~ ( in @ ( sK47_K @ SV790 @ SV763 @ SV738 @ SV265 @ SV145 ) @ SV790 ) )
= $false )
| ( ( ( SV763 != SV790 )
| ~ ( in @ SV738 @ SV790 ) )
= $true )
| ( ( in @ SV763 @ SV145 )
= $false )
| ( ( in @ SV738 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4868]) ).
thf(4943,plain,
! [SV145: $i,SV265: $i,SV763: $i,SV790: $i,SV738: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV738 @ ( sK47_K @ SV790 @ SV763 @ SV738 @ SV265 @ SV145 ) ) @ SV265 ) )
= $false )
| ( ( ( SV763 != SV790 )
| ~ ( in @ SV738 @ SV790 ) )
= $true )
| ( ( in @ SV763 @ SV145 )
= $false )
| ( ( in @ SV738 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4868]) ).
thf(4944,plain,
! [SV145: $i,SV265: $i,SV739: $i] :
( ( ( ! [SY1576: $i] :
( ~ ( in @ SY1576 @ ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV739 @ SY1576 ) @ SV265 ) ) )
= $true )
| ( ( in @ SV739 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4869]) ).
thf(4945,plain,
! [SV145: $i,SV265: $i,SV739: $i] :
( ( ( ~ ( ( ( sK45_E @ SV739 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) )
| ~ ( in @ SV739 @ ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) ) ) )
= $true )
| ( ( in @ SV739 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4870]) ).
thf(4946,plain,
! [SV145: $i,SV265: $i,SV740: $i,SV764: $i,SV791: $i] :
( ( ( ~ ( in @ ( sK47_K @ SV791 @ SV764 @ SV740 @ SV265 @ SV145 ) @ SV791 ) )
= $false )
| ( ( ( SV764 != SV791 )
| ~ ( in @ SV740 @ SV791 ) )
= $true )
| ( ( in @ SV764 @ SV145 )
= $false )
| ( ( in @ SV740 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4871]) ).
thf(4947,plain,
! [SV145: $i,SV265: $i,SV764: $i,SV791: $i,SV740: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV740 @ ( sK47_K @ SV791 @ SV764 @ SV740 @ SV265 @ SV145 ) ) @ SV265 ) )
= $false )
| ( ( ( SV764 != SV791 )
| ~ ( in @ SV740 @ SV791 ) )
= $true )
| ( ( in @ SV764 @ SV145 )
= $false )
| ( ( in @ SV740 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4871]) ).
thf(4948,plain,
! [SV145: $i,SV265: $i,SV741: $i] :
( ( ( ! [SY1579: $i] :
( ~ ( in @ SY1579 @ ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV741 @ SY1579 ) @ SV265 ) ) )
= $true )
| ( ( in @ SV741 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4872]) ).
thf(4949,plain,
! [SV145: $i,SV265: $i,SV741: $i] :
( ( ( ~ ( ( ( sK45_E @ SV741 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) )
| ~ ( in @ SV741 @ ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) ) ) )
= $true )
| ( ( in @ SV741 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4873]) ).
thf(4950,plain,
! [SV776: $i,SV272: $i,SV717: $i,SV172: $i,SV750: $i,SV820: $i] :
( ( ( ! [SY1710: $i] :
( ( ( ordered_pair @ SV820 @ SY1710 )
!= SV750 )
| ~ ( in @ SV820 @ SV172 )
| ! [SY1711: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1711 @ SY1710 @ SV820 @ SV750 @ SV717 @ SV272 @ SV172 ) @ SY1711 )
| ~ ~ ( in @ ( ordered_pair @ SY1710 @ ( sK34_R @ SY1711 @ SY1710 @ SV820 @ SV750 @ SV717 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV820 != SY1711 )
| ~ ( in @ SY1710 @ SY1711 ) ) ) )
= $true )
| ( ( SV776 = SV750 )
= $false )
| ( ( in @ SV776 @ ( cartesian_product2 @ SV172 @ SV717 ) )
= $false )
| ( ( in @ SV750 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4874]) ).
thf(4951,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( ( ( sK33_F @ SV751 @ SV717 @ SV272 @ SV172 )
!= SV751 ) )
= $false )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4875]) ).
thf(4952,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( ~ ( in @ ( sK33_F @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV717 ) ) )
= $false )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4875]) ).
thf(4953,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) )
!= SV751 )
| ~ ( in @ ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 ) @ SV172 ) ) )
= $false )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4876]) ).
thf(4954,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( ~ ~ ( ~ ! [SY1609: $i] :
( ~ ( in @ SY1609 @ ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) @ SY1609 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) ) ) ) )
= $false )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4876]) ).
thf(4955,plain,
! [SV272: $i,SV770: $i,SV172: $i,SV809: $i] :
( ( ( ! [SY1697: $i] :
( ( SY1697 != SV809 )
| ~ ( in @ SY1697 @ ( cartesian_product2 @ SV172 @ SV770 ) ) )
| ! [SY1698: $i,SY1699: $i] :
( ( ( ordered_pair @ SY1698 @ SY1699 )
!= SV809 )
| ~ ( in @ SY1698 @ SV172 )
| ! [SY1700: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1700 @ SY1699 @ SY1698 @ SV809 @ SV770 @ SV272 @ SV172 ) @ SY1700 )
| ~ ~ ( in @ ( ordered_pair @ SY1699 @ ( sK34_R @ SY1700 @ SY1699 @ SY1698 @ SV809 @ SV770 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1698 != SY1700 )
| ~ ( in @ SY1699 @ SY1700 ) ) ) )
= $true )
| ( ( in @ SV809 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4877]) ).
thf(4956,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( ~ ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK33_F @ SV810 @ SV770 @ SV272 @ SV172 )
!= SV810 )
| ~ ( in @ ( sK33_F @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV770 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) )
!= SV810 )
| ~ ( in @ ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1701: $i] :
( ~ ( in @ SY1701 @ ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) @ SY1701 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4878]) ).
thf(4957,plain,
! [SV272: $i,SV771: $i,SV172: $i,SV811: $i] :
( ( ( ! [SY1702: $i] :
( ( SY1702 != SV811 )
| ~ ( in @ SY1702 @ ( cartesian_product2 @ SV172 @ SV771 ) ) )
| ! [SY1703: $i,SY1704: $i] :
( ( ( ordered_pair @ SY1703 @ SY1704 )
!= SV811 )
| ~ ( in @ SY1703 @ SV172 )
| ! [SY1705: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1705 @ SY1704 @ SY1703 @ SV811 @ SV771 @ SV272 @ SV172 ) @ SY1705 )
| ~ ~ ( in @ ( ordered_pair @ SY1704 @ ( sK34_R @ SY1705 @ SY1704 @ SY1703 @ SV811 @ SV771 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1703 != SY1705 )
| ~ ( in @ SY1704 @ SY1705 ) ) ) )
= $true )
| ( ( in @ SV811 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4879]) ).
thf(4958,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( ~ ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK33_F @ SV812 @ SV771 @ SV272 @ SV172 )
!= SV812 )
| ~ ( in @ ( sK33_F @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV771 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) )
!= SV812 )
| ~ ( in @ ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1706: $i] :
( ~ ( in @ SY1706 @ ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) @ SY1706 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4880]) ).
thf(4959,plain,
! [SV772: $i,SV272: $i,SV803: $i,SV172: $i] :
( ( ( ~ ! [SY1674: $i] :
( ! [SY1675: $i] :
( ( SY1675 != SY1674 )
| ~ ( in @ SY1675 @ ( cartesian_product2 @ SV172 @ SV803 ) ) )
| ! [SY1676: $i,SY1677: $i] :
( ( ( ordered_pair @ SY1676 @ SY1677 )
!= SY1674 )
| ~ ( in @ SY1676 @ SV172 )
| ! [SY1678: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1678 @ SY1677 @ SY1676 @ SY1674 @ SV803 @ SV272 @ SV172 ) @ SY1678 )
| ~ ~ ( in @ ( ordered_pair @ SY1677 @ ( sK34_R @ SY1678 @ SY1677 @ SY1676 @ SY1674 @ SV803 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1676 != SY1678 )
| ~ ( in @ SY1677 @ SY1678 ) ) )
| ( in @ SY1674 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4881]) ).
thf(4960,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i] :
( ( ( ~ ! [SY1679: $i] :
( ~ ( in @ SY1679 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1679 @ SV803 @ SV272 @ SV172 )
!= SY1679 )
| ~ ( in @ ( sK33_F @ SY1679 @ SV803 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV803 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1679 @ SV803 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1679 @ SV803 @ SV272 @ SV172 ) )
!= SY1679 )
| ~ ( in @ ( sK30_O @ SY1679 @ SV803 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1680: $i] :
( ~ ( in @ SY1680 @ ( sK32_SY652 @ SY1679 @ SV803 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1679 @ SV803 @ SV272 @ SV172 ) @ SY1680 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1679 @ SV803 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1679 @ SV803 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1679 @ SV803 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1679 @ SV803 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4881]) ).
thf(4961,plain,
! [SV272: $i,SV804: $i,SV172: $i] :
( ( ( ~ ! [SY1681: $i] :
( ! [SY1682: $i] :
( ( SY1682 != SY1681 )
| ~ ( in @ SY1682 @ ( cartesian_product2 @ SV172 @ SV804 ) ) )
| ! [SY1683: $i,SY1684: $i] :
( ( ( ordered_pair @ SY1683 @ SY1684 )
!= SY1681 )
| ~ ( in @ SY1683 @ SV172 )
| ! [SY1685: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1685 @ SY1684 @ SY1683 @ SY1681 @ SV804 @ SV272 @ SV172 ) @ SY1685 )
| ~ ~ ( in @ ( ordered_pair @ SY1684 @ ( sK34_R @ SY1685 @ SY1684 @ SY1683 @ SY1681 @ SV804 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1683 != SY1685 )
| ~ ( in @ SY1684 @ SY1685 ) ) )
| ( in @ SY1681 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4882]) ).
thf(4962,plain,
! [SV172: $i,SV272: $i,SV804: $i] :
( ( ( ~ ! [SY1686: $i] :
( ~ ( in @ SY1686 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1686 @ SV804 @ SV272 @ SV172 )
!= SY1686 )
| ~ ( in @ ( sK33_F @ SY1686 @ SV804 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV804 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1686 @ SV804 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1686 @ SV804 @ SV272 @ SV172 ) )
!= SY1686 )
| ~ ( in @ ( sK30_O @ SY1686 @ SV804 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1687: $i] :
( ~ ( in @ SY1687 @ ( sK32_SY652 @ SY1686 @ SV804 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1686 @ SV804 @ SV272 @ SV172 ) @ SY1687 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1686 @ SV804 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1686 @ SV804 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1686 @ SV804 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1686 @ SV804 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4882]) ).
thf(4963,plain,
! [SV272: $i,SV805: $i,SV172: $i] :
( ( ( ~ ! [SY1688: $i] :
( ! [SY1689: $i] :
( ( SY1689 != SY1688 )
| ~ ( in @ SY1689 @ ( cartesian_product2 @ SV172 @ SV805 ) ) )
| ! [SY1690: $i,SY1691: $i] :
( ( ( ordered_pair @ SY1690 @ SY1691 )
!= SY1688 )
| ~ ( in @ SY1690 @ SV172 )
| ! [SY1692: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1692 @ SY1691 @ SY1690 @ SY1688 @ SV805 @ SV272 @ SV172 ) @ SY1692 )
| ~ ~ ( in @ ( ordered_pair @ SY1691 @ ( sK34_R @ SY1692 @ SY1691 @ SY1690 @ SY1688 @ SV805 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1690 != SY1692 )
| ~ ( in @ SY1691 @ SY1692 ) ) )
| ( in @ SY1688 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4883]) ).
thf(4964,plain,
! [SV172: $i,SV272: $i,SV805: $i] :
( ( ( ~ ! [SY1693: $i] :
( ~ ( in @ SY1693 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1693 @ SV805 @ SV272 @ SV172 )
!= SY1693 )
| ~ ( in @ ( sK33_F @ SY1693 @ SV805 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV805 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1693 @ SV805 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1693 @ SV805 @ SV272 @ SV172 ) )
!= SY1693 )
| ~ ( in @ ( sK30_O @ SY1693 @ SV805 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1694: $i] :
( ~ ( in @ SY1694 @ ( sK32_SY652 @ SY1693 @ SV805 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1693 @ SV805 @ SV272 @ SV172 ) @ SY1694 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1693 @ SV805 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1693 @ SV805 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1693 @ SV805 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1693 @ SV805 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4883]) ).
thf(4965,plain,
! [SV752: $i,SV272: $i,SV692: $i,SV172: $i,SV723: $i,SV806: $i,SV792: $i] :
( ( ( ( ( ordered_pair @ SV792 @ SV806 )
!= SV723 ) )
= $true )
| ( ( ~ ( in @ SV792 @ SV172 ) )
= $true )
| ( ( ! [SY1695: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1695 @ SV806 @ SV792 @ SV723 @ SV692 @ SV272 @ SV172 ) @ SY1695 )
| ~ ~ ( in @ ( ordered_pair @ SV806 @ ( sK34_R @ SY1695 @ SV806 @ SV792 @ SV723 @ SV692 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV792 != SY1695 )
| ~ ( in @ SV806 @ SY1695 ) ) )
= $true )
| ( ( SV752 = SV723 )
= $false )
| ( ( in @ SV752 @ ( cartesian_product2 @ SV172 @ SV692 ) )
= $false )
| ( ( in @ SV723 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4884]) ).
thf(4966,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( ( ( ordered_pair @ ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) )
!= SV724 ) )
= $false )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4885]) ).
thf(4967,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( ~ ( in @ ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 ) @ SV172 ) )
= $false )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4885]) ).
thf(4968,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( ~ ! [SY1553: $i] :
( ~ ( in @ SY1553 @ ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) @ SY1553 ) @ SV272 ) ) )
= $false )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4886]) ).
thf(4969,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( ~ ~ ( ( ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4886]) ).
thf(4970,plain,
! [SV777: $i,SV272: $i,SV718: $i,SV172: $i,SV753: $i,SV821: $i] :
( ( ( ! [SY1712: $i] :
( ( ( ordered_pair @ SV821 @ SY1712 )
!= SV753 )
| ~ ( in @ SV821 @ SV172 )
| ! [SY1713: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1713 @ SY1712 @ SV821 @ SV753 @ SV718 @ SV272 @ SV172 ) @ SY1713 )
| ~ ~ ( in @ ( ordered_pair @ SY1712 @ ( sK34_R @ SY1713 @ SY1712 @ SV821 @ SV753 @ SV718 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV821 != SY1713 )
| ~ ( in @ SY1712 @ SY1713 ) ) ) )
= $true )
| ( ( SV777 = SV753 )
= $false )
| ( ( in @ SV777 @ ( cartesian_product2 @ SV172 @ SV718 ) )
= $false )
| ( ( in @ SV753 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4887]) ).
thf(4971,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( ( ( sK33_F @ SV754 @ SV718 @ SV272 @ SV172 )
!= SV754 ) )
= $false )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4888]) ).
thf(4972,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( ~ ( in @ ( sK33_F @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV718 ) ) )
= $false )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4888]) ).
thf(4973,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) )
!= SV754 )
| ~ ( in @ ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 ) @ SV172 ) ) )
= $false )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4889]) ).
thf(4974,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( ~ ~ ( ~ ! [SY1614: $i] :
( ~ ( in @ SY1614 @ ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) @ SY1614 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) ) ) ) )
= $false )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4889]) ).
thf(4975,plain,
! [SV778: $i,SV272: $i,SV719: $i,SV172: $i,SV755: $i,SV822: $i] :
( ( ( ! [SY1714: $i] :
( ( ( ordered_pair @ SV822 @ SY1714 )
!= SV755 )
| ~ ( in @ SV822 @ SV172 )
| ! [SY1715: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1715 @ SY1714 @ SV822 @ SV755 @ SV719 @ SV272 @ SV172 ) @ SY1715 )
| ~ ~ ( in @ ( ordered_pair @ SY1714 @ ( sK34_R @ SY1715 @ SY1714 @ SV822 @ SV755 @ SV719 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV822 != SY1715 )
| ~ ( in @ SY1714 @ SY1715 ) ) ) )
= $true )
| ( ( SV778 = SV755 )
= $false )
| ( ( in @ SV778 @ ( cartesian_product2 @ SV172 @ SV719 ) )
= $false )
| ( ( in @ SV755 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4890]) ).
thf(4976,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( ( ( sK33_F @ SV756 @ SV719 @ SV272 @ SV172 )
!= SV756 ) )
= $false )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4891]) ).
thf(4977,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( ~ ( in @ ( sK33_F @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV719 ) ) )
= $false )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4891]) ).
thf(4978,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) )
!= SV756 )
| ~ ( in @ ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 ) @ SV172 ) ) )
= $false )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4892]) ).
thf(4979,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( ~ ~ ( ~ ! [SY1619: $i] :
( ~ ( in @ SY1619 @ ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) @ SY1619 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) ) ) ) )
= $false )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4892]) ).
thf(4980,plain,
! [SV720: $i,SV272: $i,SV743: $i,SV172: $i,SV779: $i,SV813: $i] :
( ( ( ( SV813 != SV779 ) )
= $true )
| ( ( ~ ( in @ SV813 @ ( cartesian_product2 @ SV172 @ SV743 ) ) )
= $true )
| ( ( ! [SY1649: $i,SY1650: $i] :
( ( ( ordered_pair @ SY1649 @ SY1650 )
!= SV779 )
| ~ ( in @ SY1649 @ SV172 )
| ! [SY1651: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1651 @ SY1650 @ SY1649 @ SV779 @ SV743 @ SV272 @ SV172 ) @ SY1651 )
| ~ ~ ( in @ ( ordered_pair @ SY1650 @ ( sK34_R @ SY1651 @ SY1650 @ SY1649 @ SV779 @ SV743 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1649 != SY1651 )
| ~ ( in @ SY1650 @ SY1651 ) ) ) )
= $true )
| ( ( in @ SV779 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4893]) ).
thf(4981,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( ~ ~ ( ( ( sK33_F @ SV780 @ SV743 @ SV272 @ SV172 )
!= SV780 )
| ~ ( in @ ( sK33_F @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV743 ) ) ) )
= $false )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4894]) ).
thf(4982,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) )
!= SV780 )
| ~ ( in @ ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1652: $i] :
( ~ ( in @ SY1652 @ ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) @ SY1652 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) ) ) ) ) )
= $false )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4894]) ).
thf(4983,plain,
! [SV272: $i,SV744: $i,SV172: $i,SV781: $i,SV814: $i] :
( ( ( ( SV814 != SV781 ) )
= $true )
| ( ( ~ ( in @ SV814 @ ( cartesian_product2 @ SV172 @ SV744 ) ) )
= $true )
| ( ( ! [SY1654: $i,SY1655: $i] :
( ( ( ordered_pair @ SY1654 @ SY1655 )
!= SV781 )
| ~ ( in @ SY1654 @ SV172 )
| ! [SY1656: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1656 @ SY1655 @ SY1654 @ SV781 @ SV744 @ SV272 @ SV172 ) @ SY1656 )
| ~ ~ ( in @ ( ordered_pair @ SY1655 @ ( sK34_R @ SY1656 @ SY1655 @ SY1654 @ SV781 @ SV744 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1654 != SY1656 )
| ~ ( in @ SY1655 @ SY1656 ) ) ) )
= $true )
| ( ( in @ SV781 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4895]) ).
thf(4984,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( ~ ~ ( ( ( sK33_F @ SV782 @ SV744 @ SV272 @ SV172 )
!= SV782 )
| ~ ( in @ ( sK33_F @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV744 ) ) ) )
= $false )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4896]) ).
thf(4985,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) )
!= SV782 )
| ~ ( in @ ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1657: $i] :
( ~ ( in @ SY1657 @ ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) @ SY1657 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) ) ) ) ) )
= $false )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4896]) ).
thf(4986,plain,
! [SV272: $i,SV745: $i,SV172: $i,SV783: $i,SV815: $i] :
( ( ( ( SV815 != SV783 ) )
= $true )
| ( ( ~ ( in @ SV815 @ ( cartesian_product2 @ SV172 @ SV745 ) ) )
= $true )
| ( ( ! [SY1659: $i,SY1660: $i] :
( ( ( ordered_pair @ SY1659 @ SY1660 )
!= SV783 )
| ~ ( in @ SY1659 @ SV172 )
| ! [SY1661: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1661 @ SY1660 @ SY1659 @ SV783 @ SV745 @ SV272 @ SV172 ) @ SY1661 )
| ~ ~ ( in @ ( ordered_pair @ SY1660 @ ( sK34_R @ SY1661 @ SY1660 @ SY1659 @ SV783 @ SV745 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1659 != SY1661 )
| ~ ( in @ SY1660 @ SY1661 ) ) ) )
= $true )
| ( ( in @ SV783 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4897]) ).
thf(4987,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( ~ ~ ( ( ( sK33_F @ SV784 @ SV745 @ SV272 @ SV172 )
!= SV784 )
| ~ ( in @ ( sK33_F @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV745 ) ) ) )
= $false )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4898]) ).
thf(4988,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) )
!= SV784 )
| ~ ( in @ ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1662: $i] :
( ~ ( in @ SY1662 @ ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) @ SY1662 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) ) ) ) ) )
= $false )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4898]) ).
thf(4989,plain,
! [SV701: $i,SV172: $i,SV272: $i,SV622: $i,SV677: $i,SV746: $i,SV757: $i,SV807: $i] :
( ( ( ~ ( in @ ( sK34_R @ SV807 @ SV757 @ SV746 @ SV677 @ SV622 @ SV272 @ SV172 ) @ SV807 )
| ~ ~ ( in @ ( ordered_pair @ SV757 @ ( sK34_R @ SV807 @ SV757 @ SV746 @ SV677 @ SV622 @ SV272 @ SV172 ) ) @ SV272 ) )
= $false )
| ( ( ( SV746 != SV807 )
| ~ ( in @ SV757 @ SV807 ) )
= $true )
| ( ( ( ordered_pair @ SV746 @ SV757 )
= SV677 )
= $false )
| ( ( in @ SV746 @ SV172 )
= $false )
| ( ( SV701 = SV677 )
= $false )
| ( ( in @ SV701 @ ( cartesian_product2 @ SV172 @ SV622 ) )
= $false )
| ( ( in @ SV677 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4899]) ).
thf(4990,plain,
! [SV660: $i,SV728: $i,SV702: $i,SV785: $i,SV139: $i,SV773: $i] :
( ( ( in @ SV773 @ SV139 )
= $false )
| ( ( ( ordered_pair @ SV773 @ SV785 )
= SV702 )
= $false )
| ( ( ( SV785
!= ( singleton @ SV773 ) ) )
= $true )
| ( ( SV728 = SV702 )
= $false )
| ( ( in @ SV728 @ ( cartesian_product2 @ SV139 @ SV660 ) )
= $false )
| ( ( in @ SV702 @ ( sK13_C @ SV660 @ SV139 ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4903]) ).
thf(4991,plain,
! [SV765: $i,SV725: $i,SV139: $i,SV794: $i] :
( ( ( in @ SV794 @ ( cartesian_product2 @ SV139 @ SV725 ) )
= $false )
| ( ( SV794 = SV765 )
= $false )
| ( ( ! [SY1626: $i,SY1627: $i] :
( ( ( ordered_pair @ SY1626 @ SY1627 )
!= SV765 )
| ~ ( in @ SY1626 @ SV139 )
| ( SY1627
!= ( singleton @ SY1626 ) ) ) )
= $true )
| ( ( in @ SV765 @ ( sK13_C @ SV725 @ SV139 ) )
= $true )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4906]) ).
thf(4992,plain,
! [SV139: $i,SV725: $i,SV766: $i] :
( ( ( ( ( sK16_E @ SV766 @ SV725 @ SV139 )
!= SV766 )
| ~ ( in @ ( sK16_E @ SV766 @ SV725 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV725 ) ) )
= $false )
| ( ( in @ SV766 @ ( sK13_C @ SV725 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4907]) ).
thf(4993,plain,
! [SV139: $i,SV725: $i,SV766: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV766 @ SV725 @ SV139 ) @ ( sK15_SY612 @ SV766 @ SV725 @ SV139 ) )
!= SV766 )
| ~ ( in @ ( sK14_J @ SV766 @ SV725 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV766 @ SV725 @ SV139 )
!= ( singleton @ ( sK14_J @ SV766 @ SV725 @ SV139 ) ) ) )
= $false )
| ( ( in @ SV766 @ ( sK13_C @ SV725 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4908]) ).
thf(4994,plain,
! [SV767: $i,SV726: $i,SV139: $i,SV795: $i] :
( ( ( in @ SV795 @ ( cartesian_product2 @ SV139 @ SV726 ) )
= $false )
| ( ( SV795 = SV767 )
= $false )
| ( ( ! [SY1629: $i,SY1630: $i] :
( ( ( ordered_pair @ SY1629 @ SY1630 )
!= SV767 )
| ~ ( in @ SY1629 @ SV139 )
| ( SY1630
!= ( singleton @ SY1629 ) ) ) )
= $true )
| ( ( in @ SV767 @ ( sK13_C @ SV726 @ SV139 ) )
= $true )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4909]) ).
thf(4995,plain,
! [SV139: $i,SV726: $i,SV768: $i] :
( ( ( ( ( sK16_E @ SV768 @ SV726 @ SV139 )
!= SV768 )
| ~ ( in @ ( sK16_E @ SV768 @ SV726 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV726 ) ) )
= $false )
| ( ( in @ SV768 @ ( sK13_C @ SV726 @ SV139 ) )
= $false )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4910]) ).
thf(4996,plain,
! [SV139: $i,SV726: $i,SV768: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV768 @ SV726 @ SV139 ) @ ( sK15_SY612 @ SV768 @ SV726 @ SV139 ) )
!= SV768 )
| ~ ( in @ ( sK14_J @ SV768 @ SV726 @ SV139 ) @ SV139 ) )
| ( ( sK15_SY612 @ SV768 @ SV726 @ SV139 )
!= ( singleton @ ( sK14_J @ SV768 @ SV726 @ SV139 ) ) ) )
= $false )
| ( ( in @ SV768 @ ( sK13_C @ SV726 @ SV139 ) )
= $false )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4911]) ).
thf(4997,plain,
! [SV694: $i,SV769: $i,SV139: $i,SV729: $i,SV816: $i,SV808: $i] :
( ( ( ( ( ordered_pair @ SV808 @ SV816 )
!= SV729 )
| ~ ( in @ SV808 @ SV139 ) )
= $true )
| ( ( ( SV816
!= ( singleton @ SV808 ) ) )
= $true )
| ( ( SV769 = SV729 )
= $false )
| ( ( in @ SV769 @ ( cartesian_product2 @ SV139 @ SV694 ) )
= $false )
| ( ( in @ SV729 @ ( sK13_C @ SV694 @ SV139 ) )
= $true )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4912]) ).
thf(4998,plain,
! [SV139: $i,SV694: $i,SV730: $i] :
( ( ( ( ( ordered_pair @ ( sK14_J @ SV730 @ SV694 @ SV139 ) @ ( sK15_SY612 @ SV730 @ SV694 @ SV139 ) )
!= SV730 )
| ~ ( in @ ( sK14_J @ SV730 @ SV694 @ SV139 ) @ SV139 ) )
= $false )
| ( ( in @ SV730 @ ( sK13_C @ SV694 @ SV139 ) )
= $false )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4915]) ).
thf(4999,plain,
! [SV661: $i,SV731: $i,SV705: $i,SV786: $i,SV139: $i,SV774: $i] :
( ( ( in @ SV774 @ SV139 )
= $false )
| ( ( ( ordered_pair @ SV774 @ SV786 )
= SV705 )
= $false )
| ( ( ( SV786
!= ( singleton @ SV774 ) ) )
= $true )
| ( ( SV731 = SV705 )
= $false )
| ( ( in @ SV731 @ ( cartesian_product2 @ SV139 @ SV661 ) )
= $false )
| ( ( in @ SV705 @ ( sK13_C @ SV661 @ SV139 ) )
= $true )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4917]) ).
thf(5000,plain,
! [SV662: $i,SV732: $i,SV707: $i,SV787: $i,SV139: $i,SV775: $i] :
( ( ( in @ SV775 @ SV139 )
= $false )
| ( ( ( ordered_pair @ SV775 @ SV787 )
= SV707 )
= $false )
| ( ( ( SV787
!= ( singleton @ SV775 ) ) )
= $true )
| ( ( SV732 = SV707 )
= $false )
| ( ( in @ SV732 @ ( cartesian_product2 @ SV139 @ SV662 ) )
= $false )
| ( ( in @ SV707 @ ( sK13_C @ SV662 @ SV139 ) )
= $true )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4920]) ).
thf(5001,plain,
! [SV733: $i,SV265: $i,SV796: $i,SV145: $i,SV817: $i] :
( ( ( ~ ( in @ SV817 @ SV145 ) )
= $true )
| ( ( ! [SY1707: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1707 @ SV817 @ SV796 @ SV265 @ SV145 ) @ SY1707 )
| ~ ~ ( in @ ( ordered_pair @ SV796 @ ( sK47_K @ SY1707 @ SV817 @ SV796 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV817 != SY1707 )
| ~ ( in @ SV796 @ SY1707 ) ) )
= $true )
| ( ( in @ SV796 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4923]) ).
thf(5002,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV797: $i] :
( ( ( ~ ( in @ ( sK45_E @ SV797 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1667: $i] :
( ~ ( in @ SY1667 @ ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV797 @ SY1667 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV797 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) )
| ~ ( in @ SV797 @ ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) ) ) ) )
= $false )
| ( ( in @ SV797 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4924]) ).
thf(5003,plain,
! [SV265: $i,SV798: $i,SV145: $i,SV818: $i] :
( ( ( ~ ( in @ SV818 @ SV145 ) )
= $true )
| ( ( ! [SY1708: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1708 @ SV818 @ SV798 @ SV265 @ SV145 ) @ SY1708 )
| ~ ~ ( in @ ( ordered_pair @ SV798 @ ( sK47_K @ SY1708 @ SV818 @ SV798 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV818 != SY1708 )
| ~ ( in @ SV798 @ SY1708 ) ) )
= $true )
| ( ( in @ SV798 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4925]) ).
thf(5004,plain,
! [SV145: $i,SV265: $i,SV799: $i] :
( ( ( ~ ( in @ ( sK45_E @ SV799 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1670: $i] :
( ~ ( in @ SY1670 @ ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV799 @ SY1670 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV799 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) )
| ~ ( in @ SV799 @ ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) ) ) ) )
= $false )
| ( ( in @ SV799 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4926]) ).
thf(5005,plain,
! [SV265: $i,SV800: $i,SV145: $i,SV819: $i] :
( ( ( ~ ( in @ SV819 @ SV145 ) )
= $true )
| ( ( ! [SY1709: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1709 @ SV819 @ SV800 @ SV265 @ SV145 ) @ SY1709 )
| ~ ~ ( in @ ( ordered_pair @ SV800 @ ( sK47_K @ SY1709 @ SV819 @ SV800 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV819 != SY1709 )
| ~ ( in @ SV800 @ SY1709 ) ) )
= $true )
| ( ( in @ SV800 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4927]) ).
thf(5006,plain,
! [SV145: $i,SV265: $i,SV801: $i] :
( ( ( ~ ( in @ ( sK45_E @ SV801 @ SV265 @ SV145 ) @ SV145 )
| ~ ~ ( ~ ! [SY1673: $i] :
( ~ ( in @ SY1673 @ ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV801 @ SY1673 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV801 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) )
| ~ ( in @ SV801 @ ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) ) ) ) )
= $false )
| ( ( in @ SV801 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4928]) ).
thf(5007,plain,
! [SV145: $i,SV265: $i,SV734: $i,SV760: $i,SV788: $i] :
( ( ( in @ ( sK47_K @ SV788 @ SV760 @ SV734 @ SV265 @ SV145 ) @ SV788 )
= $true )
| ( ( ( SV760 != SV788 )
| ~ ( in @ SV734 @ SV788 ) )
= $true )
| ( ( in @ SV760 @ SV145 )
= $false )
| ( ( in @ SV734 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4929]) ).
thf(5008,plain,
! [SV145: $i,SV265: $i,SV760: $i,SV788: $i,SV734: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV734 @ ( sK47_K @ SV788 @ SV760 @ SV734 @ SV265 @ SV145 ) ) @ SV265 ) )
= $true )
| ( ( ( SV760 != SV788 )
| ~ ( in @ SV734 @ SV788 ) )
= $true )
| ( ( in @ SV760 @ SV145 )
= $false )
| ( ( in @ SV734 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4930]) ).
thf(5009,plain,
! [SV145: $i,SV265: $i,SV735: $i,SV823: $i] :
( ( ( ~ ( in @ SV823 @ ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV735 @ SV823 ) @ SV265 ) )
= $true )
| ( ( in @ SV735 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4931]) ).
thf(5010,plain,
! [SV145: $i,SV265: $i,SV735: $i] :
( ( ( ( ( sK45_E @ SV735 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) )
| ~ ( in @ SV735 @ ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) ) )
= $false )
| ( ( in @ SV735 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4932]) ).
thf(5011,plain,
! [SV145: $i,SV265: $i,SV727: $i,SV761: $i,SV711: $i] :
( ( ( in @ SV711 @ SV761 )
= $false )
| ( ( SV727 = SV761 )
= $false )
| ( ( in @ ( sK47_K @ SV761 @ SV727 @ SV711 @ SV265 @ SV145 ) @ SV761 )
= $true )
| ( ( in @ SV727 @ SV145 )
= $false )
| ( ( in @ SV711 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4933]) ).
thf(5012,plain,
! [SV145: $i,SV265: $i,SV711: $i,SV761: $i,SV727: $i] :
( ( ( SV727 = SV761 )
= $false )
| ( ( ~ ( in @ SV711 @ SV761 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV711 @ ( sK47_K @ SV761 @ SV727 @ SV711 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( in @ SV727 @ SV145 )
= $false )
| ( ( in @ SV711 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4934]) ).
thf(5013,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV736: $i,SV762: $i,SV789: $i] :
( ( ( in @ ( sK47_K @ SV789 @ SV762 @ SV736 @ SV265 @ SV145 ) @ SV789 )
= $true )
| ( ( ( SV762 != SV789 )
| ~ ( in @ SV736 @ SV789 ) )
= $true )
| ( ( in @ SV762 @ SV145 )
= $false )
| ( ( in @ SV736 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4938]) ).
thf(5014,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV762: $i,SV789: $i,SV736: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV736 @ ( sK47_K @ SV789 @ SV762 @ SV736 @ SV265 @ SV145 ) ) @ SV265 ) )
= $true )
| ( ( ( SV762 != SV789 )
| ~ ( in @ SV736 @ SV789 ) )
= $true )
| ( ( in @ SV762 @ SV145 )
= $false )
| ( ( in @ SV736 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4939]) ).
thf(5015,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV737: $i,SV824: $i] :
( ( ( ~ ( in @ SV824 @ ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV737 @ SV824 ) @ SV265 ) )
= $true )
| ( ( in @ SV737 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4940]) ).
thf(5016,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV737: $i] :
( ( ( ( ( sK45_E @ SV737 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) )
| ~ ( in @ SV737 @ ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) ) )
= $false )
| ( ( in @ SV737 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4941]) ).
thf(5017,plain,
! [SV145: $i,SV265: $i,SV738: $i,SV763: $i,SV790: $i] :
( ( ( in @ ( sK47_K @ SV790 @ SV763 @ SV738 @ SV265 @ SV145 ) @ SV790 )
= $true )
| ( ( ( SV763 != SV790 )
| ~ ( in @ SV738 @ SV790 ) )
= $true )
| ( ( in @ SV763 @ SV145 )
= $false )
| ( ( in @ SV738 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4942]) ).
thf(5018,plain,
! [SV145: $i,SV265: $i,SV763: $i,SV790: $i,SV738: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV738 @ ( sK47_K @ SV790 @ SV763 @ SV738 @ SV265 @ SV145 ) ) @ SV265 ) )
= $true )
| ( ( ( SV763 != SV790 )
| ~ ( in @ SV738 @ SV790 ) )
= $true )
| ( ( in @ SV763 @ SV145 )
= $false )
| ( ( in @ SV738 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4943]) ).
thf(5019,plain,
! [SV145: $i,SV265: $i,SV739: $i,SV825: $i] :
( ( ( ~ ( in @ SV825 @ ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV739 @ SV825 ) @ SV265 ) )
= $true )
| ( ( in @ SV739 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4944]) ).
thf(5020,plain,
! [SV145: $i,SV265: $i,SV739: $i] :
( ( ( ( ( sK45_E @ SV739 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) )
| ~ ( in @ SV739 @ ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) ) )
= $false )
| ( ( in @ SV739 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4945]) ).
thf(5021,plain,
! [SV145: $i,SV265: $i,SV740: $i,SV764: $i,SV791: $i] :
( ( ( in @ ( sK47_K @ SV791 @ SV764 @ SV740 @ SV265 @ SV145 ) @ SV791 )
= $true )
| ( ( ( SV764 != SV791 )
| ~ ( in @ SV740 @ SV791 ) )
= $true )
| ( ( in @ SV764 @ SV145 )
= $false )
| ( ( in @ SV740 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4946]) ).
thf(5022,plain,
! [SV145: $i,SV265: $i,SV764: $i,SV791: $i,SV740: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV740 @ ( sK47_K @ SV791 @ SV764 @ SV740 @ SV265 @ SV145 ) ) @ SV265 ) )
= $true )
| ( ( ( SV764 != SV791 )
| ~ ( in @ SV740 @ SV791 ) )
= $true )
| ( ( in @ SV764 @ SV145 )
= $false )
| ( ( in @ SV740 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4947]) ).
thf(5023,plain,
! [SV145: $i,SV265: $i,SV741: $i,SV826: $i] :
( ( ( ~ ( in @ SV826 @ ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV741 @ SV826 ) @ SV265 ) )
= $true )
| ( ( in @ SV741 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4948]) ).
thf(5024,plain,
! [SV145: $i,SV265: $i,SV741: $i] :
( ( ( ( ( sK45_E @ SV741 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) )
| ~ ( in @ SV741 @ ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) ) )
= $false )
| ( ( in @ SV741 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4949]) ).
thf(5025,plain,
! [SV776: $i,SV272: $i,SV717: $i,SV172: $i,SV750: $i,SV827: $i,SV820: $i] :
( ( ( ( ( ordered_pair @ SV820 @ SV827 )
!= SV750 )
| ~ ( in @ SV820 @ SV172 )
| ! [SY1716: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1716 @ SV827 @ SV820 @ SV750 @ SV717 @ SV272 @ SV172 ) @ SY1716 )
| ~ ~ ( in @ ( ordered_pair @ SV827 @ ( sK34_R @ SY1716 @ SV827 @ SV820 @ SV750 @ SV717 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV820 != SY1716 )
| ~ ( in @ SV827 @ SY1716 ) ) )
= $true )
| ( ( SV776 = SV750 )
= $false )
| ( ( in @ SV776 @ ( cartesian_product2 @ SV172 @ SV717 ) )
= $false )
| ( ( in @ SV750 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4950]) ).
thf(5026,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( ( sK33_F @ SV751 @ SV717 @ SV272 @ SV172 )
= SV751 )
= $true )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4951]) ).
thf(5027,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( in @ ( sK33_F @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV717 ) )
= $true )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4952]) ).
thf(5028,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) )
!= SV751 )
| ~ ( in @ ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 ) @ SV172 ) ) )
= $true )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4953]) ).
thf(5029,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( ~ ( ~ ! [SY1609: $i] :
( ~ ( in @ SY1609 @ ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) @ SY1609 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) ) ) ) )
= $true )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4954]) ).
thf(5030,plain,
! [SV272: $i,SV770: $i,SV172: $i,SV809: $i] :
( ( ( ! [SY1697: $i] :
( ( SY1697 != SV809 )
| ~ ( in @ SY1697 @ ( cartesian_product2 @ SV172 @ SV770 ) ) ) )
= $true )
| ( ( ! [SY1698: $i,SY1699: $i] :
( ( ( ordered_pair @ SY1698 @ SY1699 )
!= SV809 )
| ~ ( in @ SY1698 @ SV172 )
| ! [SY1700: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1700 @ SY1699 @ SY1698 @ SV809 @ SV770 @ SV272 @ SV172 ) @ SY1700 )
| ~ ~ ( in @ ( ordered_pair @ SY1699 @ ( sK34_R @ SY1700 @ SY1699 @ SY1698 @ SV809 @ SV770 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1698 != SY1700 )
| ~ ( in @ SY1699 @ SY1700 ) ) ) )
= $true )
| ( ( in @ SV809 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4955]) ).
thf(5031,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK33_F @ SV810 @ SV770 @ SV272 @ SV172 )
!= SV810 )
| ~ ( in @ ( sK33_F @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV770 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) )
!= SV810 )
| ~ ( in @ ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1701: $i] :
( ~ ( in @ SY1701 @ ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) @ SY1701 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4956]) ).
thf(5032,plain,
! [SV272: $i,SV771: $i,SV172: $i,SV811: $i] :
( ( ( ! [SY1702: $i] :
( ( SY1702 != SV811 )
| ~ ( in @ SY1702 @ ( cartesian_product2 @ SV172 @ SV771 ) ) ) )
= $true )
| ( ( ! [SY1703: $i,SY1704: $i] :
( ( ( ordered_pair @ SY1703 @ SY1704 )
!= SV811 )
| ~ ( in @ SY1703 @ SV172 )
| ! [SY1705: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1705 @ SY1704 @ SY1703 @ SV811 @ SV771 @ SV272 @ SV172 ) @ SY1705 )
| ~ ~ ( in @ ( ordered_pair @ SY1704 @ ( sK34_R @ SY1705 @ SY1704 @ SY1703 @ SV811 @ SV771 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1703 != SY1705 )
| ~ ( in @ SY1704 @ SY1705 ) ) ) )
= $true )
| ( ( in @ SV811 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4957]) ).
thf(5033,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK33_F @ SV812 @ SV771 @ SV272 @ SV172 )
!= SV812 )
| ~ ( in @ ( sK33_F @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV771 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) )
!= SV812 )
| ~ ( in @ ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1706: $i] :
( ~ ( in @ SY1706 @ ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) @ SY1706 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4958]) ).
thf(5034,plain,
! [SV772: $i,SV272: $i,SV803: $i,SV172: $i] :
( ( ( ! [SY1674: $i] :
( ! [SY1675: $i] :
( ( SY1675 != SY1674 )
| ~ ( in @ SY1675 @ ( cartesian_product2 @ SV172 @ SV803 ) ) )
| ! [SY1676: $i,SY1677: $i] :
( ( ( ordered_pair @ SY1676 @ SY1677 )
!= SY1674 )
| ~ ( in @ SY1676 @ SV172 )
| ! [SY1678: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1678 @ SY1677 @ SY1676 @ SY1674 @ SV803 @ SV272 @ SV172 ) @ SY1678 )
| ~ ~ ( in @ ( ordered_pair @ SY1677 @ ( sK34_R @ SY1678 @ SY1677 @ SY1676 @ SY1674 @ SV803 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1676 != SY1678 )
| ~ ( in @ SY1677 @ SY1678 ) ) )
| ( in @ SY1674 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4959]) ).
thf(5035,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i] :
( ( ( ! [SY1679: $i] :
( ~ ( in @ SY1679 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1679 @ SV803 @ SV272 @ SV172 )
!= SY1679 )
| ~ ( in @ ( sK33_F @ SY1679 @ SV803 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV803 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1679 @ SV803 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1679 @ SV803 @ SV272 @ SV172 ) )
!= SY1679 )
| ~ ( in @ ( sK30_O @ SY1679 @ SV803 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1680: $i] :
( ~ ( in @ SY1680 @ ( sK32_SY652 @ SY1679 @ SV803 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1679 @ SV803 @ SV272 @ SV172 ) @ SY1680 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1679 @ SV803 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1679 @ SV803 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1679 @ SV803 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1679 @ SV803 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4960]) ).
thf(5036,plain,
! [SV272: $i,SV804: $i,SV172: $i] :
( ( ( ! [SY1681: $i] :
( ! [SY1682: $i] :
( ( SY1682 != SY1681 )
| ~ ( in @ SY1682 @ ( cartesian_product2 @ SV172 @ SV804 ) ) )
| ! [SY1683: $i,SY1684: $i] :
( ( ( ordered_pair @ SY1683 @ SY1684 )
!= SY1681 )
| ~ ( in @ SY1683 @ SV172 )
| ! [SY1685: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1685 @ SY1684 @ SY1683 @ SY1681 @ SV804 @ SV272 @ SV172 ) @ SY1685 )
| ~ ~ ( in @ ( ordered_pair @ SY1684 @ ( sK34_R @ SY1685 @ SY1684 @ SY1683 @ SY1681 @ SV804 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1683 != SY1685 )
| ~ ( in @ SY1684 @ SY1685 ) ) )
| ( in @ SY1681 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) ) ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4961]) ).
thf(5037,plain,
! [SV172: $i,SV272: $i,SV804: $i] :
( ( ( ! [SY1686: $i] :
( ~ ( in @ SY1686 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1686 @ SV804 @ SV272 @ SV172 )
!= SY1686 )
| ~ ( in @ ( sK33_F @ SY1686 @ SV804 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV804 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1686 @ SV804 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1686 @ SV804 @ SV272 @ SV172 ) )
!= SY1686 )
| ~ ( in @ ( sK30_O @ SY1686 @ SV804 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1687: $i] :
( ~ ( in @ SY1687 @ ( sK32_SY652 @ SY1686 @ SV804 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1686 @ SV804 @ SV272 @ SV172 ) @ SY1687 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1686 @ SV804 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1686 @ SV804 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1686 @ SV804 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1686 @ SV804 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4962]) ).
thf(5038,plain,
! [SV272: $i,SV805: $i,SV172: $i] :
( ( ( ! [SY1688: $i] :
( ! [SY1689: $i] :
( ( SY1689 != SY1688 )
| ~ ( in @ SY1689 @ ( cartesian_product2 @ SV172 @ SV805 ) ) )
| ! [SY1690: $i,SY1691: $i] :
( ( ( ordered_pair @ SY1690 @ SY1691 )
!= SY1688 )
| ~ ( in @ SY1690 @ SV172 )
| ! [SY1692: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1692 @ SY1691 @ SY1690 @ SY1688 @ SV805 @ SV272 @ SV172 ) @ SY1692 )
| ~ ~ ( in @ ( ordered_pair @ SY1691 @ ( sK34_R @ SY1692 @ SY1691 @ SY1690 @ SY1688 @ SV805 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1690 != SY1692 )
| ~ ( in @ SY1691 @ SY1692 ) ) )
| ( in @ SY1688 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) ) ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4963]) ).
thf(5039,plain,
! [SV172: $i,SV272: $i,SV805: $i] :
( ( ( ! [SY1693: $i] :
( ~ ( in @ SY1693 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SY1693 @ SV805 @ SV272 @ SV172 )
!= SY1693 )
| ~ ( in @ ( sK33_F @ SY1693 @ SV805 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV805 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SY1693 @ SV805 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SY1693 @ SV805 @ SV272 @ SV172 ) )
!= SY1693 )
| ~ ( in @ ( sK30_O @ SY1693 @ SV805 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1694: $i] :
( ~ ( in @ SY1694 @ ( sK32_SY652 @ SY1693 @ SV805 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SY1693 @ SV805 @ SV272 @ SV172 ) @ SY1694 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SY1693 @ SV805 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SY1693 @ SV805 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SY1693 @ SV805 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SY1693 @ SV805 @ SV272 @ SV172 ) ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4964]) ).
thf(5040,plain,
! [SV752: $i,SV272: $i,SV692: $i,SV172: $i,SV723: $i,SV806: $i,SV792: $i] :
( ( ( ( ordered_pair @ SV792 @ SV806 )
= SV723 )
= $false )
| ( ( ~ ( in @ SV792 @ SV172 ) )
= $true )
| ( ( ! [SY1695: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1695 @ SV806 @ SV792 @ SV723 @ SV692 @ SV272 @ SV172 ) @ SY1695 )
| ~ ~ ( in @ ( ordered_pair @ SV806 @ ( sK34_R @ SY1695 @ SV806 @ SV792 @ SV723 @ SV692 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV792 != SY1695 )
| ~ ( in @ SV806 @ SY1695 ) ) )
= $true )
| ( ( SV752 = SV723 )
= $false )
| ( ( in @ SV752 @ ( cartesian_product2 @ SV172 @ SV692 ) )
= $false )
| ( ( in @ SV723 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4965]) ).
thf(5041,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( ( ordered_pair @ ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) )
= SV724 )
= $true )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4966]) ).
thf(5042,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( in @ ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4967]) ).
thf(5043,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( ! [SY1553: $i] :
( ~ ( in @ SY1553 @ ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) @ SY1553 ) @ SV272 ) ) )
= $true )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4968]) ).
thf(5044,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( ~ ( ( ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) ) ) )
= $true )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4969]) ).
thf(5045,plain,
! [SV777: $i,SV272: $i,SV718: $i,SV172: $i,SV753: $i,SV828: $i,SV821: $i] :
( ( ( ( ( ordered_pair @ SV821 @ SV828 )
!= SV753 )
| ~ ( in @ SV821 @ SV172 )
| ! [SY1717: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1717 @ SV828 @ SV821 @ SV753 @ SV718 @ SV272 @ SV172 ) @ SY1717 )
| ~ ~ ( in @ ( ordered_pair @ SV828 @ ( sK34_R @ SY1717 @ SV828 @ SV821 @ SV753 @ SV718 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV821 != SY1717 )
| ~ ( in @ SV828 @ SY1717 ) ) )
= $true )
| ( ( SV777 = SV753 )
= $false )
| ( ( in @ SV777 @ ( cartesian_product2 @ SV172 @ SV718 ) )
= $false )
| ( ( in @ SV753 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4970]) ).
thf(5046,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( ( sK33_F @ SV754 @ SV718 @ SV272 @ SV172 )
= SV754 )
= $true )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4971]) ).
thf(5047,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( in @ ( sK33_F @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV718 ) )
= $true )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4972]) ).
thf(5048,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) )
!= SV754 )
| ~ ( in @ ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 ) @ SV172 ) ) )
= $true )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4973]) ).
thf(5049,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( ~ ( ~ ! [SY1614: $i] :
( ~ ( in @ SY1614 @ ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) @ SY1614 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) ) ) ) )
= $true )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4974]) ).
thf(5050,plain,
! [SV778: $i,SV272: $i,SV719: $i,SV172: $i,SV755: $i,SV829: $i,SV822: $i] :
( ( ( ( ( ordered_pair @ SV822 @ SV829 )
!= SV755 )
| ~ ( in @ SV822 @ SV172 )
| ! [SY1718: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1718 @ SV829 @ SV822 @ SV755 @ SV719 @ SV272 @ SV172 ) @ SY1718 )
| ~ ~ ( in @ ( ordered_pair @ SV829 @ ( sK34_R @ SY1718 @ SV829 @ SV822 @ SV755 @ SV719 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV822 != SY1718 )
| ~ ( in @ SV829 @ SY1718 ) ) )
= $true )
| ( ( SV778 = SV755 )
= $false )
| ( ( in @ SV778 @ ( cartesian_product2 @ SV172 @ SV719 ) )
= $false )
| ( ( in @ SV755 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4975]) ).
thf(5051,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( ( sK33_F @ SV756 @ SV719 @ SV272 @ SV172 )
= SV756 )
= $true )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4976]) ).
thf(5052,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( in @ ( sK33_F @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV719 ) )
= $true )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4977]) ).
thf(5053,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) )
!= SV756 )
| ~ ( in @ ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 ) @ SV172 ) ) )
= $true )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4978]) ).
thf(5054,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( ~ ( ~ ! [SY1619: $i] :
( ~ ( in @ SY1619 @ ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) @ SY1619 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) ) ) ) )
= $true )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4979]) ).
thf(5055,plain,
! [SV720: $i,SV272: $i,SV743: $i,SV172: $i,SV779: $i,SV813: $i] :
( ( ( SV813 = SV779 )
= $false )
| ( ( ~ ( in @ SV813 @ ( cartesian_product2 @ SV172 @ SV743 ) ) )
= $true )
| ( ( ! [SY1649: $i,SY1650: $i] :
( ( ( ordered_pair @ SY1649 @ SY1650 )
!= SV779 )
| ~ ( in @ SY1649 @ SV172 )
| ! [SY1651: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1651 @ SY1650 @ SY1649 @ SV779 @ SV743 @ SV272 @ SV172 ) @ SY1651 )
| ~ ~ ( in @ ( ordered_pair @ SY1650 @ ( sK34_R @ SY1651 @ SY1650 @ SY1649 @ SV779 @ SV743 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1649 != SY1651 )
| ~ ( in @ SY1650 @ SY1651 ) ) ) )
= $true )
| ( ( in @ SV779 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4980]) ).
thf(5056,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( ~ ( ( ( sK33_F @ SV780 @ SV743 @ SV272 @ SV172 )
!= SV780 )
| ~ ( in @ ( sK33_F @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV743 ) ) ) )
= $true )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4981]) ).
thf(5057,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) )
!= SV780 )
| ~ ( in @ ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1652: $i] :
( ~ ( in @ SY1652 @ ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) @ SY1652 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) ) ) ) ) )
= $true )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4982]) ).
