TSTP Solution File: SEU267+2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU267+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 : n023.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 12:09:19 EDT 2022
% Result : Theorem 227.55s 228.04s
% Output : CNFRefutation 231.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 178
% Syntax : Number of formulae : 3379 ( 687 unt; 137 typ; 0 def)
% Number of atoms : 41216 (13711 equ; 0 cnn)
% Maximal formula atoms : 12 ( 12 avg)
% Number of connectives : 106326 (17010 ~;17372 |; 484 &;71250 @)
% ( 96 <=>; 114 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 273 ( 273 >; 0 *; 0 +; 0 <<)
% Number of symbols : 140 ( 137 usr; 5 con; 0-5 aty)
% Number of variables : 13655 ( 0 ^13629 !; 26 ?;13655 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_antisymmetric,type,
antisymmetric: $i > $o ).
thf(tp_apply,type,
apply: $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_cartesian_product2,type,
cartesian_product2: $i > $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_disjoint,type,
disjoint: $i > $i > $o ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $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_fiber,type,
fiber: $i > $i > $i ).
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_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_meet_of_subsets,type,
meet_of_subsets: $i > $i > $i ).
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_proper_subset,type,
proper_subset: $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_sK10_D,type,
sK10_D: $i > $i > $i > $i ).
thf(tp_sK11_SY3094,type,
sK11_SY3094: $i > $i > $i > $i ).
thf(tp_sK12_C,type,
sK12_C: $i > $i > $i ).
thf(tp_sK13_SY3095,type,
sK13_SY3095: $i > $i > $i ).
thf(tp_sK14_C,type,
sK14_C: $i > $i > $i ).
thf(tp_sK15_SY3096,type,
sK15_SY3096: $i > $i > $i ).
thf(tp_sK16_D,type,
sK16_D: $i > $i > $i > $i ).
thf(tp_sK17_C,type,
sK17_C: $i > $i > $i ).
thf(tp_sK18_SY3098,type,
sK18_SY3098: $i > $i > $i ).
thf(tp_sK19_C,type,
sK19_C: $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_SY3099,type,
sK20_SY3099: $i > $i > $i ).
thf(tp_sK21_D,type,
sK21_D: $i > $i > $i > $i ).
thf(tp_sK22_C,type,
sK22_C: $i > $i > $i ).
thf(tp_sK23_SY3101,type,
sK23_SY3101: $i > $i > $i ).
thf(tp_sK24_C,type,
sK24_C: $i > $i > $i ).
thf(tp_sK25_SY3102,type,
sK25_SY3102: $i > $i > $i ).
thf(tp_sK26_E,type,
sK26_E: $i > $i > $i > $i > $i ).
thf(tp_sK27_SY3103,type,
sK27_SY3103: $i > $i > $i > $i > $i ).
thf(tp_sK28_D,type,
sK28_D: $i > $i > $i > $i ).
thf(tp_sK29_SY3106,type,
sK29_SY3106: $i > $i > $i > $i ).
thf(tp_sK2_SY3085,type,
sK2_SY3085: $i ).
thf(tp_sK30_SY3108,type,
sK30_SY3108: $i > $i > $i > $i ).
thf(tp_sK31_C,type,
sK31_C: $i > $i > $i ).
thf(tp_sK32_SY3109,type,
sK32_SY3109: $i > $i > $i ).
thf(tp_sK33_C,type,
sK33_C: $i > $i > $i ).
thf(tp_sK34_SY3110,type,
sK34_SY3110: $i > $i > $i ).
thf(tp_sK35_D,type,
sK35_D: $i > $i > $i > $i ).
thf(tp_sK36_C,type,
sK36_C: $i > $i > $i ).
thf(tp_sK37_C,type,
sK37_C: $i > $i > $i ).
thf(tp_sK38_SY3111,type,
sK38_SY3111: $i > $i > $i ).
thf(tp_sK39_B,type,
sK39_B: $i > $i ).
thf(tp_sK3_C,type,
sK3_C: $i > $i > $i ).
thf(tp_sK40_C,type,
sK40_C: $i > $i > $i ).
thf(tp_sK41_SY3114,type,
sK41_SY3114: $i > $i > $i ).
thf(tp_sK42_E,type,
sK42_E: $i > $i > $i > $i > $i ).
thf(tp_sK43_D,type,
sK43_D: $i > $i > $i > $i ).
thf(tp_sK44_SY3116,type,
sK44_SY3116: $i > $i > $i > $i ).
thf(tp_sK45_E,type,
sK45_E: $i > $i > $i > $i > $i ).
thf(tp_sK46_D,type,
sK46_D: $i > $i > $i > $i ).
thf(tp_sK47_SY3118,type,
sK47_SY3118: $i > $i > $i > $i ).
thf(tp_sK48_D,type,
sK48_D: $i > $i > $i > $i ).
thf(tp_sK49_SY3119,type,
sK49_SY3119: $i > $i > $i > $i ).
thf(tp_sK4_SY3086,type,
sK4_SY3086: $i > $i > $i ).
thf(tp_sK50_D,type,
sK50_D: $i > $i > $i > $i ).
thf(tp_sK51_SY3120,type,
sK51_SY3120: $i > $i > $i > $i ).
thf(tp_sK52_C,type,
sK52_C: $i > $i > $i ).
thf(tp_sK53_SY3121,type,
sK53_SY3121: $i > $i > $i ).
thf(tp_sK54_B,type,
sK54_B: $i > $i ).
thf(tp_sK55_SY3122,type,
sK55_SY3122: $i > $i ).
thf(tp_sK56_E,type,
sK56_E: $i > $i > $i > $i > $i ).
thf(tp_sK57_D,type,
sK57_D: $i > $i > $i > $i ).
thf(tp_sK58_E,type,
sK58_E: $i > $i > $i > $i > $i ).
thf(tp_sK59_D,type,
sK59_D: $i > $i > $i > $i ).
thf(tp_sK5_SY3088,type,
sK5_SY3088: $i > $i > $i ).
thf(tp_sK60_D,type,
sK60_D: $i > $i > $i > $i ).
thf(tp_sK61_D,type,
sK61_D: $i > $i > $i > $i ).
thf(tp_sK62_B,type,
sK62_B: $i > $i ).
thf(tp_sK63_SY3125,type,
sK63_SY3125: $i > $i ).
thf(tp_sK64_B,type,
sK64_B: $i > $i ).
thf(tp_sK65_SY3126,type,
sK65_SY3126: $i > $i ).
thf(tp_sK66_B,type,
sK66_B: $i > $i ).
thf(tp_sK67_SY3127,type,
sK67_SY3127: $i > $i ).
thf(tp_sK68_SY3129,type,
sK68_SY3129: $i > $i ).
thf(tp_sK69_B,type,
sK69_B: $i > $i ).
thf(tp_sK6_F,type,
sK6_F: $i > $i > $i > $i > $i > $i ).
thf(tp_sK7_D,type,
sK7_D: $i > $i > $i > $i ).
thf(tp_sK8_SY3089,type,
sK8_SY3089: $i > $i > $i > $i ).
thf(tp_sK9_SY3093,type,
sK9_SY3093: $i > $i > $i > $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_succ,type,
succ: $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_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(66,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(123,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( is_transitive_in @ A @ B )
<=> ! [C: $i,D: $i,E: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B )
& ( in @ E @ B )
& ( in @ ( ordered_pair @ C @ D ) @ A )
& ( in @ ( ordered_pair @ D @ E ) @ A ) )
=> ( in @ ( ordered_pair @ C @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_2) ).
thf(124,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_composition @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_1) ).
thf(127,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( relation_isomorphism @ A @ B @ C )
<=> ( ( ( relation_dom @ C )
= ( relation_field @ A ) )
& ( ( relation_rng @ C )
= ( relation_field @ B ) )
& ( one_to_one @ C )
& ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ A )
<=> ( ( in @ D @ ( relation_field @ A ) )
& ( in @ E @ ( relation_field @ A ) )
& ( in @ ( ordered_pair @ ( apply @ C @ D ) @ ( apply @ C @ E ) ) @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_wellord1) ).
thf(128,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( B
= ( relation_inverse @ A ) )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ B )
<=> ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_relat_1) ).
thf(130,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( is_connected_in @ A @ B )
<=> ! [C: $i,D: $i] :
~ ( ( in @ C @ B )
& ( in @ D @ B )
& ( C != D )
& ~ ( in @ ( ordered_pair @ C @ D ) @ A )
& ~ ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_2) ).
thf(134,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(136,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
thf(142,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( is_antisymmetric_in @ A @ B )
<=> ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B )
& ( in @ ( ordered_pair @ C @ D ) @ A )
& ( in @ ( ordered_pair @ D @ C ) @ A ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_2) ).
thf(143,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
thf(145,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( ( in @ B @ ( relation_dom @ A ) )
=> ( ( C
= ( apply @ A @ B ) )
<=> ( in @ ( ordered_pair @ B @ C ) @ A ) ) )
& ( ~ ( in @ B @ ( relation_dom @ A ) )
=> ( ( C
= ( apply @ A @ B ) )
<=> ( C = empty_set ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
thf(149,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(151,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(156,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(158,axiom,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( ordered_pair @ B @ C ) )
=> ! [B: $i] :
( ( B
= ( pair_second @ A ) )
<=> ! [C: $i,D: $i] :
( ( A
= ( ordered_pair @ C @ D ) )
=> ( B = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_mcart_1) ).
thf(161,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( fiber @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D != B )
& ( in @ ( ordered_pair @ D @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_wellord1) ).
thf(165,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( is_reflexive_in @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( ordered_pair @ C @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_2) ).
thf(166,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(168,axiom,
! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( ordered_pair @ B @ C ) )
=> ! [B: $i] :
( ( B
= ( pair_first @ A ) )
<=> ! [C: $i,D: $i] :
( ( A
= ( ordered_pair @ C @ D ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_mcart_1) ).
thf(172,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_inverse_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ A )
& ( in @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_1) ).
thf(173,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ ( ordered_pair @ E @ D ) @ A )
& ( in @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
thf(176,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_rng_restriction @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_1) ).
thf(178,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_dom_restriction @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ( ( in @ D @ B )
& ( in @ ( ordered_pair @ D @ E ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_relat_1) ).
thf(180,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( B
= ( identity_relation @ A ) )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ B )
<=> ( ( in @ C @ A )
& ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_relat_1) ).
thf(203,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ ( relation_dom @ C ) )
& ( B
= ( apply @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_1) ).
thf(208,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( relation @ D )
=> ( ( in @ ( ordered_pair @ A @ B ) @ ( relation_composition @ ( identity_relation @ C ) @ D ) )
<=> ( ( in @ A @ C )
& ( in @ ( ordered_pair @ A @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_relat_1) ).
thf(224,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(260,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(267,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_field @ C ) )
& ( in @ B @ ( relation_field @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relat_1) ).
thf(276,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(280,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(287,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ B @ ( relation_rng @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).
thf(300,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_inverse_image @ C @ B ) )
<=> ? [D: $i] :
( ( in @ D @ ( relation_rng @ C ) )
& ( in @ ( ordered_pair @ A @ D ) @ C )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t166_relat_1) ).
thf(309,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_image @ C @ B ) )
<=> ? [D: $i] :
( ( in @ D @ ( relation_dom @ C ) )
& ( in @ ( ordered_pair @ D @ A ) @ C )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_relat_1) ).
thf(323,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(326,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(329,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( connected @ A )
<=> ! [B: $i,C: $i] :
~ ( ( in @ B @ ( relation_field @ A ) )
& ( in @ C @ ( relation_field @ A ) )
& ( B != C )
& ~ ( in @ ( ordered_pair @ B @ C ) @ A )
& ~ ( in @ ( ordered_pair @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_wellord1) ).
thf(331,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( antisymmetric @ A )
<=> ! [B: $i,C: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ C @ B ) @ A ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_wellord1) ).
thf(335,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( transitive @ A )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ C @ D ) @ A ) )
=> ( in @ ( ordered_pair @ B @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_wellord1) ).
thf(341,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( reflexive @ A )
<=> ! [B: $i] :
( ( in @ B @ ( relation_field @ A ) )
=> ( in @ ( ordered_pair @ B @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_wellord1) ).
thf(342,conjecture,
! [A: $i,B: $i] :
( ( ( pair_first @ ( ordered_pair @ A @ B ) )
= A )
& ( ( pair_second @ ( ordered_pair @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_mcart_1) ).
thf(343,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( ( pair_first @ ( ordered_pair @ A @ B ) )
= A )
& ( ( pair_second @ ( ordered_pair @ A @ B ) )
= B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[342]) ).
thf(344,plain,
( ( ! [A: $i,B: $i] :
( ( ( pair_first @ ( ordered_pair @ A @ B ) )
= A )
& ( ( pair_second @ ( ordered_pair @ A @ B ) )
= B ) ) )
= $false ),
inference(unfold_def,[status(thm)],[343]) ).
thf(345,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(346,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( is_transitive_in @ A @ B )
<=> ! [C: $i,D: $i,E: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B )
& ( in @ E @ B )
& ( in @ ( ordered_pair @ C @ D ) @ A )
& ( in @ ( ordered_pair @ D @ E ) @ A ) )
=> ( in @ ( ordered_pair @ C @ E ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(347,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_composition @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(348,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( relation_isomorphism @ A @ B @ C )
<=> ( ( ( relation_dom @ C )
= ( relation_field @ A ) )
& ( ( relation_rng @ C )
= ( relation_field @ B ) )
& ( one_to_one @ C )
& ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ A )
<=> ( ( in @ D @ ( relation_field @ A ) )
& ( in @ E @ ( relation_field @ A ) )
& ( in @ ( ordered_pair @ ( apply @ C @ D ) @ ( apply @ C @ E ) ) @ B ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(349,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( B
= ( relation_inverse @ A ) )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ B )
<=> ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(350,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( is_connected_in @ A @ B )
<=> ! [C: $i,D: $i] :
~ ( ( in @ C @ B )
& ( in @ D @ B )
& ( C != D )
& ~ ( in @ ( ordered_pair @ C @ D ) @ A )
& ~ ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(351,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(352,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(353,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( is_antisymmetric_in @ A @ B )
<=> ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B )
& ( in @ ( ordered_pair @ C @ D ) @ A )
& ( in @ ( ordered_pair @ D @ C ) @ A ) )
=> ( C = D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(354,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(355,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( ( in @ B @ ( relation_dom @ A ) )
=> ( ( C
= ( apply @ A @ B ) )
<=> ( in @ ( ordered_pair @ B @ C ) @ A ) ) )
& ( ~ ( in @ B @ ( relation_dom @ A ) )
=> ( ( C
= ( apply @ A @ B ) )
<=> ( C = empty_set ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(356,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)],[149]) ).
thf(357,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)],[151]) ).
thf(358,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)],[156]) ).
thf(359,plain,
( ( ! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( ordered_pair @ B @ C ) )
=> ! [B: $i] :
( ( B
= ( pair_second @ A ) )
<=> ! [C: $i,D: $i] :
( ( A
= ( ordered_pair @ C @ D ) )
=> ( B = D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(360,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( fiber @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D != B )
& ( in @ ( ordered_pair @ D @ B ) @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(361,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( is_reflexive_in @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( ordered_pair @ C @ C ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(362,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)],[166]) ).
thf(363,plain,
( ( ! [A: $i] :
( ? [B: $i,C: $i] :
( A
= ( ordered_pair @ B @ C ) )
=> ! [B: $i] :
( ( B
= ( pair_first @ A ) )
<=> ! [C: $i,D: $i] :
( ( A
= ( ordered_pair @ C @ D ) )
=> ( B = C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(364,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_inverse_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ A )
& ( in @ E @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(365,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ ( ordered_pair @ E @ D ) @ A )
& ( in @ E @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(366,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_rng_restriction @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(367,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i,C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_dom_restriction @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ( ( in @ D @ B )
& ( in @ ( ordered_pair @ D @ E ) @ A ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(368,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( B
= ( identity_relation @ A ) )
<=> ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ B )
<=> ( ( in @ C @ A )
& ( C = D ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(369,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ ( relation_dom @ C ) )
& ( B
= ( apply @ C @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(370,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( relation @ D )
=> ( ( in @ ( ordered_pair @ A @ B ) @ ( relation_composition @ ( identity_relation @ C ) @ D ) )
<=> ( ( in @ A @ C )
& ( in @ ( ordered_pair @ A @ B ) @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(371,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i,C: $i] :
~ ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( A = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(372,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(373,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_field @ C ) )
& ( in @ B @ ( relation_field @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(374,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)],[276]) ).
thf(375,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)],[280]) ).
thf(376,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ B @ ( relation_rng @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(377,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_inverse_image @ C @ B ) )
<=> ? [D: $i] :
( ( in @ D @ ( relation_rng @ C ) )
& ( in @ ( ordered_pair @ A @ D ) @ C )
& ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(378,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_image @ C @ B ) )
<=> ? [D: $i] :
( ( in @ D @ ( relation_dom @ C ) )
& ( in @ ( ordered_pair @ D @ A ) @ C )
& ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(379,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)],[323]) ).
thf(380,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)],[326]) ).
thf(381,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( connected @ A )
<=> ! [B: $i,C: $i] :
~ ( ( in @ B @ ( relation_field @ A ) )
& ( in @ C @ ( relation_field @ A ) )
& ( B != C )
& ~ ( in @ ( ordered_pair @ B @ C ) @ A )
& ~ ( in @ ( ordered_pair @ C @ B ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(382,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( antisymmetric @ A )
<=> ! [B: $i,C: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ C @ B ) @ A ) )
=> ( B = C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(383,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( transitive @ A )
<=> ! [B: $i,C: $i,D: $i] :
( ( ( in @ ( ordered_pair @ B @ C ) @ A )
& ( in @ ( ordered_pair @ C @ D ) @ A ) )
=> ( in @ ( ordered_pair @ B @ D ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(384,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( reflexive @ A )
<=> ! [B: $i] :
( ( in @ B @ ( relation_field @ A ) )
=> ( in @ ( ordered_pair @ B @ B ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(385,plain,
( ( ! [SY3085: $i] :
( ( ( pair_first @ ( ordered_pair @ sK1_A @ SY3085 ) )
= sK1_A )
& ( ( pair_second @ ( ordered_pair @ sK1_A @ SY3085 ) )
= SY3085 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[344]) ).
thf(386,plain,
( ( ( ( pair_first @ ( ordered_pair @ sK1_A @ sK2_SY3085 ) )
= sK1_A )
& ( ( pair_second @ ( ordered_pair @ sK1_A @ sK2_SY3085 ) )
= sK2_SY3085 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[385]) ).
thf(387,plain,
( ( ( pair_first @ ( ordered_pair @ sK1_A @ sK2_SY3085 ) )
= sK1_A )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[386]) ).
thf(388,plain,
( ( ( pair_second @ ( ordered_pair @ sK1_A @ sK2_SY3085 ) )
= sK2_SY3085 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[386]) ).
thf(389,plain,
( ( ( ( pair_first @ ( ordered_pair @ sK1_A @ sK2_SY3085 ) )
!= sK1_A ) )
= $true ),
inference(polarity_switch,[status(thm)],[387]) ).
thf(390,plain,
( ( ( ( pair_second @ ( ordered_pair @ sK1_A @ sK2_SY3085 ) )
!= sK2_SY3085 ) )
= $true ),
inference(polarity_switch,[status(thm)],[388]) ).
thf(391,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK3_C @ B @ A ) @ B )
& ( in @ ( sK4_SY3086 @ B @ A ) @ B )
& ( in @ ( sK5_SY3088 @ B @ A ) @ B )
& ( in @ ( ordered_pair @ ( sK3_C @ B @ A ) @ ( sK4_SY3086 @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK4_SY3086 @ B @ A ) @ ( sK5_SY3088 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK3_C @ B @ A ) @ ( sK5_SY3088 @ B @ A ) ) @ A ) )
| ( is_transitive_in @ A @ B ) )
& ! [B: $i] :
( ~ ( is_transitive_in @ A @ B )
| ! [C: $i,D: $i,E: $i] :
( ~ ( in @ C @ B )
| ~ ( in @ D @ B )
| ~ ( in @ E @ B )
| ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ( in @ ( ordered_pair @ C @ E ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[346]) ).
thf(392,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ! [SY3092: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ C @ B @ A ) @ SY3092 ) @ A )
| ~ ( in @ ( ordered_pair @ SY3092 @ ( sK8_SY3089 @ C @ B @ A ) ) @ B ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ C @ B @ A ) @ ( sK8_SY3089 @ C @ B @ A ) ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK7_D @ C @ B @ A ) @ ( sK9_SY3093 @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK9_SY3093 @ C @ B @ A ) @ ( sK8_SY3089 @ C @ B @ A ) ) @ B ) )
| ( in @ ( ordered_pair @ ( sK7_D @ C @ B @ A ) @ ( sK8_SY3089 @ C @ B @ A ) ) @ C ) ) )
| ( C
= ( relation_composition @ A @ B ) ) )
& ! [C: $i] :
( ~ ( relation @ C )
| ( C
!= ( relation_composition @ A @ B ) )
| ( ! [D: $i,E: $i] :
( ! [F: $i] :
( ~ ( in @ ( ordered_pair @ D @ F ) @ A )
| ~ ( in @ ( ordered_pair @ F @ E ) @ B ) )
| ( in @ ( ordered_pair @ D @ E ) @ C ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( ( in @ ( ordered_pair @ D @ ( sK6_F @ E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK6_F @ E @ D @ C @ B @ A ) @ E ) @ B ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[347]) ).
thf(393,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ( ( ~ ( in @ ( sK10_D @ C @ B @ A ) @ ( relation_field @ A ) )
| ~ ( in @ ( sK11_SY3094 @ C @ B @ A ) @ ( relation_field @ A ) )
| ~ ( in @ ( ordered_pair @ ( apply @ C @ ( sK10_D @ C @ B @ A ) ) @ ( apply @ C @ ( sK11_SY3094 @ C @ B @ A ) ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ ( sK11_SY3094 @ C @ B @ A ) ) @ A ) )
& ( ( in @ ( sK10_D @ C @ B @ A ) @ ( relation_field @ A ) )
| ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ ( sK11_SY3094 @ C @ B @ A ) ) @ A ) )
& ( ( in @ ( sK11_SY3094 @ C @ B @ A ) @ ( relation_field @ A ) )
| ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ ( sK11_SY3094 @ C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( apply @ C @ ( sK10_D @ C @ B @ A ) ) @ ( apply @ C @ ( sK11_SY3094 @ C @ B @ A ) ) ) @ B )
| ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ ( sK11_SY3094 @ C @ B @ A ) ) @ A ) ) )
| ( ( relation_dom @ C )
!= ( relation_field @ A ) )
| ( ( relation_rng @ C )
!= ( relation_field @ B ) )
| ~ ( one_to_one @ C )
| ( relation_isomorphism @ A @ B @ C ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ( ! [D: $i,E: $i] :
( ~ ( in @ D @ ( relation_field @ A ) )
| ~ ( in @ E @ ( relation_field @ A ) )
| ~ ( in @ ( ordered_pair @ ( apply @ C @ D ) @ ( apply @ C @ E ) ) @ B )
| ( in @ ( ordered_pair @ D @ E ) @ A ) )
& ! [D: $i] :
( ! [E: $i] :
~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ( in @ D @ ( relation_field @ A ) ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ( in @ E @ ( relation_field @ A ) ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ( in @ ( ordered_pair @ ( apply @ C @ D ) @ ( apply @ C @ E ) ) @ B ) ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ( ( relation_dom @ C )
= ( relation_field @ A ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ( ( relation_rng @ C )
= ( relation_field @ B ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ( one_to_one @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[348]) ).
thf(394,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK12_C @ B @ A ) @ ( sK13_SY3095 @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ B @ A ) @ ( sK12_C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( sK12_C @ B @ A ) @ ( sK13_SY3095 @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ B @ A ) @ ( sK12_C @ B @ A ) ) @ A ) ) )
| ( B
= ( relation_inverse @ A ) ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ( B
!= ( relation_inverse @ A ) )
| ( ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ B )
| ( in @ ( ordered_pair @ D @ C ) @ A ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ D @ C ) @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[349]) ).
thf(395,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ( sK14_C @ B @ A )
!= ( sK15_SY3096 @ B @ A ) )
& ( in @ ( sK14_C @ B @ A ) @ B )
& ( in @ ( sK15_SY3096 @ B @ A ) @ B )
& ~ ( in @ ( ordered_pair @ ( sK14_C @ B @ A ) @ ( sK15_SY3096 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK15_SY3096 @ B @ A ) @ ( sK14_C @ B @ A ) ) @ A ) )
| ( is_connected_in @ A @ B ) )
& ! [B: $i] :
( ~ ( is_connected_in @ A @ B )
| ! [C: $i,D: $i] :
( ( C = D )
| ~ ( in @ C @ B )
| ~ ( in @ D @ B )
| ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[350]) ).
thf(396,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY3097: $i] :
~ ( in @ ( ordered_pair @ SY3097 @ ( sK17_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK17_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK18_SY3098 @ B @ A ) @ ( sK17_C @ B @ A ) ) @ A )
| ( in @ ( sK17_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_rng @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_rng @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ D @ C ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ ( sK16_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[352]) ).
thf(397,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK19_C @ B @ A ) @ B )
& ( in @ ( sK20_SY3099 @ B @ A ) @ B )
& ( in @ ( ordered_pair @ ( sK19_C @ B @ A ) @ ( sK20_SY3099 @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK20_SY3099 @ B @ A ) @ ( sK19_C @ B @ A ) ) @ A )
& ( ( sK19_C @ B @ A )
!= ( sK20_SY3099 @ B @ A ) ) )
| ( is_antisymmetric_in @ A @ B ) )
& ! [B: $i] :
( ~ ( is_antisymmetric_in @ A @ B )
| ! [C: $i,D: $i] :
( ~ ( in @ C @ B )
| ~ ( in @ D @ B )
| ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ~ ( in @ ( ordered_pair @ D @ C ) @ A )
| ( C = D ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[353]) ).
thf(398,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY3100: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ B @ A ) @ SY3100 ) @ A )
| ~ ( in @ ( sK22_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK22_C @ B @ A ) @ ( sK23_SY3101 @ B @ A ) ) @ A )
| ( in @ ( sK22_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_dom @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_dom @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ C @ ( sK21_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[354]) ).
thf(399,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C
!= ( apply @ A @ B ) )
| ( in @ ( ordered_pair @ B @ C ) @ A ) ) )
& ! [B: $i] :
( ~ ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ~ ( in @ ( ordered_pair @ B @ C ) @ A )
| ( C
= ( apply @ A @ B ) ) ) )
& ! [B: $i] :
( ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C
!= ( apply @ A @ B ) )
| ( C = empty_set ) ) )
& ! [B: $i] :
( ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C != empty_set )
| ( C
= ( apply @ A @ B ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[355]) ).
thf(400,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( in @ ( ordered_pair @ ( sK24_C @ B @ A ) @ ( sK25_SY3102 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK24_C @ B @ A ) @ ( sK25_SY3102 @ 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)],[356]) ).
thf(401,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY3104: $i,SY3105: $i] :
( ~ ( in @ SY3104 @ A )
| ~ ( in @ SY3105 @ B )
| ( ( sK28_D @ C @ B @ A )
!= ( ordered_pair @ SY3104 @ SY3105 ) ) )
| ~ ( in @ ( sK28_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK29_SY3106 @ C @ B @ A ) @ A )
& ( in @ ( sK30_SY3108 @ C @ B @ A ) @ B )
& ( ( sK28_D @ C @ B @ A )
= ( ordered_pair @ ( sK29_SY3106 @ C @ B @ A ) @ ( sK30_SY3108 @ C @ B @ A ) ) ) )
| ( in @ ( sK28_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 @ ( sK26_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK27_SY3103 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK26_E @ D @ C @ B @ A ) @ ( sK27_SY3103 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[357]) ).
thf(402,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK31_C @ B @ A ) @ ( sK32_SY3109 @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ B @ A ) @ ( sK32_SY3109 @ B @ A ) ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK31_C @ B @ A ) @ ( sK32_SY3109 @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK31_C @ B @ A ) @ ( sK32_SY3109 @ 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)],[358]) ).
thf(403,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( A
!= ( ordered_pair @ B @ C ) )
| ( ! [B: $i] :
( ( ( A
= ( ordered_pair @ ( sK33_C @ B @ A ) @ ( sK34_SY3110 @ B @ A ) ) )
& ( B
!= ( sK34_SY3110 @ B @ A ) ) )
| ( B
= ( pair_second @ A ) ) )
& ! [B: $i] :
( ( B
!= ( pair_second @ A ) )
| ! [C: $i,D: $i] :
( ( A
!= ( ordered_pair @ C @ D ) )
| ( B = D ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[359]) ).
thf(404,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ( ( sK35_D @ C @ B @ A )
= B )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ C @ B @ A ) @ B ) @ A )
| ~ ( in @ ( sK35_D @ C @ B @ A ) @ C ) )
& ( ( ( sK35_D @ C @ B @ A )
!= B )
| ( in @ ( sK35_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK35_D @ C @ B @ A ) @ B ) @ A )
| ( in @ ( sK35_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( fiber @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( fiber @ A @ B ) )
| ( ! [D: $i] :
( ( D = B )
| ~ ( in @ ( ordered_pair @ D @ B ) @ A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( D != B ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ ( ordered_pair @ D @ B ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[360]) ).
thf(405,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK36_C @ B @ A ) @ B )
& ~ ( in @ ( ordered_pair @ ( sK36_C @ B @ A ) @ ( sK36_C @ B @ A ) ) @ A ) )
| ( is_reflexive_in @ A @ B ) )
& ! [B: $i] :
( ~ ( is_reflexive_in @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ C @ C ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[361]) ).
thf(406,plain,
( ( ! [A: $i] :
( ( ! [SY3112: $i,SY3113: $i] :
( ( sK39_B @ A )
!= ( ordered_pair @ SY3112 @ SY3113 ) )
& ( in @ ( sK39_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK37_C @ B @ A ) @ ( sK38_SY3111 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[362]) ).
thf(407,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( A
!= ( ordered_pair @ B @ C ) )
| ( ! [B: $i] :
( ( ( A
= ( ordered_pair @ ( sK40_C @ B @ A ) @ ( sK41_SY3114 @ B @ A ) ) )
& ( B
!= ( sK40_C @ B @ A ) ) )
| ( B
= ( pair_first @ A ) ) )
& ! [B: $i] :
( ( B
!= ( pair_first @ A ) )
| ! [C: $i] :
( ! [D: $i] :
( A
!= ( ordered_pair @ C @ D ) )
| ( B = C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[363]) ).
thf(408,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY3115: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ C @ B @ A ) @ SY3115 ) @ A )
| ~ ( in @ SY3115 @ B ) )
| ~ ( in @ ( sK43_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK43_D @ C @ B @ A ) @ ( sK44_SY3116 @ C @ B @ A ) ) @ A )
& ( in @ ( sK44_SY3116 @ C @ B @ A ) @ B ) )
| ( in @ ( sK43_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( relation_inverse_image @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( relation_inverse_image @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ~ ( in @ E @ B ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( ordered_pair @ D @ ( sK42_E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( sK42_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[364]) ).
thf(409,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY3117: $i] :
( ~ ( in @ ( ordered_pair @ SY3117 @ ( sK46_D @ C @ B @ A ) ) @ A )
| ~ ( in @ SY3117 @ B ) )
| ~ ( in @ ( sK46_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK47_SY3118 @ C @ B @ A ) @ ( sK46_D @ C @ B @ A ) ) @ A )
& ( in @ ( sK47_SY3118 @ C @ B @ A ) @ B ) )
| ( in @ ( sK46_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( relation_image @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( relation_image @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i] :
( ~ ( in @ ( ordered_pair @ E @ D ) @ A )
| ~ ( in @ E @ B ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( ordered_pair @ ( sK45_E @ D @ C @ B @ A ) @ D ) @ A )
& ( in @ ( sK45_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[365]) ).
thf(410,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK49_SY3119 @ C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ C @ B @ A ) @ ( sK49_SY3119 @ C @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ C @ B @ A ) @ ( sK49_SY3119 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK49_SY3119 @ C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK48_D @ C @ B @ A ) @ ( sK49_SY3119 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK48_D @ C @ B @ A ) @ ( sK49_SY3119 @ C @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK48_D @ C @ B @ A ) @ ( sK49_SY3119 @ C @ B @ A ) ) @ C ) ) )
| ( C
= ( relation_rng_restriction @ A @ B ) ) )
& ! [C: $i] :
( ~ ( relation @ C )
| ( C
!= ( relation_rng_restriction @ A @ B ) )
| ( ! [D: $i,E: $i] :
( ~ ( in @ E @ A )
| ~ ( in @ ( ordered_pair @ D @ E ) @ B )
| ( in @ ( ordered_pair @ D @ E ) @ C ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ E @ A ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ ( ordered_pair @ D @ E ) @ B ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[366]) ).
thf(411,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK50_D @ C @ B @ A ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ C @ B @ A ) @ ( sK51_SY3120 @ C @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ C @ B @ A ) @ ( sK51_SY3120 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK50_D @ C @ B @ A ) @ B )
| ( in @ ( ordered_pair @ ( sK50_D @ C @ B @ A ) @ ( sK51_SY3120 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK50_D @ C @ B @ A ) @ ( sK51_SY3120 @ C @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK50_D @ C @ B @ A ) @ ( sK51_SY3120 @ C @ B @ A ) ) @ C ) ) )
| ( C
= ( relation_dom_restriction @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ( C
!= ( relation_dom_restriction @ A @ B ) )
| ( ! [D: $i,E: $i] :
( ~ ( in @ D @ B )
| ~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ( in @ ( ordered_pair @ D @ E ) @ C ) )
& ! [D: $i] :
( ! [E: $i] :
~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ D @ B ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ ( ordered_pair @ D @ E ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[367]) ).
thf(412,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( ( ( sK52_C @ B @ A )
!= ( sK53_SY3121 @ B @ A ) )
| ~ ( in @ ( sK52_C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK52_C @ B @ A ) @ ( sK53_SY3121 @ B @ A ) ) @ B ) )
& ( ( ( sK52_C @ B @ A )
= ( sK53_SY3121 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK52_C @ B @ A ) @ ( sK53_SY3121 @ B @ A ) ) @ B ) )
& ( ( in @ ( sK52_C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK52_C @ B @ A ) @ ( sK53_SY3121 @ B @ A ) ) @ B ) ) )
| ( B
= ( identity_relation @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( B
!= ( identity_relation @ A ) )
| ( ! [C: $i,D: $i] :
( ( C != D )
| ~ ( in @ C @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ B )
| ( C = D ) )
& ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ C @ D ) @ B )
| ( in @ C @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[368]) ).
thf(413,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ( B
!= ( apply @ C @ A ) )
| ~ ( in @ A @ ( relation_dom @ C ) )
| ( in @ ( ordered_pair @ A @ B ) @ C ) )
& ! [B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( B
= ( apply @ C @ A ) ) )
& ! [B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ A @ ( relation_dom @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[369]) ).
thf(414,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ~ ( relation @ D )
| ~ ( in @ A @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( relation_composition @ ( identity_relation @ C ) @ D ) ) )
& ! [C: $i,D: $i] :
( ~ ( relation @ D )
| ~ ( in @ ( ordered_pair @ A @ B ) @ ( relation_composition @ ( identity_relation @ C ) @ D ) )
| ( in @ A @ C ) )
& ! [C: $i,D: $i] :
( ~ ( relation @ D )
| ~ ( in @ ( ordered_pair @ A @ B ) @ ( relation_composition @ ( identity_relation @ C ) @ D ) )
| ( in @ ( ordered_pair @ A @ B ) @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[370]) ).
thf(415,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK54_B @ A ) @ ( sK55_SY3122 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[371]) ).
thf(416,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ( ordered_pair @ A @ B )
!= ( ordered_pair @ C @ D ) )
| ( A = C ) )
& ! [C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
!= ( ordered_pair @ C @ D ) )
| ( B = D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[372]) ).
thf(417,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ A @ ( relation_field @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ B @ ( relation_field @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[373]) ).
thf(418,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( ! [SY3123: $i] :
~ ( in @ ( ordered_pair @ SY3123 @ ( sK57_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK57_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 @ ( sK56_E @ D @ C @ B @ A ) @ D ) @ C )
| ~ ( in @ D @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[374]) ).
thf(419,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ B @ A )
| ( ! [SY3124: $i] :
~ ( in @ ( ordered_pair @ ( sK59_D @ C @ B @ A ) @ SY3124 ) @ C )
& ( in @ ( sK59_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 @ ( sK58_E @ D @ C @ B @ A ) ) @ C )
| ~ ( in @ D @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[375]) ).
thf(420,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ A @ ( relation_dom @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ B @ ( relation_rng @ C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[376]) ).
thf(421,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ! [D: $i] :
( ~ ( in @ D @ ( relation_rng @ C ) )
| ~ ( in @ ( ordered_pair @ A @ D ) @ C )
| ~ ( in @ D @ B ) )
| ( in @ A @ ( relation_inverse_image @ C @ B ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_inverse_image @ C @ B ) )
| ( ( in @ ( sK60_D @ C @ B @ A ) @ ( relation_rng @ C ) )
& ( in @ ( ordered_pair @ A @ ( sK60_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK60_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[377]) ).
thf(422,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ! [D: $i] :
( ~ ( in @ D @ ( relation_dom @ C ) )
| ~ ( in @ ( ordered_pair @ D @ A ) @ C )
| ~ ( in @ D @ B ) )
| ( in @ A @ ( relation_image @ C @ B ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_image @ C @ B ) )
| ( ( in @ ( sK61_D @ C @ B @ A ) @ ( relation_dom @ C ) )
& ( in @ ( ordered_pair @ ( sK61_D @ C @ B @ A ) @ A ) @ C )
& ( in @ ( sK61_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[378]) ).
thf(423,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)],[379]) ).
thf(424,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)],[380]) ).
thf(425,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( ( sK62_B @ A )
!= ( sK63_SY3125 @ A ) )
& ( in @ ( sK62_B @ A ) @ ( relation_field @ A ) )
& ( in @ ( sK63_SY3125 @ A ) @ ( relation_field @ A ) )
& ~ ( in @ ( ordered_pair @ ( sK62_B @ A ) @ ( sK63_SY3125 @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK63_SY3125 @ A ) @ ( sK62_B @ A ) ) @ A ) )
| ( connected @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( connected @ A )
| ! [B: $i,C: $i] :
( ( B = C )
| ~ ( in @ B @ ( relation_field @ A ) )
| ~ ( in @ C @ ( relation_field @ A ) )
| ( in @ ( ordered_pair @ B @ C ) @ A )
| ( in @ ( ordered_pair @ C @ B ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[381]) ).
thf(426,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( ordered_pair @ ( sK64_B @ A ) @ ( sK65_SY3126 @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK65_SY3126 @ A ) @ ( sK64_B @ A ) ) @ A )
& ( ( sK64_B @ A )
!= ( sK65_SY3126 @ A ) ) )
| ( antisymmetric @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( antisymmetric @ A )
| ! [B: $i,C: $i] :
( ~ ( in @ ( ordered_pair @ B @ C ) @ A )
| ~ ( in @ ( ordered_pair @ C @ B ) @ A )
| ( B = C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[382]) ).
thf(427,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( ordered_pair @ ( sK66_B @ A ) @ ( sK67_SY3127 @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK67_SY3127 @ A ) @ ( sK68_SY3129 @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK66_B @ A ) @ ( sK68_SY3129 @ A ) ) @ A ) )
| ( transitive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( transitive @ A )
| ! [B: $i,C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ B @ C ) @ A )
| ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ ( ordered_pair @ B @ D ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[383]) ).
thf(428,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( sK69_B @ A ) @ ( relation_field @ A ) )
& ~ ( in @ ( ordered_pair @ ( sK69_B @ A ) @ ( sK69_B @ A ) ) @ A ) )
| ( reflexive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( reflexive @ A )
| ! [B: $i] :
( ~ ( in @ B @ ( relation_field @ A ) )
| ( in @ ( ordered_pair @ B @ B ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[384]) ).
thf(429,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( sK69_B @ A ) @ ( relation_field @ A ) )
& ~ ( in @ ( ordered_pair @ ( sK69_B @ A ) @ ( sK69_B @ A ) ) @ A ) )
| ( reflexive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( reflexive @ A )
| ! [B: $i] :
( ~ ( in @ B @ ( relation_field @ A ) )
| ( in @ ( ordered_pair @ B @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[428]) ).
thf(430,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( ordered_pair @ ( sK66_B @ A ) @ ( sK67_SY3127 @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK67_SY3127 @ A ) @ ( sK68_SY3129 @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK66_B @ A ) @ ( sK68_SY3129 @ A ) ) @ A ) )
| ( transitive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( transitive @ A )
| ! [B: $i,C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ B @ C ) @ A )
| ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ ( ordered_pair @ B @ D ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[427]) ).
thf(431,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( ordered_pair @ ( sK64_B @ A ) @ ( sK65_SY3126 @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK65_SY3126 @ A ) @ ( sK64_B @ A ) ) @ A )
& ( ( sK64_B @ A )
!= ( sK65_SY3126 @ A ) ) )
| ( antisymmetric @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( antisymmetric @ A )
| ! [B: $i,C: $i] :
( ~ ( in @ ( ordered_pair @ B @ C ) @ A )
| ~ ( in @ ( ordered_pair @ C @ B ) @ A )
| ( B = C ) ) ) )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(432,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( ( sK62_B @ A )
!= ( sK63_SY3125 @ A ) )
& ( in @ ( sK62_B @ A ) @ ( relation_field @ A ) )
& ( in @ ( sK63_SY3125 @ A ) @ ( relation_field @ A ) )
& ~ ( in @ ( ordered_pair @ ( sK62_B @ A ) @ ( sK63_SY3125 @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK63_SY3125 @ A ) @ ( sK62_B @ A ) ) @ A ) )
| ( connected @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( connected @ A )
| ! [B: $i,C: $i] :
( ( B = C )
| ~ ( in @ B @ ( relation_field @ A ) )
| ~ ( in @ C @ ( relation_field @ A ) )
| ( in @ ( ordered_pair @ B @ C ) @ A )
| ( in @ ( ordered_pair @ C @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[425]) ).
thf(433,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)],[424]) ).
thf(434,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)],[423]) ).
thf(435,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ! [D: $i] :
( ~ ( in @ D @ ( relation_dom @ C ) )
| ~ ( in @ ( ordered_pair @ D @ A ) @ C )
| ~ ( in @ D @ B ) )
| ( in @ A @ ( relation_image @ C @ B ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_image @ C @ B ) )
| ( ( in @ ( sK61_D @ C @ B @ A ) @ ( relation_dom @ C ) )
& ( in @ ( ordered_pair @ ( sK61_D @ C @ B @ A ) @ A ) @ C )
& ( in @ ( sK61_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(436,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ! [D: $i] :
( ~ ( in @ D @ ( relation_rng @ C ) )
| ~ ( in @ ( ordered_pair @ A @ D ) @ C )
| ~ ( in @ D @ B ) )
| ( in @ A @ ( relation_inverse_image @ C @ B ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_inverse_image @ C @ B ) )
| ( ( in @ ( sK60_D @ C @ B @ A ) @ ( relation_rng @ C ) )
& ( in @ ( ordered_pair @ A @ ( sK60_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK60_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(437,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ A @ ( relation_dom @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ B @ ( relation_rng @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(438,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ B @ A )
| ( ! [SY3124: $i] :
~ ( in @ ( ordered_pair @ ( sK59_D @ C @ B @ A ) @ SY3124 ) @ C )
& ( in @ ( sK59_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 @ ( sK58_E @ D @ C @ B @ A ) ) @ C )
| ~ ( in @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(439,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( ! [SY3123: $i] :
~ ( in @ ( ordered_pair @ SY3123 @ ( sK57_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK57_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 @ ( sK56_E @ D @ C @ B @ A ) @ D ) @ C )
| ~ ( in @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[418]) ).
thf(440,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ A @ ( relation_field @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ B @ ( relation_field @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(441,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ( ordered_pair @ A @ B )
!= ( ordered_pair @ C @ D ) )
| ( A = C ) )
& ! [C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
!= ( ordered_pair @ C @ D ) )
| ( B = D ) ) ) )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(442,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK54_B @ A ) @ ( sK55_SY3122 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(443,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ~ ( relation @ D )
| ~ ( in @ A @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( relation_composition @ ( identity_relation @ C ) @ D ) ) )
& ! [C: $i,D: $i] :
( ~ ( relation @ D )
| ~ ( in @ ( ordered_pair @ A @ B ) @ ( relation_composition @ ( identity_relation @ C ) @ D ) )
| ( in @ A @ C ) )
& ! [C: $i,D: $i] :
( ~ ( relation @ D )
| ~ ( in @ ( ordered_pair @ A @ B ) @ ( relation_composition @ ( identity_relation @ C ) @ D ) )
| ( in @ ( ordered_pair @ A @ B ) @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[414]) ).
thf(444,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ( B
!= ( apply @ C @ A ) )
| ~ ( in @ A @ ( relation_dom @ C ) )
| ( in @ ( ordered_pair @ A @ B ) @ C ) )
& ! [B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( B
= ( apply @ C @ A ) ) )
& ! [B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ A @ ( relation_dom @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(445,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( ( ( sK52_C @ B @ A )
!= ( sK53_SY3121 @ B @ A ) )
| ~ ( in @ ( sK52_C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK52_C @ B @ A ) @ ( sK53_SY3121 @ B @ A ) ) @ B ) )
& ( ( ( sK52_C @ B @ A )
= ( sK53_SY3121 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK52_C @ B @ A ) @ ( sK53_SY3121 @ B @ A ) ) @ B ) )
& ( ( in @ ( sK52_C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK52_C @ B @ A ) @ ( sK53_SY3121 @ B @ A ) ) @ B ) ) )
| ( B
= ( identity_relation @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( B
!= ( identity_relation @ A ) )
| ( ! [C: $i,D: $i] :
( ( C != D )
| ~ ( in @ C @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ B )
| ( C = D ) )
& ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ C @ D ) @ B )
| ( in @ C @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(446,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK50_D @ C @ B @ A ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ C @ B @ A ) @ ( sK51_SY3120 @ C @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ C @ B @ A ) @ ( sK51_SY3120 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK50_D @ C @ B @ A ) @ B )
| ( in @ ( ordered_pair @ ( sK50_D @ C @ B @ A ) @ ( sK51_SY3120 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK50_D @ C @ B @ A ) @ ( sK51_SY3120 @ C @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK50_D @ C @ B @ A ) @ ( sK51_SY3120 @ C @ B @ A ) ) @ C ) ) )
| ( C
= ( relation_dom_restriction @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ( C
!= ( relation_dom_restriction @ A @ B ) )
| ( ! [D: $i,E: $i] :
( ~ ( in @ D @ B )
| ~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ( in @ ( ordered_pair @ D @ E ) @ C ) )
& ! [D: $i] :
( ! [E: $i] :
~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ D @ B ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ ( ordered_pair @ D @ E ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(447,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK49_SY3119 @ C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ C @ B @ A ) @ ( sK49_SY3119 @ C @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ C @ B @ A ) @ ( sK49_SY3119 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK49_SY3119 @ C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK48_D @ C @ B @ A ) @ ( sK49_SY3119 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK48_D @ C @ B @ A ) @ ( sK49_SY3119 @ C @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK48_D @ C @ B @ A ) @ ( sK49_SY3119 @ C @ B @ A ) ) @ C ) ) )
| ( C
= ( relation_rng_restriction @ A @ B ) ) )
& ! [C: $i] :
( ~ ( relation @ C )
| ( C
!= ( relation_rng_restriction @ A @ B ) )
| ( ! [D: $i,E: $i] :
( ~ ( in @ E @ A )
| ~ ( in @ ( ordered_pair @ D @ E ) @ B )
| ( in @ ( ordered_pair @ D @ E ) @ C ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ E @ A ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ ( ordered_pair @ D @ E ) @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(448,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY3117: $i] :
( ~ ( in @ ( ordered_pair @ SY3117 @ ( sK46_D @ C @ B @ A ) ) @ A )
| ~ ( in @ SY3117 @ B ) )
| ~ ( in @ ( sK46_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK47_SY3118 @ C @ B @ A ) @ ( sK46_D @ C @ B @ A ) ) @ A )
& ( in @ ( sK47_SY3118 @ C @ B @ A ) @ B ) )
| ( in @ ( sK46_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( relation_image @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( relation_image @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i] :
( ~ ( in @ ( ordered_pair @ E @ D ) @ A )
| ~ ( in @ E @ B ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( ordered_pair @ ( sK45_E @ D @ C @ B @ A ) @ D ) @ A )
& ( in @ ( sK45_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(449,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY3115: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ C @ B @ A ) @ SY3115 ) @ A )
| ~ ( in @ SY3115 @ B ) )
| ~ ( in @ ( sK43_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK43_D @ C @ B @ A ) @ ( sK44_SY3116 @ C @ B @ A ) ) @ A )
& ( in @ ( sK44_SY3116 @ C @ B @ A ) @ B ) )
| ( in @ ( sK43_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( relation_inverse_image @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( relation_inverse_image @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ~ ( in @ E @ B ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( ordered_pair @ D @ ( sK42_E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( sK42_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(450,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( A
!= ( ordered_pair @ B @ C ) )
| ( ! [B: $i] :
( ( ( A
= ( ordered_pair @ ( sK40_C @ B @ A ) @ ( sK41_SY3114 @ B @ A ) ) )
& ( B
!= ( sK40_C @ B @ A ) ) )
| ( B
= ( pair_first @ A ) ) )
& ! [B: $i] :
( ( B
!= ( pair_first @ A ) )
| ! [C: $i] :
( ! [D: $i] :
( A
!= ( ordered_pair @ C @ D ) )
| ( B = C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(451,plain,
( ( ! [A: $i] :
( ( ! [SY3112: $i,SY3113: $i] :
( ( sK39_B @ A )
!= ( ordered_pair @ SY3112 @ SY3113 ) )
& ( in @ ( sK39_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK37_C @ B @ A ) @ ( sK38_SY3111 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[406]) ).
thf(452,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK36_C @ B @ A ) @ B )
& ~ ( in @ ( ordered_pair @ ( sK36_C @ B @ A ) @ ( sK36_C @ B @ A ) ) @ A ) )
| ( is_reflexive_in @ A @ B ) )
& ! [B: $i] :
( ~ ( is_reflexive_in @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ C @ C ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(453,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ( ( sK35_D @ C @ B @ A )
= B )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ C @ B @ A ) @ B ) @ A )
| ~ ( in @ ( sK35_D @ C @ B @ A ) @ C ) )
& ( ( ( sK35_D @ C @ B @ A )
!= B )
| ( in @ ( sK35_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK35_D @ C @ B @ A ) @ B ) @ A )
| ( in @ ( sK35_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( fiber @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( fiber @ A @ B ) )
| ( ! [D: $i] :
( ( D = B )
| ~ ( in @ ( ordered_pair @ D @ B ) @ A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( D != B ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ ( ordered_pair @ D @ B ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(454,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( A
!= ( ordered_pair @ B @ C ) )
| ( ! [B: $i] :
( ( ( A
= ( ordered_pair @ ( sK33_C @ B @ A ) @ ( sK34_SY3110 @ B @ A ) ) )
& ( B
!= ( sK34_SY3110 @ B @ A ) ) )
| ( B
= ( pair_second @ A ) ) )
& ! [B: $i] :
( ( B
!= ( pair_second @ A ) )
| ! [C: $i,D: $i] :
( ( A
!= ( ordered_pair @ C @ D ) )
| ( B = D ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(455,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK31_C @ B @ A ) @ ( sK32_SY3109 @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ B @ A ) @ ( sK32_SY3109 @ B @ A ) ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK31_C @ B @ A ) @ ( sK32_SY3109 @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK31_C @ B @ A ) @ ( sK32_SY3109 @ 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)],[402]) ).
thf(456,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY3104: $i,SY3105: $i] :
( ~ ( in @ SY3104 @ A )
| ~ ( in @ SY3105 @ B )
| ( ( sK28_D @ C @ B @ A )
!= ( ordered_pair @ SY3104 @ SY3105 ) ) )
| ~ ( in @ ( sK28_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK29_SY3106 @ C @ B @ A ) @ A )
& ( in @ ( sK30_SY3108 @ C @ B @ A ) @ B )
& ( ( sK28_D @ C @ B @ A )
= ( ordered_pair @ ( sK29_SY3106 @ C @ B @ A ) @ ( sK30_SY3108 @ C @ B @ A ) ) ) )
| ( in @ ( sK28_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 @ ( sK26_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK27_SY3103 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK26_E @ D @ C @ B @ A ) @ ( sK27_SY3103 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(457,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( in @ ( ordered_pair @ ( sK24_C @ B @ A ) @ ( sK25_SY3102 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK24_C @ B @ A ) @ ( sK25_SY3102 @ 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)],[400]) ).
thf(458,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C
!= ( apply @ A @ B ) )
| ( in @ ( ordered_pair @ B @ C ) @ A ) ) )
& ! [B: $i] :
( ~ ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ~ ( in @ ( ordered_pair @ B @ C ) @ A )
| ( C
= ( apply @ A @ B ) ) ) )
& ! [B: $i] :
( ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C
!= ( apply @ A @ B ) )
| ( C = empty_set ) ) )
& ! [B: $i] :
( ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C != empty_set )
| ( C
= ( apply @ A @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[399]) ).
thf(459,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY3100: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ B @ A ) @ SY3100 ) @ A )
| ~ ( in @ ( sK22_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK22_C @ B @ A ) @ ( sK23_SY3101 @ B @ A ) ) @ A )
| ( in @ ( sK22_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_dom @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_dom @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ C @ ( sK21_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[398]) ).
thf(460,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK19_C @ B @ A ) @ B )
& ( in @ ( sK20_SY3099 @ B @ A ) @ B )
& ( in @ ( ordered_pair @ ( sK19_C @ B @ A ) @ ( sK20_SY3099 @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK20_SY3099 @ B @ A ) @ ( sK19_C @ B @ A ) ) @ A )
& ( ( sK19_C @ B @ A )
!= ( sK20_SY3099 @ B @ A ) ) )
| ( is_antisymmetric_in @ A @ B ) )
& ! [B: $i] :
( ~ ( is_antisymmetric_in @ A @ B )
| ! [C: $i,D: $i] :
( ~ ( in @ C @ B )
| ~ ( in @ D @ B )
| ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ~ ( in @ ( ordered_pair @ D @ C ) @ A )
| ( C = D ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(461,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY3097: $i] :
~ ( in @ ( ordered_pair @ SY3097 @ ( sK17_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK17_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK18_SY3098 @ B @ A ) @ ( sK17_C @ B @ A ) ) @ A )
| ( in @ ( sK17_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_rng @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_rng @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ D @ C ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ ( sK16_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(462,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[351]) ).
thf(463,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ( sK14_C @ B @ A )
!= ( sK15_SY3096 @ B @ A ) )
& ( in @ ( sK14_C @ B @ A ) @ B )
& ( in @ ( sK15_SY3096 @ B @ A ) @ B )
& ~ ( in @ ( ordered_pair @ ( sK14_C @ B @ A ) @ ( sK15_SY3096 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK15_SY3096 @ B @ A ) @ ( sK14_C @ B @ A ) ) @ A ) )
| ( is_connected_in @ A @ B ) )
& ! [B: $i] :
( ~ ( is_connected_in @ A @ B )
| ! [C: $i,D: $i] :
( ( C = D )
| ~ ( in @ C @ B )
| ~ ( in @ D @ B )
| ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[395]) ).
thf(464,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK12_C @ B @ A ) @ ( sK13_SY3095 @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ B @ A ) @ ( sK12_C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( sK12_C @ B @ A ) @ ( sK13_SY3095 @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ B @ A ) @ ( sK12_C @ B @ A ) ) @ A ) ) )
| ( B
= ( relation_inverse @ A ) ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ( B
!= ( relation_inverse @ A ) )
| ( ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ B )
| ( in @ ( ordered_pair @ D @ C ) @ A ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ D @ C ) @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[394]) ).
thf(465,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ( ( ~ ( in @ ( sK10_D @ C @ B @ A ) @ ( relation_field @ A ) )
| ~ ( in @ ( sK11_SY3094 @ C @ B @ A ) @ ( relation_field @ A ) )
| ~ ( in @ ( ordered_pair @ ( apply @ C @ ( sK10_D @ C @ B @ A ) ) @ ( apply @ C @ ( sK11_SY3094 @ C @ B @ A ) ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ ( sK11_SY3094 @ C @ B @ A ) ) @ A ) )
& ( ( in @ ( sK10_D @ C @ B @ A ) @ ( relation_field @ A ) )
| ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ ( sK11_SY3094 @ C @ B @ A ) ) @ A ) )
& ( ( in @ ( sK11_SY3094 @ C @ B @ A ) @ ( relation_field @ A ) )
| ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ ( sK11_SY3094 @ C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( apply @ C @ ( sK10_D @ C @ B @ A ) ) @ ( apply @ C @ ( sK11_SY3094 @ C @ B @ A ) ) ) @ B )
| ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ ( sK11_SY3094 @ C @ B @ A ) ) @ A ) ) )
| ( ( relation_dom @ C )
!= ( relation_field @ A ) )
| ( ( relation_rng @ C )
!= ( relation_field @ B ) )
| ~ ( one_to_one @ C )
| ( relation_isomorphism @ A @ B @ C ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ( ! [D: $i,E: $i] :
( ~ ( in @ D @ ( relation_field @ A ) )
| ~ ( in @ E @ ( relation_field @ A ) )
| ~ ( in @ ( ordered_pair @ ( apply @ C @ D ) @ ( apply @ C @ E ) ) @ B )
| ( in @ ( ordered_pair @ D @ E ) @ A ) )
& ! [D: $i] :
( ! [E: $i] :
~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ( in @ D @ ( relation_field @ A ) ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ( in @ E @ ( relation_field @ A ) ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ( in @ ( ordered_pair @ ( apply @ C @ D ) @ ( apply @ C @ E ) ) @ B ) ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ( ( relation_dom @ C )
= ( relation_field @ A ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ( ( relation_rng @ C )
= ( relation_field @ B ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ( one_to_one @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(466,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ! [SY3092: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ C @ B @ A ) @ SY3092 ) @ A )
| ~ ( in @ ( ordered_pair @ SY3092 @ ( sK8_SY3089 @ C @ B @ A ) ) @ B ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ C @ B @ A ) @ ( sK8_SY3089 @ C @ B @ A ) ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK7_D @ C @ B @ A ) @ ( sK9_SY3093 @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK9_SY3093 @ C @ B @ A ) @ ( sK8_SY3089 @ C @ B @ A ) ) @ B ) )
| ( in @ ( ordered_pair @ ( sK7_D @ C @ B @ A ) @ ( sK8_SY3089 @ C @ B @ A ) ) @ C ) ) )
| ( C
= ( relation_composition @ A @ B ) ) )
& ! [C: $i] :
( ~ ( relation @ C )
| ( C
!= ( relation_composition @ A @ B ) )
| ( ! [D: $i,E: $i] :
( ! [F: $i] :
( ~ ( in @ ( ordered_pair @ D @ F ) @ A )
| ~ ( in @ ( ordered_pair @ F @ E ) @ B ) )
| ( in @ ( ordered_pair @ D @ E ) @ C ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( ( in @ ( ordered_pair @ D @ ( sK6_F @ E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK6_F @ E @ D @ C @ B @ A ) @ E ) @ B ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(467,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK3_C @ B @ A ) @ B )
& ( in @ ( sK4_SY3086 @ B @ A ) @ B )
& ( in @ ( sK5_SY3088 @ B @ A ) @ B )
& ( in @ ( ordered_pair @ ( sK3_C @ B @ A ) @ ( sK4_SY3086 @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK4_SY3086 @ B @ A ) @ ( sK5_SY3088 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK3_C @ B @ A ) @ ( sK5_SY3088 @ B @ A ) ) @ A ) )
| ( is_transitive_in @ A @ B ) )
& ! [B: $i] :
( ~ ( is_transitive_in @ A @ B )
| ! [C: $i,D: $i,E: $i] :
( ~ ( in @ C @ B )
| ~ ( in @ D @ B )
| ~ ( in @ E @ B )
| ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ( in @ ( ordered_pair @ C @ E ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[391]) ).
thf(468,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[345]) ).
thf(469,plain,
( ( ( ( pair_first @ ( ordered_pair @ sK1_A @ sK2_SY3085 ) )
!= sK1_A ) )
= $true ),
inference(copy,[status(thm)],[389]) ).
thf(470,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK39_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK39_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK37_C @ SX1 @ SX0 ) @ ( sK38_SY3111 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[451]) ).
thf(471,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SX1 @ SX0 ) @ ( sK32_SY3109 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ SX1 @ SX0 ) @ ( sK32_SY3109 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK31_C @ SX1 @ SX0 ) @ ( sK32_SY3109 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK31_C @ SX1 @ SX0 ) @ ( sK32_SY3109 @ 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)],[455]) ).
thf(472,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK4_SY3086 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ ( sK5_SY3088 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SX1 @ SX0 ) @ ( sK4_SY3086 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( in @ ( ordered_pair @ ( sK4_SY3086 @ SX1 @ SX0 ) @ ( sK5_SY3088 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK3_C @ SX1 @ SX0 ) @ ( sK5_SY3088 @ SX1 @ SX0 ) ) @ SX0 ) )
| ( is_transitive_in @ SX0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( is_transitive_in @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i,SX4: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX3 @ SX1 )
| ~ ( in @ SX4 @ SX1 )
| ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX4 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[467]) ).
thf(473,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX1 @ SX0 )
| ~ ( ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ ( sK59_D @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX2 )
| ~ ( in @ ( sK59_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 @ ( sK58_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX2 )
| ~ ( in @ SX3 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[438]) ).
thf(474,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ ( sK8_SY3089 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ ( sK8_SY3089 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ ( sK9_SY3093 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SX2 @ SX1 @ SX0 ) @ ( sK8_SY3089 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ ( sK8_SY3089 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) ) )
| ( SX2
= ( relation_composition @ SX0 @ SX1 ) ) )
| ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ( SX2
!= ( relation_composition @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i,SX4: $i] :
( ! [SX5: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX5 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX5 @ SX4 ) @ SX1 ) )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ~ ( ~ ( in @ ( ordered_pair @ SX3 @ ( sK6_F @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX4 ) @ SX1 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[466]) ).
thf(475,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK52_C @ SX1 @ SX0 )
!= ( sK53_SY3121 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK52_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK52_C @ SX1 @ SX0 ) @ ( sK53_SY3121 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK52_C @ SX1 @ SX0 )
= ( sK53_SY3121 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK52_C @ SX1 @ SX0 ) @ ( sK53_SY3121 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK52_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK52_C @ SX1 @ SX0 ) @ ( sK53_SY3121 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( SX2 = SX3 ) )
| ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[445]) ).
thf(476,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i,SX2: $i] :
( SX0
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ( SX0
!= ( ordered_pair @ ( sK40_C @ SX1 @ SX0 ) @ ( sK41_SY3114 @ SX1 @ SX0 ) ) )
| ~ ( ( SX1
!= ( sK40_C @ SX1 @ SX0 ) ) ) )
| ( SX1
= ( pair_first @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( SX1
!= ( pair_first @ SX0 ) )
| ! [SX2: $i] :
( ! [SX3: $i] :
( SX0
!= ( ordered_pair @ SX2 @ SX3 ) )
| ( SX1 = SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[450]) ).
thf(477,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( relation @ SX3 )
| ~ ( in @ SX0 @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX3 )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( relation_composition @ ( identity_relation @ SX2 ) @ SX3 ) ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( relation @ SX3 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( relation_composition @ ( identity_relation @ SX2 ) @ SX3 ) )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( relation @ SX3 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( relation_composition @ ( identity_relation @ SX2 ) @ SX3 ) )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443]) ).
thf(478,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( relation_rng @ SX2 ) )
| ~ ( in @ ( ordered_pair @ SX0 @ SX3 ) @ SX2 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX0 @ ( relation_inverse_image @ SX2 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_inverse_image @ SX2 @ SX1 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_D @ SX2 @ SX1 @ SX0 ) @ ( relation_rng @ SX2 ) )
| ~ ( in @ ( ordered_pair @ SX0 @ ( sK60_D @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( in @ ( sK60_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[436]) ).
thf(479,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i,SX4: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX4 @ SX1 )
| ( ( sK28_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ SX3 @ SX4 ) ) )
| ~ ( in @ ( sK28_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY3106 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK30_SY3108 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( sK28_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ ( sK29_SY3106 @ SX2 @ SX1 @ SX0 ) @ ( sK30_SY3108 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( in @ ( sK28_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 @ ( sK26_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK27_SY3103 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( SX3
!= ( ordered_pair @ ( sK26_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK27_SY3103 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(480,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX0 @ ( relation_field @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX1 @ ( relation_field @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[440]) ).
thf(481,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i,SX2: $i] :
( SX0
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ( SX0
!= ( ordered_pair @ ( sK33_C @ SX1 @ SX0 ) @ ( sK34_SY3110 @ SX1 @ SX0 ) ) )
| ~ ( ( SX1
!= ( sK34_SY3110 @ SX1 @ SX0 ) ) ) )
| ( SX1
= ( pair_second @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( SX1
!= ( pair_second @ SX0 ) )
| ! [SX2: $i,SX3: $i] :
( ( SX0
!= ( ordered_pair @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[454]) ).
thf(482,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK14_C @ SX1 @ SX0 )
!= ( sK15_SY3096 @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK15_SY3096 @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK14_C @ SX1 @ SX0 ) @ ( sK15_SY3096 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK15_SY3096 @ SX1 @ SX0 ) @ ( sK14_C @ SX1 @ SX0 ) ) @ SX0 ) )
| ( is_connected_in @ SX0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( is_connected_in @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i] :
( ( SX2 = SX3 )
| ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX3 @ SX1 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(483,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( relation_dom @ SX2 ) )
| ~ ( in @ ( ordered_pair @ SX3 @ SX0 ) @ SX2 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX0 @ ( relation_image @ SX2 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_image @ SX2 @ SX1 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK61_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX2 ) )
| ~ ( in @ ( ordered_pair @ ( sK61_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) @ SX2 ) )
| ~ ( in @ ( sK61_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[435]) ).
thf(484,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ ( sK46_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ~ ( in @ ( sK46_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SX2 @ SX1 @ SX0 ) @ ( sK46_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK47_SY3118 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( in @ ( sK46_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ( SX2
= ( relation_image @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( relation_image @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX4 @ SX3 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ ( sK45_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[448]) ).
thf(485,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK64_B @ SX0 ) @ ( sK65_SY3126 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK65_SY3126 @ SX0 ) @ ( sK64_B @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK64_B @ SX0 )
!= ( sK65_SY3126 @ SX0 ) ) ) )
| ( antisymmetric @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX2 @ SX1 ) @ SX0 )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[431]) ).
thf(486,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ( SX1
!= ( apply @ SX2 @ SX0 ) )
| ~ ( in @ SX0 @ ( relation_dom @ SX2 ) )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( SX1
= ( apply @ SX2 @ SX0 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX0 @ ( relation_dom @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[444]) ).
thf(487,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ( ( sK35_D @ SX2 @ SX1 @ SX0 )
= SX1 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) @ SX0 )
| ~ ( in @ ( sK35_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( ( sK35_D @ SX2 @ SX1 @ SX0 )
!= SX1 )
| ( in @ ( sK35_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) @ SX0 )
| ( in @ ( sK35_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( fiber @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( fiber @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ( SX3 = SX1 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX1 ) @ SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( SX3 != SX1 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ ( ordered_pair @ SX3 @ SX1 ) @ SX0 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[453]) ).
thf(488,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( in @ ( sK36_C @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SX1 @ SX0 ) @ ( sK36_C @ SX1 @ SX0 ) ) @ SX0 ) )
| ( is_reflexive_in @ SX0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( is_reflexive_in @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ ( ordered_pair @ SX2 @ SX2 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[452]) ).
thf(489,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SX1 @ SX0 ) @ ( sK13_SY3095 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SX1 @ SX0 ) @ ( sK12_C @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SX1 @ SX0 ) @ ( sK13_SY3095 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ SX1 @ SX0 ) @ ( sK12_C @ SX1 @ SX0 ) ) @ SX0 ) ) )
| ( SX1
= ( relation_inverse @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ( SX1
!= ( relation_inverse @ SX0 ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[464]) ).
thf(490,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ ( sK49_SY3119 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SX2 @ SX1 @ SX0 ) @ ( sK49_SY3119 @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SX2 @ SX1 @ SX0 ) @ ( sK49_SY3119 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_SY3119 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK48_D @ SX2 @ SX1 @ SX0 ) @ ( sK49_SY3119 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SX2 @ SX1 @ SX0 ) @ ( sK49_SY3119 @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK48_D @ SX2 @ SX1 @ SX0 ) @ ( sK49_SY3119 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) ) ) )
| ( SX2
= ( relation_rng_restriction @ SX0 @ SX1 ) ) )
| ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ( SX2
!= ( relation_rng_restriction @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX1 )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ( in @ SX4 @ SX0 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[447]) ).
thf(491,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ SX2 @ ( sK17_C @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK18_SY3098 @ SX1 @ SX0 ) @ ( sK17_C @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( relation_rng @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( SX1
!= ( relation_rng @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ ( ordered_pair @ ( sK16_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[461]) ).
thf(492,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SX1 @ SX0 ) @ ( sK25_SY3102 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SX1 @ SX0 ) @ ( sK25_SY3102 @ 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)],[457]) ).
thf(493,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ ( sK50_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SX2 @ SX1 @ SX0 ) @ ( sK51_SY3120 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SX2 @ SX1 @ SX0 ) @ ( sK51_SY3120 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK50_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK50_D @ SX2 @ SX1 @ SX0 ) @ ( sK51_SY3120 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SX2 @ SX1 @ SX0 ) @ ( sK51_SY3120 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK50_D @ SX2 @ SX1 @ SX0 ) @ ( sK51_SY3120 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) ) ) )
| ( SX2
= ( relation_dom_restriction @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ( SX2
!= ( relation_dom_restriction @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ SX3 @ SX1 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ( in @ SX3 @ SX1 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446]) ).
thf(494,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ( ordered_pair @ SX0 @ SX1 )
!= ( ordered_pair @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( ( ordered_pair @ SX0 @ SX1 )
!= ( ordered_pair @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[441]) ).
thf(495,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
( ( SX2
!= ( apply @ SX0 @ SX1 ) )
| ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ( SX2
= ( apply @ SX0 @ SX1 ) ) ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
( ( SX2
!= ( apply @ SX0 @ SX1 ) )
| ( SX2 = empty_set ) ) )
| ~ ! [SX1: $i] :
( ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
( ( SX2 != empty_set )
| ( SX2
= ( apply @ SX0 @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[458]) ).
thf(496,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK62_B @ SX0 )
!= ( sK63_SY3125 @ SX0 ) ) )
| ~ ~ ( ~ ( in @ ( sK62_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ( in @ ( sK63_SY3125 @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK62_B @ SX0 ) @ ( sK63_SY3125 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK63_SY3125 @ SX0 ) @ ( sK62_B @ SX0 ) ) @ SX0 ) )
| ( connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( connected @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( SX1 = SX2 )
| ~ ( in @ SX1 @ ( relation_field @ SX0 ) )
| ~ ( in @ SX2 @ ( relation_field @ SX0 ) )
| ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[432]) ).
thf(497,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK20_SY3099 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SX1 @ SX0 ) @ ( sK20_SY3099 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( in @ ( ordered_pair @ ( sK20_SY3099 @ SX1 @ SX0 ) @ ( sK19_C @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK19_C @ SX1 @ SX0 )
!= ( sK20_SY3099 @ SX1 @ SX0 ) ) ) )
| ( is_antisymmetric_in @ SX0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( is_antisymmetric_in @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX3 @ SX1 )
| ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( SX2 = SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[460]) ).
thf(498,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)],[434]) ).
thf(499,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK66_B @ SX0 ) @ ( sK67_SY3127 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK67_SY3127 @ SX0 ) @ ( sK68_SY3129 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK66_B @ SX0 ) @ ( sK68_SY3129 @ SX0 ) ) @ SX0 ) )
| ( transitive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( transitive @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX1 @ SX3 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[430]) ).
thf(500,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)],[433]) ).
thf(501,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ~ ( in @ ( sK43_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SX2 @ SX1 @ SX0 ) @ ( sK44_SY3116 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK44_SY3116 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( in @ ( sK43_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ( SX2
= ( relation_inverse_image @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( relation_inverse_image @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ ( ordered_pair @ SX3 @ ( sK42_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK42_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(502,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX0 @ ( relation_dom @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX1 @ ( relation_rng @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[437]) ).
thf(503,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( in @ ( sK69_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK69_B @ SX0 ) @ ( sK69_B @ SX0 ) ) @ SX0 ) )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ ( relation_field @ SX0 ) )
| ( in @ ( ordered_pair @ SX1 @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[429]) ).
thf(504,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ( in @ ( sK11_SY3094 @ SX2 @ SX1 @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SX2 @ ( sK10_D @ SX2 @ SX1 @ SX0 ) ) @ ( apply @ SX2 @ ( sK11_SY3094 @ SX2 @ SX1 @ SX0 ) ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ ( sK11_SY3094 @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ ( relation_field @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ ( sK11_SY3094 @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SX2 @ SX1 @ SX0 ) @ ( relation_field @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ ( sK11_SY3094 @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SX2 @ ( sK10_D @ SX2 @ SX1 @ SX0 ) ) @ ( apply @ SX2 @ ( sK11_SY3094 @ SX2 @ SX1 @ SX0 ) ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ ( sK11_SY3094 @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) ) )
| ( ( relation_dom @ SX2 )
!= ( relation_field @ SX0 ) )
| ( ( relation_rng @ SX2 )
!= ( relation_field @ SX1 ) )
| ~ ( one_to_one @ SX2 )
| ( relation_isomorphism @ SX0 @ SX1 @ SX2 ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( relation_isomorphism @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ SX3 @ ( relation_field @ SX0 ) )
| ~ ( in @ SX4 @ ( relation_field @ SX0 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SX2 @ SX3 ) @ ( apply @ SX2 @ SX4 ) ) @ SX1 )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ( in @ SX3 @ ( relation_field @ SX0 ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ( in @ SX4 @ ( relation_field @ SX0 ) ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ( in @ ( ordered_pair @ ( apply @ SX2 @ SX3 ) @ ( apply @ SX2 @ SX4 ) ) @ SX1 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( relation_isomorphism @ SX0 @ SX1 @ SX2 )
| ( ( relation_dom @ SX2 )
= ( relation_field @ SX0 ) ) )
| ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( relation_isomorphism @ SX0 @ SX1 @ SX2 )
| ( ( relation_rng @ SX2 )
= ( relation_field @ SX1 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( relation_isomorphism @ SX0 @ SX1 @ SX2 )
| ( one_to_one @ SX2 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[465]) ).
thf(505,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ~ ( ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ ( sK57_D @ SX2 @ SX1 @ SX0 ) ) @ SX2 )
| ~ ( in @ ( sK57_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 @ ( sK56_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX2 )
| ~ ( in @ SX3 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[439]) ).
thf(506,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
| ~ ( in @ ( sK22_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SX1 @ SX0 ) @ ( sK23_SY3101 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK22_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( relation_dom @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( SX1
!= ( relation_dom @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ ( ordered_pair @ SX2 @ ( sK21_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[459]) ).
thf(507,plain,
! [SV1: $i] :
( ( ~ ( relation @ SV1 )
| ( in @ ( ordered_pair @ ( sK54_B @ SV1 ) @ ( sK55_SY3122 @ SV1 ) ) @ SV1 )
| ( SV1 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(508,plain,
! [SV2: $i] :
( ( ! [SY3130: $i] :
( ( ordered_pair @ SV2 @ SY3130 )
= ( unordered_pair @ ( unordered_pair @ SV2 @ SY3130 ) @ ( singleton @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(509,plain,
! [SV3: $i] :
( ( ! [SY3131: $i] :
~ ( empty @ ( ordered_pair @ SV3 @ SY3131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(510,plain,
( ( ( pair_first @ ( ordered_pair @ sK1_A @ sK2_SY3085 ) )
= sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(511,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK39_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK39_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK37_C @ SX1 @ SX0 ) @ ( sK38_SY3111 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(512,plain,
! [SV4: $i] :
( ( ~ ( relation @ SV4 )
| ~ ( ~ ! [SY3132: $i] :
( ~ ( relation @ SY3132 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SY3132 @ SV4 ) @ ( sK32_SY3109 @ SY3132 @ SV4 ) ) @ SV4 )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ SY3132 @ SV4 ) @ ( sK32_SY3109 @ SY3132 @ SV4 ) ) @ SY3132 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK31_C @ SY3132 @ SV4 ) @ ( sK32_SY3109 @ SY3132 @ SV4 ) ) @ SV4 )
| ( in @ ( ordered_pair @ ( sK31_C @ SY3132 @ SV4 ) @ ( sK32_SY3109 @ SY3132 @ SV4 ) ) @ SY3132 ) ) )
| ( SV4 = SY3132 ) )
| ~ ! [SY3133: $i] :
( ~ ( relation @ SY3133 )
| ( SV4 != SY3133 )
| ~ ( ~ ! [SY3134: $i,SY3135: $i] :
( ~ ( in @ ( ordered_pair @ SY3134 @ SY3135 ) @ SV4 )
| ( in @ ( ordered_pair @ SY3134 @ SY3135 ) @ SY3133 ) )
| ~ ! [SY3136: $i,SY3137: $i] :
( ~ ( in @ ( ordered_pair @ SY3136 @ SY3137 ) @ SY3133 )
| ( in @ ( ordered_pair @ SY3136 @ SY3137 ) @ SV4 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(513,plain,
! [SV5: $i] :
( ( ~ ( relation @ SV5 )
| ~ ( ~ ! [SY3138: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SY3138 @ SV5 ) @ SY3138 )
| ~ ( in @ ( sK4_SY3086 @ SY3138 @ SV5 ) @ SY3138 ) )
| ~ ( in @ ( sK5_SY3088 @ SY3138 @ SV5 ) @ SY3138 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SY3138 @ SV5 ) @ ( sK4_SY3086 @ SY3138 @ SV5 ) ) @ SV5 ) )
| ~ ( in @ ( ordered_pair @ ( sK4_SY3086 @ SY3138 @ SV5 ) @ ( sK5_SY3088 @ SY3138 @ SV5 ) ) @ SV5 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK3_C @ SY3138 @ SV5 ) @ ( sK5_SY3088 @ SY3138 @ SV5 ) ) @ SV5 ) )
| ( is_transitive_in @ SV5 @ SY3138 ) )
| ~ ! [SY3139: $i] :
( ~ ( is_transitive_in @ SV5 @ SY3139 )
| ! [SY3140: $i,SY3141: $i,SY3142: $i] :
( ~ ( in @ SY3140 @ SY3139 )
| ~ ( in @ SY3141 @ SY3139 )
| ~ ( in @ SY3142 @ SY3139 )
| ~ ( in @ ( ordered_pair @ SY3140 @ SY3141 ) @ SV5 )
| ~ ( in @ ( ordered_pair @ SY3141 @ SY3142 ) @ SV5 )
| ( in @ ( ordered_pair @ SY3140 @ SY3142 ) @ SV5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(514,plain,
! [SV6: $i] :
( ( ~ ( ~ ! [SY3143: $i,SY3144: $i] :
( ~ ( relation_of2_as_subset @ SY3144 @ SY3143 @ SV6 )
| ~ ( ~ ! [SY3145: $i] :
~ ( in @ ( ordered_pair @ ( sK59_D @ SY3144 @ SY3143 @ SV6 ) @ SY3145 ) @ SY3144 )
| ~ ( in @ ( sK59_D @ SY3144 @ SY3143 @ SV6 ) @ SY3143 ) )
| ( ( relation_dom_as_subset @ SY3143 @ SV6 @ SY3144 )
= SY3143 ) )
| ~ ! [SY3146: $i,SY3147: $i] :
( ~ ( relation_of2_as_subset @ SY3147 @ SY3146 @ SV6 )
| ( ( relation_dom_as_subset @ SY3146 @ SV6 @ SY3147 )
!= SY3146 )
| ! [SY3148: $i] :
( ( in @ ( ordered_pair @ SY3148 @ ( sK58_E @ SY3148 @ SY3147 @ SY3146 @ SV6 ) ) @ SY3147 )
| ~ ( in @ SY3148 @ SY3146 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(515,plain,
! [SV7: $i] :
( ( ~ ( relation @ SV7 )
| ! [SY3149: $i] :
( ~ ( relation @ SY3149 )
| ~ ( ~ ! [SY3150: $i] :
( ~ ( relation @ SY3150 )
| ~ ( ~ ( ! [SY3151: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3150 @ SY3149 @ SV7 ) @ SY3151 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3151 @ ( sK8_SY3089 @ SY3150 @ SY3149 @ SV7 ) ) @ SY3149 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3150 @ SY3149 @ SV7 ) @ ( sK8_SY3089 @ SY3150 @ SY3149 @ SV7 ) ) @ SY3150 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3150 @ SY3149 @ SV7 ) @ ( sK9_SY3093 @ SY3150 @ SY3149 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SY3150 @ SY3149 @ SV7 ) @ ( sK8_SY3089 @ SY3150 @ SY3149 @ SV7 ) ) @ SY3149 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SY3150 @ SY3149 @ SV7 ) @ ( sK8_SY3089 @ SY3150 @ SY3149 @ SV7 ) ) @ SY3150 ) ) )
| ( SY3150
= ( relation_composition @ SV7 @ SY3149 ) ) )
| ~ ! [SY3152: $i] :
( ~ ( relation @ SY3152 )
| ( SY3152
!= ( relation_composition @ SV7 @ SY3149 ) )
| ~ ( ~ ! [SY3153: $i,SY3154: $i] :
( ! [SY3155: $i] :
( ~ ( in @ ( ordered_pair @ SY3153 @ SY3155 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3155 @ SY3154 ) @ SY3149 ) )
| ( in @ ( ordered_pair @ SY3153 @ SY3154 ) @ SY3152 ) )
| ~ ! [SY3156: $i,SY3157: $i] :
( ~ ( in @ ( ordered_pair @ SY3156 @ SY3157 ) @ SY3152 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3156 @ ( sK6_F @ SY3157 @ SY3156 @ SY3152 @ SY3149 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY3157 @ SY3156 @ SY3152 @ SY3149 @ SV7 ) @ SY3157 ) @ SY3149 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(516,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK52_C @ SX1 @ SX0 )
!= ( sK53_SY3121 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK52_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK52_C @ SX1 @ SX0 ) @ ( sK53_SY3121 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK52_C @ SX1 @ SX0 )
= ( sK53_SY3121 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK52_C @ SX1 @ SX0 ) @ ( sK53_SY3121 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK52_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK52_C @ SX1 @ SX0 ) @ ( sK53_SY3121 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( SX2 = SX3 ) )
| ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(517,plain,
! [SV8: $i] :
( ( ! [SY3158: $i,SY3159: $i] :
( SV8
!= ( ordered_pair @ SY3158 @ SY3159 ) )
| ~ ( ~ ! [SY3160: $i] :
( ~ ( ( SV8
!= ( ordered_pair @ ( sK40_C @ SY3160 @ SV8 ) @ ( sK41_SY3114 @ SY3160 @ SV8 ) ) )
| ~ ( ( SY3160
!= ( sK40_C @ SY3160 @ SV8 ) ) ) )
| ( SY3160
= ( pair_first @ SV8 ) ) )
| ~ ! [SY3161: $i] :
( ( SY3161
!= ( pair_first @ SV8 ) )
| ! [SY3162: $i] :
( ! [SY3163: $i] :
( SV8
!= ( ordered_pair @ SY3162 @ SY3163 ) )
| ( SY3161 = SY3162 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(518,plain,
! [SV9: $i] :
( ( ! [SY3164: $i] :
~ ( ~ ! [SY3165: $i,SY3166: $i] :
( ~ ( relation @ SY3166 )
| ~ ( in @ SV9 @ SY3165 )
| ~ ( in @ ( ordered_pair @ SV9 @ SY3164 ) @ SY3166 )
| ( in @ ( ordered_pair @ SV9 @ SY3164 ) @ ( relation_composition @ ( identity_relation @ SY3165 ) @ SY3166 ) ) )
| ~ ~ ( ~ ! [SY3167: $i,SY3168: $i] :
( ~ ( relation @ SY3168 )
| ~ ( in @ ( ordered_pair @ SV9 @ SY3164 ) @ ( relation_composition @ ( identity_relation @ SY3167 ) @ SY3168 ) )
| ( in @ SV9 @ SY3167 ) )
| ~ ! [SY3169: $i,SY3170: $i] :
( ~ ( relation @ SY3170 )
| ~ ( in @ ( ordered_pair @ SV9 @ SY3164 ) @ ( relation_composition @ ( identity_relation @ SY3169 ) @ SY3170 ) )
| ( in @ ( ordered_pair @ SV9 @ SY3164 ) @ SY3170 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(519,plain,
! [SV10: $i] :
( ( ~ ( ~ ! [SY3171: $i,SY3172: $i] :
( ~ ( relation @ SY3172 )
| ! [SY3173: $i] :
( ~ ( in @ SY3173 @ ( relation_rng @ SY3172 ) )
| ~ ( in @ ( ordered_pair @ SV10 @ SY3173 ) @ SY3172 )
| ~ ( in @ SY3173 @ SY3171 ) )
| ( in @ SV10 @ ( relation_inverse_image @ SY3172 @ SY3171 ) ) )
| ~ ! [SY3174: $i,SY3175: $i] :
( ~ ( relation @ SY3175 )
| ~ ( in @ SV10 @ ( relation_inverse_image @ SY3175 @ SY3174 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_D @ SY3175 @ SY3174 @ SV10 ) @ ( relation_rng @ SY3175 ) )
| ~ ( in @ ( ordered_pair @ SV10 @ ( sK60_D @ SY3175 @ SY3174 @ SV10 ) ) @ SY3175 ) )
| ~ ( in @ ( sK60_D @ SY3175 @ SY3174 @ SV10 ) @ SY3174 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(520,plain,
! [SV11: $i] :
( ( ~ ( ~ ! [SY3176: $i,SY3177: $i] :
( ~ ( ~ ( ! [SY3178: $i,SY3179: $i] :
( ~ ( in @ SY3178 @ SV11 )
| ~ ( in @ SY3179 @ SY3176 )
| ( ( sK28_D @ SY3177 @ SY3176 @ SV11 )
!= ( ordered_pair @ SY3178 @ SY3179 ) ) )
| ~ ( in @ ( sK28_D @ SY3177 @ SY3176 @ SV11 ) @ SY3177 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY3106 @ SY3177 @ SY3176 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK30_SY3108 @ SY3177 @ SY3176 @ SV11 ) @ SY3176 ) )
| ( ( sK28_D @ SY3177 @ SY3176 @ SV11 )
!= ( ordered_pair @ ( sK29_SY3106 @ SY3177 @ SY3176 @ SV11 ) @ ( sK30_SY3108 @ SY3177 @ SY3176 @ SV11 ) ) ) )
| ( in @ ( sK28_D @ SY3177 @ SY3176 @ SV11 ) @ SY3177 ) ) )
| ( SY3177
= ( cartesian_product2 @ SV11 @ SY3176 ) ) )
| ~ ! [SY3180: $i,SY3181: $i] :
( ( SY3181
!= ( cartesian_product2 @ SV11 @ SY3180 ) )
| ~ ( ~ ! [SY3182: $i] :
( ! [SY3183: $i,SY3184: $i] :
( ~ ( in @ SY3183 @ SV11 )
| ~ ( in @ SY3184 @ SY3180 )
| ( SY3182
!= ( ordered_pair @ SY3183 @ SY3184 ) ) )
| ( in @ SY3182 @ SY3181 ) )
| ~ ! [SY3185: $i] :
( ~ ( in @ SY3185 @ SY3181 )
| ~ ( ~ ~ ( ~ ( in @ ( sK26_E @ SY3185 @ SY3181 @ SY3180 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK27_SY3103 @ SY3185 @ SY3181 @ SY3180 @ SV11 ) @ SY3180 ) )
| ( SY3185
!= ( ordered_pair @ ( sK26_E @ SY3185 @ SY3181 @ SY3180 @ SV11 ) @ ( sK27_SY3103 @ SY3185 @ SY3181 @ SY3180 @ SV11 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(521,plain,
! [SV12: $i] :
( ( ~ ( ~ ! [SY3186: $i,SY3187: $i] :
( ~ ( relation @ SY3187 )
| ~ ( in @ ( ordered_pair @ SV12 @ SY3186 ) @ SY3187 )
| ( in @ SV12 @ ( relation_field @ SY3187 ) ) )
| ~ ! [SY3188: $i,SY3189: $i] :
( ~ ( relation @ SY3189 )
| ~ ( in @ ( ordered_pair @ SV12 @ SY3188 ) @ SY3189 )
| ( in @ SY3188 @ ( relation_field @ SY3189 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(522,plain,
! [SV13: $i] :
( ( ! [SY3190: $i,SY3191: $i] :
( SV13
!= ( ordered_pair @ SY3190 @ SY3191 ) )
| ~ ( ~ ! [SY3192: $i] :
( ~ ( ( SV13
!= ( ordered_pair @ ( sK33_C @ SY3192 @ SV13 ) @ ( sK34_SY3110 @ SY3192 @ SV13 ) ) )
| ~ ( ( SY3192
!= ( sK34_SY3110 @ SY3192 @ SV13 ) ) ) )
| ( SY3192
= ( pair_second @ SV13 ) ) )
| ~ ! [SY3193: $i] :
( ( SY3193
!= ( pair_second @ SV13 ) )
| ! [SY3194: $i,SY3195: $i] :
( ( SV13
!= ( ordered_pair @ SY3194 @ SY3195 ) )
| ( SY3193 = SY3195 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(523,plain,
! [SV14: $i] :
( ( ~ ( relation @ SV14 )
| ~ ( ~ ! [SY3196: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK14_C @ SY3196 @ SV14 )
!= ( sK15_SY3096 @ SY3196 @ SV14 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SY3196 @ SV14 ) @ SY3196 )
| ~ ( in @ ( sK15_SY3096 @ SY3196 @ SV14 ) @ SY3196 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK14_C @ SY3196 @ SV14 ) @ ( sK15_SY3096 @ SY3196 @ SV14 ) ) @ SV14 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK15_SY3096 @ SY3196 @ SV14 ) @ ( sK14_C @ SY3196 @ SV14 ) ) @ SV14 ) )
| ( is_connected_in @ SV14 @ SY3196 ) )
| ~ ! [SY3197: $i] :
( ~ ( is_connected_in @ SV14 @ SY3197 )
| ! [SY3198: $i,SY3199: $i] :
( ( SY3198 = SY3199 )
| ~ ( in @ SY3198 @ SY3197 )
| ~ ( in @ SY3199 @ SY3197 )
| ( in @ ( ordered_pair @ SY3198 @ SY3199 ) @ SV14 )
| ( in @ ( ordered_pair @ SY3199 @ SY3198 ) @ SV14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(524,plain,
! [SV15: $i] :
( ( ~ ( ~ ! [SY3200: $i,SY3201: $i] :
( ~ ( relation @ SY3201 )
| ! [SY3202: $i] :
( ~ ( in @ SY3202 @ ( relation_dom @ SY3201 ) )
| ~ ( in @ ( ordered_pair @ SY3202 @ SV15 ) @ SY3201 )
| ~ ( in @ SY3202 @ SY3200 ) )
| ( in @ SV15 @ ( relation_image @ SY3201 @ SY3200 ) ) )
| ~ ! [SY3203: $i,SY3204: $i] :
( ~ ( relation @ SY3204 )
| ~ ( in @ SV15 @ ( relation_image @ SY3204 @ SY3203 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK61_D @ SY3204 @ SY3203 @ SV15 ) @ ( relation_dom @ SY3204 ) )
| ~ ( in @ ( ordered_pair @ ( sK61_D @ SY3204 @ SY3203 @ SV15 ) @ SV15 ) @ SY3204 ) )
| ~ ( in @ ( sK61_D @ SY3204 @ SY3203 @ SV15 ) @ SY3203 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(525,plain,
! [SV16: $i] :
( ( ~ ( relation @ SV16 )
| ~ ( ~ ! [SY3205: $i,SY3206: $i] :
( ~ ( ~ ( ! [SY3207: $i] :
( ~ ( in @ ( ordered_pair @ SY3207 @ ( sK46_D @ SY3206 @ SY3205 @ SV16 ) ) @ SV16 )
| ~ ( in @ SY3207 @ SY3205 ) )
| ~ ( in @ ( sK46_D @ SY3206 @ SY3205 @ SV16 ) @ SY3206 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SY3206 @ SY3205 @ SV16 ) @ ( sK46_D @ SY3206 @ SY3205 @ SV16 ) ) @ SV16 )
| ~ ( in @ ( sK47_SY3118 @ SY3206 @ SY3205 @ SV16 ) @ SY3205 ) )
| ( in @ ( sK46_D @ SY3206 @ SY3205 @ SV16 ) @ SY3206 ) ) )
| ( SY3206
= ( relation_image @ SV16 @ SY3205 ) ) )
| ~ ! [SY3208: $i,SY3209: $i] :
( ( SY3209
!= ( relation_image @ SV16 @ SY3208 ) )
| ~ ( ~ ! [SY3210: $i] :
( ! [SY3211: $i] :
( ~ ( in @ ( ordered_pair @ SY3211 @ SY3210 ) @ SV16 )
| ~ ( in @ SY3211 @ SY3208 ) )
| ( in @ SY3210 @ SY3209 ) )
| ~ ! [SY3212: $i] :
( ~ ( in @ SY3212 @ SY3209 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SY3212 @ SY3209 @ SY3208 @ SV16 ) @ SY3212 ) @ SV16 )
| ~ ( in @ ( sK45_E @ SY3212 @ SY3209 @ SY3208 @ SV16 ) @ SY3208 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(526,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK64_B @ SX0 ) @ ( sK65_SY3126 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK65_SY3126 @ SX0 ) @ ( sK64_B @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK64_B @ SX0 )
!= ( sK65_SY3126 @ SX0 ) ) ) )
| ( antisymmetric @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX2 @ SX1 ) @ SX0 )
| ( SX1 = SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(527,plain,
! [SV17: $i] :
( ( ~ ( ~ ! [SY3213: $i,SY3214: $i] :
( ~ ( function @ SY3214 )
| ~ ( relation @ SY3214 )
| ( SY3213
!= ( apply @ SY3214 @ SV17 ) )
| ~ ( in @ SV17 @ ( relation_dom @ SY3214 ) )
| ( in @ ( ordered_pair @ SV17 @ SY3213 ) @ SY3214 ) )
| ~ ~ ( ~ ! [SY3215: $i,SY3216: $i] :
( ~ ( function @ SY3216 )
| ~ ( relation @ SY3216 )
| ~ ( in @ ( ordered_pair @ SV17 @ SY3215 ) @ SY3216 )
| ( SY3215
= ( apply @ SY3216 @ SV17 ) ) )
| ~ ! [SY3217: $i,SY3218: $i] :
( ~ ( function @ SY3218 )
| ~ ( relation @ SY3218 )
| ~ ( in @ ( ordered_pair @ SV17 @ SY3217 ) @ SY3218 )
| ( in @ SV17 @ ( relation_dom @ SY3218 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(528,plain,
! [SV18: $i] :
( ( ~ ( relation @ SV18 )
| ~ ( ~ ! [SY3219: $i,SY3220: $i] :
( ~ ( ~ ( ( ( sK35_D @ SY3220 @ SY3219 @ SV18 )
= SY3219 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SY3220 @ SY3219 @ SV18 ) @ SY3219 ) @ SV18 )
| ~ ( in @ ( sK35_D @ SY3220 @ SY3219 @ SV18 ) @ SY3220 ) )
| ~ ~ ( ~ ( ( ( sK35_D @ SY3220 @ SY3219 @ SV18 )
!= SY3219 )
| ( in @ ( sK35_D @ SY3220 @ SY3219 @ SV18 ) @ SY3220 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SY3220 @ SY3219 @ SV18 ) @ SY3219 ) @ SV18 )
| ( in @ ( sK35_D @ SY3220 @ SY3219 @ SV18 ) @ SY3220 ) ) ) )
| ( SY3220
= ( fiber @ SV18 @ SY3219 ) ) )
| ~ ! [SY3221: $i,SY3222: $i] :
( ( SY3222
!= ( fiber @ SV18 @ SY3221 ) )
| ~ ( ~ ! [SY3223: $i] :
( ( SY3223 = SY3221 )
| ~ ( in @ ( ordered_pair @ SY3223 @ SY3221 ) @ SV18 )
| ( in @ SY3223 @ SY3222 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY3222 )
| ( SX3 != SY3221 ) )
| ~ ! [SY3225: $i] :
( ~ ( in @ SY3225 @ SY3222 )
| ( in @ ( ordered_pair @ SY3225 @ SY3221 ) @ SV18 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(529,plain,
! [SV19: $i] :
( ( ~ ( relation @ SV19 )
| ~ ( ~ ! [SY3226: $i] :
( ~ ( ~ ( in @ ( sK36_C @ SY3226 @ SV19 ) @ SY3226 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SY3226 @ SV19 ) @ ( sK36_C @ SY3226 @ SV19 ) ) @ SV19 ) )
| ( is_reflexive_in @ SV19 @ SY3226 ) )
| ~ ! [SY3227: $i] :
( ~ ( is_reflexive_in @ SV19 @ SY3227 )
| ! [SY3228: $i] :
( ~ ( in @ SY3228 @ SY3227 )
| ( in @ ( ordered_pair @ SY3228 @ SY3228 ) @ SV19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(530,plain,
! [SV20: $i] :
( ( ~ ( relation @ SV20 )
| ~ ( ~ ! [SY3229: $i] :
( ~ ( relation @ SY3229 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SY3229 @ SV20 ) @ ( sK13_SY3095 @ SY3229 @ SV20 ) ) @ SY3229 )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SY3229 @ SV20 ) @ ( sK12_C @ SY3229 @ SV20 ) ) @ SV20 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SY3229 @ SV20 ) @ ( sK13_SY3095 @ SY3229 @ SV20 ) ) @ SY3229 )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ SY3229 @ SV20 ) @ ( sK12_C @ SY3229 @ SV20 ) ) @ SV20 ) ) )
| ( SY3229
= ( relation_inverse @ SV20 ) ) )
| ~ ! [SY3230: $i] :
( ~ ( relation @ SY3230 )
| ( SY3230
!= ( relation_inverse @ SV20 ) )
| ~ ( ~ ! [SY3231: $i,SY3232: $i] :
( ~ ( in @ ( ordered_pair @ SY3231 @ SY3232 ) @ SY3230 )
| ( in @ ( ordered_pair @ SY3232 @ SY3231 ) @ SV20 ) )
| ~ ! [SY3233: $i,SY3234: $i] :
( ~ ( in @ ( ordered_pair @ SY3234 @ SY3233 ) @ SV20 )
| ( in @ ( ordered_pair @ SY3233 @ SY3234 ) @ SY3230 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(531,plain,
! [SV21: $i] :
( ( ! [SY3235: $i] :
( ~ ( relation @ SY3235 )
| ~ ( ~ ! [SY3236: $i] :
( ~ ( relation @ SY3236 )
| ~ ( ~ ( ~ ( in @ ( sK49_SY3119 @ SY3236 @ SY3235 @ SV21 ) @ SV21 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SY3236 @ SY3235 @ SV21 ) @ ( sK49_SY3119 @ SY3236 @ SY3235 @ SV21 ) ) @ SY3235 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SY3236 @ SY3235 @ SV21 ) @ ( sK49_SY3119 @ SY3236 @ SY3235 @ SV21 ) ) @ SY3236 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_SY3119 @ SY3236 @ SY3235 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK48_D @ SY3236 @ SY3235 @ SV21 ) @ ( sK49_SY3119 @ SY3236 @ SY3235 @ SV21 ) ) @ SY3236 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SY3236 @ SY3235 @ SV21 ) @ ( sK49_SY3119 @ SY3236 @ SY3235 @ SV21 ) ) @ SY3235 )
| ( in @ ( ordered_pair @ ( sK48_D @ SY3236 @ SY3235 @ SV21 ) @ ( sK49_SY3119 @ SY3236 @ SY3235 @ SV21 ) ) @ SY3236 ) ) ) )
| ( SY3236
= ( relation_rng_restriction @ SV21 @ SY3235 ) ) )
| ~ ! [SY3237: $i] :
( ~ ( relation @ SY3237 )
| ( SY3237
!= ( relation_rng_restriction @ SV21 @ SY3235 ) )
| ~ ( ~ ! [SY3238: $i,SY3239: $i] :
( ~ ( in @ SY3239 @ SV21 )
| ~ ( in @ ( ordered_pair @ SY3238 @ SY3239 ) @ SY3235 )
| ( in @ ( ordered_pair @ SY3238 @ SY3239 ) @ SY3237 ) )
| ~ ~ ( ~ ! [SY3240: $i,SY3241: $i] :
( ~ ( in @ ( ordered_pair @ SY3240 @ SY3241 ) @ SY3237 )
| ( in @ SY3241 @ SV21 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3237 )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3235 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(532,plain,
! [SV22: $i] :
( ( ~ ( relation @ SV22 )
| ~ ( ~ ! [SY3244: $i] :
( ~ ( ~ ( ! [SY3245: $i] :
~ ( in @ ( ordered_pair @ SY3245 @ ( sK17_C @ SY3244 @ SV22 ) ) @ SV22 )
| ~ ( in @ ( sK17_C @ SY3244 @ SV22 ) @ SY3244 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK18_SY3098 @ SY3244 @ SV22 ) @ ( sK17_C @ SY3244 @ SV22 ) ) @ SV22 )
| ( in @ ( sK17_C @ SY3244 @ SV22 ) @ SY3244 ) ) )
| ( SY3244
= ( relation_rng @ SV22 ) ) )
| ~ ! [SY3246: $i] :
( ( SY3246
!= ( relation_rng @ SV22 ) )
| ~ ( ~ ! [SY3247: $i] :
( ! [SY3248: $i] :
~ ( in @ ( ordered_pair @ SY3248 @ SY3247 ) @ SV22 )
| ( in @ SY3247 @ SY3246 ) )
| ~ ! [SY3249: $i] :
( ~ ( in @ SY3249 @ SY3246 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3249 @ SY3246 @ SV22 ) @ SY3249 ) @ SV22 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(533,plain,
! [SV23: $i] :
( ( ~ ( relation @ SV23 )
| ~ ( ~ ! [SY3250: $i] :
( ~ ( relation @ SY3250 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3250 @ SV23 ) @ ( sK25_SY3102 @ SY3250 @ SV23 ) ) @ SV23 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3250 @ SV23 ) @ ( sK25_SY3102 @ SY3250 @ SV23 ) ) @ SY3250 ) )
| ( subset @ SV23 @ SY3250 ) )
| ~ ! [SY3251: $i] :
( ~ ( relation @ SY3251 )
| ~ ( subset @ SV23 @ SY3251 )
| ! [SY3252: $i,SY3253: $i] :
( ~ ( in @ ( ordered_pair @ SY3252 @ SY3253 ) @ SV23 )
| ( in @ ( ordered_pair @ SY3252 @ SY3253 ) @ SY3251 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(534,plain,
! [SV24: $i] :
( ( ~ ( relation @ SV24 )
| ~ ( ~ ! [SY3254: $i,SY3255: $i] :
( ~ ( relation @ SY3255 )
| ~ ( ~ ( ~ ( in @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ SY3254 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ ( sK51_SY3120 @ SY3255 @ SY3254 @ SV24 ) ) @ SV24 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ ( sK51_SY3120 @ SY3255 @ SY3254 @ SV24 ) ) @ SY3255 ) )
| ~ ~ ( ~ ( ( in @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ SY3254 )
| ( in @ ( ordered_pair @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ ( sK51_SY3120 @ SY3255 @ SY3254 @ SV24 ) ) @ SY3255 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ ( sK51_SY3120 @ SY3255 @ SY3254 @ SV24 ) ) @ SV24 )
| ( in @ ( ordered_pair @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ ( sK51_SY3120 @ SY3255 @ SY3254 @ SV24 ) ) @ SY3255 ) ) ) )
| ( SY3255
= ( relation_dom_restriction @ SV24 @ SY3254 ) ) )
| ~ ! [SY3256: $i,SY3257: $i] :
( ~ ( relation @ SY3257 )
| ( SY3257
!= ( relation_dom_restriction @ SV24 @ SY3256 ) )
| ~ ( ~ ! [SY3258: $i,SY3259: $i] :
( ~ ( in @ SY3258 @ SY3256 )
| ~ ( in @ ( ordered_pair @ SY3258 @ SY3259 ) @ SV24 )
| ( in @ ( ordered_pair @ SY3258 @ SY3259 ) @ SY3257 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3257 )
| ( in @ SX3 @ SY3256 ) )
| ~ ! [SY3262: $i,SY3263: $i] :
( ~ ( in @ ( ordered_pair @ SY3262 @ SY3263 ) @ SY3257 )
| ( in @ ( ordered_pair @ SY3262 @ SY3263 ) @ SV24 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(535,plain,
! [SV25: $i] :
( ( ! [SY3264: $i] :
~ ( ~ ! [SY3265: $i] :
( ! [SY3266: $i] :
( ( ordered_pair @ SV25 @ SY3264 )
!= ( ordered_pair @ SY3265 @ SY3266 ) )
| ( SV25 = SY3265 ) )
| ~ ! [SY3267: $i,SY3268: $i] :
( ( ( ordered_pair @ SV25 @ SY3264 )
!= ( ordered_pair @ SY3267 @ SY3268 ) )
| ( SY3264 = SY3268 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(536,plain,
! [SV26: $i] :
( ( ~ ( function @ SV26 )
| ~ ( relation @ SV26 )
| ~ ( ~ ~ ( ~ ! [SY3269: $i] :
( ~ ( in @ SY3269 @ ( relation_dom @ SV26 ) )
| ! [SY3270: $i] :
( ( SY3270
!= ( apply @ SV26 @ SY3269 ) )
| ( in @ ( ordered_pair @ SY3269 @ SY3270 ) @ SV26 ) ) )
| ~ ! [SY3271: $i] :
( ~ ( in @ SY3271 @ ( relation_dom @ SV26 ) )
| ! [SY3272: $i] :
( ~ ( in @ ( ordered_pair @ SY3271 @ SY3272 ) @ SV26 )
| ( SY3272
= ( apply @ SV26 @ SY3271 ) ) ) ) )
| ~ ~ ( ~ ! [SY3273: $i] :
( ( in @ SY3273 @ ( relation_dom @ SV26 ) )
| ! [SY3274: $i] :
( ( SY3274
!= ( apply @ SV26 @ SY3273 ) )
| ( SY3274 = empty_set ) ) )
| ~ ! [SY3275: $i] :
( ( in @ SY3275 @ ( relation_dom @ SV26 ) )
| ! [SY3276: $i] :
( ( SY3276 != empty_set )
| ( SY3276
= ( apply @ SV26 @ SY3275 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(537,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK62_B @ SX0 )
!= ( sK63_SY3125 @ SX0 ) ) )
| ~ ~ ( ~ ( in @ ( sK62_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ( in @ ( sK63_SY3125 @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK62_B @ SX0 ) @ ( sK63_SY3125 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK63_SY3125 @ SX0 ) @ ( sK62_B @ SX0 ) ) @ SX0 ) )
| ( connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( connected @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( SX1 = SX2 )
| ~ ( in @ SX1 @ ( relation_field @ SX0 ) )
| ~ ( in @ SX2 @ ( relation_field @ SX0 ) )
| ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(538,plain,
! [SV27: $i] :
( ( ~ ( relation @ SV27 )
| ~ ( ~ ! [SY3277: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_C @ SY3277 @ SV27 ) @ SY3277 )
| ~ ( in @ ( sK20_SY3099 @ SY3277 @ SV27 ) @ SY3277 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SY3277 @ SV27 ) @ ( sK20_SY3099 @ SY3277 @ SV27 ) ) @ SV27 ) )
| ~ ( in @ ( ordered_pair @ ( sK20_SY3099 @ SY3277 @ SV27 ) @ ( sK19_C @ SY3277 @ SV27 ) ) @ SV27 ) )
| ~ ( ( ( sK19_C @ SY3277 @ SV27 )
!= ( sK20_SY3099 @ SY3277 @ SV27 ) ) ) )
| ( is_antisymmetric_in @ SV27 @ SY3277 ) )
| ~ ! [SY3278: $i] :
( ~ ( is_antisymmetric_in @ SV27 @ SY3278 )
| ! [SY3279: $i,SY3280: $i] :
( ~ ( in @ SY3279 @ SY3278 )
| ~ ( in @ SY3280 @ SY3278 )
| ~ ( in @ ( ordered_pair @ SY3279 @ SY3280 ) @ SV27 )
| ~ ( in @ ( ordered_pair @ SY3280 @ SY3279 ) @ SV27 )
| ( SY3279 = SY3280 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(539,plain,
! [SV28: $i] :
( ( ! [SY3281: $i] :
~ ( ~ ! [SY3282: $i,SY3283: $i] :
( ~ ( in @ SV28 @ SY3282 )
| ~ ( in @ SY3281 @ SY3283 )
| ( in @ ( ordered_pair @ SV28 @ SY3281 ) @ ( cartesian_product2 @ SY3282 @ SY3283 ) ) )
| ~ ~ ( ~ ! [SY3284: $i] :
( ! [SY3285: $i] :
~ ( in @ ( ordered_pair @ SV28 @ SY3281 ) @ ( cartesian_product2 @ SY3284 @ SY3285 ) )
| ( in @ SV28 @ SY3284 ) )
| ~ ! [SY3286: $i,SY3287: $i] :
( ~ ( in @ ( ordered_pair @ SV28 @ SY3281 ) @ ( cartesian_product2 @ SY3286 @ SY3287 ) )
| ( in @ SY3281 @ SY3287 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(540,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK66_B @ SX0 ) @ ( sK67_SY3127 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK67_SY3127 @ SX0 ) @ ( sK68_SY3129 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK66_B @ SX0 ) @ ( sK68_SY3129 @ SX0 ) ) @ SX0 ) )
| ( transitive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( transitive @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX1 @ SX3 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(541,plain,
! [SV29: $i] :
( ( ! [SY3288: $i] :
~ ( ~ ! [SY3289: $i,SY3290: $i] :
( ~ ( in @ SV29 @ SY3289 )
| ~ ( in @ SY3288 @ SY3290 )
| ( in @ ( ordered_pair @ SV29 @ SY3288 ) @ ( cartesian_product2 @ SY3289 @ SY3290 ) ) )
| ~ ~ ( ~ ! [SY3291: $i] :
( ! [SY3292: $i] :
~ ( in @ ( ordered_pair @ SV29 @ SY3288 ) @ ( cartesian_product2 @ SY3291 @ SY3292 ) )
| ( in @ SV29 @ SY3291 ) )
| ~ ! [SY3293: $i,SY3294: $i] :
( ~ ( in @ ( ordered_pair @ SV29 @ SY3288 ) @ ( cartesian_product2 @ SY3293 @ SY3294 ) )
| ( in @ SY3288 @ SY3294 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(542,plain,
! [SV30: $i] :
( ( ~ ( relation @ SV30 )
| ~ ( ~ ! [SY3295: $i,SY3296: $i] :
( ~ ( ~ ( ! [SY3297: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ SY3296 @ SY3295 @ SV30 ) @ SY3297 ) @ SV30 )
| ~ ( in @ SY3297 @ SY3295 ) )
| ~ ( in @ ( sK43_D @ SY3296 @ SY3295 @ SV30 ) @ SY3296 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SY3296 @ SY3295 @ SV30 ) @ ( sK44_SY3116 @ SY3296 @ SY3295 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK44_SY3116 @ SY3296 @ SY3295 @ SV30 ) @ SY3295 ) )
| ( in @ ( sK43_D @ SY3296 @ SY3295 @ SV30 ) @ SY3296 ) ) )
| ( SY3296
= ( relation_inverse_image @ SV30 @ SY3295 ) ) )
| ~ ! [SY3298: $i,SY3299: $i] :
( ( SY3299
!= ( relation_inverse_image @ SV30 @ SY3298 ) )
| ~ ( ~ ! [SY3300: $i] :
( ! [SY3301: $i] :
( ~ ( in @ ( ordered_pair @ SY3300 @ SY3301 ) @ SV30 )
| ~ ( in @ SY3301 @ SY3298 ) )
| ( in @ SY3300 @ SY3299 ) )
| ~ ! [SY3302: $i] :
( ~ ( in @ SY3302 @ SY3299 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3302 @ ( sK42_E @ SY3302 @ SY3299 @ SY3298 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK42_E @ SY3302 @ SY3299 @ SY3298 @ SV30 ) @ SY3298 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(543,plain,
! [SV31: $i] :
( ( ~ ( ~ ! [SY3303: $i,SY3304: $i] :
( ~ ( relation @ SY3304 )
| ~ ( in @ ( ordered_pair @ SV31 @ SY3303 ) @ SY3304 )
| ( in @ SV31 @ ( relation_dom @ SY3304 ) ) )
| ~ ! [SY3305: $i,SY3306: $i] :
( ~ ( relation @ SY3306 )
| ~ ( in @ ( ordered_pair @ SV31 @ SY3305 ) @ SY3306 )
| ( in @ SY3305 @ ( relation_rng @ SY3306 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(544,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( in @ ( sK69_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK69_B @ SX0 ) @ ( sK69_B @ SX0 ) ) @ SX0 ) )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ ( relation_field @ SX0 ) )
| ( in @ ( ordered_pair @ SX1 @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(545,plain,
! [SV32: $i] :
( ( ~ ( relation @ SV32 )
| ! [SY3307: $i] :
( ~ ( relation @ SY3307 )
| ~ ( ~ ! [SY3308: $i] :
( ~ ( function @ SY3308 )
| ~ ( relation @ SY3308 )
| ~ ( ~ ( ~ ( in @ ( sK10_D @ SY3308 @ SY3307 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( sK11_SY3094 @ SY3308 @ SY3307 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3308 @ ( sK10_D @ SY3308 @ SY3307 @ SV32 ) ) @ ( apply @ SY3308 @ ( sK11_SY3094 @ SY3308 @ SY3307 @ SV32 ) ) ) @ SY3307 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY3308 @ SY3307 @ SV32 ) @ ( sK11_SY3094 @ SY3308 @ SY3307 @ SV32 ) ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SY3308 @ SY3307 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3308 @ SY3307 @ SV32 ) @ ( sK11_SY3094 @ SY3308 @ SY3307 @ SV32 ) ) @ SV32 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SY3308 @ SY3307 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3308 @ SY3307 @ SV32 ) @ ( sK11_SY3094 @ SY3308 @ SY3307 @ SV32 ) ) @ SV32 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SY3308 @ ( sK10_D @ SY3308 @ SY3307 @ SV32 ) ) @ ( apply @ SY3308 @ ( sK11_SY3094 @ SY3308 @ SY3307 @ SV32 ) ) ) @ SY3307 )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3308 @ SY3307 @ SV32 ) @ ( sK11_SY3094 @ SY3308 @ SY3307 @ SV32 ) ) @ SV32 ) ) ) )
| ( ( relation_dom @ SY3308 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SY3308 )
!= ( relation_field @ SY3307 ) )
| ~ ( one_to_one @ SY3308 )
| ( relation_isomorphism @ SV32 @ SY3307 @ SY3308 ) )
| ~ ~ ( ~ ! [SY3309: $i] :
( ~ ( function @ SY3309 )
| ~ ( relation @ SY3309 )
| ~ ( relation_isomorphism @ SV32 @ SY3307 @ SY3309 )
| ~ ( ~ ! [SY3310: $i,SY3311: $i] :
( ~ ( in @ SY3310 @ ( relation_field @ SV32 ) )
| ~ ( in @ SY3311 @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3309 @ SY3310 ) @ ( apply @ SY3309 @ SY3311 ) ) @ SY3307 )
| ( in @ ( ordered_pair @ SY3310 @ SY3311 ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3312: $i] :
( ! [SY3313: $i] :
~ ( in @ ( ordered_pair @ SY3312 @ SY3313 ) @ SV32 )
| ( in @ SY3312 @ ( relation_field @ SV32 ) ) )
| ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV32 )
| ( in @ SY3315 @ ( relation_field @ SV32 ) ) ) )
| ~ ! [SY3316: $i,SY3317: $i] :
( ~ ( in @ ( ordered_pair @ SY3316 @ SY3317 ) @ SV32 )
| ( in @ ( ordered_pair @ ( apply @ SY3309 @ SY3316 ) @ ( apply @ SY3309 @ SY3317 ) ) @ SY3307 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3318: $i] :
( ~ ( function @ SY3318 )
| ~ ( relation @ SY3318 )
| ~ ( relation_isomorphism @ SV32 @ SY3307 @ SY3318 )
| ( ( relation_dom @ SY3318 )
= ( relation_field @ SV32 ) ) )
| ~ ! [SY3319: $i] :
( ~ ( function @ SY3319 )
| ~ ( relation @ SY3319 )
| ~ ( relation_isomorphism @ SV32 @ SY3307 @ SY3319 )
| ( ( relation_rng @ SY3319 )
= ( relation_field @ SY3307 ) ) ) )
| ~ ! [SY3320: $i] :
( ~ ( function @ SY3320 )
| ~ ( relation @ SY3320 )
| ~ ( relation_isomorphism @ SV32 @ SY3307 @ SY3320 )
| ( one_to_one @ SY3320 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(546,plain,
! [SV33: $i] :
( ( ~ ( ~ ! [SY3321: $i,SY3322: $i] :
( ~ ( relation_of2_as_subset @ SY3322 @ SV33 @ SY3321 )
| ~ ( ~ ! [SY3323: $i] :
~ ( in @ ( ordered_pair @ SY3323 @ ( sK57_D @ SY3322 @ SY3321 @ SV33 ) ) @ SY3322 )
| ~ ( in @ ( sK57_D @ SY3322 @ SY3321 @ SV33 ) @ SY3321 ) )
| ( ( relation_rng_as_subset @ SV33 @ SY3321 @ SY3322 )
= SY3321 ) )
| ~ ! [SY3324: $i,SY3325: $i] :
( ~ ( relation_of2_as_subset @ SY3325 @ SV33 @ SY3324 )
| ( ( relation_rng_as_subset @ SV33 @ SY3324 @ SY3325 )
!= SY3324 )
| ! [SY3326: $i] :
( ( in @ ( ordered_pair @ ( sK56_E @ SY3326 @ SY3325 @ SY3324 @ SV33 ) @ SY3326 ) @ SY3325 )
| ~ ( in @ SY3326 @ SY3324 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(547,plain,
! [SV34: $i] :
( ( ~ ( relation @ SV34 )
| ~ ( ~ ! [SY3327: $i] :
( ~ ( ~ ( ! [SY3328: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SY3327 @ SV34 ) @ SY3328 ) @ SV34 )
| ~ ( in @ ( sK22_C @ SY3327 @ SV34 ) @ SY3327 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SY3327 @ SV34 ) @ ( sK23_SY3101 @ SY3327 @ SV34 ) ) @ SV34 )
| ( in @ ( sK22_C @ SY3327 @ SV34 ) @ SY3327 ) ) )
| ( SY3327
= ( relation_dom @ SV34 ) ) )
| ~ ! [SY3329: $i] :
( ( SY3329
!= ( relation_dom @ SV34 ) )
| ~ ( ~ ! [SY3330: $i] :
( ! [SY3331: $i] :
~ ( in @ ( ordered_pair @ SY3330 @ SY3331 ) @ SV34 )
| ( in @ SY3330 @ SY3329 ) )
| ~ ! [SY3332: $i] :
( ~ ( in @ SY3332 @ SY3329 )
| ( in @ ( ordered_pair @ SY3332 @ ( sK21_D @ SY3332 @ SY3329 @ SV34 ) ) @ SV34 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(548,plain,
! [SV1: $i] :
( ( ( ~ ( relation @ SV1 ) )
= $true )
| ( ( ( in @ ( ordered_pair @ ( sK54_B @ SV1 ) @ ( sK55_SY3122 @ SV1 ) ) @ SV1 )
| ( SV1 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[507]) ).