thf(5058,plain,
! [SV272: $i,SV744: $i,SV172: $i,SV781: $i,SV814: $i] :
( ( ( SV814 = SV781 )
= $false )
| ( ( ~ ( in @ SV814 @ ( cartesian_product2 @ SV172 @ SV744 ) ) )
= $true )
| ( ( ! [SY1654: $i,SY1655: $i] :
( ( ( ordered_pair @ SY1654 @ SY1655 )
!= SV781 )
| ~ ( in @ SY1654 @ SV172 )
| ! [SY1656: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1656 @ SY1655 @ SY1654 @ SV781 @ SV744 @ SV272 @ SV172 ) @ SY1656 )
| ~ ~ ( in @ ( ordered_pair @ SY1655 @ ( sK34_R @ SY1656 @ SY1655 @ SY1654 @ SV781 @ SV744 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1654 != SY1656 )
| ~ ( in @ SY1655 @ SY1656 ) ) ) )
= $true )
| ( ( in @ SV781 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4983]) ).
thf(5059,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( ~ ( ( ( sK33_F @ SV782 @ SV744 @ SV272 @ SV172 )
!= SV782 )
| ~ ( in @ ( sK33_F @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV744 ) ) ) )
= $true )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4984]) ).
thf(5060,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) )
!= SV782 )
| ~ ( in @ ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1657: $i] :
( ~ ( in @ SY1657 @ ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) @ SY1657 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) ) ) ) ) )
= $true )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4985]) ).
thf(5061,plain,
! [SV272: $i,SV745: $i,SV172: $i,SV783: $i,SV815: $i] :
( ( ( SV815 = SV783 )
= $false )
| ( ( ~ ( in @ SV815 @ ( cartesian_product2 @ SV172 @ SV745 ) ) )
= $true )
| ( ( ! [SY1659: $i,SY1660: $i] :
( ( ( ordered_pair @ SY1659 @ SY1660 )
!= SV783 )
| ~ ( in @ SY1659 @ SV172 )
| ! [SY1661: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1661 @ SY1660 @ SY1659 @ SV783 @ SV745 @ SV272 @ SV172 ) @ SY1661 )
| ~ ~ ( in @ ( ordered_pair @ SY1660 @ ( sK34_R @ SY1661 @ SY1660 @ SY1659 @ SV783 @ SV745 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1659 != SY1661 )
| ~ ( in @ SY1660 @ SY1661 ) ) ) )
= $true )
| ( ( in @ SV783 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4986]) ).
thf(5062,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( ~ ( ( ( sK33_F @ SV784 @ SV745 @ SV272 @ SV172 )
!= SV784 )
| ~ ( in @ ( sK33_F @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV745 ) ) ) )
= $true )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4987]) ).
thf(5063,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) )
!= SV784 )
| ~ ( in @ ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1662: $i] :
( ~ ( in @ SY1662 @ ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) @ SY1662 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) ) ) ) ) )
= $true )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4988]) ).
thf(5064,plain,
! [SV701: $i,SV172: $i,SV272: $i,SV622: $i,SV677: $i,SV746: $i,SV757: $i,SV807: $i] :
( ( ( ~ ( in @ ( sK34_R @ SV807 @ SV757 @ SV746 @ SV677 @ SV622 @ SV272 @ SV172 ) @ SV807 ) )
= $false )
| ( ( ( SV746 != SV807 )
| ~ ( in @ SV757 @ SV807 ) )
= $true )
| ( ( ( ordered_pair @ SV746 @ SV757 )
= SV677 )
= $false )
| ( ( in @ SV746 @ SV172 )
= $false )
| ( ( SV701 = SV677 )
= $false )
| ( ( in @ SV701 @ ( cartesian_product2 @ SV172 @ SV622 ) )
= $false )
| ( ( in @ SV677 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4989]) ).
thf(5065,plain,
! [SV701: $i,SV172: $i,SV272: $i,SV622: $i,SV677: $i,SV746: $i,SV807: $i,SV757: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV757 @ ( sK34_R @ SV807 @ SV757 @ SV746 @ SV677 @ SV622 @ SV272 @ SV172 ) ) @ SV272 ) )
= $false )
| ( ( ( SV746 != SV807 )
| ~ ( in @ SV757 @ SV807 ) )
= $true )
| ( ( ( ordered_pair @ SV746 @ SV757 )
= SV677 )
= $false )
| ( ( in @ SV746 @ SV172 )
= $false )
| ( ( SV701 = SV677 )
= $false )
| ( ( in @ SV701 @ ( cartesian_product2 @ SV172 @ SV622 ) )
= $false )
| ( ( in @ SV677 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4989]) ).
thf(5066,plain,
! [SV660: $i,SV728: $i,SV139: $i,SV702: $i,SV773: $i,SV785: $i] :
( ( ( SV785
= ( singleton @ SV773 ) )
= $false )
| ( ( ( ordered_pair @ SV773 @ SV785 )
= SV702 )
= $false )
| ( ( in @ SV773 @ SV139 )
= $false )
| ( ( SV728 = SV702 )
= $false )
| ( ( in @ SV728 @ ( cartesian_product2 @ SV139 @ SV660 ) )
= $false )
| ( ( in @ SV702 @ ( sK13_C @ SV660 @ SV139 ) )
= $true )
| ( ( ( sK17_C @ SV139 )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4990]) ).
thf(5067,plain,
! [SV725: $i,SV794: $i,SV139: $i,SV765: $i,SV830: $i] :
( ( ( ! [SY1719: $i] :
( ( ( ordered_pair @ SV830 @ SY1719 )
!= SV765 )
| ~ ( in @ SV830 @ SV139 )
| ( SY1719
!= ( singleton @ SV830 ) ) ) )
= $true )
| ( ( SV794 = SV765 )
= $false )
| ( ( in @ SV794 @ ( cartesian_product2 @ SV139 @ SV725 ) )
= $false )
| ( ( in @ SV765 @ ( sK13_C @ SV725 @ SV139 ) )
= $true )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4991]) ).
thf(5068,plain,
! [SV139: $i,SV725: $i,SV766: $i] :
( ( ( ( ( sK16_E @ SV766 @ SV725 @ SV139 )
!= SV766 ) )
= $false )
| ( ( in @ SV766 @ ( sK13_C @ SV725 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4992]) ).
thf(5069,plain,
! [SV139: $i,SV725: $i,SV766: $i] :
( ( ( ~ ( in @ ( sK16_E @ SV766 @ SV725 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV725 ) ) )
= $false )
| ( ( in @ SV766 @ ( sK13_C @ SV725 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4992]) ).
thf(5070,plain,
! [SV139: $i,SV725: $i,SV766: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV766 @ SV725 @ SV139 ) @ ( sK15_SY612 @ SV766 @ SV725 @ SV139 ) )
!= SV766 )
| ~ ( in @ ( sK14_J @ SV766 @ SV725 @ SV139 ) @ SV139 ) ) )
= $false )
| ( ( in @ SV766 @ ( sK13_C @ SV725 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4993]) ).
thf(5071,plain,
! [SV139: $i,SV725: $i,SV766: $i] :
( ( ( ( ( sK15_SY612 @ SV766 @ SV725 @ SV139 )
!= ( singleton @ ( sK14_J @ SV766 @ SV725 @ SV139 ) ) ) )
= $false )
| ( ( in @ SV766 @ ( sK13_C @ SV725 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4993]) ).
thf(5072,plain,
! [SV726: $i,SV795: $i,SV139: $i,SV767: $i,SV831: $i] :
( ( ( ! [SY1720: $i] :
( ( ( ordered_pair @ SV831 @ SY1720 )
!= SV767 )
| ~ ( in @ SV831 @ SV139 )
| ( SY1720
!= ( singleton @ SV831 ) ) ) )
= $true )
| ( ( SV795 = SV767 )
= $false )
| ( ( in @ SV795 @ ( cartesian_product2 @ SV139 @ SV726 ) )
= $false )
| ( ( in @ SV767 @ ( sK13_C @ SV726 @ SV139 ) )
= $true )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4994]) ).
thf(5073,plain,
! [SV139: $i,SV726: $i,SV768: $i] :
( ( ( ( ( sK16_E @ SV768 @ SV726 @ SV139 )
!= SV768 ) )
= $false )
| ( ( in @ SV768 @ ( sK13_C @ SV726 @ SV139 ) )
= $false )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4995]) ).
thf(5074,plain,
! [SV139: $i,SV726: $i,SV768: $i] :
( ( ( ~ ( in @ ( sK16_E @ SV768 @ SV726 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV726 ) ) )
= $false )
| ( ( in @ SV768 @ ( sK13_C @ SV726 @ SV139 ) )
= $false )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4995]) ).
thf(5075,plain,
! [SV139: $i,SV726: $i,SV768: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK14_J @ SV768 @ SV726 @ SV139 ) @ ( sK15_SY612 @ SV768 @ SV726 @ SV139 ) )
!= SV768 )
| ~ ( in @ ( sK14_J @ SV768 @ SV726 @ SV139 ) @ SV139 ) ) )
= $false )
| ( ( in @ SV768 @ ( sK13_C @ SV726 @ SV139 ) )
= $false )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4996]) ).
thf(5076,plain,
! [SV139: $i,SV726: $i,SV768: $i] :
( ( ( ( ( sK15_SY612 @ SV768 @ SV726 @ SV139 )
!= ( singleton @ ( sK14_J @ SV768 @ SV726 @ SV139 ) ) ) )
= $false )
| ( ( in @ SV768 @ ( sK13_C @ SV726 @ SV139 ) )
= $false )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4996]) ).
thf(5077,plain,
! [SV694: $i,SV769: $i,SV139: $i,SV729: $i,SV816: $i,SV808: $i] :
( ( ( ( ( ordered_pair @ SV808 @ SV816 )
!= SV729 ) )
= $true )
| ( ( ~ ( in @ SV808 @ SV139 ) )
= $true )
| ( ( ( SV816
!= ( singleton @ SV808 ) ) )
= $true )
| ( ( SV769 = SV729 )
= $false )
| ( ( in @ SV769 @ ( cartesian_product2 @ SV139 @ SV694 ) )
= $false )
| ( ( in @ SV729 @ ( sK13_C @ SV694 @ SV139 ) )
= $true )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4997]) ).
thf(5078,plain,
! [SV139: $i,SV694: $i,SV730: $i] :
( ( ( ( ( ordered_pair @ ( sK14_J @ SV730 @ SV694 @ SV139 ) @ ( sK15_SY612 @ SV730 @ SV694 @ SV139 ) )
!= SV730 ) )
= $false )
| ( ( in @ SV730 @ ( sK13_C @ SV694 @ SV139 ) )
= $false )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4998]) ).
thf(5079,plain,
! [SV139: $i,SV694: $i,SV730: $i] :
( ( ( ~ ( in @ ( sK14_J @ SV730 @ SV694 @ SV139 ) @ SV139 ) )
= $false )
| ( ( in @ SV730 @ ( sK13_C @ SV694 @ SV139 ) )
= $false )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4998]) ).
thf(5080,plain,
! [SV661: $i,SV731: $i,SV139: $i,SV705: $i,SV774: $i,SV786: $i] :
( ( ( SV786
= ( singleton @ SV774 ) )
= $false )
| ( ( ( ordered_pair @ SV774 @ SV786 )
= SV705 )
= $false )
| ( ( in @ SV774 @ SV139 )
= $false )
| ( ( SV731 = SV705 )
= $false )
| ( ( in @ SV731 @ ( cartesian_product2 @ SV139 @ SV661 ) )
= $false )
| ( ( in @ SV705 @ ( sK13_C @ SV661 @ SV139 ) )
= $true )
| ( ( ( ordered_pair @ ( sK20_SY626 @ SV139 ) @ ( sK21_SY628 @ SV139 ) )
= ( sK19_SY619 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4999]) ).
thf(5081,plain,
! [SV662: $i,SV732: $i,SV139: $i,SV707: $i,SV775: $i,SV787: $i] :
( ( ( SV787
= ( singleton @ SV775 ) )
= $false )
| ( ( ( ordered_pair @ SV775 @ SV787 )
= SV707 )
= $false )
| ( ( in @ SV775 @ SV139 )
= $false )
| ( ( SV732 = SV707 )
= $false )
| ( ( in @ SV732 @ ( cartesian_product2 @ SV139 @ SV662 ) )
= $false )
| ( ( in @ SV707 @ ( sK13_C @ SV662 @ SV139 ) )
= $true )
| ( ( in @ ( sK20_SY626 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5000]) ).
thf(5082,plain,
! [SV733: $i,SV265: $i,SV796: $i,SV145: $i,SV817: $i] :
( ( ( in @ SV817 @ SV145 )
= $false )
| ( ( ! [SY1707: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1707 @ SV817 @ SV796 @ SV265 @ SV145 ) @ SY1707 )
| ~ ~ ( in @ ( ordered_pair @ SV796 @ ( sK47_K @ SY1707 @ SV817 @ SV796 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV817 != SY1707 )
| ~ ( in @ SV796 @ SY1707 ) ) )
= $true )
| ( ( in @ SV796 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5001]) ).
thf(5083,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV797: $i] :
( ( ( ~ ( in @ ( sK45_E @ SV797 @ SV265 @ SV145 ) @ SV145 ) )
= $false )
| ( ( in @ SV797 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5002]) ).
thf(5084,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV797: $i] :
( ( ( ~ ~ ( ~ ! [SY1667: $i] :
( ~ ( in @ SY1667 @ ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV797 @ SY1667 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV797 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) )
| ~ ( in @ SV797 @ ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) ) ) ) )
= $false )
| ( ( in @ SV797 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5002]) ).
thf(5085,plain,
! [SV265: $i,SV798: $i,SV145: $i,SV818: $i] :
( ( ( in @ SV818 @ SV145 )
= $false )
| ( ( ! [SY1708: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1708 @ SV818 @ SV798 @ SV265 @ SV145 ) @ SY1708 )
| ~ ~ ( in @ ( ordered_pair @ SV798 @ ( sK47_K @ SY1708 @ SV818 @ SV798 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV818 != SY1708 )
| ~ ( in @ SV798 @ SY1708 ) ) )
= $true )
| ( ( in @ SV798 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5003]) ).
thf(5086,plain,
! [SV145: $i,SV265: $i,SV799: $i] :
( ( ( ~ ( in @ ( sK45_E @ SV799 @ SV265 @ SV145 ) @ SV145 ) )
= $false )
| ( ( in @ SV799 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5004]) ).
thf(5087,plain,
! [SV145: $i,SV265: $i,SV799: $i] :
( ( ( ~ ~ ( ~ ! [SY1670: $i] :
( ~ ( in @ SY1670 @ ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV799 @ SY1670 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV799 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) )
| ~ ( in @ SV799 @ ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) ) ) ) )
= $false )
| ( ( in @ SV799 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5004]) ).
thf(5088,plain,
! [SV265: $i,SV800: $i,SV145: $i,SV819: $i] :
( ( ( in @ SV819 @ SV145 )
= $false )
| ( ( ! [SY1709: $i] :
( ~ ( ~ ( in @ ( sK47_K @ SY1709 @ SV819 @ SV800 @ SV265 @ SV145 ) @ SY1709 )
| ~ ~ ( in @ ( ordered_pair @ SV800 @ ( sK47_K @ SY1709 @ SV819 @ SV800 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV819 != SY1709 )
| ~ ( in @ SV800 @ SY1709 ) ) )
= $true )
| ( ( in @ SV800 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5005]) ).
thf(5089,plain,
! [SV145: $i,SV265: $i,SV801: $i] :
( ( ( ~ ( in @ ( sK45_E @ SV801 @ SV265 @ SV145 ) @ SV145 ) )
= $false )
| ( ( in @ SV801 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5006]) ).
thf(5090,plain,
! [SV145: $i,SV265: $i,SV801: $i] :
( ( ( ~ ~ ( ~ ! [SY1673: $i] :
( ~ ( in @ SY1673 @ ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV801 @ SY1673 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV801 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) )
| ~ ( in @ SV801 @ ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) ) ) ) )
= $false )
| ( ( in @ SV801 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5006]) ).
thf(5091,plain,
! [SV145: $i,SV265: $i,SV734: $i,SV788: $i,SV760: $i] :
( ( ( ( SV760 != SV788 ) )
= $true )
| ( ( ~ ( in @ SV734 @ SV788 ) )
= $true )
| ( ( in @ ( sK47_K @ SV788 @ SV760 @ SV734 @ SV265 @ SV145 ) @ SV788 )
= $true )
| ( ( in @ SV760 @ SV145 )
= $false )
| ( ( in @ SV734 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5007]) ).
thf(5092,plain,
! [SV145: $i,SV265: $i,SV760: $i,SV788: $i,SV734: $i] :
( ( ( in @ ( ordered_pair @ SV734 @ ( sK47_K @ SV788 @ SV760 @ SV734 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( ( SV760 != SV788 )
| ~ ( in @ SV734 @ SV788 ) )
= $true )
| ( ( in @ SV760 @ SV145 )
= $false )
| ( ( in @ SV734 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5008]) ).
thf(5093,plain,
! [SV145: $i,SV265: $i,SV735: $i,SV823: $i] :
( ( ( ~ ( in @ SV823 @ ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV735 @ SV823 ) @ SV265 )
= $true )
| ( ( in @ SV735 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5009]) ).
thf(5094,plain,
! [SV145: $i,SV265: $i,SV735: $i] :
( ( ( ( ( sK45_E @ SV735 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) ) )
= $false )
| ( ( in @ SV735 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5010]) ).
thf(5095,plain,
! [SV145: $i,SV265: $i,SV735: $i] :
( ( ( ~ ( in @ SV735 @ ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) ) )
= $false )
| ( ( in @ SV735 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5010]) ).
thf(5096,plain,
! [SV145: $i,SV265: $i,SV727: $i,SV761: $i,SV711: $i] :
( ( ( in @ SV711 @ SV761 )
= $false )
| ( ( SV727 = SV761 )
= $false )
| ( ( in @ ( ordered_pair @ SV711 @ ( sK47_K @ SV761 @ SV727 @ SV711 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( in @ SV727 @ SV145 )
= $false )
| ( ( in @ SV711 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5012]) ).
thf(5097,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV736: $i,SV789: $i,SV762: $i] :
( ( ( ( SV762 != SV789 ) )
= $true )
| ( ( ~ ( in @ SV736 @ SV789 ) )
= $true )
| ( ( in @ ( sK47_K @ SV789 @ SV762 @ SV736 @ SV265 @ SV145 ) @ SV789 )
= $true )
| ( ( in @ SV762 @ SV145 )
= $false )
| ( ( in @ SV736 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5013]) ).
thf(5098,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV762: $i,SV789: $i,SV736: $i] :
( ( ( in @ ( ordered_pair @ SV736 @ ( sK47_K @ SV789 @ SV762 @ SV736 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( ( SV762 != SV789 )
| ~ ( in @ SV736 @ SV789 ) )
= $true )
| ( ( in @ SV762 @ SV145 )
= $false )
| ( ( in @ SV736 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5014]) ).
thf(5099,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV737: $i,SV824: $i] :
( ( ( ~ ( in @ SV824 @ ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV737 @ SV824 ) @ SV265 )
= $true )
| ( ( in @ SV737 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5015]) ).
thf(5100,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV737: $i] :
( ( ( ( ( sK45_E @ SV737 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) ) )
= $false )
| ( ( in @ SV737 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5016]) ).
thf(5101,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV737: $i] :
( ( ( ~ ( in @ SV737 @ ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) ) )
= $false )
| ( ( in @ SV737 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5016]) ).
thf(5102,plain,
! [SV145: $i,SV265: $i,SV738: $i,SV790: $i,SV763: $i] :
( ( ( ( SV763 != SV790 ) )
= $true )
| ( ( ~ ( in @ SV738 @ SV790 ) )
= $true )
| ( ( in @ ( sK47_K @ SV790 @ SV763 @ SV738 @ SV265 @ SV145 ) @ SV790 )
= $true )
| ( ( in @ SV763 @ SV145 )
= $false )
| ( ( in @ SV738 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5017]) ).
thf(5103,plain,
! [SV145: $i,SV265: $i,SV763: $i,SV790: $i,SV738: $i] :
( ( ( in @ ( ordered_pair @ SV738 @ ( sK47_K @ SV790 @ SV763 @ SV738 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( ( SV763 != SV790 )
| ~ ( in @ SV738 @ SV790 ) )
= $true )
| ( ( in @ SV763 @ SV145 )
= $false )
| ( ( in @ SV738 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5018]) ).
thf(5104,plain,
! [SV145: $i,SV265: $i,SV739: $i,SV825: $i] :
( ( ( ~ ( in @ SV825 @ ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV739 @ SV825 ) @ SV265 )
= $true )
| ( ( in @ SV739 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5019]) ).
thf(5105,plain,
! [SV145: $i,SV265: $i,SV739: $i] :
( ( ( ( ( sK45_E @ SV739 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) ) )
= $false )
| ( ( in @ SV739 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5020]) ).
thf(5106,plain,
! [SV145: $i,SV265: $i,SV739: $i] :
( ( ( ~ ( in @ SV739 @ ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) ) )
= $false )
| ( ( in @ SV739 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5020]) ).
thf(5107,plain,
! [SV145: $i,SV265: $i,SV740: $i,SV791: $i,SV764: $i] :
( ( ( ( SV764 != SV791 ) )
= $true )
| ( ( ~ ( in @ SV740 @ SV791 ) )
= $true )
| ( ( in @ ( sK47_K @ SV791 @ SV764 @ SV740 @ SV265 @ SV145 ) @ SV791 )
= $true )
| ( ( in @ SV764 @ SV145 )
= $false )
| ( ( in @ SV740 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5021]) ).
thf(5108,plain,
! [SV145: $i,SV265: $i,SV764: $i,SV791: $i,SV740: $i] :
( ( ( in @ ( ordered_pair @ SV740 @ ( sK47_K @ SV791 @ SV764 @ SV740 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( ( SV764 != SV791 )
| ~ ( in @ SV740 @ SV791 ) )
= $true )
| ( ( in @ SV764 @ SV145 )
= $false )
| ( ( in @ SV740 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5022]) ).
thf(5109,plain,
! [SV145: $i,SV265: $i,SV741: $i,SV826: $i] :
( ( ( ~ ( in @ SV826 @ ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV741 @ SV826 ) @ SV265 )
= $true )
| ( ( in @ SV741 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5023]) ).
thf(5110,plain,
! [SV145: $i,SV265: $i,SV741: $i] :
( ( ( ( ( sK45_E @ SV741 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) ) )
= $false )
| ( ( in @ SV741 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5024]) ).
thf(5111,plain,
! [SV145: $i,SV265: $i,SV741: $i] :
( ( ( ~ ( in @ SV741 @ ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) ) )
= $false )
| ( ( in @ SV741 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5024]) ).
thf(5112,plain,
! [SV776: $i,SV272: $i,SV717: $i,SV172: $i,SV750: $i,SV827: $i,SV820: $i] :
( ( ( ( ( ordered_pair @ SV820 @ SV827 )
!= SV750 )
| ~ ( in @ SV820 @ SV172 ) )
= $true )
| ( ( ! [SY1716: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1716 @ SV827 @ SV820 @ SV750 @ SV717 @ SV272 @ SV172 ) @ SY1716 )
| ~ ~ ( in @ ( ordered_pair @ SV827 @ ( sK34_R @ SY1716 @ SV827 @ SV820 @ SV750 @ SV717 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV820 != SY1716 )
| ~ ( in @ SV827 @ SY1716 ) ) )
= $true )
| ( ( SV776 = SV750 )
= $false )
| ( ( in @ SV776 @ ( cartesian_product2 @ SV172 @ SV717 ) )
= $false )
| ( ( in @ SV750 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5025]) ).
thf(5113,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( ( ( ordered_pair @ ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) )
!= SV751 )
| ~ ( in @ ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 ) @ SV172 ) )
= $false )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5028]) ).
thf(5114,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( ~ ! [SY1609: $i] :
( ~ ( in @ SY1609 @ ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) @ SY1609 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5029]) ).
thf(5115,plain,
! [SV272: $i,SV770: $i,SV172: $i,SV809: $i,SV832: $i] :
( ( ( ( SV832 != SV809 )
| ~ ( in @ SV832 @ ( cartesian_product2 @ SV172 @ SV770 ) ) )
= $true )
| ( ( ! [SY1698: $i,SY1699: $i] :
( ( ( ordered_pair @ SY1698 @ SY1699 )
!= SV809 )
| ~ ( in @ SY1698 @ SV172 )
| ! [SY1700: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1700 @ SY1699 @ SY1698 @ SV809 @ SV770 @ SV272 @ SV172 ) @ SY1700 )
| ~ ~ ( in @ ( ordered_pair @ SY1699 @ ( sK34_R @ SY1700 @ SY1699 @ SY1698 @ SV809 @ SV770 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1698 != SY1700 )
| ~ ( in @ SY1699 @ SY1700 ) ) ) )
= $true )
| ( ( in @ SV809 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5030]) ).
thf(5116,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( ~ ~ ( ( ( sK33_F @ SV810 @ SV770 @ SV272 @ SV172 )
!= SV810 )
| ~ ( in @ ( sK33_F @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV770 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) )
!= SV810 )
| ~ ( in @ ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1701: $i] :
( ~ ( in @ SY1701 @ ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) @ SY1701 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) ) ) ) ) )
= $false )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5031]) ).
thf(5117,plain,
! [SV272: $i,SV771: $i,SV172: $i,SV811: $i,SV833: $i] :
( ( ( ( SV833 != SV811 )
| ~ ( in @ SV833 @ ( cartesian_product2 @ SV172 @ SV771 ) ) )
= $true )
| ( ( ! [SY1703: $i,SY1704: $i] :
( ( ( ordered_pair @ SY1703 @ SY1704 )
!= SV811 )
| ~ ( in @ SY1703 @ SV172 )
| ! [SY1705: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1705 @ SY1704 @ SY1703 @ SV811 @ SV771 @ SV272 @ SV172 ) @ SY1705 )
| ~ ~ ( in @ ( ordered_pair @ SY1704 @ ( sK34_R @ SY1705 @ SY1704 @ SY1703 @ SV811 @ SV771 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1703 != SY1705 )
| ~ ( in @ SY1704 @ SY1705 ) ) ) )
= $true )
| ( ( in @ SV811 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5032]) ).
thf(5118,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( ~ ~ ( ( ( sK33_F @ SV812 @ SV771 @ SV272 @ SV172 )
!= SV812 )
| ~ ( in @ ( sK33_F @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV771 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) )
!= SV812 )
| ~ ( in @ ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1706: $i] :
( ~ ( in @ SY1706 @ ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) @ SY1706 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) ) ) ) ) )
= $false )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5033]) ).
thf(5119,plain,
! [SV772: $i,SV272: $i,SV803: $i,SV172: $i,SV834: $i] :
( ( ( ! [SY1721: $i] :
( ( SY1721 != SV834 )
| ~ ( in @ SY1721 @ ( cartesian_product2 @ SV172 @ SV803 ) ) )
| ! [SY1722: $i,SY1723: $i] :
( ( ( ordered_pair @ SY1722 @ SY1723 )
!= SV834 )
| ~ ( in @ SY1722 @ SV172 )
| ! [SY1724: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1724 @ SY1723 @ SY1722 @ SV834 @ SV803 @ SV272 @ SV172 ) @ SY1724 )
| ~ ~ ( in @ ( ordered_pair @ SY1723 @ ( sK34_R @ SY1724 @ SY1723 @ SY1722 @ SV834 @ SV803 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1722 != SY1724 )
| ~ ( in @ SY1723 @ SY1724 ) ) )
| ( in @ SV834 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5034]) ).
thf(5120,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( ~ ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SV835 @ SV803 @ SV272 @ SV172 )
!= SV835 )
| ~ ( in @ ( sK33_F @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV803 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) )
!= SV835 )
| ~ ( in @ ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1725: $i] :
( ~ ( in @ SY1725 @ ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) @ SY1725 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5035]) ).
thf(5121,plain,
! [SV272: $i,SV804: $i,SV172: $i,SV836: $i] :
( ( ( ! [SY1726: $i] :
( ( SY1726 != SV836 )
| ~ ( in @ SY1726 @ ( cartesian_product2 @ SV172 @ SV804 ) ) )
| ! [SY1727: $i,SY1728: $i] :
( ( ( ordered_pair @ SY1727 @ SY1728 )
!= SV836 )
| ~ ( in @ SY1727 @ SV172 )
| ! [SY1729: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1729 @ SY1728 @ SY1727 @ SV836 @ SV804 @ SV272 @ SV172 ) @ SY1729 )
| ~ ~ ( in @ ( ordered_pair @ SY1728 @ ( sK34_R @ SY1729 @ SY1728 @ SY1727 @ SV836 @ SV804 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1727 != SY1729 )
| ~ ( in @ SY1728 @ SY1729 ) ) )
| ( in @ SV836 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5036]) ).
thf(5122,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( ~ ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SV837 @ SV804 @ SV272 @ SV172 )
!= SV837 )
| ~ ( in @ ( sK33_F @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV804 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) )
!= SV837 )
| ~ ( in @ ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1730: $i] :
( ~ ( in @ SY1730 @ ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) @ SY1730 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5037]) ).
thf(5123,plain,
! [SV272: $i,SV805: $i,SV172: $i,SV838: $i] :
( ( ( ! [SY1731: $i] :
( ( SY1731 != SV838 )
| ~ ( in @ SY1731 @ ( cartesian_product2 @ SV172 @ SV805 ) ) )
| ! [SY1732: $i,SY1733: $i] :
( ( ( ordered_pair @ SY1732 @ SY1733 )
!= SV838 )
| ~ ( in @ SY1732 @ SV172 )
| ! [SY1734: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1734 @ SY1733 @ SY1732 @ SV838 @ SV805 @ SV272 @ SV172 ) @ SY1734 )
| ~ ~ ( in @ ( ordered_pair @ SY1733 @ ( sK34_R @ SY1734 @ SY1733 @ SY1732 @ SV838 @ SV805 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1732 != SY1734 )
| ~ ( in @ SY1733 @ SY1734 ) ) )
| ( in @ SV838 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5038]) ).
thf(5124,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( ~ ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
| ~ ( ~ ~ ( ( ( sK33_F @ SV839 @ SV805 @ SV272 @ SV172 )
!= SV839 )
| ~ ( in @ ( sK33_F @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV805 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) )
!= SV839 )
| ~ ( in @ ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1735: $i] :
( ~ ( in @ SY1735 @ ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) @ SY1735 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5039]) ).
thf(5125,plain,
! [SV752: $i,SV272: $i,SV692: $i,SV723: $i,SV806: $i,SV172: $i,SV792: $i] :
( ( ( in @ SV792 @ SV172 )
= $false )
| ( ( ( ordered_pair @ SV792 @ SV806 )
= SV723 )
= $false )
| ( ( ! [SY1695: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1695 @ SV806 @ SV792 @ SV723 @ SV692 @ SV272 @ SV172 ) @ SY1695 )
| ~ ~ ( in @ ( ordered_pair @ SV806 @ ( sK34_R @ SY1695 @ SV806 @ SV792 @ SV723 @ SV692 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV792 != SY1695 )
| ~ ( in @ SV806 @ SY1695 ) ) )
= $true )
| ( ( SV752 = SV723 )
= $false )
| ( ( in @ SV752 @ ( cartesian_product2 @ SV172 @ SV692 ) )
= $false )
| ( ( in @ SV723 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5040]) ).
thf(5126,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i,SV840: $i] :
( ( ( ~ ( in @ SV840 @ ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) @ SV840 ) @ SV272 ) )
= $true )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5043]) ).
thf(5127,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( ( ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5044]) ).
thf(5128,plain,
! [SV777: $i,SV272: $i,SV718: $i,SV172: $i,SV753: $i,SV828: $i,SV821: $i] :
( ( ( ( ( ordered_pair @ SV821 @ SV828 )
!= SV753 )
| ~ ( in @ SV821 @ SV172 ) )
= $true )
| ( ( ! [SY1717: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1717 @ SV828 @ SV821 @ SV753 @ SV718 @ SV272 @ SV172 ) @ SY1717 )
| ~ ~ ( in @ ( ordered_pair @ SV828 @ ( sK34_R @ SY1717 @ SV828 @ SV821 @ SV753 @ SV718 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV821 != SY1717 )
| ~ ( in @ SV828 @ SY1717 ) ) )
= $true )
| ( ( SV777 = SV753 )
= $false )
| ( ( in @ SV777 @ ( cartesian_product2 @ SV172 @ SV718 ) )
= $false )
| ( ( in @ SV753 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5045]) ).
thf(5129,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( ( ( ordered_pair @ ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) )
!= SV754 )
| ~ ( in @ ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 ) @ SV172 ) )
= $false )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5048]) ).
thf(5130,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( ~ ! [SY1614: $i] :
( ~ ( in @ SY1614 @ ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) @ SY1614 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5049]) ).
thf(5131,plain,
! [SV778: $i,SV272: $i,SV719: $i,SV172: $i,SV755: $i,SV829: $i,SV822: $i] :
( ( ( ( ( ordered_pair @ SV822 @ SV829 )
!= SV755 )
| ~ ( in @ SV822 @ SV172 ) )
= $true )
| ( ( ! [SY1718: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1718 @ SV829 @ SV822 @ SV755 @ SV719 @ SV272 @ SV172 ) @ SY1718 )
| ~ ~ ( in @ ( ordered_pair @ SV829 @ ( sK34_R @ SY1718 @ SV829 @ SV822 @ SV755 @ SV719 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV822 != SY1718 )
| ~ ( in @ SV829 @ SY1718 ) ) )
= $true )
| ( ( SV778 = SV755 )
= $false )
| ( ( in @ SV778 @ ( cartesian_product2 @ SV172 @ SV719 ) )
= $false )
| ( ( in @ SV755 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5050]) ).
thf(5132,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( ( ( ordered_pair @ ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) )
!= SV756 )
| ~ ( in @ ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 ) @ SV172 ) )
= $false )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5053]) ).
thf(5133,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( ~ ! [SY1619: $i] :
( ~ ( in @ SY1619 @ ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) @ SY1619 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5054]) ).
thf(5134,plain,
! [SV720: $i,SV272: $i,SV779: $i,SV743: $i,SV172: $i,SV813: $i] :
( ( ( in @ SV813 @ ( cartesian_product2 @ SV172 @ SV743 ) )
= $false )
| ( ( SV813 = SV779 )
= $false )
| ( ( ! [SY1649: $i,SY1650: $i] :
( ( ( ordered_pair @ SY1649 @ SY1650 )
!= SV779 )
| ~ ( in @ SY1649 @ SV172 )
| ! [SY1651: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1651 @ SY1650 @ SY1649 @ SV779 @ SV743 @ SV272 @ SV172 ) @ SY1651 )
| ~ ~ ( in @ ( ordered_pair @ SY1650 @ ( sK34_R @ SY1651 @ SY1650 @ SY1649 @ SV779 @ SV743 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1649 != SY1651 )
| ~ ( in @ SY1650 @ SY1651 ) ) ) )
= $true )
| ( ( in @ SV779 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5055]) ).
thf(5135,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( ( ( sK33_F @ SV780 @ SV743 @ SV272 @ SV172 )
!= SV780 )
| ~ ( in @ ( sK33_F @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV743 ) ) )
= $false )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5056]) ).
thf(5136,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) )
!= SV780 )
| ~ ( in @ ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1652: $i] :
( ~ ( in @ SY1652 @ ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) @ SY1652 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) ) ) ) )
= $false )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5057]) ).
thf(5137,plain,
! [SV272: $i,SV781: $i,SV744: $i,SV172: $i,SV814: $i] :
( ( ( in @ SV814 @ ( cartesian_product2 @ SV172 @ SV744 ) )
= $false )
| ( ( SV814 = SV781 )
= $false )
| ( ( ! [SY1654: $i,SY1655: $i] :
( ( ( ordered_pair @ SY1654 @ SY1655 )
!= SV781 )
| ~ ( in @ SY1654 @ SV172 )
| ! [SY1656: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1656 @ SY1655 @ SY1654 @ SV781 @ SV744 @ SV272 @ SV172 ) @ SY1656 )
| ~ ~ ( in @ ( ordered_pair @ SY1655 @ ( sK34_R @ SY1656 @ SY1655 @ SY1654 @ SV781 @ SV744 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1654 != SY1656 )
| ~ ( in @ SY1655 @ SY1656 ) ) ) )
= $true )
| ( ( in @ SV781 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5058]) ).
thf(5138,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( ( ( sK33_F @ SV782 @ SV744 @ SV272 @ SV172 )
!= SV782 )
| ~ ( in @ ( sK33_F @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV744 ) ) )
= $false )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5059]) ).
thf(5139,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) )
!= SV782 )
| ~ ( in @ ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1657: $i] :
( ~ ( in @ SY1657 @ ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) @ SY1657 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) ) ) ) )
= $false )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5060]) ).
thf(5140,plain,
! [SV272: $i,SV783: $i,SV745: $i,SV172: $i,SV815: $i] :
( ( ( in @ SV815 @ ( cartesian_product2 @ SV172 @ SV745 ) )
= $false )
| ( ( SV815 = SV783 )
= $false )
| ( ( ! [SY1659: $i,SY1660: $i] :
( ( ( ordered_pair @ SY1659 @ SY1660 )
!= SV783 )
| ~ ( in @ SY1659 @ SV172 )
| ! [SY1661: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1661 @ SY1660 @ SY1659 @ SV783 @ SV745 @ SV272 @ SV172 ) @ SY1661 )
| ~ ~ ( in @ ( ordered_pair @ SY1660 @ ( sK34_R @ SY1661 @ SY1660 @ SY1659 @ SV783 @ SV745 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1659 != SY1661 )
| ~ ( in @ SY1660 @ SY1661 ) ) ) )
= $true )
| ( ( in @ SV783 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5061]) ).
thf(5141,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( ( ( sK33_F @ SV784 @ SV745 @ SV272 @ SV172 )
!= SV784 )
| ~ ( in @ ( sK33_F @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV745 ) ) )
= $false )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5062]) ).
thf(5142,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) )
!= SV784 )
| ~ ( in @ ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1662: $i] :
( ~ ( in @ SY1662 @ ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) @ SY1662 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) ) ) ) )
= $false )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5063]) ).
thf(5143,plain,
! [SV701: $i,SV172: $i,SV272: $i,SV622: $i,SV677: $i,SV746: $i,SV757: $i,SV807: $i] :
( ( ( in @ ( sK34_R @ SV807 @ SV757 @ SV746 @ SV677 @ SV622 @ SV272 @ SV172 ) @ SV807 )
= $true )
| ( ( ( SV746 != SV807 )
| ~ ( in @ SV757 @ SV807 ) )
= $true )
| ( ( ( ordered_pair @ SV746 @ SV757 )
= SV677 )
= $false )
| ( ( in @ SV746 @ SV172 )
= $false )
| ( ( SV701 = SV677 )
= $false )
| ( ( in @ SV701 @ ( cartesian_product2 @ SV172 @ SV622 ) )
= $false )
| ( ( in @ SV677 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5064]) ).
thf(5144,plain,
! [SV701: $i,SV172: $i,SV272: $i,SV622: $i,SV677: $i,SV746: $i,SV807: $i,SV757: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV757 @ ( sK34_R @ SV807 @ SV757 @ SV746 @ SV677 @ SV622 @ SV272 @ SV172 ) ) @ SV272 ) )
= $true )
| ( ( ( SV746 != SV807 )
| ~ ( in @ SV757 @ SV807 ) )
= $true )
| ( ( ( ordered_pair @ SV746 @ SV757 )
= SV677 )
= $false )
| ( ( in @ SV746 @ SV172 )
= $false )
| ( ( SV701 = SV677 )
= $false )
| ( ( in @ SV701 @ ( cartesian_product2 @ SV172 @ SV622 ) )
= $false )
| ( ( in @ SV677 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5065]) ).
thf(5145,plain,
! [SV725: $i,SV794: $i,SV139: $i,SV765: $i,SV841: $i,SV830: $i] :
( ( ( ( ( ordered_pair @ SV830 @ SV841 )
!= SV765 )
| ~ ( in @ SV830 @ SV139 )
| ( SV841
!= ( singleton @ SV830 ) ) )
= $true )
| ( ( SV794 = SV765 )
= $false )
| ( ( in @ SV794 @ ( cartesian_product2 @ SV139 @ SV725 ) )
= $false )
| ( ( in @ SV765 @ ( sK13_C @ SV725 @ SV139 ) )
= $true )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5067]) ).
thf(5146,plain,
! [SV139: $i,SV725: $i,SV766: $i] :
( ( ( ( sK16_E @ SV766 @ SV725 @ SV139 )
= SV766 )
= $true )
| ( ( in @ SV766 @ ( sK13_C @ SV725 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5068]) ).
thf(5147,plain,
! [SV139: $i,SV725: $i,SV766: $i] :
( ( ( in @ ( sK16_E @ SV766 @ SV725 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV725 ) )
= $true )
| ( ( in @ SV766 @ ( sK13_C @ SV725 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5069]) ).
thf(5148,plain,
! [SV139: $i,SV725: $i,SV766: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK14_J @ SV766 @ SV725 @ SV139 ) @ ( sK15_SY612 @ SV766 @ SV725 @ SV139 ) )
!= SV766 )
| ~ ( in @ ( sK14_J @ SV766 @ SV725 @ SV139 ) @ SV139 ) ) )
= $true )
| ( ( in @ SV766 @ ( sK13_C @ SV725 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5070]) ).
thf(5149,plain,
! [SV139: $i,SV725: $i,SV766: $i] :
( ( ( ( sK15_SY612 @ SV766 @ SV725 @ SV139 )
= ( singleton @ ( sK14_J @ SV766 @ SV725 @ SV139 ) ) )
= $true )
| ( ( in @ SV766 @ ( sK13_C @ SV725 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5071]) ).
thf(5150,plain,
! [SV726: $i,SV795: $i,SV139: $i,SV767: $i,SV842: $i,SV831: $i] :
( ( ( ( ( ordered_pair @ SV831 @ SV842 )
!= SV767 )
| ~ ( in @ SV831 @ SV139 )
| ( SV842
!= ( singleton @ SV831 ) ) )
= $true )
| ( ( SV795 = SV767 )
= $false )
| ( ( in @ SV795 @ ( cartesian_product2 @ SV139 @ SV726 ) )
= $false )
| ( ( in @ SV767 @ ( sK13_C @ SV726 @ SV139 ) )
= $true )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5072]) ).
thf(5151,plain,
! [SV139: $i,SV726: $i,SV768: $i] :
( ( ( ( sK16_E @ SV768 @ SV726 @ SV139 )
= SV768 )
= $true )
| ( ( in @ SV768 @ ( sK13_C @ SV726 @ SV139 ) )
= $false )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5073]) ).
thf(5152,plain,
! [SV139: $i,SV726: $i,SV768: $i] :
( ( ( in @ ( sK16_E @ SV768 @ SV726 @ SV139 ) @ ( cartesian_product2 @ SV139 @ SV726 ) )
= $true )
| ( ( in @ SV768 @ ( sK13_C @ SV726 @ SV139 ) )
= $false )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5074]) ).
thf(5153,plain,
! [SV139: $i,SV726: $i,SV768: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK14_J @ SV768 @ SV726 @ SV139 ) @ ( sK15_SY612 @ SV768 @ SV726 @ SV139 ) )
!= SV768 )
| ~ ( in @ ( sK14_J @ SV768 @ SV726 @ SV139 ) @ SV139 ) ) )
= $true )
| ( ( in @ SV768 @ ( sK13_C @ SV726 @ SV139 ) )
= $false )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5075]) ).
thf(5154,plain,
! [SV139: $i,SV726: $i,SV768: $i] :
( ( ( ( sK15_SY612 @ SV768 @ SV726 @ SV139 )
= ( singleton @ ( sK14_J @ SV768 @ SV726 @ SV139 ) ) )
= $true )
| ( ( in @ SV768 @ ( sK13_C @ SV726 @ SV139 ) )
= $false )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5076]) ).
thf(5155,plain,
! [SV694: $i,SV769: $i,SV139: $i,SV729: $i,SV816: $i,SV808: $i] :
( ( ( ( ordered_pair @ SV808 @ SV816 )
= SV729 )
= $false )
| ( ( ~ ( in @ SV808 @ SV139 ) )
= $true )
| ( ( ( SV816
!= ( singleton @ SV808 ) ) )
= $true )
| ( ( SV769 = SV729 )
= $false )
| ( ( in @ SV769 @ ( cartesian_product2 @ SV139 @ SV694 ) )
= $false )
| ( ( in @ SV729 @ ( sK13_C @ SV694 @ SV139 ) )
= $true )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5077]) ).
thf(5156,plain,
! [SV139: $i,SV694: $i,SV730: $i] :
( ( ( ( ordered_pair @ ( sK14_J @ SV730 @ SV694 @ SV139 ) @ ( sK15_SY612 @ SV730 @ SV694 @ SV139 ) )
= SV730 )
= $true )
| ( ( in @ SV730 @ ( sK13_C @ SV694 @ SV139 ) )
= $false )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5078]) ).
thf(5157,plain,
! [SV139: $i,SV694: $i,SV730: $i] :
( ( ( in @ ( sK14_J @ SV730 @ SV694 @ SV139 ) @ SV139 )
= $true )
| ( ( in @ SV730 @ ( sK13_C @ SV694 @ SV139 ) )
= $false )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5079]) ).
thf(5158,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV796: $i,SV817: $i,SV843: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_K @ SV843 @ SV817 @ SV796 @ SV265 @ SV145 ) @ SV843 )
| ~ ~ ( in @ ( ordered_pair @ SV796 @ ( sK47_K @ SV843 @ SV817 @ SV796 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV817 != SV843 )
| ~ ( in @ SV796 @ SV843 ) )
= $true )
| ( ( in @ SV817 @ SV145 )
= $false )
| ( ( in @ SV796 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5082]) ).
thf(5159,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV797: $i] :
( ( ( in @ ( sK45_E @ SV797 @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( in @ SV797 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5083]) ).
thf(5160,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV797: $i] :
( ( ( ~ ( ~ ! [SY1667: $i] :
( ~ ( in @ SY1667 @ ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV797 @ SY1667 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV797 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) )
| ~ ( in @ SV797 @ ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) ) ) ) )
= $true )
| ( ( in @ SV797 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5084]) ).
thf(5161,plain,
! [SV145: $i,SV265: $i,SV798: $i,SV818: $i,SV844: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_K @ SV844 @ SV818 @ SV798 @ SV265 @ SV145 ) @ SV844 )
| ~ ~ ( in @ ( ordered_pair @ SV798 @ ( sK47_K @ SV844 @ SV818 @ SV798 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV818 != SV844 )
| ~ ( in @ SV798 @ SV844 ) )
= $true )
| ( ( in @ SV818 @ SV145 )
= $false )
| ( ( in @ SV798 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5085]) ).
thf(5162,plain,
! [SV145: $i,SV265: $i,SV799: $i] :
( ( ( in @ ( sK45_E @ SV799 @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( in @ SV799 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5086]) ).
thf(5163,plain,
! [SV145: $i,SV265: $i,SV799: $i] :
( ( ( ~ ( ~ ! [SY1670: $i] :
( ~ ( in @ SY1670 @ ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV799 @ SY1670 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV799 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) )
| ~ ( in @ SV799 @ ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) ) ) ) )
= $true )
| ( ( in @ SV799 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5087]) ).
thf(5164,plain,
! [SV145: $i,SV265: $i,SV800: $i,SV819: $i,SV845: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_K @ SV845 @ SV819 @ SV800 @ SV265 @ SV145 ) @ SV845 )
| ~ ~ ( in @ ( ordered_pair @ SV800 @ ( sK47_K @ SV845 @ SV819 @ SV800 @ SV265 @ SV145 ) ) @ SV265 ) )
| ( SV819 != SV845 )
| ~ ( in @ SV800 @ SV845 ) )
= $true )
| ( ( in @ SV819 @ SV145 )
= $false )
| ( ( in @ SV800 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5088]) ).
thf(5165,plain,
! [SV145: $i,SV265: $i,SV801: $i] :
( ( ( in @ ( sK45_E @ SV801 @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( in @ SV801 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5089]) ).
thf(5166,plain,
! [SV145: $i,SV265: $i,SV801: $i] :
( ( ( ~ ( ~ ! [SY1673: $i] :
( ~ ( in @ SY1673 @ ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV801 @ SY1673 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV801 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) )
| ~ ( in @ SV801 @ ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) ) ) ) )
= $true )
| ( ( in @ SV801 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5090]) ).
thf(5167,plain,
! [SV145: $i,SV265: $i,SV734: $i,SV788: $i,SV760: $i] :
( ( ( SV760 = SV788 )
= $false )
| ( ( ~ ( in @ SV734 @ SV788 ) )
= $true )
| ( ( in @ ( sK47_K @ SV788 @ SV760 @ SV734 @ SV265 @ SV145 ) @ SV788 )
= $true )
| ( ( in @ SV760 @ SV145 )
= $false )
| ( ( in @ SV734 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5091]) ).
thf(5168,plain,
! [SV145: $i,SV265: $i,SV734: $i,SV788: $i,SV760: $i] :
( ( ( ( SV760 != SV788 ) )
= $true )
| ( ( ~ ( in @ SV734 @ SV788 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV734 @ ( sK47_K @ SV788 @ SV760 @ SV734 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( in @ SV760 @ SV145 )
= $false )
| ( ( in @ SV734 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5092]) ).
thf(5169,plain,
! [SV145: $i,SV265: $i,SV735: $i,SV823: $i] :
( ( ( in @ SV823 @ ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV735 @ SV823 ) @ SV265 )
= $true )
| ( ( in @ SV735 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5093]) ).
thf(5170,plain,
! [SV145: $i,SV265: $i,SV735: $i] :
( ( ( ( sK45_E @ SV735 @ SV265 @ SV145 )
= ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) )
= $true )
| ( ( in @ SV735 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5094]) ).
thf(5171,plain,
! [SV145: $i,SV265: $i,SV735: $i] :
( ( ( in @ SV735 @ ( sK46_SY702 @ SV735 @ SV265 @ SV145 ) )
= $true )
| ( ( in @ SV735 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5095]) ).
thf(5172,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV736: $i,SV789: $i,SV762: $i] :
( ( ( SV762 = SV789 )
= $false )
| ( ( ~ ( in @ SV736 @ SV789 ) )
= $true )
| ( ( in @ ( sK47_K @ SV789 @ SV762 @ SV736 @ SV265 @ SV145 ) @ SV789 )
= $true )
| ( ( in @ SV762 @ SV145 )
= $false )
| ( ( in @ SV736 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5097]) ).
thf(5173,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV736: $i,SV789: $i,SV762: $i] :
( ( ( ( SV762 != SV789 ) )
= $true )
| ( ( ~ ( in @ SV736 @ SV789 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV736 @ ( sK47_K @ SV789 @ SV762 @ SV736 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( in @ SV762 @ SV145 )
= $false )
| ( ( in @ SV736 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5098]) ).
thf(5174,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV737: $i,SV824: $i] :
( ( ( in @ SV824 @ ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV737 @ SV824 ) @ SV265 )
= $true )
| ( ( in @ SV737 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5099]) ).
thf(5175,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV737: $i] :
( ( ( ( sK45_E @ SV737 @ SV265 @ SV145 )
= ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) )
= $true )
| ( ( in @ SV737 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5100]) ).
thf(5176,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV737: $i] :
( ( ( in @ SV737 @ ( sK46_SY702 @ SV737 @ SV265 @ SV145 ) )
= $true )
| ( ( in @ SV737 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5101]) ).
thf(5177,plain,
! [SV145: $i,SV265: $i,SV738: $i,SV790: $i,SV763: $i] :
( ( ( SV763 = SV790 )
= $false )
| ( ( ~ ( in @ SV738 @ SV790 ) )
= $true )
| ( ( in @ ( sK47_K @ SV790 @ SV763 @ SV738 @ SV265 @ SV145 ) @ SV790 )
= $true )
| ( ( in @ SV763 @ SV145 )
= $false )
| ( ( in @ SV738 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5102]) ).
thf(5178,plain,
! [SV145: $i,SV265: $i,SV738: $i,SV790: $i,SV763: $i] :
( ( ( ( SV763 != SV790 ) )
= $true )
| ( ( ~ ( in @ SV738 @ SV790 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV738 @ ( sK47_K @ SV790 @ SV763 @ SV738 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( in @ SV763 @ SV145 )
= $false )
| ( ( in @ SV738 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5103]) ).
thf(5179,plain,
! [SV145: $i,SV265: $i,SV739: $i,SV825: $i] :
( ( ( in @ SV825 @ ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV739 @ SV825 ) @ SV265 )
= $true )
| ( ( in @ SV739 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5104]) ).
thf(5180,plain,
! [SV145: $i,SV265: $i,SV739: $i] :
( ( ( ( sK45_E @ SV739 @ SV265 @ SV145 )
= ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) )
= $true )
| ( ( in @ SV739 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5105]) ).
thf(5181,plain,
! [SV145: $i,SV265: $i,SV739: $i] :
( ( ( in @ SV739 @ ( sK46_SY702 @ SV739 @ SV265 @ SV145 ) )
= $true )
| ( ( in @ SV739 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5106]) ).
thf(5182,plain,
! [SV145: $i,SV265: $i,SV740: $i,SV791: $i,SV764: $i] :
( ( ( SV764 = SV791 )
= $false )
| ( ( ~ ( in @ SV740 @ SV791 ) )
= $true )
| ( ( in @ ( sK47_K @ SV791 @ SV764 @ SV740 @ SV265 @ SV145 ) @ SV791 )
= $true )
| ( ( in @ SV764 @ SV145 )
= $false )
| ( ( in @ SV740 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5107]) ).
thf(5183,plain,
! [SV145: $i,SV265: $i,SV740: $i,SV791: $i,SV764: $i] :
( ( ( ( SV764 != SV791 ) )
= $true )
| ( ( ~ ( in @ SV740 @ SV791 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV740 @ ( sK47_K @ SV791 @ SV764 @ SV740 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( in @ SV764 @ SV145 )
= $false )
| ( ( in @ SV740 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5108]) ).
thf(5184,plain,
! [SV145: $i,SV265: $i,SV741: $i,SV826: $i] :
( ( ( in @ SV826 @ ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV741 @ SV826 ) @ SV265 )
= $true )
| ( ( in @ SV741 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5109]) ).
thf(5185,plain,
! [SV145: $i,SV265: $i,SV741: $i] :
( ( ( ( sK45_E @ SV741 @ SV265 @ SV145 )
= ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) )
= $true )
| ( ( in @ SV741 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5110]) ).
thf(5186,plain,
! [SV145: $i,SV265: $i,SV741: $i] :
( ( ( in @ SV741 @ ( sK46_SY702 @ SV741 @ SV265 @ SV145 ) )
= $true )
| ( ( in @ SV741 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5111]) ).
thf(5187,plain,
! [SV776: $i,SV272: $i,SV717: $i,SV172: $i,SV750: $i,SV827: $i,SV820: $i] :
( ( ( ( ( ordered_pair @ SV820 @ SV827 )
!= SV750 ) )
= $true )
| ( ( ~ ( in @ SV820 @ SV172 ) )
= $true )
| ( ( ! [SY1716: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1716 @ SV827 @ SV820 @ SV750 @ SV717 @ SV272 @ SV172 ) @ SY1716 )
| ~ ~ ( in @ ( ordered_pair @ SV827 @ ( sK34_R @ SY1716 @ SV827 @ SV820 @ SV750 @ SV717 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV820 != SY1716 )
| ~ ( in @ SV827 @ SY1716 ) ) )
= $true )
| ( ( SV776 = SV750 )
= $false )
| ( ( in @ SV776 @ ( cartesian_product2 @ SV172 @ SV717 ) )
= $false )
| ( ( in @ SV750 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5112]) ).
thf(5188,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( ( ( ordered_pair @ ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) )
!= SV751 ) )
= $false )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5113]) ).
thf(5189,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( ~ ( in @ ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 ) @ SV172 ) )
= $false )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5113]) ).
thf(5190,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( ~ ! [SY1609: $i] :
( ~ ( in @ SY1609 @ ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) @ SY1609 ) @ SV272 ) ) )
= $false )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5114]) ).
thf(5191,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( ~ ~ ( ( ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5114]) ).
thf(5192,plain,
! [SV272: $i,SV770: $i,SV172: $i,SV809: $i,SV832: $i] :
( ( ( ( SV832 != SV809 ) )
= $true )
| ( ( ~ ( in @ SV832 @ ( cartesian_product2 @ SV172 @ SV770 ) ) )
= $true )
| ( ( ! [SY1698: $i,SY1699: $i] :
( ( ( ordered_pair @ SY1698 @ SY1699 )
!= SV809 )
| ~ ( in @ SY1698 @ SV172 )
| ! [SY1700: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1700 @ SY1699 @ SY1698 @ SV809 @ SV770 @ SV272 @ SV172 ) @ SY1700 )
| ~ ~ ( in @ ( ordered_pair @ SY1699 @ ( sK34_R @ SY1700 @ SY1699 @ SY1698 @ SV809 @ SV770 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1698 != SY1700 )
| ~ ( in @ SY1699 @ SY1700 ) ) ) )
= $true )
| ( ( in @ SV809 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5115]) ).
thf(5193,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( ~ ~ ( ( ( sK33_F @ SV810 @ SV770 @ SV272 @ SV172 )
!= SV810 )
| ~ ( in @ ( sK33_F @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV770 ) ) ) )
= $false )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5116]) ).
thf(5194,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) )
!= SV810 )
| ~ ( in @ ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1701: $i] :
( ~ ( in @ SY1701 @ ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) @ SY1701 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) ) ) ) ) )
= $false )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5116]) ).
thf(5195,plain,
! [SV272: $i,SV771: $i,SV172: $i,SV811: $i,SV833: $i] :
( ( ( ( SV833 != SV811 ) )
= $true )
| ( ( ~ ( in @ SV833 @ ( cartesian_product2 @ SV172 @ SV771 ) ) )
= $true )
| ( ( ! [SY1703: $i,SY1704: $i] :
( ( ( ordered_pair @ SY1703 @ SY1704 )
!= SV811 )
| ~ ( in @ SY1703 @ SV172 )
| ! [SY1705: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1705 @ SY1704 @ SY1703 @ SV811 @ SV771 @ SV272 @ SV172 ) @ SY1705 )
| ~ ~ ( in @ ( ordered_pair @ SY1704 @ ( sK34_R @ SY1705 @ SY1704 @ SY1703 @ SV811 @ SV771 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1703 != SY1705 )
| ~ ( in @ SY1704 @ SY1705 ) ) ) )
= $true )
| ( ( in @ SV811 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5117]) ).
thf(5196,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( ~ ~ ( ( ( sK33_F @ SV812 @ SV771 @ SV272 @ SV172 )
!= SV812 )
| ~ ( in @ ( sK33_F @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV771 ) ) ) )
= $false )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5118]) ).
thf(5197,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) )
!= SV812 )
| ~ ( in @ ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1706: $i] :
( ~ ( in @ SY1706 @ ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) @ SY1706 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) ) ) ) ) )
= $false )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5118]) ).
thf(5198,plain,
! [SV772: $i,SV272: $i,SV803: $i,SV172: $i,SV834: $i] :
( ( ( ! [SY1721: $i] :
( ( SY1721 != SV834 )
| ~ ( in @ SY1721 @ ( cartesian_product2 @ SV172 @ SV803 ) ) )
| ! [SY1722: $i,SY1723: $i] :
( ( ( ordered_pair @ SY1722 @ SY1723 )
!= SV834 )
| ~ ( in @ SY1722 @ SV172 )
| ! [SY1724: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1724 @ SY1723 @ SY1722 @ SV834 @ SV803 @ SV272 @ SV172 ) @ SY1724 )
| ~ ~ ( in @ ( ordered_pair @ SY1723 @ ( sK34_R @ SY1724 @ SY1723 @ SY1722 @ SV834 @ SV803 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1722 != SY1724 )
| ~ ( in @ SY1723 @ SY1724 ) ) ) )
= $true )
| ( ( in @ SV834 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5119]) ).
thf(5199,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( ~ ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK33_F @ SV835 @ SV803 @ SV272 @ SV172 )
!= SV835 )
| ~ ( in @ ( sK33_F @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV803 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) )
!= SV835 )
| ~ ( in @ ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1725: $i] :
( ~ ( in @ SY1725 @ ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) @ SY1725 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5120]) ).
thf(5200,plain,
! [SV272: $i,SV804: $i,SV172: $i,SV836: $i] :
( ( ( ! [SY1726: $i] :
( ( SY1726 != SV836 )
| ~ ( in @ SY1726 @ ( cartesian_product2 @ SV172 @ SV804 ) ) )
| ! [SY1727: $i,SY1728: $i] :
( ( ( ordered_pair @ SY1727 @ SY1728 )
!= SV836 )
| ~ ( in @ SY1727 @ SV172 )
| ! [SY1729: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1729 @ SY1728 @ SY1727 @ SV836 @ SV804 @ SV272 @ SV172 ) @ SY1729 )
| ~ ~ ( in @ ( ordered_pair @ SY1728 @ ( sK34_R @ SY1729 @ SY1728 @ SY1727 @ SV836 @ SV804 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1727 != SY1729 )
| ~ ( in @ SY1728 @ SY1729 ) ) ) )
= $true )
| ( ( in @ SV836 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5121]) ).
thf(5201,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( ~ ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK33_F @ SV837 @ SV804 @ SV272 @ SV172 )
!= SV837 )
| ~ ( in @ ( sK33_F @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV804 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) )
!= SV837 )
| ~ ( in @ ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1730: $i] :
( ~ ( in @ SY1730 @ ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) @ SY1730 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5122]) ).
thf(5202,plain,
! [SV272: $i,SV805: $i,SV172: $i,SV838: $i] :
( ( ( ! [SY1731: $i] :
( ( SY1731 != SV838 )
| ~ ( in @ SY1731 @ ( cartesian_product2 @ SV172 @ SV805 ) ) )
| ! [SY1732: $i,SY1733: $i] :
( ( ( ordered_pair @ SY1732 @ SY1733 )
!= SV838 )
| ~ ( in @ SY1732 @ SV172 )
| ! [SY1734: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1734 @ SY1733 @ SY1732 @ SV838 @ SV805 @ SV272 @ SV172 ) @ SY1734 )
| ~ ~ ( in @ ( ordered_pair @ SY1733 @ ( sK34_R @ SY1734 @ SY1733 @ SY1732 @ SV838 @ SV805 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1732 != SY1734 )
| ~ ( in @ SY1733 @ SY1734 ) ) ) )
= $true )
| ( ( in @ SV838 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5123]) ).
thf(5203,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( ~ ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( ( sK33_F @ SV839 @ SV805 @ SV272 @ SV172 )
!= SV839 )
| ~ ( in @ ( sK33_F @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV805 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) )
!= SV839 )
| ~ ( in @ ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1735: $i] :
( ~ ( in @ SY1735 @ ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) @ SY1735 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5124]) ).
thf(5204,plain,
! [SV752: $i,SV172: $i,SV272: $i,SV692: $i,SV723: $i,SV792: $i,SV806: $i,SV846: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_R @ SV846 @ SV806 @ SV792 @ SV723 @ SV692 @ SV272 @ SV172 ) @ SV846 )
| ~ ~ ( in @ ( ordered_pair @ SV806 @ ( sK34_R @ SV846 @ SV806 @ SV792 @ SV723 @ SV692 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV792 != SV846 )
| ~ ( in @ SV806 @ SV846 ) )
= $true )
| ( ( ( ordered_pair @ SV792 @ SV806 )
= SV723 )
= $false )
| ( ( in @ SV792 @ SV172 )
= $false )
| ( ( SV752 = SV723 )
= $false )
| ( ( in @ SV752 @ ( cartesian_product2 @ SV172 @ SV692 ) )
= $false )
| ( ( in @ SV723 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5125]) ).
thf(5205,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i,SV840: $i] :
( ( ( ~ ( in @ SV840 @ ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) @ SV840 ) @ SV272 )
= $true )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5126]) ).
thf(5206,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( ( ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5127]) ).
thf(5207,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( ~ ( in @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5127]) ).
thf(5208,plain,
! [SV777: $i,SV272: $i,SV718: $i,SV172: $i,SV753: $i,SV828: $i,SV821: $i] :
( ( ( ( ( ordered_pair @ SV821 @ SV828 )
!= SV753 ) )
= $true )
| ( ( ~ ( in @ SV821 @ SV172 ) )
= $true )
| ( ( ! [SY1717: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1717 @ SV828 @ SV821 @ SV753 @ SV718 @ SV272 @ SV172 ) @ SY1717 )
| ~ ~ ( in @ ( ordered_pair @ SV828 @ ( sK34_R @ SY1717 @ SV828 @ SV821 @ SV753 @ SV718 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV821 != SY1717 )
| ~ ( in @ SV828 @ SY1717 ) ) )
= $true )
| ( ( SV777 = SV753 )
= $false )
| ( ( in @ SV777 @ ( cartesian_product2 @ SV172 @ SV718 ) )
= $false )
| ( ( in @ SV753 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5128]) ).
thf(5209,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( ( ( ordered_pair @ ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) )
!= SV754 ) )
= $false )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5129]) ).
thf(5210,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( ~ ( in @ ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 ) @ SV172 ) )
= $false )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5129]) ).
thf(5211,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( ~ ! [SY1614: $i] :
( ~ ( in @ SY1614 @ ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) @ SY1614 ) @ SV272 ) ) )
= $false )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5130]) ).
thf(5212,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( ~ ~ ( ( ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5130]) ).
thf(5213,plain,
! [SV778: $i,SV272: $i,SV719: $i,SV172: $i,SV755: $i,SV829: $i,SV822: $i] :
( ( ( ( ( ordered_pair @ SV822 @ SV829 )
!= SV755 ) )
= $true )
| ( ( ~ ( in @ SV822 @ SV172 ) )
= $true )
| ( ( ! [SY1718: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1718 @ SV829 @ SV822 @ SV755 @ SV719 @ SV272 @ SV172 ) @ SY1718 )
| ~ ~ ( in @ ( ordered_pair @ SV829 @ ( sK34_R @ SY1718 @ SV829 @ SV822 @ SV755 @ SV719 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV822 != SY1718 )
| ~ ( in @ SV829 @ SY1718 ) ) )
= $true )
| ( ( SV778 = SV755 )
= $false )
| ( ( in @ SV778 @ ( cartesian_product2 @ SV172 @ SV719 ) )
= $false )
| ( ( in @ SV755 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5131]) ).
thf(5214,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( ( ( ordered_pair @ ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) )
!= SV756 ) )
= $false )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5132]) ).
thf(5215,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( ~ ( in @ ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 ) @ SV172 ) )
= $false )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5132]) ).
thf(5216,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( ~ ! [SY1619: $i] :
( ~ ( in @ SY1619 @ ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) @ SY1619 ) @ SV272 ) ) )
= $false )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5133]) ).
thf(5217,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( ~ ~ ( ( ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5133]) ).
thf(5218,plain,
! [SV720: $i,SV813: $i,SV272: $i,SV743: $i,SV172: $i,SV779: $i,SV847: $i] :
( ( ( ! [SY1736: $i] :
( ( ( ordered_pair @ SV847 @ SY1736 )
!= SV779 )
| ~ ( in @ SV847 @ SV172 )
| ! [SY1737: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1737 @ SY1736 @ SV847 @ SV779 @ SV743 @ SV272 @ SV172 ) @ SY1737 )
| ~ ~ ( in @ ( ordered_pair @ SY1736 @ ( sK34_R @ SY1737 @ SY1736 @ SV847 @ SV779 @ SV743 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV847 != SY1737 )
| ~ ( in @ SY1736 @ SY1737 ) ) ) )
= $true )
| ( ( SV813 = SV779 )
= $false )
| ( ( in @ SV813 @ ( cartesian_product2 @ SV172 @ SV743 ) )
= $false )
| ( ( in @ SV779 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5134]) ).
thf(5219,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( ( ( sK33_F @ SV780 @ SV743 @ SV272 @ SV172 )
!= SV780 ) )
= $false )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5135]) ).
thf(5220,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( ~ ( in @ ( sK33_F @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV743 ) ) )
= $false )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5135]) ).
thf(5221,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) )
!= SV780 )
| ~ ( in @ ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 ) @ SV172 ) ) )
= $false )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5136]) ).
thf(5222,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( ~ ~ ( ~ ! [SY1652: $i] :
( ~ ( in @ SY1652 @ ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) @ SY1652 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) ) ) ) )
= $false )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5136]) ).
thf(5223,plain,
! [SV814: $i,SV272: $i,SV744: $i,SV172: $i,SV781: $i,SV848: $i] :
( ( ( ! [SY1738: $i] :
( ( ( ordered_pair @ SV848 @ SY1738 )
!= SV781 )
| ~ ( in @ SV848 @ SV172 )
| ! [SY1739: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1739 @ SY1738 @ SV848 @ SV781 @ SV744 @ SV272 @ SV172 ) @ SY1739 )
| ~ ~ ( in @ ( ordered_pair @ SY1738 @ ( sK34_R @ SY1739 @ SY1738 @ SV848 @ SV781 @ SV744 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV848 != SY1739 )
| ~ ( in @ SY1738 @ SY1739 ) ) ) )
= $true )
| ( ( SV814 = SV781 )
= $false )
| ( ( in @ SV814 @ ( cartesian_product2 @ SV172 @ SV744 ) )
= $false )
| ( ( in @ SV781 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5137]) ).
thf(5224,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( ( ( sK33_F @ SV782 @ SV744 @ SV272 @ SV172 )
!= SV782 ) )
= $false )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5138]) ).
thf(5225,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( ~ ( in @ ( sK33_F @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV744 ) ) )
= $false )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5138]) ).
thf(5226,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) )
!= SV782 )
| ~ ( in @ ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 ) @ SV172 ) ) )
= $false )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5139]) ).
thf(5227,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( ~ ~ ( ~ ! [SY1657: $i] :
( ~ ( in @ SY1657 @ ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) @ SY1657 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) ) ) ) )
= $false )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5139]) ).
thf(5228,plain,
! [SV815: $i,SV272: $i,SV745: $i,SV172: $i,SV783: $i,SV849: $i] :
( ( ( ! [SY1740: $i] :
( ( ( ordered_pair @ SV849 @ SY1740 )
!= SV783 )
| ~ ( in @ SV849 @ SV172 )
| ! [SY1741: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1741 @ SY1740 @ SV849 @ SV783 @ SV745 @ SV272 @ SV172 ) @ SY1741 )
| ~ ~ ( in @ ( ordered_pair @ SY1740 @ ( sK34_R @ SY1741 @ SY1740 @ SV849 @ SV783 @ SV745 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV849 != SY1741 )
| ~ ( in @ SY1740 @ SY1741 ) ) ) )
= $true )
| ( ( SV815 = SV783 )
= $false )
| ( ( in @ SV815 @ ( cartesian_product2 @ SV172 @ SV745 ) )
= $false )
| ( ( in @ SV783 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5140]) ).
thf(5229,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( ( ( sK33_F @ SV784 @ SV745 @ SV272 @ SV172 )
!= SV784 ) )
= $false )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5141]) ).
thf(5230,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( ~ ( in @ ( sK33_F @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV745 ) ) )
= $false )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5141]) ).
thf(5231,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) )
!= SV784 )
| ~ ( in @ ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 ) @ SV172 ) ) )
= $false )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5142]) ).
thf(5232,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( ~ ~ ( ~ ! [SY1662: $i] :
( ~ ( in @ SY1662 @ ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) @ SY1662 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) ) ) ) )
= $false )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5142]) ).
thf(5233,plain,
! [SV701: $i,SV172: $i,SV272: $i,SV622: $i,SV677: $i,SV757: $i,SV807: $i,SV746: $i] :
( ( ( ( SV746 != SV807 ) )
= $true )
| ( ( ~ ( in @ SV757 @ SV807 ) )
= $true )
| ( ( in @ ( sK34_R @ SV807 @ SV757 @ SV746 @ SV677 @ SV622 @ SV272 @ SV172 ) @ SV807 )
= $true )
| ( ( ( ordered_pair @ SV746 @ SV757 )
= SV677 )
= $false )
| ( ( in @ SV746 @ SV172 )
= $false )
| ( ( SV701 = SV677 )
= $false )
| ( ( in @ SV701 @ ( cartesian_product2 @ SV172 @ SV622 ) )
= $false )
| ( ( in @ SV677 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5143]) ).
thf(5234,plain,
! [SV701: $i,SV172: $i,SV272: $i,SV622: $i,SV677: $i,SV746: $i,SV807: $i,SV757: $i] :
( ( ( in @ ( ordered_pair @ SV757 @ ( sK34_R @ SV807 @ SV757 @ SV746 @ SV677 @ SV622 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( SV746 != SV807 )
| ~ ( in @ SV757 @ SV807 ) )
= $true )
| ( ( ( ordered_pair @ SV746 @ SV757 )
= SV677 )
= $false )
| ( ( in @ SV746 @ SV172 )
= $false )
| ( ( SV701 = SV677 )
= $false )
| ( ( in @ SV701 @ ( cartesian_product2 @ SV172 @ SV622 ) )
= $false )
| ( ( in @ SV677 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5144]) ).
thf(5235,plain,
! [SV725: $i,SV794: $i,SV139: $i,SV765: $i,SV841: $i,SV830: $i] :
( ( ( ( ( ordered_pair @ SV830 @ SV841 )
!= SV765 )
| ~ ( in @ SV830 @ SV139 ) )
= $true )
| ( ( ( SV841
!= ( singleton @ SV830 ) ) )
= $true )
| ( ( SV794 = SV765 )
= $false )
| ( ( in @ SV794 @ ( cartesian_product2 @ SV139 @ SV725 ) )
= $false )
| ( ( in @ SV765 @ ( sK13_C @ SV725 @ SV139 ) )
= $true )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5145]) ).
thf(5236,plain,
! [SV139: $i,SV725: $i,SV766: $i] :
( ( ( ( ( ordered_pair @ ( sK14_J @ SV766 @ SV725 @ SV139 ) @ ( sK15_SY612 @ SV766 @ SV725 @ SV139 ) )
!= SV766 )
| ~ ( in @ ( sK14_J @ SV766 @ SV725 @ SV139 ) @ SV139 ) )
= $false )
| ( ( in @ SV766 @ ( sK13_C @ SV725 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5148]) ).
thf(5237,plain,
! [SV726: $i,SV795: $i,SV139: $i,SV767: $i,SV842: $i,SV831: $i] :
( ( ( ( ( ordered_pair @ SV831 @ SV842 )
!= SV767 )
| ~ ( in @ SV831 @ SV139 ) )
= $true )
| ( ( ( SV842
!= ( singleton @ SV831 ) ) )
= $true )
| ( ( SV795 = SV767 )
= $false )
| ( ( in @ SV795 @ ( cartesian_product2 @ SV139 @ SV726 ) )
= $false )
| ( ( in @ SV767 @ ( sK13_C @ SV726 @ SV139 ) )
= $true )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5150]) ).
thf(5238,plain,
! [SV139: $i,SV726: $i,SV768: $i] :
( ( ( ( ( ordered_pair @ ( sK14_J @ SV768 @ SV726 @ SV139 ) @ ( sK15_SY612 @ SV768 @ SV726 @ SV139 ) )
!= SV768 )
| ~ ( in @ ( sK14_J @ SV768 @ SV726 @ SV139 ) @ SV139 ) )
= $false )
| ( ( in @ SV768 @ ( sK13_C @ SV726 @ SV139 ) )
= $false )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5153]) ).
thf(5239,plain,
! [SV694: $i,SV769: $i,SV729: $i,SV816: $i,SV139: $i,SV808: $i] :
( ( ( in @ SV808 @ SV139 )
= $false )
| ( ( ( ordered_pair @ SV808 @ SV816 )
= SV729 )
= $false )
| ( ( ( SV816
!= ( singleton @ SV808 ) ) )
= $true )
| ( ( SV769 = SV729 )
= $false )
| ( ( in @ SV769 @ ( cartesian_product2 @ SV139 @ SV694 ) )
= $false )
| ( ( in @ SV729 @ ( sK13_C @ SV694 @ SV139 ) )
= $true )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5155]) ).
thf(5240,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV796: $i,SV817: $i,SV843: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_K @ SV843 @ SV817 @ SV796 @ SV265 @ SV145 ) @ SV843 )
| ~ ~ ( in @ ( ordered_pair @ SV796 @ ( sK47_K @ SV843 @ SV817 @ SV796 @ SV265 @ SV145 ) ) @ SV265 ) ) )
= $true )
| ( ( ( SV817 != SV843 )
| ~ ( in @ SV796 @ SV843 ) )
= $true )
| ( ( in @ SV817 @ SV145 )
= $false )
| ( ( in @ SV796 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5158]) ).
thf(5241,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV797: $i] :
( ( ( ~ ! [SY1667: $i] :
( ~ ( in @ SY1667 @ ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV797 @ SY1667 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV797 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) )
| ~ ( in @ SV797 @ ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( in @ SV797 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5160]) ).
thf(5242,plain,
! [SV145: $i,SV265: $i,SV798: $i,SV818: $i,SV844: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_K @ SV844 @ SV818 @ SV798 @ SV265 @ SV145 ) @ SV844 )
| ~ ~ ( in @ ( ordered_pair @ SV798 @ ( sK47_K @ SV844 @ SV818 @ SV798 @ SV265 @ SV145 ) ) @ SV265 ) ) )
= $true )
| ( ( ( SV818 != SV844 )
| ~ ( in @ SV798 @ SV844 ) )
= $true )
| ( ( in @ SV818 @ SV145 )
= $false )
| ( ( in @ SV798 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5161]) ).
thf(5243,plain,
! [SV145: $i,SV265: $i,SV799: $i] :
( ( ( ~ ! [SY1670: $i] :
( ~ ( in @ SY1670 @ ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV799 @ SY1670 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV799 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) )
| ~ ( in @ SV799 @ ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( in @ SV799 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5163]) ).
thf(5244,plain,
! [SV145: $i,SV265: $i,SV800: $i,SV819: $i,SV845: $i] :
( ( ( ~ ( ~ ( in @ ( sK47_K @ SV845 @ SV819 @ SV800 @ SV265 @ SV145 ) @ SV845 )
| ~ ~ ( in @ ( ordered_pair @ SV800 @ ( sK47_K @ SV845 @ SV819 @ SV800 @ SV265 @ SV145 ) ) @ SV265 ) ) )
= $true )
| ( ( ( SV819 != SV845 )
| ~ ( in @ SV800 @ SV845 ) )
= $true )
| ( ( in @ SV819 @ SV145 )
= $false )
| ( ( in @ SV800 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5164]) ).
thf(5245,plain,
! [SV145: $i,SV265: $i,SV801: $i] :
( ( ( ~ ! [SY1673: $i] :
( ~ ( in @ SY1673 @ ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV801 @ SY1673 ) @ SV265 ) )
| ~ ~ ( ( ( sK45_E @ SV801 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) )
| ~ ( in @ SV801 @ ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( in @ SV801 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5166]) ).
thf(5246,plain,
! [SV145: $i,SV265: $i,SV760: $i,SV788: $i,SV734: $i] :
( ( ( in @ SV734 @ SV788 )
= $false )
| ( ( SV760 = SV788 )
= $false )
| ( ( in @ ( sK47_K @ SV788 @ SV760 @ SV734 @ SV265 @ SV145 ) @ SV788 )
= $true )
| ( ( in @ SV760 @ SV145 )
= $false )
| ( ( in @ SV734 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5167]) ).
thf(5247,plain,
! [SV145: $i,SV265: $i,SV734: $i,SV788: $i,SV760: $i] :
( ( ( SV760 = SV788 )
= $false )
| ( ( ~ ( in @ SV734 @ SV788 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV734 @ ( sK47_K @ SV788 @ SV760 @ SV734 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( in @ SV760 @ SV145 )
= $false )
| ( ( in @ SV734 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5168]) ).
thf(5248,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV762: $i,SV789: $i,SV736: $i] :
( ( ( in @ SV736 @ SV789 )
= $false )
| ( ( SV762 = SV789 )
= $false )
| ( ( in @ ( sK47_K @ SV789 @ SV762 @ SV736 @ SV265 @ SV145 ) @ SV789 )
= $true )
| ( ( in @ SV762 @ SV145 )
= $false )
| ( ( in @ SV736 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5172]) ).
thf(5249,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV736: $i,SV789: $i,SV762: $i] :
( ( ( SV762 = SV789 )
= $false )
| ( ( ~ ( in @ SV736 @ SV789 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV736 @ ( sK47_K @ SV789 @ SV762 @ SV736 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( in @ SV762 @ SV145 )
= $false )
| ( ( in @ SV736 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5173]) ).
thf(5250,plain,
! [SV145: $i,SV265: $i,SV763: $i,SV790: $i,SV738: $i] :
( ( ( in @ SV738 @ SV790 )
= $false )
| ( ( SV763 = SV790 )
= $false )
| ( ( in @ ( sK47_K @ SV790 @ SV763 @ SV738 @ SV265 @ SV145 ) @ SV790 )
= $true )
| ( ( in @ SV763 @ SV145 )
= $false )
| ( ( in @ SV738 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5177]) ).
thf(5251,plain,
! [SV145: $i,SV265: $i,SV738: $i,SV790: $i,SV763: $i] :
( ( ( SV763 = SV790 )
= $false )
| ( ( ~ ( in @ SV738 @ SV790 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV738 @ ( sK47_K @ SV790 @ SV763 @ SV738 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( in @ SV763 @ SV145 )
= $false )
| ( ( in @ SV738 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5178]) ).
thf(5252,plain,
! [SV145: $i,SV265: $i,SV764: $i,SV791: $i,SV740: $i] :
( ( ( in @ SV740 @ SV791 )
= $false )
| ( ( SV764 = SV791 )
= $false )
| ( ( in @ ( sK47_K @ SV791 @ SV764 @ SV740 @ SV265 @ SV145 ) @ SV791 )
= $true )
| ( ( in @ SV764 @ SV145 )
= $false )
| ( ( in @ SV740 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5182]) ).
thf(5253,plain,
! [SV145: $i,SV265: $i,SV740: $i,SV791: $i,SV764: $i] :
( ( ( SV764 = SV791 )
= $false )
| ( ( ~ ( in @ SV740 @ SV791 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV740 @ ( sK47_K @ SV791 @ SV764 @ SV740 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( in @ SV764 @ SV145 )
= $false )
| ( ( in @ SV740 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5183]) ).
thf(5254,plain,
! [SV776: $i,SV272: $i,SV717: $i,SV172: $i,SV750: $i,SV827: $i,SV820: $i] :
( ( ( ( ordered_pair @ SV820 @ SV827 )
= SV750 )
= $false )
| ( ( ~ ( in @ SV820 @ SV172 ) )
= $true )
| ( ( ! [SY1716: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1716 @ SV827 @ SV820 @ SV750 @ SV717 @ SV272 @ SV172 ) @ SY1716 )
| ~ ~ ( in @ ( ordered_pair @ SV827 @ ( sK34_R @ SY1716 @ SV827 @ SV820 @ SV750 @ SV717 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV820 != SY1716 )
| ~ ( in @ SV827 @ SY1716 ) ) )
= $true )
| ( ( SV776 = SV750 )
= $false )
| ( ( in @ SV776 @ ( cartesian_product2 @ SV172 @ SV717 ) )
= $false )
| ( ( in @ SV750 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5187]) ).
thf(5255,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( ( ordered_pair @ ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) )
= SV751 )
= $true )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5188]) ).
thf(5256,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( in @ ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5189]) ).
thf(5257,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( ! [SY1609: $i] :
( ~ ( in @ SY1609 @ ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) @ SY1609 ) @ SV272 ) ) )
= $true )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5190]) ).
thf(5258,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( ~ ( ( ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) ) ) )
= $true )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5191]) ).
thf(5259,plain,
! [SV272: $i,SV770: $i,SV172: $i,SV809: $i,SV832: $i] :
( ( ( SV832 = SV809 )
= $false )
| ( ( ~ ( in @ SV832 @ ( cartesian_product2 @ SV172 @ SV770 ) ) )
= $true )
| ( ( ! [SY1698: $i,SY1699: $i] :
( ( ( ordered_pair @ SY1698 @ SY1699 )
!= SV809 )
| ~ ( in @ SY1698 @ SV172 )
| ! [SY1700: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1700 @ SY1699 @ SY1698 @ SV809 @ SV770 @ SV272 @ SV172 ) @ SY1700 )
| ~ ~ ( in @ ( ordered_pair @ SY1699 @ ( sK34_R @ SY1700 @ SY1699 @ SY1698 @ SV809 @ SV770 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1698 != SY1700 )
| ~ ( in @ SY1699 @ SY1700 ) ) ) )
= $true )
| ( ( in @ SV809 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5192]) ).
thf(5260,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( ~ ( ( ( sK33_F @ SV810 @ SV770 @ SV272 @ SV172 )
!= SV810 )
| ~ ( in @ ( sK33_F @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV770 ) ) ) )
= $true )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5193]) ).
thf(5261,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) )
!= SV810 )
| ~ ( in @ ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1701: $i] :
( ~ ( in @ SY1701 @ ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) @ SY1701 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) ) ) ) ) )
= $true )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5194]) ).
thf(5262,plain,
! [SV272: $i,SV771: $i,SV172: $i,SV811: $i,SV833: $i] :
( ( ( SV833 = SV811 )
= $false )
| ( ( ~ ( in @ SV833 @ ( cartesian_product2 @ SV172 @ SV771 ) ) )
= $true )
| ( ( ! [SY1703: $i,SY1704: $i] :
( ( ( ordered_pair @ SY1703 @ SY1704 )
!= SV811 )
| ~ ( in @ SY1703 @ SV172 )
| ! [SY1705: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1705 @ SY1704 @ SY1703 @ SV811 @ SV771 @ SV272 @ SV172 ) @ SY1705 )
| ~ ~ ( in @ ( ordered_pair @ SY1704 @ ( sK34_R @ SY1705 @ SY1704 @ SY1703 @ SV811 @ SV771 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1703 != SY1705 )
| ~ ( in @ SY1704 @ SY1705 ) ) ) )
= $true )
| ( ( in @ SV811 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5195]) ).
thf(5263,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( ~ ( ( ( sK33_F @ SV812 @ SV771 @ SV272 @ SV172 )
!= SV812 )
| ~ ( in @ ( sK33_F @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV771 ) ) ) )
= $true )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5196]) ).
thf(5264,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) )
!= SV812 )
| ~ ( in @ ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1706: $i] :
( ~ ( in @ SY1706 @ ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) @ SY1706 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) ) ) ) ) )
= $true )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5197]) ).
thf(5265,plain,
! [SV772: $i,SV272: $i,SV803: $i,SV172: $i,SV834: $i] :
( ( ( ! [SY1721: $i] :
( ( SY1721 != SV834 )
| ~ ( in @ SY1721 @ ( cartesian_product2 @ SV172 @ SV803 ) ) ) )
= $true )
| ( ( ! [SY1722: $i,SY1723: $i] :
( ( ( ordered_pair @ SY1722 @ SY1723 )
!= SV834 )
| ~ ( in @ SY1722 @ SV172 )
| ! [SY1724: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1724 @ SY1723 @ SY1722 @ SV834 @ SV803 @ SV272 @ SV172 ) @ SY1724 )
| ~ ~ ( in @ ( ordered_pair @ SY1723 @ ( sK34_R @ SY1724 @ SY1723 @ SY1722 @ SV834 @ SV803 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1722 != SY1724 )
| ~ ( in @ SY1723 @ SY1724 ) ) ) )
= $true )
| ( ( in @ SV834 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5198]) ).
thf(5266,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK33_F @ SV835 @ SV803 @ SV272 @ SV172 )
!= SV835 )
| ~ ( in @ ( sK33_F @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV803 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) )
!= SV835 )
| ~ ( in @ ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1725: $i] :
( ~ ( in @ SY1725 @ ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) @ SY1725 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5199]) ).
thf(5267,plain,
! [SV272: $i,SV804: $i,SV172: $i,SV836: $i] :
( ( ( ! [SY1726: $i] :
( ( SY1726 != SV836 )
| ~ ( in @ SY1726 @ ( cartesian_product2 @ SV172 @ SV804 ) ) ) )
= $true )
| ( ( ! [SY1727: $i,SY1728: $i] :
( ( ( ordered_pair @ SY1727 @ SY1728 )
!= SV836 )
| ~ ( in @ SY1727 @ SV172 )
| ! [SY1729: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1729 @ SY1728 @ SY1727 @ SV836 @ SV804 @ SV272 @ SV172 ) @ SY1729 )
| ~ ~ ( in @ ( ordered_pair @ SY1728 @ ( sK34_R @ SY1729 @ SY1728 @ SY1727 @ SV836 @ SV804 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1727 != SY1729 )
| ~ ( in @ SY1728 @ SY1729 ) ) ) )
= $true )
| ( ( in @ SV836 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5200]) ).
thf(5268,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK33_F @ SV837 @ SV804 @ SV272 @ SV172 )
!= SV837 )
| ~ ( in @ ( sK33_F @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV804 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) )
!= SV837 )
| ~ ( in @ ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1730: $i] :
( ~ ( in @ SY1730 @ ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) @ SY1730 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5201]) ).
thf(5269,plain,
! [SV272: $i,SV805: $i,SV172: $i,SV838: $i] :
( ( ( ! [SY1731: $i] :
( ( SY1731 != SV838 )
| ~ ( in @ SY1731 @ ( cartesian_product2 @ SV172 @ SV805 ) ) ) )
= $true )
| ( ( ! [SY1732: $i,SY1733: $i] :
( ( ( ordered_pair @ SY1732 @ SY1733 )
!= SV838 )
| ~ ( in @ SY1732 @ SV172 )
| ! [SY1734: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1734 @ SY1733 @ SY1732 @ SV838 @ SV805 @ SV272 @ SV172 ) @ SY1734 )
| ~ ~ ( in @ ( ordered_pair @ SY1733 @ ( sK34_R @ SY1734 @ SY1733 @ SY1732 @ SV838 @ SV805 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1732 != SY1734 )
| ~ ( in @ SY1733 @ SY1734 ) ) ) )
= $true )
| ( ( in @ SV838 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5202]) ).
thf(5270,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( ( sK33_F @ SV839 @ SV805 @ SV272 @ SV172 )
!= SV839 )
| ~ ( in @ ( sK33_F @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV805 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) )
!= SV839 )
| ~ ( in @ ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1735: $i] :
( ~ ( in @ SY1735 @ ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) @ SY1735 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5203]) ).
thf(5271,plain,
! [SV752: $i,SV172: $i,SV272: $i,SV692: $i,SV723: $i,SV792: $i,SV806: $i,SV846: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_R @ SV846 @ SV806 @ SV792 @ SV723 @ SV692 @ SV272 @ SV172 ) @ SV846 )
| ~ ~ ( in @ ( ordered_pair @ SV806 @ ( sK34_R @ SV846 @ SV806 @ SV792 @ SV723 @ SV692 @ SV272 @ SV172 ) ) @ SV272 ) ) )
= $true )
| ( ( ( SV792 != SV846 )
| ~ ( in @ SV806 @ SV846 ) )
= $true )
| ( ( ( ordered_pair @ SV792 @ SV806 )
= SV723 )
= $false )
| ( ( in @ SV792 @ SV172 )
= $false )
| ( ( SV752 = SV723 )
= $false )
| ( ( in @ SV752 @ ( cartesian_product2 @ SV172 @ SV692 ) )
= $false )
| ( ( in @ SV723 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5204]) ).
thf(5272,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i,SV840: $i] :
( ( ( in @ SV840 @ ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) @ SV840 ) @ SV272 )
= $true )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5205]) ).
thf(5273,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( ( sK30_O @ SV724 @ SV692 @ SV272 @ SV172 )
= ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5206]) ).
thf(5274,plain,
! [SV172: $i,SV272: $i,SV692: $i,SV724: $i] :
( ( ( in @ ( sK31_SY649 @ SV724 @ SV692 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV724 @ SV692 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ SV724 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5207]) ).
thf(5275,plain,
! [SV777: $i,SV272: $i,SV718: $i,SV172: $i,SV753: $i,SV828: $i,SV821: $i] :
( ( ( ( ordered_pair @ SV821 @ SV828 )
= SV753 )
= $false )
| ( ( ~ ( in @ SV821 @ SV172 ) )
= $true )
| ( ( ! [SY1717: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1717 @ SV828 @ SV821 @ SV753 @ SV718 @ SV272 @ SV172 ) @ SY1717 )
| ~ ~ ( in @ ( ordered_pair @ SV828 @ ( sK34_R @ SY1717 @ SV828 @ SV821 @ SV753 @ SV718 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV821 != SY1717 )
| ~ ( in @ SV828 @ SY1717 ) ) )
= $true )
| ( ( SV777 = SV753 )
= $false )
| ( ( in @ SV777 @ ( cartesian_product2 @ SV172 @ SV718 ) )
= $false )
| ( ( in @ SV753 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5208]) ).
thf(5276,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( ( ordered_pair @ ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) )
= SV754 )
= $true )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5209]) ).
thf(5277,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( in @ ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5210]) ).
thf(5278,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( ! [SY1614: $i] :
( ~ ( in @ SY1614 @ ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) @ SY1614 ) @ SV272 ) ) )
= $true )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5211]) ).
thf(5279,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( ~ ( ( ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) ) ) )
= $true )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5212]) ).
thf(5280,plain,
! [SV778: $i,SV272: $i,SV719: $i,SV172: $i,SV755: $i,SV829: $i,SV822: $i] :
( ( ( ( ordered_pair @ SV822 @ SV829 )
= SV755 )
= $false )
| ( ( ~ ( in @ SV822 @ SV172 ) )
= $true )
| ( ( ! [SY1718: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1718 @ SV829 @ SV822 @ SV755 @ SV719 @ SV272 @ SV172 ) @ SY1718 )
| ~ ~ ( in @ ( ordered_pair @ SV829 @ ( sK34_R @ SY1718 @ SV829 @ SV822 @ SV755 @ SV719 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV822 != SY1718 )
| ~ ( in @ SV829 @ SY1718 ) ) )
= $true )
| ( ( SV778 = SV755 )
= $false )
| ( ( in @ SV778 @ ( cartesian_product2 @ SV172 @ SV719 ) )
= $false )
| ( ( in @ SV755 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5213]) ).
thf(5281,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( ( ordered_pair @ ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) )
= SV756 )
= $true )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5214]) ).
thf(5282,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( in @ ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5215]) ).
thf(5283,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( ! [SY1619: $i] :
( ~ ( in @ SY1619 @ ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) @ SY1619 ) @ SV272 ) ) )
= $true )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5216]) ).
thf(5284,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( ~ ( ( ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) ) ) )
= $true )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5217]) ).
thf(5285,plain,
! [SV720: $i,SV813: $i,SV272: $i,SV743: $i,SV172: $i,SV779: $i,SV850: $i,SV847: $i] :
( ( ( ( ( ordered_pair @ SV847 @ SV850 )
!= SV779 )
| ~ ( in @ SV847 @ SV172 )
| ! [SY1742: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1742 @ SV850 @ SV847 @ SV779 @ SV743 @ SV272 @ SV172 ) @ SY1742 )
| ~ ~ ( in @ ( ordered_pair @ SV850 @ ( sK34_R @ SY1742 @ SV850 @ SV847 @ SV779 @ SV743 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV847 != SY1742 )
| ~ ( in @ SV850 @ SY1742 ) ) )
= $true )
| ( ( SV813 = SV779 )
= $false )
| ( ( in @ SV813 @ ( cartesian_product2 @ SV172 @ SV743 ) )
= $false )
| ( ( in @ SV779 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5218]) ).
thf(5286,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( ( sK33_F @ SV780 @ SV743 @ SV272 @ SV172 )
= SV780 )
= $true )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5219]) ).
thf(5287,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( in @ ( sK33_F @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV743 ) )
= $true )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5220]) ).
thf(5288,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) )
!= SV780 )
| ~ ( in @ ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 ) @ SV172 ) ) )
= $true )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5221]) ).
thf(5289,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( ~ ( ~ ! [SY1652: $i] :
( ~ ( in @ SY1652 @ ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) @ SY1652 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) ) ) ) )
= $true )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5222]) ).
thf(5290,plain,
! [SV814: $i,SV272: $i,SV744: $i,SV172: $i,SV781: $i,SV851: $i,SV848: $i] :
( ( ( ( ( ordered_pair @ SV848 @ SV851 )
!= SV781 )
| ~ ( in @ SV848 @ SV172 )
| ! [SY1743: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1743 @ SV851 @ SV848 @ SV781 @ SV744 @ SV272 @ SV172 ) @ SY1743 )
| ~ ~ ( in @ ( ordered_pair @ SV851 @ ( sK34_R @ SY1743 @ SV851 @ SV848 @ SV781 @ SV744 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV848 != SY1743 )
| ~ ( in @ SV851 @ SY1743 ) ) )
= $true )
| ( ( SV814 = SV781 )
= $false )
| ( ( in @ SV814 @ ( cartesian_product2 @ SV172 @ SV744 ) )
= $false )
| ( ( in @ SV781 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5223]) ).
thf(5291,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( ( sK33_F @ SV782 @ SV744 @ SV272 @ SV172 )
= SV782 )
= $true )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5224]) ).
thf(5292,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( in @ ( sK33_F @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV744 ) )
= $true )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5225]) ).
thf(5293,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) )
!= SV782 )
| ~ ( in @ ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 ) @ SV172 ) ) )
= $true )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5226]) ).
thf(5294,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( ~ ( ~ ! [SY1657: $i] :
( ~ ( in @ SY1657 @ ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) @ SY1657 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) ) ) ) )
= $true )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5227]) ).
thf(5295,plain,
! [SV815: $i,SV272: $i,SV745: $i,SV172: $i,SV783: $i,SV852: $i,SV849: $i] :
( ( ( ( ( ordered_pair @ SV849 @ SV852 )
!= SV783 )
| ~ ( in @ SV849 @ SV172 )
| ! [SY1744: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1744 @ SV852 @ SV849 @ SV783 @ SV745 @ SV272 @ SV172 ) @ SY1744 )
| ~ ~ ( in @ ( ordered_pair @ SV852 @ ( sK34_R @ SY1744 @ SV852 @ SV849 @ SV783 @ SV745 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV849 != SY1744 )
| ~ ( in @ SV852 @ SY1744 ) ) )
= $true )
| ( ( SV815 = SV783 )
= $false )
| ( ( in @ SV815 @ ( cartesian_product2 @ SV172 @ SV745 ) )
= $false )
| ( ( in @ SV783 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5228]) ).
thf(5296,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( ( sK33_F @ SV784 @ SV745 @ SV272 @ SV172 )
= SV784 )
= $true )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5229]) ).
thf(5297,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( in @ ( sK33_F @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV745 ) )
= $true )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5230]) ).
thf(5298,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) )
!= SV784 )
| ~ ( in @ ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 ) @ SV172 ) ) )
= $true )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5231]) ).
thf(5299,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( ~ ( ~ ! [SY1662: $i] :
( ~ ( in @ SY1662 @ ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) @ SY1662 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) ) ) ) )
= $true )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5232]) ).
thf(5300,plain,
! [SV701: $i,SV172: $i,SV272: $i,SV622: $i,SV677: $i,SV757: $i,SV807: $i,SV746: $i] :
( ( ( SV746 = SV807 )
= $false )
| ( ( ~ ( in @ SV757 @ SV807 ) )
= $true )
| ( ( in @ ( sK34_R @ SV807 @ SV757 @ SV746 @ SV677 @ SV622 @ SV272 @ SV172 ) @ SV807 )
= $true )
| ( ( ( ordered_pair @ SV746 @ SV757 )
= SV677 )
= $false )
| ( ( in @ SV746 @ SV172 )
= $false )
| ( ( SV701 = SV677 )
= $false )
| ( ( in @ SV701 @ ( cartesian_product2 @ SV172 @ SV622 ) )
= $false )
| ( ( in @ SV677 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5233]) ).
thf(5301,plain,
! [SV701: $i,SV172: $i,SV272: $i,SV622: $i,SV677: $i,SV757: $i,SV807: $i,SV746: $i] :
( ( ( ( SV746 != SV807 ) )
= $true )
| ( ( ~ ( in @ SV757 @ SV807 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV757 @ ( sK34_R @ SV807 @ SV757 @ SV746 @ SV677 @ SV622 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV746 @ SV757 )
= SV677 )
= $false )
| ( ( in @ SV746 @ SV172 )
= $false )
| ( ( SV701 = SV677 )
= $false )
| ( ( in @ SV701 @ ( cartesian_product2 @ SV172 @ SV622 ) )
= $false )
| ( ( in @ SV677 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5234]) ).
thf(5302,plain,
! [SV725: $i,SV794: $i,SV139: $i,SV765: $i,SV841: $i,SV830: $i] :
( ( ( ( ( ordered_pair @ SV830 @ SV841 )
!= SV765 ) )
= $true )
| ( ( ~ ( in @ SV830 @ SV139 ) )
= $true )
| ( ( ( SV841
!= ( singleton @ SV830 ) ) )
= $true )
| ( ( SV794 = SV765 )
= $false )
| ( ( in @ SV794 @ ( cartesian_product2 @ SV139 @ SV725 ) )
= $false )
| ( ( in @ SV765 @ ( sK13_C @ SV725 @ SV139 ) )
= $true )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5235]) ).
thf(5303,plain,
! [SV139: $i,SV725: $i,SV766: $i] :
( ( ( ( ( ordered_pair @ ( sK14_J @ SV766 @ SV725 @ SV139 ) @ ( sK15_SY612 @ SV766 @ SV725 @ SV139 ) )
!= SV766 ) )
= $false )
| ( ( in @ SV766 @ ( sK13_C @ SV725 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5236]) ).
thf(5304,plain,
! [SV139: $i,SV725: $i,SV766: $i] :
( ( ( ~ ( in @ ( sK14_J @ SV766 @ SV725 @ SV139 ) @ SV139 ) )
= $false )
| ( ( in @ SV766 @ ( sK13_C @ SV725 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5236]) ).
thf(5305,plain,
! [SV726: $i,SV795: $i,SV139: $i,SV767: $i,SV842: $i,SV831: $i] :
( ( ( ( ( ordered_pair @ SV831 @ SV842 )
!= SV767 ) )
= $true )
| ( ( ~ ( in @ SV831 @ SV139 ) )
= $true )
| ( ( ( SV842
!= ( singleton @ SV831 ) ) )
= $true )
| ( ( SV795 = SV767 )
= $false )
| ( ( in @ SV795 @ ( cartesian_product2 @ SV139 @ SV726 ) )
= $false )
| ( ( in @ SV767 @ ( sK13_C @ SV726 @ SV139 ) )
= $true )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5237]) ).
thf(5306,plain,
! [SV139: $i,SV726: $i,SV768: $i] :
( ( ( ( ( ordered_pair @ ( sK14_J @ SV768 @ SV726 @ SV139 ) @ ( sK15_SY612 @ SV768 @ SV726 @ SV139 ) )
!= SV768 ) )
= $false )
| ( ( in @ SV768 @ ( sK13_C @ SV726 @ SV139 ) )
= $false )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5238]) ).
thf(5307,plain,
! [SV139: $i,SV726: $i,SV768: $i] :
( ( ( ~ ( in @ ( sK14_J @ SV768 @ SV726 @ SV139 ) @ SV139 ) )
= $false )
| ( ( in @ SV768 @ ( sK13_C @ SV726 @ SV139 ) )
= $false )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5238]) ).
thf(5308,plain,
! [SV694: $i,SV769: $i,SV139: $i,SV729: $i,SV808: $i,SV816: $i] :
( ( ( SV816
= ( singleton @ SV808 ) )
= $false )
| ( ( ( ordered_pair @ SV808 @ SV816 )
= SV729 )
= $false )
| ( ( in @ SV808 @ SV139 )
= $false )
| ( ( SV769 = SV729 )
= $false )
| ( ( in @ SV769 @ ( cartesian_product2 @ SV139 @ SV694 ) )
= $false )
| ( ( in @ SV729 @ ( sK13_C @ SV694 @ SV139 ) )
= $true )
| ( ( ( sK23_SY629 @ SV139 )
= ( singleton @ ( sK22_SY620 @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5239]) ).
thf(5309,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV796: $i,SV817: $i,SV843: $i] :
( ( ( ~ ( in @ ( sK47_K @ SV843 @ SV817 @ SV796 @ SV265 @ SV145 ) @ SV843 )
| ~ ~ ( in @ ( ordered_pair @ SV796 @ ( sK47_K @ SV843 @ SV817 @ SV796 @ SV265 @ SV145 ) ) @ SV265 ) )
= $false )
| ( ( ( SV817 != SV843 )
| ~ ( in @ SV796 @ SV843 ) )
= $true )
| ( ( in @ SV817 @ SV145 )
= $false )
| ( ( in @ SV796 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5240]) ).
thf(5310,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV797: $i] :
( ( ( ~ ! [SY1667: $i] :
( ~ ( in @ SY1667 @ ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV797 @ SY1667 ) @ SV265 ) ) )
= $false )
| ( ( in @ SV797 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5241]) ).
thf(5311,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV797: $i] :
( ( ( ~ ~ ( ( ( sK45_E @ SV797 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) )
| ~ ( in @ SV797 @ ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( in @ SV797 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5241]) ).
thf(5312,plain,
! [SV145: $i,SV265: $i,SV798: $i,SV818: $i,SV844: $i] :
( ( ( ~ ( in @ ( sK47_K @ SV844 @ SV818 @ SV798 @ SV265 @ SV145 ) @ SV844 )
| ~ ~ ( in @ ( ordered_pair @ SV798 @ ( sK47_K @ SV844 @ SV818 @ SV798 @ SV265 @ SV145 ) ) @ SV265 ) )
= $false )
| ( ( ( SV818 != SV844 )
| ~ ( in @ SV798 @ SV844 ) )
= $true )
| ( ( in @ SV818 @ SV145 )
= $false )
| ( ( in @ SV798 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5242]) ).
thf(5313,plain,
! [SV145: $i,SV265: $i,SV799: $i] :
( ( ( ~ ! [SY1670: $i] :
( ~ ( in @ SY1670 @ ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV799 @ SY1670 ) @ SV265 ) ) )
= $false )
| ( ( in @ SV799 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5243]) ).
thf(5314,plain,
! [SV145: $i,SV265: $i,SV799: $i] :
( ( ( ~ ~ ( ( ( sK45_E @ SV799 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) )
| ~ ( in @ SV799 @ ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( in @ SV799 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5243]) ).
thf(5315,plain,
! [SV145: $i,SV265: $i,SV800: $i,SV819: $i,SV845: $i] :
( ( ( ~ ( in @ ( sK47_K @ SV845 @ SV819 @ SV800 @ SV265 @ SV145 ) @ SV845 )
| ~ ~ ( in @ ( ordered_pair @ SV800 @ ( sK47_K @ SV845 @ SV819 @ SV800 @ SV265 @ SV145 ) ) @ SV265 ) )
= $false )
| ( ( ( SV819 != SV845 )
| ~ ( in @ SV800 @ SV845 ) )
= $true )
| ( ( in @ SV819 @ SV145 )
= $false )
| ( ( in @ SV800 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5244]) ).
thf(5316,plain,
! [SV145: $i,SV265: $i,SV801: $i] :
( ( ( ~ ! [SY1673: $i] :
( ~ ( in @ SY1673 @ ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV801 @ SY1673 ) @ SV265 ) ) )
= $false )
| ( ( in @ SV801 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5245]) ).