thf(549,plain,
! [SV35: $i,SV2: $i] :
( ( ( ordered_pair @ SV2 @ SV35 )
= ( unordered_pair @ ( unordered_pair @ SV2 @ SV35 ) @ ( singleton @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(550,plain,
! [SV36: $i,SV3: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV3 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(551,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK39_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK39_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[511]) ).
thf(552,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK37_C @ SX1 @ SX0 ) @ ( sK38_SY3111 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[511]) ).
thf(553,plain,
! [SV4: $i] :
( ( ( ~ ( relation @ SV4 ) )
= $true )
| ( ( ~ ( ~ ! [SY3132: $i] :
( ~ ( relation @ SY3132 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SY3132 @ SV4 ) @ ( sK32_SY3109 @ SY3132 @ SV4 ) ) @ SV4 )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ SY3132 @ SV4 ) @ ( sK32_SY3109 @ SY3132 @ SV4 ) ) @ SY3132 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK31_C @ SY3132 @ SV4 ) @ ( sK32_SY3109 @ SY3132 @ SV4 ) ) @ SV4 )
| ( in @ ( ordered_pair @ ( sK31_C @ SY3132 @ SV4 ) @ ( sK32_SY3109 @ SY3132 @ SV4 ) ) @ SY3132 ) ) )
| ( SV4 = SY3132 ) )
| ~ ! [SY3133: $i] :
( ~ ( relation @ SY3133 )
| ( SV4 != SY3133 )
| ~ ( ~ ! [SY3134: $i,SY3135: $i] :
( ~ ( in @ ( ordered_pair @ SY3134 @ SY3135 ) @ SV4 )
| ( in @ ( ordered_pair @ SY3134 @ SY3135 ) @ SY3133 ) )
| ~ ! [SY3136: $i,SY3137: $i] :
( ~ ( in @ ( ordered_pair @ SY3136 @ SY3137 ) @ SY3133 )
| ( in @ ( ordered_pair @ SY3136 @ SY3137 ) @ SV4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[512]) ).
thf(554,plain,
! [SV5: $i] :
( ( ( ~ ( relation @ SV5 ) )
= $true )
| ( ( ~ ( ~ ! [SY3138: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SY3138 @ SV5 ) @ SY3138 )
| ~ ( in @ ( sK4_SY3086 @ SY3138 @ SV5 ) @ SY3138 ) )
| ~ ( in @ ( sK5_SY3088 @ SY3138 @ SV5 ) @ SY3138 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SY3138 @ SV5 ) @ ( sK4_SY3086 @ SY3138 @ SV5 ) ) @ SV5 ) )
| ~ ( in @ ( ordered_pair @ ( sK4_SY3086 @ SY3138 @ SV5 ) @ ( sK5_SY3088 @ SY3138 @ SV5 ) ) @ SV5 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK3_C @ SY3138 @ SV5 ) @ ( sK5_SY3088 @ SY3138 @ SV5 ) ) @ SV5 ) )
| ( is_transitive_in @ SV5 @ SY3138 ) )
| ~ ! [SY3139: $i] :
( ~ ( is_transitive_in @ SV5 @ SY3139 )
| ! [SY3140: $i,SY3141: $i,SY3142: $i] :
( ~ ( in @ SY3140 @ SY3139 )
| ~ ( in @ SY3141 @ SY3139 )
| ~ ( in @ SY3142 @ SY3139 )
| ~ ( in @ ( ordered_pair @ SY3140 @ SY3141 ) @ SV5 )
| ~ ( in @ ( ordered_pair @ SY3141 @ SY3142 ) @ SV5 )
| ( in @ ( ordered_pair @ SY3140 @ SY3142 ) @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[513]) ).
thf(555,plain,
! [SV6: $i] :
( ( ~ ! [SY3143: $i,SY3144: $i] :
( ~ ( relation_of2_as_subset @ SY3144 @ SY3143 @ SV6 )
| ~ ( ~ ! [SY3145: $i] :
~ ( in @ ( ordered_pair @ ( sK59_D @ SY3144 @ SY3143 @ SV6 ) @ SY3145 ) @ SY3144 )
| ~ ( in @ ( sK59_D @ SY3144 @ SY3143 @ SV6 ) @ SY3143 ) )
| ( ( relation_dom_as_subset @ SY3143 @ SV6 @ SY3144 )
= SY3143 ) )
| ~ ! [SY3146: $i,SY3147: $i] :
( ~ ( relation_of2_as_subset @ SY3147 @ SY3146 @ SV6 )
| ( ( relation_dom_as_subset @ SY3146 @ SV6 @ SY3147 )
!= SY3146 )
| ! [SY3148: $i] :
( ( in @ ( ordered_pair @ SY3148 @ ( sK58_E @ SY3148 @ SY3147 @ SY3146 @ SV6 ) ) @ SY3147 )
| ~ ( in @ SY3148 @ SY3146 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(556,plain,
! [SV7: $i] :
( ( ( ~ ( relation @ SV7 ) )
= $true )
| ( ( ! [SY3149: $i] :
( ~ ( relation @ SY3149 )
| ~ ( ~ ! [SY3150: $i] :
( ~ ( relation @ SY3150 )
| ~ ( ~ ( ! [SY3151: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3150 @ SY3149 @ SV7 ) @ SY3151 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3151 @ ( sK8_SY3089 @ SY3150 @ SY3149 @ SV7 ) ) @ SY3149 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3150 @ SY3149 @ SV7 ) @ ( sK8_SY3089 @ SY3150 @ SY3149 @ SV7 ) ) @ SY3150 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3150 @ SY3149 @ SV7 ) @ ( sK9_SY3093 @ SY3150 @ SY3149 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SY3150 @ SY3149 @ SV7 ) @ ( sK8_SY3089 @ SY3150 @ SY3149 @ SV7 ) ) @ SY3149 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SY3150 @ SY3149 @ SV7 ) @ ( sK8_SY3089 @ SY3150 @ SY3149 @ SV7 ) ) @ SY3150 ) ) )
| ( SY3150
= ( relation_composition @ SV7 @ SY3149 ) ) )
| ~ ! [SY3152: $i] :
( ~ ( relation @ SY3152 )
| ( SY3152
!= ( relation_composition @ SV7 @ SY3149 ) )
| ~ ( ~ ! [SY3153: $i,SY3154: $i] :
( ! [SY3155: $i] :
( ~ ( in @ ( ordered_pair @ SY3153 @ SY3155 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3155 @ SY3154 ) @ SY3149 ) )
| ( in @ ( ordered_pair @ SY3153 @ SY3154 ) @ SY3152 ) )
| ~ ! [SY3156: $i,SY3157: $i] :
( ~ ( in @ ( ordered_pair @ SY3156 @ SY3157 ) @ SY3152 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3156 @ ( sK6_F @ SY3157 @ SY3156 @ SY3152 @ SY3149 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY3157 @ SY3156 @ SY3152 @ SY3149 @ SV7 ) @ SY3157 ) @ SY3149 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[515]) ).
thf(557,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK52_C @ SX1 @ SX0 )
!= ( sK53_SY3121 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK52_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK52_C @ SX1 @ SX0 ) @ ( sK53_SY3121 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK52_C @ SX1 @ SX0 )
= ( sK53_SY3121 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK52_C @ SX1 @ SX0 ) @ ( sK53_SY3121 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK52_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK52_C @ SX1 @ SX0 ) @ ( sK53_SY3121 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[516]) ).
thf(558,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( SX2 = SX3 ) )
| ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[516]) ).
thf(559,plain,
! [SV8: $i] :
( ( ( ! [SY3158: $i,SY3159: $i] :
( SV8
!= ( ordered_pair @ SY3158 @ SY3159 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3160: $i] :
( ~ ( ( SV8
!= ( ordered_pair @ ( sK40_C @ SY3160 @ SV8 ) @ ( sK41_SY3114 @ SY3160 @ SV8 ) ) )
| ~ ( ( SY3160
!= ( sK40_C @ SY3160 @ SV8 ) ) ) )
| ( SY3160
= ( pair_first @ SV8 ) ) )
| ~ ! [SY3161: $i] :
( ( SY3161
!= ( pair_first @ SV8 ) )
| ! [SY3162: $i] :
( ! [SY3163: $i] :
( SV8
!= ( ordered_pair @ SY3162 @ SY3163 ) )
| ( SY3161 = SY3162 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[517]) ).
thf(560,plain,
! [SV37: $i,SV9: $i] :
( ( ~ ( ~ ! [SY3333: $i,SY3334: $i] :
( ~ ( relation @ SY3334 )
| ~ ( in @ SV9 @ SY3333 )
| ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ SY3334 )
| ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SY3333 ) @ SY3334 ) ) )
| ~ ~ ( ~ ! [SY3335: $i,SY3336: $i] :
( ~ ( relation @ SY3336 )
| ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SY3335 ) @ SY3336 ) )
| ( in @ SV9 @ SY3335 ) )
| ~ ! [SY3337: $i,SY3338: $i] :
( ~ ( relation @ SY3338 )
| ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SY3337 ) @ SY3338 ) )
| ( in @ ( ordered_pair @ SV9 @ SV37 ) @ SY3338 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(561,plain,
! [SV10: $i] :
( ( ~ ! [SY3171: $i,SY3172: $i] :
( ~ ( relation @ SY3172 )
| ! [SY3173: $i] :
( ~ ( in @ SY3173 @ ( relation_rng @ SY3172 ) )
| ~ ( in @ ( ordered_pair @ SV10 @ SY3173 ) @ SY3172 )
| ~ ( in @ SY3173 @ SY3171 ) )
| ( in @ SV10 @ ( relation_inverse_image @ SY3172 @ SY3171 ) ) )
| ~ ! [SY3174: $i,SY3175: $i] :
( ~ ( relation @ SY3175 )
| ~ ( in @ SV10 @ ( relation_inverse_image @ SY3175 @ SY3174 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_D @ SY3175 @ SY3174 @ SV10 ) @ ( relation_rng @ SY3175 ) )
| ~ ( in @ ( ordered_pair @ SV10 @ ( sK60_D @ SY3175 @ SY3174 @ SV10 ) ) @ SY3175 ) )
| ~ ( in @ ( sK60_D @ SY3175 @ SY3174 @ SV10 ) @ SY3174 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(562,plain,
! [SV11: $i] :
( ( ~ ! [SY3176: $i,SY3177: $i] :
( ~ ( ~ ( ! [SY3178: $i,SY3179: $i] :
( ~ ( in @ SY3178 @ SV11 )
| ~ ( in @ SY3179 @ SY3176 )
| ( ( sK28_D @ SY3177 @ SY3176 @ SV11 )
!= ( ordered_pair @ SY3178 @ SY3179 ) ) )
| ~ ( in @ ( sK28_D @ SY3177 @ SY3176 @ SV11 ) @ SY3177 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY3106 @ SY3177 @ SY3176 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK30_SY3108 @ SY3177 @ SY3176 @ SV11 ) @ SY3176 ) )
| ( ( sK28_D @ SY3177 @ SY3176 @ SV11 )
!= ( ordered_pair @ ( sK29_SY3106 @ SY3177 @ SY3176 @ SV11 ) @ ( sK30_SY3108 @ SY3177 @ SY3176 @ SV11 ) ) ) )
| ( in @ ( sK28_D @ SY3177 @ SY3176 @ SV11 ) @ SY3177 ) ) )
| ( SY3177
= ( cartesian_product2 @ SV11 @ SY3176 ) ) )
| ~ ! [SY3180: $i,SY3181: $i] :
( ( SY3181
!= ( cartesian_product2 @ SV11 @ SY3180 ) )
| ~ ( ~ ! [SY3182: $i] :
( ! [SY3183: $i,SY3184: $i] :
( ~ ( in @ SY3183 @ SV11 )
| ~ ( in @ SY3184 @ SY3180 )
| ( SY3182
!= ( ordered_pair @ SY3183 @ SY3184 ) ) )
| ( in @ SY3182 @ SY3181 ) )
| ~ ! [SY3185: $i] :
( ~ ( in @ SY3185 @ SY3181 )
| ~ ( ~ ~ ( ~ ( in @ ( sK26_E @ SY3185 @ SY3181 @ SY3180 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK27_SY3103 @ SY3185 @ SY3181 @ SY3180 @ SV11 ) @ SY3180 ) )
| ( SY3185
!= ( ordered_pair @ ( sK26_E @ SY3185 @ SY3181 @ SY3180 @ SV11 ) @ ( sK27_SY3103 @ SY3185 @ SY3181 @ SY3180 @ SV11 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[520]) ).
thf(563,plain,
! [SV12: $i] :
( ( ~ ! [SY3186: $i,SY3187: $i] :
( ~ ( relation @ SY3187 )
| ~ ( in @ ( ordered_pair @ SV12 @ SY3186 ) @ SY3187 )
| ( in @ SV12 @ ( relation_field @ SY3187 ) ) )
| ~ ! [SY3188: $i,SY3189: $i] :
( ~ ( relation @ SY3189 )
| ~ ( in @ ( ordered_pair @ SV12 @ SY3188 ) @ SY3189 )
| ( in @ SY3188 @ ( relation_field @ SY3189 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[521]) ).
thf(564,plain,
! [SV13: $i] :
( ( ( ! [SY3190: $i,SY3191: $i] :
( SV13
!= ( ordered_pair @ SY3190 @ SY3191 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3192: $i] :
( ~ ( ( SV13
!= ( ordered_pair @ ( sK33_C @ SY3192 @ SV13 ) @ ( sK34_SY3110 @ SY3192 @ SV13 ) ) )
| ~ ( ( SY3192
!= ( sK34_SY3110 @ SY3192 @ SV13 ) ) ) )
| ( SY3192
= ( pair_second @ SV13 ) ) )
| ~ ! [SY3193: $i] :
( ( SY3193
!= ( pair_second @ SV13 ) )
| ! [SY3194: $i,SY3195: $i] :
( ( SV13
!= ( ordered_pair @ SY3194 @ SY3195 ) )
| ( SY3193 = SY3195 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[522]) ).
thf(565,plain,
! [SV14: $i] :
( ( ( ~ ( relation @ SV14 ) )
= $true )
| ( ( ~ ( ~ ! [SY3196: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK14_C @ SY3196 @ SV14 )
!= ( sK15_SY3096 @ SY3196 @ SV14 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SY3196 @ SV14 ) @ SY3196 )
| ~ ( in @ ( sK15_SY3096 @ SY3196 @ SV14 ) @ SY3196 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK14_C @ SY3196 @ SV14 ) @ ( sK15_SY3096 @ SY3196 @ SV14 ) ) @ SV14 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK15_SY3096 @ SY3196 @ SV14 ) @ ( sK14_C @ SY3196 @ SV14 ) ) @ SV14 ) )
| ( is_connected_in @ SV14 @ SY3196 ) )
| ~ ! [SY3197: $i] :
( ~ ( is_connected_in @ SV14 @ SY3197 )
| ! [SY3198: $i,SY3199: $i] :
( ( SY3198 = SY3199 )
| ~ ( in @ SY3198 @ SY3197 )
| ~ ( in @ SY3199 @ SY3197 )
| ( in @ ( ordered_pair @ SY3198 @ SY3199 ) @ SV14 )
| ( in @ ( ordered_pair @ SY3199 @ SY3198 ) @ SV14 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[523]) ).
thf(566,plain,
! [SV15: $i] :
( ( ~ ! [SY3200: $i,SY3201: $i] :
( ~ ( relation @ SY3201 )
| ! [SY3202: $i] :
( ~ ( in @ SY3202 @ ( relation_dom @ SY3201 ) )
| ~ ( in @ ( ordered_pair @ SY3202 @ SV15 ) @ SY3201 )
| ~ ( in @ SY3202 @ SY3200 ) )
| ( in @ SV15 @ ( relation_image @ SY3201 @ SY3200 ) ) )
| ~ ! [SY3203: $i,SY3204: $i] :
( ~ ( relation @ SY3204 )
| ~ ( in @ SV15 @ ( relation_image @ SY3204 @ SY3203 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK61_D @ SY3204 @ SY3203 @ SV15 ) @ ( relation_dom @ SY3204 ) )
| ~ ( in @ ( ordered_pair @ ( sK61_D @ SY3204 @ SY3203 @ SV15 ) @ SV15 ) @ SY3204 ) )
| ~ ( in @ ( sK61_D @ SY3204 @ SY3203 @ SV15 ) @ SY3203 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(567,plain,
! [SV16: $i] :
( ( ( ~ ( relation @ SV16 ) )
= $true )
| ( ( ~ ( ~ ! [SY3205: $i,SY3206: $i] :
( ~ ( ~ ( ! [SY3207: $i] :
( ~ ( in @ ( ordered_pair @ SY3207 @ ( sK46_D @ SY3206 @ SY3205 @ SV16 ) ) @ SV16 )
| ~ ( in @ SY3207 @ SY3205 ) )
| ~ ( in @ ( sK46_D @ SY3206 @ SY3205 @ SV16 ) @ SY3206 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SY3206 @ SY3205 @ SV16 ) @ ( sK46_D @ SY3206 @ SY3205 @ SV16 ) ) @ SV16 )
| ~ ( in @ ( sK47_SY3118 @ SY3206 @ SY3205 @ SV16 ) @ SY3205 ) )
| ( in @ ( sK46_D @ SY3206 @ SY3205 @ SV16 ) @ SY3206 ) ) )
| ( SY3206
= ( relation_image @ SV16 @ SY3205 ) ) )
| ~ ! [SY3208: $i,SY3209: $i] :
( ( SY3209
!= ( relation_image @ SV16 @ SY3208 ) )
| ~ ( ~ ! [SY3210: $i] :
( ! [SY3211: $i] :
( ~ ( in @ ( ordered_pair @ SY3211 @ SY3210 ) @ SV16 )
| ~ ( in @ SY3211 @ SY3208 ) )
| ( in @ SY3210 @ SY3209 ) )
| ~ ! [SY3212: $i] :
( ~ ( in @ SY3212 @ SY3209 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SY3212 @ SY3209 @ SY3208 @ SV16 ) @ SY3212 ) @ SV16 )
| ~ ( in @ ( sK45_E @ SY3212 @ SY3209 @ SY3208 @ SV16 ) @ SY3208 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[525]) ).
thf(568,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK64_B @ SX0 ) @ ( sK65_SY3126 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK65_SY3126 @ SX0 ) @ ( sK64_B @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK64_B @ SX0 )
!= ( sK65_SY3126 @ SX0 ) ) ) )
| ( antisymmetric @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[526]) ).
thf(569,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX2 @ SX1 ) @ SX0 )
| ( SX1 = SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[526]) ).
thf(570,plain,
! [SV17: $i] :
( ( ~ ! [SY3213: $i,SY3214: $i] :
( ~ ( function @ SY3214 )
| ~ ( relation @ SY3214 )
| ( SY3213
!= ( apply @ SY3214 @ SV17 ) )
| ~ ( in @ SV17 @ ( relation_dom @ SY3214 ) )
| ( in @ ( ordered_pair @ SV17 @ SY3213 ) @ SY3214 ) )
| ~ ~ ( ~ ! [SY3215: $i,SY3216: $i] :
( ~ ( function @ SY3216 )
| ~ ( relation @ SY3216 )
| ~ ( in @ ( ordered_pair @ SV17 @ SY3215 ) @ SY3216 )
| ( SY3215
= ( apply @ SY3216 @ SV17 ) ) )
| ~ ! [SY3217: $i,SY3218: $i] :
( ~ ( function @ SY3218 )
| ~ ( relation @ SY3218 )
| ~ ( in @ ( ordered_pair @ SV17 @ SY3217 ) @ SY3218 )
| ( in @ SV17 @ ( relation_dom @ SY3218 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(571,plain,
! [SV18: $i] :
( ( ( ~ ( relation @ SV18 ) )
= $true )
| ( ( ~ ( ~ ! [SY3219: $i,SY3220: $i] :
( ~ ( ~ ( ( ( sK35_D @ SY3220 @ SY3219 @ SV18 )
= SY3219 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SY3220 @ SY3219 @ SV18 ) @ SY3219 ) @ SV18 )
| ~ ( in @ ( sK35_D @ SY3220 @ SY3219 @ SV18 ) @ SY3220 ) )
| ~ ~ ( ~ ( ( ( sK35_D @ SY3220 @ SY3219 @ SV18 )
!= SY3219 )
| ( in @ ( sK35_D @ SY3220 @ SY3219 @ SV18 ) @ SY3220 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SY3220 @ SY3219 @ SV18 ) @ SY3219 ) @ SV18 )
| ( in @ ( sK35_D @ SY3220 @ SY3219 @ SV18 ) @ SY3220 ) ) ) )
| ( SY3220
= ( fiber @ SV18 @ SY3219 ) ) )
| ~ ! [SY3221: $i,SY3222: $i] :
( ( SY3222
!= ( fiber @ SV18 @ SY3221 ) )
| ~ ( ~ ! [SY3223: $i] :
( ( SY3223 = SY3221 )
| ~ ( in @ ( ordered_pair @ SY3223 @ SY3221 ) @ SV18 )
| ( in @ SY3223 @ SY3222 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY3222 )
| ( SX3 != SY3221 ) )
| ~ ! [SY3225: $i] :
( ~ ( in @ SY3225 @ SY3222 )
| ( in @ ( ordered_pair @ SY3225 @ SY3221 ) @ SV18 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[528]) ).
thf(572,plain,
! [SV19: $i] :
( ( ( ~ ( relation @ SV19 ) )
= $true )
| ( ( ~ ( ~ ! [SY3226: $i] :
( ~ ( ~ ( in @ ( sK36_C @ SY3226 @ SV19 ) @ SY3226 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SY3226 @ SV19 ) @ ( sK36_C @ SY3226 @ SV19 ) ) @ SV19 ) )
| ( is_reflexive_in @ SV19 @ SY3226 ) )
| ~ ! [SY3227: $i] :
( ~ ( is_reflexive_in @ SV19 @ SY3227 )
| ! [SY3228: $i] :
( ~ ( in @ SY3228 @ SY3227 )
| ( in @ ( ordered_pair @ SY3228 @ SY3228 ) @ SV19 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[529]) ).
thf(573,plain,
! [SV20: $i] :
( ( ( ~ ( relation @ SV20 ) )
= $true )
| ( ( ~ ( ~ ! [SY3229: $i] :
( ~ ( relation @ SY3229 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SY3229 @ SV20 ) @ ( sK13_SY3095 @ SY3229 @ SV20 ) ) @ SY3229 )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SY3229 @ SV20 ) @ ( sK12_C @ SY3229 @ SV20 ) ) @ SV20 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SY3229 @ SV20 ) @ ( sK13_SY3095 @ SY3229 @ SV20 ) ) @ SY3229 )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ SY3229 @ SV20 ) @ ( sK12_C @ SY3229 @ SV20 ) ) @ SV20 ) ) )
| ( SY3229
= ( relation_inverse @ SV20 ) ) )
| ~ ! [SY3230: $i] :
( ~ ( relation @ SY3230 )
| ( SY3230
!= ( relation_inverse @ SV20 ) )
| ~ ( ~ ! [SY3231: $i,SY3232: $i] :
( ~ ( in @ ( ordered_pair @ SY3231 @ SY3232 ) @ SY3230 )
| ( in @ ( ordered_pair @ SY3232 @ SY3231 ) @ SV20 ) )
| ~ ! [SY3233: $i,SY3234: $i] :
( ~ ( in @ ( ordered_pair @ SY3234 @ SY3233 ) @ SV20 )
| ( in @ ( ordered_pair @ SY3233 @ SY3234 ) @ SY3230 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[530]) ).
thf(574,plain,
! [SV21: $i,SV38: $i] :
( ( ~ ( relation @ SV38 )
| ~ ( ~ ! [SY3339: $i] :
( ~ ( relation @ SY3339 )
| ~ ( ~ ( ~ ( in @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) @ SV21 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SY3339 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) ) @ SV38 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SY3339 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) ) @ SY3339 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK48_D @ SY3339 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) ) @ SY3339 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SY3339 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) ) @ SV38 )
| ( in @ ( ordered_pair @ ( sK48_D @ SY3339 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) ) @ SY3339 ) ) ) )
| ( SY3339
= ( relation_rng_restriction @ SV21 @ SV38 ) ) )
| ~ ! [SY3340: $i] :
( ~ ( relation @ SY3340 )
| ( SY3340
!= ( relation_rng_restriction @ SV21 @ SV38 ) )
| ~ ( ~ ! [SY3341: $i,SY3342: $i] :
( ~ ( in @ SY3342 @ SV21 )
| ~ ( in @ ( ordered_pair @ SY3341 @ SY3342 ) @ SV38 )
| ( in @ ( ordered_pair @ SY3341 @ SY3342 ) @ SY3340 ) )
| ~ ~ ( ~ ! [SY3240: $i,SY3241: $i] :
( ~ ( in @ ( ordered_pair @ SY3240 @ SY3241 ) @ SY3340 )
| ( in @ SY3241 @ SV21 ) )
| ~ ! [SY3345: $i,SY3346: $i] :
( ~ ( in @ ( ordered_pair @ SY3345 @ SY3346 ) @ SY3340 )
| ( in @ ( ordered_pair @ SY3345 @ SY3346 ) @ SV38 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(575,plain,
! [SV22: $i] :
( ( ( ~ ( relation @ SV22 ) )
= $true )
| ( ( ~ ( ~ ! [SY3244: $i] :
( ~ ( ~ ( ! [SY3245: $i] :
~ ( in @ ( ordered_pair @ SY3245 @ ( sK17_C @ SY3244 @ SV22 ) ) @ SV22 )
| ~ ( in @ ( sK17_C @ SY3244 @ SV22 ) @ SY3244 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK18_SY3098 @ SY3244 @ SV22 ) @ ( sK17_C @ SY3244 @ SV22 ) ) @ SV22 )
| ( in @ ( sK17_C @ SY3244 @ SV22 ) @ SY3244 ) ) )
| ( SY3244
= ( relation_rng @ SV22 ) ) )
| ~ ! [SY3246: $i] :
( ( SY3246
!= ( relation_rng @ SV22 ) )
| ~ ( ~ ! [SY3247: $i] :
( ! [SY3248: $i] :
~ ( in @ ( ordered_pair @ SY3248 @ SY3247 ) @ SV22 )
| ( in @ SY3247 @ SY3246 ) )
| ~ ! [SY3249: $i] :
( ~ ( in @ SY3249 @ SY3246 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3249 @ SY3246 @ SV22 ) @ SY3249 ) @ SV22 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[532]) ).
thf(576,plain,
! [SV23: $i] :
( ( ( ~ ( relation @ SV23 ) )
= $true )
| ( ( ~ ( ~ ! [SY3250: $i] :
( ~ ( relation @ SY3250 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3250 @ SV23 ) @ ( sK25_SY3102 @ SY3250 @ SV23 ) ) @ SV23 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3250 @ SV23 ) @ ( sK25_SY3102 @ SY3250 @ SV23 ) ) @ SY3250 ) )
| ( subset @ SV23 @ SY3250 ) )
| ~ ! [SY3251: $i] :
( ~ ( relation @ SY3251 )
| ~ ( subset @ SV23 @ SY3251 )
| ! [SY3252: $i,SY3253: $i] :
( ~ ( in @ ( ordered_pair @ SY3252 @ SY3253 ) @ SV23 )
| ( in @ ( ordered_pair @ SY3252 @ SY3253 ) @ SY3251 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[533]) ).
thf(577,plain,
! [SV24: $i] :
( ( ( ~ ( relation @ SV24 ) )
= $true )
| ( ( ~ ( ~ ! [SY3254: $i,SY3255: $i] :
( ~ ( relation @ SY3255 )
| ~ ( ~ ( ~ ( in @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ SY3254 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ ( sK51_SY3120 @ SY3255 @ SY3254 @ SV24 ) ) @ SV24 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ ( sK51_SY3120 @ SY3255 @ SY3254 @ SV24 ) ) @ SY3255 ) )
| ~ ~ ( ~ ( ( in @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ SY3254 )
| ( in @ ( ordered_pair @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ ( sK51_SY3120 @ SY3255 @ SY3254 @ SV24 ) ) @ SY3255 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ ( sK51_SY3120 @ SY3255 @ SY3254 @ SV24 ) ) @ SV24 )
| ( in @ ( ordered_pair @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ ( sK51_SY3120 @ SY3255 @ SY3254 @ SV24 ) ) @ SY3255 ) ) ) )
| ( SY3255
= ( relation_dom_restriction @ SV24 @ SY3254 ) ) )
| ~ ! [SY3256: $i,SY3257: $i] :
( ~ ( relation @ SY3257 )
| ( SY3257
!= ( relation_dom_restriction @ SV24 @ SY3256 ) )
| ~ ( ~ ! [SY3258: $i,SY3259: $i] :
( ~ ( in @ SY3258 @ SY3256 )
| ~ ( in @ ( ordered_pair @ SY3258 @ SY3259 ) @ SV24 )
| ( in @ ( ordered_pair @ SY3258 @ SY3259 ) @ SY3257 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3257 )
| ( in @ SX3 @ SY3256 ) )
| ~ ! [SY3262: $i,SY3263: $i] :
( ~ ( in @ ( ordered_pair @ SY3262 @ SY3263 ) @ SY3257 )
| ( in @ ( ordered_pair @ SY3262 @ SY3263 ) @ SV24 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[534]) ).
thf(578,plain,
! [SV39: $i,SV25: $i] :
( ( ~ ( ~ ! [SY3347: $i] :
( ! [SY3348: $i] :
( ( ordered_pair @ SV25 @ SV39 )
!= ( ordered_pair @ SY3347 @ SY3348 ) )
| ( SV25 = SY3347 ) )
| ~ ! [SY3349: $i,SY3350: $i] :
( ( ( ordered_pair @ SV25 @ SV39 )
!= ( ordered_pair @ SY3349 @ SY3350 ) )
| ( SV39 = SY3350 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(579,plain,
! [SV26: $i] :
( ( ( ~ ( function @ SV26 )
| ~ ( relation @ SV26 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY3269: $i] :
( ~ ( in @ SY3269 @ ( relation_dom @ SV26 ) )
| ! [SY3270: $i] :
( ( SY3270
!= ( apply @ SV26 @ SY3269 ) )
| ( in @ ( ordered_pair @ SY3269 @ SY3270 ) @ SV26 ) ) )
| ~ ! [SY3271: $i] :
( ~ ( in @ SY3271 @ ( relation_dom @ SV26 ) )
| ! [SY3272: $i] :
( ~ ( in @ ( ordered_pair @ SY3271 @ SY3272 ) @ SV26 )
| ( SY3272
= ( apply @ SV26 @ SY3271 ) ) ) ) )
| ~ ~ ( ~ ! [SY3273: $i] :
( ( in @ SY3273 @ ( relation_dom @ SV26 ) )
| ! [SY3274: $i] :
( ( SY3274
!= ( apply @ SV26 @ SY3273 ) )
| ( SY3274 = empty_set ) ) )
| ~ ! [SY3275: $i] :
( ( in @ SY3275 @ ( relation_dom @ SV26 ) )
| ! [SY3276: $i] :
( ( SY3276 != empty_set )
| ( SY3276
= ( apply @ SV26 @ SY3275 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[536]) ).
thf(580,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK62_B @ SX0 )
!= ( sK63_SY3125 @ SX0 ) ) )
| ~ ~ ( ~ ( in @ ( sK62_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ( in @ ( sK63_SY3125 @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK62_B @ SX0 ) @ ( sK63_SY3125 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK63_SY3125 @ SX0 ) @ ( sK62_B @ SX0 ) ) @ SX0 ) )
| ( connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[537]) ).
thf(581,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( connected @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( SX1 = SX2 )
| ~ ( in @ SX1 @ ( relation_field @ SX0 ) )
| ~ ( in @ SX2 @ ( relation_field @ SX0 ) )
| ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[537]) ).
thf(582,plain,
! [SV27: $i] :
( ( ( ~ ( relation @ SV27 ) )
= $true )
| ( ( ~ ( ~ ! [SY3277: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_C @ SY3277 @ SV27 ) @ SY3277 )
| ~ ( in @ ( sK20_SY3099 @ SY3277 @ SV27 ) @ SY3277 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SY3277 @ SV27 ) @ ( sK20_SY3099 @ SY3277 @ SV27 ) ) @ SV27 ) )
| ~ ( in @ ( ordered_pair @ ( sK20_SY3099 @ SY3277 @ SV27 ) @ ( sK19_C @ SY3277 @ SV27 ) ) @ SV27 ) )
| ~ ( ( ( sK19_C @ SY3277 @ SV27 )
!= ( sK20_SY3099 @ SY3277 @ SV27 ) ) ) )
| ( is_antisymmetric_in @ SV27 @ SY3277 ) )
| ~ ! [SY3278: $i] :
( ~ ( is_antisymmetric_in @ SV27 @ SY3278 )
| ! [SY3279: $i,SY3280: $i] :
( ~ ( in @ SY3279 @ SY3278 )
| ~ ( in @ SY3280 @ SY3278 )
| ~ ( in @ ( ordered_pair @ SY3279 @ SY3280 ) @ SV27 )
| ~ ( in @ ( ordered_pair @ SY3280 @ SY3279 ) @ SV27 )
| ( SY3279 = SY3280 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[538]) ).
thf(583,plain,
! [SV40: $i,SV28: $i] :
( ( ~ ( ~ ! [SY3351: $i,SY3352: $i] :
( ~ ( in @ SV28 @ SY3351 )
| ~ ( in @ SV40 @ SY3352 )
| ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SY3351 @ SY3352 ) ) )
| ~ ~ ( ~ ! [SY3353: $i] :
( ! [SY3354: $i] :
~ ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SY3353 @ SY3354 ) )
| ( in @ SV28 @ SY3353 ) )
| ~ ! [SY3355: $i,SY3356: $i] :
( ~ ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SY3355 @ SY3356 ) )
| ( in @ SV40 @ SY3356 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(584,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK66_B @ SX0 ) @ ( sK67_SY3127 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK67_SY3127 @ SX0 ) @ ( sK68_SY3129 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK66_B @ SX0 ) @ ( sK68_SY3129 @ SX0 ) ) @ SX0 ) )
| ( transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[540]) ).
thf(585,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( transitive @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX1 @ SX3 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[540]) ).
thf(586,plain,
! [SV41: $i,SV29: $i] :
( ( ~ ( ~ ! [SY3357: $i,SY3358: $i] :
( ~ ( in @ SV29 @ SY3357 )
| ~ ( in @ SV41 @ SY3358 )
| ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SY3357 @ SY3358 ) ) )
| ~ ~ ( ~ ! [SY3359: $i] :
( ! [SY3360: $i] :
~ ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SY3359 @ SY3360 ) )
| ( in @ SV29 @ SY3359 ) )
| ~ ! [SY3361: $i,SY3362: $i] :
( ~ ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SY3361 @ SY3362 ) )
| ( in @ SV41 @ SY3362 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(587,plain,
! [SV30: $i] :
( ( ( ~ ( relation @ SV30 ) )
= $true )
| ( ( ~ ( ~ ! [SY3295: $i,SY3296: $i] :
( ~ ( ~ ( ! [SY3297: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ SY3296 @ SY3295 @ SV30 ) @ SY3297 ) @ SV30 )
| ~ ( in @ SY3297 @ SY3295 ) )
| ~ ( in @ ( sK43_D @ SY3296 @ SY3295 @ SV30 ) @ SY3296 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SY3296 @ SY3295 @ SV30 ) @ ( sK44_SY3116 @ SY3296 @ SY3295 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK44_SY3116 @ SY3296 @ SY3295 @ SV30 ) @ SY3295 ) )
| ( in @ ( sK43_D @ SY3296 @ SY3295 @ SV30 ) @ SY3296 ) ) )
| ( SY3296
= ( relation_inverse_image @ SV30 @ SY3295 ) ) )
| ~ ! [SY3298: $i,SY3299: $i] :
( ( SY3299
!= ( relation_inverse_image @ SV30 @ SY3298 ) )
| ~ ( ~ ! [SY3300: $i] :
( ! [SY3301: $i] :
( ~ ( in @ ( ordered_pair @ SY3300 @ SY3301 ) @ SV30 )
| ~ ( in @ SY3301 @ SY3298 ) )
| ( in @ SY3300 @ SY3299 ) )
| ~ ! [SY3302: $i] :
( ~ ( in @ SY3302 @ SY3299 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3302 @ ( sK42_E @ SY3302 @ SY3299 @ SY3298 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK42_E @ SY3302 @ SY3299 @ SY3298 @ SV30 ) @ SY3298 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[542]) ).
thf(588,plain,
! [SV31: $i] :
( ( ~ ! [SY3303: $i,SY3304: $i] :
( ~ ( relation @ SY3304 )
| ~ ( in @ ( ordered_pair @ SV31 @ SY3303 ) @ SY3304 )
| ( in @ SV31 @ ( relation_dom @ SY3304 ) ) )
| ~ ! [SY3305: $i,SY3306: $i] :
( ~ ( relation @ SY3306 )
| ~ ( in @ ( ordered_pair @ SV31 @ SY3305 ) @ SY3306 )
| ( in @ SY3305 @ ( relation_rng @ SY3306 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(589,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( in @ ( sK69_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK69_B @ SX0 ) @ ( sK69_B @ SX0 ) ) @ SX0 ) )
| ( reflexive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[544]) ).
thf(590,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ ( relation_field @ SX0 ) )
| ( in @ ( ordered_pair @ SX1 @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[544]) ).
thf(591,plain,
! [SV32: $i] :
( ( ( ~ ( relation @ SV32 ) )
= $true )
| ( ( ! [SY3307: $i] :
( ~ ( relation @ SY3307 )
| ~ ( ~ ! [SY3308: $i] :
( ~ ( function @ SY3308 )
| ~ ( relation @ SY3308 )
| ~ ( ~ ( ~ ( in @ ( sK10_D @ SY3308 @ SY3307 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( sK11_SY3094 @ SY3308 @ SY3307 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3308 @ ( sK10_D @ SY3308 @ SY3307 @ SV32 ) ) @ ( apply @ SY3308 @ ( sK11_SY3094 @ SY3308 @ SY3307 @ SV32 ) ) ) @ SY3307 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY3308 @ SY3307 @ SV32 ) @ ( sK11_SY3094 @ SY3308 @ SY3307 @ SV32 ) ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SY3308 @ SY3307 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3308 @ SY3307 @ SV32 ) @ ( sK11_SY3094 @ SY3308 @ SY3307 @ SV32 ) ) @ SV32 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SY3308 @ SY3307 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3308 @ SY3307 @ SV32 ) @ ( sK11_SY3094 @ SY3308 @ SY3307 @ SV32 ) ) @ SV32 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SY3308 @ ( sK10_D @ SY3308 @ SY3307 @ SV32 ) ) @ ( apply @ SY3308 @ ( sK11_SY3094 @ SY3308 @ SY3307 @ SV32 ) ) ) @ SY3307 )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3308 @ SY3307 @ SV32 ) @ ( sK11_SY3094 @ SY3308 @ SY3307 @ SV32 ) ) @ SV32 ) ) ) )
| ( ( relation_dom @ SY3308 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SY3308 )
!= ( relation_field @ SY3307 ) )
| ~ ( one_to_one @ SY3308 )
| ( relation_isomorphism @ SV32 @ SY3307 @ SY3308 ) )
| ~ ~ ( ~ ! [SY3309: $i] :
( ~ ( function @ SY3309 )
| ~ ( relation @ SY3309 )
| ~ ( relation_isomorphism @ SV32 @ SY3307 @ SY3309 )
| ~ ( ~ ! [SY3310: $i,SY3311: $i] :
( ~ ( in @ SY3310 @ ( relation_field @ SV32 ) )
| ~ ( in @ SY3311 @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3309 @ SY3310 ) @ ( apply @ SY3309 @ SY3311 ) ) @ SY3307 )
| ( in @ ( ordered_pair @ SY3310 @ SY3311 ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3312: $i] :
( ! [SY3313: $i] :
~ ( in @ ( ordered_pair @ SY3312 @ SY3313 ) @ SV32 )
| ( in @ SY3312 @ ( relation_field @ SV32 ) ) )
| ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV32 )
| ( in @ SY3315 @ ( relation_field @ SV32 ) ) ) )
| ~ ! [SY3316: $i,SY3317: $i] :
( ~ ( in @ ( ordered_pair @ SY3316 @ SY3317 ) @ SV32 )
| ( in @ ( ordered_pair @ ( apply @ SY3309 @ SY3316 ) @ ( apply @ SY3309 @ SY3317 ) ) @ SY3307 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3318: $i] :
( ~ ( function @ SY3318 )
| ~ ( relation @ SY3318 )
| ~ ( relation_isomorphism @ SV32 @ SY3307 @ SY3318 )
| ( ( relation_dom @ SY3318 )
= ( relation_field @ SV32 ) ) )
| ~ ! [SY3319: $i] :
( ~ ( function @ SY3319 )
| ~ ( relation @ SY3319 )
| ~ ( relation_isomorphism @ SV32 @ SY3307 @ SY3319 )
| ( ( relation_rng @ SY3319 )
= ( relation_field @ SY3307 ) ) ) )
| ~ ! [SY3320: $i] :
( ~ ( function @ SY3320 )
| ~ ( relation @ SY3320 )
| ~ ( relation_isomorphism @ SV32 @ SY3307 @ SY3320 )
| ( one_to_one @ SY3320 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[545]) ).
thf(592,plain,
! [SV33: $i] :
( ( ~ ! [SY3321: $i,SY3322: $i] :
( ~ ( relation_of2_as_subset @ SY3322 @ SV33 @ SY3321 )
| ~ ( ~ ! [SY3323: $i] :
~ ( in @ ( ordered_pair @ SY3323 @ ( sK57_D @ SY3322 @ SY3321 @ SV33 ) ) @ SY3322 )
| ~ ( in @ ( sK57_D @ SY3322 @ SY3321 @ SV33 ) @ SY3321 ) )
| ( ( relation_rng_as_subset @ SV33 @ SY3321 @ SY3322 )
= SY3321 ) )
| ~ ! [SY3324: $i,SY3325: $i] :
( ~ ( relation_of2_as_subset @ SY3325 @ SV33 @ SY3324 )
| ( ( relation_rng_as_subset @ SV33 @ SY3324 @ SY3325 )
!= SY3324 )
| ! [SY3326: $i] :
( ( in @ ( ordered_pair @ ( sK56_E @ SY3326 @ SY3325 @ SY3324 @ SV33 ) @ SY3326 ) @ SY3325 )
| ~ ( in @ SY3326 @ SY3324 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(593,plain,
! [SV34: $i] :
( ( ( ~ ( relation @ SV34 ) )
= $true )
| ( ( ~ ( ~ ! [SY3327: $i] :
( ~ ( ~ ( ! [SY3328: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SY3327 @ SV34 ) @ SY3328 ) @ SV34 )
| ~ ( in @ ( sK22_C @ SY3327 @ SV34 ) @ SY3327 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SY3327 @ SV34 ) @ ( sK23_SY3101 @ SY3327 @ SV34 ) ) @ SV34 )
| ( in @ ( sK22_C @ SY3327 @ SV34 ) @ SY3327 ) ) )
| ( SY3327
= ( relation_dom @ SV34 ) ) )
| ~ ! [SY3329: $i] :
( ( SY3329
!= ( relation_dom @ SV34 ) )
| ~ ( ~ ! [SY3330: $i] :
( ! [SY3331: $i] :
~ ( in @ ( ordered_pair @ SY3330 @ SY3331 ) @ SV34 )
| ( in @ SY3330 @ SY3329 ) )
| ~ ! [SY3332: $i] :
( ~ ( in @ SY3332 @ SY3329 )
| ( in @ ( ordered_pair @ SY3332 @ ( sK21_D @ SY3332 @ SY3329 @ SV34 ) ) @ SV34 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[547]) ).
thf(594,plain,
! [SV1: $i] :
( ( ( relation @ SV1 )
= $false )
| ( ( ( in @ ( ordered_pair @ ( sK54_B @ SV1 ) @ ( sK55_SY3122 @ SV1 ) ) @ SV1 )
| ( SV1 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(595,plain,
! [SV36: $i,SV3: $i] :
( ( empty @ ( ordered_pair @ SV3 @ SV36 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[550]) ).
thf(596,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK39_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK39_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[551]) ).
thf(597,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK37_C @ SX1 @ SX0 ) @ ( sK38_SY3111 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[552]) ).
thf(598,plain,
! [SV4: $i] :
( ( ( relation @ SV4 )
= $false )
| ( ( ~ ( ~ ! [SY3132: $i] :
( ~ ( relation @ SY3132 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SY3132 @ SV4 ) @ ( sK32_SY3109 @ SY3132 @ SV4 ) ) @ SV4 )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ SY3132 @ SV4 ) @ ( sK32_SY3109 @ SY3132 @ SV4 ) ) @ SY3132 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK31_C @ SY3132 @ SV4 ) @ ( sK32_SY3109 @ SY3132 @ SV4 ) ) @ SV4 )
| ( in @ ( ordered_pair @ ( sK31_C @ SY3132 @ SV4 ) @ ( sK32_SY3109 @ SY3132 @ SV4 ) ) @ SY3132 ) ) )
| ( SV4 = SY3132 ) )
| ~ ! [SY3133: $i] :
( ~ ( relation @ SY3133 )
| ( SV4 != SY3133 )
| ~ ( ~ ! [SY3134: $i,SY3135: $i] :
( ~ ( in @ ( ordered_pair @ SY3134 @ SY3135 ) @ SV4 )
| ( in @ ( ordered_pair @ SY3134 @ SY3135 ) @ SY3133 ) )
| ~ ! [SY3136: $i,SY3137: $i] :
( ~ ( in @ ( ordered_pair @ SY3136 @ SY3137 ) @ SY3133 )
| ( in @ ( ordered_pair @ SY3136 @ SY3137 ) @ SV4 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(599,plain,
! [SV5: $i] :
( ( ( relation @ SV5 )
= $false )
| ( ( ~ ( ~ ! [SY3138: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SY3138 @ SV5 ) @ SY3138 )
| ~ ( in @ ( sK4_SY3086 @ SY3138 @ SV5 ) @ SY3138 ) )
| ~ ( in @ ( sK5_SY3088 @ SY3138 @ SV5 ) @ SY3138 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SY3138 @ SV5 ) @ ( sK4_SY3086 @ SY3138 @ SV5 ) ) @ SV5 ) )
| ~ ( in @ ( ordered_pair @ ( sK4_SY3086 @ SY3138 @ SV5 ) @ ( sK5_SY3088 @ SY3138 @ SV5 ) ) @ SV5 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK3_C @ SY3138 @ SV5 ) @ ( sK5_SY3088 @ SY3138 @ SV5 ) ) @ SV5 ) )
| ( is_transitive_in @ SV5 @ SY3138 ) )
| ~ ! [SY3139: $i] :
( ~ ( is_transitive_in @ SV5 @ SY3139 )
| ! [SY3140: $i,SY3141: $i,SY3142: $i] :
( ~ ( in @ SY3140 @ SY3139 )
| ~ ( in @ SY3141 @ SY3139 )
| ~ ( in @ SY3142 @ SY3139 )
| ~ ( in @ ( ordered_pair @ SY3140 @ SY3141 ) @ SV5 )
| ~ ( in @ ( ordered_pair @ SY3141 @ SY3142 ) @ SV5 )
| ( in @ ( ordered_pair @ SY3140 @ SY3142 ) @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(600,plain,
! [SV6: $i] :
( ( ~ ! [SY3143: $i,SY3144: $i] :
( ~ ( relation_of2_as_subset @ SY3144 @ SY3143 @ SV6 )
| ~ ( ~ ! [SY3145: $i] :
~ ( in @ ( ordered_pair @ ( sK59_D @ SY3144 @ SY3143 @ SV6 ) @ SY3145 ) @ SY3144 )
| ~ ( in @ ( sK59_D @ SY3144 @ SY3143 @ SV6 ) @ SY3143 ) )
| ( ( relation_dom_as_subset @ SY3143 @ SV6 @ SY3144 )
= SY3143 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[555]) ).
thf(601,plain,
! [SV6: $i] :
( ( ~ ! [SY3146: $i,SY3147: $i] :
( ~ ( relation_of2_as_subset @ SY3147 @ SY3146 @ SV6 )
| ( ( relation_dom_as_subset @ SY3146 @ SV6 @ SY3147 )
!= SY3146 )
| ! [SY3148: $i] :
( ( in @ ( ordered_pair @ SY3148 @ ( sK58_E @ SY3148 @ SY3147 @ SY3146 @ SV6 ) ) @ SY3147 )
| ~ ( in @ SY3148 @ SY3146 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[555]) ).
thf(602,plain,
! [SV7: $i] :
( ( ( relation @ SV7 )
= $false )
| ( ( ! [SY3149: $i] :
( ~ ( relation @ SY3149 )
| ~ ( ~ ! [SY3150: $i] :
( ~ ( relation @ SY3150 )
| ~ ( ~ ( ! [SY3151: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3150 @ SY3149 @ SV7 ) @ SY3151 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3151 @ ( sK8_SY3089 @ SY3150 @ SY3149 @ SV7 ) ) @ SY3149 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3150 @ SY3149 @ SV7 ) @ ( sK8_SY3089 @ SY3150 @ SY3149 @ SV7 ) ) @ SY3150 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3150 @ SY3149 @ SV7 ) @ ( sK9_SY3093 @ SY3150 @ SY3149 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SY3150 @ SY3149 @ SV7 ) @ ( sK8_SY3089 @ SY3150 @ SY3149 @ SV7 ) ) @ SY3149 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SY3150 @ SY3149 @ SV7 ) @ ( sK8_SY3089 @ SY3150 @ SY3149 @ SV7 ) ) @ SY3150 ) ) )
| ( SY3150
= ( relation_composition @ SV7 @ SY3149 ) ) )
| ~ ! [SY3152: $i] :
( ~ ( relation @ SY3152 )
| ( SY3152
!= ( relation_composition @ SV7 @ SY3149 ) )
| ~ ( ~ ! [SY3153: $i,SY3154: $i] :
( ! [SY3155: $i] :
( ~ ( in @ ( ordered_pair @ SY3153 @ SY3155 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3155 @ SY3154 ) @ SY3149 ) )
| ( in @ ( ordered_pair @ SY3153 @ SY3154 ) @ SY3152 ) )
| ~ ! [SY3156: $i,SY3157: $i] :
( ~ ( in @ ( ordered_pair @ SY3156 @ SY3157 ) @ SY3152 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3156 @ ( sK6_F @ SY3157 @ SY3156 @ SY3152 @ SY3149 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY3157 @ SY3156 @ SY3152 @ SY3149 @ SV7 ) @ SY3157 ) @ SY3149 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[556]) ).
thf(603,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK52_C @ SX1 @ SX0 )
!= ( sK53_SY3121 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK52_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK52_C @ SX1 @ SX0 ) @ ( sK53_SY3121 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK52_C @ SX1 @ SX0 )
= ( sK53_SY3121 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK52_C @ SX1 @ SX0 ) @ ( sK53_SY3121 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK52_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK52_C @ SX1 @ SX0 ) @ ( sK53_SY3121 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[557]) ).
thf(604,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( SX2 = SX3 ) )
| ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[558]) ).
thf(605,plain,
! [SV42: $i,SV8: $i] :
( ( ( ! [SY3363: $i] :
( SV8
!= ( ordered_pair @ SV42 @ SY3363 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3160: $i] :
( ~ ( ( SV8
!= ( ordered_pair @ ( sK40_C @ SY3160 @ SV8 ) @ ( sK41_SY3114 @ SY3160 @ SV8 ) ) )
| ~ ( ( SY3160
!= ( sK40_C @ SY3160 @ SV8 ) ) ) )
| ( SY3160
= ( pair_first @ SV8 ) ) )
| ~ ! [SY3161: $i] :
( ( SY3161
!= ( pair_first @ SV8 ) )
| ! [SY3162: $i] :
( ! [SY3163: $i] :
( SV8
!= ( ordered_pair @ SY3162 @ SY3163 ) )
| ( SY3161 = SY3162 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(606,plain,
! [SV37: $i,SV9: $i] :
( ( ~ ! [SY3333: $i,SY3334: $i] :
( ~ ( relation @ SY3334 )
| ~ ( in @ SV9 @ SY3333 )
| ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ SY3334 )
| ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SY3333 ) @ SY3334 ) ) )
| ~ ~ ( ~ ! [SY3335: $i,SY3336: $i] :
( ~ ( relation @ SY3336 )
| ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SY3335 ) @ SY3336 ) )
| ( in @ SV9 @ SY3335 ) )
| ~ ! [SY3337: $i,SY3338: $i] :
( ~ ( relation @ SY3338 )
| ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SY3337 ) @ SY3338 ) )
| ( in @ ( ordered_pair @ SV9 @ SV37 ) @ SY3338 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(607,plain,
! [SV10: $i] :
( ( ~ ! [SY3171: $i,SY3172: $i] :
( ~ ( relation @ SY3172 )
| ! [SY3173: $i] :
( ~ ( in @ SY3173 @ ( relation_rng @ SY3172 ) )
| ~ ( in @ ( ordered_pair @ SV10 @ SY3173 ) @ SY3172 )
| ~ ( in @ SY3173 @ SY3171 ) )
| ( in @ SV10 @ ( relation_inverse_image @ SY3172 @ SY3171 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[561]) ).
thf(608,plain,
! [SV10: $i] :
( ( ~ ! [SY3174: $i,SY3175: $i] :
( ~ ( relation @ SY3175 )
| ~ ( in @ SV10 @ ( relation_inverse_image @ SY3175 @ SY3174 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_D @ SY3175 @ SY3174 @ SV10 ) @ ( relation_rng @ SY3175 ) )
| ~ ( in @ ( ordered_pair @ SV10 @ ( sK60_D @ SY3175 @ SY3174 @ SV10 ) ) @ SY3175 ) )
| ~ ( in @ ( sK60_D @ SY3175 @ SY3174 @ SV10 ) @ SY3174 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[561]) ).
thf(609,plain,
! [SV11: $i] :
( ( ~ ! [SY3176: $i,SY3177: $i] :
( ~ ( ~ ( ! [SY3178: $i,SY3179: $i] :
( ~ ( in @ SY3178 @ SV11 )
| ~ ( in @ SY3179 @ SY3176 )
| ( ( sK28_D @ SY3177 @ SY3176 @ SV11 )
!= ( ordered_pair @ SY3178 @ SY3179 ) ) )
| ~ ( in @ ( sK28_D @ SY3177 @ SY3176 @ SV11 ) @ SY3177 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY3106 @ SY3177 @ SY3176 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK30_SY3108 @ SY3177 @ SY3176 @ SV11 ) @ SY3176 ) )
| ( ( sK28_D @ SY3177 @ SY3176 @ SV11 )
!= ( ordered_pair @ ( sK29_SY3106 @ SY3177 @ SY3176 @ SV11 ) @ ( sK30_SY3108 @ SY3177 @ SY3176 @ SV11 ) ) ) )
| ( in @ ( sK28_D @ SY3177 @ SY3176 @ SV11 ) @ SY3177 ) ) )
| ( SY3177
= ( cartesian_product2 @ SV11 @ SY3176 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[562]) ).
thf(610,plain,
! [SV11: $i] :
( ( ~ ! [SY3180: $i,SY3181: $i] :
( ( SY3181
!= ( cartesian_product2 @ SV11 @ SY3180 ) )
| ~ ( ~ ! [SY3182: $i] :
( ! [SY3183: $i,SY3184: $i] :
( ~ ( in @ SY3183 @ SV11 )
| ~ ( in @ SY3184 @ SY3180 )
| ( SY3182
!= ( ordered_pair @ SY3183 @ SY3184 ) ) )
| ( in @ SY3182 @ SY3181 ) )
| ~ ! [SY3185: $i] :
( ~ ( in @ SY3185 @ SY3181 )
| ~ ( ~ ~ ( ~ ( in @ ( sK26_E @ SY3185 @ SY3181 @ SY3180 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK27_SY3103 @ SY3185 @ SY3181 @ SY3180 @ SV11 ) @ SY3180 ) )
| ( SY3185
!= ( ordered_pair @ ( sK26_E @ SY3185 @ SY3181 @ SY3180 @ SV11 ) @ ( sK27_SY3103 @ SY3185 @ SY3181 @ SY3180 @ SV11 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[562]) ).
thf(611,plain,
! [SV12: $i] :
( ( ~ ! [SY3186: $i,SY3187: $i] :
( ~ ( relation @ SY3187 )
| ~ ( in @ ( ordered_pair @ SV12 @ SY3186 ) @ SY3187 )
| ( in @ SV12 @ ( relation_field @ SY3187 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[563]) ).
thf(612,plain,
! [SV12: $i] :
( ( ~ ! [SY3188: $i,SY3189: $i] :
( ~ ( relation @ SY3189 )
| ~ ( in @ ( ordered_pair @ SV12 @ SY3188 ) @ SY3189 )
| ( in @ SY3188 @ ( relation_field @ SY3189 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[563]) ).
thf(613,plain,
! [SV43: $i,SV13: $i] :
( ( ( ! [SY3364: $i] :
( SV13
!= ( ordered_pair @ SV43 @ SY3364 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3192: $i] :
( ~ ( ( SV13
!= ( ordered_pair @ ( sK33_C @ SY3192 @ SV13 ) @ ( sK34_SY3110 @ SY3192 @ SV13 ) ) )
| ~ ( ( SY3192
!= ( sK34_SY3110 @ SY3192 @ SV13 ) ) ) )
| ( SY3192
= ( pair_second @ SV13 ) ) )
| ~ ! [SY3193: $i] :
( ( SY3193
!= ( pair_second @ SV13 ) )
| ! [SY3194: $i,SY3195: $i] :
( ( SV13
!= ( ordered_pair @ SY3194 @ SY3195 ) )
| ( SY3193 = SY3195 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(614,plain,
! [SV14: $i] :
( ( ( relation @ SV14 )
= $false )
| ( ( ~ ( ~ ! [SY3196: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK14_C @ SY3196 @ SV14 )
!= ( sK15_SY3096 @ SY3196 @ SV14 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SY3196 @ SV14 ) @ SY3196 )
| ~ ( in @ ( sK15_SY3096 @ SY3196 @ SV14 ) @ SY3196 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK14_C @ SY3196 @ SV14 ) @ ( sK15_SY3096 @ SY3196 @ SV14 ) ) @ SV14 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK15_SY3096 @ SY3196 @ SV14 ) @ ( sK14_C @ SY3196 @ SV14 ) ) @ SV14 ) )
| ( is_connected_in @ SV14 @ SY3196 ) )
| ~ ! [SY3197: $i] :
( ~ ( is_connected_in @ SV14 @ SY3197 )
| ! [SY3198: $i,SY3199: $i] :
( ( SY3198 = SY3199 )
| ~ ( in @ SY3198 @ SY3197 )
| ~ ( in @ SY3199 @ SY3197 )
| ( in @ ( ordered_pair @ SY3198 @ SY3199 ) @ SV14 )
| ( in @ ( ordered_pair @ SY3199 @ SY3198 ) @ SV14 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(615,plain,
! [SV15: $i] :
( ( ~ ! [SY3200: $i,SY3201: $i] :
( ~ ( relation @ SY3201 )
| ! [SY3202: $i] :
( ~ ( in @ SY3202 @ ( relation_dom @ SY3201 ) )
| ~ ( in @ ( ordered_pair @ SY3202 @ SV15 ) @ SY3201 )
| ~ ( in @ SY3202 @ SY3200 ) )
| ( in @ SV15 @ ( relation_image @ SY3201 @ SY3200 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[566]) ).
thf(616,plain,
! [SV15: $i] :
( ( ~ ! [SY3203: $i,SY3204: $i] :
( ~ ( relation @ SY3204 )
| ~ ( in @ SV15 @ ( relation_image @ SY3204 @ SY3203 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK61_D @ SY3204 @ SY3203 @ SV15 ) @ ( relation_dom @ SY3204 ) )
| ~ ( in @ ( ordered_pair @ ( sK61_D @ SY3204 @ SY3203 @ SV15 ) @ SV15 ) @ SY3204 ) )
| ~ ( in @ ( sK61_D @ SY3204 @ SY3203 @ SV15 ) @ SY3203 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[566]) ).
thf(617,plain,
! [SV16: $i] :
( ( ( relation @ SV16 )
= $false )
| ( ( ~ ( ~ ! [SY3205: $i,SY3206: $i] :
( ~ ( ~ ( ! [SY3207: $i] :
( ~ ( in @ ( ordered_pair @ SY3207 @ ( sK46_D @ SY3206 @ SY3205 @ SV16 ) ) @ SV16 )
| ~ ( in @ SY3207 @ SY3205 ) )
| ~ ( in @ ( sK46_D @ SY3206 @ SY3205 @ SV16 ) @ SY3206 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SY3206 @ SY3205 @ SV16 ) @ ( sK46_D @ SY3206 @ SY3205 @ SV16 ) ) @ SV16 )
| ~ ( in @ ( sK47_SY3118 @ SY3206 @ SY3205 @ SV16 ) @ SY3205 ) )
| ( in @ ( sK46_D @ SY3206 @ SY3205 @ SV16 ) @ SY3206 ) ) )
| ( SY3206
= ( relation_image @ SV16 @ SY3205 ) ) )
| ~ ! [SY3208: $i,SY3209: $i] :
( ( SY3209
!= ( relation_image @ SV16 @ SY3208 ) )
| ~ ( ~ ! [SY3210: $i] :
( ! [SY3211: $i] :
( ~ ( in @ ( ordered_pair @ SY3211 @ SY3210 ) @ SV16 )
| ~ ( in @ SY3211 @ SY3208 ) )
| ( in @ SY3210 @ SY3209 ) )
| ~ ! [SY3212: $i] :
( ~ ( in @ SY3212 @ SY3209 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SY3212 @ SY3209 @ SY3208 @ SV16 ) @ SY3212 ) @ SV16 )
| ~ ( in @ ( sK45_E @ SY3212 @ SY3209 @ SY3208 @ SV16 ) @ SY3208 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(618,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK64_B @ SX0 ) @ ( sK65_SY3126 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK65_SY3126 @ SX0 ) @ ( sK64_B @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK64_B @ SX0 )
!= ( sK65_SY3126 @ SX0 ) ) ) )
| ( antisymmetric @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[568]) ).
thf(619,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX2 @ SX1 ) @ SX0 )
| ( SX1 = SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[569]) ).
thf(620,plain,
! [SV17: $i] :
( ( ~ ! [SY3213: $i,SY3214: $i] :
( ~ ( function @ SY3214 )
| ~ ( relation @ SY3214 )
| ( SY3213
!= ( apply @ SY3214 @ SV17 ) )
| ~ ( in @ SV17 @ ( relation_dom @ SY3214 ) )
| ( in @ ( ordered_pair @ SV17 @ SY3213 ) @ SY3214 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[570]) ).
thf(621,plain,
! [SV17: $i] :
( ( ~ ~ ( ~ ! [SY3215: $i,SY3216: $i] :
( ~ ( function @ SY3216 )
| ~ ( relation @ SY3216 )
| ~ ( in @ ( ordered_pair @ SV17 @ SY3215 ) @ SY3216 )
| ( SY3215
= ( apply @ SY3216 @ SV17 ) ) )
| ~ ! [SY3217: $i,SY3218: $i] :
( ~ ( function @ SY3218 )
| ~ ( relation @ SY3218 )
| ~ ( in @ ( ordered_pair @ SV17 @ SY3217 ) @ SY3218 )
| ( in @ SV17 @ ( relation_dom @ SY3218 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[570]) ).
thf(622,plain,
! [SV18: $i] :
( ( ( relation @ SV18 )
= $false )
| ( ( ~ ( ~ ! [SY3219: $i,SY3220: $i] :
( ~ ( ~ ( ( ( sK35_D @ SY3220 @ SY3219 @ SV18 )
= SY3219 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SY3220 @ SY3219 @ SV18 ) @ SY3219 ) @ SV18 )
| ~ ( in @ ( sK35_D @ SY3220 @ SY3219 @ SV18 ) @ SY3220 ) )
| ~ ~ ( ~ ( ( ( sK35_D @ SY3220 @ SY3219 @ SV18 )
!= SY3219 )
| ( in @ ( sK35_D @ SY3220 @ SY3219 @ SV18 ) @ SY3220 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SY3220 @ SY3219 @ SV18 ) @ SY3219 ) @ SV18 )
| ( in @ ( sK35_D @ SY3220 @ SY3219 @ SV18 ) @ SY3220 ) ) ) )
| ( SY3220
= ( fiber @ SV18 @ SY3219 ) ) )
| ~ ! [SY3221: $i,SY3222: $i] :
( ( SY3222
!= ( fiber @ SV18 @ SY3221 ) )
| ~ ( ~ ! [SY3223: $i] :
( ( SY3223 = SY3221 )
| ~ ( in @ ( ordered_pair @ SY3223 @ SY3221 ) @ SV18 )
| ( in @ SY3223 @ SY3222 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY3222 )
| ( SX3 != SY3221 ) )
| ~ ! [SY3225: $i] :
( ~ ( in @ SY3225 @ SY3222 )
| ( in @ ( ordered_pair @ SY3225 @ SY3221 ) @ SV18 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(623,plain,
! [SV19: $i] :
( ( ( relation @ SV19 )
= $false )
| ( ( ~ ( ~ ! [SY3226: $i] :
( ~ ( ~ ( in @ ( sK36_C @ SY3226 @ SV19 ) @ SY3226 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SY3226 @ SV19 ) @ ( sK36_C @ SY3226 @ SV19 ) ) @ SV19 ) )
| ( is_reflexive_in @ SV19 @ SY3226 ) )
| ~ ! [SY3227: $i] :
( ~ ( is_reflexive_in @ SV19 @ SY3227 )
| ! [SY3228: $i] :
( ~ ( in @ SY3228 @ SY3227 )
| ( in @ ( ordered_pair @ SY3228 @ SY3228 ) @ SV19 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(624,plain,
! [SV20: $i] :
( ( ( relation @ SV20 )
= $false )
| ( ( ~ ( ~ ! [SY3229: $i] :
( ~ ( relation @ SY3229 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SY3229 @ SV20 ) @ ( sK13_SY3095 @ SY3229 @ SV20 ) ) @ SY3229 )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SY3229 @ SV20 ) @ ( sK12_C @ SY3229 @ SV20 ) ) @ SV20 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SY3229 @ SV20 ) @ ( sK13_SY3095 @ SY3229 @ SV20 ) ) @ SY3229 )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ SY3229 @ SV20 ) @ ( sK12_C @ SY3229 @ SV20 ) ) @ SV20 ) ) )
| ( SY3229
= ( relation_inverse @ SV20 ) ) )
| ~ ! [SY3230: $i] :
( ~ ( relation @ SY3230 )
| ( SY3230
!= ( relation_inverse @ SV20 ) )
| ~ ( ~ ! [SY3231: $i,SY3232: $i] :
( ~ ( in @ ( ordered_pair @ SY3231 @ SY3232 ) @ SY3230 )
| ( in @ ( ordered_pair @ SY3232 @ SY3231 ) @ SV20 ) )
| ~ ! [SY3233: $i,SY3234: $i] :
( ~ ( in @ ( ordered_pair @ SY3234 @ SY3233 ) @ SV20 )
| ( in @ ( ordered_pair @ SY3233 @ SY3234 ) @ SY3230 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(625,plain,
! [SV21: $i,SV38: $i] :
( ( ( ~ ( relation @ SV38 ) )
= $true )
| ( ( ~ ( ~ ! [SY3339: $i] :
( ~ ( relation @ SY3339 )
| ~ ( ~ ( ~ ( in @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) @ SV21 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SY3339 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) ) @ SV38 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SY3339 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) ) @ SY3339 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK48_D @ SY3339 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) ) @ SY3339 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SY3339 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) ) @ SV38 )
| ( in @ ( ordered_pair @ ( sK48_D @ SY3339 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) ) @ SY3339 ) ) ) )
| ( SY3339
= ( relation_rng_restriction @ SV21 @ SV38 ) ) )
| ~ ! [SY3340: $i] :
( ~ ( relation @ SY3340 )
| ( SY3340
!= ( relation_rng_restriction @ SV21 @ SV38 ) )
| ~ ( ~ ! [SY3341: $i,SY3342: $i] :
( ~ ( in @ SY3342 @ SV21 )
| ~ ( in @ ( ordered_pair @ SY3341 @ SY3342 ) @ SV38 )
| ( in @ ( ordered_pair @ SY3341 @ SY3342 ) @ SY3340 ) )
| ~ ~ ( ~ ! [SY3240: $i,SY3241: $i] :
( ~ ( in @ ( ordered_pair @ SY3240 @ SY3241 ) @ SY3340 )
| ( in @ SY3241 @ SV21 ) )
| ~ ! [SY3345: $i,SY3346: $i] :
( ~ ( in @ ( ordered_pair @ SY3345 @ SY3346 ) @ SY3340 )
| ( in @ ( ordered_pair @ SY3345 @ SY3346 ) @ SV38 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[574]) ).
thf(626,plain,
! [SV22: $i] :
( ( ( relation @ SV22 )
= $false )
| ( ( ~ ( ~ ! [SY3244: $i] :
( ~ ( ~ ( ! [SY3245: $i] :
~ ( in @ ( ordered_pair @ SY3245 @ ( sK17_C @ SY3244 @ SV22 ) ) @ SV22 )
| ~ ( in @ ( sK17_C @ SY3244 @ SV22 ) @ SY3244 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK18_SY3098 @ SY3244 @ SV22 ) @ ( sK17_C @ SY3244 @ SV22 ) ) @ SV22 )
| ( in @ ( sK17_C @ SY3244 @ SV22 ) @ SY3244 ) ) )
| ( SY3244
= ( relation_rng @ SV22 ) ) )
| ~ ! [SY3246: $i] :
( ( SY3246
!= ( relation_rng @ SV22 ) )
| ~ ( ~ ! [SY3247: $i] :
( ! [SY3248: $i] :
~ ( in @ ( ordered_pair @ SY3248 @ SY3247 ) @ SV22 )
| ( in @ SY3247 @ SY3246 ) )
| ~ ! [SY3249: $i] :
( ~ ( in @ SY3249 @ SY3246 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3249 @ SY3246 @ SV22 ) @ SY3249 ) @ SV22 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[575]) ).
thf(627,plain,
! [SV23: $i] :
( ( ( relation @ SV23 )
= $false )
| ( ( ~ ( ~ ! [SY3250: $i] :
( ~ ( relation @ SY3250 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3250 @ SV23 ) @ ( sK25_SY3102 @ SY3250 @ SV23 ) ) @ SV23 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3250 @ SV23 ) @ ( sK25_SY3102 @ SY3250 @ SV23 ) ) @ SY3250 ) )
| ( subset @ SV23 @ SY3250 ) )
| ~ ! [SY3251: $i] :
( ~ ( relation @ SY3251 )
| ~ ( subset @ SV23 @ SY3251 )
| ! [SY3252: $i,SY3253: $i] :
( ~ ( in @ ( ordered_pair @ SY3252 @ SY3253 ) @ SV23 )
| ( in @ ( ordered_pair @ SY3252 @ SY3253 ) @ SY3251 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(628,plain,
! [SV24: $i] :
( ( ( relation @ SV24 )
= $false )
| ( ( ~ ( ~ ! [SY3254: $i,SY3255: $i] :
( ~ ( relation @ SY3255 )
| ~ ( ~ ( ~ ( in @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ SY3254 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ ( sK51_SY3120 @ SY3255 @ SY3254 @ SV24 ) ) @ SV24 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ ( sK51_SY3120 @ SY3255 @ SY3254 @ SV24 ) ) @ SY3255 ) )
| ~ ~ ( ~ ( ( in @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ SY3254 )
| ( in @ ( ordered_pair @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ ( sK51_SY3120 @ SY3255 @ SY3254 @ SV24 ) ) @ SY3255 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ ( sK51_SY3120 @ SY3255 @ SY3254 @ SV24 ) ) @ SV24 )
| ( in @ ( ordered_pair @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ ( sK51_SY3120 @ SY3255 @ SY3254 @ SV24 ) ) @ SY3255 ) ) ) )
| ( SY3255
= ( relation_dom_restriction @ SV24 @ SY3254 ) ) )
| ~ ! [SY3256: $i,SY3257: $i] :
( ~ ( relation @ SY3257 )
| ( SY3257
!= ( relation_dom_restriction @ SV24 @ SY3256 ) )
| ~ ( ~ ! [SY3258: $i,SY3259: $i] :
( ~ ( in @ SY3258 @ SY3256 )
| ~ ( in @ ( ordered_pair @ SY3258 @ SY3259 ) @ SV24 )
| ( in @ ( ordered_pair @ SY3258 @ SY3259 ) @ SY3257 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3257 )
| ( in @ SX3 @ SY3256 ) )
| ~ ! [SY3262: $i,SY3263: $i] :
( ~ ( in @ ( ordered_pair @ SY3262 @ SY3263 ) @ SY3257 )
| ( in @ ( ordered_pair @ SY3262 @ SY3263 ) @ SV24 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(629,plain,
! [SV39: $i,SV25: $i] :
( ( ~ ! [SY3347: $i] :
( ! [SY3348: $i] :
( ( ordered_pair @ SV25 @ SV39 )
!= ( ordered_pair @ SY3347 @ SY3348 ) )
| ( SV25 = SY3347 ) )
| ~ ! [SY3349: $i,SY3350: $i] :
( ( ( ordered_pair @ SV25 @ SV39 )
!= ( ordered_pair @ SY3349 @ SY3350 ) )
| ( SV39 = SY3350 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(630,plain,
! [SV26: $i] :
( ( ( ~ ( function @ SV26 ) )
= $true )
| ( ( ~ ( relation @ SV26 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY3269: $i] :
( ~ ( in @ SY3269 @ ( relation_dom @ SV26 ) )
| ! [SY3270: $i] :
( ( SY3270
!= ( apply @ SV26 @ SY3269 ) )
| ( in @ ( ordered_pair @ SY3269 @ SY3270 ) @ SV26 ) ) )
| ~ ! [SY3271: $i] :
( ~ ( in @ SY3271 @ ( relation_dom @ SV26 ) )
| ! [SY3272: $i] :
( ~ ( in @ ( ordered_pair @ SY3271 @ SY3272 ) @ SV26 )
| ( SY3272
= ( apply @ SV26 @ SY3271 ) ) ) ) )
| ~ ~ ( ~ ! [SY3273: $i] :
( ( in @ SY3273 @ ( relation_dom @ SV26 ) )
| ! [SY3274: $i] :
( ( SY3274
!= ( apply @ SV26 @ SY3273 ) )
| ( SY3274 = empty_set ) ) )
| ~ ! [SY3275: $i] :
( ( in @ SY3275 @ ( relation_dom @ SV26 ) )
| ! [SY3276: $i] :
( ( SY3276 != empty_set )
| ( SY3276
= ( apply @ SV26 @ SY3275 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[579]) ).
thf(631,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK62_B @ SX0 )
!= ( sK63_SY3125 @ SX0 ) ) )
| ~ ~ ( ~ ( in @ ( sK62_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ( in @ ( sK63_SY3125 @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK62_B @ SX0 ) @ ( sK63_SY3125 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK63_SY3125 @ SX0 ) @ ( sK62_B @ SX0 ) ) @ SX0 ) )
| ( connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[580]) ).
thf(632,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( connected @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( SX1 = SX2 )
| ~ ( in @ SX1 @ ( relation_field @ SX0 ) )
| ~ ( in @ SX2 @ ( relation_field @ SX0 ) )
| ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[581]) ).
thf(633,plain,
! [SV27: $i] :
( ( ( relation @ SV27 )
= $false )
| ( ( ~ ( ~ ! [SY3277: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_C @ SY3277 @ SV27 ) @ SY3277 )
| ~ ( in @ ( sK20_SY3099 @ SY3277 @ SV27 ) @ SY3277 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SY3277 @ SV27 ) @ ( sK20_SY3099 @ SY3277 @ SV27 ) ) @ SV27 ) )
| ~ ( in @ ( ordered_pair @ ( sK20_SY3099 @ SY3277 @ SV27 ) @ ( sK19_C @ SY3277 @ SV27 ) ) @ SV27 ) )
| ~ ( ( ( sK19_C @ SY3277 @ SV27 )
!= ( sK20_SY3099 @ SY3277 @ SV27 ) ) ) )
| ( is_antisymmetric_in @ SV27 @ SY3277 ) )
| ~ ! [SY3278: $i] :
( ~ ( is_antisymmetric_in @ SV27 @ SY3278 )
| ! [SY3279: $i,SY3280: $i] :
( ~ ( in @ SY3279 @ SY3278 )
| ~ ( in @ SY3280 @ SY3278 )
| ~ ( in @ ( ordered_pair @ SY3279 @ SY3280 ) @ SV27 )
| ~ ( in @ ( ordered_pair @ SY3280 @ SY3279 ) @ SV27 )
| ( SY3279 = SY3280 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[582]) ).
thf(634,plain,
! [SV40: $i,SV28: $i] :
( ( ~ ! [SY3351: $i,SY3352: $i] :
( ~ ( in @ SV28 @ SY3351 )
| ~ ( in @ SV40 @ SY3352 )
| ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SY3351 @ SY3352 ) ) )
| ~ ~ ( ~ ! [SY3353: $i] :
( ! [SY3354: $i] :
~ ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SY3353 @ SY3354 ) )
| ( in @ SV28 @ SY3353 ) )
| ~ ! [SY3355: $i,SY3356: $i] :
( ~ ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SY3355 @ SY3356 ) )
| ( in @ SV40 @ SY3356 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(635,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK66_B @ SX0 ) @ ( sK67_SY3127 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK67_SY3127 @ SX0 ) @ ( sK68_SY3129 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK66_B @ SX0 ) @ ( sK68_SY3129 @ SX0 ) ) @ SX0 ) )
| ( transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[584]) ).
thf(636,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( transitive @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX1 @ SX3 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[585]) ).
thf(637,plain,
! [SV41: $i,SV29: $i] :
( ( ~ ! [SY3357: $i,SY3358: $i] :
( ~ ( in @ SV29 @ SY3357 )
| ~ ( in @ SV41 @ SY3358 )
| ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SY3357 @ SY3358 ) ) )
| ~ ~ ( ~ ! [SY3359: $i] :
( ! [SY3360: $i] :
~ ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SY3359 @ SY3360 ) )
| ( in @ SV29 @ SY3359 ) )
| ~ ! [SY3361: $i,SY3362: $i] :
( ~ ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SY3361 @ SY3362 ) )
| ( in @ SV41 @ SY3362 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(638,plain,
! [SV30: $i] :
( ( ( relation @ SV30 )
= $false )
| ( ( ~ ( ~ ! [SY3295: $i,SY3296: $i] :
( ~ ( ~ ( ! [SY3297: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ SY3296 @ SY3295 @ SV30 ) @ SY3297 ) @ SV30 )
| ~ ( in @ SY3297 @ SY3295 ) )
| ~ ( in @ ( sK43_D @ SY3296 @ SY3295 @ SV30 ) @ SY3296 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SY3296 @ SY3295 @ SV30 ) @ ( sK44_SY3116 @ SY3296 @ SY3295 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK44_SY3116 @ SY3296 @ SY3295 @ SV30 ) @ SY3295 ) )
| ( in @ ( sK43_D @ SY3296 @ SY3295 @ SV30 ) @ SY3296 ) ) )
| ( SY3296
= ( relation_inverse_image @ SV30 @ SY3295 ) ) )
| ~ ! [SY3298: $i,SY3299: $i] :
( ( SY3299
!= ( relation_inverse_image @ SV30 @ SY3298 ) )
| ~ ( ~ ! [SY3300: $i] :
( ! [SY3301: $i] :
( ~ ( in @ ( ordered_pair @ SY3300 @ SY3301 ) @ SV30 )
| ~ ( in @ SY3301 @ SY3298 ) )
| ( in @ SY3300 @ SY3299 ) )
| ~ ! [SY3302: $i] :
( ~ ( in @ SY3302 @ SY3299 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3302 @ ( sK42_E @ SY3302 @ SY3299 @ SY3298 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK42_E @ SY3302 @ SY3299 @ SY3298 @ SV30 ) @ SY3298 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[587]) ).