thf(5317,plain,
! [SV145: $i,SV265: $i,SV801: $i] :
( ( ( ~ ~ ( ( ( sK45_E @ SV801 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) )
| ~ ( in @ SV801 @ ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) ) ) )
= $false )
| ( ( in @ SV801 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5245]) ).
thf(5318,plain,
! [SV145: $i,SV265: $i,SV760: $i,SV788: $i,SV734: $i] :
( ( ( in @ SV734 @ SV788 )
= $false )
| ( ( SV760 = SV788 )
= $false )
| ( ( in @ ( ordered_pair @ SV734 @ ( sK47_K @ SV788 @ SV760 @ SV734 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( in @ SV760 @ SV145 )
= $false )
| ( ( in @ SV734 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK48_C @ SV265 @ SV145 ) @ SV145 )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5247]) ).
thf(5319,plain,
! [SV685: $i,SV145: $i,SV265: $i,SV762: $i,SV789: $i,SV736: $i] :
( ( ( in @ SV736 @ SV789 )
= $false )
| ( ( SV762 = SV789 )
= $false )
| ( ( in @ ( ordered_pair @ SV736 @ ( sK47_K @ SV789 @ SV762 @ SV736 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( in @ SV762 @ SV145 )
= $false )
| ( ( in @ SV736 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK50_SY711 @ SV265 @ SV145 ) @ SV685 ) @ SV265 )
= $true )
| ( ( in @ SV685 @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5249]) ).
thf(5320,plain,
! [SV145: $i,SV265: $i,SV763: $i,SV790: $i,SV738: $i] :
( ( ( in @ SV738 @ SV790 )
= $false )
| ( ( SV763 = SV790 )
= $false )
| ( ( in @ ( ordered_pair @ SV738 @ ( sK47_K @ SV790 @ SV763 @ SV738 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( in @ SV763 @ SV145 )
= $false )
| ( ( in @ SV738 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5251]) ).
thf(5321,plain,
! [SV145: $i,SV265: $i,SV764: $i,SV791: $i,SV740: $i] :
( ( ( in @ SV740 @ SV791 )
= $false )
| ( ( SV764 = SV791 )
= $false )
| ( ( in @ ( ordered_pair @ SV740 @ ( sK47_K @ SV791 @ SV764 @ SV740 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( in @ SV764 @ SV145 )
= $false )
| ( ( in @ SV740 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK50_SY711 @ SV265 @ SV145 ) @ ( sK51_SY718 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5253]) ).
thf(5322,plain,
! [SV776: $i,SV272: $i,SV717: $i,SV750: $i,SV827: $i,SV172: $i,SV820: $i] :
( ( ( in @ SV820 @ SV172 )
= $false )
| ( ( ( ordered_pair @ SV820 @ SV827 )
= SV750 )
= $false )
| ( ( ! [SY1716: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1716 @ SV827 @ SV820 @ SV750 @ SV717 @ SV272 @ SV172 ) @ SY1716 )
| ~ ~ ( in @ ( ordered_pair @ SV827 @ ( sK34_R @ SY1716 @ SV827 @ SV820 @ SV750 @ SV717 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV820 != SY1716 )
| ~ ( in @ SV827 @ SY1716 ) ) )
= $true )
| ( ( SV776 = SV750 )
= $false )
| ( ( in @ SV776 @ ( cartesian_product2 @ SV172 @ SV717 ) )
= $false )
| ( ( in @ SV750 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5254]) ).
thf(5323,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i,SV853: $i] :
( ( ( ~ ( in @ SV853 @ ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) @ SV853 ) @ SV272 ) )
= $true )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5257]) ).
thf(5324,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( ( ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5258]) ).
thf(5325,plain,
! [SV272: $i,SV809: $i,SV770: $i,SV172: $i,SV832: $i] :
( ( ( in @ SV832 @ ( cartesian_product2 @ SV172 @ SV770 ) )
= $false )
| ( ( SV832 = SV809 )
= $false )
| ( ( ! [SY1698: $i,SY1699: $i] :
( ( ( ordered_pair @ SY1698 @ SY1699 )
!= SV809 )
| ~ ( in @ SY1698 @ SV172 )
| ! [SY1700: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1700 @ SY1699 @ SY1698 @ SV809 @ SV770 @ SV272 @ SV172 ) @ SY1700 )
| ~ ~ ( in @ ( ordered_pair @ SY1699 @ ( sK34_R @ SY1700 @ SY1699 @ SY1698 @ SV809 @ SV770 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1698 != SY1700 )
| ~ ( in @ SY1699 @ SY1700 ) ) ) )
= $true )
| ( ( in @ SV809 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5259]) ).
thf(5326,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( ( ( sK33_F @ SV810 @ SV770 @ SV272 @ SV172 )
!= SV810 )
| ~ ( in @ ( sK33_F @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV770 ) ) )
= $false )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5260]) ).
thf(5327,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) )
!= SV810 )
| ~ ( in @ ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1701: $i] :
( ~ ( in @ SY1701 @ ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) @ SY1701 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) ) ) ) )
= $false )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5261]) ).
thf(5328,plain,
! [SV272: $i,SV811: $i,SV771: $i,SV172: $i,SV833: $i] :
( ( ( in @ SV833 @ ( cartesian_product2 @ SV172 @ SV771 ) )
= $false )
| ( ( SV833 = SV811 )
= $false )
| ( ( ! [SY1703: $i,SY1704: $i] :
( ( ( ordered_pair @ SY1703 @ SY1704 )
!= SV811 )
| ~ ( in @ SY1703 @ SV172 )
| ! [SY1705: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1705 @ SY1704 @ SY1703 @ SV811 @ SV771 @ SV272 @ SV172 ) @ SY1705 )
| ~ ~ ( in @ ( ordered_pair @ SY1704 @ ( sK34_R @ SY1705 @ SY1704 @ SY1703 @ SV811 @ SV771 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1703 != SY1705 )
| ~ ( in @ SY1704 @ SY1705 ) ) ) )
= $true )
| ( ( in @ SV811 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5262]) ).
thf(5329,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( ( ( sK33_F @ SV812 @ SV771 @ SV272 @ SV172 )
!= SV812 )
| ~ ( in @ ( sK33_F @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV771 ) ) )
= $false )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5263]) ).
thf(5330,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) )
!= SV812 )
| ~ ( in @ ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1706: $i] :
( ~ ( in @ SY1706 @ ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) @ SY1706 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) ) ) ) )
= $false )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5264]) ).
thf(5331,plain,
! [SV772: $i,SV272: $i,SV803: $i,SV172: $i,SV834: $i,SV854: $i] :
( ( ( ( SV854 != SV834 )
| ~ ( in @ SV854 @ ( cartesian_product2 @ SV172 @ SV803 ) ) )
= $true )
| ( ( ! [SY1722: $i,SY1723: $i] :
( ( ( ordered_pair @ SY1722 @ SY1723 )
!= SV834 )
| ~ ( in @ SY1722 @ SV172 )
| ! [SY1724: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1724 @ SY1723 @ SY1722 @ SV834 @ SV803 @ SV272 @ SV172 ) @ SY1724 )
| ~ ~ ( in @ ( ordered_pair @ SY1723 @ ( sK34_R @ SY1724 @ SY1723 @ SY1722 @ SV834 @ SV803 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1722 != SY1724 )
| ~ ( in @ SY1723 @ SY1724 ) ) ) )
= $true )
| ( ( in @ SV834 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5265]) ).
thf(5332,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( ~ ~ ( ( ( sK33_F @ SV835 @ SV803 @ SV272 @ SV172 )
!= SV835 )
| ~ ( in @ ( sK33_F @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV803 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) )
!= SV835 )
| ~ ( in @ ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1725: $i] :
( ~ ( in @ SY1725 @ ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) @ SY1725 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) ) ) ) ) )
= $false )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5266]) ).
thf(5333,plain,
! [SV272: $i,SV804: $i,SV172: $i,SV836: $i,SV855: $i] :
( ( ( ( SV855 != SV836 )
| ~ ( in @ SV855 @ ( cartesian_product2 @ SV172 @ SV804 ) ) )
= $true )
| ( ( ! [SY1727: $i,SY1728: $i] :
( ( ( ordered_pair @ SY1727 @ SY1728 )
!= SV836 )
| ~ ( in @ SY1727 @ SV172 )
| ! [SY1729: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1729 @ SY1728 @ SY1727 @ SV836 @ SV804 @ SV272 @ SV172 ) @ SY1729 )
| ~ ~ ( in @ ( ordered_pair @ SY1728 @ ( sK34_R @ SY1729 @ SY1728 @ SY1727 @ SV836 @ SV804 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1727 != SY1729 )
| ~ ( in @ SY1728 @ SY1729 ) ) ) )
= $true )
| ( ( in @ SV836 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5267]) ).
thf(5334,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( ~ ~ ( ( ( sK33_F @ SV837 @ SV804 @ SV272 @ SV172 )
!= SV837 )
| ~ ( in @ ( sK33_F @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV804 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) )
!= SV837 )
| ~ ( in @ ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1730: $i] :
( ~ ( in @ SY1730 @ ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) @ SY1730 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) ) ) ) ) )
= $false )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5268]) ).
thf(5335,plain,
! [SV272: $i,SV805: $i,SV172: $i,SV838: $i,SV856: $i] :
( ( ( ( SV856 != SV838 )
| ~ ( in @ SV856 @ ( cartesian_product2 @ SV172 @ SV805 ) ) )
= $true )
| ( ( ! [SY1732: $i,SY1733: $i] :
( ( ( ordered_pair @ SY1732 @ SY1733 )
!= SV838 )
| ~ ( in @ SY1732 @ SV172 )
| ! [SY1734: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1734 @ SY1733 @ SY1732 @ SV838 @ SV805 @ SV272 @ SV172 ) @ SY1734 )
| ~ ~ ( in @ ( ordered_pair @ SY1733 @ ( sK34_R @ SY1734 @ SY1733 @ SY1732 @ SV838 @ SV805 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1732 != SY1734 )
| ~ ( in @ SY1733 @ SY1734 ) ) ) )
= $true )
| ( ( in @ SV838 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5269]) ).
thf(5336,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( ~ ~ ( ( ( sK33_F @ SV839 @ SV805 @ SV272 @ SV172 )
!= SV839 )
| ~ ( in @ ( sK33_F @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV805 ) ) )
| ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) )
!= SV839 )
| ~ ( in @ ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1735: $i] :
( ~ ( in @ SY1735 @ ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) @ SY1735 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) ) ) ) ) )
= $false )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5270]) ).
thf(5337,plain,
! [SV752: $i,SV172: $i,SV272: $i,SV692: $i,SV723: $i,SV792: $i,SV806: $i,SV846: $i] :
( ( ( ~ ( in @ ( sK34_R @ SV846 @ SV806 @ SV792 @ SV723 @ SV692 @ SV272 @ SV172 ) @ SV846 )
| ~ ~ ( in @ ( ordered_pair @ SV806 @ ( sK34_R @ SV846 @ SV806 @ SV792 @ SV723 @ SV692 @ SV272 @ SV172 ) ) @ SV272 ) )
= $false )
| ( ( ( SV792 != SV846 )
| ~ ( in @ SV806 @ SV846 ) )
= $true )
| ( ( ( ordered_pair @ SV792 @ SV806 )
= SV723 )
= $false )
| ( ( in @ SV792 @ SV172 )
= $false )
| ( ( SV752 = SV723 )
= $false )
| ( ( in @ SV752 @ ( cartesian_product2 @ SV172 @ SV692 ) )
= $false )
| ( ( in @ SV723 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5271]) ).
thf(5338,plain,
! [SV777: $i,SV272: $i,SV718: $i,SV753: $i,SV828: $i,SV172: $i,SV821: $i] :
( ( ( in @ SV821 @ SV172 )
= $false )
| ( ( ( ordered_pair @ SV821 @ SV828 )
= SV753 )
= $false )
| ( ( ! [SY1717: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1717 @ SV828 @ SV821 @ SV753 @ SV718 @ SV272 @ SV172 ) @ SY1717 )
| ~ ~ ( in @ ( ordered_pair @ SV828 @ ( sK34_R @ SY1717 @ SV828 @ SV821 @ SV753 @ SV718 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV821 != SY1717 )
| ~ ( in @ SV828 @ SY1717 ) ) )
= $true )
| ( ( SV777 = SV753 )
= $false )
| ( ( in @ SV777 @ ( cartesian_product2 @ SV172 @ SV718 ) )
= $false )
| ( ( in @ SV753 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5275]) ).
thf(5339,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i,SV857: $i] :
( ( ( ~ ( in @ SV857 @ ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) @ SV857 ) @ SV272 ) )
= $true )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5278]) ).
thf(5340,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( ( ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5279]) ).
thf(5341,plain,
! [SV778: $i,SV272: $i,SV719: $i,SV755: $i,SV829: $i,SV172: $i,SV822: $i] :
( ( ( in @ SV822 @ SV172 )
= $false )
| ( ( ( ordered_pair @ SV822 @ SV829 )
= SV755 )
= $false )
| ( ( ! [SY1718: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1718 @ SV829 @ SV822 @ SV755 @ SV719 @ SV272 @ SV172 ) @ SY1718 )
| ~ ~ ( in @ ( ordered_pair @ SV829 @ ( sK34_R @ SY1718 @ SV829 @ SV822 @ SV755 @ SV719 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV822 != SY1718 )
| ~ ( in @ SV829 @ SY1718 ) ) )
= $true )
| ( ( SV778 = SV755 )
= $false )
| ( ( in @ SV778 @ ( cartesian_product2 @ SV172 @ SV719 ) )
= $false )
| ( ( in @ SV755 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5280]) ).
thf(5342,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i,SV858: $i] :
( ( ( ~ ( in @ SV858 @ ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) @ SV858 ) @ SV272 ) )
= $true )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5283]) ).
thf(5343,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( ( ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5284]) ).
thf(5344,plain,
! [SV720: $i,SV813: $i,SV272: $i,SV743: $i,SV172: $i,SV779: $i,SV850: $i,SV847: $i] :
( ( ( ( ( ordered_pair @ SV847 @ SV850 )
!= SV779 )
| ~ ( in @ SV847 @ SV172 ) )
= $true )
| ( ( ! [SY1742: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1742 @ SV850 @ SV847 @ SV779 @ SV743 @ SV272 @ SV172 ) @ SY1742 )
| ~ ~ ( in @ ( ordered_pair @ SV850 @ ( sK34_R @ SY1742 @ SV850 @ SV847 @ SV779 @ SV743 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV847 != SY1742 )
| ~ ( in @ SV850 @ SY1742 ) ) )
= $true )
| ( ( SV813 = SV779 )
= $false )
| ( ( in @ SV813 @ ( cartesian_product2 @ SV172 @ SV743 ) )
= $false )
| ( ( in @ SV779 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5285]) ).
thf(5345,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( ( ( ordered_pair @ ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) )
!= SV780 )
| ~ ( in @ ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 ) @ SV172 ) )
= $false )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5288]) ).
thf(5346,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( ~ ! [SY1652: $i] :
( ~ ( in @ SY1652 @ ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) @ SY1652 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5289]) ).
thf(5347,plain,
! [SV814: $i,SV272: $i,SV744: $i,SV172: $i,SV781: $i,SV851: $i,SV848: $i] :
( ( ( ( ( ordered_pair @ SV848 @ SV851 )
!= SV781 )
| ~ ( in @ SV848 @ SV172 ) )
= $true )
| ( ( ! [SY1743: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1743 @ SV851 @ SV848 @ SV781 @ SV744 @ SV272 @ SV172 ) @ SY1743 )
| ~ ~ ( in @ ( ordered_pair @ SV851 @ ( sK34_R @ SY1743 @ SV851 @ SV848 @ SV781 @ SV744 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV848 != SY1743 )
| ~ ( in @ SV851 @ SY1743 ) ) )
= $true )
| ( ( SV814 = SV781 )
= $false )
| ( ( in @ SV814 @ ( cartesian_product2 @ SV172 @ SV744 ) )
= $false )
| ( ( in @ SV781 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5290]) ).
thf(5348,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( ( ( ordered_pair @ ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) )
!= SV782 )
| ~ ( in @ ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 ) @ SV172 ) )
= $false )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5293]) ).
thf(5349,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( ~ ! [SY1657: $i] :
( ~ ( in @ SY1657 @ ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) @ SY1657 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5294]) ).
thf(5350,plain,
! [SV815: $i,SV272: $i,SV745: $i,SV172: $i,SV783: $i,SV852: $i,SV849: $i] :
( ( ( ( ( ordered_pair @ SV849 @ SV852 )
!= SV783 )
| ~ ( in @ SV849 @ SV172 ) )
= $true )
| ( ( ! [SY1744: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1744 @ SV852 @ SV849 @ SV783 @ SV745 @ SV272 @ SV172 ) @ SY1744 )
| ~ ~ ( in @ ( ordered_pair @ SV852 @ ( sK34_R @ SY1744 @ SV852 @ SV849 @ SV783 @ SV745 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV849 != SY1744 )
| ~ ( in @ SV852 @ SY1744 ) ) )
= $true )
| ( ( SV815 = SV783 )
= $false )
| ( ( in @ SV815 @ ( cartesian_product2 @ SV172 @ SV745 ) )
= $false )
| ( ( in @ SV783 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5295]) ).
thf(5351,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( ( ( ordered_pair @ ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) )
!= SV784 )
| ~ ( in @ ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 ) @ SV172 ) )
= $false )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5298]) ).
thf(5352,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( ~ ! [SY1662: $i] :
( ~ ( in @ SY1662 @ ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) @ SY1662 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5299]) ).
thf(5353,plain,
! [SV701: $i,SV172: $i,SV272: $i,SV622: $i,SV677: $i,SV746: $i,SV807: $i,SV757: $i] :
( ( ( in @ SV757 @ SV807 )
= $false )
| ( ( SV746 = SV807 )
= $false )
| ( ( in @ ( sK34_R @ SV807 @ SV757 @ SV746 @ SV677 @ SV622 @ SV272 @ SV172 ) @ SV807 )
= $true )
| ( ( ( ordered_pair @ SV746 @ SV757 )
= SV677 )
= $false )
| ( ( in @ SV746 @ SV172 )
= $false )
| ( ( SV701 = SV677 )
= $false )
| ( ( in @ SV701 @ ( cartesian_product2 @ SV172 @ SV622 ) )
= $false )
| ( ( in @ SV677 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5300]) ).
thf(5354,plain,
! [SV701: $i,SV172: $i,SV272: $i,SV622: $i,SV677: $i,SV757: $i,SV807: $i,SV746: $i] :
( ( ( SV746 = SV807 )
= $false )
| ( ( ~ ( in @ SV757 @ SV807 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV757 @ ( sK34_R @ SV807 @ SV757 @ SV746 @ SV677 @ SV622 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV746 @ SV757 )
= SV677 )
= $false )
| ( ( in @ SV746 @ SV172 )
= $false )
| ( ( SV701 = SV677 )
= $false )
| ( ( in @ SV701 @ ( cartesian_product2 @ SV172 @ SV622 ) )
= $false )
| ( ( in @ SV677 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5301]) ).
thf(5355,plain,
! [SV725: $i,SV794: $i,SV139: $i,SV765: $i,SV841: $i,SV830: $i] :
( ( ( ( ordered_pair @ SV830 @ SV841 )
= SV765 )
= $false )
| ( ( ~ ( in @ SV830 @ SV139 ) )
= $true )
| ( ( ( SV841
!= ( singleton @ SV830 ) ) )
= $true )
| ( ( SV794 = SV765 )
= $false )
| ( ( in @ SV794 @ ( cartesian_product2 @ SV139 @ SV725 ) )
= $false )
| ( ( in @ SV765 @ ( sK13_C @ SV725 @ SV139 ) )
= $true )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5302]) ).
thf(5356,plain,
! [SV139: $i,SV725: $i,SV766: $i] :
( ( ( ( ordered_pair @ ( sK14_J @ SV766 @ SV725 @ SV139 ) @ ( sK15_SY612 @ SV766 @ SV725 @ SV139 ) )
= SV766 )
= $true )
| ( ( in @ SV766 @ ( sK13_C @ SV725 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5303]) ).
thf(5357,plain,
! [SV139: $i,SV725: $i,SV766: $i] :
( ( ( in @ ( sK14_J @ SV766 @ SV725 @ SV139 ) @ SV139 )
= $true )
| ( ( in @ SV766 @ ( sK13_C @ SV725 @ SV139 ) )
= $false )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5304]) ).
thf(5358,plain,
! [SV726: $i,SV795: $i,SV139: $i,SV767: $i,SV842: $i,SV831: $i] :
( ( ( ( ordered_pair @ SV831 @ SV842 )
= SV767 )
= $false )
| ( ( ~ ( in @ SV831 @ SV139 ) )
= $true )
| ( ( ( SV842
!= ( singleton @ SV831 ) ) )
= $true )
| ( ( SV795 = SV767 )
= $false )
| ( ( in @ SV795 @ ( cartesian_product2 @ SV139 @ SV726 ) )
= $false )
| ( ( in @ SV767 @ ( sK13_C @ SV726 @ SV139 ) )
= $true )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5305]) ).
thf(5359,plain,
! [SV139: $i,SV726: $i,SV768: $i] :
( ( ( ( ordered_pair @ ( sK14_J @ SV768 @ SV726 @ SV139 ) @ ( sK15_SY612 @ SV768 @ SV726 @ SV139 ) )
= SV768 )
= $true )
| ( ( in @ SV768 @ ( sK13_C @ SV726 @ SV139 ) )
= $false )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5306]) ).
thf(5360,plain,
! [SV139: $i,SV726: $i,SV768: $i] :
( ( ( in @ ( sK14_J @ SV768 @ SV726 @ SV139 ) @ SV139 )
= $true )
| ( ( in @ SV768 @ ( sK13_C @ SV726 @ SV139 ) )
= $false )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5307]) ).
thf(5361,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV796: $i,SV817: $i,SV843: $i] :
( ( ( ~ ( in @ ( sK47_K @ SV843 @ SV817 @ SV796 @ SV265 @ SV145 ) @ SV843 ) )
= $false )
| ( ( ( SV817 != SV843 )
| ~ ( in @ SV796 @ SV843 ) )
= $true )
| ( ( in @ SV817 @ SV145 )
= $false )
| ( ( in @ SV796 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5309]) ).
thf(5362,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV817: $i,SV843: $i,SV796: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV796 @ ( sK47_K @ SV843 @ SV817 @ SV796 @ SV265 @ SV145 ) ) @ SV265 ) )
= $false )
| ( ( ( SV817 != SV843 )
| ~ ( in @ SV796 @ SV843 ) )
= $true )
| ( ( in @ SV817 @ SV145 )
= $false )
| ( ( in @ SV796 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5309]) ).
thf(5363,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV797: $i] :
( ( ( ! [SY1667: $i] :
( ~ ( in @ SY1667 @ ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV797 @ SY1667 ) @ SV265 ) ) )
= $true )
| ( ( in @ SV797 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5310]) ).
thf(5364,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV797: $i] :
( ( ( ~ ( ( ( sK45_E @ SV797 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) )
| ~ ( in @ SV797 @ ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) ) ) )
= $true )
| ( ( in @ SV797 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5311]) ).
thf(5365,plain,
! [SV145: $i,SV265: $i,SV798: $i,SV818: $i,SV844: $i] :
( ( ( ~ ( in @ ( sK47_K @ SV844 @ SV818 @ SV798 @ SV265 @ SV145 ) @ SV844 ) )
= $false )
| ( ( ( SV818 != SV844 )
| ~ ( in @ SV798 @ SV844 ) )
= $true )
| ( ( in @ SV818 @ SV145 )
= $false )
| ( ( in @ SV798 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5312]) ).
thf(5366,plain,
! [SV145: $i,SV265: $i,SV818: $i,SV844: $i,SV798: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV798 @ ( sK47_K @ SV844 @ SV818 @ SV798 @ SV265 @ SV145 ) ) @ SV265 ) )
= $false )
| ( ( ( SV818 != SV844 )
| ~ ( in @ SV798 @ SV844 ) )
= $true )
| ( ( in @ SV818 @ SV145 )
= $false )
| ( ( in @ SV798 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5312]) ).
thf(5367,plain,
! [SV145: $i,SV265: $i,SV799: $i] :
( ( ( ! [SY1670: $i] :
( ~ ( in @ SY1670 @ ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV799 @ SY1670 ) @ SV265 ) ) )
= $true )
| ( ( in @ SV799 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5313]) ).
thf(5368,plain,
! [SV145: $i,SV265: $i,SV799: $i] :
( ( ( ~ ( ( ( sK45_E @ SV799 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) )
| ~ ( in @ SV799 @ ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) ) ) )
= $true )
| ( ( in @ SV799 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5314]) ).
thf(5369,plain,
! [SV145: $i,SV265: $i,SV800: $i,SV819: $i,SV845: $i] :
( ( ( ~ ( in @ ( sK47_K @ SV845 @ SV819 @ SV800 @ SV265 @ SV145 ) @ SV845 ) )
= $false )
| ( ( ( SV819 != SV845 )
| ~ ( in @ SV800 @ SV845 ) )
= $true )
| ( ( in @ SV819 @ SV145 )
= $false )
| ( ( in @ SV800 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5315]) ).
thf(5370,plain,
! [SV145: $i,SV265: $i,SV819: $i,SV845: $i,SV800: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV800 @ ( sK47_K @ SV845 @ SV819 @ SV800 @ SV265 @ SV145 ) ) @ SV265 ) )
= $false )
| ( ( ( SV819 != SV845 )
| ~ ( in @ SV800 @ SV845 ) )
= $true )
| ( ( in @ SV819 @ SV145 )
= $false )
| ( ( in @ SV800 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5315]) ).
thf(5371,plain,
! [SV145: $i,SV265: $i,SV801: $i] :
( ( ( ! [SY1673: $i] :
( ~ ( in @ SY1673 @ ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV801 @ SY1673 ) @ SV265 ) ) )
= $true )
| ( ( in @ SV801 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5316]) ).
thf(5372,plain,
! [SV145: $i,SV265: $i,SV801: $i] :
( ( ( ~ ( ( ( sK45_E @ SV801 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) )
| ~ ( in @ SV801 @ ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) ) ) )
= $true )
| ( ( in @ SV801 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5317]) ).
thf(5373,plain,
! [SV776: $i,SV172: $i,SV272: $i,SV717: $i,SV750: $i,SV820: $i,SV827: $i,SV859: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_R @ SV859 @ SV827 @ SV820 @ SV750 @ SV717 @ SV272 @ SV172 ) @ SV859 )
| ~ ~ ( in @ ( ordered_pair @ SV827 @ ( sK34_R @ SV859 @ SV827 @ SV820 @ SV750 @ SV717 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV820 != SV859 )
| ~ ( in @ SV827 @ SV859 ) )
= $true )
| ( ( ( ordered_pair @ SV820 @ SV827 )
= SV750 )
= $false )
| ( ( in @ SV820 @ SV172 )
= $false )
| ( ( SV776 = SV750 )
= $false )
| ( ( in @ SV776 @ ( cartesian_product2 @ SV172 @ SV717 ) )
= $false )
| ( ( in @ SV750 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5322]) ).
thf(5374,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i,SV853: $i] :
( ( ( ~ ( in @ SV853 @ ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) @ SV853 ) @ SV272 )
= $true )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5323]) ).
thf(5375,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( ( ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5324]) ).
thf(5376,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( ~ ( in @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5324]) ).
thf(5377,plain,
! [SV832: $i,SV272: $i,SV770: $i,SV172: $i,SV809: $i,SV860: $i] :
( ( ( ! [SY1745: $i] :
( ( ( ordered_pair @ SV860 @ SY1745 )
!= SV809 )
| ~ ( in @ SV860 @ SV172 )
| ! [SY1746: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1746 @ SY1745 @ SV860 @ SV809 @ SV770 @ SV272 @ SV172 ) @ SY1746 )
| ~ ~ ( in @ ( ordered_pair @ SY1745 @ ( sK34_R @ SY1746 @ SY1745 @ SV860 @ SV809 @ SV770 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV860 != SY1746 )
| ~ ( in @ SY1745 @ SY1746 ) ) ) )
= $true )
| ( ( SV832 = SV809 )
= $false )
| ( ( in @ SV832 @ ( cartesian_product2 @ SV172 @ SV770 ) )
= $false )
| ( ( in @ SV809 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5325]) ).
thf(5378,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( ( ( sK33_F @ SV810 @ SV770 @ SV272 @ SV172 )
!= SV810 ) )
= $false )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5326]) ).
thf(5379,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( ~ ( in @ ( sK33_F @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV770 ) ) )
= $false )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5326]) ).
thf(5380,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) )
!= SV810 )
| ~ ( in @ ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 ) @ SV172 ) ) )
= $false )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5327]) ).
thf(5381,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( ~ ~ ( ~ ! [SY1701: $i] :
( ~ ( in @ SY1701 @ ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) @ SY1701 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) ) ) ) )
= $false )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5327]) ).
thf(5382,plain,
! [SV833: $i,SV272: $i,SV771: $i,SV172: $i,SV811: $i,SV861: $i] :
( ( ( ! [SY1747: $i] :
( ( ( ordered_pair @ SV861 @ SY1747 )
!= SV811 )
| ~ ( in @ SV861 @ SV172 )
| ! [SY1748: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1748 @ SY1747 @ SV861 @ SV811 @ SV771 @ SV272 @ SV172 ) @ SY1748 )
| ~ ~ ( in @ ( ordered_pair @ SY1747 @ ( sK34_R @ SY1748 @ SY1747 @ SV861 @ SV811 @ SV771 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV861 != SY1748 )
| ~ ( in @ SY1747 @ SY1748 ) ) ) )
= $true )
| ( ( SV833 = SV811 )
= $false )
| ( ( in @ SV833 @ ( cartesian_product2 @ SV172 @ SV771 ) )
= $false )
| ( ( in @ SV811 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5328]) ).
thf(5383,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( ( ( sK33_F @ SV812 @ SV771 @ SV272 @ SV172 )
!= SV812 ) )
= $false )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5329]) ).
thf(5384,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( ~ ( in @ ( sK33_F @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV771 ) ) )
= $false )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5329]) ).
thf(5385,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) )
!= SV812 )
| ~ ( in @ ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 ) @ SV172 ) ) )
= $false )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5330]) ).
thf(5386,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( ~ ~ ( ~ ! [SY1706: $i] :
( ~ ( in @ SY1706 @ ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) @ SY1706 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) ) ) ) )
= $false )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5330]) ).
thf(5387,plain,
! [SV772: $i,SV272: $i,SV803: $i,SV172: $i,SV834: $i,SV854: $i] :
( ( ( ( SV854 != SV834 ) )
= $true )
| ( ( ~ ( in @ SV854 @ ( cartesian_product2 @ SV172 @ SV803 ) ) )
= $true )
| ( ( ! [SY1722: $i,SY1723: $i] :
( ( ( ordered_pair @ SY1722 @ SY1723 )
!= SV834 )
| ~ ( in @ SY1722 @ SV172 )
| ! [SY1724: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1724 @ SY1723 @ SY1722 @ SV834 @ SV803 @ SV272 @ SV172 ) @ SY1724 )
| ~ ~ ( in @ ( ordered_pair @ SY1723 @ ( sK34_R @ SY1724 @ SY1723 @ SY1722 @ SV834 @ SV803 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1722 != SY1724 )
| ~ ( in @ SY1723 @ SY1724 ) ) ) )
= $true )
| ( ( in @ SV834 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5331]) ).
thf(5388,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( ~ ~ ( ( ( sK33_F @ SV835 @ SV803 @ SV272 @ SV172 )
!= SV835 )
| ~ ( in @ ( sK33_F @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV803 ) ) ) )
= $false )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5332]) ).
thf(5389,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) )
!= SV835 )
| ~ ( in @ ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1725: $i] :
( ~ ( in @ SY1725 @ ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) @ SY1725 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) ) ) ) ) )
= $false )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5332]) ).
thf(5390,plain,
! [SV272: $i,SV804: $i,SV172: $i,SV836: $i,SV855: $i] :
( ( ( ( SV855 != SV836 ) )
= $true )
| ( ( ~ ( in @ SV855 @ ( cartesian_product2 @ SV172 @ SV804 ) ) )
= $true )
| ( ( ! [SY1727: $i,SY1728: $i] :
( ( ( ordered_pair @ SY1727 @ SY1728 )
!= SV836 )
| ~ ( in @ SY1727 @ SV172 )
| ! [SY1729: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1729 @ SY1728 @ SY1727 @ SV836 @ SV804 @ SV272 @ SV172 ) @ SY1729 )
| ~ ~ ( in @ ( ordered_pair @ SY1728 @ ( sK34_R @ SY1729 @ SY1728 @ SY1727 @ SV836 @ SV804 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1727 != SY1729 )
| ~ ( in @ SY1728 @ SY1729 ) ) ) )
= $true )
| ( ( in @ SV836 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5333]) ).
thf(5391,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( ~ ~ ( ( ( sK33_F @ SV837 @ SV804 @ SV272 @ SV172 )
!= SV837 )
| ~ ( in @ ( sK33_F @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV804 ) ) ) )
= $false )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5334]) ).
thf(5392,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) )
!= SV837 )
| ~ ( in @ ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1730: $i] :
( ~ ( in @ SY1730 @ ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) @ SY1730 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) ) ) ) ) )
= $false )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5334]) ).
thf(5393,plain,
! [SV272: $i,SV805: $i,SV172: $i,SV838: $i,SV856: $i] :
( ( ( ( SV856 != SV838 ) )
= $true )
| ( ( ~ ( in @ SV856 @ ( cartesian_product2 @ SV172 @ SV805 ) ) )
= $true )
| ( ( ! [SY1732: $i,SY1733: $i] :
( ( ( ordered_pair @ SY1732 @ SY1733 )
!= SV838 )
| ~ ( in @ SY1732 @ SV172 )
| ! [SY1734: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1734 @ SY1733 @ SY1732 @ SV838 @ SV805 @ SV272 @ SV172 ) @ SY1734 )
| ~ ~ ( in @ ( ordered_pair @ SY1733 @ ( sK34_R @ SY1734 @ SY1733 @ SY1732 @ SV838 @ SV805 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1732 != SY1734 )
| ~ ( in @ SY1733 @ SY1734 ) ) ) )
= $true )
| ( ( in @ SV838 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5335]) ).
thf(5394,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( ~ ~ ( ( ( sK33_F @ SV839 @ SV805 @ SV272 @ SV172 )
!= SV839 )
| ~ ( in @ ( sK33_F @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV805 ) ) ) )
= $false )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5336]) ).
thf(5395,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) )
!= SV839 )
| ~ ( in @ ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1735: $i] :
( ~ ( in @ SY1735 @ ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) @ SY1735 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) ) ) ) ) )
= $false )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5336]) ).
thf(5396,plain,
! [SV752: $i,SV172: $i,SV272: $i,SV692: $i,SV723: $i,SV792: $i,SV806: $i,SV846: $i] :
( ( ( ~ ( in @ ( sK34_R @ SV846 @ SV806 @ SV792 @ SV723 @ SV692 @ SV272 @ SV172 ) @ SV846 ) )
= $false )
| ( ( ( SV792 != SV846 )
| ~ ( in @ SV806 @ SV846 ) )
= $true )
| ( ( ( ordered_pair @ SV792 @ SV806 )
= SV723 )
= $false )
| ( ( in @ SV792 @ SV172 )
= $false )
| ( ( SV752 = SV723 )
= $false )
| ( ( in @ SV752 @ ( cartesian_product2 @ SV172 @ SV692 ) )
= $false )
| ( ( in @ SV723 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5337]) ).
thf(5397,plain,
! [SV752: $i,SV172: $i,SV272: $i,SV692: $i,SV723: $i,SV792: $i,SV846: $i,SV806: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV806 @ ( sK34_R @ SV846 @ SV806 @ SV792 @ SV723 @ SV692 @ SV272 @ SV172 ) ) @ SV272 ) )
= $false )
| ( ( ( SV792 != SV846 )
| ~ ( in @ SV806 @ SV846 ) )
= $true )
| ( ( ( ordered_pair @ SV792 @ SV806 )
= SV723 )
= $false )
| ( ( in @ SV792 @ SV172 )
= $false )
| ( ( SV752 = SV723 )
= $false )
| ( ( in @ SV752 @ ( cartesian_product2 @ SV172 @ SV692 ) )
= $false )
| ( ( in @ SV723 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5337]) ).
thf(5398,plain,
! [SV777: $i,SV172: $i,SV272: $i,SV718: $i,SV753: $i,SV821: $i,SV828: $i,SV862: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_R @ SV862 @ SV828 @ SV821 @ SV753 @ SV718 @ SV272 @ SV172 ) @ SV862 )
| ~ ~ ( in @ ( ordered_pair @ SV828 @ ( sK34_R @ SV862 @ SV828 @ SV821 @ SV753 @ SV718 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV821 != SV862 )
| ~ ( in @ SV828 @ SV862 ) )
= $true )
| ( ( ( ordered_pair @ SV821 @ SV828 )
= SV753 )
= $false )
| ( ( in @ SV821 @ SV172 )
= $false )
| ( ( SV777 = SV753 )
= $false )
| ( ( in @ SV777 @ ( cartesian_product2 @ SV172 @ SV718 ) )
= $false )
| ( ( in @ SV753 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5338]) ).
thf(5399,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i,SV857: $i] :
( ( ( ~ ( in @ SV857 @ ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) @ SV857 ) @ SV272 )
= $true )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5339]) ).
thf(5400,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( ( ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5340]) ).
thf(5401,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( ~ ( in @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5340]) ).
thf(5402,plain,
! [SV778: $i,SV172: $i,SV272: $i,SV719: $i,SV755: $i,SV822: $i,SV829: $i,SV863: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_R @ SV863 @ SV829 @ SV822 @ SV755 @ SV719 @ SV272 @ SV172 ) @ SV863 )
| ~ ~ ( in @ ( ordered_pair @ SV829 @ ( sK34_R @ SV863 @ SV829 @ SV822 @ SV755 @ SV719 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV822 != SV863 )
| ~ ( in @ SV829 @ SV863 ) )
= $true )
| ( ( ( ordered_pair @ SV822 @ SV829 )
= SV755 )
= $false )
| ( ( in @ SV822 @ SV172 )
= $false )
| ( ( SV778 = SV755 )
= $false )
| ( ( in @ SV778 @ ( cartesian_product2 @ SV172 @ SV719 ) )
= $false )
| ( ( in @ SV755 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5341]) ).
thf(5403,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i,SV858: $i] :
( ( ( ~ ( in @ SV858 @ ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) @ SV858 ) @ SV272 )
= $true )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5342]) ).
thf(5404,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( ( ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5343]) ).
thf(5405,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( ~ ( in @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5343]) ).
thf(5406,plain,
! [SV720: $i,SV813: $i,SV272: $i,SV743: $i,SV172: $i,SV779: $i,SV850: $i,SV847: $i] :
( ( ( ( ( ordered_pair @ SV847 @ SV850 )
!= SV779 ) )
= $true )
| ( ( ~ ( in @ SV847 @ SV172 ) )
= $true )
| ( ( ! [SY1742: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1742 @ SV850 @ SV847 @ SV779 @ SV743 @ SV272 @ SV172 ) @ SY1742 )
| ~ ~ ( in @ ( ordered_pair @ SV850 @ ( sK34_R @ SY1742 @ SV850 @ SV847 @ SV779 @ SV743 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV847 != SY1742 )
| ~ ( in @ SV850 @ SY1742 ) ) )
= $true )
| ( ( SV813 = SV779 )
= $false )
| ( ( in @ SV813 @ ( cartesian_product2 @ SV172 @ SV743 ) )
= $false )
| ( ( in @ SV779 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5344]) ).
thf(5407,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( ( ( ordered_pair @ ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) )
!= SV780 ) )
= $false )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5345]) ).
thf(5408,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( ~ ( in @ ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 ) @ SV172 ) )
= $false )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5345]) ).
thf(5409,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( ~ ! [SY1652: $i] :
( ~ ( in @ SY1652 @ ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) @ SY1652 ) @ SV272 ) ) )
= $false )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5346]) ).
thf(5410,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( ~ ~ ( ( ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5346]) ).
thf(5411,plain,
! [SV814: $i,SV272: $i,SV744: $i,SV172: $i,SV781: $i,SV851: $i,SV848: $i] :
( ( ( ( ( ordered_pair @ SV848 @ SV851 )
!= SV781 ) )
= $true )
| ( ( ~ ( in @ SV848 @ SV172 ) )
= $true )
| ( ( ! [SY1743: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1743 @ SV851 @ SV848 @ SV781 @ SV744 @ SV272 @ SV172 ) @ SY1743 )
| ~ ~ ( in @ ( ordered_pair @ SV851 @ ( sK34_R @ SY1743 @ SV851 @ SV848 @ SV781 @ SV744 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV848 != SY1743 )
| ~ ( in @ SV851 @ SY1743 ) ) )
= $true )
| ( ( SV814 = SV781 )
= $false )
| ( ( in @ SV814 @ ( cartesian_product2 @ SV172 @ SV744 ) )
= $false )
| ( ( in @ SV781 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5347]) ).
thf(5412,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( ( ( ordered_pair @ ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) )
!= SV782 ) )
= $false )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5348]) ).
thf(5413,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( ~ ( in @ ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 ) @ SV172 ) )
= $false )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5348]) ).
thf(5414,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( ~ ! [SY1657: $i] :
( ~ ( in @ SY1657 @ ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) @ SY1657 ) @ SV272 ) ) )
= $false )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5349]) ).
thf(5415,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( ~ ~ ( ( ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5349]) ).
thf(5416,plain,
! [SV815: $i,SV272: $i,SV745: $i,SV172: $i,SV783: $i,SV852: $i,SV849: $i] :
( ( ( ( ( ordered_pair @ SV849 @ SV852 )
!= SV783 ) )
= $true )
| ( ( ~ ( in @ SV849 @ SV172 ) )
= $true )
| ( ( ! [SY1744: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1744 @ SV852 @ SV849 @ SV783 @ SV745 @ SV272 @ SV172 ) @ SY1744 )
| ~ ~ ( in @ ( ordered_pair @ SV852 @ ( sK34_R @ SY1744 @ SV852 @ SV849 @ SV783 @ SV745 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV849 != SY1744 )
| ~ ( in @ SV852 @ SY1744 ) ) )
= $true )
| ( ( SV815 = SV783 )
= $false )
| ( ( in @ SV815 @ ( cartesian_product2 @ SV172 @ SV745 ) )
= $false )
| ( ( in @ SV783 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5350]) ).
thf(5417,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( ( ( ordered_pair @ ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) )
!= SV784 ) )
= $false )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5351]) ).
thf(5418,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( ~ ( in @ ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 ) @ SV172 ) )
= $false )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5351]) ).
thf(5419,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( ~ ! [SY1662: $i] :
( ~ ( in @ SY1662 @ ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) @ SY1662 ) @ SV272 ) ) )
= $false )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5352]) ).
thf(5420,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( ~ ~ ( ( ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5352]) ).
thf(5421,plain,
! [SV701: $i,SV172: $i,SV272: $i,SV622: $i,SV677: $i,SV746: $i,SV807: $i,SV757: $i] :
( ( ( in @ SV757 @ SV807 )
= $false )
| ( ( SV746 = SV807 )
= $false )
| ( ( in @ ( ordered_pair @ SV757 @ ( sK34_R @ SV807 @ SV757 @ SV746 @ SV677 @ SV622 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV746 @ SV757 )
= SV677 )
= $false )
| ( ( in @ SV746 @ SV172 )
= $false )
| ( ( SV701 = SV677 )
= $false )
| ( ( in @ SV701 @ ( cartesian_product2 @ SV172 @ SV622 ) )
= $false )
| ( ( in @ SV677 @ ( sK29_D @ SV622 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK36_SY655 @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5354]) ).
thf(5422,plain,
! [SV725: $i,SV794: $i,SV765: $i,SV841: $i,SV139: $i,SV830: $i] :
( ( ( in @ SV830 @ SV139 )
= $false )
| ( ( ( ordered_pair @ SV830 @ SV841 )
= SV765 )
= $false )
| ( ( ( SV841
!= ( singleton @ SV830 ) ) )
= $true )
| ( ( SV794 = SV765 )
= $false )
| ( ( in @ SV794 @ ( cartesian_product2 @ SV139 @ SV725 ) )
= $false )
| ( ( in @ SV765 @ ( sK13_C @ SV725 @ SV139 ) )
= $true )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5355]) ).
thf(5423,plain,
! [SV726: $i,SV795: $i,SV767: $i,SV842: $i,SV139: $i,SV831: $i] :
( ( ( in @ SV831 @ SV139 )
= $false )
| ( ( ( ordered_pair @ SV831 @ SV842 )
= SV767 )
= $false )
| ( ( ( SV842
!= ( singleton @ SV831 ) ) )
= $true )
| ( ( SV795 = SV767 )
= $false )
| ( ( in @ SV795 @ ( cartesian_product2 @ SV139 @ SV726 ) )
= $false )
| ( ( in @ SV767 @ ( sK13_C @ SV726 @ SV139 ) )
= $true )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5358]) ).
thf(5424,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV796: $i,SV817: $i,SV843: $i] :
( ( ( in @ ( sK47_K @ SV843 @ SV817 @ SV796 @ SV265 @ SV145 ) @ SV843 )
= $true )
| ( ( ( SV817 != SV843 )
| ~ ( in @ SV796 @ SV843 ) )
= $true )
| ( ( in @ SV817 @ SV145 )
= $false )
| ( ( in @ SV796 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5361]) ).
thf(5425,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV817: $i,SV843: $i,SV796: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV796 @ ( sK47_K @ SV843 @ SV817 @ SV796 @ SV265 @ SV145 ) ) @ SV265 ) )
= $true )
| ( ( ( SV817 != SV843 )
| ~ ( in @ SV796 @ SV843 ) )
= $true )
| ( ( in @ SV817 @ SV145 )
= $false )
| ( ( in @ SV796 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5362]) ).
thf(5426,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV797: $i,SV864: $i] :
( ( ( ~ ( in @ SV864 @ ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV797 @ SV864 ) @ SV265 ) )
= $true )
| ( ( in @ SV797 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5363]) ).
thf(5427,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV797: $i] :
( ( ( ( ( sK45_E @ SV797 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) )
| ~ ( in @ SV797 @ ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) ) )
= $false )
| ( ( in @ SV797 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5364]) ).
thf(5428,plain,
! [SV145: $i,SV265: $i,SV798: $i,SV818: $i,SV844: $i] :
( ( ( in @ ( sK47_K @ SV844 @ SV818 @ SV798 @ SV265 @ SV145 ) @ SV844 )
= $true )
| ( ( ( SV818 != SV844 )
| ~ ( in @ SV798 @ SV844 ) )
= $true )
| ( ( in @ SV818 @ SV145 )
= $false )
| ( ( in @ SV798 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5365]) ).
thf(5429,plain,
! [SV145: $i,SV265: $i,SV818: $i,SV844: $i,SV798: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV798 @ ( sK47_K @ SV844 @ SV818 @ SV798 @ SV265 @ SV145 ) ) @ SV265 ) )
= $true )
| ( ( ( SV818 != SV844 )
| ~ ( in @ SV798 @ SV844 ) )
= $true )
| ( ( in @ SV818 @ SV145 )
= $false )
| ( ( in @ SV798 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5366]) ).
thf(5430,plain,
! [SV145: $i,SV265: $i,SV799: $i,SV865: $i] :
( ( ( ~ ( in @ SV865 @ ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV799 @ SV865 ) @ SV265 ) )
= $true )
| ( ( in @ SV799 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5367]) ).
thf(5431,plain,
! [SV145: $i,SV265: $i,SV799: $i] :
( ( ( ( ( sK45_E @ SV799 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) )
| ~ ( in @ SV799 @ ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) ) )
= $false )
| ( ( in @ SV799 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5368]) ).
thf(5432,plain,
! [SV145: $i,SV265: $i,SV800: $i,SV819: $i,SV845: $i] :
( ( ( in @ ( sK47_K @ SV845 @ SV819 @ SV800 @ SV265 @ SV145 ) @ SV845 )
= $true )
| ( ( ( SV819 != SV845 )
| ~ ( in @ SV800 @ SV845 ) )
= $true )
| ( ( in @ SV819 @ SV145 )
= $false )
| ( ( in @ SV800 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5369]) ).
thf(5433,plain,
! [SV145: $i,SV265: $i,SV819: $i,SV845: $i,SV800: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV800 @ ( sK47_K @ SV845 @ SV819 @ SV800 @ SV265 @ SV145 ) ) @ SV265 ) )
= $true )
| ( ( ( SV819 != SV845 )
| ~ ( in @ SV800 @ SV845 ) )
= $true )
| ( ( in @ SV819 @ SV145 )
= $false )
| ( ( in @ SV800 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5370]) ).
thf(5434,plain,
! [SV145: $i,SV265: $i,SV801: $i,SV866: $i] :
( ( ( ~ ( in @ SV866 @ ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) )
| ( in @ ( ordered_pair @ SV801 @ SV866 ) @ SV265 ) )
= $true )
| ( ( in @ SV801 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5371]) ).
thf(5435,plain,
! [SV145: $i,SV265: $i,SV801: $i] :
( ( ( ( ( sK45_E @ SV801 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) )
| ~ ( in @ SV801 @ ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) ) )
= $false )
| ( ( in @ SV801 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5372]) ).
thf(5436,plain,
! [SV776: $i,SV172: $i,SV272: $i,SV717: $i,SV750: $i,SV820: $i,SV827: $i,SV859: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_R @ SV859 @ SV827 @ SV820 @ SV750 @ SV717 @ SV272 @ SV172 ) @ SV859 )
| ~ ~ ( in @ ( ordered_pair @ SV827 @ ( sK34_R @ SV859 @ SV827 @ SV820 @ SV750 @ SV717 @ SV272 @ SV172 ) ) @ SV272 ) ) )
= $true )
| ( ( ( SV820 != SV859 )
| ~ ( in @ SV827 @ SV859 ) )
= $true )
| ( ( ( ordered_pair @ SV820 @ SV827 )
= SV750 )
= $false )
| ( ( in @ SV820 @ SV172 )
= $false )
| ( ( SV776 = SV750 )
= $false )
| ( ( in @ SV776 @ ( cartesian_product2 @ SV172 @ SV717 ) )
= $false )
| ( ( in @ SV750 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5373]) ).
thf(5437,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i,SV853: $i] :
( ( ( in @ SV853 @ ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) @ SV853 ) @ SV272 )
= $true )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5374]) ).
thf(5438,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( ( sK30_O @ SV751 @ SV717 @ SV272 @ SV172 )
= ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5375]) ).
thf(5439,plain,
! [SV172: $i,SV272: $i,SV717: $i,SV751: $i] :
( ( ( in @ ( sK31_SY649 @ SV751 @ SV717 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV751 @ SV717 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ SV751 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5376]) ).
thf(5440,plain,
! [SV832: $i,SV272: $i,SV770: $i,SV172: $i,SV809: $i,SV867: $i,SV860: $i] :
( ( ( ( ( ordered_pair @ SV860 @ SV867 )
!= SV809 )
| ~ ( in @ SV860 @ SV172 )
| ! [SY1749: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1749 @ SV867 @ SV860 @ SV809 @ SV770 @ SV272 @ SV172 ) @ SY1749 )
| ~ ~ ( in @ ( ordered_pair @ SV867 @ ( sK34_R @ SY1749 @ SV867 @ SV860 @ SV809 @ SV770 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV860 != SY1749 )
| ~ ( in @ SV867 @ SY1749 ) ) )
= $true )
| ( ( SV832 = SV809 )
= $false )
| ( ( in @ SV832 @ ( cartesian_product2 @ SV172 @ SV770 ) )
= $false )
| ( ( in @ SV809 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5377]) ).
thf(5441,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( ( sK33_F @ SV810 @ SV770 @ SV272 @ SV172 )
= SV810 )
= $true )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5378]) ).
thf(5442,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( in @ ( sK33_F @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV770 ) )
= $true )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5379]) ).
thf(5443,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) )
!= SV810 )
| ~ ( in @ ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 ) @ SV172 ) ) )
= $true )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5380]) ).
thf(5444,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( ~ ( ~ ! [SY1701: $i] :
( ~ ( in @ SY1701 @ ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) @ SY1701 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) ) ) ) )
= $true )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5381]) ).
thf(5445,plain,
! [SV833: $i,SV272: $i,SV771: $i,SV172: $i,SV811: $i,SV868: $i,SV861: $i] :
( ( ( ( ( ordered_pair @ SV861 @ SV868 )
!= SV811 )
| ~ ( in @ SV861 @ SV172 )
| ! [SY1750: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1750 @ SV868 @ SV861 @ SV811 @ SV771 @ SV272 @ SV172 ) @ SY1750 )
| ~ ~ ( in @ ( ordered_pair @ SV868 @ ( sK34_R @ SY1750 @ SV868 @ SV861 @ SV811 @ SV771 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV861 != SY1750 )
| ~ ( in @ SV868 @ SY1750 ) ) )
= $true )
| ( ( SV833 = SV811 )
= $false )
| ( ( in @ SV833 @ ( cartesian_product2 @ SV172 @ SV771 ) )
= $false )
| ( ( in @ SV811 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5382]) ).
thf(5446,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( ( sK33_F @ SV812 @ SV771 @ SV272 @ SV172 )
= SV812 )
= $true )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5383]) ).
thf(5447,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( in @ ( sK33_F @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV771 ) )
= $true )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5384]) ).
thf(5448,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) )
!= SV812 )
| ~ ( in @ ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 ) @ SV172 ) ) )
= $true )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5385]) ).
thf(5449,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( ~ ( ~ ! [SY1706: $i] :
( ~ ( in @ SY1706 @ ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) @ SY1706 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) ) ) ) )
= $true )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5386]) ).
thf(5450,plain,
! [SV772: $i,SV272: $i,SV803: $i,SV172: $i,SV834: $i,SV854: $i] :
( ( ( SV854 = SV834 )
= $false )
| ( ( ~ ( in @ SV854 @ ( cartesian_product2 @ SV172 @ SV803 ) ) )
= $true )
| ( ( ! [SY1722: $i,SY1723: $i] :
( ( ( ordered_pair @ SY1722 @ SY1723 )
!= SV834 )
| ~ ( in @ SY1722 @ SV172 )
| ! [SY1724: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1724 @ SY1723 @ SY1722 @ SV834 @ SV803 @ SV272 @ SV172 ) @ SY1724 )
| ~ ~ ( in @ ( ordered_pair @ SY1723 @ ( sK34_R @ SY1724 @ SY1723 @ SY1722 @ SV834 @ SV803 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1722 != SY1724 )
| ~ ( in @ SY1723 @ SY1724 ) ) ) )
= $true )
| ( ( in @ SV834 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5387]) ).
thf(5451,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( ~ ( ( ( sK33_F @ SV835 @ SV803 @ SV272 @ SV172 )
!= SV835 )
| ~ ( in @ ( sK33_F @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV803 ) ) ) )
= $true )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5388]) ).
thf(5452,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) )
!= SV835 )
| ~ ( in @ ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1725: $i] :
( ~ ( in @ SY1725 @ ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) @ SY1725 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) ) ) ) ) )
= $true )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5389]) ).
thf(5453,plain,
! [SV272: $i,SV804: $i,SV172: $i,SV836: $i,SV855: $i] :
( ( ( SV855 = SV836 )
= $false )
| ( ( ~ ( in @ SV855 @ ( cartesian_product2 @ SV172 @ SV804 ) ) )
= $true )
| ( ( ! [SY1727: $i,SY1728: $i] :
( ( ( ordered_pair @ SY1727 @ SY1728 )
!= SV836 )
| ~ ( in @ SY1727 @ SV172 )
| ! [SY1729: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1729 @ SY1728 @ SY1727 @ SV836 @ SV804 @ SV272 @ SV172 ) @ SY1729 )
| ~ ~ ( in @ ( ordered_pair @ SY1728 @ ( sK34_R @ SY1729 @ SY1728 @ SY1727 @ SV836 @ SV804 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1727 != SY1729 )
| ~ ( in @ SY1728 @ SY1729 ) ) ) )
= $true )
| ( ( in @ SV836 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5390]) ).
thf(5454,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( ~ ( ( ( sK33_F @ SV837 @ SV804 @ SV272 @ SV172 )
!= SV837 )
| ~ ( in @ ( sK33_F @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV804 ) ) ) )
= $true )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5391]) ).
thf(5455,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) )
!= SV837 )
| ~ ( in @ ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1730: $i] :
( ~ ( in @ SY1730 @ ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) @ SY1730 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) ) ) ) ) )
= $true )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5392]) ).
thf(5456,plain,
! [SV272: $i,SV805: $i,SV172: $i,SV838: $i,SV856: $i] :
( ( ( SV856 = SV838 )
= $false )
| ( ( ~ ( in @ SV856 @ ( cartesian_product2 @ SV172 @ SV805 ) ) )
= $true )
| ( ( ! [SY1732: $i,SY1733: $i] :
( ( ( ordered_pair @ SY1732 @ SY1733 )
!= SV838 )
| ~ ( in @ SY1732 @ SV172 )
| ! [SY1734: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1734 @ SY1733 @ SY1732 @ SV838 @ SV805 @ SV272 @ SV172 ) @ SY1734 )
| ~ ~ ( in @ ( ordered_pair @ SY1733 @ ( sK34_R @ SY1734 @ SY1733 @ SY1732 @ SV838 @ SV805 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1732 != SY1734 )
| ~ ( in @ SY1733 @ SY1734 ) ) ) )
= $true )
| ( ( in @ SV838 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5393]) ).
thf(5457,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( ~ ( ( ( sK33_F @ SV839 @ SV805 @ SV272 @ SV172 )
!= SV839 )
| ~ ( in @ ( sK33_F @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV805 ) ) ) )
= $true )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5394]) ).
thf(5458,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( ~ ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) )
!= SV839 )
| ~ ( in @ ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1735: $i] :
( ~ ( in @ SY1735 @ ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) @ SY1735 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) ) ) ) ) )
= $true )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5395]) ).
thf(5459,plain,
! [SV752: $i,SV172: $i,SV272: $i,SV692: $i,SV723: $i,SV792: $i,SV806: $i,SV846: $i] :
( ( ( in @ ( sK34_R @ SV846 @ SV806 @ SV792 @ SV723 @ SV692 @ SV272 @ SV172 ) @ SV846 )
= $true )
| ( ( ( SV792 != SV846 )
| ~ ( in @ SV806 @ SV846 ) )
= $true )
| ( ( ( ordered_pair @ SV792 @ SV806 )
= SV723 )
= $false )
| ( ( in @ SV792 @ SV172 )
= $false )
| ( ( SV752 = SV723 )
= $false )
| ( ( in @ SV752 @ ( cartesian_product2 @ SV172 @ SV692 ) )
= $false )
| ( ( in @ SV723 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5396]) ).
thf(5460,plain,
! [SV752: $i,SV172: $i,SV272: $i,SV692: $i,SV723: $i,SV792: $i,SV846: $i,SV806: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV806 @ ( sK34_R @ SV846 @ SV806 @ SV792 @ SV723 @ SV692 @ SV272 @ SV172 ) ) @ SV272 ) )
= $true )
| ( ( ( SV792 != SV846 )
| ~ ( in @ SV806 @ SV846 ) )
= $true )
| ( ( ( ordered_pair @ SV792 @ SV806 )
= SV723 )
= $false )
| ( ( in @ SV792 @ SV172 )
= $false )
| ( ( SV752 = SV723 )
= $false )
| ( ( in @ SV752 @ ( cartesian_product2 @ SV172 @ SV692 ) )
= $false )
| ( ( in @ SV723 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5397]) ).
thf(5461,plain,
! [SV777: $i,SV172: $i,SV272: $i,SV718: $i,SV753: $i,SV821: $i,SV828: $i,SV862: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_R @ SV862 @ SV828 @ SV821 @ SV753 @ SV718 @ SV272 @ SV172 ) @ SV862 )
| ~ ~ ( in @ ( ordered_pair @ SV828 @ ( sK34_R @ SV862 @ SV828 @ SV821 @ SV753 @ SV718 @ SV272 @ SV172 ) ) @ SV272 ) ) )
= $true )
| ( ( ( SV821 != SV862 )
| ~ ( in @ SV828 @ SV862 ) )
= $true )
| ( ( ( ordered_pair @ SV821 @ SV828 )
= SV753 )
= $false )
| ( ( in @ SV821 @ SV172 )
= $false )
| ( ( SV777 = SV753 )
= $false )
| ( ( in @ SV777 @ ( cartesian_product2 @ SV172 @ SV718 ) )
= $false )
| ( ( in @ SV753 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5398]) ).
thf(5462,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i,SV857: $i] :
( ( ( in @ SV857 @ ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) @ SV857 ) @ SV272 )
= $true )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5399]) ).
thf(5463,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( ( sK30_O @ SV754 @ SV718 @ SV272 @ SV172 )
= ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5400]) ).
thf(5464,plain,
! [SV172: $i,SV272: $i,SV718: $i,SV754: $i] :
( ( ( in @ ( sK31_SY649 @ SV754 @ SV718 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV754 @ SV718 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ SV754 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5401]) ).
thf(5465,plain,
! [SV778: $i,SV172: $i,SV272: $i,SV719: $i,SV755: $i,SV822: $i,SV829: $i,SV863: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_R @ SV863 @ SV829 @ SV822 @ SV755 @ SV719 @ SV272 @ SV172 ) @ SV863 )
| ~ ~ ( in @ ( ordered_pair @ SV829 @ ( sK34_R @ SV863 @ SV829 @ SV822 @ SV755 @ SV719 @ SV272 @ SV172 ) ) @ SV272 ) ) )
= $true )
| ( ( ( SV822 != SV863 )
| ~ ( in @ SV829 @ SV863 ) )
= $true )
| ( ( ( ordered_pair @ SV822 @ SV829 )
= SV755 )
= $false )
| ( ( in @ SV822 @ SV172 )
= $false )
| ( ( SV778 = SV755 )
= $false )
| ( ( in @ SV778 @ ( cartesian_product2 @ SV172 @ SV719 ) )
= $false )
| ( ( in @ SV755 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5402]) ).
thf(5466,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i,SV858: $i] :
( ( ( in @ SV858 @ ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) @ SV858 ) @ SV272 )
= $true )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5403]) ).
thf(5467,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( ( sK30_O @ SV756 @ SV719 @ SV272 @ SV172 )
= ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5404]) ).
thf(5468,plain,
! [SV172: $i,SV272: $i,SV719: $i,SV756: $i] :
( ( ( in @ ( sK31_SY649 @ SV756 @ SV719 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV756 @ SV719 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ SV756 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5405]) ).
thf(5469,plain,
! [SV720: $i,SV813: $i,SV272: $i,SV743: $i,SV172: $i,SV779: $i,SV850: $i,SV847: $i] :
( ( ( ( ordered_pair @ SV847 @ SV850 )
= SV779 )
= $false )
| ( ( ~ ( in @ SV847 @ SV172 ) )
= $true )
| ( ( ! [SY1742: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1742 @ SV850 @ SV847 @ SV779 @ SV743 @ SV272 @ SV172 ) @ SY1742 )
| ~ ~ ( in @ ( ordered_pair @ SV850 @ ( sK34_R @ SY1742 @ SV850 @ SV847 @ SV779 @ SV743 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV847 != SY1742 )
| ~ ( in @ SV850 @ SY1742 ) ) )
= $true )
| ( ( SV813 = SV779 )
= $false )
| ( ( in @ SV813 @ ( cartesian_product2 @ SV172 @ SV743 ) )
= $false )
| ( ( in @ SV779 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5406]) ).
thf(5470,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( ( ordered_pair @ ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) )
= SV780 )
= $true )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5407]) ).
thf(5471,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( in @ ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5408]) ).
thf(5472,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( ! [SY1652: $i] :
( ~ ( in @ SY1652 @ ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) @ SY1652 ) @ SV272 ) ) )
= $true )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5409]) ).
thf(5473,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( ~ ( ( ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) ) ) )
= $true )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5410]) ).
thf(5474,plain,
! [SV814: $i,SV272: $i,SV744: $i,SV172: $i,SV781: $i,SV851: $i,SV848: $i] :
( ( ( ( ordered_pair @ SV848 @ SV851 )
= SV781 )
= $false )
| ( ( ~ ( in @ SV848 @ SV172 ) )
= $true )
| ( ( ! [SY1743: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1743 @ SV851 @ SV848 @ SV781 @ SV744 @ SV272 @ SV172 ) @ SY1743 )
| ~ ~ ( in @ ( ordered_pair @ SV851 @ ( sK34_R @ SY1743 @ SV851 @ SV848 @ SV781 @ SV744 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV848 != SY1743 )
| ~ ( in @ SV851 @ SY1743 ) ) )
= $true )
| ( ( SV814 = SV781 )
= $false )
| ( ( in @ SV814 @ ( cartesian_product2 @ SV172 @ SV744 ) )
= $false )
| ( ( in @ SV781 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5411]) ).
thf(5475,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( ( ordered_pair @ ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) )
= SV782 )
= $true )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5412]) ).
thf(5476,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( in @ ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5413]) ).
thf(5477,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( ! [SY1657: $i] :
( ~ ( in @ SY1657 @ ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) @ SY1657 ) @ SV272 ) ) )
= $true )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5414]) ).
thf(5478,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( ~ ( ( ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) ) ) )
= $true )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5415]) ).
thf(5479,plain,
! [SV815: $i,SV272: $i,SV745: $i,SV172: $i,SV783: $i,SV852: $i,SV849: $i] :
( ( ( ( ordered_pair @ SV849 @ SV852 )
= SV783 )
= $false )
| ( ( ~ ( in @ SV849 @ SV172 ) )
= $true )
| ( ( ! [SY1744: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1744 @ SV852 @ SV849 @ SV783 @ SV745 @ SV272 @ SV172 ) @ SY1744 )
| ~ ~ ( in @ ( ordered_pair @ SV852 @ ( sK34_R @ SY1744 @ SV852 @ SV849 @ SV783 @ SV745 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV849 != SY1744 )
| ~ ( in @ SV852 @ SY1744 ) ) )
= $true )
| ( ( SV815 = SV783 )
= $false )
| ( ( in @ SV815 @ ( cartesian_product2 @ SV172 @ SV745 ) )
= $false )
| ( ( in @ SV783 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5416]) ).
thf(5480,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( ( ordered_pair @ ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) )
= SV784 )
= $true )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5417]) ).
thf(5481,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( in @ ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5418]) ).
thf(5482,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( ! [SY1662: $i] :
( ~ ( in @ SY1662 @ ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) @ SY1662 ) @ SV272 ) ) )
= $true )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5419]) ).
thf(5483,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( ~ ( ( ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) ) ) )
= $true )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5420]) ).
thf(5484,plain,
! [SV725: $i,SV794: $i,SV139: $i,SV765: $i,SV830: $i,SV841: $i] :
( ( ( SV841
= ( singleton @ SV830 ) )
= $false )
| ( ( ( ordered_pair @ SV830 @ SV841 )
= SV765 )
= $false )
| ( ( in @ SV830 @ SV139 )
= $false )
| ( ( SV794 = SV765 )
= $false )
| ( ( in @ SV794 @ ( cartesian_product2 @ SV139 @ SV725 ) )
= $false )
| ( ( in @ SV765 @ ( sK13_C @ SV725 @ SV139 ) )
= $true )
| ( ( ( ordered_pair @ ( sK22_SY620 @ SV139 ) @ ( sK23_SY629 @ SV139 ) )
= ( sK18_SY613 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5422]) ).
thf(5485,plain,
! [SV726: $i,SV795: $i,SV139: $i,SV767: $i,SV831: $i,SV842: $i] :
( ( ( SV842
= ( singleton @ SV831 ) )
= $false )
| ( ( ( ordered_pair @ SV831 @ SV842 )
= SV767 )
= $false )
| ( ( in @ SV831 @ SV139 )
= $false )
| ( ( SV795 = SV767 )
= $false )
| ( ( in @ SV795 @ ( cartesian_product2 @ SV139 @ SV726 ) )
= $false )
| ( ( in @ SV767 @ ( sK13_C @ SV726 @ SV139 ) )
= $true )
| ( ( in @ ( sK22_SY620 @ SV139 ) @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5423]) ).
thf(5486,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV796: $i,SV843: $i,SV817: $i] :
( ( ( ( SV817 != SV843 ) )
= $true )
| ( ( ~ ( in @ SV796 @ SV843 ) )
= $true )
| ( ( in @ ( sK47_K @ SV843 @ SV817 @ SV796 @ SV265 @ SV145 ) @ SV843 )
= $true )
| ( ( in @ SV817 @ SV145 )
= $false )
| ( ( in @ SV796 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5424]) ).
thf(5487,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV817: $i,SV843: $i,SV796: $i] :
( ( ( in @ ( ordered_pair @ SV796 @ ( sK47_K @ SV843 @ SV817 @ SV796 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( ( SV817 != SV843 )
| ~ ( in @ SV796 @ SV843 ) )
= $true )
| ( ( in @ SV817 @ SV145 )
= $false )
| ( ( in @ SV796 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5425]) ).
thf(5488,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV797: $i,SV864: $i] :
( ( ( ~ ( in @ SV864 @ ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV797 @ SV864 ) @ SV265 )
= $true )
| ( ( in @ SV797 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5426]) ).
thf(5489,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV797: $i] :
( ( ( ( ( sK45_E @ SV797 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) ) )
= $false )
| ( ( in @ SV797 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5427]) ).
thf(5490,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV797: $i] :
( ( ( ~ ( in @ SV797 @ ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) ) )
= $false )
| ( ( in @ SV797 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5427]) ).
thf(5491,plain,
! [SV145: $i,SV265: $i,SV798: $i,SV844: $i,SV818: $i] :
( ( ( ( SV818 != SV844 ) )
= $true )
| ( ( ~ ( in @ SV798 @ SV844 ) )
= $true )
| ( ( in @ ( sK47_K @ SV844 @ SV818 @ SV798 @ SV265 @ SV145 ) @ SV844 )
= $true )
| ( ( in @ SV818 @ SV145 )
= $false )
| ( ( in @ SV798 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5428]) ).
thf(5492,plain,
! [SV145: $i,SV265: $i,SV818: $i,SV844: $i,SV798: $i] :
( ( ( in @ ( ordered_pair @ SV798 @ ( sK47_K @ SV844 @ SV818 @ SV798 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( ( SV818 != SV844 )
| ~ ( in @ SV798 @ SV844 ) )
= $true )
| ( ( in @ SV818 @ SV145 )
= $false )
| ( ( in @ SV798 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5429]) ).
thf(5493,plain,
! [SV145: $i,SV265: $i,SV799: $i,SV865: $i] :
( ( ( ~ ( in @ SV865 @ ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV799 @ SV865 ) @ SV265 )
= $true )
| ( ( in @ SV799 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5430]) ).
thf(5494,plain,
! [SV145: $i,SV265: $i,SV799: $i] :
( ( ( ( ( sK45_E @ SV799 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) ) )
= $false )
| ( ( in @ SV799 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5431]) ).
thf(5495,plain,
! [SV145: $i,SV265: $i,SV799: $i] :
( ( ( ~ ( in @ SV799 @ ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) ) )
= $false )
| ( ( in @ SV799 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5431]) ).
thf(5496,plain,
! [SV145: $i,SV265: $i,SV800: $i,SV845: $i,SV819: $i] :
( ( ( ( SV819 != SV845 ) )
= $true )
| ( ( ~ ( in @ SV800 @ SV845 ) )
= $true )
| ( ( in @ ( sK47_K @ SV845 @ SV819 @ SV800 @ SV265 @ SV145 ) @ SV845 )
= $true )
| ( ( in @ SV819 @ SV145 )
= $false )
| ( ( in @ SV800 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5432]) ).
thf(5497,plain,
! [SV145: $i,SV265: $i,SV819: $i,SV845: $i,SV800: $i] :
( ( ( in @ ( ordered_pair @ SV800 @ ( sK47_K @ SV845 @ SV819 @ SV800 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( ( SV819 != SV845 )
| ~ ( in @ SV800 @ SV845 ) )
= $true )
| ( ( in @ SV819 @ SV145 )
= $false )
| ( ( in @ SV800 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5433]) ).
thf(5498,plain,
! [SV145: $i,SV265: $i,SV801: $i,SV866: $i] :
( ( ( ~ ( in @ SV866 @ ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV801 @ SV866 ) @ SV265 )
= $true )
| ( ( in @ SV801 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5434]) ).
thf(5499,plain,
! [SV145: $i,SV265: $i,SV801: $i] :
( ( ( ( ( sK45_E @ SV801 @ SV265 @ SV145 )
!= ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) ) )
= $false )
| ( ( in @ SV801 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5435]) ).
thf(5500,plain,
! [SV145: $i,SV265: $i,SV801: $i] :
( ( ( ~ ( in @ SV801 @ ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) ) )
= $false )
| ( ( in @ SV801 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5435]) ).
thf(5501,plain,
! [SV776: $i,SV172: $i,SV272: $i,SV717: $i,SV750: $i,SV820: $i,SV827: $i,SV859: $i] :
( ( ( ~ ( in @ ( sK34_R @ SV859 @ SV827 @ SV820 @ SV750 @ SV717 @ SV272 @ SV172 ) @ SV859 )
| ~ ~ ( in @ ( ordered_pair @ SV827 @ ( sK34_R @ SV859 @ SV827 @ SV820 @ SV750 @ SV717 @ SV272 @ SV172 ) ) @ SV272 ) )
= $false )
| ( ( ( SV820 != SV859 )
| ~ ( in @ SV827 @ SV859 ) )
= $true )
| ( ( ( ordered_pair @ SV820 @ SV827 )
= SV750 )
= $false )
| ( ( in @ SV820 @ SV172 )
= $false )
| ( ( SV776 = SV750 )
= $false )
| ( ( in @ SV776 @ ( cartesian_product2 @ SV172 @ SV717 ) )
= $false )
| ( ( in @ SV750 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5436]) ).
thf(5502,plain,
! [SV832: $i,SV272: $i,SV770: $i,SV172: $i,SV809: $i,SV867: $i,SV860: $i] :
( ( ( ( ( ordered_pair @ SV860 @ SV867 )
!= SV809 )
| ~ ( in @ SV860 @ SV172 ) )
= $true )
| ( ( ! [SY1749: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1749 @ SV867 @ SV860 @ SV809 @ SV770 @ SV272 @ SV172 ) @ SY1749 )
| ~ ~ ( in @ ( ordered_pair @ SV867 @ ( sK34_R @ SY1749 @ SV867 @ SV860 @ SV809 @ SV770 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV860 != SY1749 )
| ~ ( in @ SV867 @ SY1749 ) ) )
= $true )
| ( ( SV832 = SV809 )
= $false )
| ( ( in @ SV832 @ ( cartesian_product2 @ SV172 @ SV770 ) )
= $false )
| ( ( in @ SV809 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5440]) ).
thf(5503,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( ( ( ordered_pair @ ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) )
!= SV810 )
| ~ ( in @ ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 ) @ SV172 ) )
= $false )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5443]) ).
thf(5504,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( ~ ! [SY1701: $i] :
( ~ ( in @ SY1701 @ ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) @ SY1701 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5444]) ).
thf(5505,plain,
! [SV833: $i,SV272: $i,SV771: $i,SV172: $i,SV811: $i,SV868: $i,SV861: $i] :
( ( ( ( ( ordered_pair @ SV861 @ SV868 )
!= SV811 )
| ~ ( in @ SV861 @ SV172 ) )
= $true )
| ( ( ! [SY1750: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1750 @ SV868 @ SV861 @ SV811 @ SV771 @ SV272 @ SV172 ) @ SY1750 )
| ~ ~ ( in @ ( ordered_pair @ SV868 @ ( sK34_R @ SY1750 @ SV868 @ SV861 @ SV811 @ SV771 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV861 != SY1750 )
| ~ ( in @ SV868 @ SY1750 ) ) )
= $true )
| ( ( SV833 = SV811 )
= $false )
| ( ( in @ SV833 @ ( cartesian_product2 @ SV172 @ SV771 ) )
= $false )
| ( ( in @ SV811 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5445]) ).
thf(5506,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( ( ( ordered_pair @ ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) )
!= SV812 )
| ~ ( in @ ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 ) @ SV172 ) )
= $false )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5448]) ).
thf(5507,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( ~ ! [SY1706: $i] :
( ~ ( in @ SY1706 @ ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) @ SY1706 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5449]) ).
thf(5508,plain,
! [SV772: $i,SV272: $i,SV834: $i,SV803: $i,SV172: $i,SV854: $i] :
( ( ( in @ SV854 @ ( cartesian_product2 @ SV172 @ SV803 ) )
= $false )
| ( ( SV854 = SV834 )
= $false )
| ( ( ! [SY1722: $i,SY1723: $i] :
( ( ( ordered_pair @ SY1722 @ SY1723 )
!= SV834 )
| ~ ( in @ SY1722 @ SV172 )
| ! [SY1724: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1724 @ SY1723 @ SY1722 @ SV834 @ SV803 @ SV272 @ SV172 ) @ SY1724 )
| ~ ~ ( in @ ( ordered_pair @ SY1723 @ ( sK34_R @ SY1724 @ SY1723 @ SY1722 @ SV834 @ SV803 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1722 != SY1724 )
| ~ ( in @ SY1723 @ SY1724 ) ) ) )
= $true )
| ( ( in @ SV834 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5450]) ).
thf(5509,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( ( ( sK33_F @ SV835 @ SV803 @ SV272 @ SV172 )
!= SV835 )
| ~ ( in @ ( sK33_F @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV803 ) ) )
= $false )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5451]) ).
thf(5510,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) )
!= SV835 )
| ~ ( in @ ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1725: $i] :
( ~ ( in @ SY1725 @ ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) @ SY1725 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) ) ) ) )
= $false )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5452]) ).
thf(5511,plain,
! [SV272: $i,SV836: $i,SV804: $i,SV172: $i,SV855: $i] :
( ( ( in @ SV855 @ ( cartesian_product2 @ SV172 @ SV804 ) )
= $false )
| ( ( SV855 = SV836 )
= $false )
| ( ( ! [SY1727: $i,SY1728: $i] :
( ( ( ordered_pair @ SY1727 @ SY1728 )
!= SV836 )
| ~ ( in @ SY1727 @ SV172 )
| ! [SY1729: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1729 @ SY1728 @ SY1727 @ SV836 @ SV804 @ SV272 @ SV172 ) @ SY1729 )
| ~ ~ ( in @ ( ordered_pair @ SY1728 @ ( sK34_R @ SY1729 @ SY1728 @ SY1727 @ SV836 @ SV804 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1727 != SY1729 )
| ~ ( in @ SY1728 @ SY1729 ) ) ) )
= $true )
| ( ( in @ SV836 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5453]) ).
thf(5512,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( ( ( sK33_F @ SV837 @ SV804 @ SV272 @ SV172 )
!= SV837 )
| ~ ( in @ ( sK33_F @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV804 ) ) )
= $false )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5454]) ).
thf(5513,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) )
!= SV837 )
| ~ ( in @ ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1730: $i] :
( ~ ( in @ SY1730 @ ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) @ SY1730 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) ) ) ) )
= $false )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5455]) ).
thf(5514,plain,
! [SV272: $i,SV838: $i,SV805: $i,SV172: $i,SV856: $i] :
( ( ( in @ SV856 @ ( cartesian_product2 @ SV172 @ SV805 ) )
= $false )
| ( ( SV856 = SV838 )
= $false )
| ( ( ! [SY1732: $i,SY1733: $i] :
( ( ( ordered_pair @ SY1732 @ SY1733 )
!= SV838 )
| ~ ( in @ SY1732 @ SV172 )
| ! [SY1734: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1734 @ SY1733 @ SY1732 @ SV838 @ SV805 @ SV272 @ SV172 ) @ SY1734 )
| ~ ~ ( in @ ( ordered_pair @ SY1733 @ ( sK34_R @ SY1734 @ SY1733 @ SY1732 @ SV838 @ SV805 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SY1732 != SY1734 )
| ~ ( in @ SY1733 @ SY1734 ) ) ) )
= $true )
| ( ( in @ SV838 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5456]) ).
thf(5515,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( ( ( sK33_F @ SV839 @ SV805 @ SV272 @ SV172 )
!= SV839 )
| ~ ( in @ ( sK33_F @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV805 ) ) )
= $false )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5457]) ).
thf(5516,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) )
!= SV839 )
| ~ ( in @ ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 ) @ SV172 ) )
| ~ ~ ( ~ ! [SY1735: $i] :
( ~ ( in @ SY1735 @ ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) @ SY1735 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) ) ) ) )
= $false )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5458]) ).
thf(5517,plain,
! [SV752: $i,SV172: $i,SV272: $i,SV692: $i,SV723: $i,SV806: $i,SV846: $i,SV792: $i] :
( ( ( ( SV792 != SV846 ) )
= $true )
| ( ( ~ ( in @ SV806 @ SV846 ) )
= $true )
| ( ( in @ ( sK34_R @ SV846 @ SV806 @ SV792 @ SV723 @ SV692 @ SV272 @ SV172 ) @ SV846 )
= $true )
| ( ( ( ordered_pair @ SV792 @ SV806 )
= SV723 )
= $false )
| ( ( in @ SV792 @ SV172 )
= $false )
| ( ( SV752 = SV723 )
= $false )
| ( ( in @ SV752 @ ( cartesian_product2 @ SV172 @ SV692 ) )
= $false )
| ( ( in @ SV723 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5459]) ).
thf(5518,plain,
! [SV752: $i,SV172: $i,SV272: $i,SV692: $i,SV723: $i,SV792: $i,SV846: $i,SV806: $i] :
( ( ( in @ ( ordered_pair @ SV806 @ ( sK34_R @ SV846 @ SV806 @ SV792 @ SV723 @ SV692 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( SV792 != SV846 )
| ~ ( in @ SV806 @ SV846 ) )
= $true )
| ( ( ( ordered_pair @ SV792 @ SV806 )
= SV723 )
= $false )
| ( ( in @ SV792 @ SV172 )
= $false )
| ( ( SV752 = SV723 )
= $false )
| ( ( in @ SV752 @ ( cartesian_product2 @ SV172 @ SV692 ) )
= $false )
| ( ( in @ SV723 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5460]) ).
thf(5519,plain,
! [SV777: $i,SV172: $i,SV272: $i,SV718: $i,SV753: $i,SV821: $i,SV828: $i,SV862: $i] :
( ( ( ~ ( in @ ( sK34_R @ SV862 @ SV828 @ SV821 @ SV753 @ SV718 @ SV272 @ SV172 ) @ SV862 )
| ~ ~ ( in @ ( ordered_pair @ SV828 @ ( sK34_R @ SV862 @ SV828 @ SV821 @ SV753 @ SV718 @ SV272 @ SV172 ) ) @ SV272 ) )
= $false )
| ( ( ( SV821 != SV862 )
| ~ ( in @ SV828 @ SV862 ) )
= $true )
| ( ( ( ordered_pair @ SV821 @ SV828 )
= SV753 )
= $false )
| ( ( in @ SV821 @ SV172 )
= $false )
| ( ( SV777 = SV753 )
= $false )
| ( ( in @ SV777 @ ( cartesian_product2 @ SV172 @ SV718 ) )
= $false )
| ( ( in @ SV753 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5461]) ).
thf(5520,plain,
! [SV778: $i,SV172: $i,SV272: $i,SV719: $i,SV755: $i,SV822: $i,SV829: $i,SV863: $i] :
( ( ( ~ ( in @ ( sK34_R @ SV863 @ SV829 @ SV822 @ SV755 @ SV719 @ SV272 @ SV172 ) @ SV863 )
| ~ ~ ( in @ ( ordered_pair @ SV829 @ ( sK34_R @ SV863 @ SV829 @ SV822 @ SV755 @ SV719 @ SV272 @ SV172 ) ) @ SV272 ) )
= $false )
| ( ( ( SV822 != SV863 )
| ~ ( in @ SV829 @ SV863 ) )
= $true )
| ( ( ( ordered_pair @ SV822 @ SV829 )
= SV755 )
= $false )
| ( ( in @ SV822 @ SV172 )
= $false )
| ( ( SV778 = SV755 )
= $false )
| ( ( in @ SV778 @ ( cartesian_product2 @ SV172 @ SV719 ) )
= $false )
| ( ( in @ SV755 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5465]) ).
thf(5521,plain,
! [SV720: $i,SV813: $i,SV272: $i,SV743: $i,SV779: $i,SV850: $i,SV172: $i,SV847: $i] :
( ( ( in @ SV847 @ SV172 )
= $false )
| ( ( ( ordered_pair @ SV847 @ SV850 )
= SV779 )
= $false )
| ( ( ! [SY1742: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1742 @ SV850 @ SV847 @ SV779 @ SV743 @ SV272 @ SV172 ) @ SY1742 )
| ~ ~ ( in @ ( ordered_pair @ SV850 @ ( sK34_R @ SY1742 @ SV850 @ SV847 @ SV779 @ SV743 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV847 != SY1742 )
| ~ ( in @ SV850 @ SY1742 ) ) )
= $true )
| ( ( SV813 = SV779 )
= $false )
| ( ( in @ SV813 @ ( cartesian_product2 @ SV172 @ SV743 ) )
= $false )
| ( ( in @ SV779 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5469]) ).
thf(5522,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i,SV869: $i] :
( ( ( ~ ( in @ SV869 @ ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) @ SV869 ) @ SV272 ) )
= $true )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5472]) ).
thf(5523,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( ( ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5473]) ).
thf(5524,plain,
! [SV814: $i,SV272: $i,SV744: $i,SV781: $i,SV851: $i,SV172: $i,SV848: $i] :
( ( ( in @ SV848 @ SV172 )
= $false )
| ( ( ( ordered_pair @ SV848 @ SV851 )
= SV781 )
= $false )
| ( ( ! [SY1743: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1743 @ SV851 @ SV848 @ SV781 @ SV744 @ SV272 @ SV172 ) @ SY1743 )
| ~ ~ ( in @ ( ordered_pair @ SV851 @ ( sK34_R @ SY1743 @ SV851 @ SV848 @ SV781 @ SV744 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV848 != SY1743 )
| ~ ( in @ SV851 @ SY1743 ) ) )
= $true )
| ( ( SV814 = SV781 )
= $false )
| ( ( in @ SV814 @ ( cartesian_product2 @ SV172 @ SV744 ) )
= $false )
| ( ( in @ SV781 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5474]) ).
thf(5525,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i,SV870: $i] :
( ( ( ~ ( in @ SV870 @ ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) @ SV870 ) @ SV272 ) )
= $true )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5477]) ).
thf(5526,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( ( ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5478]) ).
thf(5527,plain,
! [SV815: $i,SV272: $i,SV745: $i,SV783: $i,SV852: $i,SV172: $i,SV849: $i] :
( ( ( in @ SV849 @ SV172 )
= $false )
| ( ( ( ordered_pair @ SV849 @ SV852 )
= SV783 )
= $false )
| ( ( ! [SY1744: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1744 @ SV852 @ SV849 @ SV783 @ SV745 @ SV272 @ SV172 ) @ SY1744 )
| ~ ~ ( in @ ( ordered_pair @ SV852 @ ( sK34_R @ SY1744 @ SV852 @ SV849 @ SV783 @ SV745 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV849 != SY1744 )
| ~ ( in @ SV852 @ SY1744 ) ) )
= $true )
| ( ( SV815 = SV783 )
= $false )
| ( ( in @ SV815 @ ( cartesian_product2 @ SV172 @ SV745 ) )
= $false )
| ( ( in @ SV783 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5479]) ).
thf(5528,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i,SV871: $i] :
( ( ( ~ ( in @ SV871 @ ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) @ SV871 ) @ SV272 ) )
= $true )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5482]) ).
thf(5529,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( ( ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5483]) ).
thf(5530,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV796: $i,SV843: $i,SV817: $i] :
( ( ( SV817 = SV843 )
= $false )
| ( ( ~ ( in @ SV796 @ SV843 ) )
= $true )
| ( ( in @ ( sK47_K @ SV843 @ SV817 @ SV796 @ SV265 @ SV145 ) @ SV843 )
= $true )
| ( ( in @ SV817 @ SV145 )
= $false )
| ( ( in @ SV796 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5486]) ).
thf(5531,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV796: $i,SV843: $i,SV817: $i] :
( ( ( ( SV817 != SV843 ) )
= $true )
| ( ( ~ ( in @ SV796 @ SV843 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV796 @ ( sK47_K @ SV843 @ SV817 @ SV796 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( in @ SV817 @ SV145 )
= $false )
| ( ( in @ SV796 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5487]) ).
thf(5532,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV797: $i,SV864: $i] :
( ( ( in @ SV864 @ ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV797 @ SV864 ) @ SV265 )
= $true )
| ( ( in @ SV797 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5488]) ).
thf(5533,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV797: $i] :
( ( ( ( sK45_E @ SV797 @ SV265 @ SV145 )
= ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) )
= $true )
| ( ( in @ SV797 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5489]) ).
thf(5534,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV797: $i] :
( ( ( in @ SV797 @ ( sK46_SY702 @ SV797 @ SV265 @ SV145 ) )
= $true )
| ( ( in @ SV797 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5490]) ).
thf(5535,plain,
! [SV145: $i,SV265: $i,SV798: $i,SV844: $i,SV818: $i] :
( ( ( SV818 = SV844 )
= $false )
| ( ( ~ ( in @ SV798 @ SV844 ) )
= $true )
| ( ( in @ ( sK47_K @ SV844 @ SV818 @ SV798 @ SV265 @ SV145 ) @ SV844 )
= $true )
| ( ( in @ SV818 @ SV145 )
= $false )
| ( ( in @ SV798 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5491]) ).
thf(5536,plain,
! [SV145: $i,SV265: $i,SV798: $i,SV844: $i,SV818: $i] :
( ( ( ( SV818 != SV844 ) )
= $true )
| ( ( ~ ( in @ SV798 @ SV844 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV798 @ ( sK47_K @ SV844 @ SV818 @ SV798 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( in @ SV818 @ SV145 )
= $false )
| ( ( in @ SV798 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5492]) ).
thf(5537,plain,
! [SV145: $i,SV265: $i,SV799: $i,SV865: $i] :
( ( ( in @ SV865 @ ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV799 @ SV865 ) @ SV265 )
= $true )
| ( ( in @ SV799 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5493]) ).
thf(5538,plain,
! [SV145: $i,SV265: $i,SV799: $i] :
( ( ( ( sK45_E @ SV799 @ SV265 @ SV145 )
= ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) )
= $true )
| ( ( in @ SV799 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5494]) ).
thf(5539,plain,
! [SV145: $i,SV265: $i,SV799: $i] :
( ( ( in @ SV799 @ ( sK46_SY702 @ SV799 @ SV265 @ SV145 ) )
= $true )
| ( ( in @ SV799 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5495]) ).
thf(5540,plain,
! [SV145: $i,SV265: $i,SV800: $i,SV845: $i,SV819: $i] :
( ( ( SV819 = SV845 )
= $false )
| ( ( ~ ( in @ SV800 @ SV845 ) )
= $true )
| ( ( in @ ( sK47_K @ SV845 @ SV819 @ SV800 @ SV265 @ SV145 ) @ SV845 )
= $true )
| ( ( in @ SV819 @ SV145 )
= $false )
| ( ( in @ SV800 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5496]) ).
thf(5541,plain,
! [SV145: $i,SV265: $i,SV800: $i,SV845: $i,SV819: $i] :
( ( ( ( SV819 != SV845 ) )
= $true )
| ( ( ~ ( in @ SV800 @ SV845 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV800 @ ( sK47_K @ SV845 @ SV819 @ SV800 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( in @ SV819 @ SV145 )
= $false )
| ( ( in @ SV800 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5497]) ).
thf(5542,plain,
! [SV145: $i,SV265: $i,SV801: $i,SV866: $i] :
( ( ( in @ SV866 @ ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV801 @ SV866 ) @ SV265 )
= $true )
| ( ( in @ SV801 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5498]) ).
thf(5543,plain,
! [SV145: $i,SV265: $i,SV801: $i] :
( ( ( ( sK45_E @ SV801 @ SV265 @ SV145 )
= ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) )
= $true )
| ( ( in @ SV801 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5499]) ).
thf(5544,plain,
! [SV145: $i,SV265: $i,SV801: $i] :
( ( ( in @ SV801 @ ( sK46_SY702 @ SV801 @ SV265 @ SV145 ) )
= $true )
| ( ( in @ SV801 @ ( sK44_C @ SV265 @ SV145 ) )
= $false )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5500]) ).
thf(5545,plain,
! [SV776: $i,SV172: $i,SV272: $i,SV717: $i,SV750: $i,SV820: $i,SV827: $i,SV859: $i] :
( ( ( ~ ( in @ ( sK34_R @ SV859 @ SV827 @ SV820 @ SV750 @ SV717 @ SV272 @ SV172 ) @ SV859 ) )
= $false )
| ( ( ( SV820 != SV859 )
| ~ ( in @ SV827 @ SV859 ) )
= $true )
| ( ( ( ordered_pair @ SV820 @ SV827 )
= SV750 )
= $false )
| ( ( in @ SV820 @ SV172 )
= $false )
| ( ( SV776 = SV750 )
= $false )
| ( ( in @ SV776 @ ( cartesian_product2 @ SV172 @ SV717 ) )
= $false )
| ( ( in @ SV750 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5501]) ).
thf(5546,plain,
! [SV776: $i,SV172: $i,SV272: $i,SV717: $i,SV750: $i,SV820: $i,SV859: $i,SV827: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV827 @ ( sK34_R @ SV859 @ SV827 @ SV820 @ SV750 @ SV717 @ SV272 @ SV172 ) ) @ SV272 ) )
= $false )
| ( ( ( SV820 != SV859 )
| ~ ( in @ SV827 @ SV859 ) )
= $true )
| ( ( ( ordered_pair @ SV820 @ SV827 )
= SV750 )
= $false )
| ( ( in @ SV820 @ SV172 )
= $false )
| ( ( SV776 = SV750 )
= $false )
| ( ( in @ SV776 @ ( cartesian_product2 @ SV172 @ SV717 ) )
= $false )
| ( ( in @ SV750 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5501]) ).
thf(5547,plain,
! [SV832: $i,SV272: $i,SV770: $i,SV172: $i,SV809: $i,SV867: $i,SV860: $i] :
( ( ( ( ( ordered_pair @ SV860 @ SV867 )
!= SV809 ) )
= $true )
| ( ( ~ ( in @ SV860 @ SV172 ) )
= $true )
| ( ( ! [SY1749: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1749 @ SV867 @ SV860 @ SV809 @ SV770 @ SV272 @ SV172 ) @ SY1749 )
| ~ ~ ( in @ ( ordered_pair @ SV867 @ ( sK34_R @ SY1749 @ SV867 @ SV860 @ SV809 @ SV770 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV860 != SY1749 )
| ~ ( in @ SV867 @ SY1749 ) ) )
= $true )
| ( ( SV832 = SV809 )
= $false )
| ( ( in @ SV832 @ ( cartesian_product2 @ SV172 @ SV770 ) )
= $false )
| ( ( in @ SV809 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5502]) ).
thf(5548,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( ( ( ordered_pair @ ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) )
!= SV810 ) )
= $false )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5503]) ).
thf(5549,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( ~ ( in @ ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 ) @ SV172 ) )
= $false )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5503]) ).
thf(5550,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( ~ ! [SY1701: $i] :
( ~ ( in @ SY1701 @ ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) @ SY1701 ) @ SV272 ) ) )
= $false )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5504]) ).
thf(5551,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( ~ ~ ( ( ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5504]) ).
thf(5552,plain,
! [SV833: $i,SV272: $i,SV771: $i,SV172: $i,SV811: $i,SV868: $i,SV861: $i] :
( ( ( ( ( ordered_pair @ SV861 @ SV868 )
!= SV811 ) )
= $true )
| ( ( ~ ( in @ SV861 @ SV172 ) )
= $true )
| ( ( ! [SY1750: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1750 @ SV868 @ SV861 @ SV811 @ SV771 @ SV272 @ SV172 ) @ SY1750 )
| ~ ~ ( in @ ( ordered_pair @ SV868 @ ( sK34_R @ SY1750 @ SV868 @ SV861 @ SV811 @ SV771 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV861 != SY1750 )
| ~ ( in @ SV868 @ SY1750 ) ) )
= $true )
| ( ( SV833 = SV811 )
= $false )
| ( ( in @ SV833 @ ( cartesian_product2 @ SV172 @ SV771 ) )
= $false )
| ( ( in @ SV811 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5505]) ).
thf(5553,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( ( ( ordered_pair @ ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) )
!= SV812 ) )
= $false )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5506]) ).
thf(5554,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( ~ ( in @ ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 ) @ SV172 ) )
= $false )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5506]) ).
thf(5555,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( ~ ! [SY1706: $i] :
( ~ ( in @ SY1706 @ ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) @ SY1706 ) @ SV272 ) ) )
= $false )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5507]) ).
thf(5556,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( ~ ~ ( ( ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5507]) ).
thf(5557,plain,
! [SV772: $i,SV854: $i,SV272: $i,SV803: $i,SV172: $i,SV834: $i,SV872: $i] :
( ( ( ! [SY1751: $i] :
( ( ( ordered_pair @ SV872 @ SY1751 )
!= SV834 )
| ~ ( in @ SV872 @ SV172 )
| ! [SY1752: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1752 @ SY1751 @ SV872 @ SV834 @ SV803 @ SV272 @ SV172 ) @ SY1752 )
| ~ ~ ( in @ ( ordered_pair @ SY1751 @ ( sK34_R @ SY1752 @ SY1751 @ SV872 @ SV834 @ SV803 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV872 != SY1752 )
| ~ ( in @ SY1751 @ SY1752 ) ) ) )
= $true )
| ( ( SV854 = SV834 )
= $false )
| ( ( in @ SV854 @ ( cartesian_product2 @ SV172 @ SV803 ) )
= $false )
| ( ( in @ SV834 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5508]) ).
thf(5558,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( ( ( sK33_F @ SV835 @ SV803 @ SV272 @ SV172 )
!= SV835 ) )
= $false )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5509]) ).
thf(5559,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( ~ ( in @ ( sK33_F @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV803 ) ) )
= $false )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5509]) ).
thf(5560,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) )
!= SV835 )
| ~ ( in @ ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 ) @ SV172 ) ) )
= $false )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5510]) ).
thf(5561,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( ~ ~ ( ~ ! [SY1725: $i] :
( ~ ( in @ SY1725 @ ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) @ SY1725 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) ) ) ) )
= $false )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5510]) ).
thf(5562,plain,
! [SV855: $i,SV272: $i,SV804: $i,SV172: $i,SV836: $i,SV873: $i] :
( ( ( ! [SY1753: $i] :
( ( ( ordered_pair @ SV873 @ SY1753 )
!= SV836 )
| ~ ( in @ SV873 @ SV172 )
| ! [SY1754: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1754 @ SY1753 @ SV873 @ SV836 @ SV804 @ SV272 @ SV172 ) @ SY1754 )
| ~ ~ ( in @ ( ordered_pair @ SY1753 @ ( sK34_R @ SY1754 @ SY1753 @ SV873 @ SV836 @ SV804 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV873 != SY1754 )
| ~ ( in @ SY1753 @ SY1754 ) ) ) )
= $true )
| ( ( SV855 = SV836 )
= $false )
| ( ( in @ SV855 @ ( cartesian_product2 @ SV172 @ SV804 ) )
= $false )
| ( ( in @ SV836 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5511]) ).
thf(5563,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( ( ( sK33_F @ SV837 @ SV804 @ SV272 @ SV172 )
!= SV837 ) )
= $false )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5512]) ).
thf(5564,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( ~ ( in @ ( sK33_F @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV804 ) ) )
= $false )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5512]) ).
thf(5565,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) )
!= SV837 )
| ~ ( in @ ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 ) @ SV172 ) ) )
= $false )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5513]) ).
thf(5566,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( ~ ~ ( ~ ! [SY1730: $i] :
( ~ ( in @ SY1730 @ ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) @ SY1730 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) ) ) ) )
= $false )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5513]) ).
thf(5567,plain,
! [SV856: $i,SV272: $i,SV805: $i,SV172: $i,SV838: $i,SV874: $i] :
( ( ( ! [SY1755: $i] :
( ( ( ordered_pair @ SV874 @ SY1755 )
!= SV838 )
| ~ ( in @ SV874 @ SV172 )
| ! [SY1756: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1756 @ SY1755 @ SV874 @ SV838 @ SV805 @ SV272 @ SV172 ) @ SY1756 )
| ~ ~ ( in @ ( ordered_pair @ SY1755 @ ( sK34_R @ SY1756 @ SY1755 @ SV874 @ SV838 @ SV805 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV874 != SY1756 )
| ~ ( in @ SY1755 @ SY1756 ) ) ) )
= $true )
| ( ( SV856 = SV838 )
= $false )
| ( ( in @ SV856 @ ( cartesian_product2 @ SV172 @ SV805 ) )
= $false )
| ( ( in @ SV838 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5514]) ).
thf(5568,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( ( ( sK33_F @ SV839 @ SV805 @ SV272 @ SV172 )
!= SV839 ) )
= $false )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5515]) ).
thf(5569,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( ~ ( in @ ( sK33_F @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV805 ) ) )
= $false )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5515]) ).
thf(5570,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( ~ ~ ( ( ( ordered_pair @ ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) )
!= SV839 )
| ~ ( in @ ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 ) @ SV172 ) ) )
= $false )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5516]) ).
thf(5571,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( ~ ~ ( ~ ! [SY1735: $i] :
( ~ ( in @ SY1735 @ ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) @ SY1735 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) ) ) ) )
= $false )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5516]) ).
thf(5572,plain,
! [SV752: $i,SV172: $i,SV272: $i,SV692: $i,SV723: $i,SV806: $i,SV846: $i,SV792: $i] :
( ( ( SV792 = SV846 )
= $false )
| ( ( ~ ( in @ SV806 @ SV846 ) )
= $true )
| ( ( in @ ( sK34_R @ SV846 @ SV806 @ SV792 @ SV723 @ SV692 @ SV272 @ SV172 ) @ SV846 )
= $true )
| ( ( ( ordered_pair @ SV792 @ SV806 )
= SV723 )
= $false )
| ( ( in @ SV792 @ SV172 )
= $false )
| ( ( SV752 = SV723 )
= $false )
| ( ( in @ SV752 @ ( cartesian_product2 @ SV172 @ SV692 ) )
= $false )
| ( ( in @ SV723 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5517]) ).
thf(5573,plain,
! [SV752: $i,SV172: $i,SV272: $i,SV692: $i,SV723: $i,SV806: $i,SV846: $i,SV792: $i] :
( ( ( ( SV792 != SV846 ) )
= $true )
| ( ( ~ ( in @ SV806 @ SV846 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV806 @ ( sK34_R @ SV846 @ SV806 @ SV792 @ SV723 @ SV692 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV792 @ SV806 )
= SV723 )
= $false )
| ( ( in @ SV792 @ SV172 )
= $false )
| ( ( SV752 = SV723 )
= $false )
| ( ( in @ SV752 @ ( cartesian_product2 @ SV172 @ SV692 ) )
= $false )
| ( ( in @ SV723 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5518]) ).
thf(5574,plain,
! [SV777: $i,SV172: $i,SV272: $i,SV718: $i,SV753: $i,SV821: $i,SV828: $i,SV862: $i] :
( ( ( ~ ( in @ ( sK34_R @ SV862 @ SV828 @ SV821 @ SV753 @ SV718 @ SV272 @ SV172 ) @ SV862 ) )
= $false )
| ( ( ( SV821 != SV862 )
| ~ ( in @ SV828 @ SV862 ) )
= $true )
| ( ( ( ordered_pair @ SV821 @ SV828 )
= SV753 )
= $false )
| ( ( in @ SV821 @ SV172 )
= $false )
| ( ( SV777 = SV753 )
= $false )
| ( ( in @ SV777 @ ( cartesian_product2 @ SV172 @ SV718 ) )
= $false )
| ( ( in @ SV753 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5519]) ).
thf(5575,plain,
! [SV777: $i,SV172: $i,SV272: $i,SV718: $i,SV753: $i,SV821: $i,SV862: $i,SV828: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV828 @ ( sK34_R @ SV862 @ SV828 @ SV821 @ SV753 @ SV718 @ SV272 @ SV172 ) ) @ SV272 ) )
= $false )
| ( ( ( SV821 != SV862 )
| ~ ( in @ SV828 @ SV862 ) )
= $true )
| ( ( ( ordered_pair @ SV821 @ SV828 )
= SV753 )
= $false )
| ( ( in @ SV821 @ SV172 )
= $false )
| ( ( SV777 = SV753 )
= $false )
| ( ( in @ SV777 @ ( cartesian_product2 @ SV172 @ SV718 ) )
= $false )
| ( ( in @ SV753 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5519]) ).
thf(5576,plain,
! [SV778: $i,SV172: $i,SV272: $i,SV719: $i,SV755: $i,SV822: $i,SV829: $i,SV863: $i] :
( ( ( ~ ( in @ ( sK34_R @ SV863 @ SV829 @ SV822 @ SV755 @ SV719 @ SV272 @ SV172 ) @ SV863 ) )
= $false )
| ( ( ( SV822 != SV863 )
| ~ ( in @ SV829 @ SV863 ) )
= $true )
| ( ( ( ordered_pair @ SV822 @ SV829 )
= SV755 )
= $false )
| ( ( in @ SV822 @ SV172 )
= $false )
| ( ( SV778 = SV755 )
= $false )
| ( ( in @ SV778 @ ( cartesian_product2 @ SV172 @ SV719 ) )
= $false )
| ( ( in @ SV755 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5520]) ).
thf(5577,plain,
! [SV778: $i,SV172: $i,SV272: $i,SV719: $i,SV755: $i,SV822: $i,SV863: $i,SV829: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV829 @ ( sK34_R @ SV863 @ SV829 @ SV822 @ SV755 @ SV719 @ SV272 @ SV172 ) ) @ SV272 ) )
= $false )
| ( ( ( SV822 != SV863 )
| ~ ( in @ SV829 @ SV863 ) )
= $true )
| ( ( ( ordered_pair @ SV822 @ SV829 )
= SV755 )
= $false )
| ( ( in @ SV822 @ SV172 )
= $false )
| ( ( SV778 = SV755 )
= $false )
| ( ( in @ SV778 @ ( cartesian_product2 @ SV172 @ SV719 ) )
= $false )
| ( ( in @ SV755 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5520]) ).
thf(5578,plain,
! [SV720: $i,SV813: $i,SV172: $i,SV272: $i,SV743: $i,SV779: $i,SV847: $i,SV850: $i,SV875: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_R @ SV875 @ SV850 @ SV847 @ SV779 @ SV743 @ SV272 @ SV172 ) @ SV875 )
| ~ ~ ( in @ ( ordered_pair @ SV850 @ ( sK34_R @ SV875 @ SV850 @ SV847 @ SV779 @ SV743 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV847 != SV875 )
| ~ ( in @ SV850 @ SV875 ) )
= $true )
| ( ( ( ordered_pair @ SV847 @ SV850 )
= SV779 )
= $false )
| ( ( in @ SV847 @ SV172 )
= $false )
| ( ( SV813 = SV779 )
= $false )
| ( ( in @ SV813 @ ( cartesian_product2 @ SV172 @ SV743 ) )
= $false )
| ( ( in @ SV779 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5521]) ).