thf(639,plain,
! [SV31: $i] :
( ( ~ ! [SY3303: $i,SY3304: $i] :
( ~ ( relation @ SY3304 )
| ~ ( in @ ( ordered_pair @ SV31 @ SY3303 ) @ SY3304 )
| ( in @ SV31 @ ( relation_dom @ SY3304 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[588]) ).
thf(640,plain,
! [SV31: $i] :
( ( ~ ! [SY3305: $i,SY3306: $i] :
( ~ ( relation @ SY3306 )
| ~ ( in @ ( ordered_pair @ SV31 @ SY3305 ) @ SY3306 )
| ( in @ SY3305 @ ( relation_rng @ SY3306 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[588]) ).
thf(641,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( in @ ( sK69_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK69_B @ SX0 ) @ ( sK69_B @ SX0 ) ) @ SX0 ) )
| ( reflexive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[589]) ).
thf(642,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ ( relation_field @ SX0 ) )
| ( in @ ( ordered_pair @ SX1 @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[590]) ).
thf(643,plain,
! [SV32: $i] :
( ( ( relation @ SV32 )
= $false )
| ( ( ! [SY3307: $i] :
( ~ ( relation @ SY3307 )
| ~ ( ~ ! [SY3308: $i] :
( ~ ( function @ SY3308 )
| ~ ( relation @ SY3308 )
| ~ ( ~ ( ~ ( in @ ( sK10_D @ SY3308 @ SY3307 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( sK11_SY3094 @ SY3308 @ SY3307 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3308 @ ( sK10_D @ SY3308 @ SY3307 @ SV32 ) ) @ ( apply @ SY3308 @ ( sK11_SY3094 @ SY3308 @ SY3307 @ SV32 ) ) ) @ SY3307 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY3308 @ SY3307 @ SV32 ) @ ( sK11_SY3094 @ SY3308 @ SY3307 @ SV32 ) ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SY3308 @ SY3307 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3308 @ SY3307 @ SV32 ) @ ( sK11_SY3094 @ SY3308 @ SY3307 @ SV32 ) ) @ SV32 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SY3308 @ SY3307 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3308 @ SY3307 @ SV32 ) @ ( sK11_SY3094 @ SY3308 @ SY3307 @ SV32 ) ) @ SV32 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SY3308 @ ( sK10_D @ SY3308 @ SY3307 @ SV32 ) ) @ ( apply @ SY3308 @ ( sK11_SY3094 @ SY3308 @ SY3307 @ SV32 ) ) ) @ SY3307 )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3308 @ SY3307 @ SV32 ) @ ( sK11_SY3094 @ SY3308 @ SY3307 @ SV32 ) ) @ SV32 ) ) ) )
| ( ( relation_dom @ SY3308 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SY3308 )
!= ( relation_field @ SY3307 ) )
| ~ ( one_to_one @ SY3308 )
| ( relation_isomorphism @ SV32 @ SY3307 @ SY3308 ) )
| ~ ~ ( ~ ! [SY3309: $i] :
( ~ ( function @ SY3309 )
| ~ ( relation @ SY3309 )
| ~ ( relation_isomorphism @ SV32 @ SY3307 @ SY3309 )
| ~ ( ~ ! [SY3310: $i,SY3311: $i] :
( ~ ( in @ SY3310 @ ( relation_field @ SV32 ) )
| ~ ( in @ SY3311 @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3309 @ SY3310 ) @ ( apply @ SY3309 @ SY3311 ) ) @ SY3307 )
| ( in @ ( ordered_pair @ SY3310 @ SY3311 ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3312: $i] :
( ! [SY3313: $i] :
~ ( in @ ( ordered_pair @ SY3312 @ SY3313 ) @ SV32 )
| ( in @ SY3312 @ ( relation_field @ SV32 ) ) )
| ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV32 )
| ( in @ SY3315 @ ( relation_field @ SV32 ) ) ) )
| ~ ! [SY3316: $i,SY3317: $i] :
( ~ ( in @ ( ordered_pair @ SY3316 @ SY3317 ) @ SV32 )
| ( in @ ( ordered_pair @ ( apply @ SY3309 @ SY3316 ) @ ( apply @ SY3309 @ SY3317 ) ) @ SY3307 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3318: $i] :
( ~ ( function @ SY3318 )
| ~ ( relation @ SY3318 )
| ~ ( relation_isomorphism @ SV32 @ SY3307 @ SY3318 )
| ( ( relation_dom @ SY3318 )
= ( relation_field @ SV32 ) ) )
| ~ ! [SY3319: $i] :
( ~ ( function @ SY3319 )
| ~ ( relation @ SY3319 )
| ~ ( relation_isomorphism @ SV32 @ SY3307 @ SY3319 )
| ( ( relation_rng @ SY3319 )
= ( relation_field @ SY3307 ) ) ) )
| ~ ! [SY3320: $i] :
( ~ ( function @ SY3320 )
| ~ ( relation @ SY3320 )
| ~ ( relation_isomorphism @ SV32 @ SY3307 @ SY3320 )
| ( one_to_one @ SY3320 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[591]) ).
thf(644,plain,
! [SV33: $i] :
( ( ~ ! [SY3321: $i,SY3322: $i] :
( ~ ( relation_of2_as_subset @ SY3322 @ SV33 @ SY3321 )
| ~ ( ~ ! [SY3323: $i] :
~ ( in @ ( ordered_pair @ SY3323 @ ( sK57_D @ SY3322 @ SY3321 @ SV33 ) ) @ SY3322 )
| ~ ( in @ ( sK57_D @ SY3322 @ SY3321 @ SV33 ) @ SY3321 ) )
| ( ( relation_rng_as_subset @ SV33 @ SY3321 @ SY3322 )
= SY3321 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[592]) ).
thf(645,plain,
! [SV33: $i] :
( ( ~ ! [SY3324: $i,SY3325: $i] :
( ~ ( relation_of2_as_subset @ SY3325 @ SV33 @ SY3324 )
| ( ( relation_rng_as_subset @ SV33 @ SY3324 @ SY3325 )
!= SY3324 )
| ! [SY3326: $i] :
( ( in @ ( ordered_pair @ ( sK56_E @ SY3326 @ SY3325 @ SY3324 @ SV33 ) @ SY3326 ) @ SY3325 )
| ~ ( in @ SY3326 @ SY3324 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[592]) ).
thf(646,plain,
! [SV34: $i] :
( ( ( relation @ SV34 )
= $false )
| ( ( ~ ( ~ ! [SY3327: $i] :
( ~ ( ~ ( ! [SY3328: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SY3327 @ SV34 ) @ SY3328 ) @ SV34 )
| ~ ( in @ ( sK22_C @ SY3327 @ SV34 ) @ SY3327 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SY3327 @ SV34 ) @ ( sK23_SY3101 @ SY3327 @ SV34 ) ) @ SV34 )
| ( in @ ( sK22_C @ SY3327 @ SV34 ) @ SY3327 ) ) )
| ( SY3327
= ( relation_dom @ SV34 ) ) )
| ~ ! [SY3329: $i] :
( ( SY3329
!= ( relation_dom @ SV34 ) )
| ~ ( ~ ! [SY3330: $i] :
( ! [SY3331: $i] :
~ ( in @ ( ordered_pair @ SY3330 @ SY3331 ) @ SV34 )
| ( in @ SY3330 @ SY3329 ) )
| ~ ! [SY3332: $i] :
( ~ ( in @ SY3332 @ SY3329 )
| ( in @ ( ordered_pair @ SY3332 @ ( sK21_D @ SY3332 @ SY3329 @ SV34 ) ) @ SV34 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[593]) ).
thf(647,plain,
! [SV1: $i] :
( ( ( in @ ( ordered_pair @ ( sK54_B @ SV1 ) @ ( sK55_SY3122 @ SV1 ) ) @ SV1 )
= $true )
| ( ( SV1 = empty_set )
= $true )
| ( ( relation @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[594]) ).
thf(648,plain,
! [SV44: $i] :
( ( ~ ( ~ ! [SY3365: $i,SY3366: $i] :
( ( sK39_B @ SV44 )
!= ( ordered_pair @ SY3365 @ SY3366 ) )
| ~ ( in @ ( sK39_B @ SV44 ) @ SV44 ) )
| ( relation @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(649,plain,
! [SV45: $i] :
( ( ~ ( relation @ SV45 )
| ! [SY3367: $i] :
( ( SY3367
= ( ordered_pair @ ( sK37_C @ SY3367 @ SV45 ) @ ( sK38_SY3111 @ SY3367 @ SV45 ) ) )
| ~ ( in @ SY3367 @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(650,plain,
! [SV4: $i] :
( ( ( ~ ! [SY3132: $i] :
( ~ ( relation @ SY3132 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SY3132 @ SV4 ) @ ( sK32_SY3109 @ SY3132 @ SV4 ) ) @ SV4 )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ SY3132 @ SV4 ) @ ( sK32_SY3109 @ SY3132 @ SV4 ) ) @ SY3132 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK31_C @ SY3132 @ SV4 ) @ ( sK32_SY3109 @ SY3132 @ SV4 ) ) @ SV4 )
| ( in @ ( ordered_pair @ ( sK31_C @ SY3132 @ SV4 ) @ ( sK32_SY3109 @ SY3132 @ SV4 ) ) @ SY3132 ) ) )
| ( SV4 = SY3132 ) )
| ~ ! [SY3133: $i] :
( ~ ( relation @ SY3133 )
| ( SV4 != SY3133 )
| ~ ( ~ ! [SY3134: $i,SY3135: $i] :
( ~ ( in @ ( ordered_pair @ SY3134 @ SY3135 ) @ SV4 )
| ( in @ ( ordered_pair @ SY3134 @ SY3135 ) @ SY3133 ) )
| ~ ! [SY3136: $i,SY3137: $i] :
( ~ ( in @ ( ordered_pair @ SY3136 @ SY3137 ) @ SY3133 )
| ( in @ ( ordered_pair @ SY3136 @ SY3137 ) @ SV4 ) ) ) ) )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[598]) ).
thf(651,plain,
! [SV5: $i] :
( ( ( ~ ! [SY3138: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SY3138 @ SV5 ) @ SY3138 )
| ~ ( in @ ( sK4_SY3086 @ SY3138 @ SV5 ) @ SY3138 ) )
| ~ ( in @ ( sK5_SY3088 @ SY3138 @ SV5 ) @ SY3138 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SY3138 @ SV5 ) @ ( sK4_SY3086 @ SY3138 @ SV5 ) ) @ SV5 ) )
| ~ ( in @ ( ordered_pair @ ( sK4_SY3086 @ SY3138 @ SV5 ) @ ( sK5_SY3088 @ SY3138 @ SV5 ) ) @ SV5 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK3_C @ SY3138 @ SV5 ) @ ( sK5_SY3088 @ SY3138 @ SV5 ) ) @ SV5 ) )
| ( is_transitive_in @ SV5 @ SY3138 ) )
| ~ ! [SY3139: $i] :
( ~ ( is_transitive_in @ SV5 @ SY3139 )
| ! [SY3140: $i,SY3141: $i,SY3142: $i] :
( ~ ( in @ SY3140 @ SY3139 )
| ~ ( in @ SY3141 @ SY3139 )
| ~ ( in @ SY3142 @ SY3139 )
| ~ ( in @ ( ordered_pair @ SY3140 @ SY3141 ) @ SV5 )
| ~ ( in @ ( ordered_pair @ SY3141 @ SY3142 ) @ SV5 )
| ( in @ ( ordered_pair @ SY3140 @ SY3142 ) @ SV5 ) ) ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[599]) ).
thf(652,plain,
! [SV6: $i] :
( ( ! [SY3143: $i,SY3144: $i] :
( ~ ( relation_of2_as_subset @ SY3144 @ SY3143 @ SV6 )
| ~ ( ~ ! [SY3145: $i] :
~ ( in @ ( ordered_pair @ ( sK59_D @ SY3144 @ SY3143 @ SV6 ) @ SY3145 ) @ SY3144 )
| ~ ( in @ ( sK59_D @ SY3144 @ SY3143 @ SV6 ) @ SY3143 ) )
| ( ( relation_dom_as_subset @ SY3143 @ SV6 @ SY3144 )
= SY3143 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[600]) ).
thf(653,plain,
! [SV6: $i] :
( ( ! [SY3146: $i,SY3147: $i] :
( ~ ( relation_of2_as_subset @ SY3147 @ SY3146 @ SV6 )
| ( ( relation_dom_as_subset @ SY3146 @ SV6 @ SY3147 )
!= SY3146 )
| ! [SY3148: $i] :
( ( in @ ( ordered_pair @ SY3148 @ ( sK58_E @ SY3148 @ SY3147 @ SY3146 @ SV6 ) ) @ SY3147 )
| ~ ( in @ SY3148 @ SY3146 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[601]) ).
thf(654,plain,
! [SV7: $i,SV46: $i] :
( ( ( ~ ( relation @ SV46 )
| ~ ( ~ ! [SY3368: $i] :
( ~ ( relation @ SY3368 )
| ~ ( ~ ( ! [SY3369: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3368 @ SV46 @ SV7 ) @ SY3369 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3369 @ ( sK8_SY3089 @ SY3368 @ SV46 @ SV7 ) ) @ SV46 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3368 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SY3368 @ SV46 @ SV7 ) ) @ SY3368 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3368 @ SV46 @ SV7 ) @ ( sK9_SY3093 @ SY3368 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SY3368 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SY3368 @ SV46 @ SV7 ) ) @ SV46 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SY3368 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SY3368 @ SV46 @ SV7 ) ) @ SY3368 ) ) )
| ( SY3368
= ( relation_composition @ SV7 @ SV46 ) ) )
| ~ ! [SY3370: $i] :
( ~ ( relation @ SY3370 )
| ( SY3370
!= ( relation_composition @ SV7 @ SV46 ) )
| ~ ( ~ ! [SY3371: $i,SY3372: $i] :
( ! [SY3373: $i] :
( ~ ( in @ ( ordered_pair @ SY3371 @ SY3373 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3373 @ SY3372 ) @ SV46 ) )
| ( in @ ( ordered_pair @ SY3371 @ SY3372 ) @ SY3370 ) )
| ~ ! [SY3374: $i,SY3375: $i] :
( ~ ( in @ ( ordered_pair @ SY3374 @ SY3375 ) @ SY3370 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3374 @ ( sK6_F @ SY3375 @ SY3374 @ SY3370 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY3375 @ SY3374 @ SY3370 @ SV46 @ SV7 ) @ SY3375 ) @ SV46 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(655,plain,
! [SV47: $i] :
( ( ! [SY3376: $i] :
( ~ ( relation @ SY3376 )
| ~ ( ~ ( ( ( sK52_C @ SY3376 @ SV47 )
!= ( sK53_SY3121 @ SY3376 @ SV47 ) )
| ~ ( in @ ( sK52_C @ SY3376 @ SV47 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK52_C @ SY3376 @ SV47 ) @ ( sK53_SY3121 @ SY3376 @ SV47 ) ) @ SY3376 ) )
| ~ ~ ( ~ ( ( ( sK52_C @ SY3376 @ SV47 )
= ( sK53_SY3121 @ SY3376 @ SV47 ) )
| ( in @ ( ordered_pair @ ( sK52_C @ SY3376 @ SV47 ) @ ( sK53_SY3121 @ SY3376 @ SV47 ) ) @ SY3376 ) )
| ~ ( ( in @ ( sK52_C @ SY3376 @ SV47 ) @ SV47 )
| ( in @ ( ordered_pair @ ( sK52_C @ SY3376 @ SV47 ) @ ( sK53_SY3121 @ SY3376 @ SV47 ) ) @ SY3376 ) ) ) )
| ( SY3376
= ( identity_relation @ SV47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(656,plain,
! [SV48: $i] :
( ( ! [SY3377: $i] :
( ~ ( relation @ SY3377 )
| ( SY3377
!= ( identity_relation @ SV48 ) )
| ~ ( ~ ! [SY3378: $i,SY3379: $i] :
( ( SY3378 != SY3379 )
| ~ ( in @ SY3378 @ SV48 )
| ( in @ ( ordered_pair @ SY3378 @ SY3379 ) @ SY3377 ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SY3377 )
| ( SX2 = SX3 ) )
| ~ ! [SY3382: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SY3382 @ SX3 ) @ SY3377 )
| ( in @ SY3382 @ SV48 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(657,plain,
! [SV49: $i,SV42: $i,SV8: $i] :
( ( ( ( SV8
!= ( ordered_pair @ SV42 @ SV49 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3160: $i] :
( ~ ( ( SV8
!= ( ordered_pair @ ( sK40_C @ SY3160 @ SV8 ) @ ( sK41_SY3114 @ SY3160 @ SV8 ) ) )
| ~ ( ( SY3160
!= ( sK40_C @ SY3160 @ SV8 ) ) ) )
| ( SY3160
= ( pair_first @ SV8 ) ) )
| ~ ! [SY3161: $i] :
( ( SY3161
!= ( pair_first @ SV8 ) )
| ! [SY3162: $i] :
( ! [SY3163: $i] :
( SV8
!= ( ordered_pair @ SY3162 @ SY3163 ) )
| ( SY3161 = SY3162 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(658,plain,
! [SV37: $i,SV9: $i] :
( ( ~ ! [SY3333: $i,SY3334: $i] :
( ~ ( relation @ SY3334 )
| ~ ( in @ SV9 @ SY3333 )
| ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ SY3334 )
| ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SY3333 ) @ SY3334 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[606]) ).
thf(659,plain,
! [SV37: $i,SV9: $i] :
( ( ~ ~ ( ~ ! [SY3335: $i,SY3336: $i] :
( ~ ( relation @ SY3336 )
| ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SY3335 ) @ SY3336 ) )
| ( in @ SV9 @ SY3335 ) )
| ~ ! [SY3337: $i,SY3338: $i] :
( ~ ( relation @ SY3338 )
| ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SY3337 ) @ SY3338 ) )
| ( in @ ( ordered_pair @ SV9 @ SV37 ) @ SY3338 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[606]) ).
thf(660,plain,
! [SV10: $i] :
( ( ! [SY3171: $i,SY3172: $i] :
( ~ ( relation @ SY3172 )
| ! [SY3173: $i] :
( ~ ( in @ SY3173 @ ( relation_rng @ SY3172 ) )
| ~ ( in @ ( ordered_pair @ SV10 @ SY3173 ) @ SY3172 )
| ~ ( in @ SY3173 @ SY3171 ) )
| ( in @ SV10 @ ( relation_inverse_image @ SY3172 @ SY3171 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[607]) ).
thf(661,plain,
! [SV10: $i] :
( ( ! [SY3174: $i,SY3175: $i] :
( ~ ( relation @ SY3175 )
| ~ ( in @ SV10 @ ( relation_inverse_image @ SY3175 @ SY3174 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_D @ SY3175 @ SY3174 @ SV10 ) @ ( relation_rng @ SY3175 ) )
| ~ ( in @ ( ordered_pair @ SV10 @ ( sK60_D @ SY3175 @ SY3174 @ SV10 ) ) @ SY3175 ) )
| ~ ( in @ ( sK60_D @ SY3175 @ SY3174 @ SV10 ) @ SY3174 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[608]) ).
thf(662,plain,
! [SV11: $i] :
( ( ! [SY3176: $i,SY3177: $i] :
( ~ ( ~ ( ! [SY3178: $i,SY3179: $i] :
( ~ ( in @ SY3178 @ SV11 )
| ~ ( in @ SY3179 @ SY3176 )
| ( ( sK28_D @ SY3177 @ SY3176 @ SV11 )
!= ( ordered_pair @ SY3178 @ SY3179 ) ) )
| ~ ( in @ ( sK28_D @ SY3177 @ SY3176 @ SV11 ) @ SY3177 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY3106 @ SY3177 @ SY3176 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK30_SY3108 @ SY3177 @ SY3176 @ SV11 ) @ SY3176 ) )
| ( ( sK28_D @ SY3177 @ SY3176 @ SV11 )
!= ( ordered_pair @ ( sK29_SY3106 @ SY3177 @ SY3176 @ SV11 ) @ ( sK30_SY3108 @ SY3177 @ SY3176 @ SV11 ) ) ) )
| ( in @ ( sK28_D @ SY3177 @ SY3176 @ SV11 ) @ SY3177 ) ) )
| ( SY3177
= ( cartesian_product2 @ SV11 @ SY3176 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[609]) ).
thf(663,plain,
! [SV11: $i] :
( ( ! [SY3180: $i,SY3181: $i] :
( ( SY3181
!= ( cartesian_product2 @ SV11 @ SY3180 ) )
| ~ ( ~ ! [SY3182: $i] :
( ! [SY3183: $i,SY3184: $i] :
( ~ ( in @ SY3183 @ SV11 )
| ~ ( in @ SY3184 @ SY3180 )
| ( SY3182
!= ( ordered_pair @ SY3183 @ SY3184 ) ) )
| ( in @ SY3182 @ SY3181 ) )
| ~ ! [SY3185: $i] :
( ~ ( in @ SY3185 @ SY3181 )
| ~ ( ~ ~ ( ~ ( in @ ( sK26_E @ SY3185 @ SY3181 @ SY3180 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK27_SY3103 @ SY3185 @ SY3181 @ SY3180 @ SV11 ) @ SY3180 ) )
| ( SY3185
!= ( ordered_pair @ ( sK26_E @ SY3185 @ SY3181 @ SY3180 @ SV11 ) @ ( sK27_SY3103 @ SY3185 @ SY3181 @ SY3180 @ SV11 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[610]) ).
thf(664,plain,
! [SV12: $i] :
( ( ! [SY3186: $i,SY3187: $i] :
( ~ ( relation @ SY3187 )
| ~ ( in @ ( ordered_pair @ SV12 @ SY3186 ) @ SY3187 )
| ( in @ SV12 @ ( relation_field @ SY3187 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[611]) ).
thf(665,plain,
! [SV12: $i] :
( ( ! [SY3188: $i,SY3189: $i] :
( ~ ( relation @ SY3189 )
| ~ ( in @ ( ordered_pair @ SV12 @ SY3188 ) @ SY3189 )
| ( in @ SY3188 @ ( relation_field @ SY3189 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[612]) ).
thf(666,plain,
! [SV50: $i,SV43: $i,SV13: $i] :
( ( ( ( SV13
!= ( ordered_pair @ SV43 @ SV50 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3192: $i] :
( ~ ( ( SV13
!= ( ordered_pair @ ( sK33_C @ SY3192 @ SV13 ) @ ( sK34_SY3110 @ SY3192 @ SV13 ) ) )
| ~ ( ( SY3192
!= ( sK34_SY3110 @ SY3192 @ SV13 ) ) ) )
| ( SY3192
= ( pair_second @ SV13 ) ) )
| ~ ! [SY3193: $i] :
( ( SY3193
!= ( pair_second @ SV13 ) )
| ! [SY3194: $i,SY3195: $i] :
( ( SV13
!= ( ordered_pair @ SY3194 @ SY3195 ) )
| ( SY3193 = SY3195 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(667,plain,
! [SV14: $i] :
( ( ( ~ ! [SY3196: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK14_C @ SY3196 @ SV14 )
!= ( sK15_SY3096 @ SY3196 @ SV14 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SY3196 @ SV14 ) @ SY3196 )
| ~ ( in @ ( sK15_SY3096 @ SY3196 @ SV14 ) @ SY3196 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK14_C @ SY3196 @ SV14 ) @ ( sK15_SY3096 @ SY3196 @ SV14 ) ) @ SV14 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK15_SY3096 @ SY3196 @ SV14 ) @ ( sK14_C @ SY3196 @ SV14 ) ) @ SV14 ) )
| ( is_connected_in @ SV14 @ SY3196 ) )
| ~ ! [SY3197: $i] :
( ~ ( is_connected_in @ SV14 @ SY3197 )
| ! [SY3198: $i,SY3199: $i] :
( ( SY3198 = SY3199 )
| ~ ( in @ SY3198 @ SY3197 )
| ~ ( in @ SY3199 @ SY3197 )
| ( in @ ( ordered_pair @ SY3198 @ SY3199 ) @ SV14 )
| ( in @ ( ordered_pair @ SY3199 @ SY3198 ) @ SV14 ) ) ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[614]) ).
thf(668,plain,
! [SV15: $i] :
( ( ! [SY3200: $i,SY3201: $i] :
( ~ ( relation @ SY3201 )
| ! [SY3202: $i] :
( ~ ( in @ SY3202 @ ( relation_dom @ SY3201 ) )
| ~ ( in @ ( ordered_pair @ SY3202 @ SV15 ) @ SY3201 )
| ~ ( in @ SY3202 @ SY3200 ) )
| ( in @ SV15 @ ( relation_image @ SY3201 @ SY3200 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[615]) ).
thf(669,plain,
! [SV15: $i] :
( ( ! [SY3203: $i,SY3204: $i] :
( ~ ( relation @ SY3204 )
| ~ ( in @ SV15 @ ( relation_image @ SY3204 @ SY3203 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK61_D @ SY3204 @ SY3203 @ SV15 ) @ ( relation_dom @ SY3204 ) )
| ~ ( in @ ( ordered_pair @ ( sK61_D @ SY3204 @ SY3203 @ SV15 ) @ SV15 ) @ SY3204 ) )
| ~ ( in @ ( sK61_D @ SY3204 @ SY3203 @ SV15 ) @ SY3203 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[616]) ).
thf(670,plain,
! [SV16: $i] :
( ( ( ~ ! [SY3205: $i,SY3206: $i] :
( ~ ( ~ ( ! [SY3207: $i] :
( ~ ( in @ ( ordered_pair @ SY3207 @ ( sK46_D @ SY3206 @ SY3205 @ SV16 ) ) @ SV16 )
| ~ ( in @ SY3207 @ SY3205 ) )
| ~ ( in @ ( sK46_D @ SY3206 @ SY3205 @ SV16 ) @ SY3206 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SY3206 @ SY3205 @ SV16 ) @ ( sK46_D @ SY3206 @ SY3205 @ SV16 ) ) @ SV16 )
| ~ ( in @ ( sK47_SY3118 @ SY3206 @ SY3205 @ SV16 ) @ SY3205 ) )
| ( in @ ( sK46_D @ SY3206 @ SY3205 @ SV16 ) @ SY3206 ) ) )
| ( SY3206
= ( relation_image @ SV16 @ SY3205 ) ) )
| ~ ! [SY3208: $i,SY3209: $i] :
( ( SY3209
!= ( relation_image @ SV16 @ SY3208 ) )
| ~ ( ~ ! [SY3210: $i] :
( ! [SY3211: $i] :
( ~ ( in @ ( ordered_pair @ SY3211 @ SY3210 ) @ SV16 )
| ~ ( in @ SY3211 @ SY3208 ) )
| ( in @ SY3210 @ SY3209 ) )
| ~ ! [SY3212: $i] :
( ~ ( in @ SY3212 @ SY3209 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SY3212 @ SY3209 @ SY3208 @ SV16 ) @ SY3212 ) @ SV16 )
| ~ ( in @ ( sK45_E @ SY3212 @ SY3209 @ SY3208 @ SV16 ) @ SY3208 ) ) ) ) ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[617]) ).
thf(671,plain,
! [SV51: $i] :
( ( ~ ( relation @ SV51 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK64_B @ SV51 ) @ ( sK65_SY3126 @ SV51 ) ) @ SV51 )
| ~ ( in @ ( ordered_pair @ ( sK65_SY3126 @ SV51 ) @ ( sK64_B @ SV51 ) ) @ SV51 ) )
| ~ ( ( ( sK64_B @ SV51 )
!= ( sK65_SY3126 @ SV51 ) ) ) )
| ( antisymmetric @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(672,plain,
! [SV52: $i] :
( ( ~ ( relation @ SV52 )
| ~ ( antisymmetric @ SV52 )
| ! [SY3384: $i,SY3385: $i] :
( ~ ( in @ ( ordered_pair @ SY3384 @ SY3385 ) @ SV52 )
| ~ ( in @ ( ordered_pair @ SY3385 @ SY3384 ) @ SV52 )
| ( SY3384 = SY3385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(673,plain,
! [SV17: $i] :
( ( ! [SY3213: $i,SY3214: $i] :
( ~ ( function @ SY3214 )
| ~ ( relation @ SY3214 )
| ( SY3213
!= ( apply @ SY3214 @ SV17 ) )
| ~ ( in @ SV17 @ ( relation_dom @ SY3214 ) )
| ( in @ ( ordered_pair @ SV17 @ SY3213 ) @ SY3214 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[620]) ).
thf(674,plain,
! [SV17: $i] :
( ( ~ ( ~ ! [SY3215: $i,SY3216: $i] :
( ~ ( function @ SY3216 )
| ~ ( relation @ SY3216 )
| ~ ( in @ ( ordered_pair @ SV17 @ SY3215 ) @ SY3216 )
| ( SY3215
= ( apply @ SY3216 @ SV17 ) ) )
| ~ ! [SY3217: $i,SY3218: $i] :
( ~ ( function @ SY3218 )
| ~ ( relation @ SY3218 )
| ~ ( in @ ( ordered_pair @ SV17 @ SY3217 ) @ SY3218 )
| ( in @ SV17 @ ( relation_dom @ SY3218 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[621]) ).
thf(675,plain,
! [SV18: $i] :
( ( ( ~ ! [SY3219: $i,SY3220: $i] :
( ~ ( ~ ( ( ( sK35_D @ SY3220 @ SY3219 @ SV18 )
= SY3219 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SY3220 @ SY3219 @ SV18 ) @ SY3219 ) @ SV18 )
| ~ ( in @ ( sK35_D @ SY3220 @ SY3219 @ SV18 ) @ SY3220 ) )
| ~ ~ ( ~ ( ( ( sK35_D @ SY3220 @ SY3219 @ SV18 )
!= SY3219 )
| ( in @ ( sK35_D @ SY3220 @ SY3219 @ SV18 ) @ SY3220 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SY3220 @ SY3219 @ SV18 ) @ SY3219 ) @ SV18 )
| ( in @ ( sK35_D @ SY3220 @ SY3219 @ SV18 ) @ SY3220 ) ) ) )
| ( SY3220
= ( fiber @ SV18 @ SY3219 ) ) )
| ~ ! [SY3221: $i,SY3222: $i] :
( ( SY3222
!= ( fiber @ SV18 @ SY3221 ) )
| ~ ( ~ ! [SY3223: $i] :
( ( SY3223 = SY3221 )
| ~ ( in @ ( ordered_pair @ SY3223 @ SY3221 ) @ SV18 )
| ( in @ SY3223 @ SY3222 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY3222 )
| ( SX3 != SY3221 ) )
| ~ ! [SY3225: $i] :
( ~ ( in @ SY3225 @ SY3222 )
| ( in @ ( ordered_pair @ SY3225 @ SY3221 ) @ SV18 ) ) ) ) ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[622]) ).
thf(676,plain,
! [SV19: $i] :
( ( ( ~ ! [SY3226: $i] :
( ~ ( ~ ( in @ ( sK36_C @ SY3226 @ SV19 ) @ SY3226 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SY3226 @ SV19 ) @ ( sK36_C @ SY3226 @ SV19 ) ) @ SV19 ) )
| ( is_reflexive_in @ SV19 @ SY3226 ) )
| ~ ! [SY3227: $i] :
( ~ ( is_reflexive_in @ SV19 @ SY3227 )
| ! [SY3228: $i] :
( ~ ( in @ SY3228 @ SY3227 )
| ( in @ ( ordered_pair @ SY3228 @ SY3228 ) @ SV19 ) ) ) )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[623]) ).
thf(677,plain,
! [SV20: $i] :
( ( ( ~ ! [SY3229: $i] :
( ~ ( relation @ SY3229 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SY3229 @ SV20 ) @ ( sK13_SY3095 @ SY3229 @ SV20 ) ) @ SY3229 )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SY3229 @ SV20 ) @ ( sK12_C @ SY3229 @ SV20 ) ) @ SV20 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SY3229 @ SV20 ) @ ( sK13_SY3095 @ SY3229 @ SV20 ) ) @ SY3229 )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ SY3229 @ SV20 ) @ ( sK12_C @ SY3229 @ SV20 ) ) @ SV20 ) ) )
| ( SY3229
= ( relation_inverse @ SV20 ) ) )
| ~ ! [SY3230: $i] :
( ~ ( relation @ SY3230 )
| ( SY3230
!= ( relation_inverse @ SV20 ) )
| ~ ( ~ ! [SY3231: $i,SY3232: $i] :
( ~ ( in @ ( ordered_pair @ SY3231 @ SY3232 ) @ SY3230 )
| ( in @ ( ordered_pair @ SY3232 @ SY3231 ) @ SV20 ) )
| ~ ! [SY3233: $i,SY3234: $i] :
( ~ ( in @ ( ordered_pair @ SY3234 @ SY3233 ) @ SV20 )
| ( in @ ( ordered_pair @ SY3233 @ SY3234 ) @ SY3230 ) ) ) ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(678,plain,
! [SV21: $i,SV38: $i] :
( ( ( relation @ SV38 )
= $false )
| ( ( ~ ( ~ ! [SY3339: $i] :
( ~ ( relation @ SY3339 )
| ~ ( ~ ( ~ ( in @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) @ SV21 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SY3339 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) ) @ SV38 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SY3339 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) ) @ SY3339 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK48_D @ SY3339 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) ) @ SY3339 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SY3339 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) ) @ SV38 )
| ( in @ ( ordered_pair @ ( sK48_D @ SY3339 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) ) @ SY3339 ) ) ) )
| ( SY3339
= ( relation_rng_restriction @ SV21 @ SV38 ) ) )
| ~ ! [SY3340: $i] :
( ~ ( relation @ SY3340 )
| ( SY3340
!= ( relation_rng_restriction @ SV21 @ SV38 ) )
| ~ ( ~ ! [SY3341: $i,SY3342: $i] :
( ~ ( in @ SY3342 @ SV21 )
| ~ ( in @ ( ordered_pair @ SY3341 @ SY3342 ) @ SV38 )
| ( in @ ( ordered_pair @ SY3341 @ SY3342 ) @ SY3340 ) )
| ~ ~ ( ~ ! [SY3240: $i,SY3241: $i] :
( ~ ( in @ ( ordered_pair @ SY3240 @ SY3241 ) @ SY3340 )
| ( in @ SY3241 @ SV21 ) )
| ~ ! [SY3345: $i,SY3346: $i] :
( ~ ( in @ ( ordered_pair @ SY3345 @ SY3346 ) @ SY3340 )
| ( in @ ( ordered_pair @ SY3345 @ SY3346 ) @ SV38 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[625]) ).
thf(679,plain,
! [SV22: $i] :
( ( ( ~ ! [SY3244: $i] :
( ~ ( ~ ( ! [SY3245: $i] :
~ ( in @ ( ordered_pair @ SY3245 @ ( sK17_C @ SY3244 @ SV22 ) ) @ SV22 )
| ~ ( in @ ( sK17_C @ SY3244 @ SV22 ) @ SY3244 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK18_SY3098 @ SY3244 @ SV22 ) @ ( sK17_C @ SY3244 @ SV22 ) ) @ SV22 )
| ( in @ ( sK17_C @ SY3244 @ SV22 ) @ SY3244 ) ) )
| ( SY3244
= ( relation_rng @ SV22 ) ) )
| ~ ! [SY3246: $i] :
( ( SY3246
!= ( relation_rng @ SV22 ) )
| ~ ( ~ ! [SY3247: $i] :
( ! [SY3248: $i] :
~ ( in @ ( ordered_pair @ SY3248 @ SY3247 ) @ SV22 )
| ( in @ SY3247 @ SY3246 ) )
| ~ ! [SY3249: $i] :
( ~ ( in @ SY3249 @ SY3246 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3249 @ SY3246 @ SV22 ) @ SY3249 ) @ SV22 ) ) ) ) )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[626]) ).
thf(680,plain,
! [SV23: $i] :
( ( ( ~ ! [SY3250: $i] :
( ~ ( relation @ SY3250 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3250 @ SV23 ) @ ( sK25_SY3102 @ SY3250 @ SV23 ) ) @ SV23 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3250 @ SV23 ) @ ( sK25_SY3102 @ SY3250 @ SV23 ) ) @ SY3250 ) )
| ( subset @ SV23 @ SY3250 ) )
| ~ ! [SY3251: $i] :
( ~ ( relation @ SY3251 )
| ~ ( subset @ SV23 @ SY3251 )
| ! [SY3252: $i,SY3253: $i] :
( ~ ( in @ ( ordered_pair @ SY3252 @ SY3253 ) @ SV23 )
| ( in @ ( ordered_pair @ SY3252 @ SY3253 ) @ SY3251 ) ) ) )
= $false )
| ( ( relation @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[627]) ).
thf(681,plain,
! [SV24: $i] :
( ( ( ~ ! [SY3254: $i,SY3255: $i] :
( ~ ( relation @ SY3255 )
| ~ ( ~ ( ~ ( in @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ SY3254 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ ( sK51_SY3120 @ SY3255 @ SY3254 @ SV24 ) ) @ SV24 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ ( sK51_SY3120 @ SY3255 @ SY3254 @ SV24 ) ) @ SY3255 ) )
| ~ ~ ( ~ ( ( in @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ SY3254 )
| ( in @ ( ordered_pair @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ ( sK51_SY3120 @ SY3255 @ SY3254 @ SV24 ) ) @ SY3255 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ ( sK51_SY3120 @ SY3255 @ SY3254 @ SV24 ) ) @ SV24 )
| ( in @ ( ordered_pair @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ ( sK51_SY3120 @ SY3255 @ SY3254 @ SV24 ) ) @ SY3255 ) ) ) )
| ( SY3255
= ( relation_dom_restriction @ SV24 @ SY3254 ) ) )
| ~ ! [SY3256: $i,SY3257: $i] :
( ~ ( relation @ SY3257 )
| ( SY3257
!= ( relation_dom_restriction @ SV24 @ SY3256 ) )
| ~ ( ~ ! [SY3258: $i,SY3259: $i] :
( ~ ( in @ SY3258 @ SY3256 )
| ~ ( in @ ( ordered_pair @ SY3258 @ SY3259 ) @ SV24 )
| ( in @ ( ordered_pair @ SY3258 @ SY3259 ) @ SY3257 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3257 )
| ( in @ SX3 @ SY3256 ) )
| ~ ! [SY3262: $i,SY3263: $i] :
( ~ ( in @ ( ordered_pair @ SY3262 @ SY3263 ) @ SY3257 )
| ( in @ ( ordered_pair @ SY3262 @ SY3263 ) @ SV24 ) ) ) ) ) )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[628]) ).
thf(682,plain,
! [SV39: $i,SV25: $i] :
( ( ~ ! [SY3347: $i] :
( ! [SY3348: $i] :
( ( ordered_pair @ SV25 @ SV39 )
!= ( ordered_pair @ SY3347 @ SY3348 ) )
| ( SV25 = SY3347 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[629]) ).
thf(683,plain,
! [SV39: $i,SV25: $i] :
( ( ~ ! [SY3349: $i,SY3350: $i] :
( ( ( ordered_pair @ SV25 @ SV39 )
!= ( ordered_pair @ SY3349 @ SY3350 ) )
| ( SV39 = SY3350 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[629]) ).
thf(684,plain,
! [SV26: $i] :
( ( ( function @ SV26 )
= $false )
| ( ( ~ ( relation @ SV26 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY3269: $i] :
( ~ ( in @ SY3269 @ ( relation_dom @ SV26 ) )
| ! [SY3270: $i] :
( ( SY3270
!= ( apply @ SV26 @ SY3269 ) )
| ( in @ ( ordered_pair @ SY3269 @ SY3270 ) @ SV26 ) ) )
| ~ ! [SY3271: $i] :
( ~ ( in @ SY3271 @ ( relation_dom @ SV26 ) )
| ! [SY3272: $i] :
( ~ ( in @ ( ordered_pair @ SY3271 @ SY3272 ) @ SV26 )
| ( SY3272
= ( apply @ SV26 @ SY3271 ) ) ) ) )
| ~ ~ ( ~ ! [SY3273: $i] :
( ( in @ SY3273 @ ( relation_dom @ SV26 ) )
| ! [SY3274: $i] :
( ( SY3274
!= ( apply @ SV26 @ SY3273 ) )
| ( SY3274 = empty_set ) ) )
| ~ ! [SY3275: $i] :
( ( in @ SY3275 @ ( relation_dom @ SV26 ) )
| ! [SY3276: $i] :
( ( SY3276 != empty_set )
| ( SY3276
= ( apply @ SV26 @ SY3275 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[630]) ).
thf(685,plain,
! [SV53: $i] :
( ( ~ ( relation @ SV53 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK62_B @ SV53 )
!= ( sK63_SY3125 @ SV53 ) ) )
| ~ ~ ( ~ ( in @ ( sK62_B @ SV53 ) @ ( relation_field @ SV53 ) )
| ~ ( in @ ( sK63_SY3125 @ SV53 ) @ ( relation_field @ SV53 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK62_B @ SV53 ) @ ( sK63_SY3125 @ SV53 ) ) @ SV53 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK63_SY3125 @ SV53 ) @ ( sK62_B @ SV53 ) ) @ SV53 ) )
| ( connected @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(686,plain,
! [SV54: $i] :
( ( ~ ( relation @ SV54 )
| ~ ( connected @ SV54 )
| ! [SY3386: $i,SY3387: $i] :
( ( SY3386 = SY3387 )
| ~ ( in @ SY3386 @ ( relation_field @ SV54 ) )
| ~ ( in @ SY3387 @ ( relation_field @ SV54 ) )
| ( in @ ( ordered_pair @ SY3386 @ SY3387 ) @ SV54 )
| ( in @ ( ordered_pair @ SY3387 @ SY3386 ) @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(687,plain,
! [SV27: $i] :
( ( ( ~ ! [SY3277: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_C @ SY3277 @ SV27 ) @ SY3277 )
| ~ ( in @ ( sK20_SY3099 @ SY3277 @ SV27 ) @ SY3277 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SY3277 @ SV27 ) @ ( sK20_SY3099 @ SY3277 @ SV27 ) ) @ SV27 ) )
| ~ ( in @ ( ordered_pair @ ( sK20_SY3099 @ SY3277 @ SV27 ) @ ( sK19_C @ SY3277 @ SV27 ) ) @ SV27 ) )
| ~ ( ( ( sK19_C @ SY3277 @ SV27 )
!= ( sK20_SY3099 @ SY3277 @ SV27 ) ) ) )
| ( is_antisymmetric_in @ SV27 @ SY3277 ) )
| ~ ! [SY3278: $i] :
( ~ ( is_antisymmetric_in @ SV27 @ SY3278 )
| ! [SY3279: $i,SY3280: $i] :
( ~ ( in @ SY3279 @ SY3278 )
| ~ ( in @ SY3280 @ SY3278 )
| ~ ( in @ ( ordered_pair @ SY3279 @ SY3280 ) @ SV27 )
| ~ ( in @ ( ordered_pair @ SY3280 @ SY3279 ) @ SV27 )
| ( SY3279 = SY3280 ) ) ) )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[633]) ).
thf(688,plain,
! [SV40: $i,SV28: $i] :
( ( ~ ! [SY3351: $i,SY3352: $i] :
( ~ ( in @ SV28 @ SY3351 )
| ~ ( in @ SV40 @ SY3352 )
| ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SY3351 @ SY3352 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[634]) ).
thf(689,plain,
! [SV40: $i,SV28: $i] :
( ( ~ ~ ( ~ ! [SY3353: $i] :
( ! [SY3354: $i] :
~ ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SY3353 @ SY3354 ) )
| ( in @ SV28 @ SY3353 ) )
| ~ ! [SY3355: $i,SY3356: $i] :
( ~ ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SY3355 @ SY3356 ) )
| ( in @ SV40 @ SY3356 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[634]) ).
thf(690,plain,
! [SV55: $i] :
( ( ~ ( relation @ SV55 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK66_B @ SV55 ) @ ( sK67_SY3127 @ SV55 ) ) @ SV55 )
| ~ ( in @ ( ordered_pair @ ( sK67_SY3127 @ SV55 ) @ ( sK68_SY3129 @ SV55 ) ) @ SV55 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK66_B @ SV55 ) @ ( sK68_SY3129 @ SV55 ) ) @ SV55 ) )
| ( transitive @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(691,plain,
! [SV56: $i] :
( ( ~ ( relation @ SV56 )
| ~ ( transitive @ SV56 )
| ! [SY3388: $i,SY3389: $i,SY3390: $i] :
( ~ ( in @ ( ordered_pair @ SY3388 @ SY3389 ) @ SV56 )
| ~ ( in @ ( ordered_pair @ SY3389 @ SY3390 ) @ SV56 )
| ( in @ ( ordered_pair @ SY3388 @ SY3390 ) @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(692,plain,
! [SV41: $i,SV29: $i] :
( ( ~ ! [SY3357: $i,SY3358: $i] :
( ~ ( in @ SV29 @ SY3357 )
| ~ ( in @ SV41 @ SY3358 )
| ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SY3357 @ SY3358 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[637]) ).
thf(693,plain,
! [SV41: $i,SV29: $i] :
( ( ~ ~ ( ~ ! [SY3359: $i] :
( ! [SY3360: $i] :
~ ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SY3359 @ SY3360 ) )
| ( in @ SV29 @ SY3359 ) )
| ~ ! [SY3361: $i,SY3362: $i] :
( ~ ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SY3361 @ SY3362 ) )
| ( in @ SV41 @ SY3362 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[637]) ).
thf(694,plain,
! [SV30: $i] :
( ( ( ~ ! [SY3295: $i,SY3296: $i] :
( ~ ( ~ ( ! [SY3297: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ SY3296 @ SY3295 @ SV30 ) @ SY3297 ) @ SV30 )
| ~ ( in @ SY3297 @ SY3295 ) )
| ~ ( in @ ( sK43_D @ SY3296 @ SY3295 @ SV30 ) @ SY3296 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SY3296 @ SY3295 @ SV30 ) @ ( sK44_SY3116 @ SY3296 @ SY3295 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK44_SY3116 @ SY3296 @ SY3295 @ SV30 ) @ SY3295 ) )
| ( in @ ( sK43_D @ SY3296 @ SY3295 @ SV30 ) @ SY3296 ) ) )
| ( SY3296
= ( relation_inverse_image @ SV30 @ SY3295 ) ) )
| ~ ! [SY3298: $i,SY3299: $i] :
( ( SY3299
!= ( relation_inverse_image @ SV30 @ SY3298 ) )
| ~ ( ~ ! [SY3300: $i] :
( ! [SY3301: $i] :
( ~ ( in @ ( ordered_pair @ SY3300 @ SY3301 ) @ SV30 )
| ~ ( in @ SY3301 @ SY3298 ) )
| ( in @ SY3300 @ SY3299 ) )
| ~ ! [SY3302: $i] :
( ~ ( in @ SY3302 @ SY3299 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3302 @ ( sK42_E @ SY3302 @ SY3299 @ SY3298 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK42_E @ SY3302 @ SY3299 @ SY3298 @ SV30 ) @ SY3298 ) ) ) ) ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[638]) ).
thf(695,plain,
! [SV31: $i] :
( ( ! [SY3303: $i,SY3304: $i] :
( ~ ( relation @ SY3304 )
| ~ ( in @ ( ordered_pair @ SV31 @ SY3303 ) @ SY3304 )
| ( in @ SV31 @ ( relation_dom @ SY3304 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[639]) ).
thf(696,plain,
! [SV31: $i] :
( ( ! [SY3305: $i,SY3306: $i] :
( ~ ( relation @ SY3306 )
| ~ ( in @ ( ordered_pair @ SV31 @ SY3305 ) @ SY3306 )
| ( in @ SY3305 @ ( relation_rng @ SY3306 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[640]) ).
thf(697,plain,
! [SV57: $i] :
( ( ~ ( relation @ SV57 )
| ~ ( ~ ( in @ ( sK69_B @ SV57 ) @ ( relation_field @ SV57 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK69_B @ SV57 ) @ ( sK69_B @ SV57 ) ) @ SV57 ) )
| ( reflexive @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(698,plain,
! [SV58: $i] :
( ( ~ ( relation @ SV58 )
| ~ ( reflexive @ SV58 )
| ! [SY3391: $i] :
( ~ ( in @ SY3391 @ ( relation_field @ SV58 ) )
| ( in @ ( ordered_pair @ SY3391 @ SY3391 ) @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(699,plain,
! [SV32: $i,SV59: $i] :
( ( ( ~ ( relation @ SV59 )
| ~ ( ~ ! [SY3392: $i] :
( ~ ( function @ SY3392 )
| ~ ( relation @ SY3392 )
| ~ ( ~ ( ~ ( in @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3392 @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) ) @ ( apply @ SY3392 @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) @ SV32 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SY3392 @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) ) @ ( apply @ SY3392 @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) @ SV32 ) ) ) )
| ( ( relation_dom @ SY3392 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SY3392 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SY3392 )
| ( relation_isomorphism @ SV32 @ SV59 @ SY3392 ) )
| ~ ~ ( ~ ! [SY3393: $i] :
( ~ ( function @ SY3393 )
| ~ ( relation @ SY3393 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3393 )
| ~ ( ~ ! [SY3394: $i,SY3395: $i] :
( ~ ( in @ SY3394 @ ( relation_field @ SV32 ) )
| ~ ( in @ SY3395 @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3393 @ SY3394 ) @ ( apply @ SY3393 @ SY3395 ) ) @ SV59 )
| ( in @ ( ordered_pair @ SY3394 @ SY3395 ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3312: $i] :
( ! [SY3313: $i] :
~ ( in @ ( ordered_pair @ SY3312 @ SY3313 ) @ SV32 )
| ( in @ SY3312 @ ( relation_field @ SV32 ) ) )
| ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV32 )
| ( in @ SY3315 @ ( relation_field @ SV32 ) ) ) )
| ~ ! [SY3400: $i,SY3401: $i] :
( ~ ( in @ ( ordered_pair @ SY3400 @ SY3401 ) @ SV32 )
| ( in @ ( ordered_pair @ ( apply @ SY3393 @ SY3400 ) @ ( apply @ SY3393 @ SY3401 ) ) @ SV59 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3402: $i] :
( ~ ( function @ SY3402 )
| ~ ( relation @ SY3402 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3402 )
| ( ( relation_dom @ SY3402 )
= ( relation_field @ SV32 ) ) )
| ~ ! [SY3403: $i] :
( ~ ( function @ SY3403 )
| ~ ( relation @ SY3403 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3403 )
| ( ( relation_rng @ SY3403 )
= ( relation_field @ SV59 ) ) ) )
| ~ ! [SY3404: $i] :
( ~ ( function @ SY3404 )
| ~ ( relation @ SY3404 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3404 )
| ( one_to_one @ SY3404 ) ) ) ) ) )
= $true )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(700,plain,
! [SV33: $i] :
( ( ! [SY3321: $i,SY3322: $i] :
( ~ ( relation_of2_as_subset @ SY3322 @ SV33 @ SY3321 )
| ~ ( ~ ! [SY3323: $i] :
~ ( in @ ( ordered_pair @ SY3323 @ ( sK57_D @ SY3322 @ SY3321 @ SV33 ) ) @ SY3322 )
| ~ ( in @ ( sK57_D @ SY3322 @ SY3321 @ SV33 ) @ SY3321 ) )
| ( ( relation_rng_as_subset @ SV33 @ SY3321 @ SY3322 )
= SY3321 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[644]) ).
thf(701,plain,
! [SV33: $i] :
( ( ! [SY3324: $i,SY3325: $i] :
( ~ ( relation_of2_as_subset @ SY3325 @ SV33 @ SY3324 )
| ( ( relation_rng_as_subset @ SV33 @ SY3324 @ SY3325 )
!= SY3324 )
| ! [SY3326: $i] :
( ( in @ ( ordered_pair @ ( sK56_E @ SY3326 @ SY3325 @ SY3324 @ SV33 ) @ SY3326 ) @ SY3325 )
| ~ ( in @ SY3326 @ SY3324 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[645]) ).
thf(702,plain,
! [SV34: $i] :
( ( ( ~ ! [SY3327: $i] :
( ~ ( ~ ( ! [SY3328: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SY3327 @ SV34 ) @ SY3328 ) @ SV34 )
| ~ ( in @ ( sK22_C @ SY3327 @ SV34 ) @ SY3327 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SY3327 @ SV34 ) @ ( sK23_SY3101 @ SY3327 @ SV34 ) ) @ SV34 )
| ( in @ ( sK22_C @ SY3327 @ SV34 ) @ SY3327 ) ) )
| ( SY3327
= ( relation_dom @ SV34 ) ) )
| ~ ! [SY3329: $i] :
( ( SY3329
!= ( relation_dom @ SV34 ) )
| ~ ( ~ ! [SY3330: $i] :
( ! [SY3331: $i] :
~ ( in @ ( ordered_pair @ SY3330 @ SY3331 ) @ SV34 )
| ( in @ SY3330 @ SY3329 ) )
| ~ ! [SY3332: $i] :
( ~ ( in @ SY3332 @ SY3329 )
| ( in @ ( ordered_pair @ SY3332 @ ( sK21_D @ SY3332 @ SY3329 @ SV34 ) ) @ SV34 ) ) ) ) )
= $false )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[646]) ).
thf(703,plain,
! [SV44: $i] :
( ( ( ~ ( ~ ! [SY3365: $i,SY3366: $i] :
( ( sK39_B @ SV44 )
!= ( ordered_pair @ SY3365 @ SY3366 ) )
| ~ ( in @ ( sK39_B @ SV44 ) @ SV44 ) ) )
= $true )
| ( ( relation @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[648]) ).
thf(704,plain,
! [SV45: $i] :
( ( ( ~ ( relation @ SV45 ) )
= $true )
| ( ( ! [SY3367: $i] :
( ( SY3367
= ( ordered_pair @ ( sK37_C @ SY3367 @ SV45 ) @ ( sK38_SY3111 @ SY3367 @ SV45 ) ) )
| ~ ( in @ SY3367 @ SV45 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[649]) ).
thf(705,plain,
! [SV4: $i] :
( ( ( ~ ! [SY3132: $i] :
( ~ ( relation @ SY3132 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SY3132 @ SV4 ) @ ( sK32_SY3109 @ SY3132 @ SV4 ) ) @ SV4 )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ SY3132 @ SV4 ) @ ( sK32_SY3109 @ SY3132 @ SV4 ) ) @ SY3132 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK31_C @ SY3132 @ SV4 ) @ ( sK32_SY3109 @ SY3132 @ SV4 ) ) @ SV4 )
| ( in @ ( ordered_pair @ ( sK31_C @ SY3132 @ SV4 ) @ ( sK32_SY3109 @ SY3132 @ SV4 ) ) @ SY3132 ) ) )
| ( SV4 = SY3132 ) ) )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[650]) ).
thf(706,plain,
! [SV4: $i] :
( ( ( ~ ! [SY3133: $i] :
( ~ ( relation @ SY3133 )
| ( SV4 != SY3133 )
| ~ ( ~ ! [SY3134: $i,SY3135: $i] :
( ~ ( in @ ( ordered_pair @ SY3134 @ SY3135 ) @ SV4 )
| ( in @ ( ordered_pair @ SY3134 @ SY3135 ) @ SY3133 ) )
| ~ ! [SY3136: $i,SY3137: $i] :
( ~ ( in @ ( ordered_pair @ SY3136 @ SY3137 ) @ SY3133 )
| ( in @ ( ordered_pair @ SY3136 @ SY3137 ) @ SV4 ) ) ) ) )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[650]) ).
thf(707,plain,
! [SV5: $i] :
( ( ( ~ ! [SY3138: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SY3138 @ SV5 ) @ SY3138 )
| ~ ( in @ ( sK4_SY3086 @ SY3138 @ SV5 ) @ SY3138 ) )
| ~ ( in @ ( sK5_SY3088 @ SY3138 @ SV5 ) @ SY3138 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SY3138 @ SV5 ) @ ( sK4_SY3086 @ SY3138 @ SV5 ) ) @ SV5 ) )
| ~ ( in @ ( ordered_pair @ ( sK4_SY3086 @ SY3138 @ SV5 ) @ ( sK5_SY3088 @ SY3138 @ SV5 ) ) @ SV5 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK3_C @ SY3138 @ SV5 ) @ ( sK5_SY3088 @ SY3138 @ SV5 ) ) @ SV5 ) )
| ( is_transitive_in @ SV5 @ SY3138 ) ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[651]) ).
thf(708,plain,
! [SV5: $i] :
( ( ( ~ ! [SY3139: $i] :
( ~ ( is_transitive_in @ SV5 @ SY3139 )
| ! [SY3140: $i,SY3141: $i,SY3142: $i] :
( ~ ( in @ SY3140 @ SY3139 )
| ~ ( in @ SY3141 @ SY3139 )
| ~ ( in @ SY3142 @ SY3139 )
| ~ ( in @ ( ordered_pair @ SY3140 @ SY3141 ) @ SV5 )
| ~ ( in @ ( ordered_pair @ SY3141 @ SY3142 ) @ SV5 )
| ( in @ ( ordered_pair @ SY3140 @ SY3142 ) @ SV5 ) ) ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[651]) ).
thf(709,plain,
! [SV6: $i,SV60: $i] :
( ( ! [SY3405: $i] :
( ~ ( relation_of2_as_subset @ SY3405 @ SV60 @ SV6 )
| ~ ( ~ ! [SY3406: $i] :
~ ( in @ ( ordered_pair @ ( sK59_D @ SY3405 @ SV60 @ SV6 ) @ SY3406 ) @ SY3405 )
| ~ ( in @ ( sK59_D @ SY3405 @ SV60 @ SV6 ) @ SV60 ) )
| ( ( relation_dom_as_subset @ SV60 @ SV6 @ SY3405 )
= SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(710,plain,
! [SV6: $i,SV61: $i] :
( ( ! [SY3407: $i] :
( ~ ( relation_of2_as_subset @ SY3407 @ SV61 @ SV6 )
| ( ( relation_dom_as_subset @ SV61 @ SV6 @ SY3407 )
!= SV61 )
| ! [SY3408: $i] :
( ( in @ ( ordered_pair @ SY3408 @ ( sK58_E @ SY3408 @ SY3407 @ SV61 @ SV6 ) ) @ SY3407 )
| ~ ( in @ SY3408 @ SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(711,plain,
! [SV7: $i,SV46: $i] :
( ( ( ~ ( relation @ SV46 ) )
= $true )
| ( ( ~ ( ~ ! [SY3368: $i] :
( ~ ( relation @ SY3368 )
| ~ ( ~ ( ! [SY3369: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3368 @ SV46 @ SV7 ) @ SY3369 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3369 @ ( sK8_SY3089 @ SY3368 @ SV46 @ SV7 ) ) @ SV46 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3368 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SY3368 @ SV46 @ SV7 ) ) @ SY3368 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3368 @ SV46 @ SV7 ) @ ( sK9_SY3093 @ SY3368 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SY3368 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SY3368 @ SV46 @ SV7 ) ) @ SV46 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SY3368 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SY3368 @ SV46 @ SV7 ) ) @ SY3368 ) ) )
| ( SY3368
= ( relation_composition @ SV7 @ SV46 ) ) )
| ~ ! [SY3370: $i] :
( ~ ( relation @ SY3370 )
| ( SY3370
!= ( relation_composition @ SV7 @ SV46 ) )
| ~ ( ~ ! [SY3371: $i,SY3372: $i] :
( ! [SY3373: $i] :
( ~ ( in @ ( ordered_pair @ SY3371 @ SY3373 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3373 @ SY3372 ) @ SV46 ) )
| ( in @ ( ordered_pair @ SY3371 @ SY3372 ) @ SY3370 ) )
| ~ ! [SY3374: $i,SY3375: $i] :
( ~ ( in @ ( ordered_pair @ SY3374 @ SY3375 ) @ SY3370 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3374 @ ( sK6_F @ SY3375 @ SY3374 @ SY3370 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY3375 @ SY3374 @ SY3370 @ SV46 @ SV7 ) @ SY3375 ) @ SV46 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[654]) ).
thf(712,plain,
! [SV47: $i,SV62: $i] :
( ( ~ ( relation @ SV62 )
| ~ ( ~ ( ( ( sK52_C @ SV62 @ SV47 )
!= ( sK53_SY3121 @ SV62 @ SV47 ) )
| ~ ( in @ ( sK52_C @ SV62 @ SV47 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) )
| ~ ~ ( ~ ( ( ( sK52_C @ SV62 @ SV47 )
= ( sK53_SY3121 @ SV62 @ SV47 ) )
| ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) )
| ~ ( ( in @ ( sK52_C @ SV62 @ SV47 ) @ SV47 )
| ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) ) ) )
| ( SV62
= ( identity_relation @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(713,plain,
! [SV48: $i,SV63: $i] :
( ( ~ ( relation @ SV63 )
| ( SV63
!= ( identity_relation @ SV48 ) )
| ~ ( ~ ! [SY3409: $i,SY3410: $i] :
( ( SY3409 != SY3410 )
| ~ ( in @ SY3409 @ SV48 )
| ( in @ ( ordered_pair @ SY3409 @ SY3410 ) @ SV63 ) )
| ~ ~ ( ~ ! [SY3411: $i,SY3412: $i] :
( ~ ( in @ ( ordered_pair @ SY3411 @ SY3412 ) @ SV63 )
| ( SY3411 = SY3412 ) )
| ~ ! [SY3413: $i] :
( ! [SY3414: $i] :
~ ( in @ ( ordered_pair @ SY3413 @ SY3414 ) @ SV63 )
| ( in @ SY3413 @ SV48 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(714,plain,
! [SV49: $i,SV42: $i,SV8: $i] :
( ( ( SV8
= ( ordered_pair @ SV42 @ SV49 ) )
= $false )
| ( ( ~ ( ~ ! [SY3160: $i] :
( ~ ( ( SV8
!= ( ordered_pair @ ( sK40_C @ SY3160 @ SV8 ) @ ( sK41_SY3114 @ SY3160 @ SV8 ) ) )
| ~ ( ( SY3160
!= ( sK40_C @ SY3160 @ SV8 ) ) ) )
| ( SY3160
= ( pair_first @ SV8 ) ) )
| ~ ! [SY3161: $i] :
( ( SY3161
!= ( pair_first @ SV8 ) )
| ! [SY3162: $i] :
( ! [SY3163: $i] :
( SV8
!= ( ordered_pair @ SY3162 @ SY3163 ) )
| ( SY3161 = SY3162 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[657]) ).
thf(715,plain,
! [SV37: $i,SV9: $i] :
( ( ! [SY3333: $i,SY3334: $i] :
( ~ ( relation @ SY3334 )
| ~ ( in @ SV9 @ SY3333 )
| ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ SY3334 )
| ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SY3333 ) @ SY3334 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[658]) ).
thf(716,plain,
! [SV37: $i,SV9: $i] :
( ( ~ ( ~ ! [SY3335: $i,SY3336: $i] :
( ~ ( relation @ SY3336 )
| ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SY3335 ) @ SY3336 ) )
| ( in @ SV9 @ SY3335 ) )
| ~ ! [SY3337: $i,SY3338: $i] :
( ~ ( relation @ SY3338 )
| ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SY3337 ) @ SY3338 ) )
| ( in @ ( ordered_pair @ SV9 @ SV37 ) @ SY3338 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[659]) ).
thf(717,plain,
! [SV64: $i,SV10: $i] :
( ( ! [SY3415: $i] :
( ~ ( relation @ SY3415 )
| ! [SY3416: $i] :
( ~ ( in @ SY3416 @ ( relation_rng @ SY3415 ) )
| ~ ( in @ ( ordered_pair @ SV10 @ SY3416 ) @ SY3415 )
| ~ ( in @ SY3416 @ SV64 ) )
| ( in @ SV10 @ ( relation_inverse_image @ SY3415 @ SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(718,plain,
! [SV65: $i,SV10: $i] :
( ( ! [SY3417: $i] :
( ~ ( relation @ SY3417 )
| ~ ( in @ SV10 @ ( relation_inverse_image @ SY3417 @ SV65 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_D @ SY3417 @ SV65 @ SV10 ) @ ( relation_rng @ SY3417 ) )
| ~ ( in @ ( ordered_pair @ SV10 @ ( sK60_D @ SY3417 @ SV65 @ SV10 ) ) @ SY3417 ) )
| ~ ( in @ ( sK60_D @ SY3417 @ SV65 @ SV10 ) @ SV65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(719,plain,
! [SV66: $i,SV11: $i] :
( ( ! [SY3418: $i] :
( ~ ( ~ ( ! [SY3419: $i,SY3420: $i] :
( ~ ( in @ SY3419 @ SV11 )
| ~ ( in @ SY3420 @ SV66 )
| ( ( sK28_D @ SY3418 @ SV66 @ SV11 )
!= ( ordered_pair @ SY3419 @ SY3420 ) ) )
| ~ ( in @ ( sK28_D @ SY3418 @ SV66 @ SV11 ) @ SY3418 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY3106 @ SY3418 @ SV66 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK30_SY3108 @ SY3418 @ SV66 @ SV11 ) @ SV66 ) )
| ( ( sK28_D @ SY3418 @ SV66 @ SV11 )
!= ( ordered_pair @ ( sK29_SY3106 @ SY3418 @ SV66 @ SV11 ) @ ( sK30_SY3108 @ SY3418 @ SV66 @ SV11 ) ) ) )
| ( in @ ( sK28_D @ SY3418 @ SV66 @ SV11 ) @ SY3418 ) ) )
| ( SY3418
= ( cartesian_product2 @ SV11 @ SV66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(720,plain,
! [SV67: $i,SV11: $i] :
( ( ! [SY3421: $i] :
( ( SY3421
!= ( cartesian_product2 @ SV11 @ SV67 ) )
| ~ ( ~ ! [SY3422: $i] :
( ! [SY3423: $i,SY3424: $i] :
( ~ ( in @ SY3423 @ SV11 )
| ~ ( in @ SY3424 @ SV67 )
| ( SY3422
!= ( ordered_pair @ SY3423 @ SY3424 ) ) )
| ( in @ SY3422 @ SY3421 ) )
| ~ ! [SY3425: $i] :
( ~ ( in @ SY3425 @ SY3421 )
| ~ ( ~ ~ ( ~ ( in @ ( sK26_E @ SY3425 @ SY3421 @ SV67 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK27_SY3103 @ SY3425 @ SY3421 @ SV67 @ SV11 ) @ SV67 ) )
| ( SY3425
!= ( ordered_pair @ ( sK26_E @ SY3425 @ SY3421 @ SV67 @ SV11 ) @ ( sK27_SY3103 @ SY3425 @ SY3421 @ SV67 @ SV11 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(721,plain,
! [SV68: $i,SV12: $i] :
( ( ! [SY3426: $i] :
( ~ ( relation @ SY3426 )
| ~ ( in @ ( ordered_pair @ SV12 @ SV68 ) @ SY3426 )
| ( in @ SV12 @ ( relation_field @ SY3426 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(722,plain,
! [SV69: $i,SV12: $i] :
( ( ! [SY3427: $i] :
( ~ ( relation @ SY3427 )
| ~ ( in @ ( ordered_pair @ SV12 @ SV69 ) @ SY3427 )
| ( in @ SV69 @ ( relation_field @ SY3427 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(723,plain,
! [SV50: $i,SV43: $i,SV13: $i] :
( ( ( SV13
= ( ordered_pair @ SV43 @ SV50 ) )
= $false )
| ( ( ~ ( ~ ! [SY3192: $i] :
( ~ ( ( SV13
!= ( ordered_pair @ ( sK33_C @ SY3192 @ SV13 ) @ ( sK34_SY3110 @ SY3192 @ SV13 ) ) )
| ~ ( ( SY3192
!= ( sK34_SY3110 @ SY3192 @ SV13 ) ) ) )
| ( SY3192
= ( pair_second @ SV13 ) ) )
| ~ ! [SY3193: $i] :
( ( SY3193
!= ( pair_second @ SV13 ) )
| ! [SY3194: $i,SY3195: $i] :
( ( SV13
!= ( ordered_pair @ SY3194 @ SY3195 ) )
| ( SY3193 = SY3195 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[666]) ).
thf(724,plain,
! [SV14: $i] :
( ( ( ~ ! [SY3196: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK14_C @ SY3196 @ SV14 )
!= ( sK15_SY3096 @ SY3196 @ SV14 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SY3196 @ SV14 ) @ SY3196 )
| ~ ( in @ ( sK15_SY3096 @ SY3196 @ SV14 ) @ SY3196 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK14_C @ SY3196 @ SV14 ) @ ( sK15_SY3096 @ SY3196 @ SV14 ) ) @ SV14 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK15_SY3096 @ SY3196 @ SV14 ) @ ( sK14_C @ SY3196 @ SV14 ) ) @ SV14 ) )
| ( is_connected_in @ SV14 @ SY3196 ) ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[667]) ).
thf(725,plain,
! [SV14: $i] :
( ( ( ~ ! [SY3197: $i] :
( ~ ( is_connected_in @ SV14 @ SY3197 )
| ! [SY3198: $i,SY3199: $i] :
( ( SY3198 = SY3199 )
| ~ ( in @ SY3198 @ SY3197 )
| ~ ( in @ SY3199 @ SY3197 )
| ( in @ ( ordered_pair @ SY3198 @ SY3199 ) @ SV14 )
| ( in @ ( ordered_pair @ SY3199 @ SY3198 ) @ SV14 ) ) ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[667]) ).
thf(726,plain,
! [SV70: $i,SV15: $i] :
( ( ! [SY3428: $i] :
( ~ ( relation @ SY3428 )
| ! [SY3429: $i] :
( ~ ( in @ SY3429 @ ( relation_dom @ SY3428 ) )
| ~ ( in @ ( ordered_pair @ SY3429 @ SV15 ) @ SY3428 )
| ~ ( in @ SY3429 @ SV70 ) )
| ( in @ SV15 @ ( relation_image @ SY3428 @ SV70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(727,plain,
! [SV71: $i,SV15: $i] :
( ( ! [SY3430: $i] :
( ~ ( relation @ SY3430 )
| ~ ( in @ SV15 @ ( relation_image @ SY3430 @ SV71 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK61_D @ SY3430 @ SV71 @ SV15 ) @ ( relation_dom @ SY3430 ) )
| ~ ( in @ ( ordered_pair @ ( sK61_D @ SY3430 @ SV71 @ SV15 ) @ SV15 ) @ SY3430 ) )
| ~ ( in @ ( sK61_D @ SY3430 @ SV71 @ SV15 ) @ SV71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(728,plain,
! [SV16: $i] :
( ( ( ~ ! [SY3205: $i,SY3206: $i] :
( ~ ( ~ ( ! [SY3207: $i] :
( ~ ( in @ ( ordered_pair @ SY3207 @ ( sK46_D @ SY3206 @ SY3205 @ SV16 ) ) @ SV16 )
| ~ ( in @ SY3207 @ SY3205 ) )
| ~ ( in @ ( sK46_D @ SY3206 @ SY3205 @ SV16 ) @ SY3206 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SY3206 @ SY3205 @ SV16 ) @ ( sK46_D @ SY3206 @ SY3205 @ SV16 ) ) @ SV16 )
| ~ ( in @ ( sK47_SY3118 @ SY3206 @ SY3205 @ SV16 ) @ SY3205 ) )
| ( in @ ( sK46_D @ SY3206 @ SY3205 @ SV16 ) @ SY3206 ) ) )
| ( SY3206
= ( relation_image @ SV16 @ SY3205 ) ) ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[670]) ).
thf(729,plain,
! [SV16: $i] :
( ( ( ~ ! [SY3208: $i,SY3209: $i] :
( ( SY3209
!= ( relation_image @ SV16 @ SY3208 ) )
| ~ ( ~ ! [SY3210: $i] :
( ! [SY3211: $i] :
( ~ ( in @ ( ordered_pair @ SY3211 @ SY3210 ) @ SV16 )
| ~ ( in @ SY3211 @ SY3208 ) )
| ( in @ SY3210 @ SY3209 ) )
| ~ ! [SY3212: $i] :
( ~ ( in @ SY3212 @ SY3209 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SY3212 @ SY3209 @ SY3208 @ SV16 ) @ SY3212 ) @ SV16 )
| ~ ( in @ ( sK45_E @ SY3212 @ SY3209 @ SY3208 @ SV16 ) @ SY3208 ) ) ) ) ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[670]) ).
thf(730,plain,
! [SV51: $i] :
( ( ( ~ ( relation @ SV51 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK64_B @ SV51 ) @ ( sK65_SY3126 @ SV51 ) ) @ SV51 )
| ~ ( in @ ( ordered_pair @ ( sK65_SY3126 @ SV51 ) @ ( sK64_B @ SV51 ) ) @ SV51 ) )
| ~ ( ( ( sK64_B @ SV51 )
!= ( sK65_SY3126 @ SV51 ) ) ) )
| ( antisymmetric @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[671]) ).
thf(731,plain,
! [SV52: $i] :
( ( ( ~ ( relation @ SV52 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV52 )
| ! [SY3384: $i,SY3385: $i] :
( ~ ( in @ ( ordered_pair @ SY3384 @ SY3385 ) @ SV52 )
| ~ ( in @ ( ordered_pair @ SY3385 @ SY3384 ) @ SV52 )
| ( SY3384 = SY3385 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[672]) ).
thf(732,plain,
! [SV17: $i,SV72: $i] :
( ( ! [SY3431: $i] :
( ~ ( function @ SY3431 )
| ~ ( relation @ SY3431 )
| ( SV72
!= ( apply @ SY3431 @ SV17 ) )
| ~ ( in @ SV17 @ ( relation_dom @ SY3431 ) )
| ( in @ ( ordered_pair @ SV17 @ SV72 ) @ SY3431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(733,plain,
! [SV17: $i] :
( ( ~ ! [SY3215: $i,SY3216: $i] :
( ~ ( function @ SY3216 )
| ~ ( relation @ SY3216 )
| ~ ( in @ ( ordered_pair @ SV17 @ SY3215 ) @ SY3216 )
| ( SY3215
= ( apply @ SY3216 @ SV17 ) ) )
| ~ ! [SY3217: $i,SY3218: $i] :
( ~ ( function @ SY3218 )
| ~ ( relation @ SY3218 )
| ~ ( in @ ( ordered_pair @ SV17 @ SY3217 ) @ SY3218 )
| ( in @ SV17 @ ( relation_dom @ SY3218 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[674]) ).
thf(734,plain,
! [SV18: $i] :
( ( ( ~ ! [SY3219: $i,SY3220: $i] :
( ~ ( ~ ( ( ( sK35_D @ SY3220 @ SY3219 @ SV18 )
= SY3219 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SY3220 @ SY3219 @ SV18 ) @ SY3219 ) @ SV18 )
| ~ ( in @ ( sK35_D @ SY3220 @ SY3219 @ SV18 ) @ SY3220 ) )
| ~ ~ ( ~ ( ( ( sK35_D @ SY3220 @ SY3219 @ SV18 )
!= SY3219 )
| ( in @ ( sK35_D @ SY3220 @ SY3219 @ SV18 ) @ SY3220 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SY3220 @ SY3219 @ SV18 ) @ SY3219 ) @ SV18 )
| ( in @ ( sK35_D @ SY3220 @ SY3219 @ SV18 ) @ SY3220 ) ) ) )
| ( SY3220
= ( fiber @ SV18 @ SY3219 ) ) ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[675]) ).
thf(735,plain,
! [SV18: $i] :
( ( ( ~ ! [SY3221: $i,SY3222: $i] :
( ( SY3222
!= ( fiber @ SV18 @ SY3221 ) )
| ~ ( ~ ! [SY3223: $i] :
( ( SY3223 = SY3221 )
| ~ ( in @ ( ordered_pair @ SY3223 @ SY3221 ) @ SV18 )
| ( in @ SY3223 @ SY3222 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY3222 )
| ( SX3 != SY3221 ) )
| ~ ! [SY3225: $i] :
( ~ ( in @ SY3225 @ SY3222 )
| ( in @ ( ordered_pair @ SY3225 @ SY3221 ) @ SV18 ) ) ) ) ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[675]) ).
thf(736,plain,
! [SV19: $i] :
( ( ( ~ ! [SY3226: $i] :
( ~ ( ~ ( in @ ( sK36_C @ SY3226 @ SV19 ) @ SY3226 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SY3226 @ SV19 ) @ ( sK36_C @ SY3226 @ SV19 ) ) @ SV19 ) )
| ( is_reflexive_in @ SV19 @ SY3226 ) ) )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[676]) ).
thf(737,plain,
! [SV19: $i] :
( ( ( ~ ! [SY3227: $i] :
( ~ ( is_reflexive_in @ SV19 @ SY3227 )
| ! [SY3228: $i] :
( ~ ( in @ SY3228 @ SY3227 )
| ( in @ ( ordered_pair @ SY3228 @ SY3228 ) @ SV19 ) ) ) )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[676]) ).
thf(738,plain,
! [SV20: $i] :
( ( ( ~ ! [SY3229: $i] :
( ~ ( relation @ SY3229 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SY3229 @ SV20 ) @ ( sK13_SY3095 @ SY3229 @ SV20 ) ) @ SY3229 )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SY3229 @ SV20 ) @ ( sK12_C @ SY3229 @ SV20 ) ) @ SV20 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SY3229 @ SV20 ) @ ( sK13_SY3095 @ SY3229 @ SV20 ) ) @ SY3229 )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ SY3229 @ SV20 ) @ ( sK12_C @ SY3229 @ SV20 ) ) @ SV20 ) ) )
| ( SY3229
= ( relation_inverse @ SV20 ) ) ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[677]) ).
thf(739,plain,
! [SV20: $i] :
( ( ( ~ ! [SY3230: $i] :
( ~ ( relation @ SY3230 )
| ( SY3230
!= ( relation_inverse @ SV20 ) )
| ~ ( ~ ! [SY3231: $i,SY3232: $i] :
( ~ ( in @ ( ordered_pair @ SY3231 @ SY3232 ) @ SY3230 )
| ( in @ ( ordered_pair @ SY3232 @ SY3231 ) @ SV20 ) )
| ~ ! [SY3233: $i,SY3234: $i] :
( ~ ( in @ ( ordered_pair @ SY3234 @ SY3233 ) @ SV20 )
| ( in @ ( ordered_pair @ SY3233 @ SY3234 ) @ SY3230 ) ) ) ) )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[677]) ).
thf(740,plain,
! [SV21: $i,SV38: $i] :
( ( ( ~ ! [SY3339: $i] :
( ~ ( relation @ SY3339 )
| ~ ( ~ ( ~ ( in @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) @ SV21 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SY3339 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) ) @ SV38 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SY3339 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) ) @ SY3339 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK48_D @ SY3339 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) ) @ SY3339 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SY3339 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) ) @ SV38 )
| ( in @ ( ordered_pair @ ( sK48_D @ SY3339 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) ) @ SY3339 ) ) ) )
| ( SY3339
= ( relation_rng_restriction @ SV21 @ SV38 ) ) )
| ~ ! [SY3340: $i] :
( ~ ( relation @ SY3340 )
| ( SY3340
!= ( relation_rng_restriction @ SV21 @ SV38 ) )
| ~ ( ~ ! [SY3341: $i,SY3342: $i] :
( ~ ( in @ SY3342 @ SV21 )
| ~ ( in @ ( ordered_pair @ SY3341 @ SY3342 ) @ SV38 )
| ( in @ ( ordered_pair @ SY3341 @ SY3342 ) @ SY3340 ) )
| ~ ~ ( ~ ! [SY3240: $i,SY3241: $i] :
( ~ ( in @ ( ordered_pair @ SY3240 @ SY3241 ) @ SY3340 )
| ( in @ SY3241 @ SV21 ) )
| ~ ! [SY3345: $i,SY3346: $i] :
( ~ ( in @ ( ordered_pair @ SY3345 @ SY3346 ) @ SY3340 )
| ( in @ ( ordered_pair @ SY3345 @ SY3346 ) @ SV38 ) ) ) ) ) )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[678]) ).
thf(741,plain,
! [SV22: $i] :
( ( ( ~ ! [SY3244: $i] :
( ~ ( ~ ( ! [SY3245: $i] :
~ ( in @ ( ordered_pair @ SY3245 @ ( sK17_C @ SY3244 @ SV22 ) ) @ SV22 )
| ~ ( in @ ( sK17_C @ SY3244 @ SV22 ) @ SY3244 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK18_SY3098 @ SY3244 @ SV22 ) @ ( sK17_C @ SY3244 @ SV22 ) ) @ SV22 )
| ( in @ ( sK17_C @ SY3244 @ SV22 ) @ SY3244 ) ) )
| ( SY3244
= ( relation_rng @ SV22 ) ) ) )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[679]) ).
thf(742,plain,
! [SV22: $i] :
( ( ( ~ ! [SY3246: $i] :
( ( SY3246
!= ( relation_rng @ SV22 ) )
| ~ ( ~ ! [SY3247: $i] :
( ! [SY3248: $i] :
~ ( in @ ( ordered_pair @ SY3248 @ SY3247 ) @ SV22 )
| ( in @ SY3247 @ SY3246 ) )
| ~ ! [SY3249: $i] :
( ~ ( in @ SY3249 @ SY3246 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3249 @ SY3246 @ SV22 ) @ SY3249 ) @ SV22 ) ) ) ) )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[679]) ).
thf(743,plain,
! [SV23: $i] :
( ( ( ~ ! [SY3250: $i] :
( ~ ( relation @ SY3250 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3250 @ SV23 ) @ ( sK25_SY3102 @ SY3250 @ SV23 ) ) @ SV23 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3250 @ SV23 ) @ ( sK25_SY3102 @ SY3250 @ SV23 ) ) @ SY3250 ) )
| ( subset @ SV23 @ SY3250 ) ) )
= $false )
| ( ( relation @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[680]) ).
thf(744,plain,
! [SV23: $i] :
( ( ( ~ ! [SY3251: $i] :
( ~ ( relation @ SY3251 )
| ~ ( subset @ SV23 @ SY3251 )
| ! [SY3252: $i,SY3253: $i] :
( ~ ( in @ ( ordered_pair @ SY3252 @ SY3253 ) @ SV23 )
| ( in @ ( ordered_pair @ SY3252 @ SY3253 ) @ SY3251 ) ) ) )
= $false )
| ( ( relation @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[680]) ).
thf(745,plain,
! [SV24: $i] :
( ( ( ~ ! [SY3254: $i,SY3255: $i] :
( ~ ( relation @ SY3255 )
| ~ ( ~ ( ~ ( in @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ SY3254 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ ( sK51_SY3120 @ SY3255 @ SY3254 @ SV24 ) ) @ SV24 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ ( sK51_SY3120 @ SY3255 @ SY3254 @ SV24 ) ) @ SY3255 ) )
| ~ ~ ( ~ ( ( in @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ SY3254 )
| ( in @ ( ordered_pair @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ ( sK51_SY3120 @ SY3255 @ SY3254 @ SV24 ) ) @ SY3255 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ ( sK51_SY3120 @ SY3255 @ SY3254 @ SV24 ) ) @ SV24 )
| ( in @ ( ordered_pair @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ ( sK51_SY3120 @ SY3255 @ SY3254 @ SV24 ) ) @ SY3255 ) ) ) )
| ( SY3255
= ( relation_dom_restriction @ SV24 @ SY3254 ) ) ) )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[681]) ).
thf(746,plain,
! [SV24: $i] :
( ( ( ~ ! [SY3256: $i,SY3257: $i] :
( ~ ( relation @ SY3257 )
| ( SY3257
!= ( relation_dom_restriction @ SV24 @ SY3256 ) )
| ~ ( ~ ! [SY3258: $i,SY3259: $i] :
( ~ ( in @ SY3258 @ SY3256 )
| ~ ( in @ ( ordered_pair @ SY3258 @ SY3259 ) @ SV24 )
| ( in @ ( ordered_pair @ SY3258 @ SY3259 ) @ SY3257 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3257 )
| ( in @ SX3 @ SY3256 ) )
| ~ ! [SY3262: $i,SY3263: $i] :
( ~ ( in @ ( ordered_pair @ SY3262 @ SY3263 ) @ SY3257 )
| ( in @ ( ordered_pair @ SY3262 @ SY3263 ) @ SV24 ) ) ) ) ) )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[681]) ).
thf(747,plain,
! [SV39: $i,SV25: $i] :
( ( ! [SY3347: $i] :
( ! [SY3348: $i] :
( ( ordered_pair @ SV25 @ SV39 )
!= ( ordered_pair @ SY3347 @ SY3348 ) )
| ( SV25 = SY3347 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[682]) ).
thf(748,plain,
! [SV39: $i,SV25: $i] :
( ( ! [SY3349: $i,SY3350: $i] :
( ( ( ordered_pair @ SV25 @ SV39 )
!= ( ordered_pair @ SY3349 @ SY3350 ) )
| ( SV39 = SY3350 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[683]) ).
thf(749,plain,
! [SV26: $i] :
( ( ( relation @ SV26 )
= $false )
| ( ( function @ SV26 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY3269: $i] :
( ~ ( in @ SY3269 @ ( relation_dom @ SV26 ) )
| ! [SY3270: $i] :
( ( SY3270
!= ( apply @ SV26 @ SY3269 ) )
| ( in @ ( ordered_pair @ SY3269 @ SY3270 ) @ SV26 ) ) )
| ~ ! [SY3271: $i] :
( ~ ( in @ SY3271 @ ( relation_dom @ SV26 ) )
| ! [SY3272: $i] :
( ~ ( in @ ( ordered_pair @ SY3271 @ SY3272 ) @ SV26 )
| ( SY3272
= ( apply @ SV26 @ SY3271 ) ) ) ) )
| ~ ~ ( ~ ! [SY3273: $i] :
( ( in @ SY3273 @ ( relation_dom @ SV26 ) )
| ! [SY3274: $i] :
( ( SY3274
!= ( apply @ SV26 @ SY3273 ) )
| ( SY3274 = empty_set ) ) )
| ~ ! [SY3275: $i] :
( ( in @ SY3275 @ ( relation_dom @ SV26 ) )
| ! [SY3276: $i] :
( ( SY3276 != empty_set )
| ( SY3276
= ( apply @ SV26 @ SY3275 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(750,plain,
! [SV53: $i] :
( ( ( ~ ( relation @ SV53 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK62_B @ SV53 )
!= ( sK63_SY3125 @ SV53 ) ) )
| ~ ~ ( ~ ( in @ ( sK62_B @ SV53 ) @ ( relation_field @ SV53 ) )
| ~ ( in @ ( sK63_SY3125 @ SV53 ) @ ( relation_field @ SV53 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK62_B @ SV53 ) @ ( sK63_SY3125 @ SV53 ) ) @ SV53 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK63_SY3125 @ SV53 ) @ ( sK62_B @ SV53 ) ) @ SV53 ) )
| ( connected @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[685]) ).
thf(751,plain,
! [SV54: $i] :
( ( ( ~ ( relation @ SV54 ) )
= $true )
| ( ( ~ ( connected @ SV54 )
| ! [SY3386: $i,SY3387: $i] :
( ( SY3386 = SY3387 )
| ~ ( in @ SY3386 @ ( relation_field @ SV54 ) )
| ~ ( in @ SY3387 @ ( relation_field @ SV54 ) )
| ( in @ ( ordered_pair @ SY3386 @ SY3387 ) @ SV54 )
| ( in @ ( ordered_pair @ SY3387 @ SY3386 ) @ SV54 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[686]) ).
thf(752,plain,
! [SV27: $i] :
( ( ( ~ ! [SY3277: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_C @ SY3277 @ SV27 ) @ SY3277 )
| ~ ( in @ ( sK20_SY3099 @ SY3277 @ SV27 ) @ SY3277 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SY3277 @ SV27 ) @ ( sK20_SY3099 @ SY3277 @ SV27 ) ) @ SV27 ) )
| ~ ( in @ ( ordered_pair @ ( sK20_SY3099 @ SY3277 @ SV27 ) @ ( sK19_C @ SY3277 @ SV27 ) ) @ SV27 ) )
| ~ ( ( ( sK19_C @ SY3277 @ SV27 )
!= ( sK20_SY3099 @ SY3277 @ SV27 ) ) ) )
| ( is_antisymmetric_in @ SV27 @ SY3277 ) ) )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[687]) ).
thf(753,plain,
! [SV27: $i] :
( ( ( ~ ! [SY3278: $i] :
( ~ ( is_antisymmetric_in @ SV27 @ SY3278 )
| ! [SY3279: $i,SY3280: $i] :
( ~ ( in @ SY3279 @ SY3278 )
| ~ ( in @ SY3280 @ SY3278 )
| ~ ( in @ ( ordered_pair @ SY3279 @ SY3280 ) @ SV27 )
| ~ ( in @ ( ordered_pair @ SY3280 @ SY3279 ) @ SV27 )
| ( SY3279 = SY3280 ) ) ) )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[687]) ).
thf(754,plain,
! [SV40: $i,SV28: $i] :
( ( ! [SY3351: $i,SY3352: $i] :
( ~ ( in @ SV28 @ SY3351 )
| ~ ( in @ SV40 @ SY3352 )
| ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SY3351 @ SY3352 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[688]) ).
thf(755,plain,
! [SV40: $i,SV28: $i] :
( ( ~ ( ~ ! [SY3353: $i] :
( ! [SY3354: $i] :
~ ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SY3353 @ SY3354 ) )
| ( in @ SV28 @ SY3353 ) )
| ~ ! [SY3355: $i,SY3356: $i] :
( ~ ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SY3355 @ SY3356 ) )
| ( in @ SV40 @ SY3356 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[689]) ).
thf(756,plain,
! [SV55: $i] :
( ( ( ~ ( relation @ SV55 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK66_B @ SV55 ) @ ( sK67_SY3127 @ SV55 ) ) @ SV55 )
| ~ ( in @ ( ordered_pair @ ( sK67_SY3127 @ SV55 ) @ ( sK68_SY3129 @ SV55 ) ) @ SV55 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK66_B @ SV55 ) @ ( sK68_SY3129 @ SV55 ) ) @ SV55 ) )
| ( transitive @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[690]) ).
thf(757,plain,
! [SV56: $i] :
( ( ( ~ ( relation @ SV56 ) )
= $true )
| ( ( ~ ( transitive @ SV56 )
| ! [SY3388: $i,SY3389: $i,SY3390: $i] :
( ~ ( in @ ( ordered_pair @ SY3388 @ SY3389 ) @ SV56 )
| ~ ( in @ ( ordered_pair @ SY3389 @ SY3390 ) @ SV56 )
| ( in @ ( ordered_pair @ SY3388 @ SY3390 ) @ SV56 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[691]) ).
thf(758,plain,
! [SV41: $i,SV29: $i] :
( ( ! [SY3357: $i,SY3358: $i] :
( ~ ( in @ SV29 @ SY3357 )
| ~ ( in @ SV41 @ SY3358 )
| ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SY3357 @ SY3358 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[692]) ).
thf(759,plain,
! [SV41: $i,SV29: $i] :
( ( ~ ( ~ ! [SY3359: $i] :
( ! [SY3360: $i] :
~ ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SY3359 @ SY3360 ) )
| ( in @ SV29 @ SY3359 ) )
| ~ ! [SY3361: $i,SY3362: $i] :
( ~ ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SY3361 @ SY3362 ) )
| ( in @ SV41 @ SY3362 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[693]) ).
thf(760,plain,
! [SV30: $i] :
( ( ( ~ ! [SY3295: $i,SY3296: $i] :
( ~ ( ~ ( ! [SY3297: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ SY3296 @ SY3295 @ SV30 ) @ SY3297 ) @ SV30 )
| ~ ( in @ SY3297 @ SY3295 ) )
| ~ ( in @ ( sK43_D @ SY3296 @ SY3295 @ SV30 ) @ SY3296 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SY3296 @ SY3295 @ SV30 ) @ ( sK44_SY3116 @ SY3296 @ SY3295 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK44_SY3116 @ SY3296 @ SY3295 @ SV30 ) @ SY3295 ) )
| ( in @ ( sK43_D @ SY3296 @ SY3295 @ SV30 ) @ SY3296 ) ) )
| ( SY3296
= ( relation_inverse_image @ SV30 @ SY3295 ) ) ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[694]) ).
thf(761,plain,
! [SV30: $i] :
( ( ( ~ ! [SY3298: $i,SY3299: $i] :
( ( SY3299
!= ( relation_inverse_image @ SV30 @ SY3298 ) )
| ~ ( ~ ! [SY3300: $i] :
( ! [SY3301: $i] :
( ~ ( in @ ( ordered_pair @ SY3300 @ SY3301 ) @ SV30 )
| ~ ( in @ SY3301 @ SY3298 ) )
| ( in @ SY3300 @ SY3299 ) )
| ~ ! [SY3302: $i] :
( ~ ( in @ SY3302 @ SY3299 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3302 @ ( sK42_E @ SY3302 @ SY3299 @ SY3298 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK42_E @ SY3302 @ SY3299 @ SY3298 @ SV30 ) @ SY3298 ) ) ) ) ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[694]) ).
thf(762,plain,
! [SV73: $i,SV31: $i] :
( ( ! [SY3432: $i] :
( ~ ( relation @ SY3432 )
| ~ ( in @ ( ordered_pair @ SV31 @ SV73 ) @ SY3432 )
| ( in @ SV31 @ ( relation_dom @ SY3432 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(763,plain,
! [SV74: $i,SV31: $i] :
( ( ! [SY3433: $i] :
( ~ ( relation @ SY3433 )
| ~ ( in @ ( ordered_pair @ SV31 @ SV74 ) @ SY3433 )
| ( in @ SV74 @ ( relation_rng @ SY3433 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(764,plain,
! [SV57: $i] :
( ( ( ~ ( relation @ SV57 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK69_B @ SV57 ) @ ( relation_field @ SV57 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK69_B @ SV57 ) @ ( sK69_B @ SV57 ) ) @ SV57 ) )
| ( reflexive @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[697]) ).
thf(765,plain,
! [SV58: $i] :
( ( ( ~ ( relation @ SV58 ) )
= $true )
| ( ( ~ ( reflexive @ SV58 )
| ! [SY3391: $i] :
( ~ ( in @ SY3391 @ ( relation_field @ SV58 ) )
| ( in @ ( ordered_pair @ SY3391 @ SY3391 ) @ SV58 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[698]) ).
thf(766,plain,
! [SV32: $i,SV59: $i] :
( ( ( ~ ( relation @ SV59 ) )
= $true )
| ( ( ~ ( ~ ! [SY3392: $i] :
( ~ ( function @ SY3392 )
| ~ ( relation @ SY3392 )
| ~ ( ~ ( ~ ( in @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3392 @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) ) @ ( apply @ SY3392 @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) @ SV32 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SY3392 @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) ) @ ( apply @ SY3392 @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) @ SV32 ) ) ) )
| ( ( relation_dom @ SY3392 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SY3392 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SY3392 )
| ( relation_isomorphism @ SV32 @ SV59 @ SY3392 ) )
| ~ ~ ( ~ ! [SY3393: $i] :
( ~ ( function @ SY3393 )
| ~ ( relation @ SY3393 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3393 )
| ~ ( ~ ! [SY3394: $i,SY3395: $i] :
( ~ ( in @ SY3394 @ ( relation_field @ SV32 ) )
| ~ ( in @ SY3395 @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3393 @ SY3394 ) @ ( apply @ SY3393 @ SY3395 ) ) @ SV59 )
| ( in @ ( ordered_pair @ SY3394 @ SY3395 ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3312: $i] :
( ! [SY3313: $i] :
~ ( in @ ( ordered_pair @ SY3312 @ SY3313 ) @ SV32 )
| ( in @ SY3312 @ ( relation_field @ SV32 ) ) )
| ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV32 )
| ( in @ SY3315 @ ( relation_field @ SV32 ) ) ) )
| ~ ! [SY3400: $i,SY3401: $i] :
( ~ ( in @ ( ordered_pair @ SY3400 @ SY3401 ) @ SV32 )
| ( in @ ( ordered_pair @ ( apply @ SY3393 @ SY3400 ) @ ( apply @ SY3393 @ SY3401 ) ) @ SV59 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3402: $i] :
( ~ ( function @ SY3402 )
| ~ ( relation @ SY3402 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3402 )
| ( ( relation_dom @ SY3402 )
= ( relation_field @ SV32 ) ) )
| ~ ! [SY3403: $i] :
( ~ ( function @ SY3403 )
| ~ ( relation @ SY3403 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3403 )
| ( ( relation_rng @ SY3403 )
= ( relation_field @ SV59 ) ) ) )
| ~ ! [SY3404: $i] :
( ~ ( function @ SY3404 )
| ~ ( relation @ SY3404 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3404 )
| ( one_to_one @ SY3404 ) ) ) ) ) )
= $true )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[699]) ).
thf(767,plain,
! [SV75: $i,SV33: $i] :
( ( ! [SY3434: $i] :
( ~ ( relation_of2_as_subset @ SY3434 @ SV33 @ SV75 )
| ~ ( ~ ! [SY3435: $i] :
~ ( in @ ( ordered_pair @ SY3435 @ ( sK57_D @ SY3434 @ SV75 @ SV33 ) ) @ SY3434 )
| ~ ( in @ ( sK57_D @ SY3434 @ SV75 @ SV33 ) @ SV75 ) )
| ( ( relation_rng_as_subset @ SV33 @ SV75 @ SY3434 )
= SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(768,plain,
! [SV76: $i,SV33: $i] :
( ( ! [SY3436: $i] :
( ~ ( relation_of2_as_subset @ SY3436 @ SV33 @ SV76 )
| ( ( relation_rng_as_subset @ SV33 @ SV76 @ SY3436 )
!= SV76 )
| ! [SY3437: $i] :
( ( in @ ( ordered_pair @ ( sK56_E @ SY3437 @ SY3436 @ SV76 @ SV33 ) @ SY3437 ) @ SY3436 )
| ~ ( in @ SY3437 @ SV76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(769,plain,
! [SV34: $i] :
( ( ( ~ ! [SY3327: $i] :
( ~ ( ~ ( ! [SY3328: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SY3327 @ SV34 ) @ SY3328 ) @ SV34 )
| ~ ( in @ ( sK22_C @ SY3327 @ SV34 ) @ SY3327 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SY3327 @ SV34 ) @ ( sK23_SY3101 @ SY3327 @ SV34 ) ) @ SV34 )
| ( in @ ( sK22_C @ SY3327 @ SV34 ) @ SY3327 ) ) )
| ( SY3327
= ( relation_dom @ SV34 ) ) ) )
= $false )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[702]) ).
thf(770,plain,
! [SV34: $i] :
( ( ( ~ ! [SY3329: $i] :
( ( SY3329
!= ( relation_dom @ SV34 ) )
| ~ ( ~ ! [SY3330: $i] :
( ! [SY3331: $i] :
~ ( in @ ( ordered_pair @ SY3330 @ SY3331 ) @ SV34 )
| ( in @ SY3330 @ SY3329 ) )
| ~ ! [SY3332: $i] :
( ~ ( in @ SY3332 @ SY3329 )
| ( in @ ( ordered_pair @ SY3332 @ ( sK21_D @ SY3332 @ SY3329 @ SV34 ) ) @ SV34 ) ) ) ) )
= $false )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[702]) ).
thf(771,plain,
! [SV44: $i] :
( ( ( ~ ! [SY3365: $i,SY3366: $i] :
( ( sK39_B @ SV44 )
!= ( ordered_pair @ SY3365 @ SY3366 ) )
| ~ ( in @ ( sK39_B @ SV44 ) @ SV44 ) )
= $false )
| ( ( relation @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[703]) ).