thf(5579,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i,SV869: $i] :
( ( ( ~ ( in @ SV869 @ ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) @ SV869 ) @ SV272 )
= $true )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5522]) ).
thf(5580,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( ( ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5523]) ).
thf(5581,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( ~ ( in @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5523]) ).
thf(5582,plain,
! [SV814: $i,SV172: $i,SV272: $i,SV744: $i,SV781: $i,SV848: $i,SV851: $i,SV876: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_R @ SV876 @ SV851 @ SV848 @ SV781 @ SV744 @ SV272 @ SV172 ) @ SV876 )
| ~ ~ ( in @ ( ordered_pair @ SV851 @ ( sK34_R @ SV876 @ SV851 @ SV848 @ SV781 @ SV744 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV848 != SV876 )
| ~ ( in @ SV851 @ SV876 ) )
= $true )
| ( ( ( ordered_pair @ SV848 @ SV851 )
= SV781 )
= $false )
| ( ( in @ SV848 @ SV172 )
= $false )
| ( ( SV814 = SV781 )
= $false )
| ( ( in @ SV814 @ ( cartesian_product2 @ SV172 @ SV744 ) )
= $false )
| ( ( in @ SV781 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5524]) ).
thf(5583,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i,SV870: $i] :
( ( ( ~ ( in @ SV870 @ ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) @ SV870 ) @ SV272 )
= $true )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5525]) ).
thf(5584,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( ( ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5526]) ).
thf(5585,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( ~ ( in @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5526]) ).
thf(5586,plain,
! [SV815: $i,SV172: $i,SV272: $i,SV745: $i,SV783: $i,SV849: $i,SV852: $i,SV877: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_R @ SV877 @ SV852 @ SV849 @ SV783 @ SV745 @ SV272 @ SV172 ) @ SV877 )
| ~ ~ ( in @ ( ordered_pair @ SV852 @ ( sK34_R @ SV877 @ SV852 @ SV849 @ SV783 @ SV745 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV849 != SV877 )
| ~ ( in @ SV852 @ SV877 ) )
= $true )
| ( ( ( ordered_pair @ SV849 @ SV852 )
= SV783 )
= $false )
| ( ( in @ SV849 @ SV172 )
= $false )
| ( ( SV815 = SV783 )
= $false )
| ( ( in @ SV815 @ ( cartesian_product2 @ SV172 @ SV745 ) )
= $false )
| ( ( in @ SV783 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5527]) ).
thf(5587,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i,SV871: $i] :
( ( ( ~ ( in @ SV871 @ ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) @ SV871 ) @ SV272 )
= $true )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5528]) ).
thf(5588,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( ( ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5529]) ).
thf(5589,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( ~ ( in @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5529]) ).
thf(5590,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV817: $i,SV843: $i,SV796: $i] :
( ( ( in @ SV796 @ SV843 )
= $false )
| ( ( SV817 = SV843 )
= $false )
| ( ( in @ ( sK47_K @ SV843 @ SV817 @ SV796 @ SV265 @ SV145 ) @ SV843 )
= $true )
| ( ( in @ SV817 @ SV145 )
= $false )
| ( ( in @ SV796 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5530]) ).
thf(5591,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV796: $i,SV843: $i,SV817: $i] :
( ( ( SV817 = SV843 )
= $false )
| ( ( ~ ( in @ SV796 @ SV843 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV796 @ ( sK47_K @ SV843 @ SV817 @ SV796 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( in @ SV817 @ SV145 )
= $false )
| ( ( in @ SV796 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5531]) ).
thf(5592,plain,
! [SV145: $i,SV265: $i,SV818: $i,SV844: $i,SV798: $i] :
( ( ( in @ SV798 @ SV844 )
= $false )
| ( ( SV818 = SV844 )
= $false )
| ( ( in @ ( sK47_K @ SV844 @ SV818 @ SV798 @ SV265 @ SV145 ) @ SV844 )
= $true )
| ( ( in @ SV818 @ SV145 )
= $false )
| ( ( in @ SV798 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5535]) ).
thf(5593,plain,
! [SV145: $i,SV265: $i,SV798: $i,SV844: $i,SV818: $i] :
( ( ( SV818 = SV844 )
= $false )
| ( ( ~ ( in @ SV798 @ SV844 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV798 @ ( sK47_K @ SV844 @ SV818 @ SV798 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( in @ SV818 @ SV145 )
= $false )
| ( ( in @ SV798 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5536]) ).
thf(5594,plain,
! [SV145: $i,SV265: $i,SV819: $i,SV845: $i,SV800: $i] :
( ( ( in @ SV800 @ SV845 )
= $false )
| ( ( SV819 = SV845 )
= $false )
| ( ( in @ ( sK47_K @ SV845 @ SV819 @ SV800 @ SV265 @ SV145 ) @ SV845 )
= $true )
| ( ( in @ SV819 @ SV145 )
= $false )
| ( ( in @ SV800 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5540]) ).
thf(5595,plain,
! [SV145: $i,SV265: $i,SV800: $i,SV845: $i,SV819: $i] :
( ( ( SV819 = SV845 )
= $false )
| ( ( ~ ( in @ SV800 @ SV845 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV800 @ ( sK47_K @ SV845 @ SV819 @ SV800 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( in @ SV819 @ SV145 )
= $false )
| ( ( in @ SV800 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5541]) ).
thf(5596,plain,
! [SV776: $i,SV172: $i,SV272: $i,SV717: $i,SV750: $i,SV820: $i,SV827: $i,SV859: $i] :
( ( ( in @ ( sK34_R @ SV859 @ SV827 @ SV820 @ SV750 @ SV717 @ SV272 @ SV172 ) @ SV859 )
= $true )
| ( ( ( SV820 != SV859 )
| ~ ( in @ SV827 @ SV859 ) )
= $true )
| ( ( ( ordered_pair @ SV820 @ SV827 )
= SV750 )
= $false )
| ( ( in @ SV820 @ SV172 )
= $false )
| ( ( SV776 = SV750 )
= $false )
| ( ( in @ SV776 @ ( cartesian_product2 @ SV172 @ SV717 ) )
= $false )
| ( ( in @ SV750 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5545]) ).
thf(5597,plain,
! [SV776: $i,SV172: $i,SV272: $i,SV717: $i,SV750: $i,SV820: $i,SV859: $i,SV827: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV827 @ ( sK34_R @ SV859 @ SV827 @ SV820 @ SV750 @ SV717 @ SV272 @ SV172 ) ) @ SV272 ) )
= $true )
| ( ( ( SV820 != SV859 )
| ~ ( in @ SV827 @ SV859 ) )
= $true )
| ( ( ( ordered_pair @ SV820 @ SV827 )
= SV750 )
= $false )
| ( ( in @ SV820 @ SV172 )
= $false )
| ( ( SV776 = SV750 )
= $false )
| ( ( in @ SV776 @ ( cartesian_product2 @ SV172 @ SV717 ) )
= $false )
| ( ( in @ SV750 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5546]) ).
thf(5598,plain,
! [SV832: $i,SV272: $i,SV770: $i,SV172: $i,SV809: $i,SV867: $i,SV860: $i] :
( ( ( ( ordered_pair @ SV860 @ SV867 )
= SV809 )
= $false )
| ( ( ~ ( in @ SV860 @ SV172 ) )
= $true )
| ( ( ! [SY1749: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1749 @ SV867 @ SV860 @ SV809 @ SV770 @ SV272 @ SV172 ) @ SY1749 )
| ~ ~ ( in @ ( ordered_pair @ SV867 @ ( sK34_R @ SY1749 @ SV867 @ SV860 @ SV809 @ SV770 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV860 != SY1749 )
| ~ ( in @ SV867 @ SY1749 ) ) )
= $true )
| ( ( SV832 = SV809 )
= $false )
| ( ( in @ SV832 @ ( cartesian_product2 @ SV172 @ SV770 ) )
= $false )
| ( ( in @ SV809 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5547]) ).
thf(5599,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( ( ordered_pair @ ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) )
= SV810 )
= $true )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5548]) ).
thf(5600,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( in @ ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5549]) ).
thf(5601,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( ! [SY1701: $i] :
( ~ ( in @ SY1701 @ ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) @ SY1701 ) @ SV272 ) ) )
= $true )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5550]) ).
thf(5602,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( ~ ( ( ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) ) ) )
= $true )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5551]) ).
thf(5603,plain,
! [SV833: $i,SV272: $i,SV771: $i,SV172: $i,SV811: $i,SV868: $i,SV861: $i] :
( ( ( ( ordered_pair @ SV861 @ SV868 )
= SV811 )
= $false )
| ( ( ~ ( in @ SV861 @ SV172 ) )
= $true )
| ( ( ! [SY1750: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1750 @ SV868 @ SV861 @ SV811 @ SV771 @ SV272 @ SV172 ) @ SY1750 )
| ~ ~ ( in @ ( ordered_pair @ SV868 @ ( sK34_R @ SY1750 @ SV868 @ SV861 @ SV811 @ SV771 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV861 != SY1750 )
| ~ ( in @ SV868 @ SY1750 ) ) )
= $true )
| ( ( SV833 = SV811 )
= $false )
| ( ( in @ SV833 @ ( cartesian_product2 @ SV172 @ SV771 ) )
= $false )
| ( ( in @ SV811 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5552]) ).
thf(5604,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( ( ordered_pair @ ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) )
= SV812 )
= $true )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5553]) ).
thf(5605,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( in @ ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5554]) ).
thf(5606,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( ! [SY1706: $i] :
( ~ ( in @ SY1706 @ ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) @ SY1706 ) @ SV272 ) ) )
= $true )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5555]) ).
thf(5607,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( ~ ( ( ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) ) ) )
= $true )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5556]) ).
thf(5608,plain,
! [SV772: $i,SV854: $i,SV272: $i,SV803: $i,SV172: $i,SV834: $i,SV878: $i,SV872: $i] :
( ( ( ( ( ordered_pair @ SV872 @ SV878 )
!= SV834 )
| ~ ( in @ SV872 @ SV172 )
| ! [SY1757: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1757 @ SV878 @ SV872 @ SV834 @ SV803 @ SV272 @ SV172 ) @ SY1757 )
| ~ ~ ( in @ ( ordered_pair @ SV878 @ ( sK34_R @ SY1757 @ SV878 @ SV872 @ SV834 @ SV803 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV872 != SY1757 )
| ~ ( in @ SV878 @ SY1757 ) ) )
= $true )
| ( ( SV854 = SV834 )
= $false )
| ( ( in @ SV854 @ ( cartesian_product2 @ SV172 @ SV803 ) )
= $false )
| ( ( in @ SV834 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5557]) ).
thf(5609,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( ( sK33_F @ SV835 @ SV803 @ SV272 @ SV172 )
= SV835 )
= $true )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5558]) ).
thf(5610,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( in @ ( sK33_F @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV803 ) )
= $true )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5559]) ).
thf(5611,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) )
!= SV835 )
| ~ ( in @ ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 ) @ SV172 ) ) )
= $true )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5560]) ).
thf(5612,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( ~ ( ~ ! [SY1725: $i] :
( ~ ( in @ SY1725 @ ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) @ SY1725 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) ) ) ) )
= $true )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5561]) ).
thf(5613,plain,
! [SV855: $i,SV272: $i,SV804: $i,SV172: $i,SV836: $i,SV879: $i,SV873: $i] :
( ( ( ( ( ordered_pair @ SV873 @ SV879 )
!= SV836 )
| ~ ( in @ SV873 @ SV172 )
| ! [SY1758: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1758 @ SV879 @ SV873 @ SV836 @ SV804 @ SV272 @ SV172 ) @ SY1758 )
| ~ ~ ( in @ ( ordered_pair @ SV879 @ ( sK34_R @ SY1758 @ SV879 @ SV873 @ SV836 @ SV804 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV873 != SY1758 )
| ~ ( in @ SV879 @ SY1758 ) ) )
= $true )
| ( ( SV855 = SV836 )
= $false )
| ( ( in @ SV855 @ ( cartesian_product2 @ SV172 @ SV804 ) )
= $false )
| ( ( in @ SV836 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5562]) ).
thf(5614,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( ( sK33_F @ SV837 @ SV804 @ SV272 @ SV172 )
= SV837 )
= $true )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5563]) ).
thf(5615,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( in @ ( sK33_F @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV804 ) )
= $true )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5564]) ).
thf(5616,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) )
!= SV837 )
| ~ ( in @ ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 ) @ SV172 ) ) )
= $true )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5565]) ).
thf(5617,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( ~ ( ~ ! [SY1730: $i] :
( ~ ( in @ SY1730 @ ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) @ SY1730 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) ) ) ) )
= $true )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5566]) ).
thf(5618,plain,
! [SV856: $i,SV272: $i,SV805: $i,SV172: $i,SV838: $i,SV880: $i,SV874: $i] :
( ( ( ( ( ordered_pair @ SV874 @ SV880 )
!= SV838 )
| ~ ( in @ SV874 @ SV172 )
| ! [SY1759: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1759 @ SV880 @ SV874 @ SV838 @ SV805 @ SV272 @ SV172 ) @ SY1759 )
| ~ ~ ( in @ ( ordered_pair @ SV880 @ ( sK34_R @ SY1759 @ SV880 @ SV874 @ SV838 @ SV805 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV874 != SY1759 )
| ~ ( in @ SV880 @ SY1759 ) ) )
= $true )
| ( ( SV856 = SV838 )
= $false )
| ( ( in @ SV856 @ ( cartesian_product2 @ SV172 @ SV805 ) )
= $false )
| ( ( in @ SV838 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5567]) ).
thf(5619,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( ( sK33_F @ SV839 @ SV805 @ SV272 @ SV172 )
= SV839 )
= $true )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5568]) ).
thf(5620,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( in @ ( sK33_F @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( cartesian_product2 @ SV172 @ SV805 ) )
= $true )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5569]) ).
thf(5621,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( ~ ( ( ( ordered_pair @ ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) )
!= SV839 )
| ~ ( in @ ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 ) @ SV172 ) ) )
= $true )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5570]) ).
thf(5622,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( ~ ( ~ ! [SY1735: $i] :
( ~ ( in @ SY1735 @ ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) @ SY1735 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) ) ) ) )
= $true )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5571]) ).
thf(5623,plain,
! [SV752: $i,SV172: $i,SV272: $i,SV692: $i,SV723: $i,SV792: $i,SV846: $i,SV806: $i] :
( ( ( in @ SV806 @ SV846 )
= $false )
| ( ( SV792 = SV846 )
= $false )
| ( ( in @ ( sK34_R @ SV846 @ SV806 @ SV792 @ SV723 @ SV692 @ SV272 @ SV172 ) @ SV846 )
= $true )
| ( ( ( ordered_pair @ SV792 @ SV806 )
= SV723 )
= $false )
| ( ( in @ SV792 @ SV172 )
= $false )
| ( ( SV752 = SV723 )
= $false )
| ( ( in @ SV752 @ ( cartesian_product2 @ SV172 @ SV692 ) )
= $false )
| ( ( in @ SV723 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5572]) ).
thf(5624,plain,
! [SV752: $i,SV172: $i,SV272: $i,SV692: $i,SV723: $i,SV806: $i,SV846: $i,SV792: $i] :
( ( ( SV792 = SV846 )
= $false )
| ( ( ~ ( in @ SV806 @ SV846 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV806 @ ( sK34_R @ SV846 @ SV806 @ SV792 @ SV723 @ SV692 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV792 @ SV806 )
= SV723 )
= $false )
| ( ( in @ SV792 @ SV172 )
= $false )
| ( ( SV752 = SV723 )
= $false )
| ( ( in @ SV752 @ ( cartesian_product2 @ SV172 @ SV692 ) )
= $false )
| ( ( in @ SV723 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5573]) ).
thf(5625,plain,
! [SV777: $i,SV172: $i,SV272: $i,SV718: $i,SV753: $i,SV821: $i,SV828: $i,SV862: $i] :
( ( ( in @ ( sK34_R @ SV862 @ SV828 @ SV821 @ SV753 @ SV718 @ SV272 @ SV172 ) @ SV862 )
= $true )
| ( ( ( SV821 != SV862 )
| ~ ( in @ SV828 @ SV862 ) )
= $true )
| ( ( ( ordered_pair @ SV821 @ SV828 )
= SV753 )
= $false )
| ( ( in @ SV821 @ SV172 )
= $false )
| ( ( SV777 = SV753 )
= $false )
| ( ( in @ SV777 @ ( cartesian_product2 @ SV172 @ SV718 ) )
= $false )
| ( ( in @ SV753 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5574]) ).
thf(5626,plain,
! [SV777: $i,SV172: $i,SV272: $i,SV718: $i,SV753: $i,SV821: $i,SV862: $i,SV828: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV828 @ ( sK34_R @ SV862 @ SV828 @ SV821 @ SV753 @ SV718 @ SV272 @ SV172 ) ) @ SV272 ) )
= $true )
| ( ( ( SV821 != SV862 )
| ~ ( in @ SV828 @ SV862 ) )
= $true )
| ( ( ( ordered_pair @ SV821 @ SV828 )
= SV753 )
= $false )
| ( ( in @ SV821 @ SV172 )
= $false )
| ( ( SV777 = SV753 )
= $false )
| ( ( in @ SV777 @ ( cartesian_product2 @ SV172 @ SV718 ) )
= $false )
| ( ( in @ SV753 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5575]) ).
thf(5627,plain,
! [SV778: $i,SV172: $i,SV272: $i,SV719: $i,SV755: $i,SV822: $i,SV829: $i,SV863: $i] :
( ( ( in @ ( sK34_R @ SV863 @ SV829 @ SV822 @ SV755 @ SV719 @ SV272 @ SV172 ) @ SV863 )
= $true )
| ( ( ( SV822 != SV863 )
| ~ ( in @ SV829 @ SV863 ) )
= $true )
| ( ( ( ordered_pair @ SV822 @ SV829 )
= SV755 )
= $false )
| ( ( in @ SV822 @ SV172 )
= $false )
| ( ( SV778 = SV755 )
= $false )
| ( ( in @ SV778 @ ( cartesian_product2 @ SV172 @ SV719 ) )
= $false )
| ( ( in @ SV755 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5576]) ).
thf(5628,plain,
! [SV778: $i,SV172: $i,SV272: $i,SV719: $i,SV755: $i,SV822: $i,SV863: $i,SV829: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV829 @ ( sK34_R @ SV863 @ SV829 @ SV822 @ SV755 @ SV719 @ SV272 @ SV172 ) ) @ SV272 ) )
= $true )
| ( ( ( SV822 != SV863 )
| ~ ( in @ SV829 @ SV863 ) )
= $true )
| ( ( ( ordered_pair @ SV822 @ SV829 )
= SV755 )
= $false )
| ( ( in @ SV822 @ SV172 )
= $false )
| ( ( SV778 = SV755 )
= $false )
| ( ( in @ SV778 @ ( cartesian_product2 @ SV172 @ SV719 ) )
= $false )
| ( ( in @ SV755 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5577]) ).
thf(5629,plain,
! [SV720: $i,SV813: $i,SV172: $i,SV272: $i,SV743: $i,SV779: $i,SV847: $i,SV850: $i,SV875: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_R @ SV875 @ SV850 @ SV847 @ SV779 @ SV743 @ SV272 @ SV172 ) @ SV875 )
| ~ ~ ( in @ ( ordered_pair @ SV850 @ ( sK34_R @ SV875 @ SV850 @ SV847 @ SV779 @ SV743 @ SV272 @ SV172 ) ) @ SV272 ) ) )
= $true )
| ( ( ( SV847 != SV875 )
| ~ ( in @ SV850 @ SV875 ) )
= $true )
| ( ( ( ordered_pair @ SV847 @ SV850 )
= SV779 )
= $false )
| ( ( in @ SV847 @ SV172 )
= $false )
| ( ( SV813 = SV779 )
= $false )
| ( ( in @ SV813 @ ( cartesian_product2 @ SV172 @ SV743 ) )
= $false )
| ( ( in @ SV779 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5578]) ).
thf(5630,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i,SV869: $i] :
( ( ( in @ SV869 @ ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) @ SV869 ) @ SV272 )
= $true )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5579]) ).
thf(5631,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( ( sK30_O @ SV780 @ SV743 @ SV272 @ SV172 )
= ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5580]) ).
thf(5632,plain,
! [SV720: $i,SV172: $i,SV272: $i,SV743: $i,SV780: $i] :
( ( ( in @ ( sK31_SY649 @ SV780 @ SV743 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV780 @ SV743 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ SV780 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5581]) ).
thf(5633,plain,
! [SV814: $i,SV172: $i,SV272: $i,SV744: $i,SV781: $i,SV848: $i,SV851: $i,SV876: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_R @ SV876 @ SV851 @ SV848 @ SV781 @ SV744 @ SV272 @ SV172 ) @ SV876 )
| ~ ~ ( in @ ( ordered_pair @ SV851 @ ( sK34_R @ SV876 @ SV851 @ SV848 @ SV781 @ SV744 @ SV272 @ SV172 ) ) @ SV272 ) ) )
= $true )
| ( ( ( SV848 != SV876 )
| ~ ( in @ SV851 @ SV876 ) )
= $true )
| ( ( ( ordered_pair @ SV848 @ SV851 )
= SV781 )
= $false )
| ( ( in @ SV848 @ SV172 )
= $false )
| ( ( SV814 = SV781 )
= $false )
| ( ( in @ SV814 @ ( cartesian_product2 @ SV172 @ SV744 ) )
= $false )
| ( ( in @ SV781 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5582]) ).
thf(5634,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i,SV870: $i] :
( ( ( in @ SV870 @ ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) @ SV870 ) @ SV272 )
= $true )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5583]) ).
thf(5635,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( ( sK30_O @ SV782 @ SV744 @ SV272 @ SV172 )
= ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5584]) ).
thf(5636,plain,
! [SV172: $i,SV272: $i,SV744: $i,SV782: $i] :
( ( ( in @ ( sK31_SY649 @ SV782 @ SV744 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV782 @ SV744 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ SV782 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5585]) ).
thf(5637,plain,
! [SV815: $i,SV172: $i,SV272: $i,SV745: $i,SV783: $i,SV849: $i,SV852: $i,SV877: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_R @ SV877 @ SV852 @ SV849 @ SV783 @ SV745 @ SV272 @ SV172 ) @ SV877 )
| ~ ~ ( in @ ( ordered_pair @ SV852 @ ( sK34_R @ SV877 @ SV852 @ SV849 @ SV783 @ SV745 @ SV272 @ SV172 ) ) @ SV272 ) ) )
= $true )
| ( ( ( SV849 != SV877 )
| ~ ( in @ SV852 @ SV877 ) )
= $true )
| ( ( ( ordered_pair @ SV849 @ SV852 )
= SV783 )
= $false )
| ( ( in @ SV849 @ SV172 )
= $false )
| ( ( SV815 = SV783 )
= $false )
| ( ( in @ SV815 @ ( cartesian_product2 @ SV172 @ SV745 ) )
= $false )
| ( ( in @ SV783 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5586]) ).
thf(5638,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i,SV871: $i] :
( ( ( in @ SV871 @ ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) @ SV871 ) @ SV272 )
= $true )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5587]) ).
thf(5639,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( ( sK30_O @ SV784 @ SV745 @ SV272 @ SV172 )
= ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5588]) ).
thf(5640,plain,
! [SV172: $i,SV272: $i,SV745: $i,SV784: $i] :
( ( ( in @ ( sK31_SY649 @ SV784 @ SV745 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV784 @ SV745 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ SV784 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5589]) ).
thf(5641,plain,
! [SV733: $i,SV145: $i,SV265: $i,SV817: $i,SV843: $i,SV796: $i] :
( ( ( in @ SV796 @ SV843 )
= $false )
| ( ( SV817 = SV843 )
= $false )
| ( ( in @ ( ordered_pair @ SV796 @ ( sK47_K @ SV843 @ SV817 @ SV796 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( in @ SV817 @ SV145 )
= $false )
| ( ( in @ SV796 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK49_SY705 @ SV265 @ SV145 ) @ SV733 ) @ SV265 )
= $true )
| ( ( in @ SV733 @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $false )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5591]) ).
thf(5642,plain,
! [SV145: $i,SV265: $i,SV818: $i,SV844: $i,SV798: $i] :
( ( ( in @ SV798 @ SV844 )
= $false )
| ( ( SV818 = SV844 )
= $false )
| ( ( in @ ( ordered_pair @ SV798 @ ( sK47_K @ SV844 @ SV818 @ SV798 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( in @ SV818 @ SV145 )
= $false )
| ( ( in @ SV798 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( ( sK48_C @ SV265 @ SV145 )
= ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5593]) ).
thf(5643,plain,
! [SV145: $i,SV265: $i,SV819: $i,SV845: $i,SV800: $i] :
( ( ( in @ SV800 @ SV845 )
= $false )
| ( ( SV819 = SV845 )
= $false )
| ( ( in @ ( ordered_pair @ SV800 @ ( sK47_K @ SV845 @ SV819 @ SV800 @ SV265 @ SV145 ) ) @ SV265 )
= $false )
| ( ( in @ SV819 @ SV145 )
= $false )
| ( ( in @ SV800 @ ( sK44_C @ SV265 @ SV145 ) )
= $true )
| ( ( in @ ( sK49_SY705 @ SV265 @ SV145 ) @ ( sK52_SY712 @ SV265 @ SV145 ) )
= $true )
| ( ( empty @ SV145 )
= $true )
| ( ( relation @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5595]) ).
thf(5644,plain,
! [SV776: $i,SV172: $i,SV272: $i,SV717: $i,SV750: $i,SV827: $i,SV859: $i,SV820: $i] :
( ( ( ( SV820 != SV859 ) )
= $true )
| ( ( ~ ( in @ SV827 @ SV859 ) )
= $true )
| ( ( in @ ( sK34_R @ SV859 @ SV827 @ SV820 @ SV750 @ SV717 @ SV272 @ SV172 ) @ SV859 )
= $true )
| ( ( ( ordered_pair @ SV820 @ SV827 )
= SV750 )
= $false )
| ( ( in @ SV820 @ SV172 )
= $false )
| ( ( SV776 = SV750 )
= $false )
| ( ( in @ SV776 @ ( cartesian_product2 @ SV172 @ SV717 ) )
= $false )
| ( ( in @ SV750 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5596]) ).
thf(5645,plain,
! [SV776: $i,SV172: $i,SV272: $i,SV717: $i,SV750: $i,SV820: $i,SV859: $i,SV827: $i] :
( ( ( in @ ( ordered_pair @ SV827 @ ( sK34_R @ SV859 @ SV827 @ SV820 @ SV750 @ SV717 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( SV820 != SV859 )
| ~ ( in @ SV827 @ SV859 ) )
= $true )
| ( ( ( ordered_pair @ SV820 @ SV827 )
= SV750 )
= $false )
| ( ( in @ SV820 @ SV172 )
= $false )
| ( ( SV776 = SV750 )
= $false )
| ( ( in @ SV776 @ ( cartesian_product2 @ SV172 @ SV717 ) )
= $false )
| ( ( in @ SV750 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5597]) ).
thf(5646,plain,
! [SV832: $i,SV272: $i,SV770: $i,SV809: $i,SV867: $i,SV172: $i,SV860: $i] :
( ( ( in @ SV860 @ SV172 )
= $false )
| ( ( ( ordered_pair @ SV860 @ SV867 )
= SV809 )
= $false )
| ( ( ! [SY1749: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1749 @ SV867 @ SV860 @ SV809 @ SV770 @ SV272 @ SV172 ) @ SY1749 )
| ~ ~ ( in @ ( ordered_pair @ SV867 @ ( sK34_R @ SY1749 @ SV867 @ SV860 @ SV809 @ SV770 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV860 != SY1749 )
| ~ ( in @ SV867 @ SY1749 ) ) )
= $true )
| ( ( SV832 = SV809 )
= $false )
| ( ( in @ SV832 @ ( cartesian_product2 @ SV172 @ SV770 ) )
= $false )
| ( ( in @ SV809 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5598]) ).
thf(5647,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i,SV881: $i] :
( ( ( ~ ( in @ SV881 @ ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) @ SV881 ) @ SV272 ) )
= $true )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5601]) ).
thf(5648,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( ( ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5602]) ).
thf(5649,plain,
! [SV833: $i,SV272: $i,SV771: $i,SV811: $i,SV868: $i,SV172: $i,SV861: $i] :
( ( ( in @ SV861 @ SV172 )
= $false )
| ( ( ( ordered_pair @ SV861 @ SV868 )
= SV811 )
= $false )
| ( ( ! [SY1750: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1750 @ SV868 @ SV861 @ SV811 @ SV771 @ SV272 @ SV172 ) @ SY1750 )
| ~ ~ ( in @ ( ordered_pair @ SV868 @ ( sK34_R @ SY1750 @ SV868 @ SV861 @ SV811 @ SV771 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV861 != SY1750 )
| ~ ( in @ SV868 @ SY1750 ) ) )
= $true )
| ( ( SV833 = SV811 )
= $false )
| ( ( in @ SV833 @ ( cartesian_product2 @ SV172 @ SV771 ) )
= $false )
| ( ( in @ SV811 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5603]) ).
thf(5650,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i,SV882: $i] :
( ( ( ~ ( in @ SV882 @ ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) @ SV882 ) @ SV272 ) )
= $true )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5606]) ).
thf(5651,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( ( ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5607]) ).
thf(5652,plain,
! [SV772: $i,SV854: $i,SV272: $i,SV803: $i,SV172: $i,SV834: $i,SV878: $i,SV872: $i] :
( ( ( ( ( ordered_pair @ SV872 @ SV878 )
!= SV834 )
| ~ ( in @ SV872 @ SV172 ) )
= $true )
| ( ( ! [SY1757: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1757 @ SV878 @ SV872 @ SV834 @ SV803 @ SV272 @ SV172 ) @ SY1757 )
| ~ ~ ( in @ ( ordered_pair @ SV878 @ ( sK34_R @ SY1757 @ SV878 @ SV872 @ SV834 @ SV803 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV872 != SY1757 )
| ~ ( in @ SV878 @ SY1757 ) ) )
= $true )
| ( ( SV854 = SV834 )
= $false )
| ( ( in @ SV854 @ ( cartesian_product2 @ SV172 @ SV803 ) )
= $false )
| ( ( in @ SV834 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5608]) ).
thf(5653,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( ( ( ordered_pair @ ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) )
!= SV835 )
| ~ ( in @ ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 ) @ SV172 ) )
= $false )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5611]) ).
thf(5654,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( ~ ! [SY1725: $i] :
( ~ ( in @ SY1725 @ ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) @ SY1725 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5612]) ).
thf(5655,plain,
! [SV855: $i,SV272: $i,SV804: $i,SV172: $i,SV836: $i,SV879: $i,SV873: $i] :
( ( ( ( ( ordered_pair @ SV873 @ SV879 )
!= SV836 )
| ~ ( in @ SV873 @ SV172 ) )
= $true )
| ( ( ! [SY1758: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1758 @ SV879 @ SV873 @ SV836 @ SV804 @ SV272 @ SV172 ) @ SY1758 )
| ~ ~ ( in @ ( ordered_pair @ SV879 @ ( sK34_R @ SY1758 @ SV879 @ SV873 @ SV836 @ SV804 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV873 != SY1758 )
| ~ ( in @ SV879 @ SY1758 ) ) )
= $true )
| ( ( SV855 = SV836 )
= $false )
| ( ( in @ SV855 @ ( cartesian_product2 @ SV172 @ SV804 ) )
= $false )
| ( ( in @ SV836 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5613]) ).
thf(5656,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( ( ( ordered_pair @ ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) )
!= SV837 )
| ~ ( in @ ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 ) @ SV172 ) )
= $false )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5616]) ).
thf(5657,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( ~ ! [SY1730: $i] :
( ~ ( in @ SY1730 @ ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) @ SY1730 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5617]) ).
thf(5658,plain,
! [SV856: $i,SV272: $i,SV805: $i,SV172: $i,SV838: $i,SV880: $i,SV874: $i] :
( ( ( ( ( ordered_pair @ SV874 @ SV880 )
!= SV838 )
| ~ ( in @ SV874 @ SV172 ) )
= $true )
| ( ( ! [SY1759: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1759 @ SV880 @ SV874 @ SV838 @ SV805 @ SV272 @ SV172 ) @ SY1759 )
| ~ ~ ( in @ ( ordered_pair @ SV880 @ ( sK34_R @ SY1759 @ SV880 @ SV874 @ SV838 @ SV805 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV874 != SY1759 )
| ~ ( in @ SV880 @ SY1759 ) ) )
= $true )
| ( ( SV856 = SV838 )
= $false )
| ( ( in @ SV856 @ ( cartesian_product2 @ SV172 @ SV805 ) )
= $false )
| ( ( in @ SV838 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5618]) ).
thf(5659,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( ( ( ordered_pair @ ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) )
!= SV839 )
| ~ ( in @ ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 ) @ SV172 ) )
= $false )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5621]) ).
thf(5660,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( ~ ! [SY1735: $i] :
( ~ ( in @ SY1735 @ ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) @ SY1735 ) @ SV272 ) )
| ~ ~ ( ( ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5622]) ).
thf(5661,plain,
! [SV752: $i,SV172: $i,SV272: $i,SV692: $i,SV723: $i,SV792: $i,SV846: $i,SV806: $i] :
( ( ( in @ SV806 @ SV846 )
= $false )
| ( ( SV792 = SV846 )
= $false )
| ( ( in @ ( ordered_pair @ SV806 @ ( sK34_R @ SV846 @ SV806 @ SV792 @ SV723 @ SV692 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV792 @ SV806 )
= SV723 )
= $false )
| ( ( in @ SV792 @ SV172 )
= $false )
| ( ( SV752 = SV723 )
= $false )
| ( ( in @ SV752 @ ( cartesian_product2 @ SV172 @ SV692 ) )
= $false )
| ( ( in @ SV723 @ ( sK29_D @ SV692 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5624]) ).
thf(5662,plain,
! [SV777: $i,SV172: $i,SV272: $i,SV718: $i,SV753: $i,SV828: $i,SV862: $i,SV821: $i] :
( ( ( ( SV821 != SV862 ) )
= $true )
| ( ( ~ ( in @ SV828 @ SV862 ) )
= $true )
| ( ( in @ ( sK34_R @ SV862 @ SV828 @ SV821 @ SV753 @ SV718 @ SV272 @ SV172 ) @ SV862 )
= $true )
| ( ( ( ordered_pair @ SV821 @ SV828 )
= SV753 )
= $false )
| ( ( in @ SV821 @ SV172 )
= $false )
| ( ( SV777 = SV753 )
= $false )
| ( ( in @ SV777 @ ( cartesian_product2 @ SV172 @ SV718 ) )
= $false )
| ( ( in @ SV753 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5625]) ).
thf(5663,plain,
! [SV777: $i,SV172: $i,SV272: $i,SV718: $i,SV753: $i,SV821: $i,SV862: $i,SV828: $i] :
( ( ( in @ ( ordered_pair @ SV828 @ ( sK34_R @ SV862 @ SV828 @ SV821 @ SV753 @ SV718 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( SV821 != SV862 )
| ~ ( in @ SV828 @ SV862 ) )
= $true )
| ( ( ( ordered_pair @ SV821 @ SV828 )
= SV753 )
= $false )
| ( ( in @ SV821 @ SV172 )
= $false )
| ( ( SV777 = SV753 )
= $false )
| ( ( in @ SV777 @ ( cartesian_product2 @ SV172 @ SV718 ) )
= $false )
| ( ( in @ SV753 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5626]) ).
thf(5664,plain,
! [SV778: $i,SV172: $i,SV272: $i,SV719: $i,SV755: $i,SV829: $i,SV863: $i,SV822: $i] :
( ( ( ( SV822 != SV863 ) )
= $true )
| ( ( ~ ( in @ SV829 @ SV863 ) )
= $true )
| ( ( in @ ( sK34_R @ SV863 @ SV829 @ SV822 @ SV755 @ SV719 @ SV272 @ SV172 ) @ SV863 )
= $true )
| ( ( ( ordered_pair @ SV822 @ SV829 )
= SV755 )
= $false )
| ( ( in @ SV822 @ SV172 )
= $false )
| ( ( SV778 = SV755 )
= $false )
| ( ( in @ SV778 @ ( cartesian_product2 @ SV172 @ SV719 ) )
= $false )
| ( ( in @ SV755 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5627]) ).
thf(5665,plain,
! [SV778: $i,SV172: $i,SV272: $i,SV719: $i,SV755: $i,SV822: $i,SV863: $i,SV829: $i] :
( ( ( in @ ( ordered_pair @ SV829 @ ( sK34_R @ SV863 @ SV829 @ SV822 @ SV755 @ SV719 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( SV822 != SV863 )
| ~ ( in @ SV829 @ SV863 ) )
= $true )
| ( ( ( ordered_pair @ SV822 @ SV829 )
= SV755 )
= $false )
| ( ( in @ SV822 @ SV172 )
= $false )
| ( ( SV778 = SV755 )
= $false )
| ( ( in @ SV778 @ ( cartesian_product2 @ SV172 @ SV719 ) )
= $false )
| ( ( in @ SV755 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5628]) ).
thf(5666,plain,
! [SV720: $i,SV813: $i,SV172: $i,SV272: $i,SV743: $i,SV779: $i,SV847: $i,SV850: $i,SV875: $i] :
( ( ( ~ ( in @ ( sK34_R @ SV875 @ SV850 @ SV847 @ SV779 @ SV743 @ SV272 @ SV172 ) @ SV875 )
| ~ ~ ( in @ ( ordered_pair @ SV850 @ ( sK34_R @ SV875 @ SV850 @ SV847 @ SV779 @ SV743 @ SV272 @ SV172 ) ) @ SV272 ) )
= $false )
| ( ( ( SV847 != SV875 )
| ~ ( in @ SV850 @ SV875 ) )
= $true )
| ( ( ( ordered_pair @ SV847 @ SV850 )
= SV779 )
= $false )
| ( ( in @ SV847 @ SV172 )
= $false )
| ( ( SV813 = SV779 )
= $false )
| ( ( in @ SV813 @ ( cartesian_product2 @ SV172 @ SV743 ) )
= $false )
| ( ( in @ SV779 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5629]) ).
thf(5667,plain,
! [SV814: $i,SV172: $i,SV272: $i,SV744: $i,SV781: $i,SV848: $i,SV851: $i,SV876: $i] :
( ( ( ~ ( in @ ( sK34_R @ SV876 @ SV851 @ SV848 @ SV781 @ SV744 @ SV272 @ SV172 ) @ SV876 )
| ~ ~ ( in @ ( ordered_pair @ SV851 @ ( sK34_R @ SV876 @ SV851 @ SV848 @ SV781 @ SV744 @ SV272 @ SV172 ) ) @ SV272 ) )
= $false )
| ( ( ( SV848 != SV876 )
| ~ ( in @ SV851 @ SV876 ) )
= $true )
| ( ( ( ordered_pair @ SV848 @ SV851 )
= SV781 )
= $false )
| ( ( in @ SV848 @ SV172 )
= $false )
| ( ( SV814 = SV781 )
= $false )
| ( ( in @ SV814 @ ( cartesian_product2 @ SV172 @ SV744 ) )
= $false )
| ( ( in @ SV781 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5633]) ).
thf(5668,plain,
! [SV815: $i,SV172: $i,SV272: $i,SV745: $i,SV783: $i,SV849: $i,SV852: $i,SV877: $i] :
( ( ( ~ ( in @ ( sK34_R @ SV877 @ SV852 @ SV849 @ SV783 @ SV745 @ SV272 @ SV172 ) @ SV877 )
| ~ ~ ( in @ ( ordered_pair @ SV852 @ ( sK34_R @ SV877 @ SV852 @ SV849 @ SV783 @ SV745 @ SV272 @ SV172 ) ) @ SV272 ) )
= $false )
| ( ( ( SV849 != SV877 )
| ~ ( in @ SV852 @ SV877 ) )
= $true )
| ( ( ( ordered_pair @ SV849 @ SV852 )
= SV783 )
= $false )
| ( ( in @ SV849 @ SV172 )
= $false )
| ( ( SV815 = SV783 )
= $false )
| ( ( in @ SV815 @ ( cartesian_product2 @ SV172 @ SV745 ) )
= $false )
| ( ( in @ SV783 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5637]) ).
thf(5669,plain,
! [SV776: $i,SV172: $i,SV272: $i,SV717: $i,SV750: $i,SV827: $i,SV859: $i,SV820: $i] :
( ( ( SV820 = SV859 )
= $false )
| ( ( ~ ( in @ SV827 @ SV859 ) )
= $true )
| ( ( in @ ( sK34_R @ SV859 @ SV827 @ SV820 @ SV750 @ SV717 @ SV272 @ SV172 ) @ SV859 )
= $true )
| ( ( ( ordered_pair @ SV820 @ SV827 )
= SV750 )
= $false )
| ( ( in @ SV820 @ SV172 )
= $false )
| ( ( SV776 = SV750 )
= $false )
| ( ( in @ SV776 @ ( cartesian_product2 @ SV172 @ SV717 ) )
= $false )
| ( ( in @ SV750 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5644]) ).
thf(5670,plain,
! [SV776: $i,SV172: $i,SV272: $i,SV717: $i,SV750: $i,SV827: $i,SV859: $i,SV820: $i] :
( ( ( ( SV820 != SV859 ) )
= $true )
| ( ( ~ ( in @ SV827 @ SV859 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV827 @ ( sK34_R @ SV859 @ SV827 @ SV820 @ SV750 @ SV717 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV820 @ SV827 )
= SV750 )
= $false )
| ( ( in @ SV820 @ SV172 )
= $false )
| ( ( SV776 = SV750 )
= $false )
| ( ( in @ SV776 @ ( cartesian_product2 @ SV172 @ SV717 ) )
= $false )
| ( ( in @ SV750 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5645]) ).
thf(5671,plain,
! [SV832: $i,SV172: $i,SV272: $i,SV770: $i,SV809: $i,SV860: $i,SV867: $i,SV883: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_R @ SV883 @ SV867 @ SV860 @ SV809 @ SV770 @ SV272 @ SV172 ) @ SV883 )
| ~ ~ ( in @ ( ordered_pair @ SV867 @ ( sK34_R @ SV883 @ SV867 @ SV860 @ SV809 @ SV770 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV860 != SV883 )
| ~ ( in @ SV867 @ SV883 ) )
= $true )
| ( ( ( ordered_pair @ SV860 @ SV867 )
= SV809 )
= $false )
| ( ( in @ SV860 @ SV172 )
= $false )
| ( ( SV832 = SV809 )
= $false )
| ( ( in @ SV832 @ ( cartesian_product2 @ SV172 @ SV770 ) )
= $false )
| ( ( in @ SV809 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5646]) ).
thf(5672,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i,SV881: $i] :
( ( ( ~ ( in @ SV881 @ ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) @ SV881 ) @ SV272 )
= $true )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5647]) ).
thf(5673,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( ( ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5648]) ).
thf(5674,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( ~ ( in @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5648]) ).
thf(5675,plain,
! [SV833: $i,SV172: $i,SV272: $i,SV771: $i,SV811: $i,SV861: $i,SV868: $i,SV884: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_R @ SV884 @ SV868 @ SV861 @ SV811 @ SV771 @ SV272 @ SV172 ) @ SV884 )
| ~ ~ ( in @ ( ordered_pair @ SV868 @ ( sK34_R @ SV884 @ SV868 @ SV861 @ SV811 @ SV771 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV861 != SV884 )
| ~ ( in @ SV868 @ SV884 ) )
= $true )
| ( ( ( ordered_pair @ SV861 @ SV868 )
= SV811 )
= $false )
| ( ( in @ SV861 @ SV172 )
= $false )
| ( ( SV833 = SV811 )
= $false )
| ( ( in @ SV833 @ ( cartesian_product2 @ SV172 @ SV771 ) )
= $false )
| ( ( in @ SV811 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5649]) ).
thf(5676,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i,SV882: $i] :
( ( ( ~ ( in @ SV882 @ ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) @ SV882 ) @ SV272 )
= $true )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5650]) ).
thf(5677,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( ( ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5651]) ).
thf(5678,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( ~ ( in @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5651]) ).
thf(5679,plain,
! [SV772: $i,SV854: $i,SV272: $i,SV803: $i,SV172: $i,SV834: $i,SV878: $i,SV872: $i] :
( ( ( ( ( ordered_pair @ SV872 @ SV878 )
!= SV834 ) )
= $true )
| ( ( ~ ( in @ SV872 @ SV172 ) )
= $true )
| ( ( ! [SY1757: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1757 @ SV878 @ SV872 @ SV834 @ SV803 @ SV272 @ SV172 ) @ SY1757 )
| ~ ~ ( in @ ( ordered_pair @ SV878 @ ( sK34_R @ SY1757 @ SV878 @ SV872 @ SV834 @ SV803 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV872 != SY1757 )
| ~ ( in @ SV878 @ SY1757 ) ) )
= $true )
| ( ( SV854 = SV834 )
= $false )
| ( ( in @ SV854 @ ( cartesian_product2 @ SV172 @ SV803 ) )
= $false )
| ( ( in @ SV834 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5652]) ).
thf(5680,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( ( ( ordered_pair @ ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) )
!= SV835 ) )
= $false )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5653]) ).
thf(5681,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( ~ ( in @ ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 ) @ SV172 ) )
= $false )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5653]) ).
thf(5682,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( ~ ! [SY1725: $i] :
( ~ ( in @ SY1725 @ ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) @ SY1725 ) @ SV272 ) ) )
= $false )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5654]) ).
thf(5683,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( ~ ~ ( ( ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5654]) ).
thf(5684,plain,
! [SV855: $i,SV272: $i,SV804: $i,SV172: $i,SV836: $i,SV879: $i,SV873: $i] :
( ( ( ( ( ordered_pair @ SV873 @ SV879 )
!= SV836 ) )
= $true )
| ( ( ~ ( in @ SV873 @ SV172 ) )
= $true )
| ( ( ! [SY1758: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1758 @ SV879 @ SV873 @ SV836 @ SV804 @ SV272 @ SV172 ) @ SY1758 )
| ~ ~ ( in @ ( ordered_pair @ SV879 @ ( sK34_R @ SY1758 @ SV879 @ SV873 @ SV836 @ SV804 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV873 != SY1758 )
| ~ ( in @ SV879 @ SY1758 ) ) )
= $true )
| ( ( SV855 = SV836 )
= $false )
| ( ( in @ SV855 @ ( cartesian_product2 @ SV172 @ SV804 ) )
= $false )
| ( ( in @ SV836 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5655]) ).
thf(5685,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( ( ( ordered_pair @ ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) )
!= SV837 ) )
= $false )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5656]) ).
thf(5686,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( ~ ( in @ ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 ) @ SV172 ) )
= $false )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5656]) ).
thf(5687,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( ~ ! [SY1730: $i] :
( ~ ( in @ SY1730 @ ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) @ SY1730 ) @ SV272 ) ) )
= $false )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5657]) ).
thf(5688,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( ~ ~ ( ( ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5657]) ).
thf(5689,plain,
! [SV856: $i,SV272: $i,SV805: $i,SV172: $i,SV838: $i,SV880: $i,SV874: $i] :
( ( ( ( ( ordered_pair @ SV874 @ SV880 )
!= SV838 ) )
= $true )
| ( ( ~ ( in @ SV874 @ SV172 ) )
= $true )
| ( ( ! [SY1759: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1759 @ SV880 @ SV874 @ SV838 @ SV805 @ SV272 @ SV172 ) @ SY1759 )
| ~ ~ ( in @ ( ordered_pair @ SV880 @ ( sK34_R @ SY1759 @ SV880 @ SV874 @ SV838 @ SV805 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV874 != SY1759 )
| ~ ( in @ SV880 @ SY1759 ) ) )
= $true )
| ( ( SV856 = SV838 )
= $false )
| ( ( in @ SV856 @ ( cartesian_product2 @ SV172 @ SV805 ) )
= $false )
| ( ( in @ SV838 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5658]) ).
thf(5690,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( ( ( ordered_pair @ ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) )
!= SV839 ) )
= $false )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5659]) ).
thf(5691,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( ~ ( in @ ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 ) @ SV172 ) )
= $false )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5659]) ).
thf(5692,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( ~ ! [SY1735: $i] :
( ~ ( in @ SY1735 @ ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) @ SY1735 ) @ SV272 ) ) )
= $false )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5660]) ).
thf(5693,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( ~ ~ ( ( ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) ) ) )
= $false )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5660]) ).
thf(5694,plain,
! [SV777: $i,SV172: $i,SV272: $i,SV718: $i,SV753: $i,SV828: $i,SV862: $i,SV821: $i] :
( ( ( SV821 = SV862 )
= $false )
| ( ( ~ ( in @ SV828 @ SV862 ) )
= $true )
| ( ( in @ ( sK34_R @ SV862 @ SV828 @ SV821 @ SV753 @ SV718 @ SV272 @ SV172 ) @ SV862 )
= $true )
| ( ( ( ordered_pair @ SV821 @ SV828 )
= SV753 )
= $false )
| ( ( in @ SV821 @ SV172 )
= $false )
| ( ( SV777 = SV753 )
= $false )
| ( ( in @ SV777 @ ( cartesian_product2 @ SV172 @ SV718 ) )
= $false )
| ( ( in @ SV753 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5662]) ).
thf(5695,plain,
! [SV777: $i,SV172: $i,SV272: $i,SV718: $i,SV753: $i,SV828: $i,SV862: $i,SV821: $i] :
( ( ( ( SV821 != SV862 ) )
= $true )
| ( ( ~ ( in @ SV828 @ SV862 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV828 @ ( sK34_R @ SV862 @ SV828 @ SV821 @ SV753 @ SV718 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV821 @ SV828 )
= SV753 )
= $false )
| ( ( in @ SV821 @ SV172 )
= $false )
| ( ( SV777 = SV753 )
= $false )
| ( ( in @ SV777 @ ( cartesian_product2 @ SV172 @ SV718 ) )
= $false )
| ( ( in @ SV753 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5663]) ).
thf(5696,plain,
! [SV778: $i,SV172: $i,SV272: $i,SV719: $i,SV755: $i,SV829: $i,SV863: $i,SV822: $i] :
( ( ( SV822 = SV863 )
= $false )
| ( ( ~ ( in @ SV829 @ SV863 ) )
= $true )
| ( ( in @ ( sK34_R @ SV863 @ SV829 @ SV822 @ SV755 @ SV719 @ SV272 @ SV172 ) @ SV863 )
= $true )
| ( ( ( ordered_pair @ SV822 @ SV829 )
= SV755 )
= $false )
| ( ( in @ SV822 @ SV172 )
= $false )
| ( ( SV778 = SV755 )
= $false )
| ( ( in @ SV778 @ ( cartesian_product2 @ SV172 @ SV719 ) )
= $false )
| ( ( in @ SV755 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5664]) ).
thf(5697,plain,
! [SV778: $i,SV172: $i,SV272: $i,SV719: $i,SV755: $i,SV829: $i,SV863: $i,SV822: $i] :
( ( ( ( SV822 != SV863 ) )
= $true )
| ( ( ~ ( in @ SV829 @ SV863 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV829 @ ( sK34_R @ SV863 @ SV829 @ SV822 @ SV755 @ SV719 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV822 @ SV829 )
= SV755 )
= $false )
| ( ( in @ SV822 @ SV172 )
= $false )
| ( ( SV778 = SV755 )
= $false )
| ( ( in @ SV778 @ ( cartesian_product2 @ SV172 @ SV719 ) )
= $false )
| ( ( in @ SV755 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5665]) ).
thf(5698,plain,
! [SV720: $i,SV813: $i,SV172: $i,SV272: $i,SV743: $i,SV779: $i,SV847: $i,SV850: $i,SV875: $i] :
( ( ( ~ ( in @ ( sK34_R @ SV875 @ SV850 @ SV847 @ SV779 @ SV743 @ SV272 @ SV172 ) @ SV875 ) )
= $false )
| ( ( ( SV847 != SV875 )
| ~ ( in @ SV850 @ SV875 ) )
= $true )
| ( ( ( ordered_pair @ SV847 @ SV850 )
= SV779 )
= $false )
| ( ( in @ SV847 @ SV172 )
= $false )
| ( ( SV813 = SV779 )
= $false )
| ( ( in @ SV813 @ ( cartesian_product2 @ SV172 @ SV743 ) )
= $false )
| ( ( in @ SV779 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5666]) ).
thf(5699,plain,
! [SV720: $i,SV813: $i,SV172: $i,SV272: $i,SV743: $i,SV779: $i,SV847: $i,SV875: $i,SV850: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV850 @ ( sK34_R @ SV875 @ SV850 @ SV847 @ SV779 @ SV743 @ SV272 @ SV172 ) ) @ SV272 ) )
= $false )
| ( ( ( SV847 != SV875 )
| ~ ( in @ SV850 @ SV875 ) )
= $true )
| ( ( ( ordered_pair @ SV847 @ SV850 )
= SV779 )
= $false )
| ( ( in @ SV847 @ SV172 )
= $false )
| ( ( SV813 = SV779 )
= $false )
| ( ( in @ SV813 @ ( cartesian_product2 @ SV172 @ SV743 ) )
= $false )
| ( ( in @ SV779 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5666]) ).