thf(772,plain,
! [SV45: $i] :
( ( ( relation @ SV45 )
= $false )
| ( ( ! [SY3367: $i] :
( ( SY3367
= ( ordered_pair @ ( sK37_C @ SY3367 @ SV45 ) @ ( sK38_SY3111 @ SY3367 @ SV45 ) ) )
| ~ ( in @ SY3367 @ SV45 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[704]) ).
thf(773,plain,
! [SV4: $i] :
( ( ( ! [SY3132: $i] :
( ~ ( relation @ SY3132 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SY3132 @ SV4 ) @ ( sK32_SY3109 @ SY3132 @ SV4 ) ) @ SV4 )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ SY3132 @ SV4 ) @ ( sK32_SY3109 @ SY3132 @ SV4 ) ) @ SY3132 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK31_C @ SY3132 @ SV4 ) @ ( sK32_SY3109 @ SY3132 @ SV4 ) ) @ SV4 )
| ( in @ ( ordered_pair @ ( sK31_C @ SY3132 @ SV4 ) @ ( sK32_SY3109 @ SY3132 @ SV4 ) ) @ SY3132 ) ) )
| ( SV4 = SY3132 ) ) )
= $true )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[705]) ).
thf(774,plain,
! [SV4: $i] :
( ( ( ! [SY3133: $i] :
( ~ ( relation @ SY3133 )
| ( SV4 != SY3133 )
| ~ ( ~ ! [SY3134: $i,SY3135: $i] :
( ~ ( in @ ( ordered_pair @ SY3134 @ SY3135 ) @ SV4 )
| ( in @ ( ordered_pair @ SY3134 @ SY3135 ) @ SY3133 ) )
| ~ ! [SY3136: $i,SY3137: $i] :
( ~ ( in @ ( ordered_pair @ SY3136 @ SY3137 ) @ SY3133 )
| ( in @ ( ordered_pair @ SY3136 @ SY3137 ) @ SV4 ) ) ) ) )
= $true )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[706]) ).
thf(775,plain,
! [SV5: $i] :
( ( ( ! [SY3138: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SY3138 @ SV5 ) @ SY3138 )
| ~ ( in @ ( sK4_SY3086 @ SY3138 @ SV5 ) @ SY3138 ) )
| ~ ( in @ ( sK5_SY3088 @ SY3138 @ SV5 ) @ SY3138 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SY3138 @ SV5 ) @ ( sK4_SY3086 @ SY3138 @ SV5 ) ) @ SV5 ) )
| ~ ( in @ ( ordered_pair @ ( sK4_SY3086 @ SY3138 @ SV5 ) @ ( sK5_SY3088 @ SY3138 @ SV5 ) ) @ SV5 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK3_C @ SY3138 @ SV5 ) @ ( sK5_SY3088 @ SY3138 @ SV5 ) ) @ SV5 ) )
| ( is_transitive_in @ SV5 @ SY3138 ) ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[707]) ).
thf(776,plain,
! [SV5: $i] :
( ( ( ! [SY3139: $i] :
( ~ ( is_transitive_in @ SV5 @ SY3139 )
| ! [SY3140: $i,SY3141: $i,SY3142: $i] :
( ~ ( in @ SY3140 @ SY3139 )
| ~ ( in @ SY3141 @ SY3139 )
| ~ ( in @ SY3142 @ SY3139 )
| ~ ( in @ ( ordered_pair @ SY3140 @ SY3141 ) @ SV5 )
| ~ ( in @ ( ordered_pair @ SY3141 @ SY3142 ) @ SV5 )
| ( in @ ( ordered_pair @ SY3140 @ SY3142 ) @ SV5 ) ) ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[708]) ).
thf(777,plain,
! [SV6: $i,SV60: $i,SV77: $i] :
( ( ~ ( relation_of2_as_subset @ SV77 @ SV60 @ SV6 )
| ~ ( ~ ! [SY3438: $i] :
~ ( in @ ( ordered_pair @ ( sK59_D @ SV77 @ SV60 @ SV6 ) @ SY3438 ) @ SV77 )
| ~ ( in @ ( sK59_D @ SV77 @ SV60 @ SV6 ) @ SV60 ) )
| ( ( relation_dom_as_subset @ SV60 @ SV6 @ SV77 )
= SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(778,plain,
! [SV6: $i,SV61: $i,SV78: $i] :
( ( ~ ( relation_of2_as_subset @ SV78 @ SV61 @ SV6 )
| ( ( relation_dom_as_subset @ SV61 @ SV6 @ SV78 )
!= SV61 )
| ! [SY3439: $i] :
( ( in @ ( ordered_pair @ SY3439 @ ( sK58_E @ SY3439 @ SV78 @ SV61 @ SV6 ) ) @ SV78 )
| ~ ( in @ SY3439 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(779,plain,
! [SV7: $i,SV46: $i] :
( ( ( relation @ SV46 )
= $false )
| ( ( ~ ( ~ ! [SY3368: $i] :
( ~ ( relation @ SY3368 )
| ~ ( ~ ( ! [SY3369: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3368 @ SV46 @ SV7 ) @ SY3369 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3369 @ ( sK8_SY3089 @ SY3368 @ SV46 @ SV7 ) ) @ SV46 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3368 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SY3368 @ SV46 @ SV7 ) ) @ SY3368 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3368 @ SV46 @ SV7 ) @ ( sK9_SY3093 @ SY3368 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SY3368 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SY3368 @ SV46 @ SV7 ) ) @ SV46 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SY3368 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SY3368 @ SV46 @ SV7 ) ) @ SY3368 ) ) )
| ( SY3368
= ( relation_composition @ SV7 @ SV46 ) ) )
| ~ ! [SY3370: $i] :
( ~ ( relation @ SY3370 )
| ( SY3370
!= ( relation_composition @ SV7 @ SV46 ) )
| ~ ( ~ ! [SY3371: $i,SY3372: $i] :
( ! [SY3373: $i] :
( ~ ( in @ ( ordered_pair @ SY3371 @ SY3373 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3373 @ SY3372 ) @ SV46 ) )
| ( in @ ( ordered_pair @ SY3371 @ SY3372 ) @ SY3370 ) )
| ~ ! [SY3374: $i,SY3375: $i] :
( ~ ( in @ ( ordered_pair @ SY3374 @ SY3375 ) @ SY3370 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3374 @ ( sK6_F @ SY3375 @ SY3374 @ SY3370 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY3375 @ SY3374 @ SY3370 @ SV46 @ SV7 ) @ SY3375 ) @ SV46 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[711]) ).
thf(780,plain,
! [SV47: $i,SV62: $i] :
( ( ( ~ ( relation @ SV62 ) )
= $true )
| ( ( ~ ( ~ ( ( ( sK52_C @ SV62 @ SV47 )
!= ( sK53_SY3121 @ SV62 @ SV47 ) )
| ~ ( in @ ( sK52_C @ SV62 @ SV47 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) )
| ~ ~ ( ~ ( ( ( sK52_C @ SV62 @ SV47 )
= ( sK53_SY3121 @ SV62 @ SV47 ) )
| ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) )
| ~ ( ( in @ ( sK52_C @ SV62 @ SV47 ) @ SV47 )
| ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) ) ) )
| ( SV62
= ( identity_relation @ SV47 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[712]) ).
thf(781,plain,
! [SV48: $i,SV63: $i] :
( ( ( ~ ( relation @ SV63 ) )
= $true )
| ( ( ( SV63
!= ( identity_relation @ SV48 ) )
| ~ ( ~ ! [SY3409: $i,SY3410: $i] :
( ( SY3409 != SY3410 )
| ~ ( in @ SY3409 @ SV48 )
| ( in @ ( ordered_pair @ SY3409 @ SY3410 ) @ SV63 ) )
| ~ ~ ( ~ ! [SY3411: $i,SY3412: $i] :
( ~ ( in @ ( ordered_pair @ SY3411 @ SY3412 ) @ SV63 )
| ( SY3411 = SY3412 ) )
| ~ ! [SY3413: $i] :
( ! [SY3414: $i] :
~ ( in @ ( ordered_pair @ SY3413 @ SY3414 ) @ SV63 )
| ( in @ SY3413 @ SV48 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[713]) ).
thf(782,plain,
! [SV49: $i,SV42: $i,SV8: $i] :
( ( ( ~ ! [SY3160: $i] :
( ~ ( ( SV8
!= ( ordered_pair @ ( sK40_C @ SY3160 @ SV8 ) @ ( sK41_SY3114 @ SY3160 @ SV8 ) ) )
| ~ ( ( SY3160
!= ( sK40_C @ SY3160 @ SV8 ) ) ) )
| ( SY3160
= ( pair_first @ SV8 ) ) )
| ~ ! [SY3161: $i] :
( ( SY3161
!= ( pair_first @ SV8 ) )
| ! [SY3162: $i] :
( ! [SY3163: $i] :
( SV8
!= ( ordered_pair @ SY3162 @ SY3163 ) )
| ( SY3161 = SY3162 ) ) ) )
= $false )
| ( ( SV8
= ( ordered_pair @ SV42 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[714]) ).
thf(783,plain,
! [SV37: $i,SV79: $i,SV9: $i] :
( ( ! [SY3440: $i] :
( ~ ( relation @ SY3440 )
| ~ ( in @ SV9 @ SV79 )
| ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ SY3440 )
| ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SV79 ) @ SY3440 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(784,plain,
! [SV37: $i,SV9: $i] :
( ( ~ ! [SY3335: $i,SY3336: $i] :
( ~ ( relation @ SY3336 )
| ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SY3335 ) @ SY3336 ) )
| ( in @ SV9 @ SY3335 ) )
| ~ ! [SY3337: $i,SY3338: $i] :
( ~ ( relation @ SY3338 )
| ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SY3337 ) @ SY3338 ) )
| ( in @ ( ordered_pair @ SV9 @ SV37 ) @ SY3338 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[716]) ).
thf(785,plain,
! [SV64: $i,SV10: $i,SV80: $i] :
( ( ~ ( relation @ SV80 )
| ! [SY3441: $i] :
( ~ ( in @ SY3441 @ ( relation_rng @ SV80 ) )
| ~ ( in @ ( ordered_pair @ SV10 @ SY3441 ) @ SV80 )
| ~ ( in @ SY3441 @ SV64 ) )
| ( in @ SV10 @ ( relation_inverse_image @ SV80 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(786,plain,
! [SV65: $i,SV10: $i,SV81: $i] :
( ( ~ ( relation @ SV81 )
| ~ ( in @ SV10 @ ( relation_inverse_image @ SV81 @ SV65 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_D @ SV81 @ SV65 @ SV10 ) @ ( relation_rng @ SV81 ) )
| ~ ( in @ ( ordered_pair @ SV10 @ ( sK60_D @ SV81 @ SV65 @ SV10 ) ) @ SV81 ) )
| ~ ( in @ ( sK60_D @ SV81 @ SV65 @ SV10 ) @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(787,plain,
! [SV82: $i,SV66: $i,SV11: $i] :
( ( ~ ( ~ ( ! [SY3442: $i,SY3443: $i] :
( ~ ( in @ SY3442 @ SV11 )
| ~ ( in @ SY3443 @ SV66 )
| ( ( sK28_D @ SV82 @ SV66 @ SV11 )
!= ( ordered_pair @ SY3442 @ SY3443 ) ) )
| ~ ( in @ ( sK28_D @ SV82 @ SV66 @ SV11 ) @ SV82 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY3106 @ SV82 @ SV66 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK30_SY3108 @ SV82 @ SV66 @ SV11 ) @ SV66 ) )
| ( ( sK28_D @ SV82 @ SV66 @ SV11 )
!= ( ordered_pair @ ( sK29_SY3106 @ SV82 @ SV66 @ SV11 ) @ ( sK30_SY3108 @ SV82 @ SV66 @ SV11 ) ) ) )
| ( in @ ( sK28_D @ SV82 @ SV66 @ SV11 ) @ SV82 ) ) )
| ( SV82
= ( cartesian_product2 @ SV11 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(788,plain,
! [SV67: $i,SV11: $i,SV83: $i] :
( ( ( SV83
!= ( cartesian_product2 @ SV11 @ SV67 ) )
| ~ ( ~ ! [SY3444: $i] :
( ! [SY3423: $i,SY3424: $i] :
( ~ ( in @ SY3423 @ SV11 )
| ~ ( in @ SY3424 @ SV67 )
| ( SY3444
!= ( ordered_pair @ SY3423 @ SY3424 ) ) )
| ( in @ SY3444 @ SV83 ) )
| ~ ! [SY3447: $i] :
( ~ ( in @ SY3447 @ SV83 )
| ~ ( ~ ~ ( ~ ( in @ ( sK26_E @ SY3447 @ SV83 @ SV67 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK27_SY3103 @ SY3447 @ SV83 @ SV67 @ SV11 ) @ SV67 ) )
| ( SY3447
!= ( ordered_pair @ ( sK26_E @ SY3447 @ SV83 @ SV67 @ SV11 ) @ ( sK27_SY3103 @ SY3447 @ SV83 @ SV67 @ SV11 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(789,plain,
! [SV68: $i,SV12: $i,SV84: $i] :
( ( ~ ( relation @ SV84 )
| ~ ( in @ ( ordered_pair @ SV12 @ SV68 ) @ SV84 )
| ( in @ SV12 @ ( relation_field @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(790,plain,
! [SV69: $i,SV12: $i,SV85: $i] :
( ( ~ ( relation @ SV85 )
| ~ ( in @ ( ordered_pair @ SV12 @ SV69 ) @ SV85 )
| ( in @ SV69 @ ( relation_field @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(791,plain,
! [SV50: $i,SV43: $i,SV13: $i] :
( ( ( ~ ! [SY3192: $i] :
( ~ ( ( SV13
!= ( ordered_pair @ ( sK33_C @ SY3192 @ SV13 ) @ ( sK34_SY3110 @ SY3192 @ SV13 ) ) )
| ~ ( ( SY3192
!= ( sK34_SY3110 @ SY3192 @ SV13 ) ) ) )
| ( SY3192
= ( pair_second @ SV13 ) ) )
| ~ ! [SY3193: $i] :
( ( SY3193
!= ( pair_second @ SV13 ) )
| ! [SY3194: $i,SY3195: $i] :
( ( SV13
!= ( ordered_pair @ SY3194 @ SY3195 ) )
| ( SY3193 = SY3195 ) ) ) )
= $false )
| ( ( SV13
= ( ordered_pair @ SV43 @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[723]) ).
thf(792,plain,
! [SV14: $i] :
( ( ( ! [SY3196: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK14_C @ SY3196 @ SV14 )
!= ( sK15_SY3096 @ SY3196 @ SV14 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SY3196 @ SV14 ) @ SY3196 )
| ~ ( in @ ( sK15_SY3096 @ SY3196 @ SV14 ) @ SY3196 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK14_C @ SY3196 @ SV14 ) @ ( sK15_SY3096 @ SY3196 @ SV14 ) ) @ SV14 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK15_SY3096 @ SY3196 @ SV14 ) @ ( sK14_C @ SY3196 @ SV14 ) ) @ SV14 ) )
| ( is_connected_in @ SV14 @ SY3196 ) ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[724]) ).
thf(793,plain,
! [SV14: $i] :
( ( ( ! [SY3197: $i] :
( ~ ( is_connected_in @ SV14 @ SY3197 )
| ! [SY3198: $i,SY3199: $i] :
( ( SY3198 = SY3199 )
| ~ ( in @ SY3198 @ SY3197 )
| ~ ( in @ SY3199 @ SY3197 )
| ( in @ ( ordered_pair @ SY3198 @ SY3199 ) @ SV14 )
| ( in @ ( ordered_pair @ SY3199 @ SY3198 ) @ SV14 ) ) ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[725]) ).
thf(794,plain,
! [SV70: $i,SV15: $i,SV86: $i] :
( ( ~ ( relation @ SV86 )
| ! [SY3448: $i] :
( ~ ( in @ SY3448 @ ( relation_dom @ SV86 ) )
| ~ ( in @ ( ordered_pair @ SY3448 @ SV15 ) @ SV86 )
| ~ ( in @ SY3448 @ SV70 ) )
| ( in @ SV15 @ ( relation_image @ SV86 @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(795,plain,
! [SV71: $i,SV15: $i,SV87: $i] :
( ( ~ ( relation @ SV87 )
| ~ ( in @ SV15 @ ( relation_image @ SV87 @ SV71 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK61_D @ SV87 @ SV71 @ SV15 ) @ ( relation_dom @ SV87 ) )
| ~ ( in @ ( ordered_pair @ ( sK61_D @ SV87 @ SV71 @ SV15 ) @ SV15 ) @ SV87 ) )
| ~ ( in @ ( sK61_D @ SV87 @ SV71 @ SV15 ) @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(796,plain,
! [SV16: $i] :
( ( ( ! [SY3205: $i,SY3206: $i] :
( ~ ( ~ ( ! [SY3207: $i] :
( ~ ( in @ ( ordered_pair @ SY3207 @ ( sK46_D @ SY3206 @ SY3205 @ SV16 ) ) @ SV16 )
| ~ ( in @ SY3207 @ SY3205 ) )
| ~ ( in @ ( sK46_D @ SY3206 @ SY3205 @ SV16 ) @ SY3206 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SY3206 @ SY3205 @ SV16 ) @ ( sK46_D @ SY3206 @ SY3205 @ SV16 ) ) @ SV16 )
| ~ ( in @ ( sK47_SY3118 @ SY3206 @ SY3205 @ SV16 ) @ SY3205 ) )
| ( in @ ( sK46_D @ SY3206 @ SY3205 @ SV16 ) @ SY3206 ) ) )
| ( SY3206
= ( relation_image @ SV16 @ SY3205 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[728]) ).
thf(797,plain,
! [SV16: $i] :
( ( ( ! [SY3208: $i,SY3209: $i] :
( ( SY3209
!= ( relation_image @ SV16 @ SY3208 ) )
| ~ ( ~ ! [SY3210: $i] :
( ! [SY3211: $i] :
( ~ ( in @ ( ordered_pair @ SY3211 @ SY3210 ) @ SV16 )
| ~ ( in @ SY3211 @ SY3208 ) )
| ( in @ SY3210 @ SY3209 ) )
| ~ ! [SY3212: $i] :
( ~ ( in @ SY3212 @ SY3209 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SY3212 @ SY3209 @ SY3208 @ SV16 ) @ SY3212 ) @ SV16 )
| ~ ( in @ ( sK45_E @ SY3212 @ SY3209 @ SY3208 @ SV16 ) @ SY3208 ) ) ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[729]) ).
thf(798,plain,
! [SV51: $i] :
( ( ( relation @ SV51 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK64_B @ SV51 ) @ ( sK65_SY3126 @ SV51 ) ) @ SV51 )
| ~ ( in @ ( ordered_pair @ ( sK65_SY3126 @ SV51 ) @ ( sK64_B @ SV51 ) ) @ SV51 ) )
| ~ ( ( ( sK64_B @ SV51 )
!= ( sK65_SY3126 @ SV51 ) ) ) )
| ( antisymmetric @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[730]) ).
thf(799,plain,
! [SV52: $i] :
( ( ( relation @ SV52 )
= $false )
| ( ( ~ ( antisymmetric @ SV52 )
| ! [SY3384: $i,SY3385: $i] :
( ~ ( in @ ( ordered_pair @ SY3384 @ SY3385 ) @ SV52 )
| ~ ( in @ ( ordered_pair @ SY3385 @ SY3384 ) @ SV52 )
| ( SY3384 = SY3385 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[731]) ).
thf(800,plain,
! [SV17: $i,SV72: $i,SV88: $i] :
( ( ~ ( function @ SV88 )
| ~ ( relation @ SV88 )
| ( SV72
!= ( apply @ SV88 @ SV17 ) )
| ~ ( in @ SV17 @ ( relation_dom @ SV88 ) )
| ( in @ ( ordered_pair @ SV17 @ SV72 ) @ SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(801,plain,
! [SV17: $i] :
( ( ~ ! [SY3215: $i,SY3216: $i] :
( ~ ( function @ SY3216 )
| ~ ( relation @ SY3216 )
| ~ ( in @ ( ordered_pair @ SV17 @ SY3215 ) @ SY3216 )
| ( SY3215
= ( apply @ SY3216 @ SV17 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[733]) ).
thf(802,plain,
! [SV17: $i] :
( ( ~ ! [SY3217: $i,SY3218: $i] :
( ~ ( function @ SY3218 )
| ~ ( relation @ SY3218 )
| ~ ( in @ ( ordered_pair @ SV17 @ SY3217 ) @ SY3218 )
| ( in @ SV17 @ ( relation_dom @ SY3218 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[733]) ).
thf(803,plain,
! [SV18: $i] :
( ( ( ! [SY3219: $i,SY3220: $i] :
( ~ ( ~ ( ( ( sK35_D @ SY3220 @ SY3219 @ SV18 )
= SY3219 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SY3220 @ SY3219 @ SV18 ) @ SY3219 ) @ SV18 )
| ~ ( in @ ( sK35_D @ SY3220 @ SY3219 @ SV18 ) @ SY3220 ) )
| ~ ~ ( ~ ( ( ( sK35_D @ SY3220 @ SY3219 @ SV18 )
!= SY3219 )
| ( in @ ( sK35_D @ SY3220 @ SY3219 @ SV18 ) @ SY3220 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SY3220 @ SY3219 @ SV18 ) @ SY3219 ) @ SV18 )
| ( in @ ( sK35_D @ SY3220 @ SY3219 @ SV18 ) @ SY3220 ) ) ) )
| ( SY3220
= ( fiber @ SV18 @ SY3219 ) ) ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[734]) ).
thf(804,plain,
! [SV18: $i] :
( ( ( ! [SY3221: $i,SY3222: $i] :
( ( SY3222
!= ( fiber @ SV18 @ SY3221 ) )
| ~ ( ~ ! [SY3223: $i] :
( ( SY3223 = SY3221 )
| ~ ( in @ ( ordered_pair @ SY3223 @ SY3221 ) @ SV18 )
| ( in @ SY3223 @ SY3222 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY3222 )
| ( SX3 != SY3221 ) )
| ~ ! [SY3225: $i] :
( ~ ( in @ SY3225 @ SY3222 )
| ( in @ ( ordered_pair @ SY3225 @ SY3221 ) @ SV18 ) ) ) ) ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[735]) ).
thf(805,plain,
! [SV19: $i] :
( ( ( ! [SY3226: $i] :
( ~ ( ~ ( in @ ( sK36_C @ SY3226 @ SV19 ) @ SY3226 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SY3226 @ SV19 ) @ ( sK36_C @ SY3226 @ SV19 ) ) @ SV19 ) )
| ( is_reflexive_in @ SV19 @ SY3226 ) ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[736]) ).
thf(806,plain,
! [SV19: $i] :
( ( ( ! [SY3227: $i] :
( ~ ( is_reflexive_in @ SV19 @ SY3227 )
| ! [SY3228: $i] :
( ~ ( in @ SY3228 @ SY3227 )
| ( in @ ( ordered_pair @ SY3228 @ SY3228 ) @ SV19 ) ) ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[737]) ).
thf(807,plain,
! [SV20: $i] :
( ( ( ! [SY3229: $i] :
( ~ ( relation @ SY3229 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SY3229 @ SV20 ) @ ( sK13_SY3095 @ SY3229 @ SV20 ) ) @ SY3229 )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SY3229 @ SV20 ) @ ( sK12_C @ SY3229 @ SV20 ) ) @ SV20 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SY3229 @ SV20 ) @ ( sK13_SY3095 @ SY3229 @ SV20 ) ) @ SY3229 )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ SY3229 @ SV20 ) @ ( sK12_C @ SY3229 @ SV20 ) ) @ SV20 ) ) )
| ( SY3229
= ( relation_inverse @ SV20 ) ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[738]) ).
thf(808,plain,
! [SV20: $i] :
( ( ( ! [SY3230: $i] :
( ~ ( relation @ SY3230 )
| ( SY3230
!= ( relation_inverse @ SV20 ) )
| ~ ( ~ ! [SY3231: $i,SY3232: $i] :
( ~ ( in @ ( ordered_pair @ SY3231 @ SY3232 ) @ SY3230 )
| ( in @ ( ordered_pair @ SY3232 @ SY3231 ) @ SV20 ) )
| ~ ! [SY3233: $i,SY3234: $i] :
( ~ ( in @ ( ordered_pair @ SY3234 @ SY3233 ) @ SV20 )
| ( in @ ( ordered_pair @ SY3233 @ SY3234 ) @ SY3230 ) ) ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[739]) ).
thf(809,plain,
! [SV21: $i,SV38: $i] :
( ( ( ~ ! [SY3339: $i] :
( ~ ( relation @ SY3339 )
| ~ ( ~ ( ~ ( in @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) @ SV21 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SY3339 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) ) @ SV38 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SY3339 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) ) @ SY3339 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK48_D @ SY3339 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) ) @ SY3339 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SY3339 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) ) @ SV38 )
| ( in @ ( ordered_pair @ ( sK48_D @ SY3339 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) ) @ SY3339 ) ) ) )
| ( SY3339
= ( relation_rng_restriction @ SV21 @ SV38 ) ) ) )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[740]) ).
thf(810,plain,
! [SV38: $i,SV21: $i] :
( ( ( ~ ! [SY3340: $i] :
( ~ ( relation @ SY3340 )
| ( SY3340
!= ( relation_rng_restriction @ SV21 @ SV38 ) )
| ~ ( ~ ! [SY3341: $i,SY3342: $i] :
( ~ ( in @ SY3342 @ SV21 )
| ~ ( in @ ( ordered_pair @ SY3341 @ SY3342 ) @ SV38 )
| ( in @ ( ordered_pair @ SY3341 @ SY3342 ) @ SY3340 ) )
| ~ ~ ( ~ ! [SY3240: $i,SY3241: $i] :
( ~ ( in @ ( ordered_pair @ SY3240 @ SY3241 ) @ SY3340 )
| ( in @ SY3241 @ SV21 ) )
| ~ ! [SY3345: $i,SY3346: $i] :
( ~ ( in @ ( ordered_pair @ SY3345 @ SY3346 ) @ SY3340 )
| ( in @ ( ordered_pair @ SY3345 @ SY3346 ) @ SV38 ) ) ) ) ) )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[740]) ).
thf(811,plain,
! [SV22: $i] :
( ( ( ! [SY3244: $i] :
( ~ ( ~ ( ! [SY3245: $i] :
~ ( in @ ( ordered_pair @ SY3245 @ ( sK17_C @ SY3244 @ SV22 ) ) @ SV22 )
| ~ ( in @ ( sK17_C @ SY3244 @ SV22 ) @ SY3244 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK18_SY3098 @ SY3244 @ SV22 ) @ ( sK17_C @ SY3244 @ SV22 ) ) @ SV22 )
| ( in @ ( sK17_C @ SY3244 @ SV22 ) @ SY3244 ) ) )
| ( SY3244
= ( relation_rng @ SV22 ) ) ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[741]) ).
thf(812,plain,
! [SV22: $i] :
( ( ( ! [SY3246: $i] :
( ( SY3246
!= ( relation_rng @ SV22 ) )
| ~ ( ~ ! [SY3247: $i] :
( ! [SY3248: $i] :
~ ( in @ ( ordered_pair @ SY3248 @ SY3247 ) @ SV22 )
| ( in @ SY3247 @ SY3246 ) )
| ~ ! [SY3249: $i] :
( ~ ( in @ SY3249 @ SY3246 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3249 @ SY3246 @ SV22 ) @ SY3249 ) @ SV22 ) ) ) ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[742]) ).
thf(813,plain,
! [SV23: $i] :
( ( ( ! [SY3250: $i] :
( ~ ( relation @ SY3250 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3250 @ SV23 ) @ ( sK25_SY3102 @ SY3250 @ SV23 ) ) @ SV23 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3250 @ SV23 ) @ ( sK25_SY3102 @ SY3250 @ SV23 ) ) @ SY3250 ) )
| ( subset @ SV23 @ SY3250 ) ) )
= $true )
| ( ( relation @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[743]) ).
thf(814,plain,
! [SV23: $i] :
( ( ( ! [SY3251: $i] :
( ~ ( relation @ SY3251 )
| ~ ( subset @ SV23 @ SY3251 )
| ! [SY3252: $i,SY3253: $i] :
( ~ ( in @ ( ordered_pair @ SY3252 @ SY3253 ) @ SV23 )
| ( in @ ( ordered_pair @ SY3252 @ SY3253 ) @ SY3251 ) ) ) )
= $true )
| ( ( relation @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[744]) ).
thf(815,plain,
! [SV24: $i] :
( ( ( ! [SY3254: $i,SY3255: $i] :
( ~ ( relation @ SY3255 )
| ~ ( ~ ( ~ ( in @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ SY3254 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ ( sK51_SY3120 @ SY3255 @ SY3254 @ SV24 ) ) @ SV24 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ ( sK51_SY3120 @ SY3255 @ SY3254 @ SV24 ) ) @ SY3255 ) )
| ~ ~ ( ~ ( ( in @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ SY3254 )
| ( in @ ( ordered_pair @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ ( sK51_SY3120 @ SY3255 @ SY3254 @ SV24 ) ) @ SY3255 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ ( sK51_SY3120 @ SY3255 @ SY3254 @ SV24 ) ) @ SV24 )
| ( in @ ( ordered_pair @ ( sK50_D @ SY3255 @ SY3254 @ SV24 ) @ ( sK51_SY3120 @ SY3255 @ SY3254 @ SV24 ) ) @ SY3255 ) ) ) )
| ( SY3255
= ( relation_dom_restriction @ SV24 @ SY3254 ) ) ) )
= $true )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[745]) ).
thf(816,plain,
! [SV24: $i] :
( ( ( ! [SY3256: $i,SY3257: $i] :
( ~ ( relation @ SY3257 )
| ( SY3257
!= ( relation_dom_restriction @ SV24 @ SY3256 ) )
| ~ ( ~ ! [SY3258: $i,SY3259: $i] :
( ~ ( in @ SY3258 @ SY3256 )
| ~ ( in @ ( ordered_pair @ SY3258 @ SY3259 ) @ SV24 )
| ( in @ ( ordered_pair @ SY3258 @ SY3259 ) @ SY3257 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3257 )
| ( in @ SX3 @ SY3256 ) )
| ~ ! [SY3262: $i,SY3263: $i] :
( ~ ( in @ ( ordered_pair @ SY3262 @ SY3263 ) @ SY3257 )
| ( in @ ( ordered_pair @ SY3262 @ SY3263 ) @ SV24 ) ) ) ) ) )
= $true )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[746]) ).
thf(817,plain,
! [SV89: $i,SV39: $i,SV25: $i] :
( ( ! [SY3449: $i] :
( ( ordered_pair @ SV25 @ SV39 )
!= ( ordered_pair @ SV89 @ SY3449 ) )
| ( SV25 = SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(818,plain,
! [SV90: $i,SV39: $i,SV25: $i] :
( ( ! [SY3450: $i] :
( ( ( ordered_pair @ SV25 @ SV39 )
!= ( ordered_pair @ SV90 @ SY3450 ) )
| ( SV39 = SY3450 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(819,plain,
! [SV26: $i] :
( ( ( ~ ~ ( ~ ! [SY3269: $i] :
( ~ ( in @ SY3269 @ ( relation_dom @ SV26 ) )
| ! [SY3270: $i] :
( ( SY3270
!= ( apply @ SV26 @ SY3269 ) )
| ( in @ ( ordered_pair @ SY3269 @ SY3270 ) @ SV26 ) ) )
| ~ ! [SY3271: $i] :
( ~ ( in @ SY3271 @ ( relation_dom @ SV26 ) )
| ! [SY3272: $i] :
( ~ ( in @ ( ordered_pair @ SY3271 @ SY3272 ) @ SV26 )
| ( SY3272
= ( apply @ SV26 @ SY3271 ) ) ) ) )
| ~ ~ ( ~ ! [SY3273: $i] :
( ( in @ SY3273 @ ( relation_dom @ SV26 ) )
| ! [SY3274: $i] :
( ( SY3274
!= ( apply @ SV26 @ SY3273 ) )
| ( SY3274 = empty_set ) ) )
| ~ ! [SY3275: $i] :
( ( in @ SY3275 @ ( relation_dom @ SV26 ) )
| ! [SY3276: $i] :
( ( SY3276 != empty_set )
| ( SY3276
= ( apply @ SV26 @ SY3275 ) ) ) ) ) )
= $false )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[749]) ).
thf(820,plain,
! [SV53: $i] :
( ( ( relation @ SV53 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK62_B @ SV53 )
!= ( sK63_SY3125 @ SV53 ) ) )
| ~ ~ ( ~ ( in @ ( sK62_B @ SV53 ) @ ( relation_field @ SV53 ) )
| ~ ( in @ ( sK63_SY3125 @ SV53 ) @ ( relation_field @ SV53 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK62_B @ SV53 ) @ ( sK63_SY3125 @ SV53 ) ) @ SV53 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK63_SY3125 @ SV53 ) @ ( sK62_B @ SV53 ) ) @ SV53 ) )
| ( connected @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[750]) ).
thf(821,plain,
! [SV54: $i] :
( ( ( relation @ SV54 )
= $false )
| ( ( ~ ( connected @ SV54 )
| ! [SY3386: $i,SY3387: $i] :
( ( SY3386 = SY3387 )
| ~ ( in @ SY3386 @ ( relation_field @ SV54 ) )
| ~ ( in @ SY3387 @ ( relation_field @ SV54 ) )
| ( in @ ( ordered_pair @ SY3386 @ SY3387 ) @ SV54 )
| ( in @ ( ordered_pair @ SY3387 @ SY3386 ) @ SV54 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[751]) ).
thf(822,plain,
! [SV27: $i] :
( ( ( ! [SY3277: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_C @ SY3277 @ SV27 ) @ SY3277 )
| ~ ( in @ ( sK20_SY3099 @ SY3277 @ SV27 ) @ SY3277 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SY3277 @ SV27 ) @ ( sK20_SY3099 @ SY3277 @ SV27 ) ) @ SV27 ) )
| ~ ( in @ ( ordered_pair @ ( sK20_SY3099 @ SY3277 @ SV27 ) @ ( sK19_C @ SY3277 @ SV27 ) ) @ SV27 ) )
| ~ ( ( ( sK19_C @ SY3277 @ SV27 )
!= ( sK20_SY3099 @ SY3277 @ SV27 ) ) ) )
| ( is_antisymmetric_in @ SV27 @ SY3277 ) ) )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[752]) ).
thf(823,plain,
! [SV27: $i] :
( ( ( ! [SY3278: $i] :
( ~ ( is_antisymmetric_in @ SV27 @ SY3278 )
| ! [SY3279: $i,SY3280: $i] :
( ~ ( in @ SY3279 @ SY3278 )
| ~ ( in @ SY3280 @ SY3278 )
| ~ ( in @ ( ordered_pair @ SY3279 @ SY3280 ) @ SV27 )
| ~ ( in @ ( ordered_pair @ SY3280 @ SY3279 ) @ SV27 )
| ( SY3279 = SY3280 ) ) ) )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[753]) ).
thf(824,plain,
! [SV40: $i,SV91: $i,SV28: $i] :
( ( ! [SY3451: $i] :
( ~ ( in @ SV28 @ SV91 )
| ~ ( in @ SV40 @ SY3451 )
| ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SV91 @ SY3451 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(825,plain,
! [SV40: $i,SV28: $i] :
( ( ~ ! [SY3353: $i] :
( ! [SY3354: $i] :
~ ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SY3353 @ SY3354 ) )
| ( in @ SV28 @ SY3353 ) )
| ~ ! [SY3355: $i,SY3356: $i] :
( ~ ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SY3355 @ SY3356 ) )
| ( in @ SV40 @ SY3356 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[755]) ).
thf(826,plain,
! [SV55: $i] :
( ( ( relation @ SV55 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK66_B @ SV55 ) @ ( sK67_SY3127 @ SV55 ) ) @ SV55 )
| ~ ( in @ ( ordered_pair @ ( sK67_SY3127 @ SV55 ) @ ( sK68_SY3129 @ SV55 ) ) @ SV55 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK66_B @ SV55 ) @ ( sK68_SY3129 @ SV55 ) ) @ SV55 ) )
| ( transitive @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[756]) ).
thf(827,plain,
! [SV56: $i] :
( ( ( relation @ SV56 )
= $false )
| ( ( ~ ( transitive @ SV56 )
| ! [SY3388: $i,SY3389: $i,SY3390: $i] :
( ~ ( in @ ( ordered_pair @ SY3388 @ SY3389 ) @ SV56 )
| ~ ( in @ ( ordered_pair @ SY3389 @ SY3390 ) @ SV56 )
| ( in @ ( ordered_pair @ SY3388 @ SY3390 ) @ SV56 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[757]) ).
thf(828,plain,
! [SV41: $i,SV92: $i,SV29: $i] :
( ( ! [SY3452: $i] :
( ~ ( in @ SV29 @ SV92 )
| ~ ( in @ SV41 @ SY3452 )
| ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SV92 @ SY3452 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(829,plain,
! [SV41: $i,SV29: $i] :
( ( ~ ! [SY3359: $i] :
( ! [SY3360: $i] :
~ ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SY3359 @ SY3360 ) )
| ( in @ SV29 @ SY3359 ) )
| ~ ! [SY3361: $i,SY3362: $i] :
( ~ ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SY3361 @ SY3362 ) )
| ( in @ SV41 @ SY3362 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[759]) ).
thf(830,plain,
! [SV30: $i] :
( ( ( ! [SY3295: $i,SY3296: $i] :
( ~ ( ~ ( ! [SY3297: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ SY3296 @ SY3295 @ SV30 ) @ SY3297 ) @ SV30 )
| ~ ( in @ SY3297 @ SY3295 ) )
| ~ ( in @ ( sK43_D @ SY3296 @ SY3295 @ SV30 ) @ SY3296 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SY3296 @ SY3295 @ SV30 ) @ ( sK44_SY3116 @ SY3296 @ SY3295 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK44_SY3116 @ SY3296 @ SY3295 @ SV30 ) @ SY3295 ) )
| ( in @ ( sK43_D @ SY3296 @ SY3295 @ SV30 ) @ SY3296 ) ) )
| ( SY3296
= ( relation_inverse_image @ SV30 @ SY3295 ) ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[760]) ).
thf(831,plain,
! [SV30: $i] :
( ( ( ! [SY3298: $i,SY3299: $i] :
( ( SY3299
!= ( relation_inverse_image @ SV30 @ SY3298 ) )
| ~ ( ~ ! [SY3300: $i] :
( ! [SY3301: $i] :
( ~ ( in @ ( ordered_pair @ SY3300 @ SY3301 ) @ SV30 )
| ~ ( in @ SY3301 @ SY3298 ) )
| ( in @ SY3300 @ SY3299 ) )
| ~ ! [SY3302: $i] :
( ~ ( in @ SY3302 @ SY3299 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3302 @ ( sK42_E @ SY3302 @ SY3299 @ SY3298 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK42_E @ SY3302 @ SY3299 @ SY3298 @ SV30 ) @ SY3298 ) ) ) ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[761]) ).
thf(832,plain,
! [SV73: $i,SV31: $i,SV93: $i] :
( ( ~ ( relation @ SV93 )
| ~ ( in @ ( ordered_pair @ SV31 @ SV73 ) @ SV93 )
| ( in @ SV31 @ ( relation_dom @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(833,plain,
! [SV74: $i,SV31: $i,SV94: $i] :
( ( ~ ( relation @ SV94 )
| ~ ( in @ ( ordered_pair @ SV31 @ SV74 ) @ SV94 )
| ( in @ SV74 @ ( relation_rng @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(834,plain,
! [SV57: $i] :
( ( ( relation @ SV57 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK69_B @ SV57 ) @ ( relation_field @ SV57 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK69_B @ SV57 ) @ ( sK69_B @ SV57 ) ) @ SV57 ) )
| ( reflexive @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[764]) ).
thf(835,plain,
! [SV58: $i] :
( ( ( relation @ SV58 )
= $false )
| ( ( ~ ( reflexive @ SV58 )
| ! [SY3391: $i] :
( ~ ( in @ SY3391 @ ( relation_field @ SV58 ) )
| ( in @ ( ordered_pair @ SY3391 @ SY3391 ) @ SV58 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[765]) ).
thf(836,plain,
! [SV32: $i,SV59: $i] :
( ( ( relation @ SV59 )
= $false )
| ( ( ~ ( ~ ! [SY3392: $i] :
( ~ ( function @ SY3392 )
| ~ ( relation @ SY3392 )
| ~ ( ~ ( ~ ( in @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3392 @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) ) @ ( apply @ SY3392 @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) @ SV32 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SY3392 @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) ) @ ( apply @ SY3392 @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) @ SV32 ) ) ) )
| ( ( relation_dom @ SY3392 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SY3392 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SY3392 )
| ( relation_isomorphism @ SV32 @ SV59 @ SY3392 ) )
| ~ ~ ( ~ ! [SY3393: $i] :
( ~ ( function @ SY3393 )
| ~ ( relation @ SY3393 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3393 )
| ~ ( ~ ! [SY3394: $i,SY3395: $i] :
( ~ ( in @ SY3394 @ ( relation_field @ SV32 ) )
| ~ ( in @ SY3395 @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3393 @ SY3394 ) @ ( apply @ SY3393 @ SY3395 ) ) @ SV59 )
| ( in @ ( ordered_pair @ SY3394 @ SY3395 ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3312: $i] :
( ! [SY3313: $i] :
~ ( in @ ( ordered_pair @ SY3312 @ SY3313 ) @ SV32 )
| ( in @ SY3312 @ ( relation_field @ SV32 ) ) )
| ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV32 )
| ( in @ SY3315 @ ( relation_field @ SV32 ) ) ) )
| ~ ! [SY3400: $i,SY3401: $i] :
( ~ ( in @ ( ordered_pair @ SY3400 @ SY3401 ) @ SV32 )
| ( in @ ( ordered_pair @ ( apply @ SY3393 @ SY3400 ) @ ( apply @ SY3393 @ SY3401 ) ) @ SV59 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3402: $i] :
( ~ ( function @ SY3402 )
| ~ ( relation @ SY3402 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3402 )
| ( ( relation_dom @ SY3402 )
= ( relation_field @ SV32 ) ) )
| ~ ! [SY3403: $i] :
( ~ ( function @ SY3403 )
| ~ ( relation @ SY3403 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3403 )
| ( ( relation_rng @ SY3403 )
= ( relation_field @ SV59 ) ) ) )
| ~ ! [SY3404: $i] :
( ~ ( function @ SY3404 )
| ~ ( relation @ SY3404 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3404 )
| ( one_to_one @ SY3404 ) ) ) ) ) )
= $true )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[766]) ).
thf(837,plain,
! [SV75: $i,SV33: $i,SV95: $i] :
( ( ~ ( relation_of2_as_subset @ SV95 @ SV33 @ SV75 )
| ~ ( ~ ! [SY3453: $i] :
~ ( in @ ( ordered_pair @ SY3453 @ ( sK57_D @ SV95 @ SV75 @ SV33 ) ) @ SV95 )
| ~ ( in @ ( sK57_D @ SV95 @ SV75 @ SV33 ) @ SV75 ) )
| ( ( relation_rng_as_subset @ SV33 @ SV75 @ SV95 )
= SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(838,plain,
! [SV76: $i,SV33: $i,SV96: $i] :
( ( ~ ( relation_of2_as_subset @ SV96 @ SV33 @ SV76 )
| ( ( relation_rng_as_subset @ SV33 @ SV76 @ SV96 )
!= SV76 )
| ! [SY3454: $i] :
( ( in @ ( ordered_pair @ ( sK56_E @ SY3454 @ SV96 @ SV76 @ SV33 ) @ SY3454 ) @ SV96 )
| ~ ( in @ SY3454 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(839,plain,
! [SV34: $i] :
( ( ( ! [SY3327: $i] :
( ~ ( ~ ( ! [SY3328: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SY3327 @ SV34 ) @ SY3328 ) @ SV34 )
| ~ ( in @ ( sK22_C @ SY3327 @ SV34 ) @ SY3327 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SY3327 @ SV34 ) @ ( sK23_SY3101 @ SY3327 @ SV34 ) ) @ SV34 )
| ( in @ ( sK22_C @ SY3327 @ SV34 ) @ SY3327 ) ) )
| ( SY3327
= ( relation_dom @ SV34 ) ) ) )
= $true )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[769]) ).
thf(840,plain,
! [SV34: $i] :
( ( ( ! [SY3329: $i] :
( ( SY3329
!= ( relation_dom @ SV34 ) )
| ~ ( ~ ! [SY3330: $i] :
( ! [SY3331: $i] :
~ ( in @ ( ordered_pair @ SY3330 @ SY3331 ) @ SV34 )
| ( in @ SY3330 @ SY3329 ) )
| ~ ! [SY3332: $i] :
( ~ ( in @ SY3332 @ SY3329 )
| ( in @ ( ordered_pair @ SY3332 @ ( sK21_D @ SY3332 @ SY3329 @ SV34 ) ) @ SV34 ) ) ) ) )
= $true )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[770]) ).
thf(841,plain,
! [SV44: $i] :
( ( ( ~ ! [SY3365: $i,SY3366: $i] :
( ( sK39_B @ SV44 )
!= ( ordered_pair @ SY3365 @ SY3366 ) ) )
= $false )
| ( ( relation @ SV44 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[771]) ).
thf(842,plain,
! [SV44: $i] :
( ( ( ~ ( in @ ( sK39_B @ SV44 ) @ SV44 ) )
= $false )
| ( ( relation @ SV44 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[771]) ).
thf(843,plain,
! [SV45: $i,SV97: $i] :
( ( ( ( SV97
= ( ordered_pair @ ( sK37_C @ SV97 @ SV45 ) @ ( sK38_SY3111 @ SV97 @ SV45 ) ) )
| ~ ( in @ SV97 @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(844,plain,
! [SV4: $i,SV98: $i] :
( ( ( ~ ( relation @ SV98 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV4 )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV98 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV4 )
| ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV98 ) ) )
| ( SV4 = SV98 ) )
= $true )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(845,plain,
! [SV4: $i,SV99: $i] :
( ( ( ~ ( relation @ SV99 )
| ( SV4 != SV99 )
| ~ ( ~ ! [SY3455: $i,SY3456: $i] :
( ~ ( in @ ( ordered_pair @ SY3455 @ SY3456 ) @ SV4 )
| ( in @ ( ordered_pair @ SY3455 @ SY3456 ) @ SV99 ) )
| ~ ! [SY3457: $i,SY3458: $i] :
( ~ ( in @ ( ordered_pair @ SY3457 @ SY3458 ) @ SV99 )
| ( in @ ( ordered_pair @ SY3457 @ SY3458 ) @ SV4 ) ) ) )
= $true )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(846,plain,
! [SV5: $i,SV100: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SV100 @ SV5 ) @ SV100 )
| ~ ( in @ ( sK4_SY3086 @ SV100 @ SV5 ) @ SV100 ) )
| ~ ( in @ ( sK5_SY3088 @ SV100 @ SV5 ) @ SV100 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SV100 @ SV5 ) @ ( sK4_SY3086 @ SV100 @ SV5 ) ) @ SV5 ) )
| ~ ( in @ ( ordered_pair @ ( sK4_SY3086 @ SV100 @ SV5 ) @ ( sK5_SY3088 @ SV100 @ SV5 ) ) @ SV5 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK3_C @ SV100 @ SV5 ) @ ( sK5_SY3088 @ SV100 @ SV5 ) ) @ SV5 ) )
| ( is_transitive_in @ SV5 @ SV100 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(847,plain,
! [SV101: $i,SV5: $i] :
( ( ( ~ ( is_transitive_in @ SV5 @ SV101 )
| ! [SY3459: $i,SY3460: $i,SY3461: $i] :
( ~ ( in @ SY3459 @ SV101 )
| ~ ( in @ SY3460 @ SV101 )
| ~ ( in @ SY3461 @ SV101 )
| ~ ( in @ ( ordered_pair @ SY3459 @ SY3460 ) @ SV5 )
| ~ ( in @ ( ordered_pair @ SY3460 @ SY3461 ) @ SV5 )
| ( in @ ( ordered_pair @ SY3459 @ SY3461 ) @ SV5 ) ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(848,plain,
! [SV6: $i,SV60: $i,SV77: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV77 @ SV60 @ SV6 ) )
= $true )
| ( ( ~ ( ~ ! [SY3438: $i] :
~ ( in @ ( ordered_pair @ ( sK59_D @ SV77 @ SV60 @ SV6 ) @ SY3438 ) @ SV77 )
| ~ ( in @ ( sK59_D @ SV77 @ SV60 @ SV6 ) @ SV60 ) )
| ( ( relation_dom_as_subset @ SV60 @ SV6 @ SV77 )
= SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[777]) ).
thf(849,plain,
! [SV6: $i,SV61: $i,SV78: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV78 @ SV61 @ SV6 ) )
= $true )
| ( ( ( ( relation_dom_as_subset @ SV61 @ SV6 @ SV78 )
!= SV61 )
| ! [SY3439: $i] :
( ( in @ ( ordered_pair @ SY3439 @ ( sK58_E @ SY3439 @ SV78 @ SV61 @ SV6 ) ) @ SV78 )
| ~ ( in @ SY3439 @ SV61 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[778]) ).
thf(850,plain,
! [SV7: $i,SV46: $i] :
( ( ( ~ ! [SY3368: $i] :
( ~ ( relation @ SY3368 )
| ~ ( ~ ( ! [SY3369: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3368 @ SV46 @ SV7 ) @ SY3369 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3369 @ ( sK8_SY3089 @ SY3368 @ SV46 @ SV7 ) ) @ SV46 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3368 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SY3368 @ SV46 @ SV7 ) ) @ SY3368 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3368 @ SV46 @ SV7 ) @ ( sK9_SY3093 @ SY3368 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SY3368 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SY3368 @ SV46 @ SV7 ) ) @ SV46 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SY3368 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SY3368 @ SV46 @ SV7 ) ) @ SY3368 ) ) )
| ( SY3368
= ( relation_composition @ SV7 @ SV46 ) ) )
| ~ ! [SY3370: $i] :
( ~ ( relation @ SY3370 )
| ( SY3370
!= ( relation_composition @ SV7 @ SV46 ) )
| ~ ( ~ ! [SY3371: $i,SY3372: $i] :
( ! [SY3373: $i] :
( ~ ( in @ ( ordered_pair @ SY3371 @ SY3373 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3373 @ SY3372 ) @ SV46 ) )
| ( in @ ( ordered_pair @ SY3371 @ SY3372 ) @ SY3370 ) )
| ~ ! [SY3374: $i,SY3375: $i] :
( ~ ( in @ ( ordered_pair @ SY3374 @ SY3375 ) @ SY3370 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3374 @ ( sK6_F @ SY3375 @ SY3374 @ SY3370 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY3375 @ SY3374 @ SY3370 @ SV46 @ SV7 ) @ SY3375 ) @ SV46 ) ) ) ) ) )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[779]) ).
thf(851,plain,
! [SV47: $i,SV62: $i] :
( ( ( relation @ SV62 )
= $false )
| ( ( ~ ( ~ ( ( ( sK52_C @ SV62 @ SV47 )
!= ( sK53_SY3121 @ SV62 @ SV47 ) )
| ~ ( in @ ( sK52_C @ SV62 @ SV47 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) )
| ~ ~ ( ~ ( ( ( sK52_C @ SV62 @ SV47 )
= ( sK53_SY3121 @ SV62 @ SV47 ) )
| ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) )
| ~ ( ( in @ ( sK52_C @ SV62 @ SV47 ) @ SV47 )
| ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) ) ) )
| ( SV62
= ( identity_relation @ SV47 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[780]) ).
thf(852,plain,
! [SV48: $i,SV63: $i] :
( ( ( relation @ SV63 )
= $false )
| ( ( ( SV63
!= ( identity_relation @ SV48 ) )
| ~ ( ~ ! [SY3409: $i,SY3410: $i] :
( ( SY3409 != SY3410 )
| ~ ( in @ SY3409 @ SV48 )
| ( in @ ( ordered_pair @ SY3409 @ SY3410 ) @ SV63 ) )
| ~ ~ ( ~ ! [SY3411: $i,SY3412: $i] :
( ~ ( in @ ( ordered_pair @ SY3411 @ SY3412 ) @ SV63 )
| ( SY3411 = SY3412 ) )
| ~ ! [SY3413: $i] :
( ! [SY3414: $i] :
~ ( in @ ( ordered_pair @ SY3413 @ SY3414 ) @ SV63 )
| ( in @ SY3413 @ SV48 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[781]) ).
thf(853,plain,
! [SV49: $i,SV42: $i,SV8: $i] :
( ( ( ~ ! [SY3160: $i] :
( ~ ( ( SV8
!= ( ordered_pair @ ( sK40_C @ SY3160 @ SV8 ) @ ( sK41_SY3114 @ SY3160 @ SV8 ) ) )
| ~ ( ( SY3160
!= ( sK40_C @ SY3160 @ SV8 ) ) ) )
| ( SY3160
= ( pair_first @ SV8 ) ) ) )
= $false )
| ( ( SV8
= ( ordered_pair @ SV42 @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[782]) ).
thf(854,plain,
! [SV49: $i,SV42: $i,SV8: $i] :
( ( ( ~ ! [SY3161: $i] :
( ( SY3161
!= ( pair_first @ SV8 ) )
| ! [SY3162: $i] :
( ! [SY3163: $i] :
( SV8
!= ( ordered_pair @ SY3162 @ SY3163 ) )
| ( SY3161 = SY3162 ) ) ) )
= $false )
| ( ( SV8
= ( ordered_pair @ SV42 @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[782]) ).
thf(855,plain,
! [SV37: $i,SV79: $i,SV9: $i,SV102: $i] :
( ( ~ ( relation @ SV102 )
| ~ ( in @ SV9 @ SV79 )
| ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ SV102 )
| ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SV79 ) @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(856,plain,
! [SV37: $i,SV9: $i] :
( ( ~ ! [SY3335: $i,SY3336: $i] :
( ~ ( relation @ SY3336 )
| ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SY3335 ) @ SY3336 ) )
| ( in @ SV9 @ SY3335 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[784]) ).
thf(857,plain,
! [SV37: $i,SV9: $i] :
( ( ~ ! [SY3337: $i,SY3338: $i] :
( ~ ( relation @ SY3338 )
| ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SY3337 ) @ SY3338 ) )
| ( in @ ( ordered_pair @ SV9 @ SV37 ) @ SY3338 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[784]) ).
thf(858,plain,
! [SV64: $i,SV10: $i,SV80: $i] :
( ( ( ~ ( relation @ SV80 ) )
= $true )
| ( ( ! [SY3441: $i] :
( ~ ( in @ SY3441 @ ( relation_rng @ SV80 ) )
| ~ ( in @ ( ordered_pair @ SV10 @ SY3441 ) @ SV80 )
| ~ ( in @ SY3441 @ SV64 ) )
| ( in @ SV10 @ ( relation_inverse_image @ SV80 @ SV64 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[785]) ).
thf(859,plain,
! [SV65: $i,SV10: $i,SV81: $i] :
( ( ( ~ ( relation @ SV81 ) )
= $true )
| ( ( ~ ( in @ SV10 @ ( relation_inverse_image @ SV81 @ SV65 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_D @ SV81 @ SV65 @ SV10 ) @ ( relation_rng @ SV81 ) )
| ~ ( in @ ( ordered_pair @ SV10 @ ( sK60_D @ SV81 @ SV65 @ SV10 ) ) @ SV81 ) )
| ~ ( in @ ( sK60_D @ SV81 @ SV65 @ SV10 ) @ SV65 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[786]) ).
thf(860,plain,
! [SV82: $i,SV66: $i,SV11: $i] :
( ( ( ~ ( ~ ( ! [SY3442: $i,SY3443: $i] :
( ~ ( in @ SY3442 @ SV11 )
| ~ ( in @ SY3443 @ SV66 )
| ( ( sK28_D @ SV82 @ SV66 @ SV11 )
!= ( ordered_pair @ SY3442 @ SY3443 ) ) )
| ~ ( in @ ( sK28_D @ SV82 @ SV66 @ SV11 ) @ SV82 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY3106 @ SV82 @ SV66 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK30_SY3108 @ SV82 @ SV66 @ SV11 ) @ SV66 ) )
| ( ( sK28_D @ SV82 @ SV66 @ SV11 )
!= ( ordered_pair @ ( sK29_SY3106 @ SV82 @ SV66 @ SV11 ) @ ( sK30_SY3108 @ SV82 @ SV66 @ SV11 ) ) ) )
| ( in @ ( sK28_D @ SV82 @ SV66 @ SV11 ) @ SV82 ) ) ) )
= $true )
| ( ( SV82
= ( cartesian_product2 @ SV11 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[787]) ).
thf(861,plain,
! [SV67: $i,SV11: $i,SV83: $i] :
( ( ( ( SV83
!= ( cartesian_product2 @ SV11 @ SV67 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3444: $i] :
( ! [SY3423: $i,SY3424: $i] :
( ~ ( in @ SY3423 @ SV11 )
| ~ ( in @ SY3424 @ SV67 )
| ( SY3444
!= ( ordered_pair @ SY3423 @ SY3424 ) ) )
| ( in @ SY3444 @ SV83 ) )
| ~ ! [SY3447: $i] :
( ~ ( in @ SY3447 @ SV83 )
| ~ ( ~ ~ ( ~ ( in @ ( sK26_E @ SY3447 @ SV83 @ SV67 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK27_SY3103 @ SY3447 @ SV83 @ SV67 @ SV11 ) @ SV67 ) )
| ( SY3447
!= ( ordered_pair @ ( sK26_E @ SY3447 @ SV83 @ SV67 @ SV11 ) @ ( sK27_SY3103 @ SY3447 @ SV83 @ SV67 @ SV11 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[788]) ).
thf(862,plain,
! [SV68: $i,SV12: $i,SV84: $i] :
( ( ( ~ ( relation @ SV84 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV12 @ SV68 ) @ SV84 )
| ( in @ SV12 @ ( relation_field @ SV84 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[789]) ).
thf(863,plain,
! [SV69: $i,SV12: $i,SV85: $i] :
( ( ( ~ ( relation @ SV85 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV12 @ SV69 ) @ SV85 )
| ( in @ SV69 @ ( relation_field @ SV85 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[790]) ).
thf(864,plain,
! [SV50: $i,SV43: $i,SV13: $i] :
( ( ( ~ ! [SY3192: $i] :
( ~ ( ( SV13
!= ( ordered_pair @ ( sK33_C @ SY3192 @ SV13 ) @ ( sK34_SY3110 @ SY3192 @ SV13 ) ) )
| ~ ( ( SY3192
!= ( sK34_SY3110 @ SY3192 @ SV13 ) ) ) )
| ( SY3192
= ( pair_second @ SV13 ) ) ) )
= $false )
| ( ( SV13
= ( ordered_pair @ SV43 @ SV50 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[791]) ).
thf(865,plain,
! [SV50: $i,SV43: $i,SV13: $i] :
( ( ( ~ ! [SY3193: $i] :
( ( SY3193
!= ( pair_second @ SV13 ) )
| ! [SY3194: $i,SY3195: $i] :
( ( SV13
!= ( ordered_pair @ SY3194 @ SY3195 ) )
| ( SY3193 = SY3195 ) ) ) )
= $false )
| ( ( SV13
= ( ordered_pair @ SV43 @ SV50 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[791]) ).
thf(866,plain,
! [SV14: $i,SV103: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK14_C @ SV103 @ SV14 )
!= ( sK15_SY3096 @ SV103 @ SV14 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SV103 @ SV14 ) @ SV103 )
| ~ ( in @ ( sK15_SY3096 @ SV103 @ SV14 ) @ SV103 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK14_C @ SV103 @ SV14 ) @ ( sK15_SY3096 @ SV103 @ SV14 ) ) @ SV14 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK15_SY3096 @ SV103 @ SV14 ) @ ( sK14_C @ SV103 @ SV14 ) ) @ SV14 ) )
| ( is_connected_in @ SV14 @ SV103 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(867,plain,
! [SV104: $i,SV14: $i] :
( ( ( ~ ( is_connected_in @ SV14 @ SV104 )
| ! [SY3462: $i,SY3463: $i] :
( ( SY3462 = SY3463 )
| ~ ( in @ SY3462 @ SV104 )
| ~ ( in @ SY3463 @ SV104 )
| ( in @ ( ordered_pair @ SY3462 @ SY3463 ) @ SV14 )
| ( in @ ( ordered_pair @ SY3463 @ SY3462 ) @ SV14 ) ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(868,plain,
! [SV70: $i,SV15: $i,SV86: $i] :
( ( ( ~ ( relation @ SV86 ) )
= $true )
| ( ( ! [SY3448: $i] :
( ~ ( in @ SY3448 @ ( relation_dom @ SV86 ) )
| ~ ( in @ ( ordered_pair @ SY3448 @ SV15 ) @ SV86 )
| ~ ( in @ SY3448 @ SV70 ) )
| ( in @ SV15 @ ( relation_image @ SV86 @ SV70 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[794]) ).
thf(869,plain,
! [SV71: $i,SV15: $i,SV87: $i] :
( ( ( ~ ( relation @ SV87 ) )
= $true )
| ( ( ~ ( in @ SV15 @ ( relation_image @ SV87 @ SV71 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK61_D @ SV87 @ SV71 @ SV15 ) @ ( relation_dom @ SV87 ) )
| ~ ( in @ ( ordered_pair @ ( sK61_D @ SV87 @ SV71 @ SV15 ) @ SV15 ) @ SV87 ) )
| ~ ( in @ ( sK61_D @ SV87 @ SV71 @ SV15 ) @ SV71 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[795]) ).
thf(870,plain,
! [SV16: $i,SV105: $i] :
( ( ( ! [SY3464: $i] :
( ~ ( ~ ( ! [SY3465: $i] :
( ~ ( in @ ( ordered_pair @ SY3465 @ ( sK46_D @ SY3464 @ SV105 @ SV16 ) ) @ SV16 )
| ~ ( in @ SY3465 @ SV105 ) )
| ~ ( in @ ( sK46_D @ SY3464 @ SV105 @ SV16 ) @ SY3464 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SY3464 @ SV105 @ SV16 ) @ ( sK46_D @ SY3464 @ SV105 @ SV16 ) ) @ SV16 )
| ~ ( in @ ( sK47_SY3118 @ SY3464 @ SV105 @ SV16 ) @ SV105 ) )
| ( in @ ( sK46_D @ SY3464 @ SV105 @ SV16 ) @ SY3464 ) ) )
| ( SY3464
= ( relation_image @ SV16 @ SV105 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(871,plain,
! [SV106: $i,SV16: $i] :
( ( ( ! [SY3466: $i] :
( ( SY3466
!= ( relation_image @ SV16 @ SV106 ) )
| ~ ( ~ ! [SY3467: $i] :
( ! [SY3468: $i] :
( ~ ( in @ ( ordered_pair @ SY3468 @ SY3467 ) @ SV16 )
| ~ ( in @ SY3468 @ SV106 ) )
| ( in @ SY3467 @ SY3466 ) )
| ~ ! [SY3469: $i] :
( ~ ( in @ SY3469 @ SY3466 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SY3469 @ SY3466 @ SV106 @ SV16 ) @ SY3469 ) @ SV16 )
| ~ ( in @ ( sK45_E @ SY3469 @ SY3466 @ SV106 @ SV16 ) @ SV106 ) ) ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(872,plain,
! [SV51: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK64_B @ SV51 ) @ ( sK65_SY3126 @ SV51 ) ) @ SV51 )
| ~ ( in @ ( ordered_pair @ ( sK65_SY3126 @ SV51 ) @ ( sK64_B @ SV51 ) ) @ SV51 ) )
| ~ ( ( ( sK64_B @ SV51 )
!= ( sK65_SY3126 @ SV51 ) ) ) ) )
= $true )
| ( ( antisymmetric @ SV51 )
= $true )
| ( ( relation @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[798]) ).
thf(873,plain,
! [SV52: $i] :
( ( ( ~ ( antisymmetric @ SV52 ) )
= $true )
| ( ( ! [SY3384: $i,SY3385: $i] :
( ~ ( in @ ( ordered_pair @ SY3384 @ SY3385 ) @ SV52 )
| ~ ( in @ ( ordered_pair @ SY3385 @ SY3384 ) @ SV52 )
| ( SY3384 = SY3385 ) ) )
= $true )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[799]) ).
thf(874,plain,
! [SV17: $i,SV72: $i,SV88: $i] :
( ( ( ~ ( function @ SV88 )
| ~ ( relation @ SV88 ) )
= $true )
| ( ( ( SV72
!= ( apply @ SV88 @ SV17 ) )
| ~ ( in @ SV17 @ ( relation_dom @ SV88 ) )
| ( in @ ( ordered_pair @ SV17 @ SV72 ) @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[800]) ).
thf(875,plain,
! [SV17: $i] :
( ( ! [SY3215: $i,SY3216: $i] :
( ~ ( function @ SY3216 )
| ~ ( relation @ SY3216 )
| ~ ( in @ ( ordered_pair @ SV17 @ SY3215 ) @ SY3216 )
| ( SY3215
= ( apply @ SY3216 @ SV17 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[801]) ).
thf(876,plain,
! [SV17: $i] :
( ( ! [SY3217: $i,SY3218: $i] :
( ~ ( function @ SY3218 )
| ~ ( relation @ SY3218 )
| ~ ( in @ ( ordered_pair @ SV17 @ SY3217 ) @ SY3218 )
| ( in @ SV17 @ ( relation_dom @ SY3218 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[802]) ).
thf(877,plain,
! [SV18: $i,SV107: $i] :
( ( ( ! [SY3470: $i] :
( ~ ( ~ ( ( ( sK35_D @ SY3470 @ SV107 @ SV18 )
= SV107 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SY3470 @ SV107 @ SV18 ) @ SV107 ) @ SV18 )
| ~ ( in @ ( sK35_D @ SY3470 @ SV107 @ SV18 ) @ SY3470 ) )
| ~ ~ ( ~ ( ( ( sK35_D @ SY3470 @ SV107 @ SV18 )
!= SV107 )
| ( in @ ( sK35_D @ SY3470 @ SV107 @ SV18 ) @ SY3470 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SY3470 @ SV107 @ SV18 ) @ SV107 ) @ SV18 )
| ( in @ ( sK35_D @ SY3470 @ SV107 @ SV18 ) @ SY3470 ) ) ) )
| ( SY3470
= ( fiber @ SV18 @ SV107 ) ) ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(878,plain,
! [SV108: $i,SV18: $i] :
( ( ( ! [SY3471: $i] :
( ( SY3471
!= ( fiber @ SV18 @ SV108 ) )
| ~ ( ~ ! [SY3472: $i] :
( ( SY3472 = SV108 )
| ~ ( in @ ( ordered_pair @ SY3472 @ SV108 ) @ SV18 )
| ( in @ SY3472 @ SY3471 ) )
| ~ ~ ( ~ ! [SY3473: $i] :
( ~ ( in @ SY3473 @ SY3471 )
| ( SY3473 != SV108 ) )
| ~ ! [SY3474: $i] :
( ~ ( in @ SY3474 @ SY3471 )
| ( in @ ( ordered_pair @ SY3474 @ SV108 ) @ SV18 ) ) ) ) ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(879,plain,
! [SV19: $i,SV109: $i] :
( ( ( ~ ( ~ ( in @ ( sK36_C @ SV109 @ SV19 ) @ SV109 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SV109 @ SV19 ) @ ( sK36_C @ SV109 @ SV19 ) ) @ SV19 ) )
| ( is_reflexive_in @ SV19 @ SV109 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(880,plain,
! [SV110: $i,SV19: $i] :
( ( ( ~ ( is_reflexive_in @ SV19 @ SV110 )
| ! [SY3475: $i] :
( ~ ( in @ SY3475 @ SV110 )
| ( in @ ( ordered_pair @ SY3475 @ SY3475 ) @ SV19 ) ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(881,plain,
! [SV20: $i,SV111: $i] :
( ( ( ~ ( relation @ SV111 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SV111 @ SV20 ) @ ( sK13_SY3095 @ SV111 @ SV20 ) ) @ SV111 )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV111 @ SV20 ) @ ( sK12_C @ SV111 @ SV20 ) ) @ SV20 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SV111 @ SV20 ) @ ( sK13_SY3095 @ SV111 @ SV20 ) ) @ SV111 )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV111 @ SV20 ) @ ( sK12_C @ SV111 @ SV20 ) ) @ SV20 ) ) )
| ( SV111
= ( relation_inverse @ SV20 ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(882,plain,
! [SV20: $i,SV112: $i] :
( ( ( ~ ( relation @ SV112 )
| ( SV112
!= ( relation_inverse @ SV20 ) )
| ~ ( ~ ! [SY3476: $i,SY3477: $i] :
( ~ ( in @ ( ordered_pair @ SY3476 @ SY3477 ) @ SV112 )
| ( in @ ( ordered_pair @ SY3477 @ SY3476 ) @ SV20 ) )
| ~ ! [SY3478: $i,SY3479: $i] :
( ~ ( in @ ( ordered_pair @ SY3479 @ SY3478 ) @ SV20 )
| ( in @ ( ordered_pair @ SY3478 @ SY3479 ) @ SV112 ) ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(883,plain,
! [SV21: $i,SV38: $i] :
( ( ( ! [SY3339: $i] :
( ~ ( relation @ SY3339 )
| ~ ( ~ ( ~ ( in @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) @ SV21 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SY3339 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) ) @ SV38 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SY3339 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) ) @ SY3339 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK48_D @ SY3339 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) ) @ SY3339 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SY3339 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) ) @ SV38 )
| ( in @ ( ordered_pair @ ( sK48_D @ SY3339 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SY3339 @ SV38 @ SV21 ) ) @ SY3339 ) ) ) )
| ( SY3339
= ( relation_rng_restriction @ SV21 @ SV38 ) ) ) )
= $true )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[809]) ).
thf(884,plain,
! [SV38: $i,SV21: $i] :
( ( ( ! [SY3340: $i] :
( ~ ( relation @ SY3340 )
| ( SY3340
!= ( relation_rng_restriction @ SV21 @ SV38 ) )
| ~ ( ~ ! [SY3341: $i,SY3342: $i] :
( ~ ( in @ SY3342 @ SV21 )
| ~ ( in @ ( ordered_pair @ SY3341 @ SY3342 ) @ SV38 )
| ( in @ ( ordered_pair @ SY3341 @ SY3342 ) @ SY3340 ) )
| ~ ~ ( ~ ! [SY3240: $i,SY3241: $i] :
( ~ ( in @ ( ordered_pair @ SY3240 @ SY3241 ) @ SY3340 )
| ( in @ SY3241 @ SV21 ) )
| ~ ! [SY3345: $i,SY3346: $i] :
( ~ ( in @ ( ordered_pair @ SY3345 @ SY3346 ) @ SY3340 )
| ( in @ ( ordered_pair @ SY3345 @ SY3346 ) @ SV38 ) ) ) ) ) )
= $true )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[810]) ).
thf(885,plain,
! [SV22: $i,SV113: $i] :
( ( ( ~ ( ~ ( ! [SY3480: $i] :
~ ( in @ ( ordered_pair @ SY3480 @ ( sK17_C @ SV113 @ SV22 ) ) @ SV22 )
| ~ ( in @ ( sK17_C @ SV113 @ SV22 ) @ SV113 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK18_SY3098 @ SV113 @ SV22 ) @ ( sK17_C @ SV113 @ SV22 ) ) @ SV22 )
| ( in @ ( sK17_C @ SV113 @ SV22 ) @ SV113 ) ) )
| ( SV113
= ( relation_rng @ SV22 ) ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(886,plain,
! [SV22: $i,SV114: $i] :
( ( ( ( SV114
!= ( relation_rng @ SV22 ) )
| ~ ( ~ ! [SY3481: $i] :
( ! [SY3248: $i] :
~ ( in @ ( ordered_pair @ SY3248 @ SY3481 ) @ SV22 )
| ( in @ SY3481 @ SV114 ) )
| ~ ! [SY3483: $i] :
( ~ ( in @ SY3483 @ SV114 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3483 @ SV114 @ SV22 ) @ SY3483 ) @ SV22 ) ) ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(887,plain,
! [SV23: $i,SV115: $i] :
( ( ( ~ ( relation @ SV115 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV115 @ SV23 ) @ ( sK25_SY3102 @ SV115 @ SV23 ) ) @ SV23 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SV115 @ SV23 ) @ ( sK25_SY3102 @ SV115 @ SV23 ) ) @ SV115 ) )
| ( subset @ SV23 @ SV115 ) )
= $true )
| ( ( relation @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(888,plain,
! [SV23: $i,SV116: $i] :
( ( ( ~ ( relation @ SV116 )
| ~ ( subset @ SV23 @ SV116 )
| ! [SY3484: $i,SY3485: $i] :
( ~ ( in @ ( ordered_pair @ SY3484 @ SY3485 ) @ SV23 )
| ( in @ ( ordered_pair @ SY3484 @ SY3485 ) @ SV116 ) ) )
= $true )
| ( ( relation @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(889,plain,
! [SV24: $i,SV117: $i] :
( ( ( ! [SY3486: $i] :
( ~ ( relation @ SY3486 )
| ~ ( ~ ( ~ ( in @ ( sK50_D @ SY3486 @ SV117 @ SV24 ) @ SV117 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SY3486 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SY3486 @ SV117 @ SV24 ) ) @ SV24 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SY3486 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SY3486 @ SV117 @ SV24 ) ) @ SY3486 ) )
| ~ ~ ( ~ ( ( in @ ( sK50_D @ SY3486 @ SV117 @ SV24 ) @ SV117 )
| ( in @ ( ordered_pair @ ( sK50_D @ SY3486 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SY3486 @ SV117 @ SV24 ) ) @ SY3486 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SY3486 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SY3486 @ SV117 @ SV24 ) ) @ SV24 )
| ( in @ ( ordered_pair @ ( sK50_D @ SY3486 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SY3486 @ SV117 @ SV24 ) ) @ SY3486 ) ) ) )
| ( SY3486
= ( relation_dom_restriction @ SV24 @ SV117 ) ) ) )
= $true )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(890,plain,
! [SV118: $i,SV24: $i] :
( ( ( ! [SY3487: $i] :
( ~ ( relation @ SY3487 )
| ( SY3487
!= ( relation_dom_restriction @ SV24 @ SV118 ) )
| ~ ( ~ ! [SY3488: $i,SY3489: $i] :
( ~ ( in @ SY3488 @ SV118 )
| ~ ( in @ ( ordered_pair @ SY3488 @ SY3489 ) @ SV24 )
| ( in @ ( ordered_pair @ SY3488 @ SY3489 ) @ SY3487 ) )
| ~ ~ ( ~ ! [SY3490: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SY3490 @ SX4 ) @ SY3487 )
| ( in @ SY3490 @ SV118 ) )
| ~ ! [SY3262: $i,SY3263: $i] :
( ~ ( in @ ( ordered_pair @ SY3262 @ SY3263 ) @ SY3487 )
| ( in @ ( ordered_pair @ SY3262 @ SY3263 ) @ SV24 ) ) ) ) ) )
= $true )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(891,plain,
! [SV89: $i,SV39: $i,SV25: $i] :
( ( ( ! [SY3449: $i] :
( ( ordered_pair @ SV25 @ SV39 )
!= ( ordered_pair @ SV89 @ SY3449 ) ) )
= $true )
| ( ( SV25 = SV89 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[817]) ).
thf(892,plain,
! [SV119: $i,SV90: $i,SV39: $i,SV25: $i] :
( ( ( ( ordered_pair @ SV25 @ SV39 )
!= ( ordered_pair @ SV90 @ SV119 ) )
| ( SV39 = SV119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(893,plain,
! [SV26: $i] :
( ( ( ~ ~ ( ~ ! [SY3269: $i] :
( ~ ( in @ SY3269 @ ( relation_dom @ SV26 ) )
| ! [SY3270: $i] :
( ( SY3270
!= ( apply @ SV26 @ SY3269 ) )
| ( in @ ( ordered_pair @ SY3269 @ SY3270 ) @ SV26 ) ) )
| ~ ! [SY3271: $i] :
( ~ ( in @ SY3271 @ ( relation_dom @ SV26 ) )
| ! [SY3272: $i] :
( ~ ( in @ ( ordered_pair @ SY3271 @ SY3272 ) @ SV26 )
| ( SY3272
= ( apply @ SV26 @ SY3271 ) ) ) ) ) )
= $false )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[819]) ).
thf(894,plain,
! [SV26: $i] :
( ( ( ~ ~ ( ~ ! [SY3273: $i] :
( ( in @ SY3273 @ ( relation_dom @ SV26 ) )
| ! [SY3274: $i] :
( ( SY3274
!= ( apply @ SV26 @ SY3273 ) )
| ( SY3274 = empty_set ) ) )
| ~ ! [SY3275: $i] :
( ( in @ SY3275 @ ( relation_dom @ SV26 ) )
| ! [SY3276: $i] :
( ( SY3276 != empty_set )
| ( SY3276
= ( apply @ SV26 @ SY3275 ) ) ) ) ) )
= $false )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[819]) ).
thf(895,plain,
! [SV53: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK62_B @ SV53 )
!= ( sK63_SY3125 @ SV53 ) ) )
| ~ ~ ( ~ ( in @ ( sK62_B @ SV53 ) @ ( relation_field @ SV53 ) )
| ~ ( in @ ( sK63_SY3125 @ SV53 ) @ ( relation_field @ SV53 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK62_B @ SV53 ) @ ( sK63_SY3125 @ SV53 ) ) @ SV53 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK63_SY3125 @ SV53 ) @ ( sK62_B @ SV53 ) ) @ SV53 ) ) )
= $true )
| ( ( connected @ SV53 )
= $true )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[820]) ).
thf(896,plain,
! [SV54: $i] :
( ( ( ~ ( connected @ SV54 ) )
= $true )
| ( ( ! [SY3386: $i,SY3387: $i] :
( ( SY3386 = SY3387 )
| ~ ( in @ SY3386 @ ( relation_field @ SV54 ) )
| ~ ( in @ SY3387 @ ( relation_field @ SV54 ) )
| ( in @ ( ordered_pair @ SY3386 @ SY3387 ) @ SV54 )
| ( in @ ( ordered_pair @ SY3387 @ SY3386 ) @ SV54 ) ) )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[821]) ).
thf(897,plain,
! [SV27: $i,SV120: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_C @ SV120 @ SV27 ) @ SV120 )
| ~ ( in @ ( sK20_SY3099 @ SV120 @ SV27 ) @ SV120 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SV120 @ SV27 ) @ ( sK20_SY3099 @ SV120 @ SV27 ) ) @ SV27 ) )
| ~ ( in @ ( ordered_pair @ ( sK20_SY3099 @ SV120 @ SV27 ) @ ( sK19_C @ SV120 @ SV27 ) ) @ SV27 ) )
| ~ ( ( ( sK19_C @ SV120 @ SV27 )
!= ( sK20_SY3099 @ SV120 @ SV27 ) ) ) )
| ( is_antisymmetric_in @ SV27 @ SV120 ) )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(898,plain,
! [SV121: $i,SV27: $i] :
( ( ( ~ ( is_antisymmetric_in @ SV27 @ SV121 )
| ! [SY3494: $i,SY3495: $i] :
( ~ ( in @ SY3494 @ SV121 )
| ~ ( in @ SY3495 @ SV121 )
| ~ ( in @ ( ordered_pair @ SY3494 @ SY3495 ) @ SV27 )
| ~ ( in @ ( ordered_pair @ SY3495 @ SY3494 ) @ SV27 )
| ( SY3494 = SY3495 ) ) )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(899,plain,
! [SV122: $i,SV40: $i,SV91: $i,SV28: $i] :
( ( ~ ( in @ SV28 @ SV91 )
| ~ ( in @ SV40 @ SV122 )
| ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SV91 @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(900,plain,
! [SV40: $i,SV28: $i] :
( ( ~ ! [SY3353: $i] :
( ! [SY3354: $i] :
~ ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SY3353 @ SY3354 ) )
| ( in @ SV28 @ SY3353 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[825]) ).
thf(901,plain,
! [SV40: $i,SV28: $i] :
( ( ~ ! [SY3355: $i,SY3356: $i] :
( ~ ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SY3355 @ SY3356 ) )
| ( in @ SV40 @ SY3356 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[825]) ).
thf(902,plain,
! [SV55: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK66_B @ SV55 ) @ ( sK67_SY3127 @ SV55 ) ) @ SV55 )
| ~ ( in @ ( ordered_pair @ ( sK67_SY3127 @ SV55 ) @ ( sK68_SY3129 @ SV55 ) ) @ SV55 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK66_B @ SV55 ) @ ( sK68_SY3129 @ SV55 ) ) @ SV55 ) ) )
= $true )
| ( ( transitive @ SV55 )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[826]) ).
thf(903,plain,
! [SV56: $i] :
( ( ( ~ ( transitive @ SV56 ) )
= $true )
| ( ( ! [SY3388: $i,SY3389: $i,SY3390: $i] :
( ~ ( in @ ( ordered_pair @ SY3388 @ SY3389 ) @ SV56 )
| ~ ( in @ ( ordered_pair @ SY3389 @ SY3390 ) @ SV56 )
| ( in @ ( ordered_pair @ SY3388 @ SY3390 ) @ SV56 ) ) )
= $true )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[827]) ).
thf(904,plain,
! [SV123: $i,SV41: $i,SV92: $i,SV29: $i] :
( ( ~ ( in @ SV29 @ SV92 )
| ~ ( in @ SV41 @ SV123 )
| ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SV92 @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(905,plain,
! [SV41: $i,SV29: $i] :
( ( ~ ! [SY3359: $i] :
( ! [SY3360: $i] :
~ ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SY3359 @ SY3360 ) )
| ( in @ SV29 @ SY3359 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[829]) ).
thf(906,plain,
! [SV41: $i,SV29: $i] :
( ( ~ ! [SY3361: $i,SY3362: $i] :
( ~ ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SY3361 @ SY3362 ) )
| ( in @ SV41 @ SY3362 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[829]) ).
thf(907,plain,
! [SV30: $i,SV124: $i] :
( ( ( ! [SY3496: $i] :
( ~ ( ~ ( ! [SY3497: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ SY3496 @ SV124 @ SV30 ) @ SY3497 ) @ SV30 )
| ~ ( in @ SY3497 @ SV124 ) )
| ~ ( in @ ( sK43_D @ SY3496 @ SV124 @ SV30 ) @ SY3496 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SY3496 @ SV124 @ SV30 ) @ ( sK44_SY3116 @ SY3496 @ SV124 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK44_SY3116 @ SY3496 @ SV124 @ SV30 ) @ SV124 ) )
| ( in @ ( sK43_D @ SY3496 @ SV124 @ SV30 ) @ SY3496 ) ) )
| ( SY3496
= ( relation_inverse_image @ SV30 @ SV124 ) ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(908,plain,
! [SV125: $i,SV30: $i] :
( ( ( ! [SY3498: $i] :
( ( SY3498
!= ( relation_inverse_image @ SV30 @ SV125 ) )
| ~ ( ~ ! [SY3499: $i] :
( ! [SY3500: $i] :
( ~ ( in @ ( ordered_pair @ SY3499 @ SY3500 ) @ SV30 )
| ~ ( in @ SY3500 @ SV125 ) )
| ( in @ SY3499 @ SY3498 ) )
| ~ ! [SY3501: $i] :
( ~ ( in @ SY3501 @ SY3498 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3501 @ ( sK42_E @ SY3501 @ SY3498 @ SV125 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK42_E @ SY3501 @ SY3498 @ SV125 @ SV30 ) @ SV125 ) ) ) ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(909,plain,
! [SV73: $i,SV31: $i,SV93: $i] :
( ( ( ~ ( relation @ SV93 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV31 @ SV73 ) @ SV93 )
| ( in @ SV31 @ ( relation_dom @ SV93 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[832]) ).
thf(910,plain,
! [SV74: $i,SV31: $i,SV94: $i] :
( ( ( ~ ( relation @ SV94 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV31 @ SV74 ) @ SV94 )
| ( in @ SV74 @ ( relation_rng @ SV94 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[833]) ).
thf(911,plain,
! [SV57: $i] :
( ( ( ~ ( ~ ( in @ ( sK69_B @ SV57 ) @ ( relation_field @ SV57 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK69_B @ SV57 ) @ ( sK69_B @ SV57 ) ) @ SV57 ) ) )
= $true )
| ( ( reflexive @ SV57 )
= $true )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[834]) ).
thf(912,plain,
! [SV58: $i] :
( ( ( ~ ( reflexive @ SV58 ) )
= $true )
| ( ( ! [SY3391: $i] :
( ~ ( in @ SY3391 @ ( relation_field @ SV58 ) )
| ( in @ ( ordered_pair @ SY3391 @ SY3391 ) @ SV58 ) ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[835]) ).
thf(913,plain,
! [SV32: $i,SV59: $i] :
( ( ( ~ ! [SY3392: $i] :
( ~ ( function @ SY3392 )
| ~ ( relation @ SY3392 )
| ~ ( ~ ( ~ ( in @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3392 @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) ) @ ( apply @ SY3392 @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) @ SV32 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SY3392 @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) ) @ ( apply @ SY3392 @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) @ SV32 ) ) ) )
| ( ( relation_dom @ SY3392 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SY3392 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SY3392 )
| ( relation_isomorphism @ SV32 @ SV59 @ SY3392 ) )
| ~ ~ ( ~ ! [SY3393: $i] :
( ~ ( function @ SY3393 )
| ~ ( relation @ SY3393 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3393 )
| ~ ( ~ ! [SY3394: $i,SY3395: $i] :
( ~ ( in @ SY3394 @ ( relation_field @ SV32 ) )
| ~ ( in @ SY3395 @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3393 @ SY3394 ) @ ( apply @ SY3393 @ SY3395 ) ) @ SV59 )
| ( in @ ( ordered_pair @ SY3394 @ SY3395 ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3312: $i] :
( ! [SY3313: $i] :
~ ( in @ ( ordered_pair @ SY3312 @ SY3313 ) @ SV32 )
| ( in @ SY3312 @ ( relation_field @ SV32 ) ) )
| ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV32 )
| ( in @ SY3315 @ ( relation_field @ SV32 ) ) ) )
| ~ ! [SY3400: $i,SY3401: $i] :
( ~ ( in @ ( ordered_pair @ SY3400 @ SY3401 ) @ SV32 )
| ( in @ ( ordered_pair @ ( apply @ SY3393 @ SY3400 ) @ ( apply @ SY3393 @ SY3401 ) ) @ SV59 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3402: $i] :
( ~ ( function @ SY3402 )
| ~ ( relation @ SY3402 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3402 )
| ( ( relation_dom @ SY3402 )
= ( relation_field @ SV32 ) ) )
| ~ ! [SY3403: $i] :
( ~ ( function @ SY3403 )
| ~ ( relation @ SY3403 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3403 )
| ( ( relation_rng @ SY3403 )
= ( relation_field @ SV59 ) ) ) )
| ~ ! [SY3404: $i] :
( ~ ( function @ SY3404 )
| ~ ( relation @ SY3404 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3404 )
| ( one_to_one @ SY3404 ) ) ) ) )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[836]) ).
thf(914,plain,
! [SV75: $i,SV33: $i,SV95: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV95 @ SV33 @ SV75 ) )
= $true )
| ( ( ~ ( ~ ! [SY3453: $i] :
~ ( in @ ( ordered_pair @ SY3453 @ ( sK57_D @ SV95 @ SV75 @ SV33 ) ) @ SV95 )
| ~ ( in @ ( sK57_D @ SV95 @ SV75 @ SV33 ) @ SV75 ) )
| ( ( relation_rng_as_subset @ SV33 @ SV75 @ SV95 )
= SV75 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[837]) ).
thf(915,plain,
! [SV76: $i,SV33: $i,SV96: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV96 @ SV33 @ SV76 ) )
= $true )
| ( ( ( ( relation_rng_as_subset @ SV33 @ SV76 @ SV96 )
!= SV76 )
| ! [SY3454: $i] :
( ( in @ ( ordered_pair @ ( sK56_E @ SY3454 @ SV96 @ SV76 @ SV33 ) @ SY3454 ) @ SV96 )
| ~ ( in @ SY3454 @ SV76 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[838]) ).
thf(916,plain,
! [SV34: $i,SV126: $i] :
( ( ( ~ ( ~ ( ! [SY3502: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SV126 @ SV34 ) @ SY3502 ) @ SV34 )
| ~ ( in @ ( sK22_C @ SV126 @ SV34 ) @ SV126 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SV126 @ SV34 ) @ ( sK23_SY3101 @ SV126 @ SV34 ) ) @ SV34 )
| ( in @ ( sK22_C @ SV126 @ SV34 ) @ SV126 ) ) )
| ( SV126
= ( relation_dom @ SV34 ) ) )
= $true )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(917,plain,
! [SV34: $i,SV127: $i] :
( ( ( ( SV127
!= ( relation_dom @ SV34 ) )
| ~ ( ~ ! [SY3503: $i] :
( ! [SY3331: $i] :
~ ( in @ ( ordered_pair @ SY3503 @ SY3331 ) @ SV34 )
| ( in @ SY3503 @ SV127 ) )
| ~ ! [SY3505: $i] :
( ~ ( in @ SY3505 @ SV127 )
| ( in @ ( ordered_pair @ SY3505 @ ( sK21_D @ SY3505 @ SV127 @ SV34 ) ) @ SV34 ) ) ) )
= $true )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(918,plain,
! [SV44: $i] :
( ( ( ! [SY3365: $i,SY3366: $i] :
( ( sK39_B @ SV44 )
!= ( ordered_pair @ SY3365 @ SY3366 ) ) )
= $true )
| ( ( relation @ SV44 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[841]) ).
thf(919,plain,
! [SV44: $i] :
( ( ( in @ ( sK39_B @ SV44 ) @ SV44 )
= $true )
| ( ( relation @ SV44 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[842]) ).
thf(920,plain,
! [SV45: $i,SV97: $i] :
( ( ( SV97
= ( ordered_pair @ ( sK37_C @ SV97 @ SV45 ) @ ( sK38_SY3111 @ SV97 @ SV45 ) ) )
= $true )
| ( ( ~ ( in @ SV97 @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[843]) ).
thf(921,plain,
! [SV4: $i,SV98: $i] :
( ( ( ~ ( relation @ SV98 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV4 )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV98 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV4 )
| ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV98 ) ) )
| ( SV4 = SV98 ) )
= $true )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[844]) ).
thf(922,plain,
! [SV4: $i,SV99: $i] :
( ( ( ~ ( relation @ SV99 ) )
= $true )
| ( ( ( SV4 != SV99 )
| ~ ( ~ ! [SY3455: $i,SY3456: $i] :
( ~ ( in @ ( ordered_pair @ SY3455 @ SY3456 ) @ SV4 )
| ( in @ ( ordered_pair @ SY3455 @ SY3456 ) @ SV99 ) )
| ~ ! [SY3457: $i,SY3458: $i] :
( ~ ( in @ ( ordered_pair @ SY3457 @ SY3458 ) @ SV99 )
| ( in @ ( ordered_pair @ SY3457 @ SY3458 ) @ SV4 ) ) ) )
= $true )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[845]) ).
thf(923,plain,
! [SV5: $i,SV100: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SV100 @ SV5 ) @ SV100 )
| ~ ( in @ ( sK4_SY3086 @ SV100 @ SV5 ) @ SV100 ) )
| ~ ( in @ ( sK5_SY3088 @ SV100 @ SV5 ) @ SV100 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SV100 @ SV5 ) @ ( sK4_SY3086 @ SV100 @ SV5 ) ) @ SV5 ) )
| ~ ( in @ ( ordered_pair @ ( sK4_SY3086 @ SV100 @ SV5 ) @ ( sK5_SY3088 @ SV100 @ SV5 ) ) @ SV5 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK3_C @ SV100 @ SV5 ) @ ( sK5_SY3088 @ SV100 @ SV5 ) ) @ SV5 ) ) )
= $true )
| ( ( is_transitive_in @ SV5 @ SV100 )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[846]) ).
thf(924,plain,
! [SV101: $i,SV5: $i] :
( ( ( ~ ( is_transitive_in @ SV5 @ SV101 ) )
= $true )
| ( ( ! [SY3459: $i,SY3460: $i,SY3461: $i] :
( ~ ( in @ SY3459 @ SV101 )
| ~ ( in @ SY3460 @ SV101 )
| ~ ( in @ SY3461 @ SV101 )
| ~ ( in @ ( ordered_pair @ SY3459 @ SY3460 ) @ SV5 )
| ~ ( in @ ( ordered_pair @ SY3460 @ SY3461 ) @ SV5 )
| ( in @ ( ordered_pair @ SY3459 @ SY3461 ) @ SV5 ) ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[847]) ).
thf(925,plain,
! [SV6: $i,SV60: $i,SV77: $i] :
( ( ( relation_of2_as_subset @ SV77 @ SV60 @ SV6 )
= $false )
| ( ( ~ ( ~ ! [SY3438: $i] :
~ ( in @ ( ordered_pair @ ( sK59_D @ SV77 @ SV60 @ SV6 ) @ SY3438 ) @ SV77 )
| ~ ( in @ ( sK59_D @ SV77 @ SV60 @ SV6 ) @ SV60 ) )
| ( ( relation_dom_as_subset @ SV60 @ SV6 @ SV77 )
= SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[848]) ).
thf(926,plain,
! [SV6: $i,SV61: $i,SV78: $i] :
( ( ( relation_of2_as_subset @ SV78 @ SV61 @ SV6 )
= $false )
| ( ( ( ( relation_dom_as_subset @ SV61 @ SV6 @ SV78 )
!= SV61 )
| ! [SY3439: $i] :
( ( in @ ( ordered_pair @ SY3439 @ ( sK58_E @ SY3439 @ SV78 @ SV61 @ SV6 ) ) @ SV78 )
| ~ ( in @ SY3439 @ SV61 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[849]) ).
thf(927,plain,
! [SV7: $i,SV46: $i] :
( ( ( ~ ! [SY3368: $i] :
( ~ ( relation @ SY3368 )
| ~ ( ~ ( ! [SY3369: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3368 @ SV46 @ SV7 ) @ SY3369 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3369 @ ( sK8_SY3089 @ SY3368 @ SV46 @ SV7 ) ) @ SV46 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3368 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SY3368 @ SV46 @ SV7 ) ) @ SY3368 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3368 @ SV46 @ SV7 ) @ ( sK9_SY3093 @ SY3368 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SY3368 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SY3368 @ SV46 @ SV7 ) ) @ SV46 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SY3368 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SY3368 @ SV46 @ SV7 ) ) @ SY3368 ) ) )
| ( SY3368
= ( relation_composition @ SV7 @ SV46 ) ) ) )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[850]) ).
thf(928,plain,
! [SV46: $i,SV7: $i] :
( ( ( ~ ! [SY3370: $i] :
( ~ ( relation @ SY3370 )
| ( SY3370
!= ( relation_composition @ SV7 @ SV46 ) )
| ~ ( ~ ! [SY3371: $i,SY3372: $i] :
( ! [SY3373: $i] :
( ~ ( in @ ( ordered_pair @ SY3371 @ SY3373 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3373 @ SY3372 ) @ SV46 ) )
| ( in @ ( ordered_pair @ SY3371 @ SY3372 ) @ SY3370 ) )
| ~ ! [SY3374: $i,SY3375: $i] :
( ~ ( in @ ( ordered_pair @ SY3374 @ SY3375 ) @ SY3370 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3374 @ ( sK6_F @ SY3375 @ SY3374 @ SY3370 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY3375 @ SY3374 @ SY3370 @ SV46 @ SV7 ) @ SY3375 ) @ SV46 ) ) ) ) ) )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[850]) ).
thf(929,plain,
! [SV47: $i,SV62: $i] :
( ( ( ~ ( ~ ( ( ( sK52_C @ SV62 @ SV47 )
!= ( sK53_SY3121 @ SV62 @ SV47 ) )
| ~ ( in @ ( sK52_C @ SV62 @ SV47 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) )
| ~ ~ ( ~ ( ( ( sK52_C @ SV62 @ SV47 )
= ( sK53_SY3121 @ SV62 @ SV47 ) )
| ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) )
| ~ ( ( in @ ( sK52_C @ SV62 @ SV47 ) @ SV47 )
| ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) ) ) ) )
= $true )
| ( ( SV62
= ( identity_relation @ SV47 ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[851]) ).
thf(930,plain,
! [SV48: $i,SV63: $i] :
( ( ( ( SV63
!= ( identity_relation @ SV48 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3409: $i,SY3410: $i] :
( ( SY3409 != SY3410 )
| ~ ( in @ SY3409 @ SV48 )
| ( in @ ( ordered_pair @ SY3409 @ SY3410 ) @ SV63 ) )
| ~ ~ ( ~ ! [SY3411: $i,SY3412: $i] :
( ~ ( in @ ( ordered_pair @ SY3411 @ SY3412 ) @ SV63 )
| ( SY3411 = SY3412 ) )
| ~ ! [SY3413: $i] :
( ! [SY3414: $i] :
~ ( in @ ( ordered_pair @ SY3413 @ SY3414 ) @ SV63 )
| ( in @ SY3413 @ SV48 ) ) ) ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[852]) ).
thf(931,plain,
! [SV49: $i,SV42: $i,SV8: $i] :
( ( ( ! [SY3160: $i] :
( ~ ( ( SV8
!= ( ordered_pair @ ( sK40_C @ SY3160 @ SV8 ) @ ( sK41_SY3114 @ SY3160 @ SV8 ) ) )
| ~ ( ( SY3160
!= ( sK40_C @ SY3160 @ SV8 ) ) ) )
| ( SY3160
= ( pair_first @ SV8 ) ) ) )
= $true )
| ( ( SV8
= ( ordered_pair @ SV42 @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[853]) ).
thf(932,plain,
! [SV49: $i,SV42: $i,SV8: $i] :
( ( ( ! [SY3161: $i] :
( ( SY3161
!= ( pair_first @ SV8 ) )
| ! [SY3162: $i] :
( ! [SY3163: $i] :
( SV8
!= ( ordered_pair @ SY3162 @ SY3163 ) )
| ( SY3161 = SY3162 ) ) ) )
= $true )
| ( ( SV8
= ( ordered_pair @ SV42 @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[854]) ).
thf(933,plain,
! [SV37: $i,SV79: $i,SV9: $i,SV102: $i] :
( ( ( ~ ( relation @ SV102 ) )
= $true )
| ( ( ~ ( in @ SV9 @ SV79 )
| ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ SV102 )
| ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SV79 ) @ SV102 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[855]) ).
thf(934,plain,
! [SV37: $i,SV9: $i] :
( ( ! [SY3335: $i,SY3336: $i] :
( ~ ( relation @ SY3336 )
| ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SY3335 ) @ SY3336 ) )
| ( in @ SV9 @ SY3335 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[856]) ).
thf(935,plain,
! [SV37: $i,SV9: $i] :
( ( ! [SY3337: $i,SY3338: $i] :
( ~ ( relation @ SY3338 )
| ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SY3337 ) @ SY3338 ) )
| ( in @ ( ordered_pair @ SV9 @ SV37 ) @ SY3338 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[857]) ).
thf(936,plain,
! [SV64: $i,SV10: $i,SV80: $i] :
( ( ( relation @ SV80 )
= $false )
| ( ( ! [SY3441: $i] :
( ~ ( in @ SY3441 @ ( relation_rng @ SV80 ) )
| ~ ( in @ ( ordered_pair @ SV10 @ SY3441 ) @ SV80 )
| ~ ( in @ SY3441 @ SV64 ) )
| ( in @ SV10 @ ( relation_inverse_image @ SV80 @ SV64 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[858]) ).
thf(937,plain,
! [SV65: $i,SV10: $i,SV81: $i] :
( ( ( relation @ SV81 )
= $false )
| ( ( ~ ( in @ SV10 @ ( relation_inverse_image @ SV81 @ SV65 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_D @ SV81 @ SV65 @ SV10 ) @ ( relation_rng @ SV81 ) )
| ~ ( in @ ( ordered_pair @ SV10 @ ( sK60_D @ SV81 @ SV65 @ SV10 ) ) @ SV81 ) )
| ~ ( in @ ( sK60_D @ SV81 @ SV65 @ SV10 ) @ SV65 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[859]) ).
thf(938,plain,
! [SV82: $i,SV66: $i,SV11: $i] :
( ( ( ~ ( ! [SY3442: $i,SY3443: $i] :
( ~ ( in @ SY3442 @ SV11 )
| ~ ( in @ SY3443 @ SV66 )
| ( ( sK28_D @ SV82 @ SV66 @ SV11 )
!= ( ordered_pair @ SY3442 @ SY3443 ) ) )
| ~ ( in @ ( sK28_D @ SV82 @ SV66 @ SV11 ) @ SV82 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY3106 @ SV82 @ SV66 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK30_SY3108 @ SV82 @ SV66 @ SV11 ) @ SV66 ) )
| ( ( sK28_D @ SV82 @ SV66 @ SV11 )
!= ( ordered_pair @ ( sK29_SY3106 @ SV82 @ SV66 @ SV11 ) @ ( sK30_SY3108 @ SV82 @ SV66 @ SV11 ) ) ) )
| ( in @ ( sK28_D @ SV82 @ SV66 @ SV11 ) @ SV82 ) ) )
= $false )
| ( ( SV82
= ( cartesian_product2 @ SV11 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(939,plain,
! [SV67: $i,SV11: $i,SV83: $i] :
( ( ( SV83
= ( cartesian_product2 @ SV11 @ SV67 ) )
= $false )
| ( ( ~ ( ~ ! [SY3444: $i] :
( ! [SY3423: $i,SY3424: $i] :
( ~ ( in @ SY3423 @ SV11 )
| ~ ( in @ SY3424 @ SV67 )
| ( SY3444
!= ( ordered_pair @ SY3423 @ SY3424 ) ) )
| ( in @ SY3444 @ SV83 ) )
| ~ ! [SY3447: $i] :
( ~ ( in @ SY3447 @ SV83 )
| ~ ( ~ ~ ( ~ ( in @ ( sK26_E @ SY3447 @ SV83 @ SV67 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK27_SY3103 @ SY3447 @ SV83 @ SV67 @ SV11 ) @ SV67 ) )
| ( SY3447
!= ( ordered_pair @ ( sK26_E @ SY3447 @ SV83 @ SV67 @ SV11 ) @ ( sK27_SY3103 @ SY3447 @ SV83 @ SV67 @ SV11 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[861]) ).
thf(940,plain,
! [SV68: $i,SV12: $i,SV84: $i] :
( ( ( relation @ SV84 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV12 @ SV68 ) @ SV84 )
| ( in @ SV12 @ ( relation_field @ SV84 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[862]) ).
thf(941,plain,
! [SV69: $i,SV12: $i,SV85: $i] :
( ( ( relation @ SV85 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV12 @ SV69 ) @ SV85 )
| ( in @ SV69 @ ( relation_field @ SV85 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[863]) ).
thf(942,plain,
! [SV50: $i,SV43: $i,SV13: $i] :
( ( ( ! [SY3192: $i] :
( ~ ( ( SV13
!= ( ordered_pair @ ( sK33_C @ SY3192 @ SV13 ) @ ( sK34_SY3110 @ SY3192 @ SV13 ) ) )
| ~ ( ( SY3192
!= ( sK34_SY3110 @ SY3192 @ SV13 ) ) ) )
| ( SY3192
= ( pair_second @ SV13 ) ) ) )
= $true )
| ( ( SV13
= ( ordered_pair @ SV43 @ SV50 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[864]) ).
thf(943,plain,
! [SV50: $i,SV43: $i,SV13: $i] :
( ( ( ! [SY3193: $i] :
( ( SY3193
!= ( pair_second @ SV13 ) )
| ! [SY3194: $i,SY3195: $i] :
( ( SV13
!= ( ordered_pair @ SY3194 @ SY3195 ) )
| ( SY3193 = SY3195 ) ) ) )
= $true )
| ( ( SV13
= ( ordered_pair @ SV43 @ SV50 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[865]) ).
thf(944,plain,
! [SV14: $i,SV103: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK14_C @ SV103 @ SV14 )
!= ( sK15_SY3096 @ SV103 @ SV14 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SV103 @ SV14 ) @ SV103 )
| ~ ( in @ ( sK15_SY3096 @ SV103 @ SV14 ) @ SV103 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK14_C @ SV103 @ SV14 ) @ ( sK15_SY3096 @ SV103 @ SV14 ) ) @ SV14 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK15_SY3096 @ SV103 @ SV14 ) @ ( sK14_C @ SV103 @ SV14 ) ) @ SV14 ) ) )
= $true )
| ( ( is_connected_in @ SV14 @ SV103 )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[866]) ).
thf(945,plain,
! [SV104: $i,SV14: $i] :
( ( ( ~ ( is_connected_in @ SV14 @ SV104 ) )
= $true )
| ( ( ! [SY3462: $i,SY3463: $i] :
( ( SY3462 = SY3463 )
| ~ ( in @ SY3462 @ SV104 )
| ~ ( in @ SY3463 @ SV104 )
| ( in @ ( ordered_pair @ SY3462 @ SY3463 ) @ SV14 )
| ( in @ ( ordered_pair @ SY3463 @ SY3462 ) @ SV14 ) ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[867]) ).
thf(946,plain,
! [SV70: $i,SV15: $i,SV86: $i] :
( ( ( relation @ SV86 )
= $false )
| ( ( ! [SY3448: $i] :
( ~ ( in @ SY3448 @ ( relation_dom @ SV86 ) )
| ~ ( in @ ( ordered_pair @ SY3448 @ SV15 ) @ SV86 )
| ~ ( in @ SY3448 @ SV70 ) )
| ( in @ SV15 @ ( relation_image @ SV86 @ SV70 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[868]) ).
thf(947,plain,
! [SV71: $i,SV15: $i,SV87: $i] :
( ( ( relation @ SV87 )
= $false )
| ( ( ~ ( in @ SV15 @ ( relation_image @ SV87 @ SV71 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK61_D @ SV87 @ SV71 @ SV15 ) @ ( relation_dom @ SV87 ) )
| ~ ( in @ ( ordered_pair @ ( sK61_D @ SV87 @ SV71 @ SV15 ) @ SV15 ) @ SV87 ) )
| ~ ( in @ ( sK61_D @ SV87 @ SV71 @ SV15 ) @ SV71 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[869]) ).
thf(948,plain,
! [SV16: $i,SV105: $i,SV128: $i] :
( ( ( ~ ( ~ ( ! [SY3506: $i] :
( ~ ( in @ ( ordered_pair @ SY3506 @ ( sK46_D @ SV128 @ SV105 @ SV16 ) ) @ SV16 )
| ~ ( in @ SY3506 @ SV105 ) )
| ~ ( in @ ( sK46_D @ SV128 @ SV105 @ SV16 ) @ SV128 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SV128 @ SV105 @ SV16 ) @ ( sK46_D @ SV128 @ SV105 @ SV16 ) ) @ SV16 )
| ~ ( in @ ( sK47_SY3118 @ SV128 @ SV105 @ SV16 ) @ SV105 ) )
| ( in @ ( sK46_D @ SV128 @ SV105 @ SV16 ) @ SV128 ) ) )
| ( SV128
= ( relation_image @ SV16 @ SV105 ) ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[870]) ).
thf(949,plain,
! [SV106: $i,SV16: $i,SV129: $i] :
( ( ( ( SV129
!= ( relation_image @ SV16 @ SV106 ) )
| ~ ( ~ ! [SY3507: $i] :
( ! [SY3468: $i] :
( ~ ( in @ ( ordered_pair @ SY3468 @ SY3507 ) @ SV16 )
| ~ ( in @ SY3468 @ SV106 ) )
| ( in @ SY3507 @ SV129 ) )
| ~ ! [SY3509: $i] :
( ~ ( in @ SY3509 @ SV129 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SY3509 @ SV129 @ SV106 @ SV16 ) @ SY3509 ) @ SV16 )
| ~ ( in @ ( sK45_E @ SY3509 @ SV129 @ SV106 @ SV16 ) @ SV106 ) ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(950,plain,
! [SV51: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK64_B @ SV51 ) @ ( sK65_SY3126 @ SV51 ) ) @ SV51 )
| ~ ( in @ ( ordered_pair @ ( sK65_SY3126 @ SV51 ) @ ( sK64_B @ SV51 ) ) @ SV51 ) )
| ~ ( ( ( sK64_B @ SV51 )
!= ( sK65_SY3126 @ SV51 ) ) ) )
= $false )
| ( ( antisymmetric @ SV51 )
= $true )
| ( ( relation @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[872]) ).
thf(951,plain,
! [SV52: $i] :
( ( ( antisymmetric @ SV52 )
= $false )
| ( ( ! [SY3384: $i,SY3385: $i] :
( ~ ( in @ ( ordered_pair @ SY3384 @ SY3385 ) @ SV52 )
| ~ ( in @ ( ordered_pair @ SY3385 @ SY3384 ) @ SV52 )
| ( SY3384 = SY3385 ) ) )
= $true )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[873]) ).
thf(952,plain,
! [SV17: $i,SV72: $i,SV88: $i] :
( ( ( ~ ( function @ SV88 ) )
= $true )
| ( ( ~ ( relation @ SV88 ) )
= $true )
| ( ( ( SV72
!= ( apply @ SV88 @ SV17 ) )
| ~ ( in @ SV17 @ ( relation_dom @ SV88 ) )
| ( in @ ( ordered_pair @ SV17 @ SV72 ) @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[874]) ).
thf(953,plain,
! [SV130: $i,SV17: $i] :
( ( ! [SY3510: $i] :
( ~ ( function @ SY3510 )
| ~ ( relation @ SY3510 )
| ~ ( in @ ( ordered_pair @ SV17 @ SV130 ) @ SY3510 )
| ( SV130
= ( apply @ SY3510 @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(954,plain,
! [SV131: $i,SV17: $i] :
( ( ! [SY3511: $i] :
( ~ ( function @ SY3511 )
| ~ ( relation @ SY3511 )
| ~ ( in @ ( ordered_pair @ SV17 @ SV131 ) @ SY3511 )
| ( in @ SV17 @ ( relation_dom @ SY3511 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(955,plain,
! [SV18: $i,SV107: $i,SV132: $i] :
( ( ( ~ ( ~ ( ( ( sK35_D @ SV132 @ SV107 @ SV18 )
= SV107 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV107 ) @ SV18 )
| ~ ( in @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV132 ) )
| ~ ~ ( ~ ( ( ( sK35_D @ SV132 @ SV107 @ SV18 )
!= SV107 )
| ( in @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV132 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV107 ) @ SV18 )
| ( in @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV132 ) ) ) )
| ( SV132
= ( fiber @ SV18 @ SV107 ) ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[877]) ).
thf(956,plain,
! [SV108: $i,SV18: $i,SV133: $i] :
( ( ( ( SV133
!= ( fiber @ SV18 @ SV108 ) )
| ~ ( ~ ! [SY3512: $i] :
( ( SY3512 = SV108 )
| ~ ( in @ ( ordered_pair @ SY3512 @ SV108 ) @ SV18 )
| ( in @ SY3512 @ SV133 ) )
| ~ ~ ( ~ ! [SY3513: $i] :
( ~ ( in @ SY3513 @ SV133 )
| ( SY3513 != SV108 ) )
| ~ ! [SY3514: $i] :
( ~ ( in @ SY3514 @ SV133 )
| ( in @ ( ordered_pair @ SY3514 @ SV108 ) @ SV18 ) ) ) ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[878]) ).
thf(957,plain,
! [SV19: $i,SV109: $i] :
( ( ( ~ ( ~ ( in @ ( sK36_C @ SV109 @ SV19 ) @ SV109 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SV109 @ SV19 ) @ ( sK36_C @ SV109 @ SV19 ) ) @ SV19 ) ) )
= $true )
| ( ( is_reflexive_in @ SV19 @ SV109 )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[879]) ).
thf(958,plain,
! [SV110: $i,SV19: $i] :
( ( ( ~ ( is_reflexive_in @ SV19 @ SV110 ) )
= $true )
| ( ( ! [SY3475: $i] :
( ~ ( in @ SY3475 @ SV110 )
| ( in @ ( ordered_pair @ SY3475 @ SY3475 ) @ SV19 ) ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[880]) ).
thf(959,plain,
! [SV20: $i,SV111: $i] :
( ( ( ~ ( relation @ SV111 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SV111 @ SV20 ) @ ( sK13_SY3095 @ SV111 @ SV20 ) ) @ SV111 )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV111 @ SV20 ) @ ( sK12_C @ SV111 @ SV20 ) ) @ SV20 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SV111 @ SV20 ) @ ( sK13_SY3095 @ SV111 @ SV20 ) ) @ SV111 )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV111 @ SV20 ) @ ( sK12_C @ SV111 @ SV20 ) ) @ SV20 ) ) )
| ( SV111
= ( relation_inverse @ SV20 ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[881]) ).
thf(960,plain,
! [SV20: $i,SV112: $i] :
( ( ( ~ ( relation @ SV112 ) )
= $true )
| ( ( ( SV112
!= ( relation_inverse @ SV20 ) )
| ~ ( ~ ! [SY3476: $i,SY3477: $i] :
( ~ ( in @ ( ordered_pair @ SY3476 @ SY3477 ) @ SV112 )
| ( in @ ( ordered_pair @ SY3477 @ SY3476 ) @ SV20 ) )
| ~ ! [SY3478: $i,SY3479: $i] :
( ~ ( in @ ( ordered_pair @ SY3479 @ SY3478 ) @ SV20 )
| ( in @ ( ordered_pair @ SY3478 @ SY3479 ) @ SV112 ) ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[882]) ).
thf(961,plain,
! [SV21: $i,SV38: $i,SV134: $i] :
( ( ( ~ ( relation @ SV134 )
| ~ ( ~ ( ~ ( in @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) @ SV21 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV38 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV38 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) ) ) )
| ( SV134
= ( relation_rng_restriction @ SV21 @ SV38 ) ) )
= $true )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(962,plain,
! [SV38: $i,SV21: $i,SV135: $i] :
( ( ( ~ ( relation @ SV135 )
| ( SV135
!= ( relation_rng_restriction @ SV21 @ SV38 ) )
| ~ ( ~ ! [SY3515: $i,SY3516: $i] :
( ~ ( in @ SY3516 @ SV21 )
| ~ ( in @ ( ordered_pair @ SY3515 @ SY3516 ) @ SV38 )
| ( in @ ( ordered_pair @ SY3515 @ SY3516 ) @ SV135 ) )
| ~ ~ ( ~ ! [SY3517: $i,SY3518: $i] :
( ~ ( in @ ( ordered_pair @ SY3517 @ SY3518 ) @ SV135 )
| ( in @ SY3518 @ SV21 ) )
| ~ ! [SY3519: $i,SY3520: $i] :
( ~ ( in @ ( ordered_pair @ SY3519 @ SY3520 ) @ SV135 )
| ( in @ ( ordered_pair @ SY3519 @ SY3520 ) @ SV38 ) ) ) ) )
= $true )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(963,plain,
! [SV22: $i,SV113: $i] :
( ( ( ~ ( ~ ( ! [SY3480: $i] :
~ ( in @ ( ordered_pair @ SY3480 @ ( sK17_C @ SV113 @ SV22 ) ) @ SV22 )
| ~ ( in @ ( sK17_C @ SV113 @ SV22 ) @ SV113 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK18_SY3098 @ SV113 @ SV22 ) @ ( sK17_C @ SV113 @ SV22 ) ) @ SV22 )
| ( in @ ( sK17_C @ SV113 @ SV22 ) @ SV113 ) ) ) )
= $true )
| ( ( SV113
= ( relation_rng @ SV22 ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[885]) ).
thf(964,plain,
! [SV22: $i,SV114: $i] :
( ( ( ( SV114
!= ( relation_rng @ SV22 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3481: $i] :
( ! [SY3248: $i] :
~ ( in @ ( ordered_pair @ SY3248 @ SY3481 ) @ SV22 )
| ( in @ SY3481 @ SV114 ) )
| ~ ! [SY3483: $i] :
( ~ ( in @ SY3483 @ SV114 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3483 @ SV114 @ SV22 ) @ SY3483 ) @ SV22 ) ) ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[886]) ).
thf(965,plain,
! [SV23: $i,SV115: $i] :
( ( ( ~ ( relation @ SV115 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV115 @ SV23 ) @ ( sK25_SY3102 @ SV115 @ SV23 ) ) @ SV23 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SV115 @ SV23 ) @ ( sK25_SY3102 @ SV115 @ SV23 ) ) @ SV115 ) )
| ( subset @ SV23 @ SV115 ) )
= $true )
| ( ( relation @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[887]) ).
thf(966,plain,
! [SV23: $i,SV116: $i] :
( ( ( ~ ( relation @ SV116 ) )
= $true )
| ( ( ~ ( subset @ SV23 @ SV116 )
| ! [SY3484: $i,SY3485: $i] :
( ~ ( in @ ( ordered_pair @ SY3484 @ SY3485 ) @ SV23 )
| ( in @ ( ordered_pair @ SY3484 @ SY3485 ) @ SV116 ) ) )
= $true )
| ( ( relation @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[888]) ).
thf(967,plain,
! [SV24: $i,SV117: $i,SV136: $i] :
( ( ( ~ ( relation @ SV136 )
| ~ ( ~ ( ~ ( in @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ SV117 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV24 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) )
| ~ ~ ( ~ ( ( in @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ SV117 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV24 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) ) ) )
| ( SV136
= ( relation_dom_restriction @ SV24 @ SV117 ) ) )
= $true )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(968,plain,
! [SV118: $i,SV24: $i,SV137: $i] :
( ( ( ~ ( relation @ SV137 )
| ( SV137
!= ( relation_dom_restriction @ SV24 @ SV118 ) )
| ~ ( ~ ! [SY3521: $i,SY3522: $i] :
( ~ ( in @ SY3521 @ SV118 )
| ~ ( in @ ( ordered_pair @ SY3521 @ SY3522 ) @ SV24 )
| ( in @ ( ordered_pair @ SY3521 @ SY3522 ) @ SV137 ) )
| ~ ~ ( ~ ! [SY3523: $i] :
( ! [SY3524: $i] :
~ ( in @ ( ordered_pair @ SY3523 @ SY3524 ) @ SV137 )
| ( in @ SY3523 @ SV118 ) )
| ~ ! [SY3525: $i,SY3526: $i] :
( ~ ( in @ ( ordered_pair @ SY3525 @ SY3526 ) @ SV137 )
| ( in @ ( ordered_pair @ SY3525 @ SY3526 ) @ SV24 ) ) ) ) )
= $true )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(969,plain,
! [SV138: $i,SV89: $i,SV39: $i,SV25: $i] :
( ( ( ( ( ordered_pair @ SV25 @ SV39 )
!= ( ordered_pair @ SV89 @ SV138 ) ) )
= $true )
| ( ( SV25 = SV89 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(970,plain,
! [SV119: $i,SV90: $i,SV39: $i,SV25: $i] :
( ( ( ( ( ordered_pair @ SV25 @ SV39 )
!= ( ordered_pair @ SV90 @ SV119 ) ) )
= $true )
| ( ( SV39 = SV119 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[892]) ).
thf(971,plain,
! [SV26: $i] :
( ( ( ~ ( ~ ! [SY3269: $i] :
( ~ ( in @ SY3269 @ ( relation_dom @ SV26 ) )
| ! [SY3270: $i] :
( ( SY3270
!= ( apply @ SV26 @ SY3269 ) )
| ( in @ ( ordered_pair @ SY3269 @ SY3270 ) @ SV26 ) ) )
| ~ ! [SY3271: $i] :
( ~ ( in @ SY3271 @ ( relation_dom @ SV26 ) )
| ! [SY3272: $i] :
( ~ ( in @ ( ordered_pair @ SY3271 @ SY3272 ) @ SV26 )
| ( SY3272
= ( apply @ SV26 @ SY3271 ) ) ) ) ) )
= $true )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[893]) ).
thf(972,plain,
! [SV26: $i] :
( ( ( ~ ( ~ ! [SY3273: $i] :
( ( in @ SY3273 @ ( relation_dom @ SV26 ) )
| ! [SY3274: $i] :
( ( SY3274
!= ( apply @ SV26 @ SY3273 ) )
| ( SY3274 = empty_set ) ) )
| ~ ! [SY3275: $i] :
( ( in @ SY3275 @ ( relation_dom @ SV26 ) )
| ! [SY3276: $i] :
( ( SY3276 != empty_set )
| ( SY3276
= ( apply @ SV26 @ SY3275 ) ) ) ) ) )
= $true )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[894]) ).
thf(973,plain,
! [SV53: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK62_B @ SV53 )
!= ( sK63_SY3125 @ SV53 ) ) )
| ~ ~ ( ~ ( in @ ( sK62_B @ SV53 ) @ ( relation_field @ SV53 ) )
| ~ ( in @ ( sK63_SY3125 @ SV53 ) @ ( relation_field @ SV53 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK62_B @ SV53 ) @ ( sK63_SY3125 @ SV53 ) ) @ SV53 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK63_SY3125 @ SV53 ) @ ( sK62_B @ SV53 ) ) @ SV53 ) )
= $false )
| ( ( connected @ SV53 )
= $true )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[895]) ).
thf(974,plain,
! [SV54: $i] :
( ( ( connected @ SV54 )
= $false )
| ( ( ! [SY3386: $i,SY3387: $i] :
( ( SY3386 = SY3387 )
| ~ ( in @ SY3386 @ ( relation_field @ SV54 ) )
| ~ ( in @ SY3387 @ ( relation_field @ SV54 ) )
| ( in @ ( ordered_pair @ SY3386 @ SY3387 ) @ SV54 )
| ( in @ ( ordered_pair @ SY3387 @ SY3386 ) @ SV54 ) ) )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[896]) ).
thf(975,plain,
! [SV27: $i,SV120: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_C @ SV120 @ SV27 ) @ SV120 )
| ~ ( in @ ( sK20_SY3099 @ SV120 @ SV27 ) @ SV120 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SV120 @ SV27 ) @ ( sK20_SY3099 @ SV120 @ SV27 ) ) @ SV27 ) )
| ~ ( in @ ( ordered_pair @ ( sK20_SY3099 @ SV120 @ SV27 ) @ ( sK19_C @ SV120 @ SV27 ) ) @ SV27 ) )
| ~ ( ( ( sK19_C @ SV120 @ SV27 )
!= ( sK20_SY3099 @ SV120 @ SV27 ) ) ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV27 @ SV120 )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[897]) ).
thf(976,plain,
! [SV121: $i,SV27: $i] :
( ( ( ~ ( is_antisymmetric_in @ SV27 @ SV121 ) )
= $true )
| ( ( ! [SY3494: $i,SY3495: $i] :
( ~ ( in @ SY3494 @ SV121 )
| ~ ( in @ SY3495 @ SV121 )
| ~ ( in @ ( ordered_pair @ SY3494 @ SY3495 ) @ SV27 )
| ~ ( in @ ( ordered_pair @ SY3495 @ SY3494 ) @ SV27 )
| ( SY3494 = SY3495 ) ) )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[898]) ).
thf(977,plain,
! [SV122: $i,SV40: $i,SV91: $i,SV28: $i] :
( ( ( ~ ( in @ SV28 @ SV91 )
| ~ ( in @ SV40 @ SV122 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SV91 @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[899]) ).
thf(978,plain,
! [SV40: $i,SV28: $i] :
( ( ! [SY3353: $i] :
( ! [SY3354: $i] :
~ ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SY3353 @ SY3354 ) )
| ( in @ SV28 @ SY3353 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[900]) ).
thf(979,plain,
! [SV40: $i,SV28: $i] :
( ( ! [SY3355: $i,SY3356: $i] :
( ~ ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SY3355 @ SY3356 ) )
| ( in @ SV40 @ SY3356 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[901]) ).
thf(980,plain,
! [SV55: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK66_B @ SV55 ) @ ( sK67_SY3127 @ SV55 ) ) @ SV55 )
| ~ ( in @ ( ordered_pair @ ( sK67_SY3127 @ SV55 ) @ ( sK68_SY3129 @ SV55 ) ) @ SV55 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK66_B @ SV55 ) @ ( sK68_SY3129 @ SV55 ) ) @ SV55 ) )
= $false )
| ( ( transitive @ SV55 )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(981,plain,
! [SV56: $i] :
( ( ( transitive @ SV56 )
= $false )
| ( ( ! [SY3388: $i,SY3389: $i,SY3390: $i] :
( ~ ( in @ ( ordered_pair @ SY3388 @ SY3389 ) @ SV56 )
| ~ ( in @ ( ordered_pair @ SY3389 @ SY3390 ) @ SV56 )
| ( in @ ( ordered_pair @ SY3388 @ SY3390 ) @ SV56 ) ) )
= $true )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[903]) ).
thf(982,plain,
! [SV123: $i,SV41: $i,SV92: $i,SV29: $i] :
( ( ( ~ ( in @ SV29 @ SV92 )
| ~ ( in @ SV41 @ SV123 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SV92 @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[904]) ).
thf(983,plain,
! [SV41: $i,SV29: $i] :
( ( ! [SY3359: $i] :
( ! [SY3360: $i] :
~ ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SY3359 @ SY3360 ) )
| ( in @ SV29 @ SY3359 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[905]) ).
thf(984,plain,
! [SV41: $i,SV29: $i] :
( ( ! [SY3361: $i,SY3362: $i] :
( ~ ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SY3361 @ SY3362 ) )
| ( in @ SV41 @ SY3362 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[906]) ).
thf(985,plain,
! [SV30: $i,SV124: $i,SV139: $i] :
( ( ( ~ ( ~ ( ! [SY3527: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SY3527 ) @ SV30 )
| ~ ( in @ SY3527 @ SV124 ) )
| ~ ( in @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SV139 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ ( sK44_SY3116 @ SV139 @ SV124 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK44_SY3116 @ SV139 @ SV124 @ SV30 ) @ SV124 ) )
| ( in @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SV139 ) ) )
| ( SV139
= ( relation_inverse_image @ SV30 @ SV124 ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(986,plain,
! [SV125: $i,SV30: $i,SV140: $i] :
( ( ( ( SV140
!= ( relation_inverse_image @ SV30 @ SV125 ) )
| ~ ( ~ ! [SY3528: $i] :
( ! [SY3500: $i] :
( ~ ( in @ ( ordered_pair @ SY3528 @ SY3500 ) @ SV30 )
| ~ ( in @ SY3500 @ SV125 ) )
| ( in @ SY3528 @ SV140 ) )
| ~ ! [SY3530: $i] :
( ~ ( in @ SY3530 @ SV140 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3530 @ ( sK42_E @ SY3530 @ SV140 @ SV125 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK42_E @ SY3530 @ SV140 @ SV125 @ SV30 ) @ SV125 ) ) ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(987,plain,
! [SV73: $i,SV31: $i,SV93: $i] :
( ( ( relation @ SV93 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV31 @ SV73 ) @ SV93 )
| ( in @ SV31 @ ( relation_dom @ SV93 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[909]) ).
thf(988,plain,
! [SV74: $i,SV31: $i,SV94: $i] :
( ( ( relation @ SV94 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV31 @ SV74 ) @ SV94 )
| ( in @ SV74 @ ( relation_rng @ SV94 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[910]) ).
thf(989,plain,
! [SV57: $i] :
( ( ( ~ ( in @ ( sK69_B @ SV57 ) @ ( relation_field @ SV57 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK69_B @ SV57 ) @ ( sK69_B @ SV57 ) ) @ SV57 ) )
= $false )
| ( ( reflexive @ SV57 )
= $true )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[911]) ).
thf(990,plain,
! [SV58: $i] :
( ( ( reflexive @ SV58 )
= $false )
| ( ( ! [SY3391: $i] :
( ~ ( in @ SY3391 @ ( relation_field @ SV58 ) )
| ( in @ ( ordered_pair @ SY3391 @ SY3391 ) @ SV58 ) ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(991,plain,
! [SV32: $i,SV59: $i] :
( ( ( ~ ! [SY3392: $i] :
( ~ ( function @ SY3392 )
| ~ ( relation @ SY3392 )
| ~ ( ~ ( ~ ( in @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3392 @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) ) @ ( apply @ SY3392 @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) @ SV32 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SY3392 @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) ) @ ( apply @ SY3392 @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) @ SV32 ) ) ) )
| ( ( relation_dom @ SY3392 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SY3392 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SY3392 )
| ( relation_isomorphism @ SV32 @ SV59 @ SY3392 ) ) )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[913]) ).
thf(992,plain,
! [SV59: $i,SV32: $i] :
( ( ( ~ ~ ( ~ ! [SY3393: $i] :
( ~ ( function @ SY3393 )
| ~ ( relation @ SY3393 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3393 )
| ~ ( ~ ! [SY3394: $i,SY3395: $i] :
( ~ ( in @ SY3394 @ ( relation_field @ SV32 ) )
| ~ ( in @ SY3395 @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3393 @ SY3394 ) @ ( apply @ SY3393 @ SY3395 ) ) @ SV59 )
| ( in @ ( ordered_pair @ SY3394 @ SY3395 ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3312: $i] :
( ! [SY3313: $i] :
~ ( in @ ( ordered_pair @ SY3312 @ SY3313 ) @ SV32 )
| ( in @ SY3312 @ ( relation_field @ SV32 ) ) )
| ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV32 )
| ( in @ SY3315 @ ( relation_field @ SV32 ) ) ) )
| ~ ! [SY3400: $i,SY3401: $i] :
( ~ ( in @ ( ordered_pair @ SY3400 @ SY3401 ) @ SV32 )
| ( in @ ( ordered_pair @ ( apply @ SY3393 @ SY3400 ) @ ( apply @ SY3393 @ SY3401 ) ) @ SV59 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3402: $i] :
( ~ ( function @ SY3402 )
| ~ ( relation @ SY3402 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3402 )
| ( ( relation_dom @ SY3402 )
= ( relation_field @ SV32 ) ) )
| ~ ! [SY3403: $i] :
( ~ ( function @ SY3403 )
| ~ ( relation @ SY3403 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3403 )
| ( ( relation_rng @ SY3403 )
= ( relation_field @ SV59 ) ) ) )
| ~ ! [SY3404: $i] :
( ~ ( function @ SY3404 )
| ~ ( relation @ SY3404 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3404 )
| ( one_to_one @ SY3404 ) ) ) ) )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[913]) ).
thf(993,plain,
! [SV75: $i,SV33: $i,SV95: $i] :
( ( ( relation_of2_as_subset @ SV95 @ SV33 @ SV75 )
= $false )
| ( ( ~ ( ~ ! [SY3453: $i] :
~ ( in @ ( ordered_pair @ SY3453 @ ( sK57_D @ SV95 @ SV75 @ SV33 ) ) @ SV95 )
| ~ ( in @ ( sK57_D @ SV95 @ SV75 @ SV33 ) @ SV75 ) )
| ( ( relation_rng_as_subset @ SV33 @ SV75 @ SV95 )
= SV75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[914]) ).
thf(994,plain,
! [SV76: $i,SV33: $i,SV96: $i] :
( ( ( relation_of2_as_subset @ SV96 @ SV33 @ SV76 )
= $false )
| ( ( ( ( relation_rng_as_subset @ SV33 @ SV76 @ SV96 )
!= SV76 )
| ! [SY3454: $i] :
( ( in @ ( ordered_pair @ ( sK56_E @ SY3454 @ SV96 @ SV76 @ SV33 ) @ SY3454 ) @ SV96 )
| ~ ( in @ SY3454 @ SV76 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[915]) ).
thf(995,plain,
! [SV34: $i,SV126: $i] :
( ( ( ~ ( ~ ( ! [SY3502: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SV126 @ SV34 ) @ SY3502 ) @ SV34 )
| ~ ( in @ ( sK22_C @ SV126 @ SV34 ) @ SV126 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SV126 @ SV34 ) @ ( sK23_SY3101 @ SV126 @ SV34 ) ) @ SV34 )
| ( in @ ( sK22_C @ SV126 @ SV34 ) @ SV126 ) ) ) )
= $true )
| ( ( SV126
= ( relation_dom @ SV34 ) )
= $true )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[916]) ).
thf(996,plain,
! [SV34: $i,SV127: $i] :
( ( ( ( SV127
!= ( relation_dom @ SV34 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3503: $i] :
( ! [SY3331: $i] :
~ ( in @ ( ordered_pair @ SY3503 @ SY3331 ) @ SV34 )
| ( in @ SY3503 @ SV127 ) )
| ~ ! [SY3505: $i] :
( ~ ( in @ SY3505 @ SV127 )
| ( in @ ( ordered_pair @ SY3505 @ ( sK21_D @ SY3505 @ SV127 @ SV34 ) ) @ SV34 ) ) ) )
= $true )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[917]) ).
thf(997,plain,
! [SV141: $i,SV44: $i] :
( ( ( ! [SY3531: $i] :
( ( sK39_B @ SV44 )
!= ( ordered_pair @ SV141 @ SY3531 ) ) )
= $true )
| ( ( relation @ SV44 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(998,plain,
! [SV45: $i,SV97: $i] :
( ( ( in @ SV97 @ SV45 )
= $false )
| ( ( SV97
= ( ordered_pair @ ( sK37_C @ SV97 @ SV45 ) @ ( sK38_SY3111 @ SV97 @ SV45 ) ) )
= $true )
| ( ( relation @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[920]) ).
thf(999,plain,
! [SV4: $i,SV98: $i] :
( ( ( relation @ SV98 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV4 )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV98 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV4 )
| ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV98 ) ) )
| ( SV4 = SV98 ) )
= $true )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[921]) ).
thf(1000,plain,
! [SV4: $i,SV99: $i] :
( ( ( relation @ SV99 )
= $false )
| ( ( ( SV4 != SV99 )
| ~ ( ~ ! [SY3455: $i,SY3456: $i] :
( ~ ( in @ ( ordered_pair @ SY3455 @ SY3456 ) @ SV4 )
| ( in @ ( ordered_pair @ SY3455 @ SY3456 ) @ SV99 ) )
| ~ ! [SY3457: $i,SY3458: $i] :
( ~ ( in @ ( ordered_pair @ SY3457 @ SY3458 ) @ SV99 )
| ( in @ ( ordered_pair @ SY3457 @ SY3458 ) @ SV4 ) ) ) )
= $true )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[922]) ).
thf(1001,plain,
! [SV5: $i,SV100: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SV100 @ SV5 ) @ SV100 )
| ~ ( in @ ( sK4_SY3086 @ SV100 @ SV5 ) @ SV100 ) )
| ~ ( in @ ( sK5_SY3088 @ SV100 @ SV5 ) @ SV100 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SV100 @ SV5 ) @ ( sK4_SY3086 @ SV100 @ SV5 ) ) @ SV5 ) )
| ~ ( in @ ( ordered_pair @ ( sK4_SY3086 @ SV100 @ SV5 ) @ ( sK5_SY3088 @ SV100 @ SV5 ) ) @ SV5 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK3_C @ SV100 @ SV5 ) @ ( sK5_SY3088 @ SV100 @ SV5 ) ) @ SV5 ) )
= $false )
| ( ( is_transitive_in @ SV5 @ SV100 )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[923]) ).
thf(1002,plain,
! [SV101: $i,SV5: $i] :
( ( ( is_transitive_in @ SV5 @ SV101 )
= $false )
| ( ( ! [SY3459: $i,SY3460: $i,SY3461: $i] :
( ~ ( in @ SY3459 @ SV101 )
| ~ ( in @ SY3460 @ SV101 )
| ~ ( in @ SY3461 @ SV101 )
| ~ ( in @ ( ordered_pair @ SY3459 @ SY3460 ) @ SV5 )
| ~ ( in @ ( ordered_pair @ SY3460 @ SY3461 ) @ SV5 )
| ( in @ ( ordered_pair @ SY3459 @ SY3461 ) @ SV5 ) ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[924]) ).
thf(1003,plain,
! [SV6: $i,SV60: $i,SV77: $i] :
( ( ( ~ ( ~ ! [SY3438: $i] :
~ ( in @ ( ordered_pair @ ( sK59_D @ SV77 @ SV60 @ SV6 ) @ SY3438 ) @ SV77 )
| ~ ( in @ ( sK59_D @ SV77 @ SV60 @ SV6 ) @ SV60 ) ) )
= $true )
| ( ( ( relation_dom_as_subset @ SV60 @ SV6 @ SV77 )
= SV60 )
= $true )
| ( ( relation_of2_as_subset @ SV77 @ SV60 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[925]) ).
thf(1004,plain,
! [SV78: $i,SV6: $i,SV61: $i] :
( ( ( ( ( relation_dom_as_subset @ SV61 @ SV6 @ SV78 )
!= SV61 ) )
= $true )
| ( ( ! [SY3439: $i] :
( ( in @ ( ordered_pair @ SY3439 @ ( sK58_E @ SY3439 @ SV78 @ SV61 @ SV6 ) ) @ SV78 )
| ~ ( in @ SY3439 @ SV61 ) ) )
= $true )
| ( ( relation_of2_as_subset @ SV78 @ SV61 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[926]) ).
thf(1005,plain,
! [SV7: $i,SV46: $i] :
( ( ( ! [SY3368: $i] :
( ~ ( relation @ SY3368 )
| ~ ( ~ ( ! [SY3369: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3368 @ SV46 @ SV7 ) @ SY3369 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3369 @ ( sK8_SY3089 @ SY3368 @ SV46 @ SV7 ) ) @ SV46 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3368 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SY3368 @ SV46 @ SV7 ) ) @ SY3368 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3368 @ SV46 @ SV7 ) @ ( sK9_SY3093 @ SY3368 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SY3368 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SY3368 @ SV46 @ SV7 ) ) @ SV46 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SY3368 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SY3368 @ SV46 @ SV7 ) ) @ SY3368 ) ) )
| ( SY3368
= ( relation_composition @ SV7 @ SV46 ) ) ) )
= $true )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[927]) ).
thf(1006,plain,
! [SV46: $i,SV7: $i] :
( ( ( ! [SY3370: $i] :
( ~ ( relation @ SY3370 )
| ( SY3370
!= ( relation_composition @ SV7 @ SV46 ) )
| ~ ( ~ ! [SY3371: $i,SY3372: $i] :
( ! [SY3373: $i] :
( ~ ( in @ ( ordered_pair @ SY3371 @ SY3373 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3373 @ SY3372 ) @ SV46 ) )
| ( in @ ( ordered_pair @ SY3371 @ SY3372 ) @ SY3370 ) )
| ~ ! [SY3374: $i,SY3375: $i] :
( ~ ( in @ ( ordered_pair @ SY3374 @ SY3375 ) @ SY3370 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3374 @ ( sK6_F @ SY3375 @ SY3374 @ SY3370 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY3375 @ SY3374 @ SY3370 @ SV46 @ SV7 ) @ SY3375 ) @ SV46 ) ) ) ) ) )
= $true )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[928]) ).
thf(1007,plain,
! [SV47: $i,SV62: $i] :
( ( ( ~ ( ( ( sK52_C @ SV62 @ SV47 )
!= ( sK53_SY3121 @ SV62 @ SV47 ) )
| ~ ( in @ ( sK52_C @ SV62 @ SV47 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) )
| ~ ~ ( ~ ( ( ( sK52_C @ SV62 @ SV47 )
= ( sK53_SY3121 @ SV62 @ SV47 ) )
| ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) )
| ~ ( ( in @ ( sK52_C @ SV62 @ SV47 ) @ SV47 )
| ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) ) ) )
= $false )
| ( ( SV62
= ( identity_relation @ SV47 ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[929]) ).
thf(1008,plain,
! [SV48: $i,SV63: $i] :
( ( ( SV63
= ( identity_relation @ SV48 ) )
= $false )
| ( ( ~ ( ~ ! [SY3409: $i,SY3410: $i] :
( ( SY3409 != SY3410 )
| ~ ( in @ SY3409 @ SV48 )
| ( in @ ( ordered_pair @ SY3409 @ SY3410 ) @ SV63 ) )
| ~ ~ ( ~ ! [SY3411: $i,SY3412: $i] :
( ~ ( in @ ( ordered_pair @ SY3411 @ SY3412 ) @ SV63 )
| ( SY3411 = SY3412 ) )
| ~ ! [SY3413: $i] :
( ! [SY3414: $i] :
~ ( in @ ( ordered_pair @ SY3413 @ SY3414 ) @ SV63 )
| ( in @ SY3413 @ SV48 ) ) ) ) )
= $true )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[930]) ).
thf(1009,plain,
! [SV49: $i,SV42: $i,SV142: $i,SV8: $i] :
( ( ( ~ ( ( SV8
!= ( ordered_pair @ ( sK40_C @ SV142 @ SV8 ) @ ( sK41_SY3114 @ SV142 @ SV8 ) ) )
| ~ ( ( SV142
!= ( sK40_C @ SV142 @ SV8 ) ) ) )
| ( SV142
= ( pair_first @ SV8 ) ) )
= $true )
| ( ( SV8
= ( ordered_pair @ SV42 @ SV49 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1010,plain,
! [SV49: $i,SV42: $i,SV8: $i,SV143: $i] :
( ( ( ( SV143
!= ( pair_first @ SV8 ) )
| ! [SY3532: $i] :
( ! [SY3163: $i] :
( SV8
!= ( ordered_pair @ SY3532 @ SY3163 ) )
| ( SV143 = SY3532 ) ) )
= $true )
| ( ( SV8
= ( ordered_pair @ SV42 @ SV49 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1011,plain,
! [SV37: $i,SV79: $i,SV9: $i,SV102: $i] :
( ( ( relation @ SV102 )
= $false )
| ( ( ~ ( in @ SV9 @ SV79 )
| ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ SV102 )
| ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SV79 ) @ SV102 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[933]) ).
thf(1012,plain,
! [SV144: $i,SV37: $i,SV9: $i] :
( ( ! [SY3534: $i] :
( ~ ( relation @ SY3534 )
| ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SV144 ) @ SY3534 ) )
| ( in @ SV9 @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1013,plain,
! [SV145: $i,SV37: $i,SV9: $i] :
( ( ! [SY3535: $i] :
( ~ ( relation @ SY3535 )
| ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SV145 ) @ SY3535 ) )
| ( in @ ( ordered_pair @ SV9 @ SV37 ) @ SY3535 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1014,plain,
! [SV64: $i,SV10: $i,SV80: $i] :
( ( ( ! [SY3441: $i] :
( ~ ( in @ SY3441 @ ( relation_rng @ SV80 ) )
| ~ ( in @ ( ordered_pair @ SV10 @ SY3441 ) @ SV80 )
| ~ ( in @ SY3441 @ SV64 ) ) )
= $true )
| ( ( in @ SV10 @ ( relation_inverse_image @ SV80 @ SV64 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[936]) ).
thf(1015,plain,
! [SV65: $i,SV81: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ ( relation_inverse_image @ SV81 @ SV65 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK60_D @ SV81 @ SV65 @ SV10 ) @ ( relation_rng @ SV81 ) )
| ~ ( in @ ( ordered_pair @ SV10 @ ( sK60_D @ SV81 @ SV65 @ SV10 ) ) @ SV81 ) )
| ~ ( in @ ( sK60_D @ SV81 @ SV65 @ SV10 ) @ SV65 ) ) )
= $true )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[937]) ).
thf(1016,plain,
! [SV82: $i,SV66: $i,SV11: $i] :
( ( ( ~ ( ! [SY3442: $i,SY3443: $i] :
( ~ ( in @ SY3442 @ SV11 )
| ~ ( in @ SY3443 @ SV66 )
| ( ( sK28_D @ SV82 @ SV66 @ SV11 )
!= ( ordered_pair @ SY3442 @ SY3443 ) ) )
| ~ ( in @ ( sK28_D @ SV82 @ SV66 @ SV11 ) @ SV82 ) ) )
= $false )
| ( ( SV82
= ( cartesian_product2 @ SV11 @ SV66 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[938]) ).
thf(1017,plain,
! [SV11: $i,SV66: $i,SV82: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY3106 @ SV82 @ SV66 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK30_SY3108 @ SV82 @ SV66 @ SV11 ) @ SV66 ) )
| ( ( sK28_D @ SV82 @ SV66 @ SV11 )
!= ( ordered_pair @ ( sK29_SY3106 @ SV82 @ SV66 @ SV11 ) @ ( sK30_SY3108 @ SV82 @ SV66 @ SV11 ) ) ) )
| ( in @ ( sK28_D @ SV82 @ SV66 @ SV11 ) @ SV82 ) ) )
= $false )
| ( ( SV82
= ( cartesian_product2 @ SV11 @ SV66 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[938]) ).
thf(1018,plain,
! [SV83: $i,SV67: $i,SV11: $i] :
( ( ( ~ ! [SY3444: $i] :
( ! [SY3423: $i,SY3424: $i] :
( ~ ( in @ SY3423 @ SV11 )
| ~ ( in @ SY3424 @ SV67 )
| ( SY3444
!= ( ordered_pair @ SY3423 @ SY3424 ) ) )
| ( in @ SY3444 @ SV83 ) )
| ~ ! [SY3447: $i] :
( ~ ( in @ SY3447 @ SV83 )
| ~ ( ~ ~ ( ~ ( in @ ( sK26_E @ SY3447 @ SV83 @ SV67 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK27_SY3103 @ SY3447 @ SV83 @ SV67 @ SV11 ) @ SV67 ) )
| ( SY3447
!= ( ordered_pair @ ( sK26_E @ SY3447 @ SV83 @ SV67 @ SV11 ) @ ( sK27_SY3103 @ SY3447 @ SV83 @ SV67 @ SV11 ) ) ) ) ) )
= $false )
| ( ( SV83
= ( cartesian_product2 @ SV11 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[939]) ).
thf(1019,plain,
! [SV84: $i,SV68: $i,SV12: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV12 @ SV68 ) @ SV84 ) )
= $true )
| ( ( in @ SV12 @ ( relation_field @ SV84 ) )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[940]) ).
thf(1020,plain,
! [SV85: $i,SV69: $i,SV12: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV12 @ SV69 ) @ SV85 ) )
= $true )
| ( ( in @ SV69 @ ( relation_field @ SV85 ) )
= $true )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[941]) ).
thf(1021,plain,
! [SV50: $i,SV43: $i,SV146: $i,SV13: $i] :
( ( ( ~ ( ( SV13
!= ( ordered_pair @ ( sK33_C @ SV146 @ SV13 ) @ ( sK34_SY3110 @ SV146 @ SV13 ) ) )
| ~ ( ( SV146
!= ( sK34_SY3110 @ SV146 @ SV13 ) ) ) )
| ( SV146
= ( pair_second @ SV13 ) ) )
= $true )
| ( ( SV13
= ( ordered_pair @ SV43 @ SV50 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1022,plain,
! [SV50: $i,SV43: $i,SV13: $i,SV147: $i] :
( ( ( ( SV147
!= ( pair_second @ SV13 ) )
| ! [SY3536: $i,SY3537: $i] :
( ( SV13
!= ( ordered_pair @ SY3536 @ SY3537 ) )
| ( SV147 = SY3537 ) ) )
= $true )
| ( ( SV13
= ( ordered_pair @ SV43 @ SV50 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1023,plain,
! [SV14: $i,SV103: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK14_C @ SV103 @ SV14 )
!= ( sK15_SY3096 @ SV103 @ SV14 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SV103 @ SV14 ) @ SV103 )
| ~ ( in @ ( sK15_SY3096 @ SV103 @ SV14 ) @ SV103 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK14_C @ SV103 @ SV14 ) @ ( sK15_SY3096 @ SV103 @ SV14 ) ) @ SV14 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK15_SY3096 @ SV103 @ SV14 ) @ ( sK14_C @ SV103 @ SV14 ) ) @ SV14 ) )
= $false )
| ( ( is_connected_in @ SV14 @ SV103 )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[944]) ).
thf(1024,plain,
! [SV104: $i,SV14: $i] :
( ( ( is_connected_in @ SV14 @ SV104 )
= $false )
| ( ( ! [SY3462: $i,SY3463: $i] :
( ( SY3462 = SY3463 )
| ~ ( in @ SY3462 @ SV104 )
| ~ ( in @ SY3463 @ SV104 )
| ( in @ ( ordered_pair @ SY3462 @ SY3463 ) @ SV14 )
| ( in @ ( ordered_pair @ SY3463 @ SY3462 ) @ SV14 ) ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[945]) ).
thf(1025,plain,
! [SV70: $i,SV15: $i,SV86: $i] :
( ( ( ! [SY3448: $i] :
( ~ ( in @ SY3448 @ ( relation_dom @ SV86 ) )
| ~ ( in @ ( ordered_pair @ SY3448 @ SV15 ) @ SV86 )
| ~ ( in @ SY3448 @ SV70 ) ) )
= $true )
| ( ( in @ SV15 @ ( relation_image @ SV86 @ SV70 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[946]) ).
thf(1026,plain,
! [SV71: $i,SV87: $i,SV15: $i] :
( ( ( ~ ( in @ SV15 @ ( relation_image @ SV87 @ SV71 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK61_D @ SV87 @ SV71 @ SV15 ) @ ( relation_dom @ SV87 ) )
| ~ ( in @ ( ordered_pair @ ( sK61_D @ SV87 @ SV71 @ SV15 ) @ SV15 ) @ SV87 ) )
| ~ ( in @ ( sK61_D @ SV87 @ SV71 @ SV15 ) @ SV71 ) ) )
= $true )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[947]) ).
thf(1027,plain,
! [SV16: $i,SV105: $i,SV128: $i] :
( ( ( ~ ( ~ ( ! [SY3506: $i] :
( ~ ( in @ ( ordered_pair @ SY3506 @ ( sK46_D @ SV128 @ SV105 @ SV16 ) ) @ SV16 )
| ~ ( in @ SY3506 @ SV105 ) )
| ~ ( in @ ( sK46_D @ SV128 @ SV105 @ SV16 ) @ SV128 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SV128 @ SV105 @ SV16 ) @ ( sK46_D @ SV128 @ SV105 @ SV16 ) ) @ SV16 )
| ~ ( in @ ( sK47_SY3118 @ SV128 @ SV105 @ SV16 ) @ SV105 ) )
| ( in @ ( sK46_D @ SV128 @ SV105 @ SV16 ) @ SV128 ) ) ) )
= $true )
| ( ( SV128
= ( relation_image @ SV16 @ SV105 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[948]) ).
thf(1028,plain,
! [SV106: $i,SV16: $i,SV129: $i] :
( ( ( ( SV129
!= ( relation_image @ SV16 @ SV106 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3507: $i] :
( ! [SY3468: $i] :
( ~ ( in @ ( ordered_pair @ SY3468 @ SY3507 ) @ SV16 )
| ~ ( in @ SY3468 @ SV106 ) )
| ( in @ SY3507 @ SV129 ) )
| ~ ! [SY3509: $i] :
( ~ ( in @ SY3509 @ SV129 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SY3509 @ SV129 @ SV106 @ SV16 ) @ SY3509 ) @ SV16 )
| ~ ( in @ ( sK45_E @ SY3509 @ SV129 @ SV106 @ SV16 ) @ SV106 ) ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[949]) ).
thf(1029,plain,
! [SV51: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK64_B @ SV51 ) @ ( sK65_SY3126 @ SV51 ) ) @ SV51 )
| ~ ( in @ ( ordered_pair @ ( sK65_SY3126 @ SV51 ) @ ( sK64_B @ SV51 ) ) @ SV51 ) ) )
= $false )
| ( ( antisymmetric @ SV51 )
= $true )
| ( ( relation @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[950]) ).
thf(1030,plain,
! [SV51: $i] :
( ( ( ~ ( ( ( sK64_B @ SV51 )
!= ( sK65_SY3126 @ SV51 ) ) ) )
= $false )
| ( ( antisymmetric @ SV51 )
= $true )
| ( ( relation @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[950]) ).
thf(1031,plain,
! [SV52: $i,SV148: $i] :
( ( ( ! [SY3538: $i] :
( ~ ( in @ ( ordered_pair @ SV148 @ SY3538 ) @ SV52 )
| ~ ( in @ ( ordered_pair @ SY3538 @ SV148 ) @ SV52 )
| ( SV148 = SY3538 ) ) )
= $true )
| ( ( antisymmetric @ SV52 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1032,plain,
! [SV17: $i,SV72: $i,SV88: $i] :
( ( ( function @ SV88 )
= $false )
| ( ( ~ ( relation @ SV88 ) )
= $true )
| ( ( ( SV72
!= ( apply @ SV88 @ SV17 ) )
| ~ ( in @ SV17 @ ( relation_dom @ SV88 ) )
| ( in @ ( ordered_pair @ SV17 @ SV72 ) @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[952]) ).
thf(1033,plain,
! [SV130: $i,SV17: $i,SV149: $i] :
( ( ~ ( function @ SV149 )
| ~ ( relation @ SV149 )
| ~ ( in @ ( ordered_pair @ SV17 @ SV130 ) @ SV149 )
| ( SV130
= ( apply @ SV149 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1034,plain,
! [SV131: $i,SV17: $i,SV150: $i] :
( ( ~ ( function @ SV150 )
| ~ ( relation @ SV150 )
| ~ ( in @ ( ordered_pair @ SV17 @ SV131 ) @ SV150 )
| ( in @ SV17 @ ( relation_dom @ SV150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1035,plain,
! [SV18: $i,SV107: $i,SV132: $i] :
( ( ( ~ ( ~ ( ( ( sK35_D @ SV132 @ SV107 @ SV18 )
= SV107 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV107 ) @ SV18 )
| ~ ( in @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV132 ) )
| ~ ~ ( ~ ( ( ( sK35_D @ SV132 @ SV107 @ SV18 )
!= SV107 )
| ( in @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV132 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV107 ) @ SV18 )
| ( in @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV132 ) ) ) ) )
= $true )
| ( ( SV132
= ( fiber @ SV18 @ SV107 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[955]) ).
thf(1036,plain,
! [SV108: $i,SV18: $i,SV133: $i] :
( ( ( ( SV133
!= ( fiber @ SV18 @ SV108 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3512: $i] :
( ( SY3512 = SV108 )
| ~ ( in @ ( ordered_pair @ SY3512 @ SV108 ) @ SV18 )
| ( in @ SY3512 @ SV133 ) )
| ~ ~ ( ~ ! [SY3513: $i] :
( ~ ( in @ SY3513 @ SV133 )
| ( SY3513 != SV108 ) )
| ~ ! [SY3514: $i] :
( ~ ( in @ SY3514 @ SV133 )
| ( in @ ( ordered_pair @ SY3514 @ SV108 ) @ SV18 ) ) ) ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[956]) ).
thf(1037,plain,
! [SV19: $i,SV109: $i] :
( ( ( ~ ( in @ ( sK36_C @ SV109 @ SV19 ) @ SV109 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SV109 @ SV19 ) @ ( sK36_C @ SV109 @ SV19 ) ) @ SV19 ) )
= $false )
| ( ( is_reflexive_in @ SV19 @ SV109 )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[957]) ).
thf(1038,plain,
! [SV110: $i,SV19: $i] :
( ( ( is_reflexive_in @ SV19 @ SV110 )
= $false )
| ( ( ! [SY3475: $i] :
( ~ ( in @ SY3475 @ SV110 )
| ( in @ ( ordered_pair @ SY3475 @ SY3475 ) @ SV19 ) ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[958]) ).
thf(1039,plain,
! [SV20: $i,SV111: $i] :
( ( ( relation @ SV111 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SV111 @ SV20 ) @ ( sK13_SY3095 @ SV111 @ SV20 ) ) @ SV111 )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV111 @ SV20 ) @ ( sK12_C @ SV111 @ SV20 ) ) @ SV20 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SV111 @ SV20 ) @ ( sK13_SY3095 @ SV111 @ SV20 ) ) @ SV111 )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV111 @ SV20 ) @ ( sK12_C @ SV111 @ SV20 ) ) @ SV20 ) ) )
| ( SV111
= ( relation_inverse @ SV20 ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[959]) ).
thf(1040,plain,
! [SV20: $i,SV112: $i] :
( ( ( relation @ SV112 )
= $false )
| ( ( ( SV112
!= ( relation_inverse @ SV20 ) )
| ~ ( ~ ! [SY3476: $i,SY3477: $i] :
( ~ ( in @ ( ordered_pair @ SY3476 @ SY3477 ) @ SV112 )
| ( in @ ( ordered_pair @ SY3477 @ SY3476 ) @ SV20 ) )
| ~ ! [SY3478: $i,SY3479: $i] :
( ~ ( in @ ( ordered_pair @ SY3479 @ SY3478 ) @ SV20 )
| ( in @ ( ordered_pair @ SY3478 @ SY3479 ) @ SV112 ) ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[960]) ).
thf(1041,plain,
! [SV21: $i,SV38: $i,SV134: $i] :
( ( ( ~ ( relation @ SV134 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) @ SV21 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV38 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV38 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) ) ) )
| ( SV134
= ( relation_rng_restriction @ SV21 @ SV38 ) ) )
= $true )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[961]) ).
thf(1042,plain,
! [SV38: $i,SV21: $i,SV135: $i] :
( ( ( ~ ( relation @ SV135 ) )
= $true )
| ( ( ( SV135
!= ( relation_rng_restriction @ SV21 @ SV38 ) )
| ~ ( ~ ! [SY3515: $i,SY3516: $i] :
( ~ ( in @ SY3516 @ SV21 )
| ~ ( in @ ( ordered_pair @ SY3515 @ SY3516 ) @ SV38 )
| ( in @ ( ordered_pair @ SY3515 @ SY3516 ) @ SV135 ) )
| ~ ~ ( ~ ! [SY3517: $i,SY3518: $i] :
( ~ ( in @ ( ordered_pair @ SY3517 @ SY3518 ) @ SV135 )
| ( in @ SY3518 @ SV21 ) )
| ~ ! [SY3519: $i,SY3520: $i] :
( ~ ( in @ ( ordered_pair @ SY3519 @ SY3520 ) @ SV135 )
| ( in @ ( ordered_pair @ SY3519 @ SY3520 ) @ SV38 ) ) ) ) )
= $true )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[962]) ).
thf(1043,plain,
! [SV22: $i,SV113: $i] :
( ( ( ~ ( ! [SY3480: $i] :
~ ( in @ ( ordered_pair @ SY3480 @ ( sK17_C @ SV113 @ SV22 ) ) @ SV22 )
| ~ ( in @ ( sK17_C @ SV113 @ SV22 ) @ SV113 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK18_SY3098 @ SV113 @ SV22 ) @ ( sK17_C @ SV113 @ SV22 ) ) @ SV22 )
| ( in @ ( sK17_C @ SV113 @ SV22 ) @ SV113 ) ) )
= $false )
| ( ( SV113
= ( relation_rng @ SV22 ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[963]) ).
thf(1044,plain,
! [SV22: $i,SV114: $i] :
( ( ( SV114
= ( relation_rng @ SV22 ) )
= $false )
| ( ( ~ ( ~ ! [SY3481: $i] :
( ! [SY3248: $i] :
~ ( in @ ( ordered_pair @ SY3248 @ SY3481 ) @ SV22 )
| ( in @ SY3481 @ SV114 ) )
| ~ ! [SY3483: $i] :
( ~ ( in @ SY3483 @ SV114 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3483 @ SV114 @ SV22 ) @ SY3483 ) @ SV22 ) ) ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[964]) ).
thf(1045,plain,
! [SV23: $i,SV115: $i] :
( ( ( relation @ SV115 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV115 @ SV23 ) @ ( sK25_SY3102 @ SV115 @ SV23 ) ) @ SV23 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SV115 @ SV23 ) @ ( sK25_SY3102 @ SV115 @ SV23 ) ) @ SV115 ) )
| ( subset @ SV23 @ SV115 ) )
= $true )
| ( ( relation @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[965]) ).
thf(1046,plain,
! [SV23: $i,SV116: $i] :
( ( ( relation @ SV116 )
= $false )
| ( ( ~ ( subset @ SV23 @ SV116 )
| ! [SY3484: $i,SY3485: $i] :
( ~ ( in @ ( ordered_pair @ SY3484 @ SY3485 ) @ SV23 )
| ( in @ ( ordered_pair @ SY3484 @ SY3485 ) @ SV116 ) ) )
= $true )
| ( ( relation @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(1047,plain,
! [SV24: $i,SV117: $i,SV136: $i] :
( ( ( ~ ( relation @ SV136 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ SV117 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV24 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) )
| ~ ~ ( ~ ( ( in @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ SV117 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV24 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) ) ) )
| ( SV136
= ( relation_dom_restriction @ SV24 @ SV117 ) ) )
= $true )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[967]) ).
thf(1048,plain,
! [SV118: $i,SV24: $i,SV137: $i] :
( ( ( ~ ( relation @ SV137 ) )
= $true )
| ( ( ( SV137
!= ( relation_dom_restriction @ SV24 @ SV118 ) )
| ~ ( ~ ! [SY3521: $i,SY3522: $i] :
( ~ ( in @ SY3521 @ SV118 )
| ~ ( in @ ( ordered_pair @ SY3521 @ SY3522 ) @ SV24 )
| ( in @ ( ordered_pair @ SY3521 @ SY3522 ) @ SV137 ) )
| ~ ~ ( ~ ! [SY3523: $i] :
( ! [SY3524: $i] :
~ ( in @ ( ordered_pair @ SY3523 @ SY3524 ) @ SV137 )
| ( in @ SY3523 @ SV118 ) )
| ~ ! [SY3525: $i,SY3526: $i] :
( ~ ( in @ ( ordered_pair @ SY3525 @ SY3526 ) @ SV137 )
| ( in @ ( ordered_pair @ SY3525 @ SY3526 ) @ SV24 ) ) ) ) )
= $true )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[968]) ).
thf(1049,plain,
! [SV138: $i,SV89: $i,SV39: $i,SV25: $i] :
( ( ( ( ordered_pair @ SV25 @ SV39 )
= ( ordered_pair @ SV89 @ SV138 ) )
= $false )
| ( ( SV25 = SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[969]) ).
thf(1050,plain,
! [SV119: $i,SV90: $i,SV39: $i,SV25: $i] :
( ( ( ( ordered_pair @ SV25 @ SV39 )
= ( ordered_pair @ SV90 @ SV119 ) )
= $false )
| ( ( SV39 = SV119 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[970]) ).
thf(1051,plain,
! [SV26: $i] :
( ( ( ~ ! [SY3269: $i] :
( ~ ( in @ SY3269 @ ( relation_dom @ SV26 ) )
| ! [SY3270: $i] :
( ( SY3270
!= ( apply @ SV26 @ SY3269 ) )
| ( in @ ( ordered_pair @ SY3269 @ SY3270 ) @ SV26 ) ) )
| ~ ! [SY3271: $i] :
( ~ ( in @ SY3271 @ ( relation_dom @ SV26 ) )
| ! [SY3272: $i] :
( ~ ( in @ ( ordered_pair @ SY3271 @ SY3272 ) @ SV26 )
| ( SY3272
= ( apply @ SV26 @ SY3271 ) ) ) ) )
= $false )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[971]) ).
thf(1052,plain,
! [SV26: $i] :
( ( ( ~ ! [SY3273: $i] :
( ( in @ SY3273 @ ( relation_dom @ SV26 ) )
| ! [SY3274: $i] :
( ( SY3274
!= ( apply @ SV26 @ SY3273 ) )
| ( SY3274 = empty_set ) ) )
| ~ ! [SY3275: $i] :
( ( in @ SY3275 @ ( relation_dom @ SV26 ) )
| ! [SY3276: $i] :
( ( SY3276 != empty_set )
| ( SY3276
= ( apply @ SV26 @ SY3275 ) ) ) ) )
= $false )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(1053,plain,
! [SV53: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK62_B @ SV53 )
!= ( sK63_SY3125 @ SV53 ) ) )
| ~ ~ ( ~ ( in @ ( sK62_B @ SV53 ) @ ( relation_field @ SV53 ) )
| ~ ( in @ ( sK63_SY3125 @ SV53 ) @ ( relation_field @ SV53 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK62_B @ SV53 ) @ ( sK63_SY3125 @ SV53 ) ) @ SV53 ) ) )
= $false )
| ( ( connected @ SV53 )
= $true )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[973]) ).
thf(1054,plain,
! [SV53: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK63_SY3125 @ SV53 ) @ ( sK62_B @ SV53 ) ) @ SV53 ) )
= $false )
| ( ( connected @ SV53 )
= $true )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[973]) ).
thf(1055,plain,
! [SV54: $i,SV151: $i] :
( ( ( ! [SY3539: $i] :
( ( SV151 = SY3539 )
| ~ ( in @ SV151 @ ( relation_field @ SV54 ) )
| ~ ( in @ SY3539 @ ( relation_field @ SV54 ) )
| ( in @ ( ordered_pair @ SV151 @ SY3539 ) @ SV54 )
| ( in @ ( ordered_pair @ SY3539 @ SV151 ) @ SV54 ) ) )
= $true )
| ( ( connected @ SV54 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1056,plain,
! [SV27: $i,SV120: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_C @ SV120 @ SV27 ) @ SV120 )
| ~ ( in @ ( sK20_SY3099 @ SV120 @ SV27 ) @ SV120 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SV120 @ SV27 ) @ ( sK20_SY3099 @ SV120 @ SV27 ) ) @ SV27 ) )
| ~ ( in @ ( ordered_pair @ ( sK20_SY3099 @ SV120 @ SV27 ) @ ( sK19_C @ SV120 @ SV27 ) ) @ SV27 ) )
| ~ ( ( ( sK19_C @ SV120 @ SV27 )
!= ( sK20_SY3099 @ SV120 @ SV27 ) ) ) )
= $false )
| ( ( is_antisymmetric_in @ SV27 @ SV120 )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[975]) ).
thf(1057,plain,
! [SV121: $i,SV27: $i] :
( ( ( is_antisymmetric_in @ SV27 @ SV121 )
= $false )
| ( ( ! [SY3494: $i,SY3495: $i] :
( ~ ( in @ SY3494 @ SV121 )
| ~ ( in @ SY3495 @ SV121 )
| ~ ( in @ ( ordered_pair @ SY3494 @ SY3495 ) @ SV27 )
| ~ ( in @ ( ordered_pair @ SY3495 @ SY3494 ) @ SV27 )
| ( SY3494 = SY3495 ) ) )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[976]) ).
thf(1058,plain,
! [SV122: $i,SV40: $i,SV91: $i,SV28: $i] :
( ( ( ~ ( in @ SV28 @ SV91 ) )
= $true )
| ( ( ~ ( in @ SV40 @ SV122 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SV91 @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[977]) ).
thf(1059,plain,
! [SV152: $i,SV40: $i,SV28: $i] :
( ( ! [SY3540: $i] :
~ ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SV152 @ SY3540 ) )
| ( in @ SV28 @ SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1060,plain,
! [SV153: $i,SV40: $i,SV28: $i] :
( ( ! [SY3541: $i] :
( ~ ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SV153 @ SY3541 ) )
| ( in @ SV40 @ SY3541 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1061,plain,
! [SV55: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK66_B @ SV55 ) @ ( sK67_SY3127 @ SV55 ) ) @ SV55 )
| ~ ( in @ ( ordered_pair @ ( sK67_SY3127 @ SV55 ) @ ( sK68_SY3129 @ SV55 ) ) @ SV55 ) ) )
= $false )
| ( ( transitive @ SV55 )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[980]) ).
thf(1062,plain,
! [SV55: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK66_B @ SV55 ) @ ( sK68_SY3129 @ SV55 ) ) @ SV55 ) )
= $false )
| ( ( transitive @ SV55 )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[980]) ).
thf(1063,plain,
! [SV56: $i,SV154: $i] :
( ( ( ! [SY3542: $i,SY3543: $i] :
( ~ ( in @ ( ordered_pair @ SV154 @ SY3542 ) @ SV56 )
| ~ ( in @ ( ordered_pair @ SY3542 @ SY3543 ) @ SV56 )
| ( in @ ( ordered_pair @ SV154 @ SY3543 ) @ SV56 ) ) )
= $true )
| ( ( transitive @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1064,plain,
! [SV123: $i,SV41: $i,SV92: $i,SV29: $i] :
( ( ( ~ ( in @ SV29 @ SV92 ) )
= $true )
| ( ( ~ ( in @ SV41 @ SV123 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SV92 @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[982]) ).
thf(1065,plain,
! [SV155: $i,SV41: $i,SV29: $i] :
( ( ! [SY3544: $i] :
~ ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SV155 @ SY3544 ) )
| ( in @ SV29 @ SV155 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1066,plain,
! [SV156: $i,SV41: $i,SV29: $i] :
( ( ! [SY3545: $i] :
( ~ ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SV156 @ SY3545 ) )
| ( in @ SV41 @ SY3545 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1067,plain,
! [SV30: $i,SV124: $i,SV139: $i] :
( ( ( ~ ( ~ ( ! [SY3527: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SY3527 ) @ SV30 )
| ~ ( in @ SY3527 @ SV124 ) )
| ~ ( in @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SV139 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ ( sK44_SY3116 @ SV139 @ SV124 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK44_SY3116 @ SV139 @ SV124 @ SV30 ) @ SV124 ) )
| ( in @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SV139 ) ) ) )
= $true )
| ( ( SV139
= ( relation_inverse_image @ SV30 @ SV124 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[985]) ).
thf(1068,plain,
! [SV125: $i,SV30: $i,SV140: $i] :
( ( ( ( SV140
!= ( relation_inverse_image @ SV30 @ SV125 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3528: $i] :
( ! [SY3500: $i] :
( ~ ( in @ ( ordered_pair @ SY3528 @ SY3500 ) @ SV30 )
| ~ ( in @ SY3500 @ SV125 ) )
| ( in @ SY3528 @ SV140 ) )
| ~ ! [SY3530: $i] :
( ~ ( in @ SY3530 @ SV140 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3530 @ ( sK42_E @ SY3530 @ SV140 @ SV125 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK42_E @ SY3530 @ SV140 @ SV125 @ SV30 ) @ SV125 ) ) ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[986]) ).
thf(1069,plain,
! [SV93: $i,SV73: $i,SV31: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV31 @ SV73 ) @ SV93 ) )
= $true )
| ( ( in @ SV31 @ ( relation_dom @ SV93 ) )
= $true )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[987]) ).
thf(1070,plain,
! [SV94: $i,SV74: $i,SV31: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV31 @ SV74 ) @ SV94 ) )
= $true )
| ( ( in @ SV74 @ ( relation_rng @ SV94 ) )
= $true )
| ( ( relation @ SV94 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[988]) ).
thf(1071,plain,
! [SV57: $i] :
( ( ( ~ ( in @ ( sK69_B @ SV57 ) @ ( relation_field @ SV57 ) ) )
= $false )
| ( ( reflexive @ SV57 )
= $true )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[989]) ).
thf(1072,plain,
! [SV57: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK69_B @ SV57 ) @ ( sK69_B @ SV57 ) ) @ SV57 ) )
= $false )
| ( ( reflexive @ SV57 )
= $true )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[989]) ).
thf(1073,plain,
! [SV58: $i,SV157: $i] :
( ( ( ~ ( in @ SV157 @ ( relation_field @ SV58 ) )
| ( in @ ( ordered_pair @ SV157 @ SV157 ) @ SV58 ) )
= $true )
| ( ( reflexive @ SV58 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1074,plain,
! [SV32: $i,SV59: $i] :
( ( ( ! [SY3392: $i] :
( ~ ( function @ SY3392 )
| ~ ( relation @ SY3392 )
| ~ ( ~ ( ~ ( in @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3392 @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) ) @ ( apply @ SY3392 @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) @ SV32 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SY3392 @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) ) @ ( apply @ SY3392 @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3392 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SY3392 @ SV59 @ SV32 ) ) @ SV32 ) ) ) )
| ( ( relation_dom @ SY3392 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SY3392 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SY3392 )
| ( relation_isomorphism @ SV32 @ SV59 @ SY3392 ) ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[991]) ).
thf(1075,plain,
! [SV59: $i,SV32: $i] :
( ( ( ~ ( ~ ! [SY3393: $i] :
( ~ ( function @ SY3393 )
| ~ ( relation @ SY3393 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3393 )
| ~ ( ~ ! [SY3394: $i,SY3395: $i] :
( ~ ( in @ SY3394 @ ( relation_field @ SV32 ) )
| ~ ( in @ SY3395 @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3393 @ SY3394 ) @ ( apply @ SY3393 @ SY3395 ) ) @ SV59 )
| ( in @ ( ordered_pair @ SY3394 @ SY3395 ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3312: $i] :
( ! [SY3313: $i] :
~ ( in @ ( ordered_pair @ SY3312 @ SY3313 ) @ SV32 )
| ( in @ SY3312 @ ( relation_field @ SV32 ) ) )
| ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV32 )
| ( in @ SY3315 @ ( relation_field @ SV32 ) ) ) )
| ~ ! [SY3400: $i,SY3401: $i] :
( ~ ( in @ ( ordered_pair @ SY3400 @ SY3401 ) @ SV32 )
| ( in @ ( ordered_pair @ ( apply @ SY3393 @ SY3400 ) @ ( apply @ SY3393 @ SY3401 ) ) @ SV59 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3402: $i] :
( ~ ( function @ SY3402 )
| ~ ( relation @ SY3402 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3402 )
| ( ( relation_dom @ SY3402 )
= ( relation_field @ SV32 ) ) )
| ~ ! [SY3403: $i] :
( ~ ( function @ SY3403 )
| ~ ( relation @ SY3403 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3403 )
| ( ( relation_rng @ SY3403 )
= ( relation_field @ SV59 ) ) ) )
| ~ ! [SY3404: $i] :
( ~ ( function @ SY3404 )
| ~ ( relation @ SY3404 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3404 )
| ( one_to_one @ SY3404 ) ) ) ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[992]) ).
thf(1076,plain,
! [SV33: $i,SV75: $i,SV95: $i] :
( ( ( ~ ( ~ ! [SY3453: $i] :
~ ( in @ ( ordered_pair @ SY3453 @ ( sK57_D @ SV95 @ SV75 @ SV33 ) ) @ SV95 )
| ~ ( in @ ( sK57_D @ SV95 @ SV75 @ SV33 ) @ SV75 ) ) )
= $true )
| ( ( ( relation_rng_as_subset @ SV33 @ SV75 @ SV95 )
= SV75 )
= $true )
| ( ( relation_of2_as_subset @ SV95 @ SV33 @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[993]) ).
thf(1077,plain,
! [SV96: $i,SV76: $i,SV33: $i] :
( ( ( ( ( relation_rng_as_subset @ SV33 @ SV76 @ SV96 )
!= SV76 ) )
= $true )
| ( ( ! [SY3454: $i] :
( ( in @ ( ordered_pair @ ( sK56_E @ SY3454 @ SV96 @ SV76 @ SV33 ) @ SY3454 ) @ SV96 )
| ~ ( in @ SY3454 @ SV76 ) ) )
= $true )
| ( ( relation_of2_as_subset @ SV96 @ SV33 @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[994]) ).
thf(1078,plain,
! [SV34: $i,SV126: $i] :
( ( ( ~ ( ! [SY3502: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SV126 @ SV34 ) @ SY3502 ) @ SV34 )
| ~ ( in @ ( sK22_C @ SV126 @ SV34 ) @ SV126 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SV126 @ SV34 ) @ ( sK23_SY3101 @ SV126 @ SV34 ) ) @ SV34 )
| ( in @ ( sK22_C @ SV126 @ SV34 ) @ SV126 ) ) )
= $false )
| ( ( SV126
= ( relation_dom @ SV34 ) )
= $true )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[995]) ).
thf(1079,plain,
! [SV34: $i,SV127: $i] :
( ( ( SV127
= ( relation_dom @ SV34 ) )
= $false )
| ( ( ~ ( ~ ! [SY3503: $i] :
( ! [SY3331: $i] :
~ ( in @ ( ordered_pair @ SY3503 @ SY3331 ) @ SV34 )
| ( in @ SY3503 @ SV127 ) )
| ~ ! [SY3505: $i] :
( ~ ( in @ SY3505 @ SV127 )
| ( in @ ( ordered_pair @ SY3505 @ ( sK21_D @ SY3505 @ SV127 @ SV34 ) ) @ SV34 ) ) ) )
= $true )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[996]) ).
thf(1080,plain,
! [SV158: $i,SV141: $i,SV44: $i] :
( ( ( ( ( sK39_B @ SV44 )
!= ( ordered_pair @ SV141 @ SV158 ) ) )
= $true )
| ( ( relation @ SV44 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1081,plain,
! [SV4: $i,SV98: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV4 )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV98 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV4 )
| ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV98 ) ) ) )
= $true )
| ( ( SV4 = SV98 )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[999]) ).
thf(1082,plain,
! [SV99: $i,SV4: $i] :
( ( ( ( SV4 != SV99 ) )
= $true )
| ( ( ~ ( ~ ! [SY3455: $i,SY3456: $i] :
( ~ ( in @ ( ordered_pair @ SY3455 @ SY3456 ) @ SV4 )
| ( in @ ( ordered_pair @ SY3455 @ SY3456 ) @ SV99 ) )
| ~ ! [SY3457: $i,SY3458: $i] :
( ~ ( in @ ( ordered_pair @ SY3457 @ SY3458 ) @ SV99 )
| ( in @ ( ordered_pair @ SY3457 @ SY3458 ) @ SV4 ) ) ) )
= $true )
| ( ( relation @ SV99 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1000]) ).
thf(1083,plain,
! [SV5: $i,SV100: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SV100 @ SV5 ) @ SV100 )
| ~ ( in @ ( sK4_SY3086 @ SV100 @ SV5 ) @ SV100 ) )
| ~ ( in @ ( sK5_SY3088 @ SV100 @ SV5 ) @ SV100 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SV100 @ SV5 ) @ ( sK4_SY3086 @ SV100 @ SV5 ) ) @ SV5 ) )
| ~ ( in @ ( ordered_pair @ ( sK4_SY3086 @ SV100 @ SV5 ) @ ( sK5_SY3088 @ SV100 @ SV5 ) ) @ SV5 ) ) )
= $false )
| ( ( is_transitive_in @ SV5 @ SV100 )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1001]) ).
thf(1084,plain,
! [SV5: $i,SV100: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK3_C @ SV100 @ SV5 ) @ ( sK5_SY3088 @ SV100 @ SV5 ) ) @ SV5 ) )
= $false )
| ( ( is_transitive_in @ SV5 @ SV100 )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1001]) ).
thf(1085,plain,
! [SV5: $i,SV101: $i,SV159: $i] :
( ( ( ! [SY3546: $i,SY3547: $i] :
( ~ ( in @ SV159 @ SV101 )
| ~ ( in @ SY3546 @ SV101 )
| ~ ( in @ SY3547 @ SV101 )
| ~ ( in @ ( ordered_pair @ SV159 @ SY3546 ) @ SV5 )
| ~ ( in @ ( ordered_pair @ SY3546 @ SY3547 ) @ SV5 )
| ( in @ ( ordered_pair @ SV159 @ SY3547 ) @ SV5 ) ) )
= $true )
| ( ( is_transitive_in @ SV5 @ SV101 )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1086,plain,
! [SV6: $i,SV60: $i,SV77: $i] :
( ( ( ~ ! [SY3438: $i] :
~ ( in @ ( ordered_pair @ ( sK59_D @ SV77 @ SV60 @ SV6 ) @ SY3438 ) @ SV77 )
| ~ ( in @ ( sK59_D @ SV77 @ SV60 @ SV6 ) @ SV60 ) )
= $false )
| ( ( ( relation_dom_as_subset @ SV60 @ SV6 @ SV77 )
= SV60 )
= $true )
| ( ( relation_of2_as_subset @ SV77 @ SV60 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1003]) ).
thf(1087,plain,
! [SV78: $i,SV6: $i,SV61: $i] :
( ( ( ( relation_dom_as_subset @ SV61 @ SV6 @ SV78 )
= SV61 )
= $false )
| ( ( ! [SY3439: $i] :
( ( in @ ( ordered_pair @ SY3439 @ ( sK58_E @ SY3439 @ SV78 @ SV61 @ SV6 ) ) @ SV78 )
| ~ ( in @ SY3439 @ SV61 ) ) )
= $true )
| ( ( relation_of2_as_subset @ SV78 @ SV61 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1004]) ).
thf(1088,plain,
! [SV7: $i,SV46: $i,SV160: $i] :
( ( ( ~ ( relation @ SV160 )
| ~ ( ~ ( ! [SY3548: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ SY3548 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3548 @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV46 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV160 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK9_SY3093 @ SV160 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV46 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV160 ) ) )
| ( SV160
= ( relation_composition @ SV7 @ SV46 ) ) )
= $true )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1089,plain,
! [SV46: $i,SV7: $i,SV161: $i] :
( ( ( ~ ( relation @ SV161 )
| ( SV161
!= ( relation_composition @ SV7 @ SV46 ) )
| ~ ( ~ ! [SY3549: $i,SY3550: $i] :
( ! [SY3373: $i] :
( ~ ( in @ ( ordered_pair @ SY3549 @ SY3373 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3373 @ SY3550 ) @ SV46 ) )
| ( in @ ( ordered_pair @ SY3549 @ SY3550 ) @ SV161 ) )
| ~ ! [SY3552: $i,SY3553: $i] :
( ~ ( in @ ( ordered_pair @ SY3552 @ SY3553 ) @ SV161 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3552 @ ( sK6_F @ SY3553 @ SY3552 @ SV161 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY3553 @ SY3552 @ SV161 @ SV46 @ SV7 ) @ SY3553 ) @ SV46 ) ) ) ) )
= $true )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1090,plain,
! [SV47: $i,SV62: $i] :
( ( ( ~ ( ( ( sK52_C @ SV62 @ SV47 )
!= ( sK53_SY3121 @ SV62 @ SV47 ) )
| ~ ( in @ ( sK52_C @ SV62 @ SV47 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) ) )
= $false )
| ( ( SV62
= ( identity_relation @ SV47 ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1007]) ).
thf(1091,plain,
! [SV47: $i,SV62: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK52_C @ SV62 @ SV47 )
= ( sK53_SY3121 @ SV62 @ SV47 ) )
| ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) )
| ~ ( ( in @ ( sK52_C @ SV62 @ SV47 ) @ SV47 )
| ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) ) ) )
= $false )
| ( ( SV62
= ( identity_relation @ SV47 ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1007]) ).
thf(1092,plain,
! [SV63: $i,SV48: $i] :
( ( ( ~ ! [SY3409: $i,SY3410: $i] :
( ( SY3409 != SY3410 )
| ~ ( in @ SY3409 @ SV48 )
| ( in @ ( ordered_pair @ SY3409 @ SY3410 ) @ SV63 ) )
| ~ ~ ( ~ ! [SY3411: $i,SY3412: $i] :
( ~ ( in @ ( ordered_pair @ SY3411 @ SY3412 ) @ SV63 )
| ( SY3411 = SY3412 ) )
| ~ ! [SY3413: $i] :
( ! [SY3414: $i] :
~ ( in @ ( ordered_pair @ SY3413 @ SY3414 ) @ SV63 )
| ( in @ SY3413 @ SV48 ) ) ) )
= $false )
| ( ( SV63
= ( identity_relation @ SV48 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1008]) ).
thf(1093,plain,
! [SV49: $i,SV42: $i,SV142: $i,SV8: $i] :
( ( ( ~ ( ( SV8
!= ( ordered_pair @ ( sK40_C @ SV142 @ SV8 ) @ ( sK41_SY3114 @ SV142 @ SV8 ) ) )
| ~ ( ( SV142
!= ( sK40_C @ SV142 @ SV8 ) ) ) ) )
= $true )
| ( ( SV142
= ( pair_first @ SV8 ) )
= $true )
| ( ( SV8
= ( ordered_pair @ SV42 @ SV49 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1009]) ).
thf(1094,plain,
! [SV49: $i,SV42: $i,SV8: $i,SV143: $i] :
( ( ( ( SV143
!= ( pair_first @ SV8 ) ) )
= $true )
| ( ( ! [SY3532: $i] :
( ! [SY3163: $i] :
( SV8
!= ( ordered_pair @ SY3532 @ SY3163 ) )
| ( SV143 = SY3532 ) ) )
= $true )
| ( ( SV8
= ( ordered_pair @ SV42 @ SV49 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1010]) ).
thf(1095,plain,
! [SV102: $i,SV37: $i,SV79: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV79 )
| ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ SV102 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SV79 ) @ SV102 ) )
= $true )
| ( ( relation @ SV102 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1011]) ).
thf(1096,plain,
! [SV144: $i,SV37: $i,SV9: $i,SV162: $i] :
( ( ~ ( relation @ SV162 )
| ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SV144 ) @ SV162 ) )
| ( in @ SV9 @ SV144 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1097,plain,
! [SV145: $i,SV37: $i,SV9: $i,SV163: $i] :
( ( ~ ( relation @ SV163 )
| ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SV145 ) @ SV163 ) )
| ( in @ ( ordered_pair @ SV9 @ SV37 ) @ SV163 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1013]) ).
thf(1098,plain,
! [SV64: $i,SV10: $i,SV80: $i,SV164: $i] :
( ( ( ~ ( in @ SV164 @ ( relation_rng @ SV80 ) )
| ~ ( in @ ( ordered_pair @ SV10 @ SV164 ) @ SV80 )
| ~ ( in @ SV164 @ SV64 ) )
= $true )
| ( ( in @ SV10 @ ( relation_inverse_image @ SV80 @ SV64 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1099,plain,
! [SV65: $i,SV81: $i,SV10: $i] :
( ( ( in @ SV10 @ ( relation_inverse_image @ SV81 @ SV65 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK60_D @ SV81 @ SV65 @ SV10 ) @ ( relation_rng @ SV81 ) )
| ~ ( in @ ( ordered_pair @ SV10 @ ( sK60_D @ SV81 @ SV65 @ SV10 ) ) @ SV81 ) )
| ~ ( in @ ( sK60_D @ SV81 @ SV65 @ SV10 ) @ SV65 ) ) )
= $true )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1100,plain,
! [SV82: $i,SV66: $i,SV11: $i] :
( ( ( ! [SY3442: $i,SY3443: $i] :
( ~ ( in @ SY3442 @ SV11 )
| ~ ( in @ SY3443 @ SV66 )
| ( ( sK28_D @ SV82 @ SV66 @ SV11 )
!= ( ordered_pair @ SY3442 @ SY3443 ) ) )
| ~ ( in @ ( sK28_D @ SV82 @ SV66 @ SV11 ) @ SV82 ) )
= $true )
| ( ( SV82
= ( cartesian_product2 @ SV11 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1016]) ).
thf(1101,plain,
! [SV11: $i,SV66: $i,SV82: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY3106 @ SV82 @ SV66 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK30_SY3108 @ SV82 @ SV66 @ SV11 ) @ SV66 ) )
| ( ( sK28_D @ SV82 @ SV66 @ SV11 )
!= ( ordered_pair @ ( sK29_SY3106 @ SV82 @ SV66 @ SV11 ) @ ( sK30_SY3108 @ SV82 @ SV66 @ SV11 ) ) ) )
| ( in @ ( sK28_D @ SV82 @ SV66 @ SV11 ) @ SV82 ) )
= $true )
| ( ( SV82
= ( cartesian_product2 @ SV11 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1017]) ).
thf(1102,plain,
! [SV83: $i,SV67: $i,SV11: $i] :
( ( ( ~ ! [SY3444: $i] :
( ! [SY3423: $i,SY3424: $i] :
( ~ ( in @ SY3423 @ SV11 )
| ~ ( in @ SY3424 @ SV67 )
| ( SY3444
!= ( ordered_pair @ SY3423 @ SY3424 ) ) )
| ( in @ SY3444 @ SV83 ) ) )
= $false )
| ( ( SV83
= ( cartesian_product2 @ SV11 @ SV67 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1018]) ).
thf(1103,plain,
! [SV11: $i,SV67: $i,SV83: $i] :
( ( ( ~ ! [SY3447: $i] :
( ~ ( in @ SY3447 @ SV83 )
| ~ ( ~ ~ ( ~ ( in @ ( sK26_E @ SY3447 @ SV83 @ SV67 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK27_SY3103 @ SY3447 @ SV83 @ SV67 @ SV11 ) @ SV67 ) )
| ( SY3447
!= ( ordered_pair @ ( sK26_E @ SY3447 @ SV83 @ SV67 @ SV11 ) @ ( sK27_SY3103 @ SY3447 @ SV83 @ SV67 @ SV11 ) ) ) ) ) )
= $false )
| ( ( SV83
= ( cartesian_product2 @ SV11 @ SV67 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1018]) ).
thf(1104,plain,
! [SV84: $i,SV68: $i,SV12: $i] :
( ( ( in @ ( ordered_pair @ SV12 @ SV68 ) @ SV84 )
= $false )
| ( ( in @ SV12 @ ( relation_field @ SV84 ) )
= $true )
| ( ( relation @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1019]) ).
thf(1105,plain,
! [SV85: $i,SV69: $i,SV12: $i] :
( ( ( in @ ( ordered_pair @ SV12 @ SV69 ) @ SV85 )
= $false )
| ( ( in @ SV69 @ ( relation_field @ SV85 ) )
= $true )
| ( ( relation @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1020]) ).
thf(1106,plain,
! [SV50: $i,SV43: $i,SV146: $i,SV13: $i] :
( ( ( ~ ( ( SV13
!= ( ordered_pair @ ( sK33_C @ SV146 @ SV13 ) @ ( sK34_SY3110 @ SV146 @ SV13 ) ) )
| ~ ( ( SV146
!= ( sK34_SY3110 @ SV146 @ SV13 ) ) ) ) )
= $true )
| ( ( SV146
= ( pair_second @ SV13 ) )
= $true )
| ( ( SV13
= ( ordered_pair @ SV43 @ SV50 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1021]) ).
thf(1107,plain,
! [SV50: $i,SV43: $i,SV13: $i,SV147: $i] :
( ( ( ( SV147
!= ( pair_second @ SV13 ) ) )
= $true )
| ( ( ! [SY3536: $i,SY3537: $i] :
( ( SV13
!= ( ordered_pair @ SY3536 @ SY3537 ) )
| ( SV147 = SY3537 ) ) )
= $true )
| ( ( SV13
= ( ordered_pair @ SV43 @ SV50 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1022]) ).
thf(1108,plain,
! [SV14: $i,SV103: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK14_C @ SV103 @ SV14 )
!= ( sK15_SY3096 @ SV103 @ SV14 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SV103 @ SV14 ) @ SV103 )
| ~ ( in @ ( sK15_SY3096 @ SV103 @ SV14 ) @ SV103 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK14_C @ SV103 @ SV14 ) @ ( sK15_SY3096 @ SV103 @ SV14 ) ) @ SV14 ) ) )
= $false )
| ( ( is_connected_in @ SV14 @ SV103 )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1023]) ).
thf(1109,plain,
! [SV14: $i,SV103: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK15_SY3096 @ SV103 @ SV14 ) @ ( sK14_C @ SV103 @ SV14 ) ) @ SV14 ) )
= $false )
| ( ( is_connected_in @ SV14 @ SV103 )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1023]) ).
thf(1110,plain,
! [SV14: $i,SV104: $i,SV165: $i] :
( ( ( ! [SY3554: $i] :
( ( SV165 = SY3554 )
| ~ ( in @ SV165 @ SV104 )
| ~ ( in @ SY3554 @ SV104 )
| ( in @ ( ordered_pair @ SV165 @ SY3554 ) @ SV14 )
| ( in @ ( ordered_pair @ SY3554 @ SV165 ) @ SV14 ) ) )
= $true )
| ( ( is_connected_in @ SV14 @ SV104 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1111,plain,
! [SV70: $i,SV15: $i,SV86: $i,SV166: $i] :
( ( ( ~ ( in @ SV166 @ ( relation_dom @ SV86 ) )
| ~ ( in @ ( ordered_pair @ SV166 @ SV15 ) @ SV86 )
| ~ ( in @ SV166 @ SV70 ) )
= $true )
| ( ( in @ SV15 @ ( relation_image @ SV86 @ SV70 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1112,plain,
! [SV71: $i,SV87: $i,SV15: $i] :
( ( ( in @ SV15 @ ( relation_image @ SV87 @ SV71 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK61_D @ SV87 @ SV71 @ SV15 ) @ ( relation_dom @ SV87 ) )
| ~ ( in @ ( ordered_pair @ ( sK61_D @ SV87 @ SV71 @ SV15 ) @ SV15 ) @ SV87 ) )
| ~ ( in @ ( sK61_D @ SV87 @ SV71 @ SV15 ) @ SV71 ) ) )
= $true )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1026]) ).
thf(1113,plain,
! [SV16: $i,SV105: $i,SV128: $i] :
( ( ( ~ ( ! [SY3506: $i] :
( ~ ( in @ ( ordered_pair @ SY3506 @ ( sK46_D @ SV128 @ SV105 @ SV16 ) ) @ SV16 )
| ~ ( in @ SY3506 @ SV105 ) )
| ~ ( in @ ( sK46_D @ SV128 @ SV105 @ SV16 ) @ SV128 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SV128 @ SV105 @ SV16 ) @ ( sK46_D @ SV128 @ SV105 @ SV16 ) ) @ SV16 )
| ~ ( in @ ( sK47_SY3118 @ SV128 @ SV105 @ SV16 ) @ SV105 ) )
| ( in @ ( sK46_D @ SV128 @ SV105 @ SV16 ) @ SV128 ) ) )
= $false )
| ( ( SV128
= ( relation_image @ SV16 @ SV105 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1027]) ).
thf(1114,plain,
! [SV106: $i,SV16: $i,SV129: $i] :
( ( ( SV129
= ( relation_image @ SV16 @ SV106 ) )
= $false )
| ( ( ~ ( ~ ! [SY3507: $i] :
( ! [SY3468: $i] :
( ~ ( in @ ( ordered_pair @ SY3468 @ SY3507 ) @ SV16 )
| ~ ( in @ SY3468 @ SV106 ) )
| ( in @ SY3507 @ SV129 ) )
| ~ ! [SY3509: $i] :
( ~ ( in @ SY3509 @ SV129 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SY3509 @ SV129 @ SV106 @ SV16 ) @ SY3509 ) @ SV16 )
| ~ ( in @ ( sK45_E @ SY3509 @ SV129 @ SV106 @ SV16 ) @ SV106 ) ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1028]) ).
thf(1115,plain,
! [SV51: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK64_B @ SV51 ) @ ( sK65_SY3126 @ SV51 ) ) @ SV51 )
| ~ ( in @ ( ordered_pair @ ( sK65_SY3126 @ SV51 ) @ ( sK64_B @ SV51 ) ) @ SV51 ) ) )
= $true )
| ( ( antisymmetric @ SV51 )
= $true )
| ( ( relation @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1029]) ).
thf(1116,plain,
! [SV51: $i] :
( ( ( ( ( sK64_B @ SV51 )
!= ( sK65_SY3126 @ SV51 ) ) )
= $true )
| ( ( antisymmetric @ SV51 )
= $true )
| ( ( relation @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1030]) ).
thf(1117,plain,
! [SV52: $i,SV167: $i,SV148: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV148 @ SV167 ) @ SV52 )
| ~ ( in @ ( ordered_pair @ SV167 @ SV148 ) @ SV52 )
| ( SV148 = SV167 ) )
= $true )
| ( ( antisymmetric @ SV52 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1118,plain,
! [SV17: $i,SV72: $i,SV88: $i] :
( ( ( relation @ SV88 )
= $false )
| ( ( function @ SV88 )
= $false )
| ( ( ( SV72
!= ( apply @ SV88 @ SV17 ) )
| ~ ( in @ SV17 @ ( relation_dom @ SV88 ) )
| ( in @ ( ordered_pair @ SV17 @ SV72 ) @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1032]) ).
thf(1119,plain,
! [SV130: $i,SV17: $i,SV149: $i] :
( ( ( ~ ( function @ SV149 )
| ~ ( relation @ SV149 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV17 @ SV130 ) @ SV149 )
| ( SV130
= ( apply @ SV149 @ SV17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1033]) ).
thf(1120,plain,
! [SV131: $i,SV17: $i,SV150: $i] :
( ( ( ~ ( function @ SV150 )
| ~ ( relation @ SV150 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV17 @ SV131 ) @ SV150 )
| ( in @ SV17 @ ( relation_dom @ SV150 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1034]) ).
thf(1121,plain,
! [SV18: $i,SV107: $i,SV132: $i] :
( ( ( ~ ( ( ( sK35_D @ SV132 @ SV107 @ SV18 )
= SV107 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV107 ) @ SV18 )
| ~ ( in @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV132 ) )
| ~ ~ ( ~ ( ( ( sK35_D @ SV132 @ SV107 @ SV18 )
!= SV107 )
| ( in @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV132 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV107 ) @ SV18 )
| ( in @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV132 ) ) ) )
= $false )
| ( ( SV132
= ( fiber @ SV18 @ SV107 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1035]) ).
thf(1122,plain,
! [SV108: $i,SV18: $i,SV133: $i] :
( ( ( SV133
= ( fiber @ SV18 @ SV108 ) )
= $false )
| ( ( ~ ( ~ ! [SY3512: $i] :
( ( SY3512 = SV108 )
| ~ ( in @ ( ordered_pair @ SY3512 @ SV108 ) @ SV18 )
| ( in @ SY3512 @ SV133 ) )
| ~ ~ ( ~ ! [SY3513: $i] :
( ~ ( in @ SY3513 @ SV133 )
| ( SY3513 != SV108 ) )
| ~ ! [SY3514: $i] :
( ~ ( in @ SY3514 @ SV133 )
| ( in @ ( ordered_pair @ SY3514 @ SV108 ) @ SV18 ) ) ) ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1036]) ).
thf(1123,plain,
! [SV19: $i,SV109: $i] :
( ( ( ~ ( in @ ( sK36_C @ SV109 @ SV19 ) @ SV109 ) )
= $false )
| ( ( is_reflexive_in @ SV19 @ SV109 )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1037]) ).
thf(1124,plain,
! [SV19: $i,SV109: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SV109 @ SV19 ) @ ( sK36_C @ SV109 @ SV19 ) ) @ SV19 ) )
= $false )
| ( ( is_reflexive_in @ SV19 @ SV109 )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1037]) ).
thf(1125,plain,
! [SV19: $i,SV110: $i,SV168: $i] :
( ( ( ~ ( in @ SV168 @ SV110 )
| ( in @ ( ordered_pair @ SV168 @ SV168 ) @ SV19 ) )
= $true )
| ( ( is_reflexive_in @ SV19 @ SV110 )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1126,plain,
! [SV20: $i,SV111: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SV111 @ SV20 ) @ ( sK13_SY3095 @ SV111 @ SV20 ) ) @ SV111 )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV111 @ SV20 ) @ ( sK12_C @ SV111 @ SV20 ) ) @ SV20 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SV111 @ SV20 ) @ ( sK13_SY3095 @ SV111 @ SV20 ) ) @ SV111 )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV111 @ SV20 ) @ ( sK12_C @ SV111 @ SV20 ) ) @ SV20 ) ) ) )
= $true )
| ( ( SV111
= ( relation_inverse @ SV20 ) )
= $true )
| ( ( relation @ SV111 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1039]) ).
thf(1127,plain,
! [SV20: $i,SV112: $i] :
( ( ( ( SV112
!= ( relation_inverse @ SV20 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3476: $i,SY3477: $i] :
( ~ ( in @ ( ordered_pair @ SY3476 @ SY3477 ) @ SV112 )
| ( in @ ( ordered_pair @ SY3477 @ SY3476 ) @ SV20 ) )
| ~ ! [SY3478: $i,SY3479: $i] :
( ~ ( in @ ( ordered_pair @ SY3479 @ SY3478 ) @ SV20 )
| ( in @ ( ordered_pair @ SY3478 @ SY3479 ) @ SV112 ) ) ) )
= $true )
| ( ( relation @ SV112 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1040]) ).