thf(5700,plain,
! [SV814: $i,SV172: $i,SV272: $i,SV744: $i,SV781: $i,SV848: $i,SV851: $i,SV876: $i] :
( ( ( ~ ( in @ ( sK34_R @ SV876 @ SV851 @ SV848 @ SV781 @ SV744 @ SV272 @ SV172 ) @ SV876 ) )
= $false )
| ( ( ( SV848 != SV876 )
| ~ ( in @ SV851 @ SV876 ) )
= $true )
| ( ( ( ordered_pair @ SV848 @ SV851 )
= SV781 )
= $false )
| ( ( in @ SV848 @ SV172 )
= $false )
| ( ( SV814 = SV781 )
= $false )
| ( ( in @ SV814 @ ( cartesian_product2 @ SV172 @ SV744 ) )
= $false )
| ( ( in @ SV781 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5667]) ).
thf(5701,plain,
! [SV814: $i,SV172: $i,SV272: $i,SV744: $i,SV781: $i,SV848: $i,SV876: $i,SV851: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV851 @ ( sK34_R @ SV876 @ SV851 @ SV848 @ SV781 @ SV744 @ SV272 @ SV172 ) ) @ SV272 ) )
= $false )
| ( ( ( SV848 != SV876 )
| ~ ( in @ SV851 @ SV876 ) )
= $true )
| ( ( ( ordered_pair @ SV848 @ SV851 )
= SV781 )
= $false )
| ( ( in @ SV848 @ SV172 )
= $false )
| ( ( SV814 = SV781 )
= $false )
| ( ( in @ SV814 @ ( cartesian_product2 @ SV172 @ SV744 ) )
= $false )
| ( ( in @ SV781 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5667]) ).
thf(5702,plain,
! [SV815: $i,SV172: $i,SV272: $i,SV745: $i,SV783: $i,SV849: $i,SV852: $i,SV877: $i] :
( ( ( ~ ( in @ ( sK34_R @ SV877 @ SV852 @ SV849 @ SV783 @ SV745 @ SV272 @ SV172 ) @ SV877 ) )
= $false )
| ( ( ( SV849 != SV877 )
| ~ ( in @ SV852 @ SV877 ) )
= $true )
| ( ( ( ordered_pair @ SV849 @ SV852 )
= SV783 )
= $false )
| ( ( in @ SV849 @ SV172 )
= $false )
| ( ( SV815 = SV783 )
= $false )
| ( ( in @ SV815 @ ( cartesian_product2 @ SV172 @ SV745 ) )
= $false )
| ( ( in @ SV783 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5668]) ).
thf(5703,plain,
! [SV815: $i,SV172: $i,SV272: $i,SV745: $i,SV783: $i,SV849: $i,SV877: $i,SV852: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV852 @ ( sK34_R @ SV877 @ SV852 @ SV849 @ SV783 @ SV745 @ SV272 @ SV172 ) ) @ SV272 ) )
= $false )
| ( ( ( SV849 != SV877 )
| ~ ( in @ SV852 @ SV877 ) )
= $true )
| ( ( ( ordered_pair @ SV849 @ SV852 )
= SV783 )
= $false )
| ( ( in @ SV849 @ SV172 )
= $false )
| ( ( SV815 = SV783 )
= $false )
| ( ( in @ SV815 @ ( cartesian_product2 @ SV172 @ SV745 ) )
= $false )
| ( ( in @ SV783 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5668]) ).
thf(5704,plain,
! [SV776: $i,SV172: $i,SV272: $i,SV717: $i,SV750: $i,SV820: $i,SV859: $i,SV827: $i] :
( ( ( in @ SV827 @ SV859 )
= $false )
| ( ( SV820 = SV859 )
= $false )
| ( ( in @ ( sK34_R @ SV859 @ SV827 @ SV820 @ SV750 @ SV717 @ SV272 @ SV172 ) @ SV859 )
= $true )
| ( ( ( ordered_pair @ SV820 @ SV827 )
= SV750 )
= $false )
| ( ( in @ SV820 @ SV172 )
= $false )
| ( ( SV776 = SV750 )
= $false )
| ( ( in @ SV776 @ ( cartesian_product2 @ SV172 @ SV717 ) )
= $false )
| ( ( in @ SV750 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5669]) ).
thf(5705,plain,
! [SV776: $i,SV172: $i,SV272: $i,SV717: $i,SV750: $i,SV827: $i,SV859: $i,SV820: $i] :
( ( ( SV820 = SV859 )
= $false )
| ( ( ~ ( in @ SV827 @ SV859 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV827 @ ( sK34_R @ SV859 @ SV827 @ SV820 @ SV750 @ SV717 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV820 @ SV827 )
= SV750 )
= $false )
| ( ( in @ SV820 @ SV172 )
= $false )
| ( ( SV776 = SV750 )
= $false )
| ( ( in @ SV776 @ ( cartesian_product2 @ SV172 @ SV717 ) )
= $false )
| ( ( in @ SV750 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5670]) ).
thf(5706,plain,
! [SV832: $i,SV172: $i,SV272: $i,SV770: $i,SV809: $i,SV860: $i,SV867: $i,SV883: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_R @ SV883 @ SV867 @ SV860 @ SV809 @ SV770 @ SV272 @ SV172 ) @ SV883 )
| ~ ~ ( in @ ( ordered_pair @ SV867 @ ( sK34_R @ SV883 @ SV867 @ SV860 @ SV809 @ SV770 @ SV272 @ SV172 ) ) @ SV272 ) ) )
= $true )
| ( ( ( SV860 != SV883 )
| ~ ( in @ SV867 @ SV883 ) )
= $true )
| ( ( ( ordered_pair @ SV860 @ SV867 )
= SV809 )
= $false )
| ( ( in @ SV860 @ SV172 )
= $false )
| ( ( SV832 = SV809 )
= $false )
| ( ( in @ SV832 @ ( cartesian_product2 @ SV172 @ SV770 ) )
= $false )
| ( ( in @ SV809 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5671]) ).
thf(5707,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i,SV881: $i] :
( ( ( in @ SV881 @ ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) @ SV881 ) @ SV272 )
= $true )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5672]) ).
thf(5708,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( ( sK30_O @ SV810 @ SV770 @ SV272 @ SV172 )
= ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5673]) ).
thf(5709,plain,
! [SV172: $i,SV272: $i,SV770: $i,SV810: $i] :
( ( ( in @ ( sK31_SY649 @ SV810 @ SV770 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV810 @ SV770 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ SV810 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $false )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5674]) ).
thf(5710,plain,
! [SV833: $i,SV172: $i,SV272: $i,SV771: $i,SV811: $i,SV861: $i,SV868: $i,SV884: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_R @ SV884 @ SV868 @ SV861 @ SV811 @ SV771 @ SV272 @ SV172 ) @ SV884 )
| ~ ~ ( in @ ( ordered_pair @ SV868 @ ( sK34_R @ SV884 @ SV868 @ SV861 @ SV811 @ SV771 @ SV272 @ SV172 ) ) @ SV272 ) ) )
= $true )
| ( ( ( SV861 != SV884 )
| ~ ( in @ SV868 @ SV884 ) )
= $true )
| ( ( ( ordered_pair @ SV861 @ SV868 )
= SV811 )
= $false )
| ( ( in @ SV861 @ SV172 )
= $false )
| ( ( SV833 = SV811 )
= $false )
| ( ( in @ SV833 @ ( cartesian_product2 @ SV172 @ SV771 ) )
= $false )
| ( ( in @ SV811 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5675]) ).
thf(5711,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i,SV882: $i] :
( ( ( in @ SV882 @ ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) @ SV882 ) @ SV272 )
= $true )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5676]) ).
thf(5712,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( ( sK30_O @ SV812 @ SV771 @ SV272 @ SV172 )
= ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5677]) ).
thf(5713,plain,
! [SV172: $i,SV272: $i,SV771: $i,SV812: $i] :
( ( ( in @ ( sK31_SY649 @ SV812 @ SV771 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV812 @ SV771 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ SV812 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5678]) ).
thf(5714,plain,
! [SV772: $i,SV854: $i,SV272: $i,SV803: $i,SV172: $i,SV834: $i,SV878: $i,SV872: $i] :
( ( ( ( ordered_pair @ SV872 @ SV878 )
= SV834 )
= $false )
| ( ( ~ ( in @ SV872 @ SV172 ) )
= $true )
| ( ( ! [SY1757: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1757 @ SV878 @ SV872 @ SV834 @ SV803 @ SV272 @ SV172 ) @ SY1757 )
| ~ ~ ( in @ ( ordered_pair @ SV878 @ ( sK34_R @ SY1757 @ SV878 @ SV872 @ SV834 @ SV803 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV872 != SY1757 )
| ~ ( in @ SV878 @ SY1757 ) ) )
= $true )
| ( ( SV854 = SV834 )
= $false )
| ( ( in @ SV854 @ ( cartesian_product2 @ SV172 @ SV803 ) )
= $false )
| ( ( in @ SV834 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5679]) ).
thf(5715,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( ( ordered_pair @ ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) )
= SV835 )
= $true )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5680]) ).
thf(5716,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( in @ ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5681]) ).
thf(5717,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( ! [SY1725: $i] :
( ~ ( in @ SY1725 @ ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) @ SY1725 ) @ SV272 ) ) )
= $true )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5682]) ).
thf(5718,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( ~ ( ( ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) ) ) )
= $true )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5683]) ).
thf(5719,plain,
! [SV855: $i,SV272: $i,SV804: $i,SV172: $i,SV836: $i,SV879: $i,SV873: $i] :
( ( ( ( ordered_pair @ SV873 @ SV879 )
= SV836 )
= $false )
| ( ( ~ ( in @ SV873 @ SV172 ) )
= $true )
| ( ( ! [SY1758: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1758 @ SV879 @ SV873 @ SV836 @ SV804 @ SV272 @ SV172 ) @ SY1758 )
| ~ ~ ( in @ ( ordered_pair @ SV879 @ ( sK34_R @ SY1758 @ SV879 @ SV873 @ SV836 @ SV804 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV873 != SY1758 )
| ~ ( in @ SV879 @ SY1758 ) ) )
= $true )
| ( ( SV855 = SV836 )
= $false )
| ( ( in @ SV855 @ ( cartesian_product2 @ SV172 @ SV804 ) )
= $false )
| ( ( in @ SV836 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5684]) ).
thf(5720,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( ( ordered_pair @ ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) )
= SV837 )
= $true )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5685]) ).
thf(5721,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( in @ ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5686]) ).
thf(5722,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( ! [SY1730: $i] :
( ~ ( in @ SY1730 @ ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) @ SY1730 ) @ SV272 ) ) )
= $true )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5687]) ).
thf(5723,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( ~ ( ( ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) ) ) )
= $true )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5688]) ).
thf(5724,plain,
! [SV856: $i,SV272: $i,SV805: $i,SV172: $i,SV838: $i,SV880: $i,SV874: $i] :
( ( ( ( ordered_pair @ SV874 @ SV880 )
= SV838 )
= $false )
| ( ( ~ ( in @ SV874 @ SV172 ) )
= $true )
| ( ( ! [SY1759: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1759 @ SV880 @ SV874 @ SV838 @ SV805 @ SV272 @ SV172 ) @ SY1759 )
| ~ ~ ( in @ ( ordered_pair @ SV880 @ ( sK34_R @ SY1759 @ SV880 @ SV874 @ SV838 @ SV805 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV874 != SY1759 )
| ~ ( in @ SV880 @ SY1759 ) ) )
= $true )
| ( ( SV856 = SV838 )
= $false )
| ( ( in @ SV856 @ ( cartesian_product2 @ SV172 @ SV805 ) )
= $false )
| ( ( in @ SV838 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5689]) ).
thf(5725,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( ( ordered_pair @ ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) )
= SV839 )
= $true )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5690]) ).
thf(5726,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( in @ ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5691]) ).
thf(5727,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( ! [SY1735: $i] :
( ~ ( in @ SY1735 @ ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) @ SY1735 ) @ SV272 ) ) )
= $true )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5692]) ).
thf(5728,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( ~ ( ( ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) ) ) )
= $true )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5693]) ).
thf(5729,plain,
! [SV777: $i,SV172: $i,SV272: $i,SV718: $i,SV753: $i,SV821: $i,SV862: $i,SV828: $i] :
( ( ( in @ SV828 @ SV862 )
= $false )
| ( ( SV821 = SV862 )
= $false )
| ( ( in @ ( sK34_R @ SV862 @ SV828 @ SV821 @ SV753 @ SV718 @ SV272 @ SV172 ) @ SV862 )
= $true )
| ( ( ( ordered_pair @ SV821 @ SV828 )
= SV753 )
= $false )
| ( ( in @ SV821 @ SV172 )
= $false )
| ( ( SV777 = SV753 )
= $false )
| ( ( in @ SV777 @ ( cartesian_product2 @ SV172 @ SV718 ) )
= $false )
| ( ( in @ SV753 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5694]) ).
thf(5730,plain,
! [SV777: $i,SV172: $i,SV272: $i,SV718: $i,SV753: $i,SV828: $i,SV862: $i,SV821: $i] :
( ( ( SV821 = SV862 )
= $false )
| ( ( ~ ( in @ SV828 @ SV862 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV828 @ ( sK34_R @ SV862 @ SV828 @ SV821 @ SV753 @ SV718 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV821 @ SV828 )
= SV753 )
= $false )
| ( ( in @ SV821 @ SV172 )
= $false )
| ( ( SV777 = SV753 )
= $false )
| ( ( in @ SV777 @ ( cartesian_product2 @ SV172 @ SV718 ) )
= $false )
| ( ( in @ SV753 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5695]) ).
thf(5731,plain,
! [SV778: $i,SV172: $i,SV272: $i,SV719: $i,SV755: $i,SV822: $i,SV863: $i,SV829: $i] :
( ( ( in @ SV829 @ SV863 )
= $false )
| ( ( SV822 = SV863 )
= $false )
| ( ( in @ ( sK34_R @ SV863 @ SV829 @ SV822 @ SV755 @ SV719 @ SV272 @ SV172 ) @ SV863 )
= $true )
| ( ( ( ordered_pair @ SV822 @ SV829 )
= SV755 )
= $false )
| ( ( in @ SV822 @ SV172 )
= $false )
| ( ( SV778 = SV755 )
= $false )
| ( ( in @ SV778 @ ( cartesian_product2 @ SV172 @ SV719 ) )
= $false )
| ( ( in @ SV755 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5696]) ).
thf(5732,plain,
! [SV778: $i,SV172: $i,SV272: $i,SV719: $i,SV755: $i,SV829: $i,SV863: $i,SV822: $i] :
( ( ( SV822 = SV863 )
= $false )
| ( ( ~ ( in @ SV829 @ SV863 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV829 @ ( sK34_R @ SV863 @ SV829 @ SV822 @ SV755 @ SV719 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV822 @ SV829 )
= SV755 )
= $false )
| ( ( in @ SV822 @ SV172 )
= $false )
| ( ( SV778 = SV755 )
= $false )
| ( ( in @ SV778 @ ( cartesian_product2 @ SV172 @ SV719 ) )
= $false )
| ( ( in @ SV755 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5697]) ).
thf(5733,plain,
! [SV720: $i,SV813: $i,SV172: $i,SV272: $i,SV743: $i,SV779: $i,SV847: $i,SV850: $i,SV875: $i] :
( ( ( in @ ( sK34_R @ SV875 @ SV850 @ SV847 @ SV779 @ SV743 @ SV272 @ SV172 ) @ SV875 )
= $true )
| ( ( ( SV847 != SV875 )
| ~ ( in @ SV850 @ SV875 ) )
= $true )
| ( ( ( ordered_pair @ SV847 @ SV850 )
= SV779 )
= $false )
| ( ( in @ SV847 @ SV172 )
= $false )
| ( ( SV813 = SV779 )
= $false )
| ( ( in @ SV813 @ ( cartesian_product2 @ SV172 @ SV743 ) )
= $false )
| ( ( in @ SV779 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5698]) ).
thf(5734,plain,
! [SV720: $i,SV813: $i,SV172: $i,SV272: $i,SV743: $i,SV779: $i,SV847: $i,SV875: $i,SV850: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV850 @ ( sK34_R @ SV875 @ SV850 @ SV847 @ SV779 @ SV743 @ SV272 @ SV172 ) ) @ SV272 ) )
= $true )
| ( ( ( SV847 != SV875 )
| ~ ( in @ SV850 @ SV875 ) )
= $true )
| ( ( ( ordered_pair @ SV847 @ SV850 )
= SV779 )
= $false )
| ( ( in @ SV847 @ SV172 )
= $false )
| ( ( SV813 = SV779 )
= $false )
| ( ( in @ SV813 @ ( cartesian_product2 @ SV172 @ SV743 ) )
= $false )
| ( ( in @ SV779 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5699]) ).
thf(5735,plain,
! [SV814: $i,SV172: $i,SV272: $i,SV744: $i,SV781: $i,SV848: $i,SV851: $i,SV876: $i] :
( ( ( in @ ( sK34_R @ SV876 @ SV851 @ SV848 @ SV781 @ SV744 @ SV272 @ SV172 ) @ SV876 )
= $true )
| ( ( ( SV848 != SV876 )
| ~ ( in @ SV851 @ SV876 ) )
= $true )
| ( ( ( ordered_pair @ SV848 @ SV851 )
= SV781 )
= $false )
| ( ( in @ SV848 @ SV172 )
= $false )
| ( ( SV814 = SV781 )
= $false )
| ( ( in @ SV814 @ ( cartesian_product2 @ SV172 @ SV744 ) )
= $false )
| ( ( in @ SV781 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5700]) ).
thf(5736,plain,
! [SV814: $i,SV172: $i,SV272: $i,SV744: $i,SV781: $i,SV848: $i,SV876: $i,SV851: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV851 @ ( sK34_R @ SV876 @ SV851 @ SV848 @ SV781 @ SV744 @ SV272 @ SV172 ) ) @ SV272 ) )
= $true )
| ( ( ( SV848 != SV876 )
| ~ ( in @ SV851 @ SV876 ) )
= $true )
| ( ( ( ordered_pair @ SV848 @ SV851 )
= SV781 )
= $false )
| ( ( in @ SV848 @ SV172 )
= $false )
| ( ( SV814 = SV781 )
= $false )
| ( ( in @ SV814 @ ( cartesian_product2 @ SV172 @ SV744 ) )
= $false )
| ( ( in @ SV781 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5701]) ).
thf(5737,plain,
! [SV815: $i,SV172: $i,SV272: $i,SV745: $i,SV783: $i,SV849: $i,SV852: $i,SV877: $i] :
( ( ( in @ ( sK34_R @ SV877 @ SV852 @ SV849 @ SV783 @ SV745 @ SV272 @ SV172 ) @ SV877 )
= $true )
| ( ( ( SV849 != SV877 )
| ~ ( in @ SV852 @ SV877 ) )
= $true )
| ( ( ( ordered_pair @ SV849 @ SV852 )
= SV783 )
= $false )
| ( ( in @ SV849 @ SV172 )
= $false )
| ( ( SV815 = SV783 )
= $false )
| ( ( in @ SV815 @ ( cartesian_product2 @ SV172 @ SV745 ) )
= $false )
| ( ( in @ SV783 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5702]) ).
thf(5738,plain,
! [SV815: $i,SV172: $i,SV272: $i,SV745: $i,SV783: $i,SV849: $i,SV877: $i,SV852: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV852 @ ( sK34_R @ SV877 @ SV852 @ SV849 @ SV783 @ SV745 @ SV272 @ SV172 ) ) @ SV272 ) )
= $true )
| ( ( ( SV849 != SV877 )
| ~ ( in @ SV852 @ SV877 ) )
= $true )
| ( ( ( ordered_pair @ SV849 @ SV852 )
= SV783 )
= $false )
| ( ( in @ SV849 @ SV172 )
= $false )
| ( ( SV815 = SV783 )
= $false )
| ( ( in @ SV815 @ ( cartesian_product2 @ SV172 @ SV745 ) )
= $false )
| ( ( in @ SV783 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5703]) ).
thf(5739,plain,
! [SV776: $i,SV172: $i,SV272: $i,SV717: $i,SV750: $i,SV820: $i,SV859: $i,SV827: $i] :
( ( ( in @ SV827 @ SV859 )
= $false )
| ( ( SV820 = SV859 )
= $false )
| ( ( in @ ( ordered_pair @ SV827 @ ( sK34_R @ SV859 @ SV827 @ SV820 @ SV750 @ SV717 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV820 @ SV827 )
= SV750 )
= $false )
| ( ( in @ SV820 @ SV172 )
= $false )
| ( ( SV776 = SV750 )
= $false )
| ( ( in @ SV776 @ ( cartesian_product2 @ SV172 @ SV717 ) )
= $false )
| ( ( in @ SV750 @ ( sK29_D @ SV717 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK35_D @ SV272 @ SV172 )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5705]) ).
thf(5740,plain,
! [SV832: $i,SV172: $i,SV272: $i,SV770: $i,SV809: $i,SV860: $i,SV867: $i,SV883: $i] :
( ( ( ~ ( in @ ( sK34_R @ SV883 @ SV867 @ SV860 @ SV809 @ SV770 @ SV272 @ SV172 ) @ SV883 )
| ~ ~ ( in @ ( ordered_pair @ SV867 @ ( sK34_R @ SV883 @ SV867 @ SV860 @ SV809 @ SV770 @ SV272 @ SV172 ) ) @ SV272 ) )
= $false )
| ( ( ( SV860 != SV883 )
| ~ ( in @ SV867 @ SV883 ) )
= $true )
| ( ( ( ordered_pair @ SV860 @ SV867 )
= SV809 )
= $false )
| ( ( in @ SV860 @ SV172 )
= $false )
| ( ( SV832 = SV809 )
= $false )
| ( ( in @ SV832 @ ( cartesian_product2 @ SV172 @ SV770 ) )
= $false )
| ( ( in @ SV809 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5706]) ).
thf(5741,plain,
! [SV833: $i,SV172: $i,SV272: $i,SV771: $i,SV811: $i,SV861: $i,SV868: $i,SV884: $i] :
( ( ( ~ ( in @ ( sK34_R @ SV884 @ SV868 @ SV861 @ SV811 @ SV771 @ SV272 @ SV172 ) @ SV884 )
| ~ ~ ( in @ ( ordered_pair @ SV868 @ ( sK34_R @ SV884 @ SV868 @ SV861 @ SV811 @ SV771 @ SV272 @ SV172 ) ) @ SV272 ) )
= $false )
| ( ( ( SV861 != SV884 )
| ~ ( in @ SV868 @ SV884 ) )
= $true )
| ( ( ( ordered_pair @ SV861 @ SV868 )
= SV811 )
= $false )
| ( ( in @ SV861 @ SV172 )
= $false )
| ( ( SV833 = SV811 )
= $false )
| ( ( in @ SV833 @ ( cartesian_product2 @ SV172 @ SV771 ) )
= $false )
| ( ( in @ SV811 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5710]) ).
thf(5742,plain,
! [SV772: $i,SV854: $i,SV272: $i,SV803: $i,SV834: $i,SV878: $i,SV172: $i,SV872: $i] :
( ( ( in @ SV872 @ SV172 )
= $false )
| ( ( ( ordered_pair @ SV872 @ SV878 )
= SV834 )
= $false )
| ( ( ! [SY1757: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1757 @ SV878 @ SV872 @ SV834 @ SV803 @ SV272 @ SV172 ) @ SY1757 )
| ~ ~ ( in @ ( ordered_pair @ SV878 @ ( sK34_R @ SY1757 @ SV878 @ SV872 @ SV834 @ SV803 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV872 != SY1757 )
| ~ ( in @ SV878 @ SY1757 ) ) )
= $true )
| ( ( SV854 = SV834 )
= $false )
| ( ( in @ SV854 @ ( cartesian_product2 @ SV172 @ SV803 ) )
= $false )
| ( ( in @ SV834 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5714]) ).
thf(5743,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i,SV885: $i] :
( ( ( ~ ( in @ SV885 @ ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) @ SV885 ) @ SV272 ) )
= $true )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5717]) ).
thf(5744,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( ( ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5718]) ).
thf(5745,plain,
! [SV855: $i,SV272: $i,SV804: $i,SV836: $i,SV879: $i,SV172: $i,SV873: $i] :
( ( ( in @ SV873 @ SV172 )
= $false )
| ( ( ( ordered_pair @ SV873 @ SV879 )
= SV836 )
= $false )
| ( ( ! [SY1758: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1758 @ SV879 @ SV873 @ SV836 @ SV804 @ SV272 @ SV172 ) @ SY1758 )
| ~ ~ ( in @ ( ordered_pair @ SV879 @ ( sK34_R @ SY1758 @ SV879 @ SV873 @ SV836 @ SV804 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV873 != SY1758 )
| ~ ( in @ SV879 @ SY1758 ) ) )
= $true )
| ( ( SV855 = SV836 )
= $false )
| ( ( in @ SV855 @ ( cartesian_product2 @ SV172 @ SV804 ) )
= $false )
| ( ( in @ SV836 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5719]) ).
thf(5746,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i,SV886: $i] :
( ( ( ~ ( in @ SV886 @ ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) @ SV886 ) @ SV272 ) )
= $true )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5722]) ).
thf(5747,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( ( ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5723]) ).
thf(5748,plain,
! [SV856: $i,SV272: $i,SV805: $i,SV838: $i,SV880: $i,SV172: $i,SV874: $i] :
( ( ( in @ SV874 @ SV172 )
= $false )
| ( ( ( ordered_pair @ SV874 @ SV880 )
= SV838 )
= $false )
| ( ( ! [SY1759: $i] :
( ~ ( ~ ( in @ ( sK34_R @ SY1759 @ SV880 @ SV874 @ SV838 @ SV805 @ SV272 @ SV172 ) @ SY1759 )
| ~ ~ ( in @ ( ordered_pair @ SV880 @ ( sK34_R @ SY1759 @ SV880 @ SV874 @ SV838 @ SV805 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV874 != SY1759 )
| ~ ( in @ SV880 @ SY1759 ) ) )
= $true )
| ( ( SV856 = SV838 )
= $false )
| ( ( in @ SV856 @ ( cartesian_product2 @ SV172 @ SV805 ) )
= $false )
| ( ( in @ SV838 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5724]) ).
thf(5749,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i,SV887: $i] :
( ( ( ~ ( in @ SV887 @ ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) )
| ( in @ ( ordered_pair @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) @ SV887 ) @ SV272 ) )
= $true )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5727]) ).
thf(5750,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( ( ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) )
| ~ ( in @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5728]) ).
thf(5751,plain,
! [SV777: $i,SV172: $i,SV272: $i,SV718: $i,SV753: $i,SV821: $i,SV862: $i,SV828: $i] :
( ( ( in @ SV828 @ SV862 )
= $false )
| ( ( SV821 = SV862 )
= $false )
| ( ( in @ ( ordered_pair @ SV828 @ ( sK34_R @ SV862 @ SV828 @ SV821 @ SV753 @ SV718 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV821 @ SV828 )
= SV753 )
= $false )
| ( ( in @ SV821 @ SV172 )
= $false )
| ( ( SV777 = SV753 )
= $false )
| ( ( in @ SV777 @ ( cartesian_product2 @ SV172 @ SV718 ) )
= $false )
| ( ( in @ SV753 @ ( sK29_D @ SV718 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK38_SY678 @ SV272 @ SV172 ) @ ( sK39_SY682 @ SV272 @ SV172 ) )
= ( sK37_SY665 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5730]) ).
thf(5752,plain,
! [SV778: $i,SV172: $i,SV272: $i,SV719: $i,SV755: $i,SV822: $i,SV863: $i,SV829: $i] :
( ( ( in @ SV829 @ SV863 )
= $false )
| ( ( SV822 = SV863 )
= $false )
| ( ( in @ ( ordered_pair @ SV829 @ ( sK34_R @ SV863 @ SV829 @ SV822 @ SV755 @ SV719 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV822 @ SV829 )
= SV755 )
= $false )
| ( ( in @ SV822 @ SV172 )
= $false )
| ( ( SV778 = SV755 )
= $false )
| ( ( in @ SV778 @ ( cartesian_product2 @ SV172 @ SV719 ) )
= $false )
| ( ( in @ SV755 @ ( sK29_D @ SV719 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK38_SY678 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5732]) ).
thf(5753,plain,
! [SV720: $i,SV813: $i,SV172: $i,SV272: $i,SV743: $i,SV779: $i,SV850: $i,SV875: $i,SV847: $i] :
( ( ( ( SV847 != SV875 ) )
= $true )
| ( ( ~ ( in @ SV850 @ SV875 ) )
= $true )
| ( ( in @ ( sK34_R @ SV875 @ SV850 @ SV847 @ SV779 @ SV743 @ SV272 @ SV172 ) @ SV875 )
= $true )
| ( ( ( ordered_pair @ SV847 @ SV850 )
= SV779 )
= $false )
| ( ( in @ SV847 @ SV172 )
= $false )
| ( ( SV813 = SV779 )
= $false )
| ( ( in @ SV813 @ ( cartesian_product2 @ SV172 @ SV743 ) )
= $false )
| ( ( in @ SV779 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5733]) ).
thf(5754,plain,
! [SV720: $i,SV813: $i,SV172: $i,SV272: $i,SV743: $i,SV779: $i,SV847: $i,SV875: $i,SV850: $i] :
( ( ( in @ ( ordered_pair @ SV850 @ ( sK34_R @ SV875 @ SV850 @ SV847 @ SV779 @ SV743 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( SV847 != SV875 )
| ~ ( in @ SV850 @ SV875 ) )
= $true )
| ( ( ( ordered_pair @ SV847 @ SV850 )
= SV779 )
= $false )
| ( ( in @ SV847 @ SV172 )
= $false )
| ( ( SV813 = SV779 )
= $false )
| ( ( in @ SV813 @ ( cartesian_product2 @ SV172 @ SV743 ) )
= $false )
| ( ( in @ SV779 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5734]) ).
thf(5755,plain,
! [SV814: $i,SV172: $i,SV272: $i,SV744: $i,SV781: $i,SV851: $i,SV876: $i,SV848: $i] :
( ( ( ( SV848 != SV876 ) )
= $true )
| ( ( ~ ( in @ SV851 @ SV876 ) )
= $true )
| ( ( in @ ( sK34_R @ SV876 @ SV851 @ SV848 @ SV781 @ SV744 @ SV272 @ SV172 ) @ SV876 )
= $true )
| ( ( ( ordered_pair @ SV848 @ SV851 )
= SV781 )
= $false )
| ( ( in @ SV848 @ SV172 )
= $false )
| ( ( SV814 = SV781 )
= $false )
| ( ( in @ SV814 @ ( cartesian_product2 @ SV172 @ SV744 ) )
= $false )
| ( ( in @ SV781 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5735]) ).
thf(5756,plain,
! [SV814: $i,SV172: $i,SV272: $i,SV744: $i,SV781: $i,SV848: $i,SV876: $i,SV851: $i] :
( ( ( in @ ( ordered_pair @ SV851 @ ( sK34_R @ SV876 @ SV851 @ SV848 @ SV781 @ SV744 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( SV848 != SV876 )
| ~ ( in @ SV851 @ SV876 ) )
= $true )
| ( ( ( ordered_pair @ SV848 @ SV851 )
= SV781 )
= $false )
| ( ( in @ SV848 @ SV172 )
= $false )
| ( ( SV814 = SV781 )
= $false )
| ( ( in @ SV814 @ ( cartesian_product2 @ SV172 @ SV744 ) )
= $false )
| ( ( in @ SV781 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5736]) ).
thf(5757,plain,
! [SV815: $i,SV172: $i,SV272: $i,SV745: $i,SV783: $i,SV852: $i,SV877: $i,SV849: $i] :
( ( ( ( SV849 != SV877 ) )
= $true )
| ( ( ~ ( in @ SV852 @ SV877 ) )
= $true )
| ( ( in @ ( sK34_R @ SV877 @ SV852 @ SV849 @ SV783 @ SV745 @ SV272 @ SV172 ) @ SV877 )
= $true )
| ( ( ( ordered_pair @ SV849 @ SV852 )
= SV783 )
= $false )
| ( ( in @ SV849 @ SV172 )
= $false )
| ( ( SV815 = SV783 )
= $false )
| ( ( in @ SV815 @ ( cartesian_product2 @ SV172 @ SV745 ) )
= $false )
| ( ( in @ SV783 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5737]) ).
thf(5758,plain,
! [SV815: $i,SV172: $i,SV272: $i,SV745: $i,SV783: $i,SV849: $i,SV877: $i,SV852: $i] :
( ( ( in @ ( ordered_pair @ SV852 @ ( sK34_R @ SV877 @ SV852 @ SV849 @ SV783 @ SV745 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( SV849 != SV877 )
| ~ ( in @ SV852 @ SV877 ) )
= $true )
| ( ( ( ordered_pair @ SV849 @ SV852 )
= SV783 )
= $false )
| ( ( in @ SV849 @ SV172 )
= $false )
| ( ( SV815 = SV783 )
= $false )
| ( ( in @ SV815 @ ( cartesian_product2 @ SV172 @ SV745 ) )
= $false )
| ( ( in @ SV783 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5738]) ).
thf(5759,plain,
! [SV832: $i,SV172: $i,SV272: $i,SV770: $i,SV809: $i,SV860: $i,SV867: $i,SV883: $i] :
( ( ( ~ ( in @ ( sK34_R @ SV883 @ SV867 @ SV860 @ SV809 @ SV770 @ SV272 @ SV172 ) @ SV883 ) )
= $false )
| ( ( ( SV860 != SV883 )
| ~ ( in @ SV867 @ SV883 ) )
= $true )
| ( ( ( ordered_pair @ SV860 @ SV867 )
= SV809 )
= $false )
| ( ( in @ SV860 @ SV172 )
= $false )
| ( ( SV832 = SV809 )
= $false )
| ( ( in @ SV832 @ ( cartesian_product2 @ SV172 @ SV770 ) )
= $false )
| ( ( in @ SV809 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5740]) ).
thf(5760,plain,
! [SV832: $i,SV172: $i,SV272: $i,SV770: $i,SV809: $i,SV860: $i,SV883: $i,SV867: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV867 @ ( sK34_R @ SV883 @ SV867 @ SV860 @ SV809 @ SV770 @ SV272 @ SV172 ) ) @ SV272 ) )
= $false )
| ( ( ( SV860 != SV883 )
| ~ ( in @ SV867 @ SV883 ) )
= $true )
| ( ( ( ordered_pair @ SV860 @ SV867 )
= SV809 )
= $false )
| ( ( in @ SV860 @ SV172 )
= $false )
| ( ( SV832 = SV809 )
= $false )
| ( ( in @ SV832 @ ( cartesian_product2 @ SV172 @ SV770 ) )
= $false )
| ( ( in @ SV809 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5740]) ).
thf(5761,plain,
! [SV833: $i,SV172: $i,SV272: $i,SV771: $i,SV811: $i,SV861: $i,SV868: $i,SV884: $i] :
( ( ( ~ ( in @ ( sK34_R @ SV884 @ SV868 @ SV861 @ SV811 @ SV771 @ SV272 @ SV172 ) @ SV884 ) )
= $false )
| ( ( ( SV861 != SV884 )
| ~ ( in @ SV868 @ SV884 ) )
= $true )
| ( ( ( ordered_pair @ SV861 @ SV868 )
= SV811 )
= $false )
| ( ( in @ SV861 @ SV172 )
= $false )
| ( ( SV833 = SV811 )
= $false )
| ( ( in @ SV833 @ ( cartesian_product2 @ SV172 @ SV771 ) )
= $false )
| ( ( in @ SV811 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5741]) ).
thf(5762,plain,
! [SV833: $i,SV172: $i,SV272: $i,SV771: $i,SV811: $i,SV861: $i,SV884: $i,SV868: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV868 @ ( sK34_R @ SV884 @ SV868 @ SV861 @ SV811 @ SV771 @ SV272 @ SV172 ) ) @ SV272 ) )
= $false )
| ( ( ( SV861 != SV884 )
| ~ ( in @ SV868 @ SV884 ) )
= $true )
| ( ( ( ordered_pair @ SV861 @ SV868 )
= SV811 )
= $false )
| ( ( in @ SV861 @ SV172 )
= $false )
| ( ( SV833 = SV811 )
= $false )
| ( ( in @ SV833 @ ( cartesian_product2 @ SV172 @ SV771 ) )
= $false )
| ( ( in @ SV811 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5741]) ).
thf(5763,plain,
! [SV772: $i,SV854: $i,SV172: $i,SV272: $i,SV803: $i,SV834: $i,SV872: $i,SV878: $i,SV888: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_R @ SV888 @ SV878 @ SV872 @ SV834 @ SV803 @ SV272 @ SV172 ) @ SV888 )
| ~ ~ ( in @ ( ordered_pair @ SV878 @ ( sK34_R @ SV888 @ SV878 @ SV872 @ SV834 @ SV803 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV872 != SV888 )
| ~ ( in @ SV878 @ SV888 ) )
= $true )
| ( ( ( ordered_pair @ SV872 @ SV878 )
= SV834 )
= $false )
| ( ( in @ SV872 @ SV172 )
= $false )
| ( ( SV854 = SV834 )
= $false )
| ( ( in @ SV854 @ ( cartesian_product2 @ SV172 @ SV803 ) )
= $false )
| ( ( in @ SV834 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5742]) ).
thf(5764,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i,SV885: $i] :
( ( ( ~ ( in @ SV885 @ ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) @ SV885 ) @ SV272 )
= $true )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5743]) ).
thf(5765,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( ( ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5744]) ).
thf(5766,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( ~ ( in @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5744]) ).
thf(5767,plain,
! [SV855: $i,SV172: $i,SV272: $i,SV804: $i,SV836: $i,SV873: $i,SV879: $i,SV889: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_R @ SV889 @ SV879 @ SV873 @ SV836 @ SV804 @ SV272 @ SV172 ) @ SV889 )
| ~ ~ ( in @ ( ordered_pair @ SV879 @ ( sK34_R @ SV889 @ SV879 @ SV873 @ SV836 @ SV804 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV873 != SV889 )
| ~ ( in @ SV879 @ SV889 ) )
= $true )
| ( ( ( ordered_pair @ SV873 @ SV879 )
= SV836 )
= $false )
| ( ( in @ SV873 @ SV172 )
= $false )
| ( ( SV855 = SV836 )
= $false )
| ( ( in @ SV855 @ ( cartesian_product2 @ SV172 @ SV804 ) )
= $false )
| ( ( in @ SV836 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5745]) ).
thf(5768,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i,SV886: $i] :
( ( ( ~ ( in @ SV886 @ ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) @ SV886 ) @ SV272 )
= $true )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5746]) ).
thf(5769,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( ( ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5747]) ).
thf(5770,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( ~ ( in @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5747]) ).
thf(5771,plain,
! [SV856: $i,SV172: $i,SV272: $i,SV805: $i,SV838: $i,SV874: $i,SV880: $i,SV890: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_R @ SV890 @ SV880 @ SV874 @ SV838 @ SV805 @ SV272 @ SV172 ) @ SV890 )
| ~ ~ ( in @ ( ordered_pair @ SV880 @ ( sK34_R @ SV890 @ SV880 @ SV874 @ SV838 @ SV805 @ SV272 @ SV172 ) ) @ SV272 ) )
| ( SV874 != SV890 )
| ~ ( in @ SV880 @ SV890 ) )
= $true )
| ( ( ( ordered_pair @ SV874 @ SV880 )
= SV838 )
= $false )
| ( ( in @ SV874 @ SV172 )
= $false )
| ( ( SV856 = SV838 )
= $false )
| ( ( in @ SV856 @ ( cartesian_product2 @ SV172 @ SV805 ) )
= $false )
| ( ( in @ SV838 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5748]) ).
thf(5772,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i,SV887: $i] :
( ( ( ~ ( in @ SV887 @ ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) @ SV887 ) @ SV272 )
= $true )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5749]) ).
thf(5773,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( ( ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 )
!= ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5750]) ).
thf(5774,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( ~ ( in @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) ) )
= $false )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5750]) ).
thf(5775,plain,
! [SV720: $i,SV813: $i,SV172: $i,SV272: $i,SV743: $i,SV779: $i,SV850: $i,SV875: $i,SV847: $i] :
( ( ( SV847 = SV875 )
= $false )
| ( ( ~ ( in @ SV850 @ SV875 ) )
= $true )
| ( ( in @ ( sK34_R @ SV875 @ SV850 @ SV847 @ SV779 @ SV743 @ SV272 @ SV172 ) @ SV875 )
= $true )
| ( ( ( ordered_pair @ SV847 @ SV850 )
= SV779 )
= $false )
| ( ( in @ SV847 @ SV172 )
= $false )
| ( ( SV813 = SV779 )
= $false )
| ( ( in @ SV813 @ ( cartesian_product2 @ SV172 @ SV743 ) )
= $false )
| ( ( in @ SV779 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5753]) ).
thf(5776,plain,
! [SV720: $i,SV813: $i,SV172: $i,SV272: $i,SV743: $i,SV779: $i,SV850: $i,SV875: $i,SV847: $i] :
( ( ( ( SV847 != SV875 ) )
= $true )
| ( ( ~ ( in @ SV850 @ SV875 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV850 @ ( sK34_R @ SV875 @ SV850 @ SV847 @ SV779 @ SV743 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV847 @ SV850 )
= SV779 )
= $false )
| ( ( in @ SV847 @ SV172 )
= $false )
| ( ( SV813 = SV779 )
= $false )
| ( ( in @ SV813 @ ( cartesian_product2 @ SV172 @ SV743 ) )
= $false )
| ( ( in @ SV779 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5754]) ).
thf(5777,plain,
! [SV814: $i,SV172: $i,SV272: $i,SV744: $i,SV781: $i,SV851: $i,SV876: $i,SV848: $i] :
( ( ( SV848 = SV876 )
= $false )
| ( ( ~ ( in @ SV851 @ SV876 ) )
= $true )
| ( ( in @ ( sK34_R @ SV876 @ SV851 @ SV848 @ SV781 @ SV744 @ SV272 @ SV172 ) @ SV876 )
= $true )
| ( ( ( ordered_pair @ SV848 @ SV851 )
= SV781 )
= $false )
| ( ( in @ SV848 @ SV172 )
= $false )
| ( ( SV814 = SV781 )
= $false )
| ( ( in @ SV814 @ ( cartesian_product2 @ SV172 @ SV744 ) )
= $false )
| ( ( in @ SV781 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5755]) ).
thf(5778,plain,
! [SV814: $i,SV172: $i,SV272: $i,SV744: $i,SV781: $i,SV851: $i,SV876: $i,SV848: $i] :
( ( ( ( SV848 != SV876 ) )
= $true )
| ( ( ~ ( in @ SV851 @ SV876 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV851 @ ( sK34_R @ SV876 @ SV851 @ SV848 @ SV781 @ SV744 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV848 @ SV851 )
= SV781 )
= $false )
| ( ( in @ SV848 @ SV172 )
= $false )
| ( ( SV814 = SV781 )
= $false )
| ( ( in @ SV814 @ ( cartesian_product2 @ SV172 @ SV744 ) )
= $false )
| ( ( in @ SV781 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5756]) ).
thf(5779,plain,
! [SV815: $i,SV172: $i,SV272: $i,SV745: $i,SV783: $i,SV852: $i,SV877: $i,SV849: $i] :
( ( ( SV849 = SV877 )
= $false )
| ( ( ~ ( in @ SV852 @ SV877 ) )
= $true )
| ( ( in @ ( sK34_R @ SV877 @ SV852 @ SV849 @ SV783 @ SV745 @ SV272 @ SV172 ) @ SV877 )
= $true )
| ( ( ( ordered_pair @ SV849 @ SV852 )
= SV783 )
= $false )
| ( ( in @ SV849 @ SV172 )
= $false )
| ( ( SV815 = SV783 )
= $false )
| ( ( in @ SV815 @ ( cartesian_product2 @ SV172 @ SV745 ) )
= $false )
| ( ( in @ SV783 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5757]) ).
thf(5780,plain,
! [SV815: $i,SV172: $i,SV272: $i,SV745: $i,SV783: $i,SV852: $i,SV877: $i,SV849: $i] :
( ( ( ( SV849 != SV877 ) )
= $true )
| ( ( ~ ( in @ SV852 @ SV877 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV852 @ ( sK34_R @ SV877 @ SV852 @ SV849 @ SV783 @ SV745 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV849 @ SV852 )
= SV783 )
= $false )
| ( ( in @ SV849 @ SV172 )
= $false )
| ( ( SV815 = SV783 )
= $false )
| ( ( in @ SV815 @ ( cartesian_product2 @ SV172 @ SV745 ) )
= $false )
| ( ( in @ SV783 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5758]) ).
thf(5781,plain,
! [SV832: $i,SV172: $i,SV272: $i,SV770: $i,SV809: $i,SV860: $i,SV867: $i,SV883: $i] :
( ( ( in @ ( sK34_R @ SV883 @ SV867 @ SV860 @ SV809 @ SV770 @ SV272 @ SV172 ) @ SV883 )
= $true )
| ( ( ( SV860 != SV883 )
| ~ ( in @ SV867 @ SV883 ) )
= $true )
| ( ( ( ordered_pair @ SV860 @ SV867 )
= SV809 )
= $false )
| ( ( in @ SV860 @ SV172 )
= $false )
| ( ( SV832 = SV809 )
= $false )
| ( ( in @ SV832 @ ( cartesian_product2 @ SV172 @ SV770 ) )
= $false )
| ( ( in @ SV809 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5759]) ).
thf(5782,plain,
! [SV832: $i,SV172: $i,SV272: $i,SV770: $i,SV809: $i,SV860: $i,SV883: $i,SV867: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV867 @ ( sK34_R @ SV883 @ SV867 @ SV860 @ SV809 @ SV770 @ SV272 @ SV172 ) ) @ SV272 ) )
= $true )
| ( ( ( SV860 != SV883 )
| ~ ( in @ SV867 @ SV883 ) )
= $true )
| ( ( ( ordered_pair @ SV860 @ SV867 )
= SV809 )
= $false )
| ( ( in @ SV860 @ SV172 )
= $false )
| ( ( SV832 = SV809 )
= $false )
| ( ( in @ SV832 @ ( cartesian_product2 @ SV172 @ SV770 ) )
= $false )
| ( ( in @ SV809 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5760]) ).
thf(5783,plain,
! [SV833: $i,SV172: $i,SV272: $i,SV771: $i,SV811: $i,SV861: $i,SV868: $i,SV884: $i] :
( ( ( in @ ( sK34_R @ SV884 @ SV868 @ SV861 @ SV811 @ SV771 @ SV272 @ SV172 ) @ SV884 )
= $true )
| ( ( ( SV861 != SV884 )
| ~ ( in @ SV868 @ SV884 ) )
= $true )
| ( ( ( ordered_pair @ SV861 @ SV868 )
= SV811 )
= $false )
| ( ( in @ SV861 @ SV172 )
= $false )
| ( ( SV833 = SV811 )
= $false )
| ( ( in @ SV833 @ ( cartesian_product2 @ SV172 @ SV771 ) )
= $false )
| ( ( in @ SV811 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5761]) ).
thf(5784,plain,
! [SV833: $i,SV172: $i,SV272: $i,SV771: $i,SV811: $i,SV861: $i,SV884: $i,SV868: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV868 @ ( sK34_R @ SV884 @ SV868 @ SV861 @ SV811 @ SV771 @ SV272 @ SV172 ) ) @ SV272 ) )
= $true )
| ( ( ( SV861 != SV884 )
| ~ ( in @ SV868 @ SV884 ) )
= $true )
| ( ( ( ordered_pair @ SV861 @ SV868 )
= SV811 )
= $false )
| ( ( in @ SV861 @ SV172 )
= $false )
| ( ( SV833 = SV811 )
= $false )
| ( ( in @ SV833 @ ( cartesian_product2 @ SV172 @ SV771 ) )
= $false )
| ( ( in @ SV811 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5762]) ).
thf(5785,plain,
! [SV772: $i,SV854: $i,SV172: $i,SV272: $i,SV803: $i,SV834: $i,SV872: $i,SV878: $i,SV888: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_R @ SV888 @ SV878 @ SV872 @ SV834 @ SV803 @ SV272 @ SV172 ) @ SV888 )
| ~ ~ ( in @ ( ordered_pair @ SV878 @ ( sK34_R @ SV888 @ SV878 @ SV872 @ SV834 @ SV803 @ SV272 @ SV172 ) ) @ SV272 ) ) )
= $true )
| ( ( ( SV872 != SV888 )
| ~ ( in @ SV878 @ SV888 ) )
= $true )
| ( ( ( ordered_pair @ SV872 @ SV878 )
= SV834 )
= $false )
| ( ( in @ SV872 @ SV172 )
= $false )
| ( ( SV854 = SV834 )
= $false )
| ( ( in @ SV854 @ ( cartesian_product2 @ SV172 @ SV803 ) )
= $false )
| ( ( in @ SV834 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5763]) ).
thf(5786,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i,SV885: $i] :
( ( ( in @ SV885 @ ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) @ SV885 ) @ SV272 )
= $true )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5764]) ).
thf(5787,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( ( sK30_O @ SV835 @ SV803 @ SV272 @ SV172 )
= ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5765]) ).
thf(5788,plain,
! [SV772: $i,SV172: $i,SV272: $i,SV803: $i,SV835: $i] :
( ( ( in @ ( sK31_SY649 @ SV835 @ SV803 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV835 @ SV803 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ SV835 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5766]) ).
thf(5789,plain,
! [SV855: $i,SV172: $i,SV272: $i,SV804: $i,SV836: $i,SV873: $i,SV879: $i,SV889: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_R @ SV889 @ SV879 @ SV873 @ SV836 @ SV804 @ SV272 @ SV172 ) @ SV889 )
| ~ ~ ( in @ ( ordered_pair @ SV879 @ ( sK34_R @ SV889 @ SV879 @ SV873 @ SV836 @ SV804 @ SV272 @ SV172 ) ) @ SV272 ) ) )
= $true )
| ( ( ( SV873 != SV889 )
| ~ ( in @ SV879 @ SV889 ) )
= $true )
| ( ( ( ordered_pair @ SV873 @ SV879 )
= SV836 )
= $false )
| ( ( in @ SV873 @ SV172 )
= $false )
| ( ( SV855 = SV836 )
= $false )
| ( ( in @ SV855 @ ( cartesian_product2 @ SV172 @ SV804 ) )
= $false )
| ( ( in @ SV836 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5767]) ).
thf(5790,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i,SV886: $i] :
( ( ( in @ SV886 @ ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) @ SV886 ) @ SV272 )
= $true )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5768]) ).
thf(5791,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( ( sK30_O @ SV837 @ SV804 @ SV272 @ SV172 )
= ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5769]) ).
thf(5792,plain,
! [SV172: $i,SV272: $i,SV804: $i,SV837: $i] :
( ( ( in @ ( sK31_SY649 @ SV837 @ SV804 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV837 @ SV804 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ SV837 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $false )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5770]) ).
thf(5793,plain,
! [SV856: $i,SV172: $i,SV272: $i,SV805: $i,SV838: $i,SV874: $i,SV880: $i,SV890: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_R @ SV890 @ SV880 @ SV874 @ SV838 @ SV805 @ SV272 @ SV172 ) @ SV890 )
| ~ ~ ( in @ ( ordered_pair @ SV880 @ ( sK34_R @ SV890 @ SV880 @ SV874 @ SV838 @ SV805 @ SV272 @ SV172 ) ) @ SV272 ) ) )
= $true )
| ( ( ( SV874 != SV890 )
| ~ ( in @ SV880 @ SV890 ) )
= $true )
| ( ( ( ordered_pair @ SV874 @ SV880 )
= SV838 )
= $false )
| ( ( in @ SV874 @ SV172 )
= $false )
| ( ( SV856 = SV838 )
= $false )
| ( ( in @ SV856 @ ( cartesian_product2 @ SV172 @ SV805 ) )
= $false )
| ( ( in @ SV838 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5771]) ).
thf(5794,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i,SV887: $i] :
( ( ( in @ SV887 @ ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) @ SV887 ) @ SV272 )
= $true )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5772]) ).
thf(5795,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( ( sK30_O @ SV839 @ SV805 @ SV272 @ SV172 )
= ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5773]) ).
thf(5796,plain,
! [SV172: $i,SV272: $i,SV805: $i,SV839: $i] :
( ( ( in @ ( sK31_SY649 @ SV839 @ SV805 @ SV272 @ SV172 ) @ ( sK32_SY652 @ SV839 @ SV805 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ SV839 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $false )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5774]) ).
thf(5797,plain,
! [SV720: $i,SV813: $i,SV172: $i,SV272: $i,SV743: $i,SV779: $i,SV847: $i,SV875: $i,SV850: $i] :
( ( ( in @ SV850 @ SV875 )
= $false )
| ( ( SV847 = SV875 )
= $false )
| ( ( in @ ( sK34_R @ SV875 @ SV850 @ SV847 @ SV779 @ SV743 @ SV272 @ SV172 ) @ SV875 )
= $true )
| ( ( ( ordered_pair @ SV847 @ SV850 )
= SV779 )
= $false )
| ( ( in @ SV847 @ SV172 )
= $false )
| ( ( SV813 = SV779 )
= $false )
| ( ( in @ SV813 @ ( cartesian_product2 @ SV172 @ SV743 ) )
= $false )
| ( ( in @ SV779 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5775]) ).
thf(5798,plain,
! [SV720: $i,SV813: $i,SV172: $i,SV272: $i,SV743: $i,SV779: $i,SV850: $i,SV875: $i,SV847: $i] :
( ( ( SV847 = SV875 )
= $false )
| ( ( ~ ( in @ SV850 @ SV875 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV850 @ ( sK34_R @ SV875 @ SV850 @ SV847 @ SV779 @ SV743 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV847 @ SV850 )
= SV779 )
= $false )
| ( ( in @ SV847 @ SV172 )
= $false )
| ( ( SV813 = SV779 )
= $false )
| ( ( in @ SV813 @ ( cartesian_product2 @ SV172 @ SV743 ) )
= $false )
| ( ( in @ SV779 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5776]) ).