thf(1128,plain,
! [SV21: $i,SV38: $i,SV134: $i] :
( ( ( relation @ SV134 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) @ SV21 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV38 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV38 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) ) ) )
| ( SV134
= ( relation_rng_restriction @ SV21 @ SV38 ) ) )
= $true )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1041]) ).
thf(1129,plain,
! [SV38: $i,SV21: $i,SV135: $i] :
( ( ( relation @ SV135 )
= $false )
| ( ( ( SV135
!= ( relation_rng_restriction @ SV21 @ SV38 ) )
| ~ ( ~ ! [SY3515: $i,SY3516: $i] :
( ~ ( in @ SY3516 @ SV21 )
| ~ ( in @ ( ordered_pair @ SY3515 @ SY3516 ) @ SV38 )
| ( in @ ( ordered_pair @ SY3515 @ SY3516 ) @ SV135 ) )
| ~ ~ ( ~ ! [SY3517: $i,SY3518: $i] :
( ~ ( in @ ( ordered_pair @ SY3517 @ SY3518 ) @ SV135 )
| ( in @ SY3518 @ SV21 ) )
| ~ ! [SY3519: $i,SY3520: $i] :
( ~ ( in @ ( ordered_pair @ SY3519 @ SY3520 ) @ SV135 )
| ( in @ ( ordered_pair @ SY3519 @ SY3520 ) @ SV38 ) ) ) ) )
= $true )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1042]) ).
thf(1130,plain,
! [SV22: $i,SV113: $i] :
( ( ( ~ ( ! [SY3480: $i] :
~ ( in @ ( ordered_pair @ SY3480 @ ( sK17_C @ SV113 @ SV22 ) ) @ SV22 )
| ~ ( in @ ( sK17_C @ SV113 @ SV22 ) @ SV113 ) ) )
= $false )
| ( ( SV113
= ( relation_rng @ SV22 ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1043]) ).
thf(1131,plain,
! [SV22: $i,SV113: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK18_SY3098 @ SV113 @ SV22 ) @ ( sK17_C @ SV113 @ SV22 ) ) @ SV22 )
| ( in @ ( sK17_C @ SV113 @ SV22 ) @ SV113 ) ) )
= $false )
| ( ( SV113
= ( relation_rng @ SV22 ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1043]) ).
thf(1132,plain,
! [SV114: $i,SV22: $i] :
( ( ( ~ ! [SY3481: $i] :
( ! [SY3248: $i] :
~ ( in @ ( ordered_pair @ SY3248 @ SY3481 ) @ SV22 )
| ( in @ SY3481 @ SV114 ) )
| ~ ! [SY3483: $i] :
( ~ ( in @ SY3483 @ SV114 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3483 @ SV114 @ SV22 ) @ SY3483 ) @ SV22 ) ) )
= $false )
| ( ( SV114
= ( relation_rng @ SV22 ) )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1044]) ).
thf(1133,plain,
! [SV23: $i,SV115: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV115 @ SV23 ) @ ( sK25_SY3102 @ SV115 @ SV23 ) ) @ SV23 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SV115 @ SV23 ) @ ( sK25_SY3102 @ SV115 @ SV23 ) ) @ SV115 ) ) )
= $true )
| ( ( subset @ SV23 @ SV115 )
= $true )
| ( ( relation @ SV115 )
= $false )
| ( ( relation @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1045]) ).
thf(1134,plain,
! [SV116: $i,SV23: $i] :
( ( ( ~ ( subset @ SV23 @ SV116 ) )
= $true )
| ( ( ! [SY3484: $i,SY3485: $i] :
( ~ ( in @ ( ordered_pair @ SY3484 @ SY3485 ) @ SV23 )
| ( in @ ( ordered_pair @ SY3484 @ SY3485 ) @ SV116 ) ) )
= $true )
| ( ( relation @ SV116 )
= $false )
| ( ( relation @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1046]) ).
thf(1135,plain,
! [SV24: $i,SV117: $i,SV136: $i] :
( ( ( relation @ SV136 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ SV117 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV24 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) )
| ~ ~ ( ~ ( ( in @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ SV117 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV24 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) ) ) )
| ( SV136
= ( relation_dom_restriction @ SV24 @ SV117 ) ) )
= $true )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1047]) ).
thf(1136,plain,
! [SV118: $i,SV24: $i,SV137: $i] :
( ( ( relation @ SV137 )
= $false )
| ( ( ( SV137
!= ( relation_dom_restriction @ SV24 @ SV118 ) )
| ~ ( ~ ! [SY3521: $i,SY3522: $i] :
( ~ ( in @ SY3521 @ SV118 )
| ~ ( in @ ( ordered_pair @ SY3521 @ SY3522 ) @ SV24 )
| ( in @ ( ordered_pair @ SY3521 @ SY3522 ) @ SV137 ) )
| ~ ~ ( ~ ! [SY3523: $i] :
( ! [SY3524: $i] :
~ ( in @ ( ordered_pair @ SY3523 @ SY3524 ) @ SV137 )
| ( in @ SY3523 @ SV118 ) )
| ~ ! [SY3525: $i,SY3526: $i] :
( ~ ( in @ ( ordered_pair @ SY3525 @ SY3526 ) @ SV137 )
| ( in @ ( ordered_pair @ SY3525 @ SY3526 ) @ SV24 ) ) ) ) )
= $true )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1048]) ).
thf(1137,plain,
! [SV26: $i] :
( ( ( ~ ! [SY3269: $i] :
( ~ ( in @ SY3269 @ ( relation_dom @ SV26 ) )
| ! [SY3270: $i] :
( ( SY3270
!= ( apply @ SV26 @ SY3269 ) )
| ( in @ ( ordered_pair @ SY3269 @ SY3270 ) @ SV26 ) ) ) )
= $false )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1051]) ).
thf(1138,plain,
! [SV26: $i] :
( ( ( ~ ! [SY3271: $i] :
( ~ ( in @ SY3271 @ ( relation_dom @ SV26 ) )
| ! [SY3272: $i] :
( ~ ( in @ ( ordered_pair @ SY3271 @ SY3272 ) @ SV26 )
| ( SY3272
= ( apply @ SV26 @ SY3271 ) ) ) ) )
= $false )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1051]) ).
thf(1139,plain,
! [SV26: $i] :
( ( ( ~ ! [SY3273: $i] :
( ( in @ SY3273 @ ( relation_dom @ SV26 ) )
| ! [SY3274: $i] :
( ( SY3274
!= ( apply @ SV26 @ SY3273 ) )
| ( SY3274 = empty_set ) ) ) )
= $false )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1052]) ).
thf(1140,plain,
! [SV26: $i] :
( ( ( ~ ! [SY3275: $i] :
( ( in @ SY3275 @ ( relation_dom @ SV26 ) )
| ! [SY3276: $i] :
( ( SY3276 != empty_set )
| ( SY3276
= ( apply @ SV26 @ SY3275 ) ) ) ) )
= $false )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1052]) ).
thf(1141,plain,
! [SV53: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK62_B @ SV53 )
!= ( sK63_SY3125 @ SV53 ) ) )
| ~ ~ ( ~ ( in @ ( sK62_B @ SV53 ) @ ( relation_field @ SV53 ) )
| ~ ( in @ ( sK63_SY3125 @ SV53 ) @ ( relation_field @ SV53 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK62_B @ SV53 ) @ ( sK63_SY3125 @ SV53 ) ) @ SV53 ) ) )
= $true )
| ( ( connected @ SV53 )
= $true )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1053]) ).
thf(1142,plain,
! [SV53: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK63_SY3125 @ SV53 ) @ ( sK62_B @ SV53 ) ) @ SV53 ) )
= $true )
| ( ( connected @ SV53 )
= $true )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1054]) ).
thf(1143,plain,
! [SV54: $i,SV169: $i,SV151: $i] :
( ( ( ( SV151 = SV169 )
| ~ ( in @ SV151 @ ( relation_field @ SV54 ) )
| ~ ( in @ SV169 @ ( relation_field @ SV54 ) )
| ( in @ ( ordered_pair @ SV151 @ SV169 ) @ SV54 )
| ( in @ ( ordered_pair @ SV169 @ SV151 ) @ SV54 ) )
= $true )
| ( ( connected @ SV54 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1144,plain,
! [SV27: $i,SV120: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_C @ SV120 @ SV27 ) @ SV120 )
| ~ ( in @ ( sK20_SY3099 @ SV120 @ SV27 ) @ SV120 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SV120 @ SV27 ) @ ( sK20_SY3099 @ SV120 @ SV27 ) ) @ SV27 ) )
| ~ ( in @ ( ordered_pair @ ( sK20_SY3099 @ SV120 @ SV27 ) @ ( sK19_C @ SV120 @ SV27 ) ) @ SV27 ) ) )
= $false )
| ( ( is_antisymmetric_in @ SV27 @ SV120 )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1056]) ).
thf(1145,plain,
! [SV27: $i,SV120: $i] :
( ( ( ~ ( ( ( sK19_C @ SV120 @ SV27 )
!= ( sK20_SY3099 @ SV120 @ SV27 ) ) ) )
= $false )
| ( ( is_antisymmetric_in @ SV27 @ SV120 )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1056]) ).
thf(1146,plain,
! [SV27: $i,SV121: $i,SV170: $i] :
( ( ( ! [SY3555: $i] :
( ~ ( in @ SV170 @ SV121 )
| ~ ( in @ SY3555 @ SV121 )
| ~ ( in @ ( ordered_pair @ SV170 @ SY3555 ) @ SV27 )
| ~ ( in @ ( ordered_pair @ SY3555 @ SV170 ) @ SV27 )
| ( SV170 = SY3555 ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV27 @ SV121 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1147,plain,
! [SV122: $i,SV40: $i,SV91: $i,SV28: $i] :
( ( ( in @ SV28 @ SV91 )
= $false )
| ( ( ~ ( in @ SV40 @ SV122 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SV91 @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1058]) ).
thf(1148,plain,
! [SV152: $i,SV40: $i,SV28: $i] :
( ( ( ! [SY3540: $i] :
~ ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SV152 @ SY3540 ) ) )
= $true )
| ( ( in @ SV28 @ SV152 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1059]) ).
thf(1149,plain,
! [SV171: $i,SV153: $i,SV40: $i,SV28: $i] :
( ( ~ ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SV153 @ SV171 ) )
| ( in @ SV40 @ SV171 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1150,plain,
! [SV55: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK66_B @ SV55 ) @ ( sK67_SY3127 @ SV55 ) ) @ SV55 )
| ~ ( in @ ( ordered_pair @ ( sK67_SY3127 @ SV55 ) @ ( sK68_SY3129 @ SV55 ) ) @ SV55 ) ) )
= $true )
| ( ( transitive @ SV55 )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1061]) ).
thf(1151,plain,
! [SV55: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK66_B @ SV55 ) @ ( sK68_SY3129 @ SV55 ) ) @ SV55 ) )
= $true )
| ( ( transitive @ SV55 )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1062]) ).
thf(1152,plain,
! [SV56: $i,SV172: $i,SV154: $i] :
( ( ( ! [SY3556: $i] :
( ~ ( in @ ( ordered_pair @ SV154 @ SV172 ) @ SV56 )
| ~ ( in @ ( ordered_pair @ SV172 @ SY3556 ) @ SV56 )
| ( in @ ( ordered_pair @ SV154 @ SY3556 ) @ SV56 ) ) )
= $true )
| ( ( transitive @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1153,plain,
! [SV123: $i,SV41: $i,SV92: $i,SV29: $i] :
( ( ( in @ SV29 @ SV92 )
= $false )
| ( ( ~ ( in @ SV41 @ SV123 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SV92 @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1064]) ).
thf(1154,plain,
! [SV155: $i,SV41: $i,SV29: $i] :
( ( ( ! [SY3544: $i] :
~ ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SV155 @ SY3544 ) ) )
= $true )
| ( ( in @ SV29 @ SV155 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1065]) ).
thf(1155,plain,
! [SV173: $i,SV156: $i,SV41: $i,SV29: $i] :
( ( ~ ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SV156 @ SV173 ) )
| ( in @ SV41 @ SV173 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1156,plain,
! [SV30: $i,SV124: $i,SV139: $i] :
( ( ( ~ ( ! [SY3527: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SY3527 ) @ SV30 )
| ~ ( in @ SY3527 @ SV124 ) )
| ~ ( in @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SV139 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ ( sK44_SY3116 @ SV139 @ SV124 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK44_SY3116 @ SV139 @ SV124 @ SV30 ) @ SV124 ) )
| ( in @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SV139 ) ) )
= $false )
| ( ( SV139
= ( relation_inverse_image @ SV30 @ SV124 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1067]) ).
thf(1157,plain,
! [SV125: $i,SV30: $i,SV140: $i] :
( ( ( SV140
= ( relation_inverse_image @ SV30 @ SV125 ) )
= $false )
| ( ( ~ ( ~ ! [SY3528: $i] :
( ! [SY3500: $i] :
( ~ ( in @ ( ordered_pair @ SY3528 @ SY3500 ) @ SV30 )
| ~ ( in @ SY3500 @ SV125 ) )
| ( in @ SY3528 @ SV140 ) )
| ~ ! [SY3530: $i] :
( ~ ( in @ SY3530 @ SV140 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3530 @ ( sK42_E @ SY3530 @ SV140 @ SV125 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK42_E @ SY3530 @ SV140 @ SV125 @ SV30 ) @ SV125 ) ) ) ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1068]) ).
thf(1158,plain,
! [SV93: $i,SV73: $i,SV31: $i] :
( ( ( in @ ( ordered_pair @ SV31 @ SV73 ) @ SV93 )
= $false )
| ( ( in @ SV31 @ ( relation_dom @ SV93 ) )
= $true )
| ( ( relation @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1069]) ).
thf(1159,plain,
! [SV94: $i,SV74: $i,SV31: $i] :
( ( ( in @ ( ordered_pair @ SV31 @ SV74 ) @ SV94 )
= $false )
| ( ( in @ SV74 @ ( relation_rng @ SV94 ) )
= $true )
| ( ( relation @ SV94 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1070]) ).
thf(1160,plain,
! [SV57: $i] :
( ( ( in @ ( sK69_B @ SV57 ) @ ( relation_field @ SV57 ) )
= $true )
| ( ( reflexive @ SV57 )
= $true )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1071]) ).
thf(1161,plain,
! [SV57: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK69_B @ SV57 ) @ ( sK69_B @ SV57 ) ) @ SV57 ) )
= $true )
| ( ( reflexive @ SV57 )
= $true )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1072]) ).
thf(1162,plain,
! [SV58: $i,SV157: $i] :
( ( ( ~ ( in @ SV157 @ ( relation_field @ SV58 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV157 @ SV157 ) @ SV58 )
= $true )
| ( ( reflexive @ SV58 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1073]) ).
thf(1163,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( ~ ( function @ SV174 )
| ~ ( relation @ SV174 )
| ~ ( ~ ( ~ ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) ) ) )
| ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 )
| ( relation_isomorphism @ SV32 @ SV59 @ SV174 ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1164,plain,
! [SV59: $i,SV32: $i] :
( ( ( ~ ! [SY3393: $i] :
( ~ ( function @ SY3393 )
| ~ ( relation @ SY3393 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3393 )
| ~ ( ~ ! [SY3394: $i,SY3395: $i] :
( ~ ( in @ SY3394 @ ( relation_field @ SV32 ) )
| ~ ( in @ SY3395 @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3393 @ SY3394 ) @ ( apply @ SY3393 @ SY3395 ) ) @ SV59 )
| ( in @ ( ordered_pair @ SY3394 @ SY3395 ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3312: $i] :
( ! [SY3313: $i] :
~ ( in @ ( ordered_pair @ SY3312 @ SY3313 ) @ SV32 )
| ( in @ SY3312 @ ( relation_field @ SV32 ) ) )
| ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV32 )
| ( in @ SY3315 @ ( relation_field @ SV32 ) ) ) )
| ~ ! [SY3400: $i,SY3401: $i] :
( ~ ( in @ ( ordered_pair @ SY3400 @ SY3401 ) @ SV32 )
| ( in @ ( ordered_pair @ ( apply @ SY3393 @ SY3400 ) @ ( apply @ SY3393 @ SY3401 ) ) @ SV59 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3402: $i] :
( ~ ( function @ SY3402 )
| ~ ( relation @ SY3402 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3402 )
| ( ( relation_dom @ SY3402 )
= ( relation_field @ SV32 ) ) )
| ~ ! [SY3403: $i] :
( ~ ( function @ SY3403 )
| ~ ( relation @ SY3403 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3403 )
| ( ( relation_rng @ SY3403 )
= ( relation_field @ SV59 ) ) ) )
| ~ ! [SY3404: $i] :
( ~ ( function @ SY3404 )
| ~ ( relation @ SY3404 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3404 )
| ( one_to_one @ SY3404 ) ) ) )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1075]) ).
thf(1165,plain,
! [SV33: $i,SV75: $i,SV95: $i] :
( ( ( ~ ! [SY3453: $i] :
~ ( in @ ( ordered_pair @ SY3453 @ ( sK57_D @ SV95 @ SV75 @ SV33 ) ) @ SV95 )
| ~ ( in @ ( sK57_D @ SV95 @ SV75 @ SV33 ) @ SV75 ) )
= $false )
| ( ( ( relation_rng_as_subset @ SV33 @ SV75 @ SV95 )
= SV75 )
= $true )
| ( ( relation_of2_as_subset @ SV95 @ SV33 @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1076]) ).
thf(1166,plain,
! [SV96: $i,SV76: $i,SV33: $i] :
( ( ( ( relation_rng_as_subset @ SV33 @ SV76 @ SV96 )
= SV76 )
= $false )
| ( ( ! [SY3454: $i] :
( ( in @ ( ordered_pair @ ( sK56_E @ SY3454 @ SV96 @ SV76 @ SV33 ) @ SY3454 ) @ SV96 )
| ~ ( in @ SY3454 @ SV76 ) ) )
= $true )
| ( ( relation_of2_as_subset @ SV96 @ SV33 @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1077]) ).
thf(1167,plain,
! [SV34: $i,SV126: $i] :
( ( ( ~ ( ! [SY3502: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SV126 @ SV34 ) @ SY3502 ) @ SV34 )
| ~ ( in @ ( sK22_C @ SV126 @ SV34 ) @ SV126 ) ) )
= $false )
| ( ( SV126
= ( relation_dom @ SV34 ) )
= $true )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1078]) ).
thf(1168,plain,
! [SV34: $i,SV126: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SV126 @ SV34 ) @ ( sK23_SY3101 @ SV126 @ SV34 ) ) @ SV34 )
| ( in @ ( sK22_C @ SV126 @ SV34 ) @ SV126 ) ) )
= $false )
| ( ( SV126
= ( relation_dom @ SV34 ) )
= $true )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1078]) ).
thf(1169,plain,
! [SV127: $i,SV34: $i] :
( ( ( ~ ! [SY3503: $i] :
( ! [SY3331: $i] :
~ ( in @ ( ordered_pair @ SY3503 @ SY3331 ) @ SV34 )
| ( in @ SY3503 @ SV127 ) )
| ~ ! [SY3505: $i] :
( ~ ( in @ SY3505 @ SV127 )
| ( in @ ( ordered_pair @ SY3505 @ ( sK21_D @ SY3505 @ SV127 @ SV34 ) ) @ SV34 ) ) )
= $false )
| ( ( SV127
= ( relation_dom @ SV34 ) )
= $false )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1079]) ).
thf(1170,plain,
! [SV158: $i,SV141: $i,SV44: $i] :
( ( ( ( sK39_B @ SV44 )
= ( ordered_pair @ SV141 @ SV158 ) )
= $false )
| ( ( relation @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1080]) ).
thf(1171,plain,
! [SV4: $i,SV98: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV4 )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV98 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV4 )
| ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV98 ) ) )
= $false )
| ( ( SV4 = SV98 )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1081]) ).
thf(1172,plain,
! [SV99: $i,SV4: $i] :
( ( ( SV4 = SV99 )
= $false )
| ( ( ~ ( ~ ! [SY3455: $i,SY3456: $i] :
( ~ ( in @ ( ordered_pair @ SY3455 @ SY3456 ) @ SV4 )
| ( in @ ( ordered_pair @ SY3455 @ SY3456 ) @ SV99 ) )
| ~ ! [SY3457: $i,SY3458: $i] :
( ~ ( in @ ( ordered_pair @ SY3457 @ SY3458 ) @ SV99 )
| ( in @ ( ordered_pair @ SY3457 @ SY3458 ) @ SV4 ) ) ) )
= $true )
| ( ( relation @ SV99 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1082]) ).
thf(1173,plain,
! [SV5: $i,SV100: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SV100 @ SV5 ) @ SV100 )
| ~ ( in @ ( sK4_SY3086 @ SV100 @ SV5 ) @ SV100 ) )
| ~ ( in @ ( sK5_SY3088 @ SV100 @ SV5 ) @ SV100 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SV100 @ SV5 ) @ ( sK4_SY3086 @ SV100 @ SV5 ) ) @ SV5 ) )
| ~ ( in @ ( ordered_pair @ ( sK4_SY3086 @ SV100 @ SV5 ) @ ( sK5_SY3088 @ SV100 @ SV5 ) ) @ SV5 ) ) )
= $true )
| ( ( is_transitive_in @ SV5 @ SV100 )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1083]) ).
thf(1174,plain,
! [SV5: $i,SV100: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK3_C @ SV100 @ SV5 ) @ ( sK5_SY3088 @ SV100 @ SV5 ) ) @ SV5 ) )
= $true )
| ( ( is_transitive_in @ SV5 @ SV100 )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1084]) ).
thf(1175,plain,
! [SV5: $i,SV175: $i,SV101: $i,SV159: $i] :
( ( ( ! [SY3557: $i] :
( ~ ( in @ SV159 @ SV101 )
| ~ ( in @ SV175 @ SV101 )
| ~ ( in @ SY3557 @ SV101 )
| ~ ( in @ ( ordered_pair @ SV159 @ SV175 ) @ SV5 )
| ~ ( in @ ( ordered_pair @ SV175 @ SY3557 ) @ SV5 )
| ( in @ ( ordered_pair @ SV159 @ SY3557 ) @ SV5 ) ) )
= $true )
| ( ( is_transitive_in @ SV5 @ SV101 )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1176,plain,
! [SV6: $i,SV60: $i,SV77: $i] :
( ( ( ~ ! [SY3438: $i] :
~ ( in @ ( ordered_pair @ ( sK59_D @ SV77 @ SV60 @ SV6 ) @ SY3438 ) @ SV77 ) )
= $false )
| ( ( ( relation_dom_as_subset @ SV60 @ SV6 @ SV77 )
= SV60 )
= $true )
| ( ( relation_of2_as_subset @ SV77 @ SV60 @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1086]) ).
thf(1177,plain,
! [SV6: $i,SV60: $i,SV77: $i] :
( ( ( ~ ( in @ ( sK59_D @ SV77 @ SV60 @ SV6 ) @ SV60 ) )
= $false )
| ( ( ( relation_dom_as_subset @ SV60 @ SV6 @ SV77 )
= SV60 )
= $true )
| ( ( relation_of2_as_subset @ SV77 @ SV60 @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1086]) ).
thf(1178,plain,
! [SV6: $i,SV61: $i,SV78: $i,SV176: $i] :
( ( ( ( in @ ( ordered_pair @ SV176 @ ( sK58_E @ SV176 @ SV78 @ SV61 @ SV6 ) ) @ SV78 )
| ~ ( in @ SV176 @ SV61 ) )
= $true )
| ( ( ( relation_dom_as_subset @ SV61 @ SV6 @ SV78 )
= SV61 )
= $false )
| ( ( relation_of2_as_subset @ SV78 @ SV61 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1179,plain,
! [SV7: $i,SV46: $i,SV160: $i] :
( ( ( ~ ( relation @ SV160 ) )
= $true )
| ( ( ~ ( ~ ( ! [SY3548: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ SY3548 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3548 @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV46 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV160 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK9_SY3093 @ SV160 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV46 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV160 ) ) )
| ( SV160
= ( relation_composition @ SV7 @ SV46 ) ) )
= $true )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1088]) ).
thf(1180,plain,
! [SV46: $i,SV7: $i,SV161: $i] :
( ( ( ~ ( relation @ SV161 ) )
= $true )
| ( ( ( SV161
!= ( relation_composition @ SV7 @ SV46 ) )
| ~ ( ~ ! [SY3549: $i,SY3550: $i] :
( ! [SY3373: $i] :
( ~ ( in @ ( ordered_pair @ SY3549 @ SY3373 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3373 @ SY3550 ) @ SV46 ) )
| ( in @ ( ordered_pair @ SY3549 @ SY3550 ) @ SV161 ) )
| ~ ! [SY3552: $i,SY3553: $i] :
( ~ ( in @ ( ordered_pair @ SY3552 @ SY3553 ) @ SV161 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3552 @ ( sK6_F @ SY3553 @ SY3552 @ SV161 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY3553 @ SY3552 @ SV161 @ SV46 @ SV7 ) @ SY3553 ) @ SV46 ) ) ) ) )
= $true )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1089]) ).
thf(1181,plain,
! [SV47: $i,SV62: $i] :
( ( ( ( ( sK52_C @ SV62 @ SV47 )
!= ( sK53_SY3121 @ SV62 @ SV47 ) )
| ~ ( in @ ( sK52_C @ SV62 @ SV47 ) @ SV47 )
| ~ ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) )
= $true )
| ( ( SV62
= ( identity_relation @ SV47 ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1090]) ).
thf(1182,plain,
! [SV47: $i,SV62: $i] :
( ( ( ~ ( ~ ( ( ( sK52_C @ SV62 @ SV47 )
= ( sK53_SY3121 @ SV62 @ SV47 ) )
| ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) )
| ~ ( ( in @ ( sK52_C @ SV62 @ SV47 ) @ SV47 )
| ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) ) ) )
= $true )
| ( ( SV62
= ( identity_relation @ SV47 ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1091]) ).
thf(1183,plain,
! [SV63: $i,SV48: $i] :
( ( ( ~ ! [SY3409: $i,SY3410: $i] :
( ( SY3409 != SY3410 )
| ~ ( in @ SY3409 @ SV48 )
| ( in @ ( ordered_pair @ SY3409 @ SY3410 ) @ SV63 ) ) )
= $false )
| ( ( SV63
= ( identity_relation @ SV48 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1092]) ).
thf(1184,plain,
! [SV48: $i,SV63: $i] :
( ( ( ~ ~ ( ~ ! [SY3411: $i,SY3412: $i] :
( ~ ( in @ ( ordered_pair @ SY3411 @ SY3412 ) @ SV63 )
| ( SY3411 = SY3412 ) )
| ~ ! [SY3413: $i] :
( ! [SY3414: $i] :
~ ( in @ ( ordered_pair @ SY3413 @ SY3414 ) @ SV63 )
| ( in @ SY3413 @ SV48 ) ) ) )
= $false )
| ( ( SV63
= ( identity_relation @ SV48 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1092]) ).
thf(1185,plain,
! [SV49: $i,SV42: $i,SV142: $i,SV8: $i] :
( ( ( ( SV8
!= ( ordered_pair @ ( sK40_C @ SV142 @ SV8 ) @ ( sK41_SY3114 @ SV142 @ SV8 ) ) )
| ~ ( ( SV142
!= ( sK40_C @ SV142 @ SV8 ) ) ) )
= $false )
| ( ( SV142
= ( pair_first @ SV8 ) )
= $true )
| ( ( SV8
= ( ordered_pair @ SV42 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1093]) ).
thf(1186,plain,
! [SV49: $i,SV42: $i,SV8: $i,SV143: $i] :
( ( ( SV143
= ( pair_first @ SV8 ) )
= $false )
| ( ( ! [SY3532: $i] :
( ! [SY3163: $i] :
( SV8
!= ( ordered_pair @ SY3532 @ SY3163 ) )
| ( SV143 = SY3532 ) ) )
= $true )
| ( ( SV8
= ( ordered_pair @ SV42 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1094]) ).
thf(1187,plain,
! [SV102: $i,SV37: $i,SV79: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV79 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ SV102 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SV79 ) @ SV102 ) )
= $true )
| ( ( relation @ SV102 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1095]) ).
thf(1188,plain,
! [SV144: $i,SV37: $i,SV9: $i,SV162: $i] :
( ( ( ~ ( relation @ SV162 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SV144 ) @ SV162 ) )
| ( in @ SV9 @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1096]) ).
thf(1189,plain,
! [SV145: $i,SV37: $i,SV9: $i,SV163: $i] :
( ( ( ~ ( relation @ SV163 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SV145 ) @ SV163 ) )
| ( in @ ( ordered_pair @ SV9 @ SV37 ) @ SV163 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1097]) ).
thf(1190,plain,
! [SV64: $i,SV10: $i,SV80: $i,SV164: $i] :
( ( ( ~ ( in @ SV164 @ ( relation_rng @ SV80 ) )
| ~ ( in @ ( ordered_pair @ SV10 @ SV164 ) @ SV80 ) )
= $true )
| ( ( ~ ( in @ SV164 @ SV64 ) )
= $true )
| ( ( in @ SV10 @ ( relation_inverse_image @ SV80 @ SV64 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1098]) ).
thf(1191,plain,
! [SV10: $i,SV65: $i,SV81: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK60_D @ SV81 @ SV65 @ SV10 ) @ ( relation_rng @ SV81 ) )
| ~ ( in @ ( ordered_pair @ SV10 @ ( sK60_D @ SV81 @ SV65 @ SV10 ) ) @ SV81 ) )
| ~ ( in @ ( sK60_D @ SV81 @ SV65 @ SV10 ) @ SV65 ) )
= $false )
| ( ( in @ SV10 @ ( relation_inverse_image @ SV81 @ SV65 ) )
= $false )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1099]) ).
thf(1192,plain,
! [SV82: $i,SV66: $i,SV11: $i] :
( ( ( ! [SY3442: $i,SY3443: $i] :
( ~ ( in @ SY3442 @ SV11 )
| ~ ( in @ SY3443 @ SV66 )
| ( ( sK28_D @ SV82 @ SV66 @ SV11 )
!= ( ordered_pair @ SY3442 @ SY3443 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK28_D @ SV82 @ SV66 @ SV11 ) @ SV82 ) )
= $true )
| ( ( SV82
= ( cartesian_product2 @ SV11 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1100]) ).
thf(1193,plain,
! [SV11: $i,SV66: $i,SV82: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY3106 @ SV82 @ SV66 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK30_SY3108 @ SV82 @ SV66 @ SV11 ) @ SV66 ) )
| ( ( sK28_D @ SV82 @ SV66 @ SV11 )
!= ( ordered_pair @ ( sK29_SY3106 @ SV82 @ SV66 @ SV11 ) @ ( sK30_SY3108 @ SV82 @ SV66 @ SV11 ) ) ) ) )
= $true )
| ( ( in @ ( sK28_D @ SV82 @ SV66 @ SV11 ) @ SV82 )
= $true )
| ( ( SV82
= ( cartesian_product2 @ SV11 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1101]) ).
thf(1194,plain,
! [SV83: $i,SV67: $i,SV11: $i] :
( ( ( ! [SY3444: $i] :
( ! [SY3423: $i,SY3424: $i] :
( ~ ( in @ SY3423 @ SV11 )
| ~ ( in @ SY3424 @ SV67 )
| ( SY3444
!= ( ordered_pair @ SY3423 @ SY3424 ) ) )
| ( in @ SY3444 @ SV83 ) ) )
= $true )
| ( ( SV83
= ( cartesian_product2 @ SV11 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1102]) ).
thf(1195,plain,
! [SV11: $i,SV67: $i,SV83: $i] :
( ( ( ! [SY3447: $i] :
( ~ ( in @ SY3447 @ SV83 )
| ~ ( ~ ~ ( ~ ( in @ ( sK26_E @ SY3447 @ SV83 @ SV67 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK27_SY3103 @ SY3447 @ SV83 @ SV67 @ SV11 ) @ SV67 ) )
| ( SY3447
!= ( ordered_pair @ ( sK26_E @ SY3447 @ SV83 @ SV67 @ SV11 ) @ ( sK27_SY3103 @ SY3447 @ SV83 @ SV67 @ SV11 ) ) ) ) ) )
= $true )
| ( ( SV83
= ( cartesian_product2 @ SV11 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1103]) ).
thf(1196,plain,
! [SV50: $i,SV43: $i,SV146: $i,SV13: $i] :
( ( ( ( SV13
!= ( ordered_pair @ ( sK33_C @ SV146 @ SV13 ) @ ( sK34_SY3110 @ SV146 @ SV13 ) ) )
| ~ ( ( SV146
!= ( sK34_SY3110 @ SV146 @ SV13 ) ) ) )
= $false )
| ( ( SV146
= ( pair_second @ SV13 ) )
= $true )
| ( ( SV13
= ( ordered_pair @ SV43 @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1106]) ).
thf(1197,plain,
! [SV50: $i,SV43: $i,SV13: $i,SV147: $i] :
( ( ( SV147
= ( pair_second @ SV13 ) )
= $false )
| ( ( ! [SY3536: $i,SY3537: $i] :
( ( SV13
!= ( ordered_pair @ SY3536 @ SY3537 ) )
| ( SV147 = SY3537 ) ) )
= $true )
| ( ( SV13
= ( ordered_pair @ SV43 @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1107]) ).
thf(1198,plain,
! [SV14: $i,SV103: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK14_C @ SV103 @ SV14 )
!= ( sK15_SY3096 @ SV103 @ SV14 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SV103 @ SV14 ) @ SV103 )
| ~ ( in @ ( sK15_SY3096 @ SV103 @ SV14 ) @ SV103 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK14_C @ SV103 @ SV14 ) @ ( sK15_SY3096 @ SV103 @ SV14 ) ) @ SV14 ) ) )
= $true )
| ( ( is_connected_in @ SV14 @ SV103 )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1108]) ).
thf(1199,plain,
! [SV14: $i,SV103: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK15_SY3096 @ SV103 @ SV14 ) @ ( sK14_C @ SV103 @ SV14 ) ) @ SV14 ) )
= $true )
| ( ( is_connected_in @ SV14 @ SV103 )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1109]) ).
thf(1200,plain,
! [SV14: $i,SV104: $i,SV177: $i,SV165: $i] :
( ( ( ( SV165 = SV177 )
| ~ ( in @ SV165 @ SV104 )
| ~ ( in @ SV177 @ SV104 )
| ( in @ ( ordered_pair @ SV165 @ SV177 ) @ SV14 )
| ( in @ ( ordered_pair @ SV177 @ SV165 ) @ SV14 ) )
= $true )
| ( ( is_connected_in @ SV14 @ SV104 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1201,plain,
! [SV70: $i,SV15: $i,SV86: $i,SV166: $i] :
( ( ( ~ ( in @ SV166 @ ( relation_dom @ SV86 ) )
| ~ ( in @ ( ordered_pair @ SV166 @ SV15 ) @ SV86 ) )
= $true )
| ( ( ~ ( in @ SV166 @ SV70 ) )
= $true )
| ( ( in @ SV15 @ ( relation_image @ SV86 @ SV70 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1111]) ).
thf(1202,plain,
! [SV15: $i,SV71: $i,SV87: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK61_D @ SV87 @ SV71 @ SV15 ) @ ( relation_dom @ SV87 ) )
| ~ ( in @ ( ordered_pair @ ( sK61_D @ SV87 @ SV71 @ SV15 ) @ SV15 ) @ SV87 ) )
| ~ ( in @ ( sK61_D @ SV87 @ SV71 @ SV15 ) @ SV71 ) )
= $false )
| ( ( in @ SV15 @ ( relation_image @ SV87 @ SV71 ) )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1112]) ).
thf(1203,plain,
! [SV16: $i,SV105: $i,SV128: $i] :
( ( ( ~ ( ! [SY3506: $i] :
( ~ ( in @ ( ordered_pair @ SY3506 @ ( sK46_D @ SV128 @ SV105 @ SV16 ) ) @ SV16 )
| ~ ( in @ SY3506 @ SV105 ) )
| ~ ( in @ ( sK46_D @ SV128 @ SV105 @ SV16 ) @ SV128 ) ) )
= $false )
| ( ( SV128
= ( relation_image @ SV16 @ SV105 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1113]) ).
thf(1204,plain,
! [SV16: $i,SV105: $i,SV128: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SV128 @ SV105 @ SV16 ) @ ( sK46_D @ SV128 @ SV105 @ SV16 ) ) @ SV16 )
| ~ ( in @ ( sK47_SY3118 @ SV128 @ SV105 @ SV16 ) @ SV105 ) )
| ( in @ ( sK46_D @ SV128 @ SV105 @ SV16 ) @ SV128 ) ) )
= $false )
| ( ( SV128
= ( relation_image @ SV16 @ SV105 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1113]) ).
thf(1205,plain,
! [SV129: $i,SV106: $i,SV16: $i] :
( ( ( ~ ! [SY3507: $i] :
( ! [SY3468: $i] :
( ~ ( in @ ( ordered_pair @ SY3468 @ SY3507 ) @ SV16 )
| ~ ( in @ SY3468 @ SV106 ) )
| ( in @ SY3507 @ SV129 ) )
| ~ ! [SY3509: $i] :
( ~ ( in @ SY3509 @ SV129 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SY3509 @ SV129 @ SV106 @ SV16 ) @ SY3509 ) @ SV16 )
| ~ ( in @ ( sK45_E @ SY3509 @ SV129 @ SV106 @ SV16 ) @ SV106 ) ) ) )
= $false )
| ( ( SV129
= ( relation_image @ SV16 @ SV106 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1114]) ).
thf(1206,plain,
! [SV51: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK64_B @ SV51 ) @ ( sK65_SY3126 @ SV51 ) ) @ SV51 )
| ~ ( in @ ( ordered_pair @ ( sK65_SY3126 @ SV51 ) @ ( sK64_B @ SV51 ) ) @ SV51 ) )
= $false )
| ( ( antisymmetric @ SV51 )
= $true )
| ( ( relation @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1115]) ).
thf(1207,plain,
! [SV51: $i] :
( ( ( ( sK64_B @ SV51 )
= ( sK65_SY3126 @ SV51 ) )
= $false )
| ( ( antisymmetric @ SV51 )
= $true )
| ( ( relation @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1116]) ).
thf(1208,plain,
! [SV52: $i,SV167: $i,SV148: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV148 @ SV167 ) @ SV52 )
| ~ ( in @ ( ordered_pair @ SV167 @ SV148 ) @ SV52 ) )
= $true )
| ( ( SV148 = SV167 )
= $true )
| ( ( antisymmetric @ SV52 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1117]) ).
thf(1209,plain,
! [SV17: $i,SV88: $i,SV72: $i] :
( ( ( ( SV72
!= ( apply @ SV88 @ SV17 ) )
| ~ ( in @ SV17 @ ( relation_dom @ SV88 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV17 @ SV72 ) @ SV88 )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1118]) ).
thf(1210,plain,
! [SV130: $i,SV17: $i,SV149: $i] :
( ( ( ~ ( function @ SV149 ) )
= $true )
| ( ( ~ ( relation @ SV149 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV17 @ SV130 ) @ SV149 )
| ( SV130
= ( apply @ SV149 @ SV17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1119]) ).
thf(1211,plain,
! [SV131: $i,SV17: $i,SV150: $i] :
( ( ( ~ ( function @ SV150 ) )
= $true )
| ( ( ~ ( relation @ SV150 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV17 @ SV131 ) @ SV150 )
| ( in @ SV17 @ ( relation_dom @ SV150 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1120]) ).
thf(1212,plain,
! [SV18: $i,SV107: $i,SV132: $i] :
( ( ( ~ ( ( ( sK35_D @ SV132 @ SV107 @ SV18 )
= SV107 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV107 ) @ SV18 )
| ~ ( in @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV132 ) ) )
= $false )
| ( ( SV132
= ( fiber @ SV18 @ SV107 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1121]) ).
thf(1213,plain,
! [SV18: $i,SV107: $i,SV132: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK35_D @ SV132 @ SV107 @ SV18 )
!= SV107 )
| ( in @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV132 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV107 ) @ SV18 )
| ( in @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV132 ) ) ) )
= $false )
| ( ( SV132
= ( fiber @ SV18 @ SV107 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1121]) ).
thf(1214,plain,
! [SV133: $i,SV18: $i,SV108: $i] :
( ( ( ~ ! [SY3512: $i] :
( ( SY3512 = SV108 )
| ~ ( in @ ( ordered_pair @ SY3512 @ SV108 ) @ SV18 )
| ( in @ SY3512 @ SV133 ) )
| ~ ~ ( ~ ! [SY3513: $i] :
( ~ ( in @ SY3513 @ SV133 )
| ( SY3513 != SV108 ) )
| ~ ! [SY3514: $i] :
( ~ ( in @ SY3514 @ SV133 )
| ( in @ ( ordered_pair @ SY3514 @ SV108 ) @ SV18 ) ) ) )
= $false )
| ( ( SV133
= ( fiber @ SV18 @ SV108 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1122]) ).
thf(1215,plain,
! [SV19: $i,SV109: $i] :
( ( ( in @ ( sK36_C @ SV109 @ SV19 ) @ SV109 )
= $true )
| ( ( is_reflexive_in @ SV19 @ SV109 )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1123]) ).
thf(1216,plain,
! [SV19: $i,SV109: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SV109 @ SV19 ) @ ( sK36_C @ SV109 @ SV19 ) ) @ SV19 ) )
= $true )
| ( ( is_reflexive_in @ SV19 @ SV109 )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1124]) ).
thf(1217,plain,
! [SV19: $i,SV110: $i,SV168: $i] :
( ( ( ~ ( in @ SV168 @ SV110 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV168 @ SV168 ) @ SV19 )
= $true )
| ( ( is_reflexive_in @ SV19 @ SV110 )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1125]) ).
thf(1218,plain,
! [SV20: $i,SV111: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SV111 @ SV20 ) @ ( sK13_SY3095 @ SV111 @ SV20 ) ) @ SV111 )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV111 @ SV20 ) @ ( sK12_C @ SV111 @ SV20 ) ) @ SV20 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SV111 @ SV20 ) @ ( sK13_SY3095 @ SV111 @ SV20 ) ) @ SV111 )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV111 @ SV20 ) @ ( sK12_C @ SV111 @ SV20 ) ) @ SV20 ) ) )
= $false )
| ( ( SV111
= ( relation_inverse @ SV20 ) )
= $true )
| ( ( relation @ SV111 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1126]) ).
thf(1219,plain,
! [SV20: $i,SV112: $i] :
( ( ( SV112
= ( relation_inverse @ SV20 ) )
= $false )
| ( ( ~ ( ~ ! [SY3476: $i,SY3477: $i] :
( ~ ( in @ ( ordered_pair @ SY3476 @ SY3477 ) @ SV112 )
| ( in @ ( ordered_pair @ SY3477 @ SY3476 ) @ SV20 ) )
| ~ ! [SY3478: $i,SY3479: $i] :
( ~ ( in @ ( ordered_pair @ SY3479 @ SY3478 ) @ SV20 )
| ( in @ ( ordered_pair @ SY3478 @ SY3479 ) @ SV112 ) ) ) )
= $true )
| ( ( relation @ SV112 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1127]) ).
thf(1220,plain,
! [SV21: $i,SV38: $i,SV134: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) @ SV21 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV38 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV38 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) ) ) ) )
= $true )
| ( ( SV134
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $true )
| ( ( relation @ SV134 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1128]) ).
thf(1221,plain,
! [SV38: $i,SV21: $i,SV135: $i] :
( ( ( ( SV135
!= ( relation_rng_restriction @ SV21 @ SV38 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3515: $i,SY3516: $i] :
( ~ ( in @ SY3516 @ SV21 )
| ~ ( in @ ( ordered_pair @ SY3515 @ SY3516 ) @ SV38 )
| ( in @ ( ordered_pair @ SY3515 @ SY3516 ) @ SV135 ) )
| ~ ~ ( ~ ! [SY3517: $i,SY3518: $i] :
( ~ ( in @ ( ordered_pair @ SY3517 @ SY3518 ) @ SV135 )
| ( in @ SY3518 @ SV21 ) )
| ~ ! [SY3519: $i,SY3520: $i] :
( ~ ( in @ ( ordered_pair @ SY3519 @ SY3520 ) @ SV135 )
| ( in @ ( ordered_pair @ SY3519 @ SY3520 ) @ SV38 ) ) ) ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1129]) ).
thf(1222,plain,
! [SV22: $i,SV113: $i] :
( ( ( ! [SY3480: $i] :
~ ( in @ ( ordered_pair @ SY3480 @ ( sK17_C @ SV113 @ SV22 ) ) @ SV22 )
| ~ ( in @ ( sK17_C @ SV113 @ SV22 ) @ SV113 ) )
= $true )
| ( ( SV113
= ( relation_rng @ SV22 ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1130]) ).
thf(1223,plain,
! [SV22: $i,SV113: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK18_SY3098 @ SV113 @ SV22 ) @ ( sK17_C @ SV113 @ SV22 ) ) @ SV22 )
| ( in @ ( sK17_C @ SV113 @ SV22 ) @ SV113 ) )
= $true )
| ( ( SV113
= ( relation_rng @ SV22 ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1131]) ).
thf(1224,plain,
! [SV114: $i,SV22: $i] :
( ( ( ~ ! [SY3481: $i] :
( ! [SY3248: $i] :
~ ( in @ ( ordered_pair @ SY3248 @ SY3481 ) @ SV22 )
| ( in @ SY3481 @ SV114 ) ) )
= $false )
| ( ( SV114
= ( relation_rng @ SV22 ) )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1132]) ).
thf(1225,plain,
! [SV22: $i,SV114: $i] :
( ( ( ~ ! [SY3483: $i] :
( ~ ( in @ SY3483 @ SV114 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3483 @ SV114 @ SV22 ) @ SY3483 ) @ SV22 ) ) )
= $false )
| ( ( SV114
= ( relation_rng @ SV22 ) )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1132]) ).
thf(1226,plain,
! [SV23: $i,SV115: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV115 @ SV23 ) @ ( sK25_SY3102 @ SV115 @ SV23 ) ) @ SV23 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SV115 @ SV23 ) @ ( sK25_SY3102 @ SV115 @ SV23 ) ) @ SV115 ) )
= $false )
| ( ( subset @ SV23 @ SV115 )
= $true )
| ( ( relation @ SV115 )
= $false )
| ( ( relation @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1133]) ).
thf(1227,plain,
! [SV116: $i,SV23: $i] :
( ( ( subset @ SV23 @ SV116 )
= $false )
| ( ( ! [SY3484: $i,SY3485: $i] :
( ~ ( in @ ( ordered_pair @ SY3484 @ SY3485 ) @ SV23 )
| ( in @ ( ordered_pair @ SY3484 @ SY3485 ) @ SV116 ) ) )
= $true )
| ( ( relation @ SV116 )
= $false )
| ( ( relation @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1134]) ).
thf(1228,plain,
! [SV24: $i,SV117: $i,SV136: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ SV117 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV24 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) )
| ~ ~ ( ~ ( ( in @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ SV117 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV24 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) ) ) ) )
= $true )
| ( ( SV136
= ( relation_dom_restriction @ SV24 @ SV117 ) )
= $true )
| ( ( relation @ SV136 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1135]) ).
thf(1229,plain,
! [SV118: $i,SV24: $i,SV137: $i] :
( ( ( ( SV137
!= ( relation_dom_restriction @ SV24 @ SV118 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3521: $i,SY3522: $i] :
( ~ ( in @ SY3521 @ SV118 )
| ~ ( in @ ( ordered_pair @ SY3521 @ SY3522 ) @ SV24 )
| ( in @ ( ordered_pair @ SY3521 @ SY3522 ) @ SV137 ) )
| ~ ~ ( ~ ! [SY3523: $i] :
( ! [SY3524: $i] :
~ ( in @ ( ordered_pair @ SY3523 @ SY3524 ) @ SV137 )
| ( in @ SY3523 @ SV118 ) )
| ~ ! [SY3525: $i,SY3526: $i] :
( ~ ( in @ ( ordered_pair @ SY3525 @ SY3526 ) @ SV137 )
| ( in @ ( ordered_pair @ SY3525 @ SY3526 ) @ SV24 ) ) ) ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1136]) ).
thf(1230,plain,
! [SV26: $i] :
( ( ( ! [SY3269: $i] :
( ~ ( in @ SY3269 @ ( relation_dom @ SV26 ) )
| ! [SY3270: $i] :
( ( SY3270
!= ( apply @ SV26 @ SY3269 ) )
| ( in @ ( ordered_pair @ SY3269 @ SY3270 ) @ SV26 ) ) ) )
= $true )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1137]) ).
thf(1231,plain,
! [SV26: $i] :
( ( ( ! [SY3271: $i] :
( ~ ( in @ SY3271 @ ( relation_dom @ SV26 ) )
| ! [SY3272: $i] :
( ~ ( in @ ( ordered_pair @ SY3271 @ SY3272 ) @ SV26 )
| ( SY3272
= ( apply @ SV26 @ SY3271 ) ) ) ) )
= $true )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1138]) ).
thf(1232,plain,
! [SV26: $i] :
( ( ( ! [SY3273: $i] :
( ( in @ SY3273 @ ( relation_dom @ SV26 ) )
| ! [SY3274: $i] :
( ( SY3274
!= ( apply @ SV26 @ SY3273 ) )
| ( SY3274 = empty_set ) ) ) )
= $true )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1139]) ).
thf(1233,plain,
! [SV26: $i] :
( ( ( ! [SY3275: $i] :
( ( in @ SY3275 @ ( relation_dom @ SV26 ) )
| ! [SY3276: $i] :
( ( SY3276 != empty_set )
| ( SY3276
= ( apply @ SV26 @ SY3275 ) ) ) ) )
= $true )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1140]) ).
thf(1234,plain,
! [SV53: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK62_B @ SV53 )
!= ( sK63_SY3125 @ SV53 ) ) )
| ~ ~ ( ~ ( in @ ( sK62_B @ SV53 ) @ ( relation_field @ SV53 ) )
| ~ ( in @ ( sK63_SY3125 @ SV53 ) @ ( relation_field @ SV53 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK62_B @ SV53 ) @ ( sK63_SY3125 @ SV53 ) ) @ SV53 ) )
= $false )
| ( ( connected @ SV53 )
= $true )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1141]) ).
thf(1235,plain,
! [SV53: $i] :
( ( ( in @ ( ordered_pair @ ( sK63_SY3125 @ SV53 ) @ ( sK62_B @ SV53 ) ) @ SV53 )
= $false )
| ( ( connected @ SV53 )
= $true )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1142]) ).
thf(1236,plain,
! [SV54: $i,SV169: $i,SV151: $i] :
( ( ( ( SV151 = SV169 )
| ~ ( in @ SV151 @ ( relation_field @ SV54 ) )
| ~ ( in @ SV169 @ ( relation_field @ SV54 ) )
| ( in @ ( ordered_pair @ SV151 @ SV169 ) @ SV54 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV169 @ SV151 ) @ SV54 )
= $true )
| ( ( connected @ SV54 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1143]) ).
thf(1237,plain,
! [SV27: $i,SV120: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_C @ SV120 @ SV27 ) @ SV120 )
| ~ ( in @ ( sK20_SY3099 @ SV120 @ SV27 ) @ SV120 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SV120 @ SV27 ) @ ( sK20_SY3099 @ SV120 @ SV27 ) ) @ SV27 ) )
| ~ ( in @ ( ordered_pair @ ( sK20_SY3099 @ SV120 @ SV27 ) @ ( sK19_C @ SV120 @ SV27 ) ) @ SV27 ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV27 @ SV120 )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1144]) ).
thf(1238,plain,
! [SV27: $i,SV120: $i] :
( ( ( ( ( sK19_C @ SV120 @ SV27 )
!= ( sK20_SY3099 @ SV120 @ SV27 ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV27 @ SV120 )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1145]) ).
thf(1239,plain,
! [SV27: $i,SV178: $i,SV121: $i,SV170: $i] :
( ( ( ~ ( in @ SV170 @ SV121 )
| ~ ( in @ SV178 @ SV121 )
| ~ ( in @ ( ordered_pair @ SV170 @ SV178 ) @ SV27 )
| ~ ( in @ ( ordered_pair @ SV178 @ SV170 ) @ SV27 )
| ( SV170 = SV178 ) )
= $true )
| ( ( is_antisymmetric_in @ SV27 @ SV121 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1240,plain,
! [SV91: $i,SV28: $i,SV122: $i,SV40: $i] :
( ( ( in @ SV40 @ SV122 )
= $false )
| ( ( in @ SV28 @ SV91 )
= $false )
| ( ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SV91 @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1147]) ).
thf(1241,plain,
! [SV179: $i,SV152: $i,SV40: $i,SV28: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SV152 @ SV179 ) ) )
= $true )
| ( ( in @ SV28 @ SV152 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1148]) ).
thf(1242,plain,
! [SV171: $i,SV153: $i,SV40: $i,SV28: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SV153 @ SV171 ) ) )
= $true )
| ( ( in @ SV40 @ SV171 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1149]) ).
thf(1243,plain,
! [SV55: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK66_B @ SV55 ) @ ( sK67_SY3127 @ SV55 ) ) @ SV55 )
| ~ ( in @ ( ordered_pair @ ( sK67_SY3127 @ SV55 ) @ ( sK68_SY3129 @ SV55 ) ) @ SV55 ) )
= $false )
| ( ( transitive @ SV55 )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1150]) ).
thf(1244,plain,
! [SV55: $i] :
( ( ( in @ ( ordered_pair @ ( sK66_B @ SV55 ) @ ( sK68_SY3129 @ SV55 ) ) @ SV55 )
= $false )
| ( ( transitive @ SV55 )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1151]) ).
thf(1245,plain,
! [SV180: $i,SV56: $i,SV172: $i,SV154: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV154 @ SV172 ) @ SV56 )
| ~ ( in @ ( ordered_pair @ SV172 @ SV180 ) @ SV56 )
| ( in @ ( ordered_pair @ SV154 @ SV180 ) @ SV56 ) )
= $true )
| ( ( transitive @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1246,plain,
! [SV92: $i,SV29: $i,SV123: $i,SV41: $i] :
( ( ( in @ SV41 @ SV123 )
= $false )
| ( ( in @ SV29 @ SV92 )
= $false )
| ( ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SV92 @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1153]) ).
thf(1247,plain,
! [SV181: $i,SV155: $i,SV41: $i,SV29: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SV155 @ SV181 ) ) )
= $true )
| ( ( in @ SV29 @ SV155 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1248,plain,
! [SV173: $i,SV156: $i,SV41: $i,SV29: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SV156 @ SV173 ) ) )
= $true )
| ( ( in @ SV41 @ SV173 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1155]) ).
thf(1249,plain,
! [SV30: $i,SV124: $i,SV139: $i] :
( ( ( ~ ( ! [SY3527: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SY3527 ) @ SV30 )
| ~ ( in @ SY3527 @ SV124 ) )
| ~ ( in @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SV139 ) ) )
= $false )
| ( ( SV139
= ( relation_inverse_image @ SV30 @ SV124 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1156]) ).
thf(1250,plain,
! [SV30: $i,SV124: $i,SV139: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ ( sK44_SY3116 @ SV139 @ SV124 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK44_SY3116 @ SV139 @ SV124 @ SV30 ) @ SV124 ) )
| ( in @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SV139 ) ) )
= $false )
| ( ( SV139
= ( relation_inverse_image @ SV30 @ SV124 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1156]) ).
thf(1251,plain,
! [SV140: $i,SV125: $i,SV30: $i] :
( ( ( ~ ! [SY3528: $i] :
( ! [SY3500: $i] :
( ~ ( in @ ( ordered_pair @ SY3528 @ SY3500 ) @ SV30 )
| ~ ( in @ SY3500 @ SV125 ) )
| ( in @ SY3528 @ SV140 ) )
| ~ ! [SY3530: $i] :
( ~ ( in @ SY3530 @ SV140 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3530 @ ( sK42_E @ SY3530 @ SV140 @ SV125 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK42_E @ SY3530 @ SV140 @ SV125 @ SV30 ) @ SV125 ) ) ) )
= $false )
| ( ( SV140
= ( relation_inverse_image @ SV30 @ SV125 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1157]) ).
thf(1252,plain,
! [SV57: $i] :
( ( ( in @ ( ordered_pair @ ( sK69_B @ SV57 ) @ ( sK69_B @ SV57 ) ) @ SV57 )
= $false )
| ( ( reflexive @ SV57 )
= $true )
| ( ( relation @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1161]) ).
thf(1253,plain,
! [SV58: $i,SV157: $i] :
( ( ( in @ SV157 @ ( relation_field @ SV58 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV157 @ SV157 ) @ SV58 )
= $true )
| ( ( reflexive @ SV58 )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1162]) ).
thf(1254,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( ~ ( function @ SV174 )
| ~ ( relation @ SV174 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) ) ) )
| ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 )
| ( relation_isomorphism @ SV32 @ SV59 @ SV174 ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1163]) ).
thf(1255,plain,
! [SV59: $i,SV32: $i] :
( ( ( ~ ! [SY3393: $i] :
( ~ ( function @ SY3393 )
| ~ ( relation @ SY3393 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3393 )
| ~ ( ~ ! [SY3394: $i,SY3395: $i] :
( ~ ( in @ SY3394 @ ( relation_field @ SV32 ) )
| ~ ( in @ SY3395 @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3393 @ SY3394 ) @ ( apply @ SY3393 @ SY3395 ) ) @ SV59 )
| ( in @ ( ordered_pair @ SY3394 @ SY3395 ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3312: $i] :
( ! [SY3313: $i] :
~ ( in @ ( ordered_pair @ SY3312 @ SY3313 ) @ SV32 )
| ( in @ SY3312 @ ( relation_field @ SV32 ) ) )
| ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV32 )
| ( in @ SY3315 @ ( relation_field @ SV32 ) ) ) )
| ~ ! [SY3400: $i,SY3401: $i] :
( ~ ( in @ ( ordered_pair @ SY3400 @ SY3401 ) @ SV32 )
| ( in @ ( ordered_pair @ ( apply @ SY3393 @ SY3400 ) @ ( apply @ SY3393 @ SY3401 ) ) @ SV59 ) ) ) ) ) )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1164]) ).
thf(1256,plain,
! [SV59: $i,SV32: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY3402: $i] :
( ~ ( function @ SY3402 )
| ~ ( relation @ SY3402 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3402 )
| ( ( relation_dom @ SY3402 )
= ( relation_field @ SV32 ) ) )
| ~ ! [SY3403: $i] :
( ~ ( function @ SY3403 )
| ~ ( relation @ SY3403 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3403 )
| ( ( relation_rng @ SY3403 )
= ( relation_field @ SV59 ) ) ) )
| ~ ! [SY3404: $i] :
( ~ ( function @ SY3404 )
| ~ ( relation @ SY3404 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3404 )
| ( one_to_one @ SY3404 ) ) ) )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1164]) ).
thf(1257,plain,
! [SV33: $i,SV75: $i,SV95: $i] :
( ( ( ~ ! [SY3453: $i] :
~ ( in @ ( ordered_pair @ SY3453 @ ( sK57_D @ SV95 @ SV75 @ SV33 ) ) @ SV95 ) )
= $false )
| ( ( ( relation_rng_as_subset @ SV33 @ SV75 @ SV95 )
= SV75 )
= $true )
| ( ( relation_of2_as_subset @ SV95 @ SV33 @ SV75 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1165]) ).
thf(1258,plain,
! [SV33: $i,SV75: $i,SV95: $i] :
( ( ( ~ ( in @ ( sK57_D @ SV95 @ SV75 @ SV33 ) @ SV75 ) )
= $false )
| ( ( ( relation_rng_as_subset @ SV33 @ SV75 @ SV95 )
= SV75 )
= $true )
| ( ( relation_of2_as_subset @ SV95 @ SV33 @ SV75 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1165]) ).
thf(1259,plain,
! [SV33: $i,SV76: $i,SV96: $i,SV182: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK56_E @ SV182 @ SV96 @ SV76 @ SV33 ) @ SV182 ) @ SV96 )
| ~ ( in @ SV182 @ SV76 ) )
= $true )
| ( ( ( relation_rng_as_subset @ SV33 @ SV76 @ SV96 )
= SV76 )
= $false )
| ( ( relation_of2_as_subset @ SV96 @ SV33 @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1260,plain,
! [SV34: $i,SV126: $i] :
( ( ( ! [SY3502: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SV126 @ SV34 ) @ SY3502 ) @ SV34 )
| ~ ( in @ ( sK22_C @ SV126 @ SV34 ) @ SV126 ) )
= $true )
| ( ( SV126
= ( relation_dom @ SV34 ) )
= $true )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1167]) ).
thf(1261,plain,
! [SV34: $i,SV126: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK22_C @ SV126 @ SV34 ) @ ( sK23_SY3101 @ SV126 @ SV34 ) ) @ SV34 )
| ( in @ ( sK22_C @ SV126 @ SV34 ) @ SV126 ) )
= $true )
| ( ( SV126
= ( relation_dom @ SV34 ) )
= $true )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1168]) ).
thf(1262,plain,
! [SV127: $i,SV34: $i] :
( ( ( ~ ! [SY3503: $i] :
( ! [SY3331: $i] :
~ ( in @ ( ordered_pair @ SY3503 @ SY3331 ) @ SV34 )
| ( in @ SY3503 @ SV127 ) ) )
= $false )
| ( ( SV127
= ( relation_dom @ SV34 ) )
= $false )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1169]) ).
thf(1263,plain,
! [SV34: $i,SV127: $i] :
( ( ( ~ ! [SY3505: $i] :
( ~ ( in @ SY3505 @ SV127 )
| ( in @ ( ordered_pair @ SY3505 @ ( sK21_D @ SY3505 @ SV127 @ SV34 ) ) @ SV34 ) ) )
= $false )
| ( ( SV127
= ( relation_dom @ SV34 ) )
= $false )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1169]) ).
thf(1264,plain,
! [SV4: $i,SV98: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV4 )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV98 ) ) )
= $false )
| ( ( SV4 = SV98 )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1171]) ).
thf(1265,plain,
! [SV4: $i,SV98: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV4 )
| ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV98 ) ) )
= $false )
| ( ( SV4 = SV98 )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1171]) ).
thf(1266,plain,
! [SV99: $i,SV4: $i] :
( ( ( ~ ! [SY3455: $i,SY3456: $i] :
( ~ ( in @ ( ordered_pair @ SY3455 @ SY3456 ) @ SV4 )
| ( in @ ( ordered_pair @ SY3455 @ SY3456 ) @ SV99 ) )
| ~ ! [SY3457: $i,SY3458: $i] :
( ~ ( in @ ( ordered_pair @ SY3457 @ SY3458 ) @ SV99 )
| ( in @ ( ordered_pair @ SY3457 @ SY3458 ) @ SV4 ) ) )
= $false )
| ( ( SV4 = SV99 )
= $false )
| ( ( relation @ SV99 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1172]) ).
thf(1267,plain,
! [SV5: $i,SV100: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SV100 @ SV5 ) @ SV100 )
| ~ ( in @ ( sK4_SY3086 @ SV100 @ SV5 ) @ SV100 ) )
| ~ ( in @ ( sK5_SY3088 @ SV100 @ SV5 ) @ SV100 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SV100 @ SV5 ) @ ( sK4_SY3086 @ SV100 @ SV5 ) ) @ SV5 ) )
| ~ ( in @ ( ordered_pair @ ( sK4_SY3086 @ SV100 @ SV5 ) @ ( sK5_SY3088 @ SV100 @ SV5 ) ) @ SV5 ) )
= $false )
| ( ( is_transitive_in @ SV5 @ SV100 )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1173]) ).
thf(1268,plain,
! [SV5: $i,SV100: $i] :
( ( ( in @ ( ordered_pair @ ( sK3_C @ SV100 @ SV5 ) @ ( sK5_SY3088 @ SV100 @ SV5 ) ) @ SV5 )
= $false )
| ( ( is_transitive_in @ SV5 @ SV100 )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1174]) ).
thf(1269,plain,
! [SV5: $i,SV183: $i,SV175: $i,SV101: $i,SV159: $i] :
( ( ( ~ ( in @ SV159 @ SV101 )
| ~ ( in @ SV175 @ SV101 )
| ~ ( in @ SV183 @ SV101 )
| ~ ( in @ ( ordered_pair @ SV159 @ SV175 ) @ SV5 )
| ~ ( in @ ( ordered_pair @ SV175 @ SV183 ) @ SV5 )
| ( in @ ( ordered_pair @ SV159 @ SV183 ) @ SV5 ) )
= $true )
| ( ( is_transitive_in @ SV5 @ SV101 )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1270,plain,
! [SV6: $i,SV60: $i,SV77: $i] :
( ( ( ! [SY3438: $i] :
~ ( in @ ( ordered_pair @ ( sK59_D @ SV77 @ SV60 @ SV6 ) @ SY3438 ) @ SV77 ) )
= $true )
| ( ( ( relation_dom_as_subset @ SV60 @ SV6 @ SV77 )
= SV60 )
= $true )
| ( ( relation_of2_as_subset @ SV77 @ SV60 @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1176]) ).
thf(1271,plain,
! [SV6: $i,SV60: $i,SV77: $i] :
( ( ( in @ ( sK59_D @ SV77 @ SV60 @ SV6 ) @ SV60 )
= $true )
| ( ( ( relation_dom_as_subset @ SV60 @ SV6 @ SV77 )
= SV60 )
= $true )
| ( ( relation_of2_as_subset @ SV77 @ SV60 @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1177]) ).
thf(1272,plain,
! [SV6: $i,SV61: $i,SV78: $i,SV176: $i] :
( ( ( in @ ( ordered_pair @ SV176 @ ( sK58_E @ SV176 @ SV78 @ SV61 @ SV6 ) ) @ SV78 )
= $true )
| ( ( ~ ( in @ SV176 @ SV61 ) )
= $true )
| ( ( ( relation_dom_as_subset @ SV61 @ SV6 @ SV78 )
= SV61 )
= $false )
| ( ( relation_of2_as_subset @ SV78 @ SV61 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1178]) ).
thf(1273,plain,
! [SV7: $i,SV46: $i,SV160: $i] :
( ( ( relation @ SV160 )
= $false )
| ( ( ~ ( ~ ( ! [SY3548: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ SY3548 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3548 @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV46 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV160 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK9_SY3093 @ SV160 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV46 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV160 ) ) )
| ( SV160
= ( relation_composition @ SV7 @ SV46 ) ) )
= $true )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1179]) ).
thf(1274,plain,
! [SV46: $i,SV7: $i,SV161: $i] :
( ( ( relation @ SV161 )
= $false )
| ( ( ( SV161
!= ( relation_composition @ SV7 @ SV46 ) )
| ~ ( ~ ! [SY3549: $i,SY3550: $i] :
( ! [SY3373: $i] :
( ~ ( in @ ( ordered_pair @ SY3549 @ SY3373 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3373 @ SY3550 ) @ SV46 ) )
| ( in @ ( ordered_pair @ SY3549 @ SY3550 ) @ SV161 ) )
| ~ ! [SY3552: $i,SY3553: $i] :
( ~ ( in @ ( ordered_pair @ SY3552 @ SY3553 ) @ SV161 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3552 @ ( sK6_F @ SY3553 @ SY3552 @ SV161 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY3553 @ SY3552 @ SV161 @ SV46 @ SV7 ) @ SY3553 ) @ SV46 ) ) ) ) )
= $true )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1180]) ).
thf(1275,plain,
! [SV47: $i,SV62: $i] :
( ( ( ( ( sK52_C @ SV62 @ SV47 )
!= ( sK53_SY3121 @ SV62 @ SV47 ) )
| ~ ( in @ ( sK52_C @ SV62 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) )
= $true )
| ( ( SV62
= ( identity_relation @ SV47 ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1181]) ).
thf(1276,plain,
! [SV47: $i,SV62: $i] :
( ( ( ~ ( ( ( sK52_C @ SV62 @ SV47 )
= ( sK53_SY3121 @ SV62 @ SV47 ) )
| ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) )
| ~ ( ( in @ ( sK52_C @ SV62 @ SV47 ) @ SV47 )
| ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) ) )
= $false )
| ( ( SV62
= ( identity_relation @ SV47 ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1182]) ).
thf(1277,plain,
! [SV63: $i,SV48: $i] :
( ( ( ! [SY3409: $i,SY3410: $i] :
( ( SY3409 != SY3410 )
| ~ ( in @ SY3409 @ SV48 )
| ( in @ ( ordered_pair @ SY3409 @ SY3410 ) @ SV63 ) ) )
= $true )
| ( ( SV63
= ( identity_relation @ SV48 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1183]) ).
thf(1278,plain,
! [SV48: $i,SV63: $i] :
( ( ( ~ ( ~ ! [SY3411: $i,SY3412: $i] :
( ~ ( in @ ( ordered_pair @ SY3411 @ SY3412 ) @ SV63 )
| ( SY3411 = SY3412 ) )
| ~ ! [SY3413: $i] :
( ! [SY3414: $i] :
~ ( in @ ( ordered_pair @ SY3413 @ SY3414 ) @ SV63 )
| ( in @ SY3413 @ SV48 ) ) ) )
= $true )
| ( ( SV63
= ( identity_relation @ SV48 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1184]) ).
thf(1279,plain,
! [SV49: $i,SV42: $i,SV142: $i,SV8: $i] :
( ( ( ( SV8
!= ( ordered_pair @ ( sK40_C @ SV142 @ SV8 ) @ ( sK41_SY3114 @ SV142 @ SV8 ) ) ) )
= $false )
| ( ( SV142
= ( pair_first @ SV8 ) )
= $true )
| ( ( SV8
= ( ordered_pair @ SV42 @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1185]) ).
thf(1280,plain,
! [SV49: $i,SV42: $i,SV8: $i,SV142: $i] :
( ( ( ~ ( ( SV142
!= ( sK40_C @ SV142 @ SV8 ) ) ) )
= $false )
| ( ( SV142
= ( pair_first @ SV8 ) )
= $true )
| ( ( SV8
= ( ordered_pair @ SV42 @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1185]) ).
thf(1281,plain,
! [SV49: $i,SV42: $i,SV143: $i,SV184: $i,SV8: $i] :
( ( ( ! [SY3558: $i] :
( SV8
!= ( ordered_pair @ SV184 @ SY3558 ) )
| ( SV143 = SV184 ) )
= $true )
| ( ( SV143
= ( pair_first @ SV8 ) )
= $false )
| ( ( SV8
= ( ordered_pair @ SV42 @ SV49 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1186]) ).
thf(1282,plain,
! [SV102: $i,SV37: $i,SV79: $i,SV9: $i] :
( ( ( in @ SV9 @ SV79 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ SV102 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SV79 ) @ SV102 ) )
= $true )
| ( ( relation @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1187]) ).
thf(1283,plain,
! [SV144: $i,SV37: $i,SV9: $i,SV162: $i] :
( ( ( relation @ SV162 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SV144 ) @ SV162 ) )
| ( in @ SV9 @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1188]) ).
thf(1284,plain,
! [SV145: $i,SV37: $i,SV9: $i,SV163: $i] :
( ( ( relation @ SV163 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SV145 ) @ SV163 ) )
| ( in @ ( ordered_pair @ SV9 @ SV37 ) @ SV163 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1189]) ).
thf(1285,plain,
! [SV64: $i,SV10: $i,SV80: $i,SV164: $i] :
( ( ( ~ ( in @ SV164 @ ( relation_rng @ SV80 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV10 @ SV164 ) @ SV80 ) )
= $true )
| ( ( ~ ( in @ SV164 @ SV64 ) )
= $true )
| ( ( in @ SV10 @ ( relation_inverse_image @ SV80 @ SV64 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1190]) ).
thf(1286,plain,
! [SV10: $i,SV65: $i,SV81: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK60_D @ SV81 @ SV65 @ SV10 ) @ ( relation_rng @ SV81 ) )
| ~ ( in @ ( ordered_pair @ SV10 @ ( sK60_D @ SV81 @ SV65 @ SV10 ) ) @ SV81 ) ) )
= $false )
| ( ( in @ SV10 @ ( relation_inverse_image @ SV81 @ SV65 ) )
= $false )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1191]) ).
thf(1287,plain,
! [SV10: $i,SV65: $i,SV81: $i] :
( ( ( ~ ( in @ ( sK60_D @ SV81 @ SV65 @ SV10 ) @ SV65 ) )
= $false )
| ( ( in @ SV10 @ ( relation_inverse_image @ SV81 @ SV65 ) )
= $false )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1191]) ).
thf(1288,plain,
! [SV82: $i,SV66: $i,SV11: $i,SV185: $i] :
( ( ( ! [SY3559: $i] :
( ~ ( in @ SV185 @ SV11 )
| ~ ( in @ SY3559 @ SV66 )
| ( ( sK28_D @ SV82 @ SV66 @ SV11 )
!= ( ordered_pair @ SV185 @ SY3559 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK28_D @ SV82 @ SV66 @ SV11 ) @ SV82 ) )
= $true )
| ( ( SV82
= ( cartesian_product2 @ SV11 @ SV66 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1192]) ).
thf(1289,plain,
! [SV11: $i,SV66: $i,SV82: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK29_SY3106 @ SV82 @ SV66 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK30_SY3108 @ SV82 @ SV66 @ SV11 ) @ SV66 ) )
| ( ( sK28_D @ SV82 @ SV66 @ SV11 )
!= ( ordered_pair @ ( sK29_SY3106 @ SV82 @ SV66 @ SV11 ) @ ( sK30_SY3108 @ SV82 @ SV66 @ SV11 ) ) ) )
= $false )
| ( ( in @ ( sK28_D @ SV82 @ SV66 @ SV11 ) @ SV82 )
= $true )
| ( ( SV82
= ( cartesian_product2 @ SV11 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1193]) ).
thf(1290,plain,
! [SV83: $i,SV186: $i,SV67: $i,SV11: $i] :
( ( ( ! [SY3560: $i,SY3561: $i] :
( ~ ( in @ SY3560 @ SV11 )
| ~ ( in @ SY3561 @ SV67 )
| ( SV186
!= ( ordered_pair @ SY3560 @ SY3561 ) ) )
| ( in @ SV186 @ SV83 ) )
= $true )
| ( ( SV83
= ( cartesian_product2 @ SV11 @ SV67 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1291,plain,
! [SV11: $i,SV67: $i,SV83: $i,SV187: $i] :
( ( ( ~ ( in @ SV187 @ SV83 )
| ~ ( ~ ~ ( ~ ( in @ ( sK26_E @ SV187 @ SV83 @ SV67 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK27_SY3103 @ SV187 @ SV83 @ SV67 @ SV11 ) @ SV67 ) )
| ( SV187
!= ( ordered_pair @ ( sK26_E @ SV187 @ SV83 @ SV67 @ SV11 ) @ ( sK27_SY3103 @ SV187 @ SV83 @ SV67 @ SV11 ) ) ) ) )
= $true )
| ( ( SV83
= ( cartesian_product2 @ SV11 @ SV67 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1292,plain,
! [SV50: $i,SV43: $i,SV146: $i,SV13: $i] :
( ( ( ( SV13
!= ( ordered_pair @ ( sK33_C @ SV146 @ SV13 ) @ ( sK34_SY3110 @ SV146 @ SV13 ) ) ) )
= $false )
| ( ( SV146
= ( pair_second @ SV13 ) )
= $true )
| ( ( SV13
= ( ordered_pair @ SV43 @ SV50 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1196]) ).
thf(1293,plain,
! [SV50: $i,SV43: $i,SV13: $i,SV146: $i] :
( ( ( ~ ( ( SV146
!= ( sK34_SY3110 @ SV146 @ SV13 ) ) ) )
= $false )
| ( ( SV146
= ( pair_second @ SV13 ) )
= $true )
| ( ( SV13
= ( ordered_pair @ SV43 @ SV50 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1196]) ).
thf(1294,plain,
! [SV50: $i,SV43: $i,SV147: $i,SV188: $i,SV13: $i] :
( ( ( ! [SY3562: $i] :
( ( SV13
!= ( ordered_pair @ SV188 @ SY3562 ) )
| ( SV147 = SY3562 ) ) )
= $true )
| ( ( SV147
= ( pair_second @ SV13 ) )
= $false )
| ( ( SV13
= ( ordered_pair @ SV43 @ SV50 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1295,plain,
! [SV14: $i,SV103: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK14_C @ SV103 @ SV14 )
!= ( sK15_SY3096 @ SV103 @ SV14 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SV103 @ SV14 ) @ SV103 )
| ~ ( in @ ( sK15_SY3096 @ SV103 @ SV14 ) @ SV103 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK14_C @ SV103 @ SV14 ) @ ( sK15_SY3096 @ SV103 @ SV14 ) ) @ SV14 ) )
= $false )
| ( ( is_connected_in @ SV14 @ SV103 )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1198]) ).
thf(1296,plain,
! [SV14: $i,SV103: $i] :
( ( ( in @ ( ordered_pair @ ( sK15_SY3096 @ SV103 @ SV14 ) @ ( sK14_C @ SV103 @ SV14 ) ) @ SV14 )
= $false )
| ( ( is_connected_in @ SV14 @ SV103 )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1199]) ).
thf(1297,plain,
! [SV14: $i,SV104: $i,SV177: $i,SV165: $i] :
( ( ( ( SV165 = SV177 )
| ~ ( in @ SV165 @ SV104 )
| ~ ( in @ SV177 @ SV104 )
| ( in @ ( ordered_pair @ SV165 @ SV177 ) @ SV14 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV177 @ SV165 ) @ SV14 )
= $true )
| ( ( is_connected_in @ SV14 @ SV104 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1200]) ).
thf(1298,plain,
! [SV70: $i,SV15: $i,SV86: $i,SV166: $i] :
( ( ( ~ ( in @ SV166 @ ( relation_dom @ SV86 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV166 @ SV15 ) @ SV86 ) )
= $true )
| ( ( ~ ( in @ SV166 @ SV70 ) )
= $true )
| ( ( in @ SV15 @ ( relation_image @ SV86 @ SV70 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1201]) ).
thf(1299,plain,
! [SV15: $i,SV71: $i,SV87: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK61_D @ SV87 @ SV71 @ SV15 ) @ ( relation_dom @ SV87 ) )
| ~ ( in @ ( ordered_pair @ ( sK61_D @ SV87 @ SV71 @ SV15 ) @ SV15 ) @ SV87 ) ) )
= $false )
| ( ( in @ SV15 @ ( relation_image @ SV87 @ SV71 ) )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1202]) ).
thf(1300,plain,
! [SV15: $i,SV71: $i,SV87: $i] :
( ( ( ~ ( in @ ( sK61_D @ SV87 @ SV71 @ SV15 ) @ SV71 ) )
= $false )
| ( ( in @ SV15 @ ( relation_image @ SV87 @ SV71 ) )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1202]) ).
thf(1301,plain,
! [SV16: $i,SV105: $i,SV128: $i] :
( ( ( ! [SY3506: $i] :
( ~ ( in @ ( ordered_pair @ SY3506 @ ( sK46_D @ SV128 @ SV105 @ SV16 ) ) @ SV16 )
| ~ ( in @ SY3506 @ SV105 ) )
| ~ ( in @ ( sK46_D @ SV128 @ SV105 @ SV16 ) @ SV128 ) )
= $true )
| ( ( SV128
= ( relation_image @ SV16 @ SV105 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1203]) ).
thf(1302,plain,
! [SV16: $i,SV105: $i,SV128: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SV128 @ SV105 @ SV16 ) @ ( sK46_D @ SV128 @ SV105 @ SV16 ) ) @ SV16 )
| ~ ( in @ ( sK47_SY3118 @ SV128 @ SV105 @ SV16 ) @ SV105 ) )
| ( in @ ( sK46_D @ SV128 @ SV105 @ SV16 ) @ SV128 ) )
= $true )
| ( ( SV128
= ( relation_image @ SV16 @ SV105 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1204]) ).
thf(1303,plain,
! [SV129: $i,SV106: $i,SV16: $i] :
( ( ( ~ ! [SY3507: $i] :
( ! [SY3468: $i] :
( ~ ( in @ ( ordered_pair @ SY3468 @ SY3507 ) @ SV16 )
| ~ ( in @ SY3468 @ SV106 ) )
| ( in @ SY3507 @ SV129 ) ) )
= $false )
| ( ( SV129
= ( relation_image @ SV16 @ SV106 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1205]) ).
thf(1304,plain,
! [SV16: $i,SV106: $i,SV129: $i] :
( ( ( ~ ! [SY3509: $i] :
( ~ ( in @ SY3509 @ SV129 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SY3509 @ SV129 @ SV106 @ SV16 ) @ SY3509 ) @ SV16 )
| ~ ( in @ ( sK45_E @ SY3509 @ SV129 @ SV106 @ SV16 ) @ SV106 ) ) ) )
= $false )
| ( ( SV129
= ( relation_image @ SV16 @ SV106 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1205]) ).
thf(1305,plain,
! [SV51: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK64_B @ SV51 ) @ ( sK65_SY3126 @ SV51 ) ) @ SV51 ) )
= $false )
| ( ( antisymmetric @ SV51 )
= $true )
| ( ( relation @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1206]) ).
thf(1306,plain,
! [SV51: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK65_SY3126 @ SV51 ) @ ( sK64_B @ SV51 ) ) @ SV51 ) )
= $false )
| ( ( antisymmetric @ SV51 )
= $true )
| ( ( relation @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1206]) ).
thf(1307,plain,
! [SV52: $i,SV167: $i,SV148: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV148 @ SV167 ) @ SV52 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV167 @ SV148 ) @ SV52 ) )
= $true )
| ( ( SV148 = SV167 )
= $true )
| ( ( antisymmetric @ SV52 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1208]) ).
thf(1308,plain,
! [SV17: $i,SV88: $i,SV72: $i] :
( ( ( ( SV72
!= ( apply @ SV88 @ SV17 ) ) )
= $true )
| ( ( ~ ( in @ SV17 @ ( relation_dom @ SV88 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV17 @ SV72 ) @ SV88 )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1209]) ).
thf(1309,plain,
! [SV130: $i,SV17: $i,SV149: $i] :
( ( ( function @ SV149 )
= $false )
| ( ( ~ ( relation @ SV149 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV17 @ SV130 ) @ SV149 )
| ( SV130
= ( apply @ SV149 @ SV17 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1210]) ).
thf(1310,plain,
! [SV131: $i,SV17: $i,SV150: $i] :
( ( ( function @ SV150 )
= $false )
| ( ( ~ ( relation @ SV150 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV17 @ SV131 ) @ SV150 )
| ( in @ SV17 @ ( relation_dom @ SV150 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1211]) ).
thf(1311,plain,
! [SV18: $i,SV107: $i,SV132: $i] :
( ( ( ( ( sK35_D @ SV132 @ SV107 @ SV18 )
= SV107 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV107 ) @ SV18 )
| ~ ( in @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV132 ) )
= $true )
| ( ( SV132
= ( fiber @ SV18 @ SV107 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1212]) ).
thf(1312,plain,
! [SV18: $i,SV107: $i,SV132: $i] :
( ( ( ~ ( ~ ( ( ( sK35_D @ SV132 @ SV107 @ SV18 )
!= SV107 )
| ( in @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV132 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV107 ) @ SV18 )
| ( in @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV132 ) ) ) )
= $true )
| ( ( SV132
= ( fiber @ SV18 @ SV107 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1213]) ).
thf(1313,plain,
! [SV133: $i,SV18: $i,SV108: $i] :
( ( ( ~ ! [SY3512: $i] :
( ( SY3512 = SV108 )
| ~ ( in @ ( ordered_pair @ SY3512 @ SV108 ) @ SV18 )
| ( in @ SY3512 @ SV133 ) ) )
= $false )
| ( ( SV133
= ( fiber @ SV18 @ SV108 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1214]) ).
thf(1314,plain,
! [SV18: $i,SV108: $i,SV133: $i] :
( ( ( ~ ~ ( ~ ! [SY3513: $i] :
( ~ ( in @ SY3513 @ SV133 )
| ( SY3513 != SV108 ) )
| ~ ! [SY3514: $i] :
( ~ ( in @ SY3514 @ SV133 )
| ( in @ ( ordered_pair @ SY3514 @ SV108 ) @ SV18 ) ) ) )
= $false )
| ( ( SV133
= ( fiber @ SV18 @ SV108 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1214]) ).
thf(1315,plain,
! [SV19: $i,SV109: $i] :
( ( ( in @ ( ordered_pair @ ( sK36_C @ SV109 @ SV19 ) @ ( sK36_C @ SV109 @ SV19 ) ) @ SV19 )
= $false )
| ( ( is_reflexive_in @ SV19 @ SV109 )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1316,plain,
! [SV19: $i,SV110: $i,SV168: $i] :
( ( ( in @ SV168 @ SV110 )
= $false )
| ( ( in @ ( ordered_pair @ SV168 @ SV168 ) @ SV19 )
= $true )
| ( ( is_reflexive_in @ SV19 @ SV110 )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1217]) ).
thf(1317,plain,
! [SV20: $i,SV111: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SV111 @ SV20 ) @ ( sK13_SY3095 @ SV111 @ SV20 ) ) @ SV111 )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV111 @ SV20 ) @ ( sK12_C @ SV111 @ SV20 ) ) @ SV20 ) ) )
= $false )
| ( ( SV111
= ( relation_inverse @ SV20 ) )
= $true )
| ( ( relation @ SV111 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1218]) ).
thf(1318,plain,
! [SV20: $i,SV111: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SV111 @ SV20 ) @ ( sK13_SY3095 @ SV111 @ SV20 ) ) @ SV111 )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV111 @ SV20 ) @ ( sK12_C @ SV111 @ SV20 ) ) @ SV20 ) ) )
= $false )
| ( ( SV111
= ( relation_inverse @ SV20 ) )
= $true )
| ( ( relation @ SV111 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1218]) ).
thf(1319,plain,
! [SV20: $i,SV112: $i] :
( ( ( ~ ! [SY3476: $i,SY3477: $i] :
( ~ ( in @ ( ordered_pair @ SY3476 @ SY3477 ) @ SV112 )
| ( in @ ( ordered_pair @ SY3477 @ SY3476 ) @ SV20 ) )
| ~ ! [SY3478: $i,SY3479: $i] :
( ~ ( in @ ( ordered_pair @ SY3479 @ SY3478 ) @ SV20 )
| ( in @ ( ordered_pair @ SY3478 @ SY3479 ) @ SV112 ) ) )
= $false )
| ( ( SV112
= ( relation_inverse @ SV20 ) )
= $false )
| ( ( relation @ SV112 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1219]) ).
thf(1320,plain,
! [SV21: $i,SV38: $i,SV134: $i] :
( ( ( ~ ( ~ ( in @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) @ SV21 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV38 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV38 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) ) ) )
= $false )
| ( ( SV134
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $true )
| ( ( relation @ SV134 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1220]) ).
thf(1321,plain,
! [SV38: $i,SV21: $i,SV135: $i] :
( ( ( SV135
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $false )
| ( ( ~ ( ~ ! [SY3515: $i,SY3516: $i] :
( ~ ( in @ SY3516 @ SV21 )
| ~ ( in @ ( ordered_pair @ SY3515 @ SY3516 ) @ SV38 )
| ( in @ ( ordered_pair @ SY3515 @ SY3516 ) @ SV135 ) )
| ~ ~ ( ~ ! [SY3517: $i,SY3518: $i] :
( ~ ( in @ ( ordered_pair @ SY3517 @ SY3518 ) @ SV135 )
| ( in @ SY3518 @ SV21 ) )
| ~ ! [SY3519: $i,SY3520: $i] :
( ~ ( in @ ( ordered_pair @ SY3519 @ SY3520 ) @ SV135 )
| ( in @ ( ordered_pair @ SY3519 @ SY3520 ) @ SV38 ) ) ) ) )
= $true )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1221]) ).
thf(1322,plain,
! [SV22: $i,SV113: $i] :
( ( ( ! [SY3480: $i] :
~ ( in @ ( ordered_pair @ SY3480 @ ( sK17_C @ SV113 @ SV22 ) ) @ SV22 ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV113 @ SV22 ) @ SV113 ) )
= $true )
| ( ( SV113
= ( relation_rng @ SV22 ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1222]) ).
thf(1323,plain,
! [SV22: $i,SV113: $i] :
( ( ( in @ ( ordered_pair @ ( sK18_SY3098 @ SV113 @ SV22 ) @ ( sK17_C @ SV113 @ SV22 ) ) @ SV22 )
= $true )
| ( ( in @ ( sK17_C @ SV113 @ SV22 ) @ SV113 )
= $true )
| ( ( SV113
= ( relation_rng @ SV22 ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1223]) ).
thf(1324,plain,
! [SV114: $i,SV22: $i] :
( ( ( ! [SY3481: $i] :
( ! [SY3248: $i] :
~ ( in @ ( ordered_pair @ SY3248 @ SY3481 ) @ SV22 )
| ( in @ SY3481 @ SV114 ) ) )
= $true )
| ( ( SV114
= ( relation_rng @ SV22 ) )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1224]) ).
thf(1325,plain,
! [SV22: $i,SV114: $i] :
( ( ( ! [SY3483: $i] :
( ~ ( in @ SY3483 @ SV114 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3483 @ SV114 @ SV22 ) @ SY3483 ) @ SV22 ) ) )
= $true )
| ( ( SV114
= ( relation_rng @ SV22 ) )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1225]) ).
thf(1326,plain,
! [SV23: $i,SV115: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV115 @ SV23 ) @ ( sK25_SY3102 @ SV115 @ SV23 ) ) @ SV23 ) )
= $false )
| ( ( subset @ SV23 @ SV115 )
= $true )
| ( ( relation @ SV115 )
= $false )
| ( ( relation @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1226]) ).
thf(1327,plain,
! [SV23: $i,SV115: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SV115 @ SV23 ) @ ( sK25_SY3102 @ SV115 @ SV23 ) ) @ SV115 ) )
= $false )
| ( ( subset @ SV23 @ SV115 )
= $true )
| ( ( relation @ SV115 )
= $false )
| ( ( relation @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1226]) ).
thf(1328,plain,
! [SV116: $i,SV23: $i,SV189: $i] :
( ( ( ! [SY3563: $i] :
( ~ ( in @ ( ordered_pair @ SV189 @ SY3563 ) @ SV23 )
| ( in @ ( ordered_pair @ SV189 @ SY3563 ) @ SV116 ) ) )
= $true )
| ( ( subset @ SV23 @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false )
| ( ( relation @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1329,plain,
! [SV24: $i,SV117: $i,SV136: $i] :
( ( ( ~ ( ~ ( in @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ SV117 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV24 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) )
| ~ ~ ( ~ ( ( in @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ SV117 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV24 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) ) ) )
= $false )
| ( ( SV136
= ( relation_dom_restriction @ SV24 @ SV117 ) )
= $true )
| ( ( relation @ SV136 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1330,plain,
! [SV118: $i,SV24: $i,SV137: $i] :
( ( ( SV137
= ( relation_dom_restriction @ SV24 @ SV118 ) )
= $false )
| ( ( ~ ( ~ ! [SY3521: $i,SY3522: $i] :
( ~ ( in @ SY3521 @ SV118 )
| ~ ( in @ ( ordered_pair @ SY3521 @ SY3522 ) @ SV24 )
| ( in @ ( ordered_pair @ SY3521 @ SY3522 ) @ SV137 ) )
| ~ ~ ( ~ ! [SY3523: $i] :
( ! [SY3524: $i] :
~ ( in @ ( ordered_pair @ SY3523 @ SY3524 ) @ SV137 )
| ( in @ SY3523 @ SV118 ) )
| ~ ! [SY3525: $i,SY3526: $i] :
( ~ ( in @ ( ordered_pair @ SY3525 @ SY3526 ) @ SV137 )
| ( in @ ( ordered_pair @ SY3525 @ SY3526 ) @ SV24 ) ) ) ) )
= $true )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1229]) ).
thf(1331,plain,
! [SV26: $i,SV190: $i] :
( ( ( ~ ( in @ SV190 @ ( relation_dom @ SV26 ) )
| ! [SY3564: $i] :
( ( SY3564
!= ( apply @ SV26 @ SV190 ) )
| ( in @ ( ordered_pair @ SV190 @ SY3564 ) @ SV26 ) ) )
= $true )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1230]) ).
thf(1332,plain,
! [SV26: $i,SV191: $i] :
( ( ( ~ ( in @ SV191 @ ( relation_dom @ SV26 ) )
| ! [SY3565: $i] :
( ~ ( in @ ( ordered_pair @ SV191 @ SY3565 ) @ SV26 )
| ( SY3565
= ( apply @ SV26 @ SV191 ) ) ) )
= $true )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1231]) ).
thf(1333,plain,
! [SV26: $i,SV192: $i] :
( ( ( ( in @ SV192 @ ( relation_dom @ SV26 ) )
| ! [SY3566: $i] :
( ( SY3566
!= ( apply @ SV26 @ SV192 ) )
| ( SY3566 = empty_set ) ) )
= $true )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1334,plain,
! [SV26: $i,SV193: $i] :
( ( ( ( in @ SV193 @ ( relation_dom @ SV26 ) )
| ! [SY3567: $i] :
( ( SY3567 != empty_set )
| ( SY3567
= ( apply @ SV26 @ SV193 ) ) ) )
= $true )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1233]) ).
thf(1335,plain,
! [SV53: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK62_B @ SV53 )
!= ( sK63_SY3125 @ SV53 ) ) )
| ~ ~ ( ~ ( in @ ( sK62_B @ SV53 ) @ ( relation_field @ SV53 ) )
| ~ ( in @ ( sK63_SY3125 @ SV53 ) @ ( relation_field @ SV53 ) ) ) ) )
= $false )
| ( ( connected @ SV53 )
= $true )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1234]) ).
thf(1336,plain,
! [SV53: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK62_B @ SV53 ) @ ( sK63_SY3125 @ SV53 ) ) @ SV53 ) )
= $false )
| ( ( connected @ SV53 )
= $true )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1234]) ).
thf(1337,plain,
! [SV54: $i,SV169: $i,SV151: $i] :
( ( ( ( SV151 = SV169 )
| ~ ( in @ SV151 @ ( relation_field @ SV54 ) )
| ~ ( in @ SV169 @ ( relation_field @ SV54 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV151 @ SV169 ) @ SV54 )
= $true )
| ( ( in @ ( ordered_pair @ SV169 @ SV151 ) @ SV54 )
= $true )
| ( ( connected @ SV54 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1236]) ).
thf(1338,plain,
! [SV27: $i,SV120: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_C @ SV120 @ SV27 ) @ SV120 )
| ~ ( in @ ( sK20_SY3099 @ SV120 @ SV27 ) @ SV120 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SV120 @ SV27 ) @ ( sK20_SY3099 @ SV120 @ SV27 ) ) @ SV27 ) )
| ~ ( in @ ( ordered_pair @ ( sK20_SY3099 @ SV120 @ SV27 ) @ ( sK19_C @ SV120 @ SV27 ) ) @ SV27 ) )
= $false )
| ( ( is_antisymmetric_in @ SV27 @ SV120 )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1237]) ).
thf(1339,plain,
! [SV27: $i,SV120: $i] :
( ( ( ( sK19_C @ SV120 @ SV27 )
= ( sK20_SY3099 @ SV120 @ SV27 ) )
= $false )
| ( ( is_antisymmetric_in @ SV27 @ SV120 )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1238]) ).
thf(1340,plain,
! [SV27: $i,SV178: $i,SV121: $i,SV170: $i] :
( ( ( ~ ( in @ SV170 @ SV121 )
| ~ ( in @ SV178 @ SV121 )
| ~ ( in @ ( ordered_pair @ SV170 @ SV178 ) @ SV27 )
| ~ ( in @ ( ordered_pair @ SV178 @ SV170 ) @ SV27 ) )
= $true )
| ( ( SV170 = SV178 )
= $true )
| ( ( is_antisymmetric_in @ SV27 @ SV121 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1239]) ).
thf(1341,plain,
! [SV179: $i,SV152: $i,SV40: $i,SV28: $i] :
( ( ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SV152 @ SV179 ) )
= $false )
| ( ( in @ SV28 @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1241]) ).
thf(1342,plain,
! [SV171: $i,SV153: $i,SV40: $i,SV28: $i] :
( ( ( in @ ( ordered_pair @ SV28 @ SV40 ) @ ( cartesian_product2 @ SV153 @ SV171 ) )
= $false )
| ( ( in @ SV40 @ SV171 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1242]) ).
thf(1343,plain,
! [SV55: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK66_B @ SV55 ) @ ( sK67_SY3127 @ SV55 ) ) @ SV55 ) )
= $false )
| ( ( transitive @ SV55 )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1243]) ).
thf(1344,plain,
! [SV55: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK67_SY3127 @ SV55 ) @ ( sK68_SY3129 @ SV55 ) ) @ SV55 ) )
= $false )
| ( ( transitive @ SV55 )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1243]) ).
thf(1345,plain,
! [SV180: $i,SV56: $i,SV172: $i,SV154: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV154 @ SV172 ) @ SV56 )
| ~ ( in @ ( ordered_pair @ SV172 @ SV180 ) @ SV56 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV154 @ SV180 ) @ SV56 )
= $true )
| ( ( transitive @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1245]) ).
thf(1346,plain,
! [SV181: $i,SV155: $i,SV41: $i,SV29: $i] :
( ( ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SV155 @ SV181 ) )
= $false )
| ( ( in @ SV29 @ SV155 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1247]) ).
thf(1347,plain,
! [SV173: $i,SV156: $i,SV41: $i,SV29: $i] :
( ( ( in @ ( ordered_pair @ SV29 @ SV41 ) @ ( cartesian_product2 @ SV156 @ SV173 ) )
= $false )
| ( ( in @ SV41 @ SV173 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1248]) ).
thf(1348,plain,
! [SV30: $i,SV124: $i,SV139: $i] :
( ( ( ! [SY3527: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SY3527 ) @ SV30 )
| ~ ( in @ SY3527 @ SV124 ) )
| ~ ( in @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SV139 ) )
= $true )
| ( ( SV139
= ( relation_inverse_image @ SV30 @ SV124 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1249]) ).
thf(1349,plain,
! [SV30: $i,SV124: $i,SV139: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ ( sK44_SY3116 @ SV139 @ SV124 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK44_SY3116 @ SV139 @ SV124 @ SV30 ) @ SV124 ) )
| ( in @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SV139 ) )
= $true )
| ( ( SV139
= ( relation_inverse_image @ SV30 @ SV124 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1250]) ).
thf(1350,plain,
! [SV140: $i,SV125: $i,SV30: $i] :
( ( ( ~ ! [SY3528: $i] :
( ! [SY3500: $i] :
( ~ ( in @ ( ordered_pair @ SY3528 @ SY3500 ) @ SV30 )
| ~ ( in @ SY3500 @ SV125 ) )
| ( in @ SY3528 @ SV140 ) ) )
= $false )
| ( ( SV140
= ( relation_inverse_image @ SV30 @ SV125 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1251]) ).
thf(1351,plain,
! [SV30: $i,SV125: $i,SV140: $i] :
( ( ( ~ ! [SY3530: $i] :
( ~ ( in @ SY3530 @ SV140 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3530 @ ( sK42_E @ SY3530 @ SV140 @ SV125 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK42_E @ SY3530 @ SV140 @ SV125 @ SV30 ) @ SV125 ) ) ) )
= $false )
| ( ( SV140
= ( relation_inverse_image @ SV30 @ SV125 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1251]) ).
thf(1352,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( ~ ( function @ SV174 ) )
= $true )
| ( ( ~ ( relation @ SV174 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) ) ) )
| ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 )
| ( relation_isomorphism @ SV32 @ SV59 @ SV174 ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1254]) ).