thf(5799,plain,
! [SV814: $i,SV172: $i,SV272: $i,SV744: $i,SV781: $i,SV848: $i,SV876: $i,SV851: $i] :
( ( ( in @ SV851 @ SV876 )
= $false )
| ( ( SV848 = SV876 )
= $false )
| ( ( in @ ( sK34_R @ SV876 @ SV851 @ SV848 @ SV781 @ SV744 @ SV272 @ SV172 ) @ SV876 )
= $true )
| ( ( ( ordered_pair @ SV848 @ SV851 )
= SV781 )
= $false )
| ( ( in @ SV848 @ SV172 )
= $false )
| ( ( SV814 = SV781 )
= $false )
| ( ( in @ SV814 @ ( cartesian_product2 @ SV172 @ SV744 ) )
= $false )
| ( ( in @ SV781 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5777]) ).
thf(5800,plain,
! [SV814: $i,SV172: $i,SV272: $i,SV744: $i,SV781: $i,SV851: $i,SV876: $i,SV848: $i] :
( ( ( SV848 = SV876 )
= $false )
| ( ( ~ ( in @ SV851 @ SV876 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV851 @ ( sK34_R @ SV876 @ SV851 @ SV848 @ SV781 @ SV744 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV848 @ SV851 )
= SV781 )
= $false )
| ( ( in @ SV848 @ SV172 )
= $false )
| ( ( SV814 = SV781 )
= $false )
| ( ( in @ SV814 @ ( cartesian_product2 @ SV172 @ SV744 ) )
= $false )
| ( ( in @ SV781 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5778]) ).
thf(5801,plain,
! [SV815: $i,SV172: $i,SV272: $i,SV745: $i,SV783: $i,SV849: $i,SV877: $i,SV852: $i] :
( ( ( in @ SV852 @ SV877 )
= $false )
| ( ( SV849 = SV877 )
= $false )
| ( ( in @ ( sK34_R @ SV877 @ SV852 @ SV849 @ SV783 @ SV745 @ SV272 @ SV172 ) @ SV877 )
= $true )
| ( ( ( ordered_pair @ SV849 @ SV852 )
= SV783 )
= $false )
| ( ( in @ SV849 @ SV172 )
= $false )
| ( ( SV815 = SV783 )
= $false )
| ( ( in @ SV815 @ ( cartesian_product2 @ SV172 @ SV745 ) )
= $false )
| ( ( in @ SV783 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5779]) ).
thf(5802,plain,
! [SV815: $i,SV172: $i,SV272: $i,SV745: $i,SV783: $i,SV852: $i,SV877: $i,SV849: $i] :
( ( ( SV849 = SV877 )
= $false )
| ( ( ~ ( in @ SV852 @ SV877 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV852 @ ( sK34_R @ SV877 @ SV852 @ SV849 @ SV783 @ SV745 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV849 @ SV852 )
= SV783 )
= $false )
| ( ( in @ SV849 @ SV172 )
= $false )
| ( ( SV815 = SV783 )
= $false )
| ( ( in @ SV815 @ ( cartesian_product2 @ SV172 @ SV745 ) )
= $false )
| ( ( in @ SV783 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5780]) ).
thf(5803,plain,
! [SV832: $i,SV172: $i,SV272: $i,SV770: $i,SV809: $i,SV867: $i,SV883: $i,SV860: $i] :
( ( ( ( SV860 != SV883 ) )
= $true )
| ( ( ~ ( in @ SV867 @ SV883 ) )
= $true )
| ( ( in @ ( sK34_R @ SV883 @ SV867 @ SV860 @ SV809 @ SV770 @ SV272 @ SV172 ) @ SV883 )
= $true )
| ( ( ( ordered_pair @ SV860 @ SV867 )
= SV809 )
= $false )
| ( ( in @ SV860 @ SV172 )
= $false )
| ( ( SV832 = SV809 )
= $false )
| ( ( in @ SV832 @ ( cartesian_product2 @ SV172 @ SV770 ) )
= $false )
| ( ( in @ SV809 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5781]) ).
thf(5804,plain,
! [SV832: $i,SV172: $i,SV272: $i,SV770: $i,SV809: $i,SV860: $i,SV883: $i,SV867: $i] :
( ( ( in @ ( ordered_pair @ SV867 @ ( sK34_R @ SV883 @ SV867 @ SV860 @ SV809 @ SV770 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( SV860 != SV883 )
| ~ ( in @ SV867 @ SV883 ) )
= $true )
| ( ( ( ordered_pair @ SV860 @ SV867 )
= SV809 )
= $false )
| ( ( in @ SV860 @ SV172 )
= $false )
| ( ( SV832 = SV809 )
= $false )
| ( ( in @ SV832 @ ( cartesian_product2 @ SV172 @ SV770 ) )
= $false )
| ( ( in @ SV809 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5782]) ).
thf(5805,plain,
! [SV833: $i,SV172: $i,SV272: $i,SV771: $i,SV811: $i,SV868: $i,SV884: $i,SV861: $i] :
( ( ( ( SV861 != SV884 ) )
= $true )
| ( ( ~ ( in @ SV868 @ SV884 ) )
= $true )
| ( ( in @ ( sK34_R @ SV884 @ SV868 @ SV861 @ SV811 @ SV771 @ SV272 @ SV172 ) @ SV884 )
= $true )
| ( ( ( ordered_pair @ SV861 @ SV868 )
= SV811 )
= $false )
| ( ( in @ SV861 @ SV172 )
= $false )
| ( ( SV833 = SV811 )
= $false )
| ( ( in @ SV833 @ ( cartesian_product2 @ SV172 @ SV771 ) )
= $false )
| ( ( in @ SV811 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5783]) ).
thf(5806,plain,
! [SV833: $i,SV172: $i,SV272: $i,SV771: $i,SV811: $i,SV861: $i,SV884: $i,SV868: $i] :
( ( ( in @ ( ordered_pair @ SV868 @ ( sK34_R @ SV884 @ SV868 @ SV861 @ SV811 @ SV771 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( SV861 != SV884 )
| ~ ( in @ SV868 @ SV884 ) )
= $true )
| ( ( ( ordered_pair @ SV861 @ SV868 )
= SV811 )
= $false )
| ( ( in @ SV861 @ SV172 )
= $false )
| ( ( SV833 = SV811 )
= $false )
| ( ( in @ SV833 @ ( cartesian_product2 @ SV172 @ SV771 ) )
= $false )
| ( ( in @ SV811 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5784]) ).
thf(5807,plain,
! [SV772: $i,SV854: $i,SV172: $i,SV272: $i,SV803: $i,SV834: $i,SV872: $i,SV878: $i,SV888: $i] :
( ( ( ~ ( in @ ( sK34_R @ SV888 @ SV878 @ SV872 @ SV834 @ SV803 @ SV272 @ SV172 ) @ SV888 )
| ~ ~ ( in @ ( ordered_pair @ SV878 @ ( sK34_R @ SV888 @ SV878 @ SV872 @ SV834 @ SV803 @ SV272 @ SV172 ) ) @ SV272 ) )
= $false )
| ( ( ( SV872 != SV888 )
| ~ ( in @ SV878 @ SV888 ) )
= $true )
| ( ( ( ordered_pair @ SV872 @ SV878 )
= SV834 )
= $false )
| ( ( in @ SV872 @ SV172 )
= $false )
| ( ( SV854 = SV834 )
= $false )
| ( ( in @ SV854 @ ( cartesian_product2 @ SV172 @ SV803 ) )
= $false )
| ( ( in @ SV834 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5785]) ).
thf(5808,plain,
! [SV855: $i,SV172: $i,SV272: $i,SV804: $i,SV836: $i,SV873: $i,SV879: $i,SV889: $i] :
( ( ( ~ ( in @ ( sK34_R @ SV889 @ SV879 @ SV873 @ SV836 @ SV804 @ SV272 @ SV172 ) @ SV889 )
| ~ ~ ( in @ ( ordered_pair @ SV879 @ ( sK34_R @ SV889 @ SV879 @ SV873 @ SV836 @ SV804 @ SV272 @ SV172 ) ) @ SV272 ) )
= $false )
| ( ( ( SV873 != SV889 )
| ~ ( in @ SV879 @ SV889 ) )
= $true )
| ( ( ( ordered_pair @ SV873 @ SV879 )
= SV836 )
= $false )
| ( ( in @ SV873 @ SV172 )
= $false )
| ( ( SV855 = SV836 )
= $false )
| ( ( in @ SV855 @ ( cartesian_product2 @ SV172 @ SV804 ) )
= $false )
| ( ( in @ SV836 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5789]) ).
thf(5809,plain,
! [SV856: $i,SV172: $i,SV272: $i,SV805: $i,SV838: $i,SV874: $i,SV880: $i,SV890: $i] :
( ( ( ~ ( in @ ( sK34_R @ SV890 @ SV880 @ SV874 @ SV838 @ SV805 @ SV272 @ SV172 ) @ SV890 )
| ~ ~ ( in @ ( ordered_pair @ SV880 @ ( sK34_R @ SV890 @ SV880 @ SV874 @ SV838 @ SV805 @ SV272 @ SV172 ) ) @ SV272 ) )
= $false )
| ( ( ( SV874 != SV890 )
| ~ ( in @ SV880 @ SV890 ) )
= $true )
| ( ( ( ordered_pair @ SV874 @ SV880 )
= SV838 )
= $false )
| ( ( in @ SV874 @ SV172 )
= $false )
| ( ( SV856 = SV838 )
= $false )
| ( ( in @ SV856 @ ( cartesian_product2 @ SV172 @ SV805 ) )
= $false )
| ( ( in @ SV838 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5793]) ).
thf(5810,plain,
! [SV720: $i,SV813: $i,SV172: $i,SV272: $i,SV743: $i,SV779: $i,SV847: $i,SV875: $i,SV850: $i] :
( ( ( in @ SV850 @ SV875 )
= $false )
| ( ( SV847 = SV875 )
= $false )
| ( ( in @ ( ordered_pair @ SV850 @ ( sK34_R @ SV875 @ SV850 @ SV847 @ SV779 @ SV743 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV847 @ SV850 )
= SV779 )
= $false )
| ( ( in @ SV847 @ SV172 )
= $false )
| ( ( SV813 = SV779 )
= $false )
| ( ( in @ SV813 @ ( cartesian_product2 @ SV172 @ SV743 ) )
= $false )
| ( ( in @ SV779 @ ( sK29_D @ SV743 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK39_SY682 @ SV272 @ SV172 ) @ SV720 ) @ SV272 )
= $true )
| ( ( in @ SV720 @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5798]) ).
thf(5811,plain,
! [SV814: $i,SV172: $i,SV272: $i,SV744: $i,SV781: $i,SV848: $i,SV876: $i,SV851: $i] :
( ( ( in @ SV851 @ SV876 )
= $false )
| ( ( SV848 = SV876 )
= $false )
| ( ( in @ ( ordered_pair @ SV851 @ ( sK34_R @ SV876 @ SV851 @ SV848 @ SV781 @ SV744 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV848 @ SV851 )
= SV781 )
= $false )
| ( ( in @ SV848 @ SV172 )
= $false )
| ( ( SV814 = SV781 )
= $false )
| ( ( in @ SV814 @ ( cartesian_product2 @ SV172 @ SV744 ) )
= $false )
| ( ( in @ SV781 @ ( sK29_D @ SV744 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK38_SY678 @ SV272 @ SV172 )
= ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5800]) ).
thf(5812,plain,
! [SV815: $i,SV172: $i,SV272: $i,SV745: $i,SV783: $i,SV849: $i,SV877: $i,SV852: $i] :
( ( ( in @ SV852 @ SV877 )
= $false )
| ( ( SV849 = SV877 )
= $false )
| ( ( in @ ( ordered_pair @ SV852 @ ( sK34_R @ SV877 @ SV852 @ SV849 @ SV783 @ SV745 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV849 @ SV852 )
= SV783 )
= $false )
| ( ( in @ SV849 @ SV172 )
= $false )
| ( ( SV815 = SV783 )
= $false )
| ( ( in @ SV815 @ ( cartesian_product2 @ SV172 @ SV745 ) )
= $false )
| ( ( in @ SV783 @ ( sK29_D @ SV745 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK39_SY682 @ SV272 @ SV172 ) @ ( sK40_SY685 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5802]) ).
thf(5813,plain,
! [SV832: $i,SV172: $i,SV272: $i,SV770: $i,SV809: $i,SV867: $i,SV883: $i,SV860: $i] :
( ( ( SV860 = SV883 )
= $false )
| ( ( ~ ( in @ SV867 @ SV883 ) )
= $true )
| ( ( in @ ( sK34_R @ SV883 @ SV867 @ SV860 @ SV809 @ SV770 @ SV272 @ SV172 ) @ SV883 )
= $true )
| ( ( ( ordered_pair @ SV860 @ SV867 )
= SV809 )
= $false )
| ( ( in @ SV860 @ SV172 )
= $false )
| ( ( SV832 = SV809 )
= $false )
| ( ( in @ SV832 @ ( cartesian_product2 @ SV172 @ SV770 ) )
= $false )
| ( ( in @ SV809 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5803]) ).
thf(5814,plain,
! [SV832: $i,SV172: $i,SV272: $i,SV770: $i,SV809: $i,SV867: $i,SV883: $i,SV860: $i] :
( ( ( ( SV860 != SV883 ) )
= $true )
| ( ( ~ ( in @ SV867 @ SV883 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV867 @ ( sK34_R @ SV883 @ SV867 @ SV860 @ SV809 @ SV770 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV860 @ SV867 )
= SV809 )
= $false )
| ( ( in @ SV860 @ SV172 )
= $false )
| ( ( SV832 = SV809 )
= $false )
| ( ( in @ SV832 @ ( cartesian_product2 @ SV172 @ SV770 ) )
= $false )
| ( ( in @ SV809 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5804]) ).
thf(5815,plain,
! [SV833: $i,SV172: $i,SV272: $i,SV771: $i,SV811: $i,SV868: $i,SV884: $i,SV861: $i] :
( ( ( SV861 = SV884 )
= $false )
| ( ( ~ ( in @ SV868 @ SV884 ) )
= $true )
| ( ( in @ ( sK34_R @ SV884 @ SV868 @ SV861 @ SV811 @ SV771 @ SV272 @ SV172 ) @ SV884 )
= $true )
| ( ( ( ordered_pair @ SV861 @ SV868 )
= SV811 )
= $false )
| ( ( in @ SV861 @ SV172 )
= $false )
| ( ( SV833 = SV811 )
= $false )
| ( ( in @ SV833 @ ( cartesian_product2 @ SV172 @ SV771 ) )
= $false )
| ( ( in @ SV811 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5805]) ).
thf(5816,plain,
! [SV833: $i,SV172: $i,SV272: $i,SV771: $i,SV811: $i,SV868: $i,SV884: $i,SV861: $i] :
( ( ( ( SV861 != SV884 ) )
= $true )
| ( ( ~ ( in @ SV868 @ SV884 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV868 @ ( sK34_R @ SV884 @ SV868 @ SV861 @ SV811 @ SV771 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV861 @ SV868 )
= SV811 )
= $false )
| ( ( in @ SV861 @ SV172 )
= $false )
| ( ( SV833 = SV811 )
= $false )
| ( ( in @ SV833 @ ( cartesian_product2 @ SV172 @ SV771 ) )
= $false )
| ( ( in @ SV811 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5806]) ).
thf(5817,plain,
! [SV772: $i,SV854: $i,SV172: $i,SV272: $i,SV803: $i,SV834: $i,SV872: $i,SV878: $i,SV888: $i] :
( ( ( ~ ( in @ ( sK34_R @ SV888 @ SV878 @ SV872 @ SV834 @ SV803 @ SV272 @ SV172 ) @ SV888 ) )
= $false )
| ( ( ( SV872 != SV888 )
| ~ ( in @ SV878 @ SV888 ) )
= $true )
| ( ( ( ordered_pair @ SV872 @ SV878 )
= SV834 )
= $false )
| ( ( in @ SV872 @ SV172 )
= $false )
| ( ( SV854 = SV834 )
= $false )
| ( ( in @ SV854 @ ( cartesian_product2 @ SV172 @ SV803 ) )
= $false )
| ( ( in @ SV834 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5807]) ).
thf(5818,plain,
! [SV772: $i,SV854: $i,SV172: $i,SV272: $i,SV803: $i,SV834: $i,SV872: $i,SV888: $i,SV878: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV878 @ ( sK34_R @ SV888 @ SV878 @ SV872 @ SV834 @ SV803 @ SV272 @ SV172 ) ) @ SV272 ) )
= $false )
| ( ( ( SV872 != SV888 )
| ~ ( in @ SV878 @ SV888 ) )
= $true )
| ( ( ( ordered_pair @ SV872 @ SV878 )
= SV834 )
= $false )
| ( ( in @ SV872 @ SV172 )
= $false )
| ( ( SV854 = SV834 )
= $false )
| ( ( in @ SV854 @ ( cartesian_product2 @ SV172 @ SV803 ) )
= $false )
| ( ( in @ SV834 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5807]) ).
thf(5819,plain,
! [SV855: $i,SV172: $i,SV272: $i,SV804: $i,SV836: $i,SV873: $i,SV879: $i,SV889: $i] :
( ( ( ~ ( in @ ( sK34_R @ SV889 @ SV879 @ SV873 @ SV836 @ SV804 @ SV272 @ SV172 ) @ SV889 ) )
= $false )
| ( ( ( SV873 != SV889 )
| ~ ( in @ SV879 @ SV889 ) )
= $true )
| ( ( ( ordered_pair @ SV873 @ SV879 )
= SV836 )
= $false )
| ( ( in @ SV873 @ SV172 )
= $false )
| ( ( SV855 = SV836 )
= $false )
| ( ( in @ SV855 @ ( cartesian_product2 @ SV172 @ SV804 ) )
= $false )
| ( ( in @ SV836 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5808]) ).
thf(5820,plain,
! [SV855: $i,SV172: $i,SV272: $i,SV804: $i,SV836: $i,SV873: $i,SV889: $i,SV879: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV879 @ ( sK34_R @ SV889 @ SV879 @ SV873 @ SV836 @ SV804 @ SV272 @ SV172 ) ) @ SV272 ) )
= $false )
| ( ( ( SV873 != SV889 )
| ~ ( in @ SV879 @ SV889 ) )
= $true )
| ( ( ( ordered_pair @ SV873 @ SV879 )
= SV836 )
= $false )
| ( ( in @ SV873 @ SV172 )
= $false )
| ( ( SV855 = SV836 )
= $false )
| ( ( in @ SV855 @ ( cartesian_product2 @ SV172 @ SV804 ) )
= $false )
| ( ( in @ SV836 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5808]) ).
thf(5821,plain,
! [SV856: $i,SV172: $i,SV272: $i,SV805: $i,SV838: $i,SV874: $i,SV880: $i,SV890: $i] :
( ( ( ~ ( in @ ( sK34_R @ SV890 @ SV880 @ SV874 @ SV838 @ SV805 @ SV272 @ SV172 ) @ SV890 ) )
= $false )
| ( ( ( SV874 != SV890 )
| ~ ( in @ SV880 @ SV890 ) )
= $true )
| ( ( ( ordered_pair @ SV874 @ SV880 )
= SV838 )
= $false )
| ( ( in @ SV874 @ SV172 )
= $false )
| ( ( SV856 = SV838 )
= $false )
| ( ( in @ SV856 @ ( cartesian_product2 @ SV172 @ SV805 ) )
= $false )
| ( ( in @ SV838 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5809]) ).
thf(5822,plain,
! [SV856: $i,SV172: $i,SV272: $i,SV805: $i,SV838: $i,SV874: $i,SV890: $i,SV880: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ SV880 @ ( sK34_R @ SV890 @ SV880 @ SV874 @ SV838 @ SV805 @ SV272 @ SV172 ) ) @ SV272 ) )
= $false )
| ( ( ( SV874 != SV890 )
| ~ ( in @ SV880 @ SV890 ) )
= $true )
| ( ( ( ordered_pair @ SV874 @ SV880 )
= SV838 )
= $false )
| ( ( in @ SV874 @ SV172 )
= $false )
| ( ( SV856 = SV838 )
= $false )
| ( ( in @ SV856 @ ( cartesian_product2 @ SV172 @ SV805 ) )
= $false )
| ( ( in @ SV838 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5809]) ).
thf(5823,plain,
! [SV832: $i,SV172: $i,SV272: $i,SV770: $i,SV809: $i,SV860: $i,SV883: $i,SV867: $i] :
( ( ( in @ SV867 @ SV883 )
= $false )
| ( ( SV860 = SV883 )
= $false )
| ( ( in @ ( sK34_R @ SV883 @ SV867 @ SV860 @ SV809 @ SV770 @ SV272 @ SV172 ) @ SV883 )
= $true )
| ( ( ( ordered_pair @ SV860 @ SV867 )
= SV809 )
= $false )
| ( ( in @ SV860 @ SV172 )
= $false )
| ( ( SV832 = SV809 )
= $false )
| ( ( in @ SV832 @ ( cartesian_product2 @ SV172 @ SV770 ) )
= $false )
| ( ( in @ SV809 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5813]) ).
thf(5824,plain,
! [SV832: $i,SV172: $i,SV272: $i,SV770: $i,SV809: $i,SV867: $i,SV883: $i,SV860: $i] :
( ( ( SV860 = SV883 )
= $false )
| ( ( ~ ( in @ SV867 @ SV883 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV867 @ ( sK34_R @ SV883 @ SV867 @ SV860 @ SV809 @ SV770 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV860 @ SV867 )
= SV809 )
= $false )
| ( ( in @ SV860 @ SV172 )
= $false )
| ( ( SV832 = SV809 )
= $false )
| ( ( in @ SV832 @ ( cartesian_product2 @ SV172 @ SV770 ) )
= $false )
| ( ( in @ SV809 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5814]) ).
thf(5825,plain,
! [SV833: $i,SV172: $i,SV272: $i,SV771: $i,SV811: $i,SV861: $i,SV884: $i,SV868: $i] :
( ( ( in @ SV868 @ SV884 )
= $false )
| ( ( SV861 = SV884 )
= $false )
| ( ( in @ ( sK34_R @ SV884 @ SV868 @ SV861 @ SV811 @ SV771 @ SV272 @ SV172 ) @ SV884 )
= $true )
| ( ( ( ordered_pair @ SV861 @ SV868 )
= SV811 )
= $false )
| ( ( in @ SV861 @ SV172 )
= $false )
| ( ( SV833 = SV811 )
= $false )
| ( ( in @ SV833 @ ( cartesian_product2 @ SV172 @ SV771 ) )
= $false )
| ( ( in @ SV811 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5815]) ).
thf(5826,plain,
! [SV833: $i,SV172: $i,SV272: $i,SV771: $i,SV811: $i,SV868: $i,SV884: $i,SV861: $i] :
( ( ( SV861 = SV884 )
= $false )
| ( ( ~ ( in @ SV868 @ SV884 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV868 @ ( sK34_R @ SV884 @ SV868 @ SV861 @ SV811 @ SV771 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV861 @ SV868 )
= SV811 )
= $false )
| ( ( in @ SV861 @ SV172 )
= $false )
| ( ( SV833 = SV811 )
= $false )
| ( ( in @ SV833 @ ( cartesian_product2 @ SV172 @ SV771 ) )
= $false )
| ( ( in @ SV811 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5816]) ).
thf(5827,plain,
! [SV772: $i,SV854: $i,SV172: $i,SV272: $i,SV803: $i,SV834: $i,SV872: $i,SV878: $i,SV888: $i] :
( ( ( in @ ( sK34_R @ SV888 @ SV878 @ SV872 @ SV834 @ SV803 @ SV272 @ SV172 ) @ SV888 )
= $true )
| ( ( ( SV872 != SV888 )
| ~ ( in @ SV878 @ SV888 ) )
= $true )
| ( ( ( ordered_pair @ SV872 @ SV878 )
= SV834 )
= $false )
| ( ( in @ SV872 @ SV172 )
= $false )
| ( ( SV854 = SV834 )
= $false )
| ( ( in @ SV854 @ ( cartesian_product2 @ SV172 @ SV803 ) )
= $false )
| ( ( in @ SV834 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5817]) ).
thf(5828,plain,
! [SV772: $i,SV854: $i,SV172: $i,SV272: $i,SV803: $i,SV834: $i,SV872: $i,SV888: $i,SV878: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV878 @ ( sK34_R @ SV888 @ SV878 @ SV872 @ SV834 @ SV803 @ SV272 @ SV172 ) ) @ SV272 ) )
= $true )
| ( ( ( SV872 != SV888 )
| ~ ( in @ SV878 @ SV888 ) )
= $true )
| ( ( ( ordered_pair @ SV872 @ SV878 )
= SV834 )
= $false )
| ( ( in @ SV872 @ SV172 )
= $false )
| ( ( SV854 = SV834 )
= $false )
| ( ( in @ SV854 @ ( cartesian_product2 @ SV172 @ SV803 ) )
= $false )
| ( ( in @ SV834 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5818]) ).
thf(5829,plain,
! [SV855: $i,SV172: $i,SV272: $i,SV804: $i,SV836: $i,SV873: $i,SV879: $i,SV889: $i] :
( ( ( in @ ( sK34_R @ SV889 @ SV879 @ SV873 @ SV836 @ SV804 @ SV272 @ SV172 ) @ SV889 )
= $true )
| ( ( ( SV873 != SV889 )
| ~ ( in @ SV879 @ SV889 ) )
= $true )
| ( ( ( ordered_pair @ SV873 @ SV879 )
= SV836 )
= $false )
| ( ( in @ SV873 @ SV172 )
= $false )
| ( ( SV855 = SV836 )
= $false )
| ( ( in @ SV855 @ ( cartesian_product2 @ SV172 @ SV804 ) )
= $false )
| ( ( in @ SV836 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5819]) ).
thf(5830,plain,
! [SV855: $i,SV172: $i,SV272: $i,SV804: $i,SV836: $i,SV873: $i,SV889: $i,SV879: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV879 @ ( sK34_R @ SV889 @ SV879 @ SV873 @ SV836 @ SV804 @ SV272 @ SV172 ) ) @ SV272 ) )
= $true )
| ( ( ( SV873 != SV889 )
| ~ ( in @ SV879 @ SV889 ) )
= $true )
| ( ( ( ordered_pair @ SV873 @ SV879 )
= SV836 )
= $false )
| ( ( in @ SV873 @ SV172 )
= $false )
| ( ( SV855 = SV836 )
= $false )
| ( ( in @ SV855 @ ( cartesian_product2 @ SV172 @ SV804 ) )
= $false )
| ( ( in @ SV836 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5820]) ).
thf(5831,plain,
! [SV856: $i,SV172: $i,SV272: $i,SV805: $i,SV838: $i,SV874: $i,SV880: $i,SV890: $i] :
( ( ( in @ ( sK34_R @ SV890 @ SV880 @ SV874 @ SV838 @ SV805 @ SV272 @ SV172 ) @ SV890 )
= $true )
| ( ( ( SV874 != SV890 )
| ~ ( in @ SV880 @ SV890 ) )
= $true )
| ( ( ( ordered_pair @ SV874 @ SV880 )
= SV838 )
= $false )
| ( ( in @ SV874 @ SV172 )
= $false )
| ( ( SV856 = SV838 )
= $false )
| ( ( in @ SV856 @ ( cartesian_product2 @ SV172 @ SV805 ) )
= $false )
| ( ( in @ SV838 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5821]) ).
thf(5832,plain,
! [SV856: $i,SV172: $i,SV272: $i,SV805: $i,SV838: $i,SV874: $i,SV890: $i,SV880: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV880 @ ( sK34_R @ SV890 @ SV880 @ SV874 @ SV838 @ SV805 @ SV272 @ SV172 ) ) @ SV272 ) )
= $true )
| ( ( ( SV874 != SV890 )
| ~ ( in @ SV880 @ SV890 ) )
= $true )
| ( ( ( ordered_pair @ SV874 @ SV880 )
= SV838 )
= $false )
| ( ( in @ SV874 @ SV172 )
= $false )
| ( ( SV856 = SV838 )
= $false )
| ( ( in @ SV856 @ ( cartesian_product2 @ SV172 @ SV805 ) )
= $false )
| ( ( in @ SV838 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5822]) ).
thf(5833,plain,
! [SV832: $i,SV172: $i,SV272: $i,SV770: $i,SV809: $i,SV860: $i,SV883: $i,SV867: $i] :
( ( ( in @ SV867 @ SV883 )
= $false )
| ( ( SV860 = SV883 )
= $false )
| ( ( in @ ( ordered_pair @ SV867 @ ( sK34_R @ SV883 @ SV867 @ SV860 @ SV809 @ SV770 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV860 @ SV867 )
= SV809 )
= $false )
| ( ( in @ SV860 @ SV172 )
= $false )
| ( ( SV832 = SV809 )
= $false )
| ( ( in @ SV832 @ ( cartesian_product2 @ SV172 @ SV770 ) )
= $false )
| ( ( in @ SV809 @ ( sK29_D @ SV770 @ SV272 @ SV172 ) )
= $true )
| ( ( ( ordered_pair @ ( sK41_SY666 @ SV272 @ SV172 ) @ ( sK42_SY688 @ SV272 @ SV172 ) )
= ( sK36_SY655 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5824]) ).
thf(5834,plain,
! [SV833: $i,SV172: $i,SV272: $i,SV771: $i,SV811: $i,SV861: $i,SV884: $i,SV868: $i] :
( ( ( in @ SV868 @ SV884 )
= $false )
| ( ( SV861 = SV884 )
= $false )
| ( ( in @ ( ordered_pair @ SV868 @ ( sK34_R @ SV884 @ SV868 @ SV861 @ SV811 @ SV771 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV861 @ SV868 )
= SV811 )
= $false )
| ( ( in @ SV861 @ SV172 )
= $false )
| ( ( SV833 = SV811 )
= $false )
| ( ( in @ SV833 @ ( cartesian_product2 @ SV172 @ SV771 ) )
= $false )
| ( ( in @ SV811 @ ( sK29_D @ SV771 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK41_SY666 @ SV272 @ SV172 ) @ SV172 )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5826]) ).
thf(5835,plain,
! [SV772: $i,SV854: $i,SV172: $i,SV272: $i,SV803: $i,SV834: $i,SV878: $i,SV888: $i,SV872: $i] :
( ( ( ( SV872 != SV888 ) )
= $true )
| ( ( ~ ( in @ SV878 @ SV888 ) )
= $true )
| ( ( in @ ( sK34_R @ SV888 @ SV878 @ SV872 @ SV834 @ SV803 @ SV272 @ SV172 ) @ SV888 )
= $true )
| ( ( ( ordered_pair @ SV872 @ SV878 )
= SV834 )
= $false )
| ( ( in @ SV872 @ SV172 )
= $false )
| ( ( SV854 = SV834 )
= $false )
| ( ( in @ SV854 @ ( cartesian_product2 @ SV172 @ SV803 ) )
= $false )
| ( ( in @ SV834 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5827]) ).
thf(5836,plain,
! [SV772: $i,SV854: $i,SV172: $i,SV272: $i,SV803: $i,SV834: $i,SV872: $i,SV888: $i,SV878: $i] :
( ( ( in @ ( ordered_pair @ SV878 @ ( sK34_R @ SV888 @ SV878 @ SV872 @ SV834 @ SV803 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( SV872 != SV888 )
| ~ ( in @ SV878 @ SV888 ) )
= $true )
| ( ( ( ordered_pair @ SV872 @ SV878 )
= SV834 )
= $false )
| ( ( in @ SV872 @ SV172 )
= $false )
| ( ( SV854 = SV834 )
= $false )
| ( ( in @ SV854 @ ( cartesian_product2 @ SV172 @ SV803 ) )
= $false )
| ( ( in @ SV834 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5828]) ).
thf(5837,plain,
! [SV855: $i,SV172: $i,SV272: $i,SV804: $i,SV836: $i,SV879: $i,SV889: $i,SV873: $i] :
( ( ( ( SV873 != SV889 ) )
= $true )
| ( ( ~ ( in @ SV879 @ SV889 ) )
= $true )
| ( ( in @ ( sK34_R @ SV889 @ SV879 @ SV873 @ SV836 @ SV804 @ SV272 @ SV172 ) @ SV889 )
= $true )
| ( ( ( ordered_pair @ SV873 @ SV879 )
= SV836 )
= $false )
| ( ( in @ SV873 @ SV172 )
= $false )
| ( ( SV855 = SV836 )
= $false )
| ( ( in @ SV855 @ ( cartesian_product2 @ SV172 @ SV804 ) )
= $false )
| ( ( in @ SV836 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5829]) ).
thf(5838,plain,
! [SV855: $i,SV172: $i,SV272: $i,SV804: $i,SV836: $i,SV873: $i,SV889: $i,SV879: $i] :
( ( ( in @ ( ordered_pair @ SV879 @ ( sK34_R @ SV889 @ SV879 @ SV873 @ SV836 @ SV804 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( SV873 != SV889 )
| ~ ( in @ SV879 @ SV889 ) )
= $true )
| ( ( ( ordered_pair @ SV873 @ SV879 )
= SV836 )
= $false )
| ( ( in @ SV873 @ SV172 )
= $false )
| ( ( SV855 = SV836 )
= $false )
| ( ( in @ SV855 @ ( cartesian_product2 @ SV172 @ SV804 ) )
= $false )
| ( ( in @ SV836 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5830]) ).
thf(5839,plain,
! [SV856: $i,SV172: $i,SV272: $i,SV805: $i,SV838: $i,SV880: $i,SV890: $i,SV874: $i] :
( ( ( ( SV874 != SV890 ) )
= $true )
| ( ( ~ ( in @ SV880 @ SV890 ) )
= $true )
| ( ( in @ ( sK34_R @ SV890 @ SV880 @ SV874 @ SV838 @ SV805 @ SV272 @ SV172 ) @ SV890 )
= $true )
| ( ( ( ordered_pair @ SV874 @ SV880 )
= SV838 )
= $false )
| ( ( in @ SV874 @ SV172 )
= $false )
| ( ( SV856 = SV838 )
= $false )
| ( ( in @ SV856 @ ( cartesian_product2 @ SV172 @ SV805 ) )
= $false )
| ( ( in @ SV838 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5831]) ).
thf(5840,plain,
! [SV856: $i,SV172: $i,SV272: $i,SV805: $i,SV838: $i,SV874: $i,SV890: $i,SV880: $i] :
( ( ( in @ ( ordered_pair @ SV880 @ ( sK34_R @ SV890 @ SV880 @ SV874 @ SV838 @ SV805 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( SV874 != SV890 )
| ~ ( in @ SV880 @ SV890 ) )
= $true )
| ( ( ( ordered_pair @ SV874 @ SV880 )
= SV838 )
= $false )
| ( ( in @ SV874 @ SV172 )
= $false )
| ( ( SV856 = SV838 )
= $false )
| ( ( in @ SV856 @ ( cartesian_product2 @ SV172 @ SV805 ) )
= $false )
| ( ( in @ SV838 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5832]) ).
thf(5841,plain,
! [SV772: $i,SV854: $i,SV172: $i,SV272: $i,SV803: $i,SV834: $i,SV878: $i,SV888: $i,SV872: $i] :
( ( ( SV872 = SV888 )
= $false )
| ( ( ~ ( in @ SV878 @ SV888 ) )
= $true )
| ( ( in @ ( sK34_R @ SV888 @ SV878 @ SV872 @ SV834 @ SV803 @ SV272 @ SV172 ) @ SV888 )
= $true )
| ( ( ( ordered_pair @ SV872 @ SV878 )
= SV834 )
= $false )
| ( ( in @ SV872 @ SV172 )
= $false )
| ( ( SV854 = SV834 )
= $false )
| ( ( in @ SV854 @ ( cartesian_product2 @ SV172 @ SV803 ) )
= $false )
| ( ( in @ SV834 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5835]) ).
thf(5842,plain,
! [SV772: $i,SV854: $i,SV172: $i,SV272: $i,SV803: $i,SV834: $i,SV878: $i,SV888: $i,SV872: $i] :
( ( ( ( SV872 != SV888 ) )
= $true )
| ( ( ~ ( in @ SV878 @ SV888 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV878 @ ( sK34_R @ SV888 @ SV878 @ SV872 @ SV834 @ SV803 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV872 @ SV878 )
= SV834 )
= $false )
| ( ( in @ SV872 @ SV172 )
= $false )
| ( ( SV854 = SV834 )
= $false )
| ( ( in @ SV854 @ ( cartesian_product2 @ SV172 @ SV803 ) )
= $false )
| ( ( in @ SV834 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5836]) ).
thf(5843,plain,
! [SV855: $i,SV172: $i,SV272: $i,SV804: $i,SV836: $i,SV879: $i,SV889: $i,SV873: $i] :
( ( ( SV873 = SV889 )
= $false )
| ( ( ~ ( in @ SV879 @ SV889 ) )
= $true )
| ( ( in @ ( sK34_R @ SV889 @ SV879 @ SV873 @ SV836 @ SV804 @ SV272 @ SV172 ) @ SV889 )
= $true )
| ( ( ( ordered_pair @ SV873 @ SV879 )
= SV836 )
= $false )
| ( ( in @ SV873 @ SV172 )
= $false )
| ( ( SV855 = SV836 )
= $false )
| ( ( in @ SV855 @ ( cartesian_product2 @ SV172 @ SV804 ) )
= $false )
| ( ( in @ SV836 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5837]) ).
thf(5844,plain,
! [SV855: $i,SV172: $i,SV272: $i,SV804: $i,SV836: $i,SV879: $i,SV889: $i,SV873: $i] :
( ( ( ( SV873 != SV889 ) )
= $true )
| ( ( ~ ( in @ SV879 @ SV889 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV879 @ ( sK34_R @ SV889 @ SV879 @ SV873 @ SV836 @ SV804 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV873 @ SV879 )
= SV836 )
= $false )
| ( ( in @ SV873 @ SV172 )
= $false )
| ( ( SV855 = SV836 )
= $false )
| ( ( in @ SV855 @ ( cartesian_product2 @ SV172 @ SV804 ) )
= $false )
| ( ( in @ SV836 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5838]) ).
thf(5845,plain,
! [SV856: $i,SV172: $i,SV272: $i,SV805: $i,SV838: $i,SV880: $i,SV890: $i,SV874: $i] :
( ( ( SV874 = SV890 )
= $false )
| ( ( ~ ( in @ SV880 @ SV890 ) )
= $true )
| ( ( in @ ( sK34_R @ SV890 @ SV880 @ SV874 @ SV838 @ SV805 @ SV272 @ SV172 ) @ SV890 )
= $true )
| ( ( ( ordered_pair @ SV874 @ SV880 )
= SV838 )
= $false )
| ( ( in @ SV874 @ SV172 )
= $false )
| ( ( SV856 = SV838 )
= $false )
| ( ( in @ SV856 @ ( cartesian_product2 @ SV172 @ SV805 ) )
= $false )
| ( ( in @ SV838 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5839]) ).
thf(5846,plain,
! [SV856: $i,SV172: $i,SV272: $i,SV805: $i,SV838: $i,SV880: $i,SV890: $i,SV874: $i] :
( ( ( ( SV874 != SV890 ) )
= $true )
| ( ( ~ ( in @ SV880 @ SV890 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV880 @ ( sK34_R @ SV890 @ SV880 @ SV874 @ SV838 @ SV805 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV874 @ SV880 )
= SV838 )
= $false )
| ( ( in @ SV874 @ SV172 )
= $false )
| ( ( SV856 = SV838 )
= $false )
| ( ( in @ SV856 @ ( cartesian_product2 @ SV172 @ SV805 ) )
= $false )
| ( ( in @ SV838 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5840]) ).
thf(5847,plain,
! [SV772: $i,SV854: $i,SV172: $i,SV272: $i,SV803: $i,SV834: $i,SV872: $i,SV888: $i,SV878: $i] :
( ( ( in @ SV878 @ SV888 )
= $false )
| ( ( SV872 = SV888 )
= $false )
| ( ( in @ ( sK34_R @ SV888 @ SV878 @ SV872 @ SV834 @ SV803 @ SV272 @ SV172 ) @ SV888 )
= $true )
| ( ( ( ordered_pair @ SV872 @ SV878 )
= SV834 )
= $false )
| ( ( in @ SV872 @ SV172 )
= $false )
| ( ( SV854 = SV834 )
= $false )
| ( ( in @ SV854 @ ( cartesian_product2 @ SV172 @ SV803 ) )
= $false )
| ( ( in @ SV834 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5841]) ).
thf(5848,plain,
! [SV772: $i,SV854: $i,SV172: $i,SV272: $i,SV803: $i,SV834: $i,SV878: $i,SV888: $i,SV872: $i] :
( ( ( SV872 = SV888 )
= $false )
| ( ( ~ ( in @ SV878 @ SV888 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV878 @ ( sK34_R @ SV888 @ SV878 @ SV872 @ SV834 @ SV803 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV872 @ SV878 )
= SV834 )
= $false )
| ( ( in @ SV872 @ SV172 )
= $false )
| ( ( SV854 = SV834 )
= $false )
| ( ( in @ SV854 @ ( cartesian_product2 @ SV172 @ SV803 ) )
= $false )
| ( ( in @ SV834 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5842]) ).
thf(5849,plain,
! [SV855: $i,SV172: $i,SV272: $i,SV804: $i,SV836: $i,SV873: $i,SV889: $i,SV879: $i] :
( ( ( in @ SV879 @ SV889 )
= $false )
| ( ( SV873 = SV889 )
= $false )
| ( ( in @ ( sK34_R @ SV889 @ SV879 @ SV873 @ SV836 @ SV804 @ SV272 @ SV172 ) @ SV889 )
= $true )
| ( ( ( ordered_pair @ SV873 @ SV879 )
= SV836 )
= $false )
| ( ( in @ SV873 @ SV172 )
= $false )
| ( ( SV855 = SV836 )
= $false )
| ( ( in @ SV855 @ ( cartesian_product2 @ SV172 @ SV804 ) )
= $false )
| ( ( in @ SV836 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5843]) ).
thf(5850,plain,
! [SV855: $i,SV172: $i,SV272: $i,SV804: $i,SV836: $i,SV879: $i,SV889: $i,SV873: $i] :
( ( ( SV873 = SV889 )
= $false )
| ( ( ~ ( in @ SV879 @ SV889 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV879 @ ( sK34_R @ SV889 @ SV879 @ SV873 @ SV836 @ SV804 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV873 @ SV879 )
= SV836 )
= $false )
| ( ( in @ SV873 @ SV172 )
= $false )
| ( ( SV855 = SV836 )
= $false )
| ( ( in @ SV855 @ ( cartesian_product2 @ SV172 @ SV804 ) )
= $false )
| ( ( in @ SV836 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5844]) ).
thf(5851,plain,
! [SV856: $i,SV172: $i,SV272: $i,SV805: $i,SV838: $i,SV874: $i,SV890: $i,SV880: $i] :
( ( ( in @ SV880 @ SV890 )
= $false )
| ( ( SV874 = SV890 )
= $false )
| ( ( in @ ( sK34_R @ SV890 @ SV880 @ SV874 @ SV838 @ SV805 @ SV272 @ SV172 ) @ SV890 )
= $true )
| ( ( ( ordered_pair @ SV874 @ SV880 )
= SV838 )
= $false )
| ( ( in @ SV874 @ SV172 )
= $false )
| ( ( SV856 = SV838 )
= $false )
| ( ( in @ SV856 @ ( cartesian_product2 @ SV172 @ SV805 ) )
= $false )
| ( ( in @ SV838 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5845]) ).
thf(5852,plain,
! [SV856: $i,SV172: $i,SV272: $i,SV805: $i,SV838: $i,SV880: $i,SV890: $i,SV874: $i] :
( ( ( SV874 = SV890 )
= $false )
| ( ( ~ ( in @ SV880 @ SV890 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV880 @ ( sK34_R @ SV890 @ SV880 @ SV874 @ SV838 @ SV805 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV874 @ SV880 )
= SV838 )
= $false )
| ( ( in @ SV874 @ SV172 )
= $false )
| ( ( SV856 = SV838 )
= $false )
| ( ( in @ SV856 @ ( cartesian_product2 @ SV172 @ SV805 ) )
= $false )
| ( ( in @ SV838 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5846]) ).
thf(5853,plain,
! [SV772: $i,SV854: $i,SV172: $i,SV272: $i,SV803: $i,SV834: $i,SV872: $i,SV888: $i,SV878: $i] :
( ( ( in @ SV878 @ SV888 )
= $false )
| ( ( SV872 = SV888 )
= $false )
| ( ( in @ ( ordered_pair @ SV878 @ ( sK34_R @ SV888 @ SV878 @ SV872 @ SV834 @ SV803 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV872 @ SV878 )
= SV834 )
= $false )
| ( ( in @ SV872 @ SV172 )
= $false )
| ( ( SV854 = SV834 )
= $false )
| ( ( in @ SV854 @ ( cartesian_product2 @ SV172 @ SV803 ) )
= $false )
| ( ( in @ SV834 @ ( sK29_D @ SV803 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK42_SY688 @ SV272 @ SV172 ) @ SV772 ) @ SV272 )
= $true )
| ( ( in @ SV772 @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $false )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5848]) ).
thf(5854,plain,
! [SV855: $i,SV172: $i,SV272: $i,SV804: $i,SV836: $i,SV873: $i,SV889: $i,SV879: $i] :
( ( ( in @ SV879 @ SV889 )
= $false )
| ( ( SV873 = SV889 )
= $false )
| ( ( in @ ( ordered_pair @ SV879 @ ( sK34_R @ SV889 @ SV879 @ SV873 @ SV836 @ SV804 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV873 @ SV879 )
= SV836 )
= $false )
| ( ( in @ SV873 @ SV172 )
= $false )
| ( ( SV855 = SV836 )
= $false )
| ( ( in @ SV855 @ ( cartesian_product2 @ SV172 @ SV804 ) )
= $false )
| ( ( in @ SV836 @ ( sK29_D @ SV804 @ SV272 @ SV172 ) )
= $true )
| ( ( ( sK41_SY666 @ SV272 @ SV172 )
= ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5850]) ).
thf(5855,plain,
! [SV856: $i,SV172: $i,SV272: $i,SV805: $i,SV838: $i,SV874: $i,SV890: $i,SV880: $i] :
( ( ( in @ SV880 @ SV890 )
= $false )
| ( ( SV874 = SV890 )
= $false )
| ( ( in @ ( ordered_pair @ SV880 @ ( sK34_R @ SV890 @ SV880 @ SV874 @ SV838 @ SV805 @ SV272 @ SV172 ) ) @ SV272 )
= $false )
| ( ( ( ordered_pair @ SV874 @ SV880 )
= SV838 )
= $false )
| ( ( in @ SV874 @ SV172 )
= $false )
| ( ( SV856 = SV838 )
= $false )
| ( ( in @ SV856 @ ( cartesian_product2 @ SV172 @ SV805 ) )
= $false )
| ( ( in @ SV838 @ ( sK29_D @ SV805 @ SV272 @ SV172 ) )
= $true )
| ( ( in @ ( sK42_SY688 @ SV272 @ SV172 ) @ ( sK43_SY691 @ SV272 @ SV172 ) )
= $true )
| ( ( empty @ SV172 )
= $true )
| ( ( relation @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5852]) ).
thf(5856,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[951,5855,5854,5853,5851,5849,5847,5834,5833,5825,5823,5812,5811,5810,5801,5799,5797,5796,5795,5794,5792,5791,5790,5788,5787,5786,5752,5751,5739,5731,5729,5726,5725,5721,5720,5716,5715,5713,5712,5711,5709,5708,5707,5704,5661,5643,5642,5641,5640,5639,5638,5636,5635,5634,5632,5631,5630,5623,5620,5619,5615,5614,5610,5609,5605,5604,5600,5599,5594,5592,5590,5544,5543,5542,5539,5538,5537,5534,5533,5532,5485,5484,5481,5480,5476,5475,5471,5470,5468,5467,5466,5464,5463,5462,5447,5446,5442,5441,5439,5438,5437,5421,5360,5359,5357,5356,5353,5321,5320,5319,5318,5308,5297,5296,5292,5291,5287,5286,5282,5281,5277,5276,5274,5273,5272,5256,5255,5252,5250,5248,5246,5186,5185,5184,5181,5180,5179,5176,5175,5174,5171,5170,5169,5165,5162,5159,5157,5156,5154,5152,5151,5149,5147,5146,5096,5081,5080,5066,5052,5051,5047,5046,5042,5041,5027,5026,5011,4937,4936,4935,4922,4921,4919,4918,4916,4914,4913,4905,4904,4902,4901,4900,4850,4843,4810,4809,4797,4732,4731,4729,4726,4723,4716,4708,4707,4705,4703,4702,4700,4698,4697,4695,4694,4685,4683,4682,4678,4677,4652,4576,4575,4574,4517,4516,4515,4500,4493,4492,4490,4489,4481,4479,4478,4465,4464,4442,4441,4440,4439,4438,4437,4348,4347,4311,4310,4304,4303,4250,4249,4248,4243,4242,4241,4240,4239,4238,4237,4236,4233,4232,4175,4172,4171,4162,4153,4151,4150,4125,4124,4107,4106,4105,4102,4098,4095,4067,4066,4065,4064,4052,4051,4047,4046,4045,4038,4035,4034,4032,4031,4028,4023,4022,4021,4020,4019,4018,4010,4007,4005,3995,3994,3976,3975,3972,3963,3949,3948,3939,3938,3932,3931,3922,3917,3910,3909,3908,3897,3882,3868,3866,3863,3862,3861,3846,3827,3817,3816,3813,3812,3802,3785,3774,3772,3757,3752,3734,3732,3726,3724,3719,3716,3707,3706,3696,3695,3653,3650,3643,3642,3626,3625,3614,3607,3605,3604,3601,3600,3571,3566,3565,3556,3552,3551,3543,3532,3531,3530,3527,3524,3523,3511,3496,3492,3491,3490,3474,3473,3457,3452,3448,3437,3415,3397,3376,3375,3365,3355,3354,3347,3339,3338,3329,3328,3311,3308,3307,3300,3274,3273,3272,3271,3266,3265,3264,3262,3254,3244,3237,3236,3225,3224,3223,3216,3214,3213,3209,3198,3196,3195,3189,3171,3161,3159,3158,3157,3156,3139,3135,3134,3133,3132,3121,3113,3095,3094,3090,3087,3068,3065,3064,3057,3056,3026,3025,3024,3015,3014,3010,2981,2978,2968,2962,2951,2949,2944,2929,2926,2920,2917,2916,2915,2914,2913,2912,2911,2905,2903,2899,2898,2897,2896,2895,2892,2891,2885,2884,2881,2880,2875,2847,2846,2815,2814,2785,2784,2780,2779,2771,2757,2753,2749,2748,2742,2741,2738,2737,2736,2731,2730,2729,2728,2727,2726,2725,2722,2721,2713,2701,2700,2694,2693,2690,2675,2674,2652,2651,2648,2647,2632,2631,2592,2591,2586,2550,2549,2548,2547,2546,2545,2538,2532,2530,2521,2520,2519,2516,2515,2512,2490,2481,2396,2376,2358,2345,2344,2343,2341,2340,2339,2332,2331,2330,2327,2326,2325,2323,2322,2311,2308,2304,2303,2300,2299,2296,2276,2273,2270,2269,2255,2220,2218,2217,2198,2131,2124,2122,2121,2119,2118,2116,2115,2114,2113,2112,2110,2107,2104,2101,2100,2097,2094,2093,2090,2082,2079,2077,2076,2073,2069,2067,2065,2064,2063,2059,2057,2055,2052,2051,2030,2026,2001,2000,1992,1990,1989,1979,1978,1968,1960,1959,1947,1942,1879,1875,1869,1862,1854,1849,1848,1847,1846,1845,1830,1811,1795,1794,1785,1783,1773,1614,1608,1604,1603,1594,1582,1577,1572,1569,1568,1560,1546,1534,1412,1411,1410,1409,1407,1404,1402,1378,1373,1370,1355,1340,1324,1304,1292,1283,1183,1157,1127,1115,1114,981]) ).
thf(5857,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[5856]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU308+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 19 18:21:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.53 ................
% 0.74/0.90
% 0.74/0.90 No.of.Axioms: 494
% 0.74/0.90
% 0.74/0.90 Length.of.Defs: 0
% 0.74/0.90
% 0.74/0.90 Contains.Choice.Funs: false
% 0.85/1.04 ..............................
% 0.93/1.15 (rf:2,axioms:236,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:496,loop_count:0,foatp_calls:0,translation:fof_full)...........................................................................................................................................................................................................................................................................................................................................................................................................
% 22.23/22.39
% 22.23/22.39 ********************************
% 22.23/22.39 * All subproblems solved! *
% 22.23/22.39 ********************************
% 22.23/22.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:2,axioms:237,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:72,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:5856,loop_count:0,foatp_calls:1,translation:fof_full)
% 37.47/37.69
% 37.47/37.69 %**** Beginning of derivation protocol ****
% 37.47/37.69 % SZS output start CNFRefutation
% See solution above
% 37.54/37.72
% 37.54/37.72 %**** End of derivation protocol ****
% 37.54/37.72 %**** no. of clauses in derivation: 5599 ****
% 37.54/37.72 %**** clause counter: 5856 ****
% 37.54/37.72
% 37.54/37.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:2,axioms:237,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:72,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:5856,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------