thf(1353,plain,
! [SV59: $i,SV32: $i] :
( ( ( ! [SY3393: $i] :
( ~ ( function @ SY3393 )
| ~ ( relation @ SY3393 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3393 )
| ~ ( ~ ! [SY3394: $i,SY3395: $i] :
( ~ ( in @ SY3394 @ ( relation_field @ SV32 ) )
| ~ ( in @ SY3395 @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3393 @ SY3394 ) @ ( apply @ SY3393 @ SY3395 ) ) @ SV59 )
| ( in @ ( ordered_pair @ SY3394 @ SY3395 ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3312: $i] :
( ! [SY3313: $i] :
~ ( in @ ( ordered_pair @ SY3312 @ SY3313 ) @ SV32 )
| ( in @ SY3312 @ ( relation_field @ SV32 ) ) )
| ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV32 )
| ( in @ SY3315 @ ( relation_field @ SV32 ) ) ) )
| ~ ! [SY3400: $i,SY3401: $i] :
( ~ ( in @ ( ordered_pair @ SY3400 @ SY3401 ) @ SV32 )
| ( in @ ( ordered_pair @ ( apply @ SY3393 @ SY3400 ) @ ( apply @ SY3393 @ SY3401 ) ) @ SV59 ) ) ) ) ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1255]) ).
thf(1354,plain,
! [SV59: $i,SV32: $i] :
( ( ( ~ ( ~ ~ ( ~ ! [SY3402: $i] :
( ~ ( function @ SY3402 )
| ~ ( relation @ SY3402 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3402 )
| ( ( relation_dom @ SY3402 )
= ( relation_field @ SV32 ) ) )
| ~ ! [SY3403: $i] :
( ~ ( function @ SY3403 )
| ~ ( relation @ SY3403 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3403 )
| ( ( relation_rng @ SY3403 )
= ( relation_field @ SV59 ) ) ) )
| ~ ! [SY3404: $i] :
( ~ ( function @ SY3404 )
| ~ ( relation @ SY3404 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3404 )
| ( one_to_one @ SY3404 ) ) ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1256]) ).
thf(1355,plain,
! [SV33: $i,SV75: $i,SV95: $i] :
( ( ( ! [SY3453: $i] :
~ ( in @ ( ordered_pair @ SY3453 @ ( sK57_D @ SV95 @ SV75 @ SV33 ) ) @ SV95 ) )
= $true )
| ( ( ( relation_rng_as_subset @ SV33 @ SV75 @ SV95 )
= SV75 )
= $true )
| ( ( relation_of2_as_subset @ SV95 @ SV33 @ SV75 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1257]) ).
thf(1356,plain,
! [SV33: $i,SV75: $i,SV95: $i] :
( ( ( in @ ( sK57_D @ SV95 @ SV75 @ SV33 ) @ SV75 )
= $true )
| ( ( ( relation_rng_as_subset @ SV33 @ SV75 @ SV95 )
= SV75 )
= $true )
| ( ( relation_of2_as_subset @ SV95 @ SV33 @ SV75 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1258]) ).
thf(1357,plain,
! [SV33: $i,SV76: $i,SV96: $i,SV182: $i] :
( ( ( in @ ( ordered_pair @ ( sK56_E @ SV182 @ SV96 @ SV76 @ SV33 ) @ SV182 ) @ SV96 )
= $true )
| ( ( ~ ( in @ SV182 @ SV76 ) )
= $true )
| ( ( ( relation_rng_as_subset @ SV33 @ SV76 @ SV96 )
= SV76 )
= $false )
| ( ( relation_of2_as_subset @ SV96 @ SV33 @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1259]) ).
thf(1358,plain,
! [SV34: $i,SV126: $i] :
( ( ( ! [SY3502: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SV126 @ SV34 ) @ SY3502 ) @ SV34 ) )
= $true )
| ( ( ~ ( in @ ( sK22_C @ SV126 @ SV34 ) @ SV126 ) )
= $true )
| ( ( SV126
= ( relation_dom @ SV34 ) )
= $true )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1260]) ).
thf(1359,plain,
! [SV34: $i,SV126: $i] :
( ( ( in @ ( ordered_pair @ ( sK22_C @ SV126 @ SV34 ) @ ( sK23_SY3101 @ SV126 @ SV34 ) ) @ SV34 )
= $true )
| ( ( in @ ( sK22_C @ SV126 @ SV34 ) @ SV126 )
= $true )
| ( ( SV126
= ( relation_dom @ SV34 ) )
= $true )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1261]) ).
thf(1360,plain,
! [SV127: $i,SV34: $i] :
( ( ( ! [SY3503: $i] :
( ! [SY3331: $i] :
~ ( in @ ( ordered_pair @ SY3503 @ SY3331 ) @ SV34 )
| ( in @ SY3503 @ SV127 ) ) )
= $true )
| ( ( SV127
= ( relation_dom @ SV34 ) )
= $false )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1262]) ).
thf(1361,plain,
! [SV34: $i,SV127: $i] :
( ( ( ! [SY3505: $i] :
( ~ ( in @ SY3505 @ SV127 )
| ( in @ ( ordered_pair @ SY3505 @ ( sK21_D @ SY3505 @ SV127 @ SV34 ) ) @ SV34 ) ) )
= $true )
| ( ( SV127
= ( relation_dom @ SV34 ) )
= $false )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1263]) ).
thf(1362,plain,
! [SV4: $i,SV98: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV4 )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV98 ) )
= $true )
| ( ( SV4 = SV98 )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1264]) ).
thf(1363,plain,
! [SV4: $i,SV98: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV4 )
| ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV98 ) )
= $true )
| ( ( SV4 = SV98 )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1265]) ).
thf(1364,plain,
! [SV99: $i,SV4: $i] :
( ( ( ~ ! [SY3455: $i,SY3456: $i] :
( ~ ( in @ ( ordered_pair @ SY3455 @ SY3456 ) @ SV4 )
| ( in @ ( ordered_pair @ SY3455 @ SY3456 ) @ SV99 ) ) )
= $false )
| ( ( SV4 = SV99 )
= $false )
| ( ( relation @ SV99 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1266]) ).
thf(1365,plain,
! [SV4: $i,SV99: $i] :
( ( ( ~ ! [SY3457: $i,SY3458: $i] :
( ~ ( in @ ( ordered_pair @ SY3457 @ SY3458 ) @ SV99 )
| ( in @ ( ordered_pair @ SY3457 @ SY3458 ) @ SV4 ) ) )
= $false )
| ( ( SV4 = SV99 )
= $false )
| ( ( relation @ SV99 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1266]) ).
thf(1366,plain,
! [SV5: $i,SV100: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SV100 @ SV5 ) @ SV100 )
| ~ ( in @ ( sK4_SY3086 @ SV100 @ SV5 ) @ SV100 ) )
| ~ ( in @ ( sK5_SY3088 @ SV100 @ SV5 ) @ SV100 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SV100 @ SV5 ) @ ( sK4_SY3086 @ SV100 @ SV5 ) ) @ SV5 ) ) )
= $false )
| ( ( is_transitive_in @ SV5 @ SV100 )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1267]) ).
thf(1367,plain,
! [SV5: $i,SV100: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK4_SY3086 @ SV100 @ SV5 ) @ ( sK5_SY3088 @ SV100 @ SV5 ) ) @ SV5 ) )
= $false )
| ( ( is_transitive_in @ SV5 @ SV100 )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1267]) ).
thf(1368,plain,
! [SV5: $i,SV183: $i,SV175: $i,SV101: $i,SV159: $i] :
( ( ( ~ ( in @ SV159 @ SV101 )
| ~ ( in @ SV175 @ SV101 )
| ~ ( in @ SV183 @ SV101 )
| ~ ( in @ ( ordered_pair @ SV159 @ SV175 ) @ SV5 )
| ~ ( in @ ( ordered_pair @ SV175 @ SV183 ) @ SV5 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV159 @ SV183 ) @ SV5 )
= $true )
| ( ( is_transitive_in @ SV5 @ SV101 )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1269]) ).
thf(1369,plain,
! [SV194: $i,SV6: $i,SV60: $i,SV77: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK59_D @ SV77 @ SV60 @ SV6 ) @ SV194 ) @ SV77 ) )
= $true )
| ( ( ( relation_dom_as_subset @ SV60 @ SV6 @ SV77 )
= SV60 )
= $true )
| ( ( relation_of2_as_subset @ SV77 @ SV60 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1270]) ).
thf(1370,plain,
! [SV6: $i,SV78: $i,SV61: $i,SV176: $i] :
( ( ( in @ SV176 @ SV61 )
= $false )
| ( ( in @ ( ordered_pair @ SV176 @ ( sK58_E @ SV176 @ SV78 @ SV61 @ SV6 ) ) @ SV78 )
= $true )
| ( ( ( relation_dom_as_subset @ SV61 @ SV6 @ SV78 )
= SV61 )
= $false )
| ( ( relation_of2_as_subset @ SV78 @ SV61 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1272]) ).
thf(1371,plain,
! [SV7: $i,SV46: $i,SV160: $i] :
( ( ( ~ ( ~ ( ! [SY3548: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ SY3548 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3548 @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV46 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV160 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK9_SY3093 @ SV160 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV46 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV160 ) ) ) )
= $true )
| ( ( SV160
= ( relation_composition @ SV7 @ SV46 ) )
= $true )
| ( ( relation @ SV160 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1273]) ).
thf(1372,plain,
! [SV46: $i,SV7: $i,SV161: $i] :
( ( ( ( SV161
!= ( relation_composition @ SV7 @ SV46 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3549: $i,SY3550: $i] :
( ! [SY3373: $i] :
( ~ ( in @ ( ordered_pair @ SY3549 @ SY3373 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3373 @ SY3550 ) @ SV46 ) )
| ( in @ ( ordered_pair @ SY3549 @ SY3550 ) @ SV161 ) )
| ~ ! [SY3552: $i,SY3553: $i] :
( ~ ( in @ ( ordered_pair @ SY3552 @ SY3553 ) @ SV161 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3552 @ ( sK6_F @ SY3553 @ SY3552 @ SV161 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY3553 @ SY3552 @ SV161 @ SV46 @ SV7 ) @ SY3553 ) @ SV46 ) ) ) ) )
= $true )
| ( ( relation @ SV161 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1274]) ).
thf(1373,plain,
! [SV47: $i,SV62: $i] :
( ( ( ( ( sK52_C @ SV62 @ SV47 )
!= ( sK53_SY3121 @ SV62 @ SV47 ) ) )
= $true )
| ( ( ~ ( in @ ( sK52_C @ SV62 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) )
= $true )
| ( ( SV62
= ( identity_relation @ SV47 ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1275]) ).
thf(1374,plain,
! [SV47: $i,SV62: $i] :
( ( ( ~ ( ( ( sK52_C @ SV62 @ SV47 )
= ( sK53_SY3121 @ SV62 @ SV47 ) )
| ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) ) )
= $false )
| ( ( SV62
= ( identity_relation @ SV47 ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1276]) ).
thf(1375,plain,
! [SV47: $i,SV62: $i] :
( ( ( ~ ( ( in @ ( sK52_C @ SV62 @ SV47 ) @ SV47 )
| ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) ) )
= $false )
| ( ( SV62
= ( identity_relation @ SV47 ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1276]) ).
thf(1376,plain,
! [SV63: $i,SV48: $i,SV195: $i] :
( ( ( ! [SY3568: $i] :
( ( SV195 != SY3568 )
| ~ ( in @ SV195 @ SV48 )
| ( in @ ( ordered_pair @ SV195 @ SY3568 ) @ SV63 ) ) )
= $true )
| ( ( SV63
= ( identity_relation @ SV48 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1377,plain,
! [SV48: $i,SV63: $i] :
( ( ( ~ ! [SY3411: $i,SY3412: $i] :
( ~ ( in @ ( ordered_pair @ SY3411 @ SY3412 ) @ SV63 )
| ( SY3411 = SY3412 ) )
| ~ ! [SY3413: $i] :
( ! [SY3414: $i] :
~ ( in @ ( ordered_pair @ SY3413 @ SY3414 ) @ SV63 )
| ( in @ SY3413 @ SV48 ) ) )
= $false )
| ( ( SV63
= ( identity_relation @ SV48 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1378,plain,
! [SV49: $i,SV42: $i,SV142: $i,SV8: $i] :
( ( ( SV8
= ( ordered_pair @ ( sK40_C @ SV142 @ SV8 ) @ ( sK41_SY3114 @ SV142 @ SV8 ) ) )
= $true )
| ( ( SV142
= ( pair_first @ SV8 ) )
= $true )
| ( ( SV8
= ( ordered_pair @ SV42 @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1279]) ).
thf(1379,plain,
! [SV49: $i,SV42: $i,SV8: $i,SV142: $i] :
( ( ( ( SV142
!= ( sK40_C @ SV142 @ SV8 ) ) )
= $true )
| ( ( SV142
= ( pair_first @ SV8 ) )
= $true )
| ( ( SV8
= ( ordered_pair @ SV42 @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1280]) ).
thf(1380,plain,
! [SV49: $i,SV42: $i,SV143: $i,SV184: $i,SV8: $i] :
( ( ( ! [SY3558: $i] :
( SV8
!= ( ordered_pair @ SV184 @ SY3558 ) ) )
= $true )
| ( ( SV143 = SV184 )
= $true )
| ( ( SV143
= ( pair_first @ SV8 ) )
= $false )
| ( ( SV8
= ( ordered_pair @ SV42 @ SV49 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1281]) ).
thf(1381,plain,
! [SV79: $i,SV102: $i,SV37: $i,SV9: $i] :
( ( ( in @ ( ordered_pair @ SV9 @ SV37 ) @ SV102 )
= $false )
| ( ( in @ SV9 @ SV79 )
= $false )
| ( ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SV79 ) @ SV102 ) )
= $true )
| ( ( relation @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1282]) ).
thf(1382,plain,
! [SV162: $i,SV144: $i,SV37: $i,SV9: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SV144 ) @ SV162 ) ) )
= $true )
| ( ( in @ SV9 @ SV144 )
= $true )
| ( ( relation @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1283]) ).
thf(1383,plain,
! [SV163: $i,SV145: $i,SV37: $i,SV9: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SV145 ) @ SV163 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV9 @ SV37 ) @ SV163 )
= $true )
| ( ( relation @ SV163 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1284]) ).
thf(1384,plain,
! [SV64: $i,SV10: $i,SV80: $i,SV164: $i] :
( ( ( in @ SV164 @ ( relation_rng @ SV80 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV10 @ SV164 ) @ SV80 ) )
= $true )
| ( ( ~ ( in @ SV164 @ SV64 ) )
= $true )
| ( ( in @ SV10 @ ( relation_inverse_image @ SV80 @ SV64 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1285]) ).
thf(1385,plain,
! [SV10: $i,SV65: $i,SV81: $i] :
( ( ( ~ ( ~ ( in @ ( sK60_D @ SV81 @ SV65 @ SV10 ) @ ( relation_rng @ SV81 ) )
| ~ ( in @ ( ordered_pair @ SV10 @ ( sK60_D @ SV81 @ SV65 @ SV10 ) ) @ SV81 ) ) )
= $true )
| ( ( in @ SV10 @ ( relation_inverse_image @ SV81 @ SV65 ) )
= $false )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1286]) ).
thf(1386,plain,
! [SV10: $i,SV65: $i,SV81: $i] :
( ( ( in @ ( sK60_D @ SV81 @ SV65 @ SV10 ) @ SV65 )
= $true )
| ( ( in @ SV10 @ ( relation_inverse_image @ SV81 @ SV65 ) )
= $false )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1287]) ).
thf(1387,plain,
! [SV82: $i,SV66: $i,SV196: $i,SV11: $i,SV185: $i] :
( ( ( ~ ( in @ SV185 @ SV11 )
| ~ ( in @ SV196 @ SV66 )
| ( ( sK28_D @ SV82 @ SV66 @ SV11 )
!= ( ordered_pair @ SV185 @ SV196 ) ) )
= $true )
| ( ( ~ ( in @ ( sK28_D @ SV82 @ SV66 @ SV11 ) @ SV82 ) )
= $true )
| ( ( SV82
= ( cartesian_product2 @ SV11 @ SV66 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1388,plain,
! [SV11: $i,SV66: $i,SV82: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK29_SY3106 @ SV82 @ SV66 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK30_SY3108 @ SV82 @ SV66 @ SV11 ) @ SV66 ) ) )
= $false )
| ( ( in @ ( sK28_D @ SV82 @ SV66 @ SV11 ) @ SV82 )
= $true )
| ( ( SV82
= ( cartesian_product2 @ SV11 @ SV66 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1289]) ).
thf(1389,plain,
! [SV11: $i,SV66: $i,SV82: $i] :
( ( ( ( ( sK28_D @ SV82 @ SV66 @ SV11 )
!= ( ordered_pair @ ( sK29_SY3106 @ SV82 @ SV66 @ SV11 ) @ ( sK30_SY3108 @ SV82 @ SV66 @ SV11 ) ) ) )
= $false )
| ( ( in @ ( sK28_D @ SV82 @ SV66 @ SV11 ) @ SV82 )
= $true )
| ( ( SV82
= ( cartesian_product2 @ SV11 @ SV66 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1289]) ).
thf(1390,plain,
! [SV83: $i,SV186: $i,SV67: $i,SV11: $i] :
( ( ( ! [SY3560: $i,SY3561: $i] :
( ~ ( in @ SY3560 @ SV11 )
| ~ ( in @ SY3561 @ SV67 )
| ( SV186
!= ( ordered_pair @ SY3560 @ SY3561 ) ) ) )
= $true )
| ( ( in @ SV186 @ SV83 )
= $true )
| ( ( SV83
= ( cartesian_product2 @ SV11 @ SV67 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1290]) ).
thf(1391,plain,
! [SV11: $i,SV67: $i,SV83: $i,SV187: $i] :
( ( ( ~ ( in @ SV187 @ SV83 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK26_E @ SV187 @ SV83 @ SV67 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK27_SY3103 @ SV187 @ SV83 @ SV67 @ SV11 ) @ SV67 ) )
| ( SV187
!= ( ordered_pair @ ( sK26_E @ SV187 @ SV83 @ SV67 @ SV11 ) @ ( sK27_SY3103 @ SV187 @ SV83 @ SV67 @ SV11 ) ) ) ) )
= $true )
| ( ( SV83
= ( cartesian_product2 @ SV11 @ SV67 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1291]) ).
thf(1392,plain,
! [SV50: $i,SV43: $i,SV146: $i,SV13: $i] :
( ( ( SV13
= ( ordered_pair @ ( sK33_C @ SV146 @ SV13 ) @ ( sK34_SY3110 @ SV146 @ SV13 ) ) )
= $true )
| ( ( SV146
= ( pair_second @ SV13 ) )
= $true )
| ( ( SV13
= ( ordered_pair @ SV43 @ SV50 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1292]) ).
thf(1393,plain,
! [SV50: $i,SV43: $i,SV13: $i,SV146: $i] :
( ( ( ( SV146
!= ( sK34_SY3110 @ SV146 @ SV13 ) ) )
= $true )
| ( ( SV146
= ( pair_second @ SV13 ) )
= $true )
| ( ( SV13
= ( ordered_pair @ SV43 @ SV50 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1293]) ).
thf(1394,plain,
! [SV50: $i,SV43: $i,SV147: $i,SV197: $i,SV188: $i,SV13: $i] :
( ( ( ( SV13
!= ( ordered_pair @ SV188 @ SV197 ) )
| ( SV147 = SV197 ) )
= $true )
| ( ( SV147
= ( pair_second @ SV13 ) )
= $false )
| ( ( SV13
= ( ordered_pair @ SV43 @ SV50 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1395,plain,
! [SV14: $i,SV103: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK14_C @ SV103 @ SV14 )
!= ( sK15_SY3096 @ SV103 @ SV14 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SV103 @ SV14 ) @ SV103 )
| ~ ( in @ ( sK15_SY3096 @ SV103 @ SV14 ) @ SV103 ) ) ) )
= $false )
| ( ( is_connected_in @ SV14 @ SV103 )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1295]) ).
thf(1396,plain,
! [SV14: $i,SV103: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK14_C @ SV103 @ SV14 ) @ ( sK15_SY3096 @ SV103 @ SV14 ) ) @ SV14 ) )
= $false )
| ( ( is_connected_in @ SV14 @ SV103 )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1295]) ).
thf(1397,plain,
! [SV14: $i,SV104: $i,SV177: $i,SV165: $i] :
( ( ( ( SV165 = SV177 )
| ~ ( in @ SV165 @ SV104 )
| ~ ( in @ SV177 @ SV104 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV165 @ SV177 ) @ SV14 )
= $true )
| ( ( in @ ( ordered_pair @ SV177 @ SV165 ) @ SV14 )
= $true )
| ( ( is_connected_in @ SV14 @ SV104 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1297]) ).
thf(1398,plain,
! [SV70: $i,SV15: $i,SV86: $i,SV166: $i] :
( ( ( in @ SV166 @ ( relation_dom @ SV86 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV166 @ SV15 ) @ SV86 ) )
= $true )
| ( ( ~ ( in @ SV166 @ SV70 ) )
= $true )
| ( ( in @ SV15 @ ( relation_image @ SV86 @ SV70 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1298]) ).
thf(1399,plain,
! [SV15: $i,SV71: $i,SV87: $i] :
( ( ( ~ ( ~ ( in @ ( sK61_D @ SV87 @ SV71 @ SV15 ) @ ( relation_dom @ SV87 ) )
| ~ ( in @ ( ordered_pair @ ( sK61_D @ SV87 @ SV71 @ SV15 ) @ SV15 ) @ SV87 ) ) )
= $true )
| ( ( in @ SV15 @ ( relation_image @ SV87 @ SV71 ) )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1299]) ).
thf(1400,plain,
! [SV15: $i,SV71: $i,SV87: $i] :
( ( ( in @ ( sK61_D @ SV87 @ SV71 @ SV15 ) @ SV71 )
= $true )
| ( ( in @ SV15 @ ( relation_image @ SV87 @ SV71 ) )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1300]) ).
thf(1401,plain,
! [SV16: $i,SV105: $i,SV128: $i] :
( ( ( ! [SY3506: $i] :
( ~ ( in @ ( ordered_pair @ SY3506 @ ( sK46_D @ SV128 @ SV105 @ SV16 ) ) @ SV16 )
| ~ ( in @ SY3506 @ SV105 ) ) )
= $true )
| ( ( ~ ( in @ ( sK46_D @ SV128 @ SV105 @ SV16 ) @ SV128 ) )
= $true )
| ( ( SV128
= ( relation_image @ SV16 @ SV105 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1301]) ).
thf(1402,plain,
! [SV16: $i,SV105: $i,SV128: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SV128 @ SV105 @ SV16 ) @ ( sK46_D @ SV128 @ SV105 @ SV16 ) ) @ SV16 )
| ~ ( in @ ( sK47_SY3118 @ SV128 @ SV105 @ SV16 ) @ SV105 ) ) )
= $true )
| ( ( in @ ( sK46_D @ SV128 @ SV105 @ SV16 ) @ SV128 )
= $true )
| ( ( SV128
= ( relation_image @ SV16 @ SV105 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1302]) ).
thf(1403,plain,
! [SV129: $i,SV106: $i,SV16: $i] :
( ( ( ! [SY3507: $i] :
( ! [SY3468: $i] :
( ~ ( in @ ( ordered_pair @ SY3468 @ SY3507 ) @ SV16 )
| ~ ( in @ SY3468 @ SV106 ) )
| ( in @ SY3507 @ SV129 ) ) )
= $true )
| ( ( SV129
= ( relation_image @ SV16 @ SV106 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1303]) ).
thf(1404,plain,
! [SV16: $i,SV106: $i,SV129: $i] :
( ( ( ! [SY3509: $i] :
( ~ ( in @ SY3509 @ SV129 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SY3509 @ SV129 @ SV106 @ SV16 ) @ SY3509 ) @ SV16 )
| ~ ( in @ ( sK45_E @ SY3509 @ SV129 @ SV106 @ SV16 ) @ SV106 ) ) ) )
= $true )
| ( ( SV129
= ( relation_image @ SV16 @ SV106 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1304]) ).
thf(1405,plain,
! [SV51: $i] :
( ( ( in @ ( ordered_pair @ ( sK64_B @ SV51 ) @ ( sK65_SY3126 @ SV51 ) ) @ SV51 )
= $true )
| ( ( antisymmetric @ SV51 )
= $true )
| ( ( relation @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1305]) ).
thf(1406,plain,
! [SV51: $i] :
( ( ( in @ ( ordered_pair @ ( sK65_SY3126 @ SV51 ) @ ( sK64_B @ SV51 ) ) @ SV51 )
= $true )
| ( ( antisymmetric @ SV51 )
= $true )
| ( ( relation @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1306]) ).
thf(1407,plain,
! [SV52: $i,SV167: $i,SV148: $i] :
( ( ( in @ ( ordered_pair @ SV148 @ SV167 ) @ SV52 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV167 @ SV148 ) @ SV52 ) )
= $true )
| ( ( SV148 = SV167 )
= $true )
| ( ( antisymmetric @ SV52 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1307]) ).
thf(1408,plain,
! [SV17: $i,SV88: $i,SV72: $i] :
( ( ( SV72
= ( apply @ SV88 @ SV17 ) )
= $false )
| ( ( ~ ( in @ SV17 @ ( relation_dom @ SV88 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV17 @ SV72 ) @ SV88 )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1308]) ).
thf(1409,plain,
! [SV130: $i,SV17: $i,SV149: $i] :
( ( ( relation @ SV149 )
= $false )
| ( ( function @ SV149 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV17 @ SV130 ) @ SV149 )
| ( SV130
= ( apply @ SV149 @ SV17 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1309]) ).
thf(1410,plain,
! [SV131: $i,SV17: $i,SV150: $i] :
( ( ( relation @ SV150 )
= $false )
| ( ( function @ SV150 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV17 @ SV131 ) @ SV150 )
| ( in @ SV17 @ ( relation_dom @ SV150 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1310]) ).
thf(1411,plain,
! [SV18: $i,SV107: $i,SV132: $i] :
( ( ( ( ( sK35_D @ SV132 @ SV107 @ SV18 )
= SV107 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV107 ) @ SV18 ) )
= $true )
| ( ( ~ ( in @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV132 ) )
= $true )
| ( ( SV132
= ( fiber @ SV18 @ SV107 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1311]) ).
thf(1412,plain,
! [SV18: $i,SV107: $i,SV132: $i] :
( ( ( ~ ( ( ( sK35_D @ SV132 @ SV107 @ SV18 )
!= SV107 )
| ( in @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV132 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV107 ) @ SV18 )
| ( in @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV132 ) ) )
= $false )
| ( ( SV132
= ( fiber @ SV18 @ SV107 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1312]) ).
thf(1413,plain,
! [SV133: $i,SV18: $i,SV108: $i] :
( ( ( ! [SY3512: $i] :
( ( SY3512 = SV108 )
| ~ ( in @ ( ordered_pair @ SY3512 @ SV108 ) @ SV18 )
| ( in @ SY3512 @ SV133 ) ) )
= $true )
| ( ( SV133
= ( fiber @ SV18 @ SV108 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1313]) ).
thf(1414,plain,
! [SV18: $i,SV108: $i,SV133: $i] :
( ( ( ~ ( ~ ! [SY3513: $i] :
( ~ ( in @ SY3513 @ SV133 )
| ( SY3513 != SV108 ) )
| ~ ! [SY3514: $i] :
( ~ ( in @ SY3514 @ SV133 )
| ( in @ ( ordered_pair @ SY3514 @ SV108 ) @ SV18 ) ) ) )
= $true )
| ( ( SV133
= ( fiber @ SV18 @ SV108 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1314]) ).
thf(1415,plain,
! [SV20: $i,SV111: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SV111 @ SV20 ) @ ( sK13_SY3095 @ SV111 @ SV20 ) ) @ SV111 )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV111 @ SV20 ) @ ( sK12_C @ SV111 @ SV20 ) ) @ SV20 ) )
= $true )
| ( ( SV111
= ( relation_inverse @ SV20 ) )
= $true )
| ( ( relation @ SV111 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1317]) ).
thf(1416,plain,
! [SV20: $i,SV111: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK12_C @ SV111 @ SV20 ) @ ( sK13_SY3095 @ SV111 @ SV20 ) ) @ SV111 )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV111 @ SV20 ) @ ( sK12_C @ SV111 @ SV20 ) ) @ SV20 ) )
= $true )
| ( ( SV111
= ( relation_inverse @ SV20 ) )
= $true )
| ( ( relation @ SV111 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1318]) ).
thf(1417,plain,
! [SV20: $i,SV112: $i] :
( ( ( ~ ! [SY3476: $i,SY3477: $i] :
( ~ ( in @ ( ordered_pair @ SY3476 @ SY3477 ) @ SV112 )
| ( in @ ( ordered_pair @ SY3477 @ SY3476 ) @ SV20 ) ) )
= $false )
| ( ( SV112
= ( relation_inverse @ SV20 ) )
= $false )
| ( ( relation @ SV112 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1319]) ).
thf(1418,plain,
! [SV112: $i,SV20: $i] :
( ( ( ~ ! [SY3478: $i,SY3479: $i] :
( ~ ( in @ ( ordered_pair @ SY3479 @ SY3478 ) @ SV20 )
| ( in @ ( ordered_pair @ SY3478 @ SY3479 ) @ SV112 ) ) )
= $false )
| ( ( SV112
= ( relation_inverse @ SV20 ) )
= $false )
| ( ( relation @ SV112 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1319]) ).
thf(1419,plain,
! [SV21: $i,SV38: $i,SV134: $i] :
( ( ( ~ ( ~ ( in @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) @ SV21 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV38 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) ) )
= $false )
| ( ( SV134
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $true )
| ( ( relation @ SV134 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1320]) ).
thf(1420,plain,
! [SV21: $i,SV38: $i,SV134: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV38 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) ) ) )
= $false )
| ( ( SV134
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $true )
| ( ( relation @ SV134 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1320]) ).
thf(1421,plain,
! [SV135: $i,SV38: $i,SV21: $i] :
( ( ( ~ ! [SY3515: $i,SY3516: $i] :
( ~ ( in @ SY3516 @ SV21 )
| ~ ( in @ ( ordered_pair @ SY3515 @ SY3516 ) @ SV38 )
| ( in @ ( ordered_pair @ SY3515 @ SY3516 ) @ SV135 ) )
| ~ ~ ( ~ ! [SY3517: $i,SY3518: $i] :
( ~ ( in @ ( ordered_pair @ SY3517 @ SY3518 ) @ SV135 )
| ( in @ SY3518 @ SV21 ) )
| ~ ! [SY3519: $i,SY3520: $i] :
( ~ ( in @ ( ordered_pair @ SY3519 @ SY3520 ) @ SV135 )
| ( in @ ( ordered_pair @ SY3519 @ SY3520 ) @ SV38 ) ) ) )
= $false )
| ( ( SV135
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1321]) ).
thf(1422,plain,
! [SV22: $i,SV113: $i,SV198: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV198 @ ( sK17_C @ SV113 @ SV22 ) ) @ SV22 ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV113 @ SV22 ) @ SV113 ) )
= $true )
| ( ( SV113
= ( relation_rng @ SV22 ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1423,plain,
! [SV114: $i,SV22: $i,SV199: $i] :
( ( ( ! [SY3569: $i] :
~ ( in @ ( ordered_pair @ SY3569 @ SV199 ) @ SV22 )
| ( in @ SV199 @ SV114 ) )
= $true )
| ( ( SV114
= ( relation_rng @ SV22 ) )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1424,plain,
! [SV22: $i,SV114: $i,SV200: $i] :
( ( ( ~ ( in @ SV200 @ SV114 )
| ( in @ ( ordered_pair @ ( sK16_D @ SV200 @ SV114 @ SV22 ) @ SV200 ) @ SV22 ) )
= $true )
| ( ( SV114
= ( relation_rng @ SV22 ) )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1425,plain,
! [SV23: $i,SV115: $i] :
( ( ( in @ ( ordered_pair @ ( sK24_C @ SV115 @ SV23 ) @ ( sK25_SY3102 @ SV115 @ SV23 ) ) @ SV23 )
= $true )
| ( ( subset @ SV23 @ SV115 )
= $true )
| ( ( relation @ SV115 )
= $false )
| ( ( relation @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1326]) ).
thf(1426,plain,
! [SV23: $i,SV115: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV115 @ SV23 ) @ ( sK25_SY3102 @ SV115 @ SV23 ) ) @ SV115 ) )
= $true )
| ( ( subset @ SV23 @ SV115 )
= $true )
| ( ( relation @ SV115 )
= $false )
| ( ( relation @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1327]) ).
thf(1427,plain,
! [SV116: $i,SV23: $i,SV201: $i,SV189: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV189 @ SV201 ) @ SV23 )
| ( in @ ( ordered_pair @ SV189 @ SV201 ) @ SV116 ) )
= $true )
| ( ( subset @ SV23 @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false )
| ( ( relation @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1328]) ).
thf(1428,plain,
! [SV24: $i,SV117: $i,SV136: $i] :
( ( ( ~ ( ~ ( in @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ SV117 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV24 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) ) )
= $false )
| ( ( SV136
= ( relation_dom_restriction @ SV24 @ SV117 ) )
= $true )
| ( ( relation @ SV136 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1329]) ).
thf(1429,plain,
! [SV24: $i,SV117: $i,SV136: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ SV117 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV24 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) ) ) )
= $false )
| ( ( SV136
= ( relation_dom_restriction @ SV24 @ SV117 ) )
= $true )
| ( ( relation @ SV136 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1329]) ).
thf(1430,plain,
! [SV137: $i,SV24: $i,SV118: $i] :
( ( ( ~ ! [SY3521: $i,SY3522: $i] :
( ~ ( in @ SY3521 @ SV118 )
| ~ ( in @ ( ordered_pair @ SY3521 @ SY3522 ) @ SV24 )
| ( in @ ( ordered_pair @ SY3521 @ SY3522 ) @ SV137 ) )
| ~ ~ ( ~ ! [SY3523: $i] :
( ! [SY3524: $i] :
~ ( in @ ( ordered_pair @ SY3523 @ SY3524 ) @ SV137 )
| ( in @ SY3523 @ SV118 ) )
| ~ ! [SY3525: $i,SY3526: $i] :
( ~ ( in @ ( ordered_pair @ SY3525 @ SY3526 ) @ SV137 )
| ( in @ ( ordered_pair @ SY3525 @ SY3526 ) @ SV24 ) ) ) )
= $false )
| ( ( SV137
= ( relation_dom_restriction @ SV24 @ SV118 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1330]) ).
thf(1431,plain,
! [SV26: $i,SV190: $i] :
( ( ( ~ ( in @ SV190 @ ( relation_dom @ SV26 ) ) )
= $true )
| ( ( ! [SY3564: $i] :
( ( SY3564
!= ( apply @ SV26 @ SV190 ) )
| ( in @ ( ordered_pair @ SV190 @ SY3564 ) @ SV26 ) ) )
= $true )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1331]) ).
thf(1432,plain,
! [SV26: $i,SV191: $i] :
( ( ( ~ ( in @ SV191 @ ( relation_dom @ SV26 ) ) )
= $true )
| ( ( ! [SY3565: $i] :
( ~ ( in @ ( ordered_pair @ SV191 @ SY3565 ) @ SV26 )
| ( SY3565
= ( apply @ SV26 @ SV191 ) ) ) )
= $true )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1332]) ).
thf(1433,plain,
! [SV26: $i,SV192: $i] :
( ( ( in @ SV192 @ ( relation_dom @ SV26 ) )
= $true )
| ( ( ! [SY3566: $i] :
( ( SY3566
!= ( apply @ SV26 @ SV192 ) )
| ( SY3566 = empty_set ) ) )
= $true )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1333]) ).
thf(1434,plain,
! [SV26: $i,SV193: $i] :
( ( ( in @ SV193 @ ( relation_dom @ SV26 ) )
= $true )
| ( ( ! [SY3567: $i] :
( ( SY3567 != empty_set )
| ( SY3567
= ( apply @ SV26 @ SV193 ) ) ) )
= $true )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1334]) ).
thf(1435,plain,
! [SV53: $i] :
( ( ( ~ ( ~ ( ( ( sK62_B @ SV53 )
!= ( sK63_SY3125 @ SV53 ) ) )
| ~ ~ ( ~ ( in @ ( sK62_B @ SV53 ) @ ( relation_field @ SV53 ) )
| ~ ( in @ ( sK63_SY3125 @ SV53 ) @ ( relation_field @ SV53 ) ) ) ) )
= $true )
| ( ( connected @ SV53 )
= $true )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1335]) ).
thf(1436,plain,
! [SV53: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK62_B @ SV53 ) @ ( sK63_SY3125 @ SV53 ) ) @ SV53 ) )
= $true )
| ( ( connected @ SV53 )
= $true )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1336]) ).
thf(1437,plain,
! [SV54: $i,SV169: $i,SV151: $i] :
( ( ( SV151 = SV169 )
= $true )
| ( ( ~ ( in @ SV151 @ ( relation_field @ SV54 ) )
| ~ ( in @ SV169 @ ( relation_field @ SV54 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV151 @ SV169 ) @ SV54 )
= $true )
| ( ( in @ ( ordered_pair @ SV169 @ SV151 ) @ SV54 )
= $true )
| ( ( connected @ SV54 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1337]) ).
thf(1438,plain,
! [SV27: $i,SV120: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_C @ SV120 @ SV27 ) @ SV120 )
| ~ ( in @ ( sK20_SY3099 @ SV120 @ SV27 ) @ SV120 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SV120 @ SV27 ) @ ( sK20_SY3099 @ SV120 @ SV27 ) ) @ SV27 ) ) )
= $false )
| ( ( is_antisymmetric_in @ SV27 @ SV120 )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1338]) ).
thf(1439,plain,
! [SV27: $i,SV120: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK20_SY3099 @ SV120 @ SV27 ) @ ( sK19_C @ SV120 @ SV27 ) ) @ SV27 ) )
= $false )
| ( ( is_antisymmetric_in @ SV27 @ SV120 )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1338]) ).
thf(1440,plain,
! [SV27: $i,SV178: $i,SV121: $i,SV170: $i] :
( ( ( ~ ( in @ SV170 @ SV121 )
| ~ ( in @ SV178 @ SV121 )
| ~ ( in @ ( ordered_pair @ SV170 @ SV178 ) @ SV27 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV178 @ SV170 ) @ SV27 ) )
= $true )
| ( ( SV170 = SV178 )
= $true )
| ( ( is_antisymmetric_in @ SV27 @ SV121 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1340]) ).
thf(1441,plain,
! [SV55: $i] :
( ( ( in @ ( ordered_pair @ ( sK66_B @ SV55 ) @ ( sK67_SY3127 @ SV55 ) ) @ SV55 )
= $true )
| ( ( transitive @ SV55 )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1343]) ).
thf(1442,plain,
! [SV55: $i] :
( ( ( in @ ( ordered_pair @ ( sK67_SY3127 @ SV55 ) @ ( sK68_SY3129 @ SV55 ) ) @ SV55 )
= $true )
| ( ( transitive @ SV55 )
= $true )
| ( ( relation @ SV55 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1344]) ).
thf(1443,plain,
! [SV180: $i,SV56: $i,SV172: $i,SV154: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV154 @ SV172 ) @ SV56 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV172 @ SV180 ) @ SV56 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV154 @ SV180 ) @ SV56 )
= $true )
| ( ( transitive @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1345]) ).
thf(1444,plain,
! [SV30: $i,SV124: $i,SV139: $i] :
( ( ( ! [SY3527: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SY3527 ) @ SV30 )
| ~ ( in @ SY3527 @ SV124 ) ) )
= $true )
| ( ( ~ ( in @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SV139 ) )
= $true )
| ( ( SV139
= ( relation_inverse_image @ SV30 @ SV124 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1348]) ).
thf(1445,plain,
! [SV30: $i,SV124: $i,SV139: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ ( sK44_SY3116 @ SV139 @ SV124 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK44_SY3116 @ SV139 @ SV124 @ SV30 ) @ SV124 ) ) )
= $true )
| ( ( in @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SV139 )
= $true )
| ( ( SV139
= ( relation_inverse_image @ SV30 @ SV124 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1349]) ).
thf(1446,plain,
! [SV140: $i,SV125: $i,SV30: $i] :
( ( ( ! [SY3528: $i] :
( ! [SY3500: $i] :
( ~ ( in @ ( ordered_pair @ SY3528 @ SY3500 ) @ SV30 )
| ~ ( in @ SY3500 @ SV125 ) )
| ( in @ SY3528 @ SV140 ) ) )
= $true )
| ( ( SV140
= ( relation_inverse_image @ SV30 @ SV125 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1350]) ).
thf(1447,plain,
! [SV30: $i,SV125: $i,SV140: $i] :
( ( ( ! [SY3530: $i] :
( ~ ( in @ SY3530 @ SV140 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3530 @ ( sK42_E @ SY3530 @ SV140 @ SV125 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK42_E @ SY3530 @ SV140 @ SV125 @ SV30 ) @ SV125 ) ) ) )
= $true )
| ( ( SV140
= ( relation_inverse_image @ SV30 @ SV125 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1351]) ).
thf(1448,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( function @ SV174 )
= $false )
| ( ( ~ ( relation @ SV174 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) ) ) )
| ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 )
| ( relation_isomorphism @ SV32 @ SV59 @ SV174 ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1352]) ).
thf(1449,plain,
! [SV59: $i,SV32: $i,SV202: $i] :
( ( ( ~ ( function @ SV202 )
| ~ ( relation @ SV202 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
| ~ ( ~ ! [SY3570: $i,SY3571: $i] :
( ~ ( in @ SY3570 @ ( relation_field @ SV32 ) )
| ~ ( in @ SY3571 @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV202 @ SY3570 ) @ ( apply @ SV202 @ SY3571 ) ) @ SV59 )
| ( in @ ( ordered_pair @ SY3570 @ SY3571 ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3312: $i] :
( ! [SY3313: $i] :
~ ( in @ ( ordered_pair @ SY3312 @ SY3313 ) @ SV32 )
| ( in @ SY3312 @ ( relation_field @ SV32 ) ) )
| ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV32 )
| ( in @ SY3315 @ ( relation_field @ SV32 ) ) ) )
| ~ ! [SY3576: $i,SY3577: $i] :
( ~ ( in @ ( ordered_pair @ SY3576 @ SY3577 ) @ SV32 )
| ( in @ ( ordered_pair @ ( apply @ SV202 @ SY3576 ) @ ( apply @ SV202 @ SY3577 ) ) @ SV59 ) ) ) ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1353]) ).
thf(1450,plain,
! [SV59: $i,SV32: $i] :
( ( ( ~ ~ ( ~ ! [SY3402: $i] :
( ~ ( function @ SY3402 )
| ~ ( relation @ SY3402 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3402 )
| ( ( relation_dom @ SY3402 )
= ( relation_field @ SV32 ) ) )
| ~ ! [SY3403: $i] :
( ~ ( function @ SY3403 )
| ~ ( relation @ SY3403 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3403 )
| ( ( relation_rng @ SY3403 )
= ( relation_field @ SV59 ) ) ) )
| ~ ! [SY3404: $i] :
( ~ ( function @ SY3404 )
| ~ ( relation @ SY3404 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3404 )
| ( one_to_one @ SY3404 ) ) )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1354]) ).
thf(1451,plain,
! [SV33: $i,SV75: $i,SV95: $i,SV203: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV203 @ ( sK57_D @ SV95 @ SV75 @ SV33 ) ) @ SV95 ) )
= $true )
| ( ( ( relation_rng_as_subset @ SV33 @ SV75 @ SV95 )
= SV75 )
= $true )
| ( ( relation_of2_as_subset @ SV95 @ SV33 @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1355]) ).
thf(1452,plain,
! [SV33: $i,SV96: $i,SV76: $i,SV182: $i] :
( ( ( in @ SV182 @ SV76 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK56_E @ SV182 @ SV96 @ SV76 @ SV33 ) @ SV182 ) @ SV96 )
= $true )
| ( ( ( relation_rng_as_subset @ SV33 @ SV76 @ SV96 )
= SV76 )
= $false )
| ( ( relation_of2_as_subset @ SV96 @ SV33 @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1357]) ).
thf(1453,plain,
! [SV204: $i,SV34: $i,SV126: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SV126 @ SV34 ) @ SV204 ) @ SV34 ) )
= $true )
| ( ( ~ ( in @ ( sK22_C @ SV126 @ SV34 ) @ SV126 ) )
= $true )
| ( ( SV126
= ( relation_dom @ SV34 ) )
= $true )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1358]) ).
thf(1454,plain,
! [SV127: $i,SV34: $i,SV205: $i] :
( ( ( ! [SY3578: $i] :
~ ( in @ ( ordered_pair @ SV205 @ SY3578 ) @ SV34 )
| ( in @ SV205 @ SV127 ) )
= $true )
| ( ( SV127
= ( relation_dom @ SV34 ) )
= $false )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1360]) ).
thf(1455,plain,
! [SV34: $i,SV127: $i,SV206: $i] :
( ( ( ~ ( in @ SV206 @ SV127 )
| ( in @ ( ordered_pair @ SV206 @ ( sK21_D @ SV206 @ SV127 @ SV34 ) ) @ SV34 ) )
= $true )
| ( ( SV127
= ( relation_dom @ SV34 ) )
= $false )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1361]) ).
thf(1456,plain,
! [SV4: $i,SV98: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV4 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV98 ) )
= $true )
| ( ( SV4 = SV98 )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1362]) ).
thf(1457,plain,
! [SV4: $i,SV98: $i] :
( ( ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV4 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV98 )
= $true )
| ( ( SV4 = SV98 )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1363]) ).
thf(1458,plain,
! [SV99: $i,SV4: $i] :
( ( ( ! [SY3455: $i,SY3456: $i] :
( ~ ( in @ ( ordered_pair @ SY3455 @ SY3456 ) @ SV4 )
| ( in @ ( ordered_pair @ SY3455 @ SY3456 ) @ SV99 ) ) )
= $true )
| ( ( SV4 = SV99 )
= $false )
| ( ( relation @ SV99 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1364]) ).
thf(1459,plain,
! [SV4: $i,SV99: $i] :
( ( ( ! [SY3457: $i,SY3458: $i] :
( ~ ( in @ ( ordered_pair @ SY3457 @ SY3458 ) @ SV99 )
| ( in @ ( ordered_pair @ SY3457 @ SY3458 ) @ SV4 ) ) )
= $true )
| ( ( SV4 = SV99 )
= $false )
| ( ( relation @ SV99 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1365]) ).
thf(1460,plain,
! [SV5: $i,SV100: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SV100 @ SV5 ) @ SV100 )
| ~ ( in @ ( sK4_SY3086 @ SV100 @ SV5 ) @ SV100 ) )
| ~ ( in @ ( sK5_SY3088 @ SV100 @ SV5 ) @ SV100 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SV100 @ SV5 ) @ ( sK4_SY3086 @ SV100 @ SV5 ) ) @ SV5 ) ) )
= $true )
| ( ( is_transitive_in @ SV5 @ SV100 )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1366]) ).
thf(1461,plain,
! [SV5: $i,SV100: $i] :
( ( ( in @ ( ordered_pair @ ( sK4_SY3086 @ SV100 @ SV5 ) @ ( sK5_SY3088 @ SV100 @ SV5 ) ) @ SV5 )
= $true )
| ( ( is_transitive_in @ SV5 @ SV100 )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1367]) ).
thf(1462,plain,
! [SV5: $i,SV183: $i,SV175: $i,SV101: $i,SV159: $i] :
( ( ( ~ ( in @ SV159 @ SV101 )
| ~ ( in @ SV175 @ SV101 )
| ~ ( in @ SV183 @ SV101 )
| ~ ( in @ ( ordered_pair @ SV159 @ SV175 ) @ SV5 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV175 @ SV183 ) @ SV5 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV159 @ SV183 ) @ SV5 )
= $true )
| ( ( is_transitive_in @ SV5 @ SV101 )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1368]) ).
thf(1463,plain,
! [SV194: $i,SV6: $i,SV60: $i,SV77: $i] :
( ( ( in @ ( ordered_pair @ ( sK59_D @ SV77 @ SV60 @ SV6 ) @ SV194 ) @ SV77 )
= $false )
| ( ( ( relation_dom_as_subset @ SV60 @ SV6 @ SV77 )
= SV60 )
= $true )
| ( ( relation_of2_as_subset @ SV77 @ SV60 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1369]) ).
thf(1464,plain,
! [SV7: $i,SV46: $i,SV160: $i] :
( ( ( ~ ( ! [SY3548: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ SY3548 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3548 @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV46 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV160 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK9_SY3093 @ SV160 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV46 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV160 ) ) )
= $false )
| ( ( SV160
= ( relation_composition @ SV7 @ SV46 ) )
= $true )
| ( ( relation @ SV160 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1371]) ).
thf(1465,plain,
! [SV46: $i,SV7: $i,SV161: $i] :
( ( ( SV161
= ( relation_composition @ SV7 @ SV46 ) )
= $false )
| ( ( ~ ( ~ ! [SY3549: $i,SY3550: $i] :
( ! [SY3373: $i] :
( ~ ( in @ ( ordered_pair @ SY3549 @ SY3373 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3373 @ SY3550 ) @ SV46 ) )
| ( in @ ( ordered_pair @ SY3549 @ SY3550 ) @ SV161 ) )
| ~ ! [SY3552: $i,SY3553: $i] :
( ~ ( in @ ( ordered_pair @ SY3552 @ SY3553 ) @ SV161 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3552 @ ( sK6_F @ SY3553 @ SY3552 @ SV161 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY3553 @ SY3552 @ SV161 @ SV46 @ SV7 ) @ SY3553 ) @ SV46 ) ) ) ) )
= $true )
| ( ( relation @ SV161 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1372]) ).
thf(1466,plain,
! [SV47: $i,SV62: $i] :
( ( ( ( sK52_C @ SV62 @ SV47 )
= ( sK53_SY3121 @ SV62 @ SV47 ) )
= $false )
| ( ( ~ ( in @ ( sK52_C @ SV62 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) )
= $true )
| ( ( SV62
= ( identity_relation @ SV47 ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1373]) ).
thf(1467,plain,
! [SV47: $i,SV62: $i] :
( ( ( ( ( sK52_C @ SV62 @ SV47 )
= ( sK53_SY3121 @ SV62 @ SV47 ) )
| ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) )
= $true )
| ( ( SV62
= ( identity_relation @ SV47 ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1374]) ).
thf(1468,plain,
! [SV47: $i,SV62: $i] :
( ( ( ( in @ ( sK52_C @ SV62 @ SV47 ) @ SV47 )
| ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) )
= $true )
| ( ( SV62
= ( identity_relation @ SV47 ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1375]) ).
thf(1469,plain,
! [SV63: $i,SV48: $i,SV207: $i,SV195: $i] :
( ( ( ( SV195 != SV207 )
| ~ ( in @ SV195 @ SV48 )
| ( in @ ( ordered_pair @ SV195 @ SV207 ) @ SV63 ) )
= $true )
| ( ( SV63
= ( identity_relation @ SV48 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1376]) ).
thf(1470,plain,
! [SV48: $i,SV63: $i] :
( ( ( ~ ! [SY3411: $i,SY3412: $i] :
( ~ ( in @ ( ordered_pair @ SY3411 @ SY3412 ) @ SV63 )
| ( SY3411 = SY3412 ) ) )
= $false )
| ( ( SV63
= ( identity_relation @ SV48 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1377]) ).
thf(1471,plain,
! [SV48: $i,SV63: $i] :
( ( ( ~ ! [SY3413: $i] :
( ! [SY3414: $i] :
~ ( in @ ( ordered_pair @ SY3413 @ SY3414 ) @ SV63 )
| ( in @ SY3413 @ SV48 ) ) )
= $false )
| ( ( SV63
= ( identity_relation @ SV48 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1377]) ).
thf(1472,plain,
! [SV49: $i,SV42: $i,SV8: $i,SV142: $i] :
( ( ( SV142
= ( sK40_C @ SV142 @ SV8 ) )
= $false )
| ( ( SV142
= ( pair_first @ SV8 ) )
= $true )
| ( ( SV8
= ( ordered_pair @ SV42 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1379]) ).
thf(1473,plain,
! [SV49: $i,SV42: $i,SV143: $i,SV208: $i,SV184: $i,SV8: $i] :
( ( ( ( SV8
!= ( ordered_pair @ SV184 @ SV208 ) ) )
= $true )
| ( ( SV143 = SV184 )
= $true )
| ( ( SV143
= ( pair_first @ SV8 ) )
= $false )
| ( ( SV8
= ( ordered_pair @ SV42 @ SV49 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1380]) ).
thf(1474,plain,
! [SV162: $i,SV144: $i,SV37: $i,SV9: $i] :
( ( ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SV144 ) @ SV162 ) )
= $false )
| ( ( in @ SV9 @ SV144 )
= $true )
| ( ( relation @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1382]) ).
thf(1475,plain,
! [SV163: $i,SV145: $i,SV37: $i,SV9: $i] :
( ( ( in @ ( ordered_pair @ SV9 @ SV37 ) @ ( relation_composition @ ( identity_relation @ SV145 ) @ SV163 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV9 @ SV37 ) @ SV163 )
= $true )
| ( ( relation @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1383]) ).
thf(1476,plain,
! [SV64: $i,SV80: $i,SV164: $i,SV10: $i] :
( ( ( in @ ( ordered_pair @ SV10 @ SV164 ) @ SV80 )
= $false )
| ( ( in @ SV164 @ ( relation_rng @ SV80 ) )
= $false )
| ( ( ~ ( in @ SV164 @ SV64 ) )
= $true )
| ( ( in @ SV10 @ ( relation_inverse_image @ SV80 @ SV64 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1384]) ).
thf(1477,plain,
! [SV10: $i,SV65: $i,SV81: $i] :
( ( ( ~ ( in @ ( sK60_D @ SV81 @ SV65 @ SV10 ) @ ( relation_rng @ SV81 ) )
| ~ ( in @ ( ordered_pair @ SV10 @ ( sK60_D @ SV81 @ SV65 @ SV10 ) ) @ SV81 ) )
= $false )
| ( ( in @ SV10 @ ( relation_inverse_image @ SV81 @ SV65 ) )
= $false )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1385]) ).
thf(1478,plain,
! [SV82: $i,SV66: $i,SV196: $i,SV11: $i,SV185: $i] :
( ( ( ~ ( in @ SV185 @ SV11 )
| ~ ( in @ SV196 @ SV66 ) )
= $true )
| ( ( ( ( sK28_D @ SV82 @ SV66 @ SV11 )
!= ( ordered_pair @ SV185 @ SV196 ) ) )
= $true )
| ( ( ~ ( in @ ( sK28_D @ SV82 @ SV66 @ SV11 ) @ SV82 ) )
= $true )
| ( ( SV82
= ( cartesian_product2 @ SV11 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1387]) ).
thf(1479,plain,
! [SV11: $i,SV66: $i,SV82: $i] :
( ( ( ~ ( ~ ( in @ ( sK29_SY3106 @ SV82 @ SV66 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK30_SY3108 @ SV82 @ SV66 @ SV11 ) @ SV66 ) ) )
= $true )
| ( ( in @ ( sK28_D @ SV82 @ SV66 @ SV11 ) @ SV82 )
= $true )
| ( ( SV82
= ( cartesian_product2 @ SV11 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1388]) ).
thf(1480,plain,
! [SV11: $i,SV66: $i,SV82: $i] :
( ( ( ( sK28_D @ SV82 @ SV66 @ SV11 )
= ( ordered_pair @ ( sK29_SY3106 @ SV82 @ SV66 @ SV11 ) @ ( sK30_SY3108 @ SV82 @ SV66 @ SV11 ) ) )
= $true )
| ( ( in @ ( sK28_D @ SV82 @ SV66 @ SV11 ) @ SV82 )
= $true )
| ( ( SV82
= ( cartesian_product2 @ SV11 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1389]) ).
thf(1481,plain,
! [SV83: $i,SV186: $i,SV67: $i,SV11: $i,SV209: $i] :
( ( ( ! [SY3579: $i] :
( ~ ( in @ SV209 @ SV11 )
| ~ ( in @ SY3579 @ SV67 )
| ( SV186
!= ( ordered_pair @ SV209 @ SY3579 ) ) ) )
= $true )
| ( ( in @ SV186 @ SV83 )
= $true )
| ( ( SV83
= ( cartesian_product2 @ SV11 @ SV67 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1390]) ).
thf(1482,plain,
! [SV11: $i,SV67: $i,SV83: $i,SV187: $i] :
( ( ( in @ SV187 @ SV83 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK26_E @ SV187 @ SV83 @ SV67 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK27_SY3103 @ SV187 @ SV83 @ SV67 @ SV11 ) @ SV67 ) )
| ( SV187
!= ( ordered_pair @ ( sK26_E @ SV187 @ SV83 @ SV67 @ SV11 ) @ ( sK27_SY3103 @ SV187 @ SV83 @ SV67 @ SV11 ) ) ) ) )
= $true )
| ( ( SV83
= ( cartesian_product2 @ SV11 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1391]) ).
thf(1483,plain,
! [SV50: $i,SV43: $i,SV13: $i,SV146: $i] :
( ( ( SV146
= ( sK34_SY3110 @ SV146 @ SV13 ) )
= $false )
| ( ( SV146
= ( pair_second @ SV13 ) )
= $true )
| ( ( SV13
= ( ordered_pair @ SV43 @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1393]) ).
thf(1484,plain,
! [SV50: $i,SV43: $i,SV147: $i,SV197: $i,SV188: $i,SV13: $i] :
( ( ( ( SV13
!= ( ordered_pair @ SV188 @ SV197 ) ) )
= $true )
| ( ( SV147 = SV197 )
= $true )
| ( ( SV147
= ( pair_second @ SV13 ) )
= $false )
| ( ( SV13
= ( ordered_pair @ SV43 @ SV50 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1394]) ).
thf(1485,plain,
! [SV14: $i,SV103: $i] :
( ( ( ~ ( ~ ( ( ( sK14_C @ SV103 @ SV14 )
!= ( sK15_SY3096 @ SV103 @ SV14 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SV103 @ SV14 ) @ SV103 )
| ~ ( in @ ( sK15_SY3096 @ SV103 @ SV14 ) @ SV103 ) ) ) )
= $true )
| ( ( is_connected_in @ SV14 @ SV103 )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1395]) ).
thf(1486,plain,
! [SV14: $i,SV103: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK14_C @ SV103 @ SV14 ) @ ( sK15_SY3096 @ SV103 @ SV14 ) ) @ SV14 ) )
= $true )
| ( ( is_connected_in @ SV14 @ SV103 )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1396]) ).
thf(1487,plain,
! [SV14: $i,SV104: $i,SV177: $i,SV165: $i] :
( ( ( SV165 = SV177 )
= $true )
| ( ( ~ ( in @ SV165 @ SV104 )
| ~ ( in @ SV177 @ SV104 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV165 @ SV177 ) @ SV14 )
= $true )
| ( ( in @ ( ordered_pair @ SV177 @ SV165 ) @ SV14 )
= $true )
| ( ( is_connected_in @ SV14 @ SV104 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1397]) ).
thf(1488,plain,
! [SV70: $i,SV86: $i,SV15: $i,SV166: $i] :
( ( ( in @ ( ordered_pair @ SV166 @ SV15 ) @ SV86 )
= $false )
| ( ( in @ SV166 @ ( relation_dom @ SV86 ) )
= $false )
| ( ( ~ ( in @ SV166 @ SV70 ) )
= $true )
| ( ( in @ SV15 @ ( relation_image @ SV86 @ SV70 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1398]) ).
thf(1489,plain,
! [SV15: $i,SV71: $i,SV87: $i] :
( ( ( ~ ( in @ ( sK61_D @ SV87 @ SV71 @ SV15 ) @ ( relation_dom @ SV87 ) )
| ~ ( in @ ( ordered_pair @ ( sK61_D @ SV87 @ SV71 @ SV15 ) @ SV15 ) @ SV87 ) )
= $false )
| ( ( in @ SV15 @ ( relation_image @ SV87 @ SV71 ) )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1399]) ).
thf(1490,plain,
! [SV16: $i,SV105: $i,SV128: $i,SV210: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV210 @ ( sK46_D @ SV128 @ SV105 @ SV16 ) ) @ SV16 )
| ~ ( in @ SV210 @ SV105 ) )
= $true )
| ( ( ~ ( in @ ( sK46_D @ SV128 @ SV105 @ SV16 ) @ SV128 ) )
= $true )
| ( ( SV128
= ( relation_image @ SV16 @ SV105 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1401]) ).
thf(1491,plain,
! [SV16: $i,SV105: $i,SV128: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SV128 @ SV105 @ SV16 ) @ ( sK46_D @ SV128 @ SV105 @ SV16 ) ) @ SV16 )
| ~ ( in @ ( sK47_SY3118 @ SV128 @ SV105 @ SV16 ) @ SV105 ) )
= $false )
| ( ( in @ ( sK46_D @ SV128 @ SV105 @ SV16 ) @ SV128 )
= $true )
| ( ( SV128
= ( relation_image @ SV16 @ SV105 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1402]) ).
thf(1492,plain,
! [SV129: $i,SV106: $i,SV16: $i,SV211: $i] :
( ( ( ! [SY3580: $i] :
( ~ ( in @ ( ordered_pair @ SY3580 @ SV211 ) @ SV16 )
| ~ ( in @ SY3580 @ SV106 ) )
| ( in @ SV211 @ SV129 ) )
= $true )
| ( ( SV129
= ( relation_image @ SV16 @ SV106 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1403]) ).
thf(1493,plain,
! [SV16: $i,SV106: $i,SV129: $i,SV212: $i] :
( ( ( ~ ( in @ SV212 @ SV129 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SV212 @ SV129 @ SV106 @ SV16 ) @ SV212 ) @ SV16 )
| ~ ( in @ ( sK45_E @ SV212 @ SV129 @ SV106 @ SV16 ) @ SV106 ) ) )
= $true )
| ( ( SV129
= ( relation_image @ SV16 @ SV106 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1404]) ).
thf(1494,plain,
! [SV52: $i,SV148: $i,SV167: $i] :
( ( ( in @ ( ordered_pair @ SV167 @ SV148 ) @ SV52 )
= $false )
| ( ( in @ ( ordered_pair @ SV148 @ SV167 ) @ SV52 )
= $false )
| ( ( SV148 = SV167 )
= $true )
| ( ( antisymmetric @ SV52 )
= $false )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1407]) ).
thf(1495,plain,
! [SV72: $i,SV88: $i,SV17: $i] :
( ( ( in @ SV17 @ ( relation_dom @ SV88 ) )
= $false )
| ( ( SV72
= ( apply @ SV88 @ SV17 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV17 @ SV72 ) @ SV88 )
= $true )
| ( ( function @ SV88 )
= $false )
| ( ( relation @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1408]) ).
thf(1496,plain,
! [SV149: $i,SV130: $i,SV17: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV17 @ SV130 ) @ SV149 ) )
= $true )
| ( ( SV130
= ( apply @ SV149 @ SV17 ) )
= $true )
| ( ( function @ SV149 )
= $false )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1409]) ).
thf(1497,plain,
! [SV150: $i,SV131: $i,SV17: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV17 @ SV131 ) @ SV150 ) )
= $true )
| ( ( in @ SV17 @ ( relation_dom @ SV150 ) )
= $true )
| ( ( function @ SV150 )
= $false )
| ( ( relation @ SV150 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1410]) ).
thf(1498,plain,
! [SV18: $i,SV107: $i,SV132: $i] :
( ( ( ( sK35_D @ SV132 @ SV107 @ SV18 )
= SV107 )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV107 ) @ SV18 ) )
= $true )
| ( ( ~ ( in @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV132 ) )
= $true )
| ( ( SV132
= ( fiber @ SV18 @ SV107 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1411]) ).
thf(1499,plain,
! [SV18: $i,SV107: $i,SV132: $i] :
( ( ( ~ ( ( ( sK35_D @ SV132 @ SV107 @ SV18 )
!= SV107 )
| ( in @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV132 ) ) )
= $false )
| ( ( SV132
= ( fiber @ SV18 @ SV107 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1412]) ).
thf(1500,plain,
! [SV18: $i,SV107: $i,SV132: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV107 ) @ SV18 )
| ( in @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV132 ) ) )
= $false )
| ( ( SV132
= ( fiber @ SV18 @ SV107 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1412]) ).
thf(1501,plain,
! [SV133: $i,SV18: $i,SV108: $i,SV213: $i] :
( ( ( ( SV213 = SV108 )
| ~ ( in @ ( ordered_pair @ SV213 @ SV108 ) @ SV18 )
| ( in @ SV213 @ SV133 ) )
= $true )
| ( ( SV133
= ( fiber @ SV18 @ SV108 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1413]) ).
thf(1502,plain,
! [SV18: $i,SV108: $i,SV133: $i] :
( ( ( ~ ! [SY3513: $i] :
( ~ ( in @ SY3513 @ SV133 )
| ( SY3513 != SV108 ) )
| ~ ! [SY3514: $i] :
( ~ ( in @ SY3514 @ SV133 )
| ( in @ ( ordered_pair @ SY3514 @ SV108 ) @ SV18 ) ) )
= $false )
| ( ( SV133
= ( fiber @ SV18 @ SV108 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1414]) ).
thf(1503,plain,
! [SV20: $i,SV111: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SV111 @ SV20 ) @ ( sK13_SY3095 @ SV111 @ SV20 ) ) @ SV111 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV111 @ SV20 ) @ ( sK12_C @ SV111 @ SV20 ) ) @ SV20 ) )
= $true )
| ( ( SV111
= ( relation_inverse @ SV20 ) )
= $true )
| ( ( relation @ SV111 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1415]) ).
thf(1504,plain,
! [SV20: $i,SV111: $i] :
( ( ( in @ ( ordered_pair @ ( sK12_C @ SV111 @ SV20 ) @ ( sK13_SY3095 @ SV111 @ SV20 ) ) @ SV111 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV111 @ SV20 ) @ ( sK12_C @ SV111 @ SV20 ) ) @ SV20 )
= $true )
| ( ( SV111
= ( relation_inverse @ SV20 ) )
= $true )
| ( ( relation @ SV111 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1416]) ).
thf(1505,plain,
! [SV20: $i,SV112: $i] :
( ( ( ! [SY3476: $i,SY3477: $i] :
( ~ ( in @ ( ordered_pair @ SY3476 @ SY3477 ) @ SV112 )
| ( in @ ( ordered_pair @ SY3477 @ SY3476 ) @ SV20 ) ) )
= $true )
| ( ( SV112
= ( relation_inverse @ SV20 ) )
= $false )
| ( ( relation @ SV112 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1417]) ).
thf(1506,plain,
! [SV112: $i,SV20: $i] :
( ( ( ! [SY3478: $i,SY3479: $i] :
( ~ ( in @ ( ordered_pair @ SY3479 @ SY3478 ) @ SV20 )
| ( in @ ( ordered_pair @ SY3478 @ SY3479 ) @ SV112 ) ) )
= $true )
| ( ( SV112
= ( relation_inverse @ SV20 ) )
= $false )
| ( ( relation @ SV112 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1418]) ).
thf(1507,plain,
! [SV21: $i,SV38: $i,SV134: $i] :
( ( ( ~ ( in @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) @ SV21 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV38 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) )
= $true )
| ( ( SV134
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $true )
| ( ( relation @ SV134 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1419]) ).
thf(1508,plain,
! [SV21: $i,SV38: $i,SV134: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV38 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) ) ) )
= $true )
| ( ( SV134
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $true )
| ( ( relation @ SV134 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1420]) ).
thf(1509,plain,
! [SV135: $i,SV38: $i,SV21: $i] :
( ( ( ~ ! [SY3515: $i,SY3516: $i] :
( ~ ( in @ SY3516 @ SV21 )
| ~ ( in @ ( ordered_pair @ SY3515 @ SY3516 ) @ SV38 )
| ( in @ ( ordered_pair @ SY3515 @ SY3516 ) @ SV135 ) ) )
= $false )
| ( ( SV135
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1421]) ).
thf(1510,plain,
! [SV38: $i,SV21: $i,SV135: $i] :
( ( ( ~ ~ ( ~ ! [SY3517: $i,SY3518: $i] :
( ~ ( in @ ( ordered_pair @ SY3517 @ SY3518 ) @ SV135 )
| ( in @ SY3518 @ SV21 ) )
| ~ ! [SY3519: $i,SY3520: $i] :
( ~ ( in @ ( ordered_pair @ SY3519 @ SY3520 ) @ SV135 )
| ( in @ ( ordered_pair @ SY3519 @ SY3520 ) @ SV38 ) ) ) )
= $false )
| ( ( SV135
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1421]) ).
thf(1511,plain,
! [SV22: $i,SV113: $i,SV198: $i] :
( ( ( in @ ( ordered_pair @ SV198 @ ( sK17_C @ SV113 @ SV22 ) ) @ SV22 )
= $false )
| ( ( ~ ( in @ ( sK17_C @ SV113 @ SV22 ) @ SV113 ) )
= $true )
| ( ( SV113
= ( relation_rng @ SV22 ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1422]) ).
thf(1512,plain,
! [SV114: $i,SV22: $i,SV199: $i] :
( ( ( ! [SY3569: $i] :
~ ( in @ ( ordered_pair @ SY3569 @ SV199 ) @ SV22 ) )
= $true )
| ( ( in @ SV199 @ SV114 )
= $true )
| ( ( SV114
= ( relation_rng @ SV22 ) )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1423]) ).
thf(1513,plain,
! [SV22: $i,SV114: $i,SV200: $i] :
( ( ( ~ ( in @ SV200 @ SV114 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK16_D @ SV200 @ SV114 @ SV22 ) @ SV200 ) @ SV22 )
= $true )
| ( ( SV114
= ( relation_rng @ SV22 ) )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1424]) ).
thf(1514,plain,
! [SV23: $i,SV115: $i] :
( ( ( in @ ( ordered_pair @ ( sK24_C @ SV115 @ SV23 ) @ ( sK25_SY3102 @ SV115 @ SV23 ) ) @ SV115 )
= $false )
| ( ( subset @ SV23 @ SV115 )
= $true )
| ( ( relation @ SV115 )
= $false )
| ( ( relation @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1426]) ).
thf(1515,plain,
! [SV116: $i,SV23: $i,SV201: $i,SV189: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV189 @ SV201 ) @ SV23 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV189 @ SV201 ) @ SV116 )
= $true )
| ( ( subset @ SV23 @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false )
| ( ( relation @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1427]) ).
thf(1516,plain,
! [SV24: $i,SV117: $i,SV136: $i] :
( ( ( ~ ( in @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ SV117 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV24 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) )
= $true )
| ( ( SV136
= ( relation_dom_restriction @ SV24 @ SV117 ) )
= $true )
| ( ( relation @ SV136 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1428]) ).
thf(1517,plain,
! [SV24: $i,SV117: $i,SV136: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ SV117 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV24 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) ) ) )
= $true )
| ( ( SV136
= ( relation_dom_restriction @ SV24 @ SV117 ) )
= $true )
| ( ( relation @ SV136 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1429]) ).
thf(1518,plain,
! [SV137: $i,SV24: $i,SV118: $i] :
( ( ( ~ ! [SY3521: $i,SY3522: $i] :
( ~ ( in @ SY3521 @ SV118 )
| ~ ( in @ ( ordered_pair @ SY3521 @ SY3522 ) @ SV24 )
| ( in @ ( ordered_pair @ SY3521 @ SY3522 ) @ SV137 ) ) )
= $false )
| ( ( SV137
= ( relation_dom_restriction @ SV24 @ SV118 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1430]) ).
thf(1519,plain,
! [SV24: $i,SV118: $i,SV137: $i] :
( ( ( ~ ~ ( ~ ! [SY3523: $i] :
( ! [SY3524: $i] :
~ ( in @ ( ordered_pair @ SY3523 @ SY3524 ) @ SV137 )
| ( in @ SY3523 @ SV118 ) )
| ~ ! [SY3525: $i,SY3526: $i] :
( ~ ( in @ ( ordered_pair @ SY3525 @ SY3526 ) @ SV137 )
| ( in @ ( ordered_pair @ SY3525 @ SY3526 ) @ SV24 ) ) ) )
= $false )
| ( ( SV137
= ( relation_dom_restriction @ SV24 @ SV118 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1430]) ).
thf(1520,plain,
! [SV26: $i,SV190: $i] :
( ( ( in @ SV190 @ ( relation_dom @ SV26 ) )
= $false )
| ( ( ! [SY3564: $i] :
( ( SY3564
!= ( apply @ SV26 @ SV190 ) )
| ( in @ ( ordered_pair @ SV190 @ SY3564 ) @ SV26 ) ) )
= $true )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1431]) ).
thf(1521,plain,
! [SV26: $i,SV191: $i] :
( ( ( in @ SV191 @ ( relation_dom @ SV26 ) )
= $false )
| ( ( ! [SY3565: $i] :
( ~ ( in @ ( ordered_pair @ SV191 @ SY3565 ) @ SV26 )
| ( SY3565
= ( apply @ SV26 @ SV191 ) ) ) )
= $true )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1432]) ).
thf(1522,plain,
! [SV192: $i,SV26: $i,SV214: $i] :
( ( ( ( SV214
!= ( apply @ SV26 @ SV192 ) )
| ( SV214 = empty_set ) )
= $true )
| ( ( in @ SV192 @ ( relation_dom @ SV26 ) )
= $true )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1433]) ).
thf(1523,plain,
! [SV193: $i,SV26: $i,SV215: $i] :
( ( ( ( SV215 != empty_set )
| ( SV215
= ( apply @ SV26 @ SV193 ) ) )
= $true )
| ( ( in @ SV193 @ ( relation_dom @ SV26 ) )
= $true )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1434]) ).
thf(1524,plain,
! [SV53: $i] :
( ( ( ~ ( ( ( sK62_B @ SV53 )
!= ( sK63_SY3125 @ SV53 ) ) )
| ~ ~ ( ~ ( in @ ( sK62_B @ SV53 ) @ ( relation_field @ SV53 ) )
| ~ ( in @ ( sK63_SY3125 @ SV53 ) @ ( relation_field @ SV53 ) ) ) )
= $false )
| ( ( connected @ SV53 )
= $true )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1435]) ).
thf(1525,plain,
! [SV53: $i] :
( ( ( in @ ( ordered_pair @ ( sK62_B @ SV53 ) @ ( sK63_SY3125 @ SV53 ) ) @ SV53 )
= $false )
| ( ( connected @ SV53 )
= $true )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1436]) ).
thf(1526,plain,
! [SV169: $i,SV54: $i,SV151: $i] :
( ( ( ~ ( in @ SV151 @ ( relation_field @ SV54 ) ) )
= $true )
| ( ( ~ ( in @ SV169 @ ( relation_field @ SV54 ) ) )
= $true )
| ( ( SV151 = SV169 )
= $true )
| ( ( in @ ( ordered_pair @ SV151 @ SV169 ) @ SV54 )
= $true )
| ( ( in @ ( ordered_pair @ SV169 @ SV151 ) @ SV54 )
= $true )
| ( ( connected @ SV54 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1437]) ).
thf(1527,plain,
! [SV27: $i,SV120: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK19_C @ SV120 @ SV27 ) @ SV120 )
| ~ ( in @ ( sK20_SY3099 @ SV120 @ SV27 ) @ SV120 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SV120 @ SV27 ) @ ( sK20_SY3099 @ SV120 @ SV27 ) ) @ SV27 ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV27 @ SV120 )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1438]) ).
thf(1528,plain,
! [SV27: $i,SV120: $i] :
( ( ( in @ ( ordered_pair @ ( sK20_SY3099 @ SV120 @ SV27 ) @ ( sK19_C @ SV120 @ SV27 ) ) @ SV27 )
= $true )
| ( ( is_antisymmetric_in @ SV27 @ SV120 )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1439]) ).
thf(1529,plain,
! [SV27: $i,SV178: $i,SV121: $i,SV170: $i] :
( ( ( ~ ( in @ SV170 @ SV121 )
| ~ ( in @ SV178 @ SV121 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV170 @ SV178 ) @ SV27 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV178 @ SV170 ) @ SV27 ) )
= $true )
| ( ( SV170 = SV178 )
= $true )
| ( ( is_antisymmetric_in @ SV27 @ SV121 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1440]) ).
thf(1530,plain,
! [SV180: $i,SV56: $i,SV172: $i,SV154: $i] :
( ( ( in @ ( ordered_pair @ SV154 @ SV172 ) @ SV56 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV172 @ SV180 ) @ SV56 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV154 @ SV180 ) @ SV56 )
= $true )
| ( ( transitive @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1443]) ).
thf(1531,plain,
! [SV216: $i,SV30: $i,SV124: $i,SV139: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SV216 ) @ SV30 )
| ~ ( in @ SV216 @ SV124 ) )
= $true )
| ( ( ~ ( in @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SV139 ) )
= $true )
| ( ( SV139
= ( relation_inverse_image @ SV30 @ SV124 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1444]) ).
thf(1532,plain,
! [SV30: $i,SV124: $i,SV139: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ ( sK44_SY3116 @ SV139 @ SV124 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK44_SY3116 @ SV139 @ SV124 @ SV30 ) @ SV124 ) )
= $false )
| ( ( in @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SV139 )
= $true )
| ( ( SV139
= ( relation_inverse_image @ SV30 @ SV124 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1445]) ).
thf(1533,plain,
! [SV140: $i,SV125: $i,SV30: $i,SV217: $i] :
( ( ( ! [SY3581: $i] :
( ~ ( in @ ( ordered_pair @ SV217 @ SY3581 ) @ SV30 )
| ~ ( in @ SY3581 @ SV125 ) )
| ( in @ SV217 @ SV140 ) )
= $true )
| ( ( SV140
= ( relation_inverse_image @ SV30 @ SV125 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(1534,plain,
! [SV30: $i,SV125: $i,SV140: $i,SV218: $i] :
( ( ( ~ ( in @ SV218 @ SV140 )
| ~ ( ~ ( in @ ( ordered_pair @ SV218 @ ( sK42_E @ SV218 @ SV140 @ SV125 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK42_E @ SV218 @ SV140 @ SV125 @ SV30 ) @ SV125 ) ) )
= $true )
| ( ( SV140
= ( relation_inverse_image @ SV30 @ SV125 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(1535,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( relation @ SV174 )
= $false )
| ( ( function @ SV174 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) ) ) )
| ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 )
| ( relation_isomorphism @ SV32 @ SV59 @ SV174 ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1448]) ).
thf(1536,plain,
! [SV59: $i,SV32: $i,SV202: $i] :
( ( ( ~ ( function @ SV202 )
| ~ ( relation @ SV202 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
| ~ ( ~ ! [SY3570: $i,SY3571: $i] :
( ~ ( in @ SY3570 @ ( relation_field @ SV32 ) )
| ~ ( in @ SY3571 @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV202 @ SY3570 ) @ ( apply @ SV202 @ SY3571 ) ) @ SV59 )
| ( in @ ( ordered_pair @ SY3570 @ SY3571 ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3312: $i] :
( ! [SY3313: $i] :
~ ( in @ ( ordered_pair @ SY3312 @ SY3313 ) @ SV32 )
| ( in @ SY3312 @ ( relation_field @ SV32 ) ) )
| ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV32 )
| ( in @ SY3315 @ ( relation_field @ SV32 ) ) ) )
| ~ ! [SY3576: $i,SY3577: $i] :
( ~ ( in @ ( ordered_pair @ SY3576 @ SY3577 ) @ SV32 )
| ( in @ ( ordered_pair @ ( apply @ SV202 @ SY3576 ) @ ( apply @ SV202 @ SY3577 ) ) @ SV59 ) ) ) ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1449]) ).
thf(1537,plain,
! [SV59: $i,SV32: $i] :
( ( ( ~ ~ ( ~ ! [SY3402: $i] :
( ~ ( function @ SY3402 )
| ~ ( relation @ SY3402 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3402 )
| ( ( relation_dom @ SY3402 )
= ( relation_field @ SV32 ) ) )
| ~ ! [SY3403: $i] :
( ~ ( function @ SY3403 )
| ~ ( relation @ SY3403 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3403 )
| ( ( relation_rng @ SY3403 )
= ( relation_field @ SV59 ) ) ) ) )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1450]) ).
thf(1538,plain,
! [SV59: $i,SV32: $i] :
( ( ( ~ ! [SY3404: $i] :
( ~ ( function @ SY3404 )
| ~ ( relation @ SY3404 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3404 )
| ( one_to_one @ SY3404 ) ) )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1450]) ).
thf(1539,plain,
! [SV33: $i,SV75: $i,SV95: $i,SV203: $i] :
( ( ( in @ ( ordered_pair @ SV203 @ ( sK57_D @ SV95 @ SV75 @ SV33 ) ) @ SV95 )
= $false )
| ( ( ( relation_rng_as_subset @ SV33 @ SV75 @ SV95 )
= SV75 )
= $true )
| ( ( relation_of2_as_subset @ SV95 @ SV33 @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1451]) ).
thf(1540,plain,
! [SV204: $i,SV34: $i,SV126: $i] :
( ( ( in @ ( ordered_pair @ ( sK22_C @ SV126 @ SV34 ) @ SV204 ) @ SV34 )
= $false )
| ( ( ~ ( in @ ( sK22_C @ SV126 @ SV34 ) @ SV126 ) )
= $true )
| ( ( SV126
= ( relation_dom @ SV34 ) )
= $true )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1453]) ).
thf(1541,plain,
! [SV127: $i,SV34: $i,SV205: $i] :
( ( ( ! [SY3578: $i] :
~ ( in @ ( ordered_pair @ SV205 @ SY3578 ) @ SV34 ) )
= $true )
| ( ( in @ SV205 @ SV127 )
= $true )
| ( ( SV127
= ( relation_dom @ SV34 ) )
= $false )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1454]) ).
thf(1542,plain,
! [SV34: $i,SV127: $i,SV206: $i] :
( ( ( ~ ( in @ SV206 @ SV127 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV206 @ ( sK21_D @ SV206 @ SV127 @ SV34 ) ) @ SV34 )
= $true )
| ( ( SV127
= ( relation_dom @ SV34 ) )
= $false )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1455]) ).
thf(1543,plain,
! [SV4: $i,SV98: $i] :
( ( ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV4 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV98 ) )
= $true )
| ( ( SV4 = SV98 )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1456]) ).
thf(1544,plain,
! [SV99: $i,SV4: $i,SV219: $i] :
( ( ( ! [SY3582: $i] :
( ~ ( in @ ( ordered_pair @ SV219 @ SY3582 ) @ SV4 )
| ( in @ ( ordered_pair @ SV219 @ SY3582 ) @ SV99 ) ) )
= $true )
| ( ( SV4 = SV99 )
= $false )
| ( ( relation @ SV99 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1458]) ).
thf(1545,plain,
! [SV4: $i,SV99: $i,SV220: $i] :
( ( ( ! [SY3583: $i] :
( ~ ( in @ ( ordered_pair @ SV220 @ SY3583 ) @ SV99 )
| ( in @ ( ordered_pair @ SV220 @ SY3583 ) @ SV4 ) ) )
= $true )
| ( ( SV4 = SV99 )
= $false )
| ( ( relation @ SV99 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(1546,plain,
! [SV5: $i,SV100: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SV100 @ SV5 ) @ SV100 )
| ~ ( in @ ( sK4_SY3086 @ SV100 @ SV5 ) @ SV100 ) )
| ~ ( in @ ( sK5_SY3088 @ SV100 @ SV5 ) @ SV100 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SV100 @ SV5 ) @ ( sK4_SY3086 @ SV100 @ SV5 ) ) @ SV5 ) )
= $false )
| ( ( is_transitive_in @ SV5 @ SV100 )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1460]) ).
thf(1547,plain,
! [SV5: $i,SV183: $i,SV175: $i,SV101: $i,SV159: $i] :
( ( ( ~ ( in @ SV159 @ SV101 )
| ~ ( in @ SV175 @ SV101 )
| ~ ( in @ SV183 @ SV101 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV159 @ SV175 ) @ SV5 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV175 @ SV183 ) @ SV5 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV159 @ SV183 ) @ SV5 )
= $true )
| ( ( is_transitive_in @ SV5 @ SV101 )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1462]) ).
thf(1548,plain,
! [SV7: $i,SV46: $i,SV160: $i] :
( ( ( ~ ( ! [SY3548: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ SY3548 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3548 @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV46 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV160 ) ) )
= $false )
| ( ( SV160
= ( relation_composition @ SV7 @ SV46 ) )
= $true )
| ( ( relation @ SV160 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1464]) ).
thf(1549,plain,
! [SV7: $i,SV46: $i,SV160: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK9_SY3093 @ SV160 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV46 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV160 ) ) )
= $false )
| ( ( SV160
= ( relation_composition @ SV7 @ SV46 ) )
= $true )
| ( ( relation @ SV160 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1464]) ).
thf(1550,plain,
! [SV161: $i,SV46: $i,SV7: $i] :
( ( ( ~ ! [SY3549: $i,SY3550: $i] :
( ! [SY3373: $i] :
( ~ ( in @ ( ordered_pair @ SY3549 @ SY3373 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3373 @ SY3550 ) @ SV46 ) )
| ( in @ ( ordered_pair @ SY3549 @ SY3550 ) @ SV161 ) )
| ~ ! [SY3552: $i,SY3553: $i] :
( ~ ( in @ ( ordered_pair @ SY3552 @ SY3553 ) @ SV161 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3552 @ ( sK6_F @ SY3553 @ SY3552 @ SV161 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY3553 @ SY3552 @ SV161 @ SV46 @ SV7 ) @ SY3553 ) @ SV46 ) ) ) )
= $false )
| ( ( SV161
= ( relation_composition @ SV7 @ SV46 ) )
= $false )
| ( ( relation @ SV161 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1465]) ).
thf(1551,plain,
! [SV47: $i,SV62: $i] :
( ( ( in @ ( sK52_C @ SV62 @ SV47 ) @ SV47 )
= $false )
| ( ( ( sK52_C @ SV62 @ SV47 )
= ( sK53_SY3121 @ SV62 @ SV47 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 ) )
= $true )
| ( ( SV62
= ( identity_relation @ SV47 ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1466]) ).
thf(1552,plain,
! [SV47: $i,SV62: $i] :
( ( ( ( sK52_C @ SV62 @ SV47 )
= ( sK53_SY3121 @ SV62 @ SV47 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 )
= $true )
| ( ( SV62
= ( identity_relation @ SV47 ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1467]) ).
thf(1553,plain,
! [SV47: $i,SV62: $i] :
( ( ( in @ ( sK52_C @ SV62 @ SV47 ) @ SV47 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 )
= $true )
| ( ( SV62
= ( identity_relation @ SV47 ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1468]) ).
thf(1554,plain,
! [SV63: $i,SV48: $i,SV207: $i,SV195: $i] :
( ( ( ( SV195 != SV207 )
| ~ ( in @ SV195 @ SV48 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV195 @ SV207 ) @ SV63 )
= $true )
| ( ( SV63
= ( identity_relation @ SV48 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1469]) ).
thf(1555,plain,
! [SV48: $i,SV63: $i] :
( ( ( ! [SY3411: $i,SY3412: $i] :
( ~ ( in @ ( ordered_pair @ SY3411 @ SY3412 ) @ SV63 )
| ( SY3411 = SY3412 ) ) )
= $true )
| ( ( SV63
= ( identity_relation @ SV48 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1470]) ).
thf(1556,plain,
! [SV48: $i,SV63: $i] :
( ( ( ! [SY3413: $i] :
( ! [SY3414: $i] :
~ ( in @ ( ordered_pair @ SY3413 @ SY3414 ) @ SV63 )
| ( in @ SY3413 @ SV48 ) ) )
= $true )
| ( ( SV63
= ( identity_relation @ SV48 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1471]) ).
thf(1557,plain,
! [SV49: $i,SV42: $i,SV143: $i,SV208: $i,SV184: $i,SV8: $i] :
( ( ( SV8
= ( ordered_pair @ SV184 @ SV208 ) )
= $false )
| ( ( SV143 = SV184 )
= $true )
| ( ( SV143
= ( pair_first @ SV8 ) )
= $false )
| ( ( SV8
= ( ordered_pair @ SV42 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1473]) ).
thf(1558,plain,
! [SV10: $i,SV80: $i,SV64: $i,SV164: $i] :
( ( ( in @ SV164 @ SV64 )
= $false )
| ( ( in @ SV164 @ ( relation_rng @ SV80 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV10 @ SV164 ) @ SV80 )
= $false )
| ( ( in @ SV10 @ ( relation_inverse_image @ SV80 @ SV64 ) )
= $true )
| ( ( relation @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1476]) ).
thf(1559,plain,
! [SV10: $i,SV65: $i,SV81: $i] :
( ( ( ~ ( in @ ( sK60_D @ SV81 @ SV65 @ SV10 ) @ ( relation_rng @ SV81 ) ) )
= $false )
| ( ( in @ SV10 @ ( relation_inverse_image @ SV81 @ SV65 ) )
= $false )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1477]) ).
thf(1560,plain,
! [SV65: $i,SV81: $i,SV10: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV10 @ ( sK60_D @ SV81 @ SV65 @ SV10 ) ) @ SV81 ) )
= $false )
| ( ( in @ SV10 @ ( relation_inverse_image @ SV81 @ SV65 ) )
= $false )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1477]) ).
thf(1561,plain,
! [SV82: $i,SV66: $i,SV196: $i,SV11: $i,SV185: $i] :
( ( ( ~ ( in @ SV185 @ SV11 ) )
= $true )
| ( ( ~ ( in @ SV196 @ SV66 ) )
= $true )
| ( ( ( ( sK28_D @ SV82 @ SV66 @ SV11 )
!= ( ordered_pair @ SV185 @ SV196 ) ) )
= $true )
| ( ( ~ ( in @ ( sK28_D @ SV82 @ SV66 @ SV11 ) @ SV82 ) )
= $true )
| ( ( SV82
= ( cartesian_product2 @ SV11 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1478]) ).
thf(1562,plain,
! [SV11: $i,SV66: $i,SV82: $i] :
( ( ( ~ ( in @ ( sK29_SY3106 @ SV82 @ SV66 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK30_SY3108 @ SV82 @ SV66 @ SV11 ) @ SV66 ) )
= $false )
| ( ( in @ ( sK28_D @ SV82 @ SV66 @ SV11 ) @ SV82 )
= $true )
| ( ( SV82
= ( cartesian_product2 @ SV11 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1479]) ).
thf(1563,plain,
! [SV83: $i,SV186: $i,SV67: $i,SV221: $i,SV11: $i,SV209: $i] :
( ( ( ~ ( in @ SV209 @ SV11 )
| ~ ( in @ SV221 @ SV67 )
| ( SV186
!= ( ordered_pair @ SV209 @ SV221 ) ) )
= $true )
| ( ( in @ SV186 @ SV83 )
= $true )
| ( ( SV83
= ( cartesian_product2 @ SV11 @ SV67 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1481]) ).
thf(1564,plain,
! [SV11: $i,SV67: $i,SV83: $i,SV187: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK26_E @ SV187 @ SV83 @ SV67 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK27_SY3103 @ SV187 @ SV83 @ SV67 @ SV11 ) @ SV67 ) )
| ( SV187
!= ( ordered_pair @ ( sK26_E @ SV187 @ SV83 @ SV67 @ SV11 ) @ ( sK27_SY3103 @ SV187 @ SV83 @ SV67 @ SV11 ) ) ) )
= $false )
| ( ( in @ SV187 @ SV83 )
= $false )
| ( ( SV83
= ( cartesian_product2 @ SV11 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1482]) ).
thf(1565,plain,
! [SV50: $i,SV43: $i,SV147: $i,SV197: $i,SV188: $i,SV13: $i] :
( ( ( SV13
= ( ordered_pair @ SV188 @ SV197 ) )
= $false )
| ( ( SV147 = SV197 )
= $true )
| ( ( SV147
= ( pair_second @ SV13 ) )
= $false )
| ( ( SV13
= ( ordered_pair @ SV43 @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1484]) ).
thf(1566,plain,
! [SV14: $i,SV103: $i] :
( ( ( ~ ( ( ( sK14_C @ SV103 @ SV14 )
!= ( sK15_SY3096 @ SV103 @ SV14 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SV103 @ SV14 ) @ SV103 )
| ~ ( in @ ( sK15_SY3096 @ SV103 @ SV14 ) @ SV103 ) ) )
= $false )
| ( ( is_connected_in @ SV14 @ SV103 )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1485]) ).
thf(1567,plain,
! [SV14: $i,SV103: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_C @ SV103 @ SV14 ) @ ( sK15_SY3096 @ SV103 @ SV14 ) ) @ SV14 )
= $false )
| ( ( is_connected_in @ SV14 @ SV103 )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1486]) ).
thf(1568,plain,
! [SV14: $i,SV177: $i,SV104: $i,SV165: $i] :
( ( ( ~ ( in @ SV165 @ SV104 ) )
= $true )
| ( ( ~ ( in @ SV177 @ SV104 ) )
= $true )
| ( ( SV165 = SV177 )
= $true )
| ( ( in @ ( ordered_pair @ SV165 @ SV177 ) @ SV14 )
= $true )
| ( ( in @ ( ordered_pair @ SV177 @ SV165 ) @ SV14 )
= $true )
| ( ( is_connected_in @ SV14 @ SV104 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1487]) ).
thf(1569,plain,
! [SV15: $i,SV86: $i,SV70: $i,SV166: $i] :
( ( ( in @ SV166 @ SV70 )
= $false )
| ( ( in @ SV166 @ ( relation_dom @ SV86 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV166 @ SV15 ) @ SV86 )
= $false )
| ( ( in @ SV15 @ ( relation_image @ SV86 @ SV70 ) )
= $true )
| ( ( relation @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1488]) ).
thf(1570,plain,
! [SV15: $i,SV71: $i,SV87: $i] :
( ( ( ~ ( in @ ( sK61_D @ SV87 @ SV71 @ SV15 ) @ ( relation_dom @ SV87 ) ) )
= $false )
| ( ( in @ SV15 @ ( relation_image @ SV87 @ SV71 ) )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1489]) ).
thf(1571,plain,
! [SV15: $i,SV71: $i,SV87: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK61_D @ SV87 @ SV71 @ SV15 ) @ SV15 ) @ SV87 ) )
= $false )
| ( ( in @ SV15 @ ( relation_image @ SV87 @ SV71 ) )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1489]) ).
thf(1572,plain,
! [SV16: $i,SV105: $i,SV128: $i,SV210: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV210 @ ( sK46_D @ SV128 @ SV105 @ SV16 ) ) @ SV16 ) )
= $true )
| ( ( ~ ( in @ SV210 @ SV105 ) )
= $true )
| ( ( ~ ( in @ ( sK46_D @ SV128 @ SV105 @ SV16 ) @ SV128 ) )
= $true )
| ( ( SV128
= ( relation_image @ SV16 @ SV105 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1490]) ).
thf(1573,plain,
! [SV16: $i,SV105: $i,SV128: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SV128 @ SV105 @ SV16 ) @ ( sK46_D @ SV128 @ SV105 @ SV16 ) ) @ SV16 ) )
= $false )
| ( ( in @ ( sK46_D @ SV128 @ SV105 @ SV16 ) @ SV128 )
= $true )
| ( ( SV128
= ( relation_image @ SV16 @ SV105 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1491]) ).
thf(1574,plain,
! [SV16: $i,SV105: $i,SV128: $i] :
( ( ( ~ ( in @ ( sK47_SY3118 @ SV128 @ SV105 @ SV16 ) @ SV105 ) )
= $false )
| ( ( in @ ( sK46_D @ SV128 @ SV105 @ SV16 ) @ SV128 )
= $true )
| ( ( SV128
= ( relation_image @ SV16 @ SV105 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1491]) ).
thf(1575,plain,
! [SV129: $i,SV106: $i,SV16: $i,SV211: $i] :
( ( ( ! [SY3580: $i] :
( ~ ( in @ ( ordered_pair @ SY3580 @ SV211 ) @ SV16 )
| ~ ( in @ SY3580 @ SV106 ) ) )
= $true )
| ( ( in @ SV211 @ SV129 )
= $true )
| ( ( SV129
= ( relation_image @ SV16 @ SV106 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1492]) ).
thf(1576,plain,
! [SV16: $i,SV106: $i,SV129: $i,SV212: $i] :
( ( ( ~ ( in @ SV212 @ SV129 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SV212 @ SV129 @ SV106 @ SV16 ) @ SV212 ) @ SV16 )
| ~ ( in @ ( sK45_E @ SV212 @ SV129 @ SV106 @ SV16 ) @ SV106 ) ) )
= $true )
| ( ( SV129
= ( relation_image @ SV16 @ SV106 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1493]) ).
thf(1577,plain,
! [SV149: $i,SV130: $i,SV17: $i] :
( ( ( in @ ( ordered_pair @ SV17 @ SV130 ) @ SV149 )
= $false )
| ( ( SV130
= ( apply @ SV149 @ SV17 ) )
= $true )
| ( ( function @ SV149 )
= $false )
| ( ( relation @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1496]) ).
thf(1578,plain,
! [SV150: $i,SV131: $i,SV17: $i] :
( ( ( in @ ( ordered_pair @ SV17 @ SV131 ) @ SV150 )
= $false )
| ( ( in @ SV17 @ ( relation_dom @ SV150 ) )
= $true )
| ( ( function @ SV150 )
= $false )
| ( ( relation @ SV150 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1497]) ).
thf(1579,plain,
! [SV18: $i,SV107: $i,SV132: $i] :
( ( ( in @ ( ordered_pair @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV107 ) @ SV18 )
= $false )
| ( ( ( sK35_D @ SV132 @ SV107 @ SV18 )
= SV107 )
= $true )
| ( ( ~ ( in @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV132 ) )
= $true )
| ( ( SV132
= ( fiber @ SV18 @ SV107 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1498]) ).
thf(1580,plain,
! [SV18: $i,SV107: $i,SV132: $i] :
( ( ( ( ( sK35_D @ SV132 @ SV107 @ SV18 )
!= SV107 )
| ( in @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV132 ) )
= $true )
| ( ( SV132
= ( fiber @ SV18 @ SV107 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1499]) ).
thf(1581,plain,
! [SV18: $i,SV107: $i,SV132: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV107 ) @ SV18 )
| ( in @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV132 ) )
= $true )
| ( ( SV132
= ( fiber @ SV18 @ SV107 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1500]) ).
thf(1582,plain,
! [SV133: $i,SV18: $i,SV108: $i,SV213: $i] :
( ( ( ( SV213 = SV108 )
| ~ ( in @ ( ordered_pair @ SV213 @ SV108 ) @ SV18 ) )
= $true )
| ( ( in @ SV213 @ SV133 )
= $true )
| ( ( SV133
= ( fiber @ SV18 @ SV108 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1501]) ).
thf(1583,plain,
! [SV18: $i,SV108: $i,SV133: $i] :
( ( ( ~ ! [SY3513: $i] :
( ~ ( in @ SY3513 @ SV133 )
| ( SY3513 != SV108 ) ) )
= $false )
| ( ( SV133
= ( fiber @ SV18 @ SV108 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1502]) ).
thf(1584,plain,
! [SV18: $i,SV108: $i,SV133: $i] :
( ( ( ~ ! [SY3514: $i] :
( ~ ( in @ SY3514 @ SV133 )
| ( in @ ( ordered_pair @ SY3514 @ SV108 ) @ SV18 ) ) )
= $false )
| ( ( SV133
= ( fiber @ SV18 @ SV108 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1502]) ).
thf(1585,plain,
! [SV20: $i,SV111: $i] :
( ( ( in @ ( ordered_pair @ ( sK12_C @ SV111 @ SV20 ) @ ( sK13_SY3095 @ SV111 @ SV20 ) ) @ SV111 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV111 @ SV20 ) @ ( sK12_C @ SV111 @ SV20 ) ) @ SV20 ) )
= $true )
| ( ( SV111
= ( relation_inverse @ SV20 ) )
= $true )
| ( ( relation @ SV111 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1503]) ).
thf(1586,plain,
! [SV20: $i,SV112: $i,SV222: $i] :
( ( ( ! [SY3584: $i] :
( ~ ( in @ ( ordered_pair @ SV222 @ SY3584 ) @ SV112 )
| ( in @ ( ordered_pair @ SY3584 @ SV222 ) @ SV20 ) ) )
= $true )
| ( ( SV112
= ( relation_inverse @ SV20 ) )
= $false )
| ( ( relation @ SV112 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1505]) ).
thf(1587,plain,
! [SV112: $i,SV20: $i,SV223: $i] :
( ( ( ! [SY3585: $i] :
( ~ ( in @ ( ordered_pair @ SY3585 @ SV223 ) @ SV20 )
| ( in @ ( ordered_pair @ SV223 @ SY3585 ) @ SV112 ) ) )
= $true )
| ( ( SV112
= ( relation_inverse @ SV20 ) )
= $false )
| ( ( relation @ SV112 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(1588,plain,
! [SV21: $i,SV38: $i,SV134: $i] :
( ( ( ~ ( in @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) @ SV21 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV38 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) )
= $true )
| ( ( SV134
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $true )
| ( ( relation @ SV134 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1507]) ).
thf(1589,plain,
! [SV21: $i,SV38: $i,SV134: $i] :
( ( ( ~ ( ( in @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV38 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) ) )
= $false )
| ( ( SV134
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $true )
| ( ( relation @ SV134 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1508]) ).
thf(1590,plain,
! [SV135: $i,SV38: $i,SV21: $i] :
( ( ( ! [SY3515: $i,SY3516: $i] :
( ~ ( in @ SY3516 @ SV21 )
| ~ ( in @ ( ordered_pair @ SY3515 @ SY3516 ) @ SV38 )
| ( in @ ( ordered_pair @ SY3515 @ SY3516 ) @ SV135 ) ) )
= $true )
| ( ( SV135
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1509]) ).
thf(1591,plain,
! [SV38: $i,SV21: $i,SV135: $i] :
( ( ( ~ ( ~ ! [SY3517: $i,SY3518: $i] :
( ~ ( in @ ( ordered_pair @ SY3517 @ SY3518 ) @ SV135 )
| ( in @ SY3518 @ SV21 ) )
| ~ ! [SY3519: $i,SY3520: $i] :
( ~ ( in @ ( ordered_pair @ SY3519 @ SY3520 ) @ SV135 )
| ( in @ ( ordered_pair @ SY3519 @ SY3520 ) @ SV38 ) ) ) )
= $true )
| ( ( SV135
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1510]) ).
thf(1592,plain,
! [SV198: $i,SV22: $i,SV113: $i] :
( ( ( in @ ( sK17_C @ SV113 @ SV22 ) @ SV113 )
= $false )
| ( ( in @ ( ordered_pair @ SV198 @ ( sK17_C @ SV113 @ SV22 ) ) @ SV22 )
= $false )
| ( ( SV113
= ( relation_rng @ SV22 ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1511]) ).
thf(1593,plain,
! [SV114: $i,SV22: $i,SV199: $i,SV224: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV224 @ SV199 ) @ SV22 ) )
= $true )
| ( ( in @ SV199 @ SV114 )
= $true )
| ( ( SV114
= ( relation_rng @ SV22 ) )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1512]) ).
thf(1594,plain,
! [SV22: $i,SV114: $i,SV200: $i] :
( ( ( in @ SV200 @ SV114 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK16_D @ SV200 @ SV114 @ SV22 ) @ SV200 ) @ SV22 )
= $true )
| ( ( SV114
= ( relation_rng @ SV22 ) )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1513]) ).
thf(1595,plain,
! [SV116: $i,SV23: $i,SV201: $i,SV189: $i] :
( ( ( in @ ( ordered_pair @ SV189 @ SV201 ) @ SV23 )
= $false )
| ( ( in @ ( ordered_pair @ SV189 @ SV201 ) @ SV116 )
= $true )
| ( ( subset @ SV23 @ SV116 )
= $false )
| ( ( relation @ SV116 )
= $false )
| ( ( relation @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1515]) ).
thf(1596,plain,
! [SV24: $i,SV117: $i,SV136: $i] :
( ( ( ~ ( in @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ SV117 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV24 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) )
= $true )
| ( ( SV136
= ( relation_dom_restriction @ SV24 @ SV117 ) )
= $true )
| ( ( relation @ SV136 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1516]) ).
thf(1597,plain,
! [SV24: $i,SV117: $i,SV136: $i] :
( ( ( ~ ( ( in @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ SV117 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV24 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) ) )
= $false )
| ( ( SV136
= ( relation_dom_restriction @ SV24 @ SV117 ) )
= $true )
| ( ( relation @ SV136 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1517]) ).
thf(1598,plain,
! [SV137: $i,SV24: $i,SV118: $i] :
( ( ( ! [SY3521: $i,SY3522: $i] :
( ~ ( in @ SY3521 @ SV118 )
| ~ ( in @ ( ordered_pair @ SY3521 @ SY3522 ) @ SV24 )
| ( in @ ( ordered_pair @ SY3521 @ SY3522 ) @ SV137 ) ) )
= $true )
| ( ( SV137
= ( relation_dom_restriction @ SV24 @ SV118 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1518]) ).
thf(1599,plain,
! [SV24: $i,SV118: $i,SV137: $i] :
( ( ( ~ ( ~ ! [SY3523: $i] :
( ! [SY3524: $i] :
~ ( in @ ( ordered_pair @ SY3523 @ SY3524 ) @ SV137 )
| ( in @ SY3523 @ SV118 ) )
| ~ ! [SY3525: $i,SY3526: $i] :
( ~ ( in @ ( ordered_pair @ SY3525 @ SY3526 ) @ SV137 )
| ( in @ ( ordered_pair @ SY3525 @ SY3526 ) @ SV24 ) ) ) )
= $true )
| ( ( SV137
= ( relation_dom_restriction @ SV24 @ SV118 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1519]) ).
thf(1600,plain,
! [SV190: $i,SV26: $i,SV225: $i] :
( ( ( ( SV225
!= ( apply @ SV26 @ SV190 ) )
| ( in @ ( ordered_pair @ SV190 @ SV225 ) @ SV26 ) )
= $true )
| ( ( in @ SV190 @ ( relation_dom @ SV26 ) )
= $false )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(1601,plain,
! [SV26: $i,SV226: $i,SV191: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV191 @ SV226 ) @ SV26 )
| ( SV226
= ( apply @ SV26 @ SV191 ) ) )
= $true )
| ( ( in @ SV191 @ ( relation_dom @ SV26 ) )
= $false )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1521]) ).
thf(1602,plain,
! [SV192: $i,SV26: $i,SV214: $i] :
( ( ( ( SV214
!= ( apply @ SV26 @ SV192 ) ) )
= $true )
| ( ( SV214 = empty_set )
= $true )
| ( ( in @ SV192 @ ( relation_dom @ SV26 ) )
= $true )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1522]) ).
thf(1603,plain,
! [SV193: $i,SV26: $i,SV215: $i] :
( ( ( ( SV215 != empty_set ) )
= $true )
| ( ( SV215
= ( apply @ SV26 @ SV193 ) )
= $true )
| ( ( in @ SV193 @ ( relation_dom @ SV26 ) )
= $true )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1523]) ).
thf(1604,plain,
! [SV53: $i] :
( ( ( ~ ( ( ( sK62_B @ SV53 )
!= ( sK63_SY3125 @ SV53 ) ) ) )
= $false )
| ( ( connected @ SV53 )
= $true )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1524]) ).
thf(1605,plain,
! [SV53: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK62_B @ SV53 ) @ ( relation_field @ SV53 ) )
| ~ ( in @ ( sK63_SY3125 @ SV53 ) @ ( relation_field @ SV53 ) ) ) )
= $false )
| ( ( connected @ SV53 )
= $true )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1524]) ).
thf(1606,plain,
! [SV169: $i,SV54: $i,SV151: $i] :
( ( ( in @ SV151 @ ( relation_field @ SV54 ) )
= $false )
| ( ( ~ ( in @ SV169 @ ( relation_field @ SV54 ) ) )
= $true )
| ( ( SV151 = SV169 )
= $true )
| ( ( in @ ( ordered_pair @ SV151 @ SV169 ) @ SV54 )
= $true )
| ( ( in @ ( ordered_pair @ SV169 @ SV151 ) @ SV54 )
= $true )
| ( ( connected @ SV54 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1526]) ).
thf(1607,plain,
! [SV27: $i,SV120: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK19_C @ SV120 @ SV27 ) @ SV120 )
| ~ ( in @ ( sK20_SY3099 @ SV120 @ SV27 ) @ SV120 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SV120 @ SV27 ) @ ( sK20_SY3099 @ SV120 @ SV27 ) ) @ SV27 ) )
= $false )
| ( ( is_antisymmetric_in @ SV27 @ SV120 )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1527]) ).
thf(1608,plain,
! [SV27: $i,SV178: $i,SV121: $i,SV170: $i] :
( ( ( ~ ( in @ SV170 @ SV121 ) )
= $true )
| ( ( ~ ( in @ SV178 @ SV121 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV170 @ SV178 ) @ SV27 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV178 @ SV170 ) @ SV27 ) )
= $true )
| ( ( SV170 = SV178 )
= $true )
| ( ( is_antisymmetric_in @ SV27 @ SV121 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1529]) ).
thf(1609,plain,
! [SV154: $i,SV56: $i,SV180: $i,SV172: $i] :
( ( ( in @ ( ordered_pair @ SV172 @ SV180 ) @ SV56 )
= $false )
| ( ( in @ ( ordered_pair @ SV154 @ SV172 ) @ SV56 )
= $false )
| ( ( in @ ( ordered_pair @ SV154 @ SV180 ) @ SV56 )
= $true )
| ( ( transitive @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1530]) ).
thf(1610,plain,
! [SV216: $i,SV30: $i,SV124: $i,SV139: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SV216 ) @ SV30 ) )
= $true )
| ( ( ~ ( in @ SV216 @ SV124 ) )
= $true )
| ( ( ~ ( in @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SV139 ) )
= $true )
| ( ( SV139
= ( relation_inverse_image @ SV30 @ SV124 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1531]) ).
thf(1611,plain,
! [SV30: $i,SV124: $i,SV139: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ ( sK44_SY3116 @ SV139 @ SV124 @ SV30 ) ) @ SV30 ) )
= $false )
| ( ( in @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SV139 )
= $true )
| ( ( SV139
= ( relation_inverse_image @ SV30 @ SV124 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1532]) ).
thf(1612,plain,
! [SV30: $i,SV124: $i,SV139: $i] :
( ( ( ~ ( in @ ( sK44_SY3116 @ SV139 @ SV124 @ SV30 ) @ SV124 ) )
= $false )
| ( ( in @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SV139 )
= $true )
| ( ( SV139
= ( relation_inverse_image @ SV30 @ SV124 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1532]) ).
thf(1613,plain,
! [SV140: $i,SV125: $i,SV30: $i,SV217: $i] :
( ( ( ! [SY3581: $i] :
( ~ ( in @ ( ordered_pair @ SV217 @ SY3581 ) @ SV30 )
| ~ ( in @ SY3581 @ SV125 ) ) )
= $true )
| ( ( in @ SV217 @ SV140 )
= $true )
| ( ( SV140
= ( relation_inverse_image @ SV30 @ SV125 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1533]) ).
thf(1614,plain,
! [SV30: $i,SV125: $i,SV140: $i,SV218: $i] :
( ( ( ~ ( in @ SV218 @ SV140 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV218 @ ( sK42_E @ SV218 @ SV140 @ SV125 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK42_E @ SV218 @ SV140 @ SV125 @ SV30 ) @ SV125 ) ) )
= $true )
| ( ( SV140
= ( relation_inverse_image @ SV30 @ SV125 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1534]) ).
thf(1615,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) ) ) )
| ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1535]) ).
thf(1616,plain,
! [SV59: $i,SV32: $i,SV202: $i] :
( ( ( ~ ( function @ SV202 ) )
= $true )
| ( ( ~ ( relation @ SV202 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
| ~ ( ~ ! [SY3570: $i,SY3571: $i] :
( ~ ( in @ SY3570 @ ( relation_field @ SV32 ) )
| ~ ( in @ SY3571 @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV202 @ SY3570 ) @ ( apply @ SV202 @ SY3571 ) ) @ SV59 )
| ( in @ ( ordered_pair @ SY3570 @ SY3571 ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3312: $i] :
( ! [SY3313: $i] :
~ ( in @ ( ordered_pair @ SY3312 @ SY3313 ) @ SV32 )
| ( in @ SY3312 @ ( relation_field @ SV32 ) ) )
| ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV32 )
| ( in @ SY3315 @ ( relation_field @ SV32 ) ) ) )
| ~ ! [SY3576: $i,SY3577: $i] :
( ~ ( in @ ( ordered_pair @ SY3576 @ SY3577 ) @ SV32 )
| ( in @ ( ordered_pair @ ( apply @ SV202 @ SY3576 ) @ ( apply @ SV202 @ SY3577 ) ) @ SV59 ) ) ) ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1536]) ).
thf(1617,plain,
! [SV59: $i,SV32: $i] :
( ( ( ~ ( ~ ! [SY3402: $i] :
( ~ ( function @ SY3402 )
| ~ ( relation @ SY3402 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3402 )
| ( ( relation_dom @ SY3402 )
= ( relation_field @ SV32 ) ) )
| ~ ! [SY3403: $i] :
( ~ ( function @ SY3403 )
| ~ ( relation @ SY3403 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3403 )
| ( ( relation_rng @ SY3403 )
= ( relation_field @ SV59 ) ) ) ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1537]) ).
thf(1618,plain,
! [SV59: $i,SV32: $i] :
( ( ( ! [SY3404: $i] :
( ~ ( function @ SY3404 )
| ~ ( relation @ SY3404 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3404 )
| ( one_to_one @ SY3404 ) ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1538]) ).
thf(1619,plain,
! [SV204: $i,SV34: $i,SV126: $i] :
( ( ( in @ ( sK22_C @ SV126 @ SV34 ) @ SV126 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK22_C @ SV126 @ SV34 ) @ SV204 ) @ SV34 )
= $false )
| ( ( SV126
= ( relation_dom @ SV34 ) )
= $true )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1540]) ).
thf(1620,plain,
! [SV127: $i,SV34: $i,SV227: $i,SV205: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV205 @ SV227 ) @ SV34 ) )
= $true )
| ( ( in @ SV205 @ SV127 )
= $true )
| ( ( SV127
= ( relation_dom @ SV34 ) )
= $false )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1541]) ).
thf(1621,plain,
! [SV34: $i,SV127: $i,SV206: $i] :
( ( ( in @ SV206 @ SV127 )
= $false )
| ( ( in @ ( ordered_pair @ SV206 @ ( sK21_D @ SV206 @ SV127 @ SV34 ) ) @ SV34 )
= $true )
| ( ( SV127
= ( relation_dom @ SV34 ) )
= $false )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1542]) ).
thf(1622,plain,
! [SV4: $i,SV98: $i] :
( ( ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV98 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK31_C @ SV98 @ SV4 ) @ ( sK32_SY3109 @ SV98 @ SV4 ) ) @ SV4 )
= $false )
| ( ( SV4 = SV98 )
= $true )
| ( ( relation @ SV98 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1543]) ).
thf(1623,plain,
! [SV99: $i,SV4: $i,SV228: $i,SV219: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV219 @ SV228 ) @ SV4 )
| ( in @ ( ordered_pair @ SV219 @ SV228 ) @ SV99 ) )
= $true )
| ( ( SV4 = SV99 )
= $false )
| ( ( relation @ SV99 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1544]) ).
thf(1624,plain,
! [SV4: $i,SV99: $i,SV229: $i,SV220: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV220 @ SV229 ) @ SV99 )
| ( in @ ( ordered_pair @ SV220 @ SV229 ) @ SV4 ) )
= $true )
| ( ( SV4 = SV99 )
= $false )
| ( ( relation @ SV99 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(1625,plain,
! [SV5: $i,SV100: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SV100 @ SV5 ) @ SV100 )
| ~ ( in @ ( sK4_SY3086 @ SV100 @ SV5 ) @ SV100 ) )
| ~ ( in @ ( sK5_SY3088 @ SV100 @ SV5 ) @ SV100 ) ) )
= $false )
| ( ( is_transitive_in @ SV5 @ SV100 )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1546]) ).
thf(1626,plain,
! [SV5: $i,SV100: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK3_C @ SV100 @ SV5 ) @ ( sK4_SY3086 @ SV100 @ SV5 ) ) @ SV5 ) )
= $false )
| ( ( is_transitive_in @ SV5 @ SV100 )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1546]) ).
thf(1627,plain,
! [SV5: $i,SV183: $i,SV175: $i,SV101: $i,SV159: $i] :
( ( ( ~ ( in @ SV159 @ SV101 )
| ~ ( in @ SV175 @ SV101 ) )
= $true )
| ( ( ~ ( in @ SV183 @ SV101 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV159 @ SV175 ) @ SV5 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV175 @ SV183 ) @ SV5 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV159 @ SV183 ) @ SV5 )
= $true )
| ( ( is_transitive_in @ SV5 @ SV101 )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1547]) ).
thf(1628,plain,
! [SV7: $i,SV46: $i,SV160: $i] :
( ( ( ! [SY3548: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ SY3548 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3548 @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV46 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV160 ) )
= $true )
| ( ( SV160
= ( relation_composition @ SV7 @ SV46 ) )
= $true )
| ( ( relation @ SV160 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1548]) ).
thf(1629,plain,
! [SV7: $i,SV46: $i,SV160: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK9_SY3093 @ SV160 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV46 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV160 ) )
= $true )
| ( ( SV160
= ( relation_composition @ SV7 @ SV46 ) )
= $true )
| ( ( relation @ SV160 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1549]) ).
thf(1630,plain,
! [SV161: $i,SV46: $i,SV7: $i] :
( ( ( ~ ! [SY3549: $i,SY3550: $i] :
( ! [SY3373: $i] :
( ~ ( in @ ( ordered_pair @ SY3549 @ SY3373 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3373 @ SY3550 ) @ SV46 ) )
| ( in @ ( ordered_pair @ SY3549 @ SY3550 ) @ SV161 ) ) )
= $false )
| ( ( SV161
= ( relation_composition @ SV7 @ SV46 ) )
= $false )
| ( ( relation @ SV161 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1550]) ).
thf(1631,plain,
! [SV7: $i,SV46: $i,SV161: $i] :
( ( ( ~ ! [SY3552: $i,SY3553: $i] :
( ~ ( in @ ( ordered_pair @ SY3552 @ SY3553 ) @ SV161 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3552 @ ( sK6_F @ SY3553 @ SY3552 @ SV161 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY3553 @ SY3552 @ SV161 @ SV46 @ SV7 ) @ SY3553 ) @ SV46 ) ) ) )
= $false )
| ( ( SV161
= ( relation_composition @ SV7 @ SV46 ) )
= $false )
| ( ( relation @ SV161 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1550]) ).
thf(1632,plain,
! [SV47: $i,SV62: $i] :
( ( ( in @ ( ordered_pair @ ( sK52_C @ SV62 @ SV47 ) @ ( sK53_SY3121 @ SV62 @ SV47 ) ) @ SV62 )
= $false )
| ( ( ( sK52_C @ SV62 @ SV47 )
= ( sK53_SY3121 @ SV62 @ SV47 ) )
= $false )
| ( ( in @ ( sK52_C @ SV62 @ SV47 ) @ SV47 )
= $false )
| ( ( SV62
= ( identity_relation @ SV47 ) )
= $true )
| ( ( relation @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1551]) ).
thf(1633,plain,
! [SV63: $i,SV48: $i,SV207: $i,SV195: $i] :
( ( ( ( SV195 != SV207 ) )
= $true )
| ( ( ~ ( in @ SV195 @ SV48 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV195 @ SV207 ) @ SV63 )
= $true )
| ( ( SV63
= ( identity_relation @ SV48 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1554]) ).
thf(1634,plain,
! [SV48: $i,SV63: $i,SV230: $i] :
( ( ( ! [SY3586: $i] :
( ~ ( in @ ( ordered_pair @ SV230 @ SY3586 ) @ SV63 )
| ( SV230 = SY3586 ) ) )
= $true )
| ( ( SV63
= ( identity_relation @ SV48 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1555]) ).
thf(1635,plain,
! [SV48: $i,SV63: $i,SV231: $i] :
( ( ( ! [SY3587: $i] :
~ ( in @ ( ordered_pair @ SV231 @ SY3587 ) @ SV63 )
| ( in @ SV231 @ SV48 ) )
= $true )
| ( ( SV63
= ( identity_relation @ SV48 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1556]) ).
thf(1636,plain,
! [SV10: $i,SV65: $i,SV81: $i] :
( ( ( in @ ( sK60_D @ SV81 @ SV65 @ SV10 ) @ ( relation_rng @ SV81 ) )
= $true )
| ( ( in @ SV10 @ ( relation_inverse_image @ SV81 @ SV65 ) )
= $false )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1559]) ).
thf(1637,plain,
! [SV65: $i,SV81: $i,SV10: $i] :
( ( ( in @ ( ordered_pair @ SV10 @ ( sK60_D @ SV81 @ SV65 @ SV10 ) ) @ SV81 )
= $true )
| ( ( in @ SV10 @ ( relation_inverse_image @ SV81 @ SV65 ) )
= $false )
| ( ( relation @ SV81 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1560]) ).
thf(1638,plain,
! [SV82: $i,SV66: $i,SV196: $i,SV11: $i,SV185: $i] :
( ( ( in @ SV185 @ SV11 )
= $false )
| ( ( ~ ( in @ SV196 @ SV66 ) )
= $true )
| ( ( ( ( sK28_D @ SV82 @ SV66 @ SV11 )
!= ( ordered_pair @ SV185 @ SV196 ) ) )
= $true )
| ( ( ~ ( in @ ( sK28_D @ SV82 @ SV66 @ SV11 ) @ SV82 ) )
= $true )
| ( ( SV82
= ( cartesian_product2 @ SV11 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1561]) ).
thf(1639,plain,
! [SV11: $i,SV66: $i,SV82: $i] :
( ( ( ~ ( in @ ( sK29_SY3106 @ SV82 @ SV66 @ SV11 ) @ SV11 ) )
= $false )
| ( ( in @ ( sK28_D @ SV82 @ SV66 @ SV11 ) @ SV82 )
= $true )
| ( ( SV82
= ( cartesian_product2 @ SV11 @ SV66 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1562]) ).
thf(1640,plain,
! [SV11: $i,SV66: $i,SV82: $i] :
( ( ( ~ ( in @ ( sK30_SY3108 @ SV82 @ SV66 @ SV11 ) @ SV66 ) )
= $false )
| ( ( in @ ( sK28_D @ SV82 @ SV66 @ SV11 ) @ SV82 )
= $true )
| ( ( SV82
= ( cartesian_product2 @ SV11 @ SV66 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1562]) ).
thf(1641,plain,
! [SV83: $i,SV186: $i,SV67: $i,SV221: $i,SV11: $i,SV209: $i] :
( ( ( ~ ( in @ SV209 @ SV11 )
| ~ ( in @ SV221 @ SV67 ) )
= $true )
| ( ( ( SV186
!= ( ordered_pair @ SV209 @ SV221 ) ) )
= $true )
| ( ( in @ SV186 @ SV83 )
= $true )
| ( ( SV83
= ( cartesian_product2 @ SV11 @ SV67 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1563]) ).
thf(1642,plain,
! [SV11: $i,SV67: $i,SV83: $i,SV187: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK26_E @ SV187 @ SV83 @ SV67 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK27_SY3103 @ SV187 @ SV83 @ SV67 @ SV11 ) @ SV67 ) ) )
= $false )
| ( ( in @ SV187 @ SV83 )
= $false )
| ( ( SV83
= ( cartesian_product2 @ SV11 @ SV67 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1564]) ).
thf(1643,plain,
! [SV11: $i,SV67: $i,SV83: $i,SV187: $i] :
( ( ( ( SV187
!= ( ordered_pair @ ( sK26_E @ SV187 @ SV83 @ SV67 @ SV11 ) @ ( sK27_SY3103 @ SV187 @ SV83 @ SV67 @ SV11 ) ) ) )
= $false )
| ( ( in @ SV187 @ SV83 )
= $false )
| ( ( SV83
= ( cartesian_product2 @ SV11 @ SV67 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1564]) ).
thf(1644,plain,
! [SV14: $i,SV103: $i] :
( ( ( ~ ( ( ( sK14_C @ SV103 @ SV14 )
!= ( sK15_SY3096 @ SV103 @ SV14 ) ) ) )
= $false )
| ( ( is_connected_in @ SV14 @ SV103 )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1566]) ).
thf(1645,plain,
! [SV14: $i,SV103: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK14_C @ SV103 @ SV14 ) @ SV103 )
| ~ ( in @ ( sK15_SY3096 @ SV103 @ SV14 ) @ SV103 ) ) )
= $false )
| ( ( is_connected_in @ SV14 @ SV103 )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1566]) ).
thf(1646,plain,
! [SV14: $i,SV177: $i,SV104: $i,SV165: $i] :
( ( ( in @ SV165 @ SV104 )
= $false )
| ( ( ~ ( in @ SV177 @ SV104 ) )
= $true )
| ( ( SV165 = SV177 )
= $true )
| ( ( in @ ( ordered_pair @ SV165 @ SV177 ) @ SV14 )
= $true )
| ( ( in @ ( ordered_pair @ SV177 @ SV165 ) @ SV14 )
= $true )
| ( ( is_connected_in @ SV14 @ SV104 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1568]) ).
thf(1647,plain,
! [SV15: $i,SV71: $i,SV87: $i] :
( ( ( in @ ( sK61_D @ SV87 @ SV71 @ SV15 ) @ ( relation_dom @ SV87 ) )
= $true )
| ( ( in @ SV15 @ ( relation_image @ SV87 @ SV71 ) )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1570]) ).
thf(1648,plain,
! [SV15: $i,SV71: $i,SV87: $i] :
( ( ( in @ ( ordered_pair @ ( sK61_D @ SV87 @ SV71 @ SV15 ) @ SV15 ) @ SV87 )
= $true )
| ( ( in @ SV15 @ ( relation_image @ SV87 @ SV71 ) )
= $false )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1571]) ).
thf(1649,plain,
! [SV16: $i,SV105: $i,SV128: $i,SV210: $i] :
( ( ( in @ ( ordered_pair @ SV210 @ ( sK46_D @ SV128 @ SV105 @ SV16 ) ) @ SV16 )
= $false )
| ( ( ~ ( in @ SV210 @ SV105 ) )
= $true )
| ( ( ~ ( in @ ( sK46_D @ SV128 @ SV105 @ SV16 ) @ SV128 ) )
= $true )
| ( ( SV128
= ( relation_image @ SV16 @ SV105 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1572]) ).
thf(1650,plain,
! [SV16: $i,SV105: $i,SV128: $i] :
( ( ( in @ ( ordered_pair @ ( sK47_SY3118 @ SV128 @ SV105 @ SV16 ) @ ( sK46_D @ SV128 @ SV105 @ SV16 ) ) @ SV16 )
= $true )
| ( ( in @ ( sK46_D @ SV128 @ SV105 @ SV16 ) @ SV128 )
= $true )
| ( ( SV128
= ( relation_image @ SV16 @ SV105 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1573]) ).
thf(1651,plain,
! [SV16: $i,SV105: $i,SV128: $i] :
( ( ( in @ ( sK47_SY3118 @ SV128 @ SV105 @ SV16 ) @ SV105 )
= $true )
| ( ( in @ ( sK46_D @ SV128 @ SV105 @ SV16 ) @ SV128 )
= $true )
| ( ( SV128
= ( relation_image @ SV16 @ SV105 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1574]) ).
thf(1652,plain,
! [SV129: $i,SV106: $i,SV16: $i,SV211: $i,SV232: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV232 @ SV211 ) @ SV16 )
| ~ ( in @ SV232 @ SV106 ) )
= $true )
| ( ( in @ SV211 @ SV129 )
= $true )
| ( ( SV129
= ( relation_image @ SV16 @ SV106 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1575]) ).
thf(1653,plain,
! [SV16: $i,SV106: $i,SV129: $i,SV212: $i] :
( ( ( in @ SV212 @ SV129 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SV212 @ SV129 @ SV106 @ SV16 ) @ SV212 ) @ SV16 )
| ~ ( in @ ( sK45_E @ SV212 @ SV129 @ SV106 @ SV16 ) @ SV106 ) ) )
= $true )
| ( ( SV129
= ( relation_image @ SV16 @ SV106 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1576]) ).
thf(1654,plain,
! [SV18: $i,SV107: $i,SV132: $i] :
( ( ( in @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV132 )
= $false )
| ( ( ( sK35_D @ SV132 @ SV107 @ SV18 )
= SV107 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV107 ) @ SV18 )
= $false )
| ( ( SV132
= ( fiber @ SV18 @ SV107 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1579]) ).
thf(1655,plain,
! [SV18: $i,SV107: $i,SV132: $i] :
( ( ( ( ( sK35_D @ SV132 @ SV107 @ SV18 )
!= SV107 ) )
= $true )
| ( ( in @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV132 )
= $true )
| ( ( SV132
= ( fiber @ SV18 @ SV107 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1580]) ).
thf(1656,plain,
! [SV18: $i,SV107: $i,SV132: $i] :
( ( ( in @ ( ordered_pair @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV107 ) @ SV18 )
= $true )
| ( ( in @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV132 )
= $true )
| ( ( SV132
= ( fiber @ SV18 @ SV107 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1581]) ).
thf(1657,plain,
! [SV133: $i,SV18: $i,SV108: $i,SV213: $i] :
( ( ( SV213 = SV108 )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV213 @ SV108 ) @ SV18 ) )
= $true )
| ( ( in @ SV213 @ SV133 )
= $true )
| ( ( SV133
= ( fiber @ SV18 @ SV108 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1582]) ).
thf(1658,plain,
! [SV18: $i,SV108: $i,SV133: $i] :
( ( ( ! [SY3513: $i] :
( ~ ( in @ SY3513 @ SV133 )
| ( SY3513 != SV108 ) ) )
= $true )
| ( ( SV133
= ( fiber @ SV18 @ SV108 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1583]) ).
thf(1659,plain,
! [SV18: $i,SV108: $i,SV133: $i] :
( ( ( ! [SY3514: $i] :
( ~ ( in @ SY3514 @ SV133 )
| ( in @ ( ordered_pair @ SY3514 @ SV108 ) @ SV18 ) ) )
= $true )
| ( ( SV133
= ( fiber @ SV18 @ SV108 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1584]) ).
thf(1660,plain,
! [SV20: $i,SV111: $i] :
( ( ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV111 @ SV20 ) @ ( sK12_C @ SV111 @ SV20 ) ) @ SV20 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK12_C @ SV111 @ SV20 ) @ ( sK13_SY3095 @ SV111 @ SV20 ) ) @ SV111 )
= $false )
| ( ( SV111
= ( relation_inverse @ SV20 ) )
= $true )
| ( ( relation @ SV111 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1585]) ).
thf(1661,plain,
! [SV20: $i,SV112: $i,SV233: $i,SV222: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV222 @ SV233 ) @ SV112 )
| ( in @ ( ordered_pair @ SV233 @ SV222 ) @ SV20 ) )
= $true )
| ( ( SV112
= ( relation_inverse @ SV20 ) )
= $false )
| ( ( relation @ SV112 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(1662,plain,
! [SV112: $i,SV20: $i,SV223: $i,SV234: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV234 @ SV223 ) @ SV20 )
| ( in @ ( ordered_pair @ SV223 @ SV234 ) @ SV112 ) )
= $true )
| ( ( SV112
= ( relation_inverse @ SV20 ) )
= $false )
| ( ( relation @ SV112 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1587]) ).
thf(1663,plain,
! [SV21: $i,SV38: $i,SV134: $i] :
( ( ( ~ ( in @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) @ SV21 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV38 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) )
= $true )
| ( ( SV134
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $true )
| ( ( relation @ SV134 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1588]) ).
thf(1664,plain,
! [SV21: $i,SV38: $i,SV134: $i] :
( ( ( ~ ( ( in @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) ) )
= $false )
| ( ( SV134
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $true )
| ( ( relation @ SV134 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1589]) ).
thf(1665,plain,
! [SV21: $i,SV38: $i,SV134: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV38 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) ) )
= $false )
| ( ( SV134
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $true )
| ( ( relation @ SV134 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1589]) ).
thf(1666,plain,
! [SV135: $i,SV38: $i,SV235: $i,SV21: $i] :
( ( ( ! [SY3588: $i] :
( ~ ( in @ SY3588 @ SV21 )
| ~ ( in @ ( ordered_pair @ SV235 @ SY3588 ) @ SV38 )
| ( in @ ( ordered_pair @ SV235 @ SY3588 ) @ SV135 ) ) )
= $true )
| ( ( SV135
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(1667,plain,
! [SV38: $i,SV21: $i,SV135: $i] :
( ( ( ~ ! [SY3517: $i,SY3518: $i] :
( ~ ( in @ ( ordered_pair @ SY3517 @ SY3518 ) @ SV135 )
| ( in @ SY3518 @ SV21 ) )
| ~ ! [SY3519: $i,SY3520: $i] :
( ~ ( in @ ( ordered_pair @ SY3519 @ SY3520 ) @ SV135 )
| ( in @ ( ordered_pair @ SY3519 @ SY3520 ) @ SV38 ) ) )
= $false )
| ( ( SV135
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1591]) ).
thf(1668,plain,
! [SV114: $i,SV22: $i,SV199: $i,SV224: $i] :
( ( ( in @ ( ordered_pair @ SV224 @ SV199 ) @ SV22 )
= $false )
| ( ( in @ SV199 @ SV114 )
= $true )
| ( ( SV114
= ( relation_rng @ SV22 ) )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1593]) ).
thf(1669,plain,
! [SV24: $i,SV117: $i,SV136: $i] :
( ( ( ~ ( in @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ SV117 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV24 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) )
= $true )
| ( ( SV136
= ( relation_dom_restriction @ SV24 @ SV117 ) )
= $true )
| ( ( relation @ SV136 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1596]) ).
thf(1670,plain,
! [SV24: $i,SV117: $i,SV136: $i] :
( ( ( ~ ( ( in @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ SV117 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) ) )
= $false )
| ( ( SV136
= ( relation_dom_restriction @ SV24 @ SV117 ) )
= $true )
| ( ( relation @ SV136 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1597]) ).
thf(1671,plain,
! [SV24: $i,SV117: $i,SV136: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV24 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) ) )
= $false )
| ( ( SV136
= ( relation_dom_restriction @ SV24 @ SV117 ) )
= $true )
| ( ( relation @ SV136 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1597]) ).
thf(1672,plain,
! [SV137: $i,SV24: $i,SV118: $i,SV236: $i] :
( ( ( ! [SY3589: $i] :
( ~ ( in @ SV236 @ SV118 )
| ~ ( in @ ( ordered_pair @ SV236 @ SY3589 ) @ SV24 )
| ( in @ ( ordered_pair @ SV236 @ SY3589 ) @ SV137 ) ) )
= $true )
| ( ( SV137
= ( relation_dom_restriction @ SV24 @ SV118 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1598]) ).
thf(1673,plain,
! [SV24: $i,SV118: $i,SV137: $i] :
( ( ( ~ ! [SY3523: $i] :
( ! [SY3524: $i] :
~ ( in @ ( ordered_pair @ SY3523 @ SY3524 ) @ SV137 )
| ( in @ SY3523 @ SV118 ) )
| ~ ! [SY3525: $i,SY3526: $i] :
( ~ ( in @ ( ordered_pair @ SY3525 @ SY3526 ) @ SV137 )
| ( in @ ( ordered_pair @ SY3525 @ SY3526 ) @ SV24 ) ) )
= $false )
| ( ( SV137
= ( relation_dom_restriction @ SV24 @ SV118 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1599]) ).
thf(1674,plain,
! [SV190: $i,SV26: $i,SV225: $i] :
( ( ( ( SV225
!= ( apply @ SV26 @ SV190 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV190 @ SV225 ) @ SV26 )
= $true )
| ( ( in @ SV190 @ ( relation_dom @ SV26 ) )
= $false )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1600]) ).
thf(1675,plain,
! [SV26: $i,SV226: $i,SV191: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV191 @ SV226 ) @ SV26 ) )
= $true )
| ( ( SV226
= ( apply @ SV26 @ SV191 ) )
= $true )
| ( ( in @ SV191 @ ( relation_dom @ SV26 ) )
= $false )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1601]) ).
thf(1676,plain,
! [SV192: $i,SV26: $i,SV214: $i] :
( ( ( SV214
= ( apply @ SV26 @ SV192 ) )
= $false )
| ( ( SV214 = empty_set )
= $true )
| ( ( in @ SV192 @ ( relation_dom @ SV26 ) )
= $true )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1602]) ).
thf(1677,plain,
! [SV193: $i,SV26: $i,SV215: $i] :
( ( ( SV215 = empty_set )
= $false )
| ( ( SV215
= ( apply @ SV26 @ SV193 ) )
= $true )
| ( ( in @ SV193 @ ( relation_dom @ SV26 ) )
= $true )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1603]) ).
thf(1678,plain,
! [SV53: $i] :
( ( ( ( ( sK62_B @ SV53 )
!= ( sK63_SY3125 @ SV53 ) ) )
= $true )
| ( ( connected @ SV53 )
= $true )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1604]) ).
thf(1679,plain,
! [SV53: $i] :
( ( ( ~ ( ~ ( in @ ( sK62_B @ SV53 ) @ ( relation_field @ SV53 ) )
| ~ ( in @ ( sK63_SY3125 @ SV53 ) @ ( relation_field @ SV53 ) ) ) )
= $true )
| ( ( connected @ SV53 )
= $true )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1605]) ).
thf(1680,plain,
! [SV151: $i,SV54: $i,SV169: $i] :
( ( ( in @ SV169 @ ( relation_field @ SV54 ) )
= $false )
| ( ( in @ SV151 @ ( relation_field @ SV54 ) )
= $false )
| ( ( SV151 = SV169 )
= $true )
| ( ( in @ ( ordered_pair @ SV151 @ SV169 ) @ SV54 )
= $true )
| ( ( in @ ( ordered_pair @ SV169 @ SV151 ) @ SV54 )
= $true )
| ( ( connected @ SV54 )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1606]) ).
thf(1681,plain,
! [SV27: $i,SV120: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK19_C @ SV120 @ SV27 ) @ SV120 )
| ~ ( in @ ( sK20_SY3099 @ SV120 @ SV27 ) @ SV120 ) ) )
= $false )
| ( ( is_antisymmetric_in @ SV27 @ SV120 )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1607]) ).
thf(1682,plain,
! [SV27: $i,SV120: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV120 @ SV27 ) @ ( sK20_SY3099 @ SV120 @ SV27 ) ) @ SV27 ) )
= $false )
| ( ( is_antisymmetric_in @ SV27 @ SV120 )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1607]) ).
thf(1683,plain,
! [SV27: $i,SV178: $i,SV121: $i,SV170: $i] :
( ( ( in @ SV170 @ SV121 )
= $false )
| ( ( ~ ( in @ SV178 @ SV121 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV170 @ SV178 ) @ SV27 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV178 @ SV170 ) @ SV27 ) )
= $true )
| ( ( SV170 = SV178 )
= $true )
| ( ( is_antisymmetric_in @ SV27 @ SV121 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1608]) ).
thf(1684,plain,
! [SV216: $i,SV30: $i,SV124: $i,SV139: $i] :
( ( ( in @ ( ordered_pair @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SV216 ) @ SV30 )
= $false )
| ( ( ~ ( in @ SV216 @ SV124 ) )
= $true )
| ( ( ~ ( in @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SV139 ) )
= $true )
| ( ( SV139
= ( relation_inverse_image @ SV30 @ SV124 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1610]) ).
thf(1685,plain,
! [SV30: $i,SV124: $i,SV139: $i] :
( ( ( in @ ( ordered_pair @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ ( sK44_SY3116 @ SV139 @ SV124 @ SV30 ) ) @ SV30 )
= $true )
| ( ( in @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SV139 )
= $true )
| ( ( SV139
= ( relation_inverse_image @ SV30 @ SV124 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1611]) ).
thf(1686,plain,
! [SV30: $i,SV124: $i,SV139: $i] :
( ( ( in @ ( sK44_SY3116 @ SV139 @ SV124 @ SV30 ) @ SV124 )
= $true )
| ( ( in @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SV139 )
= $true )
| ( ( SV139
= ( relation_inverse_image @ SV30 @ SV124 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1612]) ).
thf(1687,plain,
! [SV140: $i,SV125: $i,SV30: $i,SV237: $i,SV217: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV217 @ SV237 ) @ SV30 )
| ~ ( in @ SV237 @ SV125 ) )
= $true )
| ( ( in @ SV217 @ SV140 )
= $true )
| ( ( SV140
= ( relation_inverse_image @ SV30 @ SV125 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(1688,plain,
! [SV30: $i,SV125: $i,SV140: $i,SV218: $i] :
( ( ( in @ SV218 @ SV140 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV218 @ ( sK42_E @ SV218 @ SV140 @ SV125 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK42_E @ SV218 @ SV140 @ SV125 @ SV30 ) @ SV125 ) ) )
= $true )
| ( ( SV140
= ( relation_inverse_image @ SV30 @ SV125 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1614]) ).
thf(1689,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1615]) ).
thf(1690,plain,
! [SV59: $i,SV32: $i,SV202: $i] :
( ( ( function @ SV202 )
= $false )
| ( ( ~ ( relation @ SV202 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
| ~ ( ~ ! [SY3570: $i,SY3571: $i] :
( ~ ( in @ SY3570 @ ( relation_field @ SV32 ) )
| ~ ( in @ SY3571 @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV202 @ SY3570 ) @ ( apply @ SV202 @ SY3571 ) ) @ SV59 )
| ( in @ ( ordered_pair @ SY3570 @ SY3571 ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3312: $i] :
( ! [SY3313: $i] :
~ ( in @ ( ordered_pair @ SY3312 @ SY3313 ) @ SV32 )
| ( in @ SY3312 @ ( relation_field @ SV32 ) ) )
| ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV32 )
| ( in @ SY3315 @ ( relation_field @ SV32 ) ) ) )
| ~ ! [SY3576: $i,SY3577: $i] :
( ~ ( in @ ( ordered_pair @ SY3576 @ SY3577 ) @ SV32 )
| ( in @ ( ordered_pair @ ( apply @ SV202 @ SY3576 ) @ ( apply @ SV202 @ SY3577 ) ) @ SV59 ) ) ) ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1616]) ).
thf(1691,plain,
! [SV59: $i,SV32: $i] :
( ( ( ~ ! [SY3402: $i] :
( ~ ( function @ SY3402 )
| ~ ( relation @ SY3402 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3402 )
| ( ( relation_dom @ SY3402 )
= ( relation_field @ SV32 ) ) )
| ~ ! [SY3403: $i] :
( ~ ( function @ SY3403 )
| ~ ( relation @ SY3403 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3403 )
| ( ( relation_rng @ SY3403 )
= ( relation_field @ SV59 ) ) ) )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1617]) ).
thf(1692,plain,
! [SV59: $i,SV32: $i,SV238: $i] :
( ( ( ~ ( function @ SV238 )
| ~ ( relation @ SV238 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SV238 )
| ( one_to_one @ SV238 ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1618]) ).
thf(1693,plain,
! [SV127: $i,SV34: $i,SV227: $i,SV205: $i] :
( ( ( in @ ( ordered_pair @ SV205 @ SV227 ) @ SV34 )
= $false )
| ( ( in @ SV205 @ SV127 )
= $true )
| ( ( SV127
= ( relation_dom @ SV34 ) )
= $false )
| ( ( relation @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1620]) ).
thf(1694,plain,
! [SV99: $i,SV4: $i,SV228: $i,SV219: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV219 @ SV228 ) @ SV4 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV219 @ SV228 ) @ SV99 )
= $true )
| ( ( SV4 = SV99 )
= $false )
| ( ( relation @ SV99 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1623]) ).
thf(1695,plain,
! [SV4: $i,SV99: $i,SV229: $i,SV220: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV220 @ SV229 ) @ SV99 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV220 @ SV229 ) @ SV4 )
= $true )
| ( ( SV4 = SV99 )
= $false )
| ( ( relation @ SV99 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1624]) ).
thf(1696,plain,
! [SV5: $i,SV100: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SV100 @ SV5 ) @ SV100 )
| ~ ( in @ ( sK4_SY3086 @ SV100 @ SV5 ) @ SV100 ) )
| ~ ( in @ ( sK5_SY3088 @ SV100 @ SV5 ) @ SV100 ) ) )
= $true )
| ( ( is_transitive_in @ SV5 @ SV100 )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1625]) ).
thf(1697,plain,
! [SV5: $i,SV100: $i] :
( ( ( in @ ( ordered_pair @ ( sK3_C @ SV100 @ SV5 ) @ ( sK4_SY3086 @ SV100 @ SV5 ) ) @ SV5 )
= $true )
| ( ( is_transitive_in @ SV5 @ SV100 )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1626]) ).
thf(1698,plain,
! [SV5: $i,SV183: $i,SV175: $i,SV101: $i,SV159: $i] :
( ( ( ~ ( in @ SV159 @ SV101 ) )
= $true )
| ( ( ~ ( in @ SV175 @ SV101 ) )
= $true )
| ( ( ~ ( in @ SV183 @ SV101 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV159 @ SV175 ) @ SV5 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV175 @ SV183 ) @ SV5 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV159 @ SV183 ) @ SV5 )
= $true )
| ( ( is_transitive_in @ SV5 @ SV101 )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1627]) ).
thf(1699,plain,
! [SV7: $i,SV46: $i,SV160: $i] :
( ( ( ! [SY3548: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ SY3548 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3548 @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV46 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV160 ) )
= $true )
| ( ( SV160
= ( relation_composition @ SV7 @ SV46 ) )
= $true )
| ( ( relation @ SV160 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1628]) ).
thf(1700,plain,
! [SV7: $i,SV46: $i,SV160: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK9_SY3093 @ SV160 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV46 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV160 )
= $true )
| ( ( SV160
= ( relation_composition @ SV7 @ SV46 ) )
= $true )
| ( ( relation @ SV160 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1629]) ).
thf(1701,plain,
! [SV161: $i,SV46: $i,SV7: $i] :
( ( ( ! [SY3549: $i,SY3550: $i] :
( ! [SY3373: $i] :
( ~ ( in @ ( ordered_pair @ SY3549 @ SY3373 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3373 @ SY3550 ) @ SV46 ) )
| ( in @ ( ordered_pair @ SY3549 @ SY3550 ) @ SV161 ) ) )
= $true )
| ( ( SV161
= ( relation_composition @ SV7 @ SV46 ) )
= $false )
| ( ( relation @ SV161 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1630]) ).
thf(1702,plain,
! [SV7: $i,SV46: $i,SV161: $i] :
( ( ( ! [SY3552: $i,SY3553: $i] :
( ~ ( in @ ( ordered_pair @ SY3552 @ SY3553 ) @ SV161 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3552 @ ( sK6_F @ SY3553 @ SY3552 @ SV161 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY3553 @ SY3552 @ SV161 @ SV46 @ SV7 ) @ SY3553 ) @ SV46 ) ) ) )
= $true )
| ( ( SV161
= ( relation_composition @ SV7 @ SV46 ) )
= $false )
| ( ( relation @ SV161 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1631]) ).
thf(1703,plain,
! [SV63: $i,SV48: $i,SV207: $i,SV195: $i] :
( ( ( SV195 = SV207 )
= $false )
| ( ( ~ ( in @ SV195 @ SV48 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV195 @ SV207 ) @ SV63 )
= $true )
| ( ( SV63
= ( identity_relation @ SV48 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1633]) ).
thf(1704,plain,
! [SV48: $i,SV63: $i,SV239: $i,SV230: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV230 @ SV239 ) @ SV63 )
| ( SV230 = SV239 ) )
= $true )
| ( ( SV63
= ( identity_relation @ SV48 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(1705,plain,
! [SV48: $i,SV63: $i,SV231: $i] :
( ( ( ! [SY3587: $i] :
~ ( in @ ( ordered_pair @ SV231 @ SY3587 ) @ SV63 ) )
= $true )
| ( ( in @ SV231 @ SV48 )
= $true )
| ( ( SV63
= ( identity_relation @ SV48 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1635]) ).
thf(1706,plain,
! [SV82: $i,SV11: $i,SV185: $i,SV66: $i,SV196: $i] :
( ( ( in @ SV196 @ SV66 )
= $false )
| ( ( in @ SV185 @ SV11 )
= $false )
| ( ( ( ( sK28_D @ SV82 @ SV66 @ SV11 )
!= ( ordered_pair @ SV185 @ SV196 ) ) )
= $true )
| ( ( ~ ( in @ ( sK28_D @ SV82 @ SV66 @ SV11 ) @ SV82 ) )
= $true )
| ( ( SV82
= ( cartesian_product2 @ SV11 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1638]) ).
thf(1707,plain,
! [SV11: $i,SV66: $i,SV82: $i] :
( ( ( in @ ( sK29_SY3106 @ SV82 @ SV66 @ SV11 ) @ SV11 )
= $true )
| ( ( in @ ( sK28_D @ SV82 @ SV66 @ SV11 ) @ SV82 )
= $true )
| ( ( SV82
= ( cartesian_product2 @ SV11 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1639]) ).
thf(1708,plain,
! [SV11: $i,SV66: $i,SV82: $i] :
( ( ( in @ ( sK30_SY3108 @ SV82 @ SV66 @ SV11 ) @ SV66 )
= $true )
| ( ( in @ ( sK28_D @ SV82 @ SV66 @ SV11 ) @ SV82 )
= $true )
| ( ( SV82
= ( cartesian_product2 @ SV11 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1640]) ).
thf(1709,plain,
! [SV83: $i,SV186: $i,SV67: $i,SV221: $i,SV11: $i,SV209: $i] :
( ( ( ~ ( in @ SV209 @ SV11 ) )
= $true )
| ( ( ~ ( in @ SV221 @ SV67 ) )
= $true )
| ( ( ( SV186
!= ( ordered_pair @ SV209 @ SV221 ) ) )
= $true )
| ( ( in @ SV186 @ SV83 )
= $true )
| ( ( SV83
= ( cartesian_product2 @ SV11 @ SV67 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1641]) ).
thf(1710,plain,
! [SV11: $i,SV67: $i,SV83: $i,SV187: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_E @ SV187 @ SV83 @ SV67 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK27_SY3103 @ SV187 @ SV83 @ SV67 @ SV11 ) @ SV67 ) ) )
= $true )
| ( ( in @ SV187 @ SV83 )
= $false )
| ( ( SV83
= ( cartesian_product2 @ SV11 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1642]) ).
thf(1711,plain,
! [SV11: $i,SV67: $i,SV83: $i,SV187: $i] :
( ( ( SV187
= ( ordered_pair @ ( sK26_E @ SV187 @ SV83 @ SV67 @ SV11 ) @ ( sK27_SY3103 @ SV187 @ SV83 @ SV67 @ SV11 ) ) )
= $true )
| ( ( in @ SV187 @ SV83 )
= $false )
| ( ( SV83
= ( cartesian_product2 @ SV11 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1643]) ).
thf(1712,plain,
! [SV14: $i,SV103: $i] :
( ( ( ( ( sK14_C @ SV103 @ SV14 )
!= ( sK15_SY3096 @ SV103 @ SV14 ) ) )
= $true )
| ( ( is_connected_in @ SV14 @ SV103 )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1644]) ).
thf(1713,plain,
! [SV14: $i,SV103: $i] :
( ( ( ~ ( ~ ( in @ ( sK14_C @ SV103 @ SV14 ) @ SV103 )
| ~ ( in @ ( sK15_SY3096 @ SV103 @ SV14 ) @ SV103 ) ) )
= $true )
| ( ( is_connected_in @ SV14 @ SV103 )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1645]) ).
thf(1714,plain,
! [SV14: $i,SV165: $i,SV104: $i,SV177: $i] :
( ( ( in @ SV177 @ SV104 )
= $false )
| ( ( in @ SV165 @ SV104 )
= $false )
| ( ( SV165 = SV177 )
= $true )
| ( ( in @ ( ordered_pair @ SV165 @ SV177 ) @ SV14 )
= $true )
| ( ( in @ ( ordered_pair @ SV177 @ SV165 ) @ SV14 )
= $true )
| ( ( is_connected_in @ SV14 @ SV104 )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1646]) ).
thf(1715,plain,
! [SV16: $i,SV128: $i,SV105: $i,SV210: $i] :
( ( ( in @ SV210 @ SV105 )
= $false )
| ( ( in @ ( ordered_pair @ SV210 @ ( sK46_D @ SV128 @ SV105 @ SV16 ) ) @ SV16 )
= $false )
| ( ( ~ ( in @ ( sK46_D @ SV128 @ SV105 @ SV16 ) @ SV128 ) )
= $true )
| ( ( SV128
= ( relation_image @ SV16 @ SV105 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1649]) ).
thf(1716,plain,
! [SV129: $i,SV106: $i,SV16: $i,SV211: $i,SV232: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV232 @ SV211 ) @ SV16 ) )
= $true )
| ( ( ~ ( in @ SV232 @ SV106 ) )
= $true )
| ( ( in @ SV211 @ SV129 )
= $true )
| ( ( SV129
= ( relation_image @ SV16 @ SV106 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1652]) ).
thf(1717,plain,
! [SV16: $i,SV106: $i,SV129: $i,SV212: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SV212 @ SV129 @ SV106 @ SV16 ) @ SV212 ) @ SV16 )
| ~ ( in @ ( sK45_E @ SV212 @ SV129 @ SV106 @ SV16 ) @ SV106 ) )
= $false )
| ( ( in @ SV212 @ SV129 )
= $false )
| ( ( SV129
= ( relation_image @ SV16 @ SV106 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1653]) ).
thf(1718,plain,
! [SV18: $i,SV107: $i,SV132: $i] :
( ( ( ( sK35_D @ SV132 @ SV107 @ SV18 )
= SV107 )
= $false )
| ( ( in @ ( sK35_D @ SV132 @ SV107 @ SV18 ) @ SV132 )
= $true )
| ( ( SV132
= ( fiber @ SV18 @ SV107 ) )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1655]) ).
thf(1719,plain,
! [SV133: $i,SV18: $i,SV108: $i,SV213: $i] :
( ( ( in @ ( ordered_pair @ SV213 @ SV108 ) @ SV18 )
= $false )
| ( ( SV213 = SV108 )
= $true )
| ( ( in @ SV213 @ SV133 )
= $true )
| ( ( SV133
= ( fiber @ SV18 @ SV108 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1657]) ).
thf(1720,plain,
! [SV18: $i,SV108: $i,SV133: $i,SV240: $i] :
( ( ( ~ ( in @ SV240 @ SV133 )
| ( SV240 != SV108 ) )
= $true )
| ( ( SV133
= ( fiber @ SV18 @ SV108 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1658]) ).
thf(1721,plain,
! [SV18: $i,SV108: $i,SV133: $i,SV241: $i] :
( ( ( ~ ( in @ SV241 @ SV133 )
| ( in @ ( ordered_pair @ SV241 @ SV108 ) @ SV18 ) )
= $true )
| ( ( SV133
= ( fiber @ SV18 @ SV108 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1659]) ).
thf(1722,plain,
! [SV20: $i,SV112: $i,SV233: $i,SV222: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV222 @ SV233 ) @ SV112 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV233 @ SV222 ) @ SV20 )
= $true )
| ( ( SV112
= ( relation_inverse @ SV20 ) )
= $false )
| ( ( relation @ SV112 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1661]) ).
thf(1723,plain,
! [SV112: $i,SV20: $i,SV223: $i,SV234: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV234 @ SV223 ) @ SV20 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV223 @ SV234 ) @ SV112 )
= $true )
| ( ( SV112
= ( relation_inverse @ SV20 ) )
= $false )
| ( ( relation @ SV112 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1662]) ).
thf(1724,plain,
! [SV21: $i,SV38: $i,SV134: $i] :
( ( ( in @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) @ SV21 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV38 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) )
= $true )
| ( ( SV134
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $true )
| ( ( relation @ SV134 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1663]) ).
thf(1725,plain,
! [SV21: $i,SV38: $i,SV134: $i] :
( ( ( ( in @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) @ SV21 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) )
= $true )
| ( ( SV134
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $true )
| ( ( relation @ SV134 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1664]) ).
thf(1726,plain,
! [SV21: $i,SV38: $i,SV134: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV38 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) )
= $true )
| ( ( SV134
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $true )
| ( ( relation @ SV134 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1665]) ).
thf(1727,plain,
! [SV135: $i,SV38: $i,SV235: $i,SV21: $i,SV242: $i] :
( ( ( ~ ( in @ SV242 @ SV21 )
| ~ ( in @ ( ordered_pair @ SV235 @ SV242 ) @ SV38 )
| ( in @ ( ordered_pair @ SV235 @ SV242 ) @ SV135 ) )
= $true )
| ( ( SV135
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1666]) ).
thf(1728,plain,
! [SV38: $i,SV21: $i,SV135: $i] :
( ( ( ~ ! [SY3517: $i,SY3518: $i] :
( ~ ( in @ ( ordered_pair @ SY3517 @ SY3518 ) @ SV135 )
| ( in @ SY3518 @ SV21 ) ) )
= $false )
| ( ( SV135
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1667]) ).
thf(1729,plain,
! [SV21: $i,SV38: $i,SV135: $i] :
( ( ( ~ ! [SY3519: $i,SY3520: $i] :
( ~ ( in @ ( ordered_pair @ SY3519 @ SY3520 ) @ SV135 )
| ( in @ ( ordered_pair @ SY3519 @ SY3520 ) @ SV38 ) ) )
= $false )
| ( ( SV135
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1667]) ).
thf(1730,plain,
! [SV24: $i,SV117: $i,SV136: $i] :
( ( ( in @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ SV117 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV24 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) )
= $true )
| ( ( SV136
= ( relation_dom_restriction @ SV24 @ SV117 ) )
= $true )
| ( ( relation @ SV136 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1669]) ).
thf(1731,plain,
! [SV24: $i,SV117: $i,SV136: $i] :
( ( ( ( in @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ SV117 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) )
= $true )
| ( ( SV136
= ( relation_dom_restriction @ SV24 @ SV117 ) )
= $true )
| ( ( relation @ SV136 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1670]) ).
thf(1732,plain,
! [SV24: $i,SV117: $i,SV136: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV24 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) )
= $true )
| ( ( SV136
= ( relation_dom_restriction @ SV24 @ SV117 ) )
= $true )
| ( ( relation @ SV136 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1671]) ).
thf(1733,plain,
! [SV137: $i,SV24: $i,SV243: $i,SV118: $i,SV236: $i] :
( ( ( ~ ( in @ SV236 @ SV118 )
| ~ ( in @ ( ordered_pair @ SV236 @ SV243 ) @ SV24 )
| ( in @ ( ordered_pair @ SV236 @ SV243 ) @ SV137 ) )
= $true )
| ( ( SV137
= ( relation_dom_restriction @ SV24 @ SV118 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1672]) ).
thf(1734,plain,
! [SV24: $i,SV118: $i,SV137: $i] :
( ( ( ~ ! [SY3523: $i] :
( ! [SY3524: $i] :
~ ( in @ ( ordered_pair @ SY3523 @ SY3524 ) @ SV137 )
| ( in @ SY3523 @ SV118 ) ) )
= $false )
| ( ( SV137
= ( relation_dom_restriction @ SV24 @ SV118 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1673]) ).
thf(1735,plain,
! [SV118: $i,SV24: $i,SV137: $i] :
( ( ( ~ ! [SY3525: $i,SY3526: $i] :
( ~ ( in @ ( ordered_pair @ SY3525 @ SY3526 ) @ SV137 )
| ( in @ ( ordered_pair @ SY3525 @ SY3526 ) @ SV24 ) ) )
= $false )
| ( ( SV137
= ( relation_dom_restriction @ SV24 @ SV118 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1673]) ).
thf(1736,plain,
! [SV190: $i,SV26: $i,SV225: $i] :
( ( ( SV225
= ( apply @ SV26 @ SV190 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV190 @ SV225 ) @ SV26 )
= $true )
| ( ( in @ SV190 @ ( relation_dom @ SV26 ) )
= $false )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1674]) ).
thf(1737,plain,
! [SV26: $i,SV226: $i,SV191: $i] :
( ( ( in @ ( ordered_pair @ SV191 @ SV226 ) @ SV26 )
= $false )
| ( ( SV226
= ( apply @ SV26 @ SV191 ) )
= $true )
| ( ( in @ SV191 @ ( relation_dom @ SV26 ) )
= $false )
| ( ( function @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1675]) ).
thf(1738,plain,
! [SV53: $i] :
( ( ( ( sK62_B @ SV53 )
= ( sK63_SY3125 @ SV53 ) )
= $false )
| ( ( connected @ SV53 )
= $true )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1678]) ).
thf(1739,plain,
! [SV53: $i] :
( ( ( ~ ( in @ ( sK62_B @ SV53 ) @ ( relation_field @ SV53 ) )
| ~ ( in @ ( sK63_SY3125 @ SV53 ) @ ( relation_field @ SV53 ) ) )
= $false )
| ( ( connected @ SV53 )
= $true )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1679]) ).
thf(1740,plain,
! [SV27: $i,SV120: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_C @ SV120 @ SV27 ) @ SV120 )
| ~ ( in @ ( sK20_SY3099 @ SV120 @ SV27 ) @ SV120 ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV27 @ SV120 )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1681]) ).
thf(1741,plain,
! [SV27: $i,SV120: $i] :
( ( ( in @ ( ordered_pair @ ( sK19_C @ SV120 @ SV27 ) @ ( sK20_SY3099 @ SV120 @ SV27 ) ) @ SV27 )
= $true )
| ( ( is_antisymmetric_in @ SV27 @ SV120 )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1682]) ).
thf(1742,plain,
! [SV27: $i,SV170: $i,SV121: $i,SV178: $i] :
( ( ( in @ SV178 @ SV121 )
= $false )
| ( ( in @ SV170 @ SV121 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV170 @ SV178 ) @ SV27 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV178 @ SV170 ) @ SV27 ) )
= $true )
| ( ( SV170 = SV178 )
= $true )
| ( ( is_antisymmetric_in @ SV27 @ SV121 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1683]) ).
thf(1743,plain,
! [SV30: $i,SV139: $i,SV124: $i,SV216: $i] :
( ( ( in @ SV216 @ SV124 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SV216 ) @ SV30 )
= $false )
| ( ( ~ ( in @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SV139 ) )
= $true )
| ( ( SV139
= ( relation_inverse_image @ SV30 @ SV124 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1684]) ).
thf(1744,plain,
! [SV140: $i,SV125: $i,SV30: $i,SV237: $i,SV217: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV217 @ SV237 ) @ SV30 ) )
= $true )
| ( ( ~ ( in @ SV237 @ SV125 ) )
= $true )
| ( ( in @ SV217 @ SV140 )
= $true )
| ( ( SV140
= ( relation_inverse_image @ SV30 @ SV125 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1687]) ).
thf(1745,plain,
! [SV30: $i,SV125: $i,SV140: $i,SV218: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV218 @ ( sK42_E @ SV218 @ SV140 @ SV125 @ SV30 ) ) @ SV30 )
| ~ ( in @ ( sK42_E @ SV218 @ SV140 @ SV125 @ SV30 ) @ SV125 ) )
= $false )
| ( ( in @ SV218 @ SV140 )
= $false )
| ( ( SV140
= ( relation_inverse_image @ SV30 @ SV125 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1688]) ).
thf(1746,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1689]) ).
thf(1747,plain,
! [SV59: $i,SV32: $i,SV202: $i] :
( ( ( relation @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( ~ ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
| ~ ( ~ ! [SY3570: $i,SY3571: $i] :
( ~ ( in @ SY3570 @ ( relation_field @ SV32 ) )
| ~ ( in @ SY3571 @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV202 @ SY3570 ) @ ( apply @ SV202 @ SY3571 ) ) @ SV59 )
| ( in @ ( ordered_pair @ SY3570 @ SY3571 ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3312: $i] :
( ! [SY3313: $i] :
~ ( in @ ( ordered_pair @ SY3312 @ SY3313 ) @ SV32 )
| ( in @ SY3312 @ ( relation_field @ SV32 ) ) )
| ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV32 )
| ( in @ SY3315 @ ( relation_field @ SV32 ) ) ) )
| ~ ! [SY3576: $i,SY3577: $i] :
( ~ ( in @ ( ordered_pair @ SY3576 @ SY3577 ) @ SV32 )
| ( in @ ( ordered_pair @ ( apply @ SV202 @ SY3576 ) @ ( apply @ SV202 @ SY3577 ) ) @ SV59 ) ) ) ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1690]) ).
thf(1748,plain,
! [SV59: $i,SV32: $i] :
( ( ( ~ ! [SY3402: $i] :
( ~ ( function @ SY3402 )
| ~ ( relation @ SY3402 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3402 )
| ( ( relation_dom @ SY3402 )
= ( relation_field @ SV32 ) ) ) )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1691]) ).
thf(1749,plain,
! [SV59: $i,SV32: $i] :
( ( ( ~ ! [SY3403: $i] :
( ~ ( function @ SY3403 )
| ~ ( relation @ SY3403 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3403 )
| ( ( relation_rng @ SY3403 )
= ( relation_field @ SV59 ) ) ) )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1691]) ).
thf(1750,plain,
! [SV59: $i,SV32: $i,SV238: $i] :
( ( ( ~ ( function @ SV238 )
| ~ ( relation @ SV238 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV32 @ SV59 @ SV238 )
| ( one_to_one @ SV238 ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1692]) ).
thf(1751,plain,
! [SV99: $i,SV4: $i,SV228: $i,SV219: $i] :
( ( ( in @ ( ordered_pair @ SV219 @ SV228 ) @ SV4 )
= $false )
| ( ( in @ ( ordered_pair @ SV219 @ SV228 ) @ SV99 )
= $true )
| ( ( SV4 = SV99 )
= $false )
| ( ( relation @ SV99 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1694]) ).
thf(1752,plain,
! [SV4: $i,SV99: $i,SV229: $i,SV220: $i] :
( ( ( in @ ( ordered_pair @ SV220 @ SV229 ) @ SV99 )
= $false )
| ( ( in @ ( ordered_pair @ SV220 @ SV229 ) @ SV4 )
= $true )
| ( ( SV4 = SV99 )
= $false )
| ( ( relation @ SV99 )
= $false )
| ( ( relation @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1695]) ).
thf(1753,plain,
! [SV5: $i,SV100: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK3_C @ SV100 @ SV5 ) @ SV100 )
| ~ ( in @ ( sK4_SY3086 @ SV100 @ SV5 ) @ SV100 ) )
| ~ ( in @ ( sK5_SY3088 @ SV100 @ SV5 ) @ SV100 ) )
= $false )
| ( ( is_transitive_in @ SV5 @ SV100 )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1696]) ).
thf(1754,plain,
! [SV5: $i,SV183: $i,SV175: $i,SV101: $i,SV159: $i] :
( ( ( in @ SV159 @ SV101 )
= $false )
| ( ( ~ ( in @ SV175 @ SV101 ) )
= $true )
| ( ( ~ ( in @ SV183 @ SV101 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV159 @ SV175 ) @ SV5 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV175 @ SV183 ) @ SV5 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV159 @ SV183 ) @ SV5 )
= $true )
| ( ( is_transitive_in @ SV5 @ SV101 )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1698]) ).
thf(1755,plain,
! [SV244: $i,SV7: $i,SV46: $i,SV160: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ SV244 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SV244 @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV46 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV160 ) )
= $true )
| ( ( SV160
= ( relation_composition @ SV7 @ SV46 ) )
= $true )
| ( ( relation @ SV160 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1699]) ).
thf(1756,plain,
! [SV7: $i,SV46: $i,SV160: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK9_SY3093 @ SV160 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV46 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV160 )
= $true )
| ( ( SV160
= ( relation_composition @ SV7 @ SV46 ) )
= $true )
| ( ( relation @ SV160 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1700]) ).
thf(1757,plain,
! [SV161: $i,SV46: $i,SV7: $i,SV245: $i] :
( ( ( ! [SY3590: $i] :
( ! [SY3591: $i] :
( ~ ( in @ ( ordered_pair @ SV245 @ SY3591 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3591 @ SY3590 ) @ SV46 ) )
| ( in @ ( ordered_pair @ SV245 @ SY3590 ) @ SV161 ) ) )
= $true )
| ( ( SV161
= ( relation_composition @ SV7 @ SV46 ) )
= $false )
| ( ( relation @ SV161 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1701]) ).
thf(1758,plain,
! [SV7: $i,SV46: $i,SV161: $i,SV246: $i] :
( ( ( ! [SY3592: $i] :
( ~ ( in @ ( ordered_pair @ SV246 @ SY3592 ) @ SV161 )
| ~ ( ~ ( in @ ( ordered_pair @ SV246 @ ( sK6_F @ SY3592 @ SV246 @ SV161 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY3592 @ SV246 @ SV161 @ SV46 @ SV7 ) @ SY3592 ) @ SV46 ) ) ) )
= $true )
| ( ( SV161
= ( relation_composition @ SV7 @ SV46 ) )
= $false )
| ( ( relation @ SV161 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1702]) ).
thf(1759,plain,
! [SV63: $i,SV207: $i,SV48: $i,SV195: $i] :
( ( ( in @ SV195 @ SV48 )
= $false )
| ( ( SV195 = SV207 )
= $false )
| ( ( in @ ( ordered_pair @ SV195 @ SV207 ) @ SV63 )
= $true )
| ( ( SV63
= ( identity_relation @ SV48 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1703]) ).
thf(1760,plain,
! [SV48: $i,SV63: $i,SV239: $i,SV230: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV230 @ SV239 ) @ SV63 ) )
= $true )
| ( ( SV230 = SV239 )
= $true )
| ( ( SV63
= ( identity_relation @ SV48 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1704]) ).
thf(1761,plain,
! [SV48: $i,SV63: $i,SV247: $i,SV231: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV231 @ SV247 ) @ SV63 ) )
= $true )
| ( ( in @ SV231 @ SV48 )
= $true )
| ( ( SV63
= ( identity_relation @ SV48 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1705]) ).
thf(1762,plain,
! [SV196: $i,SV185: $i,SV11: $i,SV66: $i,SV82: $i] :
( ( ( ( sK28_D @ SV82 @ SV66 @ SV11 )
= ( ordered_pair @ SV185 @ SV196 ) )
= $false )
| ( ( in @ SV185 @ SV11 )
= $false )
| ( ( in @ SV196 @ SV66 )
= $false )
| ( ( ~ ( in @ ( sK28_D @ SV82 @ SV66 @ SV11 ) @ SV82 ) )
= $true )
| ( ( SV82
= ( cartesian_product2 @ SV11 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1706]) ).
thf(1763,plain,
! [SV83: $i,SV186: $i,SV67: $i,SV221: $i,SV11: $i,SV209: $i] :
( ( ( in @ SV209 @ SV11 )
= $false )
| ( ( ~ ( in @ SV221 @ SV67 ) )
= $true )
| ( ( ( SV186
!= ( ordered_pair @ SV209 @ SV221 ) ) )
= $true )
| ( ( in @ SV186 @ SV83 )
= $true )
| ( ( SV83
= ( cartesian_product2 @ SV11 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1709]) ).
thf(1764,plain,
! [SV11: $i,SV67: $i,SV83: $i,SV187: $i] :
( ( ( ~ ( in @ ( sK26_E @ SV187 @ SV83 @ SV67 @ SV11 ) @ SV11 )
| ~ ( in @ ( sK27_SY3103 @ SV187 @ SV83 @ SV67 @ SV11 ) @ SV67 ) )
= $false )
| ( ( in @ SV187 @ SV83 )
= $false )
| ( ( SV83
= ( cartesian_product2 @ SV11 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1710]) ).
thf(1765,plain,
! [SV14: $i,SV103: $i] :
( ( ( ( sK14_C @ SV103 @ SV14 )
= ( sK15_SY3096 @ SV103 @ SV14 ) )
= $false )
| ( ( is_connected_in @ SV14 @ SV103 )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1712]) ).
thf(1766,plain,
! [SV14: $i,SV103: $i] :
( ( ( ~ ( in @ ( sK14_C @ SV103 @ SV14 ) @ SV103 )
| ~ ( in @ ( sK15_SY3096 @ SV103 @ SV14 ) @ SV103 ) )
= $false )
| ( ( is_connected_in @ SV14 @ SV103 )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1713]) ).
thf(1767,plain,
! [SV210: $i,SV16: $i,SV105: $i,SV128: $i] :
( ( ( in @ ( sK46_D @ SV128 @ SV105 @ SV16 ) @ SV128 )
= $false )
| ( ( in @ ( ordered_pair @ SV210 @ ( sK46_D @ SV128 @ SV105 @ SV16 ) ) @ SV16 )
= $false )
| ( ( in @ SV210 @ SV105 )
= $false )
| ( ( SV128
= ( relation_image @ SV16 @ SV105 ) )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1715]) ).
thf(1768,plain,
! [SV129: $i,SV106: $i,SV16: $i,SV211: $i,SV232: $i] :
( ( ( in @ ( ordered_pair @ SV232 @ SV211 ) @ SV16 )
= $false )
| ( ( ~ ( in @ SV232 @ SV106 ) )
= $true )
| ( ( in @ SV211 @ SV129 )
= $true )
| ( ( SV129
= ( relation_image @ SV16 @ SV106 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1716]) ).
thf(1769,plain,
! [SV16: $i,SV106: $i,SV129: $i,SV212: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SV212 @ SV129 @ SV106 @ SV16 ) @ SV212 ) @ SV16 ) )
= $false )
| ( ( in @ SV212 @ SV129 )
= $false )
| ( ( SV129
= ( relation_image @ SV16 @ SV106 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1717]) ).
thf(1770,plain,
! [SV16: $i,SV106: $i,SV129: $i,SV212: $i] :
( ( ( ~ ( in @ ( sK45_E @ SV212 @ SV129 @ SV106 @ SV16 ) @ SV106 ) )
= $false )
| ( ( in @ SV212 @ SV129 )
= $false )
| ( ( SV129
= ( relation_image @ SV16 @ SV106 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1717]) ).
thf(1771,plain,
! [SV18: $i,SV108: $i,SV133: $i,SV240: $i] :
( ( ( ~ ( in @ SV240 @ SV133 ) )
= $true )
| ( ( ( SV240 != SV108 ) )
= $true )
| ( ( SV133
= ( fiber @ SV18 @ SV108 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1720]) ).
thf(1772,plain,
! [SV18: $i,SV108: $i,SV133: $i,SV241: $i] :
( ( ( ~ ( in @ SV241 @ SV133 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV241 @ SV108 ) @ SV18 )
= $true )
| ( ( SV133
= ( fiber @ SV18 @ SV108 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1721]) ).
thf(1773,plain,
! [SV20: $i,SV112: $i,SV233: $i,SV222: $i] :
( ( ( in @ ( ordered_pair @ SV222 @ SV233 ) @ SV112 )
= $false )
| ( ( in @ ( ordered_pair @ SV233 @ SV222 ) @ SV20 )
= $true )
| ( ( SV112
= ( relation_inverse @ SV20 ) )
= $false )
| ( ( relation @ SV112 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1722]) ).
thf(1774,plain,
! [SV112: $i,SV20: $i,SV223: $i,SV234: $i] :
( ( ( in @ ( ordered_pair @ SV234 @ SV223 ) @ SV20 )
= $false )
| ( ( in @ ( ordered_pair @ SV223 @ SV234 ) @ SV112 )
= $true )
| ( ( SV112
= ( relation_inverse @ SV20 ) )
= $false )
| ( ( relation @ SV112 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1723]) ).
thf(1775,plain,
! [SV21: $i,SV38: $i,SV134: $i] :
( ( ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV38 )
= $false )
| ( ( in @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) @ SV21 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 ) )
= $true )
| ( ( SV134
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $true )
| ( ( relation @ SV134 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1724]) ).
thf(1776,plain,
! [SV21: $i,SV38: $i,SV134: $i] :
( ( ( in @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) @ SV21 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 )
= $true )
| ( ( SV134
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $true )
| ( ( relation @ SV134 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1725]) ).
thf(1777,plain,
! [SV21: $i,SV38: $i,SV134: $i] :
( ( ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV38 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 )
= $true )
| ( ( SV134
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $true )
| ( ( relation @ SV134 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1726]) ).
thf(1778,plain,
! [SV135: $i,SV38: $i,SV235: $i,SV21: $i,SV242: $i] :
( ( ( ~ ( in @ SV242 @ SV21 )
| ~ ( in @ ( ordered_pair @ SV235 @ SV242 ) @ SV38 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV235 @ SV242 ) @ SV135 )
= $true )
| ( ( SV135
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1727]) ).
thf(1779,plain,
! [SV38: $i,SV21: $i,SV135: $i] :
( ( ( ! [SY3517: $i,SY3518: $i] :
( ~ ( in @ ( ordered_pair @ SY3517 @ SY3518 ) @ SV135 )
| ( in @ SY3518 @ SV21 ) ) )
= $true )
| ( ( SV135
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1728]) ).
thf(1780,plain,
! [SV21: $i,SV38: $i,SV135: $i] :
( ( ( ! [SY3519: $i,SY3520: $i] :
( ~ ( in @ ( ordered_pair @ SY3519 @ SY3520 ) @ SV135 )
| ( in @ ( ordered_pair @ SY3519 @ SY3520 ) @ SV38 ) ) )
= $true )
| ( ( SV135
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1729]) ).
thf(1781,plain,
! [SV24: $i,SV117: $i,SV136: $i] :
( ( ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV24 )
= $false )
| ( ( in @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ SV117 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 ) )
= $true )
| ( ( SV136
= ( relation_dom_restriction @ SV24 @ SV117 ) )
= $true )
| ( ( relation @ SV136 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1730]) ).
thf(1782,plain,
! [SV24: $i,SV117: $i,SV136: $i] :
( ( ( in @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ SV117 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 )
= $true )
| ( ( SV136
= ( relation_dom_restriction @ SV24 @ SV117 ) )
= $true )
| ( ( relation @ SV136 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1731]) ).
thf(1783,plain,
! [SV24: $i,SV117: $i,SV136: $i] :
( ( ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV24 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 )
= $true )
| ( ( SV136
= ( relation_dom_restriction @ SV24 @ SV117 ) )
= $true )
| ( ( relation @ SV136 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1732]) ).
thf(1784,plain,
! [SV137: $i,SV24: $i,SV243: $i,SV118: $i,SV236: $i] :
( ( ( ~ ( in @ SV236 @ SV118 )
| ~ ( in @ ( ordered_pair @ SV236 @ SV243 ) @ SV24 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV236 @ SV243 ) @ SV137 )
= $true )
| ( ( SV137
= ( relation_dom_restriction @ SV24 @ SV118 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1733]) ).
thf(1785,plain,
! [SV24: $i,SV118: $i,SV137: $i] :
( ( ( ! [SY3523: $i] :
( ! [SY3524: $i] :
~ ( in @ ( ordered_pair @ SY3523 @ SY3524 ) @ SV137 )
| ( in @ SY3523 @ SV118 ) ) )
= $true )
| ( ( SV137
= ( relation_dom_restriction @ SV24 @ SV118 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1734]) ).
thf(1786,plain,
! [SV118: $i,SV24: $i,SV137: $i] :
( ( ( ! [SY3525: $i,SY3526: $i] :
( ~ ( in @ ( ordered_pair @ SY3525 @ SY3526 ) @ SV137 )
| ( in @ ( ordered_pair @ SY3525 @ SY3526 ) @ SV24 ) ) )
= $true )
| ( ( SV137
= ( relation_dom_restriction @ SV24 @ SV118 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1735]) ).
thf(1787,plain,
! [SV53: $i] :
( ( ( ~ ( in @ ( sK62_B @ SV53 ) @ ( relation_field @ SV53 ) ) )
= $false )
| ( ( connected @ SV53 )
= $true )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1739]) ).
thf(1788,plain,
! [SV53: $i] :
( ( ( ~ ( in @ ( sK63_SY3125 @ SV53 ) @ ( relation_field @ SV53 ) ) )
= $false )
| ( ( connected @ SV53 )
= $true )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1739]) ).
thf(1789,plain,
! [SV27: $i,SV120: $i] :
( ( ( ~ ( in @ ( sK19_C @ SV120 @ SV27 ) @ SV120 )
| ~ ( in @ ( sK20_SY3099 @ SV120 @ SV27 ) @ SV120 ) )
= $false )
| ( ( is_antisymmetric_in @ SV27 @ SV120 )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1740]) ).
thf(1790,plain,
! [SV121: $i,SV27: $i,SV178: $i,SV170: $i] :
( ( ( in @ ( ordered_pair @ SV170 @ SV178 ) @ SV27 )
= $false )
| ( ( in @ SV170 @ SV121 )
= $false )
| ( ( in @ SV178 @ SV121 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV178 @ SV170 ) @ SV27 ) )
= $true )
| ( ( SV170 = SV178 )
= $true )
| ( ( is_antisymmetric_in @ SV27 @ SV121 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1742]) ).
thf(1791,plain,
! [SV216: $i,SV30: $i,SV124: $i,SV139: $i] :
( ( ( in @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SV139 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK43_D @ SV139 @ SV124 @ SV30 ) @ SV216 ) @ SV30 )
= $false )
| ( ( in @ SV216 @ SV124 )
= $false )
| ( ( SV139
= ( relation_inverse_image @ SV30 @ SV124 ) )
= $true )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1743]) ).
thf(1792,plain,
! [SV140: $i,SV125: $i,SV30: $i,SV237: $i,SV217: $i] :
( ( ( in @ ( ordered_pair @ SV217 @ SV237 ) @ SV30 )
= $false )
| ( ( ~ ( in @ SV237 @ SV125 ) )
= $true )
| ( ( in @ SV217 @ SV140 )
= $true )
| ( ( SV140
= ( relation_inverse_image @ SV30 @ SV125 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1744]) ).
thf(1793,plain,
! [SV30: $i,SV125: $i,SV140: $i,SV218: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV218 @ ( sK42_E @ SV218 @ SV140 @ SV125 @ SV30 ) ) @ SV30 ) )
= $false )
| ( ( in @ SV218 @ SV140 )
= $false )
| ( ( SV140
= ( relation_inverse_image @ SV30 @ SV125 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1745]) ).
thf(1794,plain,
! [SV30: $i,SV125: $i,SV140: $i,SV218: $i] :
( ( ( ~ ( in @ ( sK42_E @ SV218 @ SV140 @ SV125 @ SV30 ) @ SV125 ) )
= $false )
| ( ( in @ SV218 @ SV140 )
= $false )
| ( ( SV140
= ( relation_inverse_image @ SV30 @ SV125 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1745]) ).
thf(1795,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) ) )
= $false )
| ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1746]) ).
thf(1796,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1746]) ).
thf(1797,plain,
! [SV202: $i,SV59: $i,SV32: $i] :
( ( ( ~ ( relation_isomorphism @ SV32 @ SV59 @ SV202 ) )
= $true )
| ( ( ~ ( ~ ! [SY3570: $i,SY3571: $i] :
( ~ ( in @ SY3570 @ ( relation_field @ SV32 ) )
| ~ ( in @ SY3571 @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV202 @ SY3570 ) @ ( apply @ SV202 @ SY3571 ) ) @ SV59 )
| ( in @ ( ordered_pair @ SY3570 @ SY3571 ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3312: $i] :
( ! [SY3313: $i] :
~ ( in @ ( ordered_pair @ SY3312 @ SY3313 ) @ SV32 )
| ( in @ SY3312 @ ( relation_field @ SV32 ) ) )
| ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV32 )
| ( in @ SY3315 @ ( relation_field @ SV32 ) ) ) )
| ~ ! [SY3576: $i,SY3577: $i] :
( ~ ( in @ ( ordered_pair @ SY3576 @ SY3577 ) @ SV32 )
| ( in @ ( ordered_pair @ ( apply @ SV202 @ SY3576 ) @ ( apply @ SV202 @ SY3577 ) ) @ SV59 ) ) ) ) )
= $true )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1747]) ).
thf(1798,plain,
! [SV59: $i,SV32: $i] :
( ( ( ! [SY3402: $i] :
( ~ ( function @ SY3402 )
| ~ ( relation @ SY3402 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3402 )
| ( ( relation_dom @ SY3402 )
= ( relation_field @ SV32 ) ) ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1748]) ).
thf(1799,plain,
! [SV59: $i,SV32: $i] :
( ( ( ! [SY3403: $i] :
( ~ ( function @ SY3403 )
| ~ ( relation @ SY3403 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SY3403 )
| ( ( relation_rng @ SY3403 )
= ( relation_field @ SV59 ) ) ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1749]) ).
thf(1800,plain,
! [SV59: $i,SV32: $i,SV238: $i] :
( ( ( ~ ( function @ SV238 ) )
= $true )
| ( ( ~ ( relation @ SV238 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV32 @ SV59 @ SV238 )
| ( one_to_one @ SV238 ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1750]) ).
thf(1801,plain,
! [SV5: $i,SV100: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK3_C @ SV100 @ SV5 ) @ SV100 )
| ~ ( in @ ( sK4_SY3086 @ SV100 @ SV5 ) @ SV100 ) ) )
= $false )
| ( ( is_transitive_in @ SV5 @ SV100 )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1753]) ).
thf(1802,plain,
! [SV5: $i,SV100: $i] :
( ( ( ~ ( in @ ( sK5_SY3088 @ SV100 @ SV5 ) @ SV100 ) )
= $false )
| ( ( is_transitive_in @ SV5 @ SV100 )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1753]) ).
thf(1803,plain,
! [SV5: $i,SV183: $i,SV159: $i,SV101: $i,SV175: $i] :
( ( ( in @ SV175 @ SV101 )
= $false )
| ( ( in @ SV159 @ SV101 )
= $false )
| ( ( ~ ( in @ SV183 @ SV101 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV159 @ SV175 ) @ SV5 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV175 @ SV183 ) @ SV5 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV159 @ SV183 ) @ SV5 )
= $true )
| ( ( is_transitive_in @ SV5 @ SV101 )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1754]) ).
thf(1804,plain,
! [SV244: $i,SV7: $i,SV46: $i,SV160: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ SV244 ) @ SV7 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV244 @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV46 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV160 ) )
= $true )
| ( ( SV160
= ( relation_composition @ SV7 @ SV46 ) )
= $true )
| ( ( relation @ SV160 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1755]) ).
thf(1805,plain,
! [SV7: $i,SV46: $i,SV160: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK9_SY3093 @ SV160 @ SV46 @ SV7 ) ) @ SV7 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV160 )
= $true )
| ( ( SV160
= ( relation_composition @ SV7 @ SV46 ) )
= $true )
| ( ( relation @ SV160 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1756]) ).
thf(1806,plain,
! [SV7: $i,SV46: $i,SV160: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV46 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV160 )
= $true )
| ( ( SV160
= ( relation_composition @ SV7 @ SV46 ) )
= $true )
| ( ( relation @ SV160 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1756]) ).
thf(1807,plain,
! [SV161: $i,SV46: $i,SV248: $i,SV7: $i,SV245: $i] :
( ( ( ! [SY3593: $i] :
( ~ ( in @ ( ordered_pair @ SV245 @ SY3593 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3593 @ SV248 ) @ SV46 ) )
| ( in @ ( ordered_pair @ SV245 @ SV248 ) @ SV161 ) )
= $true )
| ( ( SV161
= ( relation_composition @ SV7 @ SV46 ) )
= $false )
| ( ( relation @ SV161 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1757]) ).
thf(1808,plain,
! [SV7: $i,SV46: $i,SV161: $i,SV249: $i,SV246: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV246 @ SV249 ) @ SV161 )
| ~ ( ~ ( in @ ( ordered_pair @ SV246 @ ( sK6_F @ SV249 @ SV246 @ SV161 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SV249 @ SV246 @ SV161 @ SV46 @ SV7 ) @ SV249 ) @ SV46 ) ) )
= $true )
| ( ( SV161
= ( relation_composition @ SV7 @ SV46 ) )
= $false )
| ( ( relation @ SV161 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1758]) ).
thf(1809,plain,
! [SV48: $i,SV63: $i,SV239: $i,SV230: $i] :
( ( ( in @ ( ordered_pair @ SV230 @ SV239 ) @ SV63 )
= $false )
| ( ( SV230 = SV239 )
= $true )
| ( ( SV63
= ( identity_relation @ SV48 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1760]) ).
thf(1810,plain,
! [SV48: $i,SV63: $i,SV247: $i,SV231: $i] :
( ( ( in @ ( ordered_pair @ SV231 @ SV247 ) @ SV63 )
= $false )
| ( ( in @ SV231 @ SV48 )
= $true )
| ( ( SV63
= ( identity_relation @ SV48 ) )
= $false )
| ( ( relation @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1761]) ).
thf(1811,plain,
! [SV185: $i,SV196: $i,SV11: $i,SV66: $i,SV82: $i] :
( ( ( in @ ( sK28_D @ SV82 @ SV66 @ SV11 ) @ SV82 )
= $false )
| ( ( in @ SV196 @ SV66 )
= $false )
| ( ( in @ SV185 @ SV11 )
= $false )
| ( ( ( sK28_D @ SV82 @ SV66 @ SV11 )
= ( ordered_pair @ SV185 @ SV196 ) )
= $false )
| ( ( SV82
= ( cartesian_product2 @ SV11 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1762]) ).
thf(1812,plain,
! [SV83: $i,SV186: $i,SV11: $i,SV209: $i,SV67: $i,SV221: $i] :
( ( ( in @ SV221 @ SV67 )
= $false )
| ( ( in @ SV209 @ SV11 )
= $false )
| ( ( ( SV186
!= ( ordered_pair @ SV209 @ SV221 ) ) )
= $true )
| ( ( in @ SV186 @ SV83 )
= $true )
| ( ( SV83
= ( cartesian_product2 @ SV11 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1763]) ).
thf(1813,plain,
! [SV11: $i,SV67: $i,SV83: $i,SV187: $i] :
( ( ( ~ ( in @ ( sK26_E @ SV187 @ SV83 @ SV67 @ SV11 ) @ SV11 ) )
= $false )
| ( ( in @ SV187 @ SV83 )
= $false )
| ( ( SV83
= ( cartesian_product2 @ SV11 @ SV67 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1764]) ).
thf(1814,plain,
! [SV11: $i,SV67: $i,SV83: $i,SV187: $i] :
( ( ( ~ ( in @ ( sK27_SY3103 @ SV187 @ SV83 @ SV67 @ SV11 ) @ SV67 ) )
= $false )
| ( ( in @ SV187 @ SV83 )
= $false )
| ( ( SV83
= ( cartesian_product2 @ SV11 @ SV67 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1764]) ).
thf(1815,plain,
! [SV14: $i,SV103: $i] :
( ( ( ~ ( in @ ( sK14_C @ SV103 @ SV14 ) @ SV103 ) )
= $false )
| ( ( is_connected_in @ SV14 @ SV103 )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1766]) ).
thf(1816,plain,
! [SV14: $i,SV103: $i] :
( ( ( ~ ( in @ ( sK15_SY3096 @ SV103 @ SV14 ) @ SV103 ) )
= $false )
| ( ( is_connected_in @ SV14 @ SV103 )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1766]) ).
thf(1817,plain,
! [SV129: $i,SV16: $i,SV211: $i,SV106: $i,SV232: $i] :
( ( ( in @ SV232 @ SV106 )
= $false )
| ( ( in @ ( ordered_pair @ SV232 @ SV211 ) @ SV16 )
= $false )
| ( ( in @ SV211 @ SV129 )
= $true )
| ( ( SV129
= ( relation_image @ SV16 @ SV106 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1768]) ).
thf(1818,plain,
! [SV16: $i,SV106: $i,SV129: $i,SV212: $i] :
( ( ( in @ ( ordered_pair @ ( sK45_E @ SV212 @ SV129 @ SV106 @ SV16 ) @ SV212 ) @ SV16 )
= $true )
| ( ( in @ SV212 @ SV129 )
= $false )
| ( ( SV129
= ( relation_image @ SV16 @ SV106 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1769]) ).
thf(1819,plain,
! [SV16: $i,SV106: $i,SV129: $i,SV212: $i] :
( ( ( in @ ( sK45_E @ SV212 @ SV129 @ SV106 @ SV16 ) @ SV106 )
= $true )
| ( ( in @ SV212 @ SV129 )
= $false )
| ( ( SV129
= ( relation_image @ SV16 @ SV106 ) )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1770]) ).
thf(1820,plain,
! [SV18: $i,SV108: $i,SV133: $i,SV240: $i] :
( ( ( in @ SV240 @ SV133 )
= $false )
| ( ( ( SV240 != SV108 ) )
= $true )
| ( ( SV133
= ( fiber @ SV18 @ SV108 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1771]) ).
thf(1821,plain,
! [SV18: $i,SV108: $i,SV133: $i,SV241: $i] :
( ( ( in @ SV241 @ SV133 )
= $false )
| ( ( in @ ( ordered_pair @ SV241 @ SV108 ) @ SV18 )
= $true )
| ( ( SV133
= ( fiber @ SV18 @ SV108 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1772]) ).
thf(1822,plain,
! [SV21: $i,SV38: $i,SV134: $i] :
( ( ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV134 )
= $false )
| ( ( in @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) @ SV21 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK48_D @ SV134 @ SV38 @ SV21 ) @ ( sK49_SY3119 @ SV134 @ SV38 @ SV21 ) ) @ SV38 )
= $false )
| ( ( SV134
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $true )
| ( ( relation @ SV134 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1775]) ).
thf(1823,plain,
! [SV135: $i,SV38: $i,SV235: $i,SV21: $i,SV242: $i] :
( ( ( ~ ( in @ SV242 @ SV21 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV235 @ SV242 ) @ SV38 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV235 @ SV242 ) @ SV135 )
= $true )
| ( ( SV135
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1778]) ).
thf(1824,plain,
! [SV38: $i,SV21: $i,SV135: $i,SV250: $i] :
( ( ( ! [SY3594: $i] :
( ~ ( in @ ( ordered_pair @ SV250 @ SY3594 ) @ SV135 )
| ( in @ SY3594 @ SV21 ) ) )
= $true )
| ( ( SV135
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1779]) ).
thf(1825,plain,
! [SV21: $i,SV38: $i,SV135: $i,SV251: $i] :
( ( ( ! [SY3595: $i] :
( ~ ( in @ ( ordered_pair @ SV251 @ SY3595 ) @ SV135 )
| ( in @ ( ordered_pair @ SV251 @ SY3595 ) @ SV38 ) ) )
= $true )
| ( ( SV135
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1780]) ).
thf(1826,plain,
! [SV24: $i,SV117: $i,SV136: $i] :
( ( ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV136 )
= $false )
| ( ( in @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ SV117 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK50_D @ SV136 @ SV117 @ SV24 ) @ ( sK51_SY3120 @ SV136 @ SV117 @ SV24 ) ) @ SV24 )
= $false )
| ( ( SV136
= ( relation_dom_restriction @ SV24 @ SV117 ) )
= $true )
| ( ( relation @ SV136 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1781]) ).
thf(1827,plain,
! [SV137: $i,SV24: $i,SV243: $i,SV118: $i,SV236: $i] :
( ( ( ~ ( in @ SV236 @ SV118 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV236 @ SV243 ) @ SV24 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV236 @ SV243 ) @ SV137 )
= $true )
| ( ( SV137
= ( relation_dom_restriction @ SV24 @ SV118 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1784]) ).
thf(1828,plain,
! [SV24: $i,SV118: $i,SV137: $i,SV252: $i] :
( ( ( ! [SY3596: $i] :
~ ( in @ ( ordered_pair @ SV252 @ SY3596 ) @ SV137 )
| ( in @ SV252 @ SV118 ) )
= $true )
| ( ( SV137
= ( relation_dom_restriction @ SV24 @ SV118 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1785]) ).
thf(1829,plain,
! [SV118: $i,SV24: $i,SV137: $i,SV253: $i] :
( ( ( ! [SY3597: $i] :
( ~ ( in @ ( ordered_pair @ SV253 @ SY3597 ) @ SV137 )
| ( in @ ( ordered_pair @ SV253 @ SY3597 ) @ SV24 ) ) )
= $true )
| ( ( SV137
= ( relation_dom_restriction @ SV24 @ SV118 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1786]) ).
thf(1830,plain,
! [SV53: $i] :
( ( ( in @ ( sK62_B @ SV53 ) @ ( relation_field @ SV53 ) )
= $true )
| ( ( connected @ SV53 )
= $true )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1787]) ).
thf(1831,plain,
! [SV53: $i] :
( ( ( in @ ( sK63_SY3125 @ SV53 ) @ ( relation_field @ SV53 ) )
= $true )
| ( ( connected @ SV53 )
= $true )
| ( ( relation @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1788]) ).
thf(1832,plain,
! [SV27: $i,SV120: $i] :
( ( ( ~ ( in @ ( sK19_C @ SV120 @ SV27 ) @ SV120 ) )
= $false )
| ( ( is_antisymmetric_in @ SV27 @ SV120 )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1789]) ).
thf(1833,plain,
! [SV27: $i,SV120: $i] :
( ( ( ~ ( in @ ( sK20_SY3099 @ SV120 @ SV27 ) @ SV120 ) )
= $false )
| ( ( is_antisymmetric_in @ SV27 @ SV120 )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1789]) ).
thf(1834,plain,
! [SV121: $i,SV27: $i,SV170: $i,SV178: $i] :
( ( ( in @ ( ordered_pair @ SV178 @ SV170 ) @ SV27 )
= $false )
| ( ( in @ SV178 @ SV121 )
= $false )
| ( ( in @ SV170 @ SV121 )
= $false )
| ( ( in @ ( ordered_pair @ SV170 @ SV178 ) @ SV27 )
= $false )
| ( ( SV170 = SV178 )
= $true )
| ( ( is_antisymmetric_in @ SV27 @ SV121 )
= $false )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1790]) ).
thf(1835,plain,
! [SV140: $i,SV30: $i,SV217: $i,SV125: $i,SV237: $i] :
( ( ( in @ SV237 @ SV125 )
= $false )
| ( ( in @ ( ordered_pair @ SV217 @ SV237 ) @ SV30 )
= $false )
| ( ( in @ SV217 @ SV140 )
= $true )
| ( ( SV140
= ( relation_inverse_image @ SV30 @ SV125 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1792]) ).
thf(1836,plain,
! [SV30: $i,SV125: $i,SV140: $i,SV218: $i] :
( ( ( in @ ( ordered_pair @ SV218 @ ( sK42_E @ SV218 @ SV140 @ SV125 @ SV30 ) ) @ SV30 )
= $true )
| ( ( in @ SV218 @ SV140 )
= $false )
| ( ( SV140
= ( relation_inverse_image @ SV30 @ SV125 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1793]) ).
thf(1837,plain,
! [SV30: $i,SV125: $i,SV140: $i,SV218: $i] :
( ( ( in @ ( sK42_E @ SV218 @ SV140 @ SV125 @ SV30 ) @ SV125 )
= $true )
| ( ( in @ SV218 @ SV140 )
= $false )
| ( ( SV140
= ( relation_inverse_image @ SV30 @ SV125 ) )
= $false )
| ( ( relation @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1794]) ).
thf(1838,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( ~ ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
= $true )
| ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1795]) ).
thf(1839,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1796]) ).
thf(1840,plain,
! [SV202: $i,SV59: $i,SV32: $i] :
( ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( ~ ( ~ ! [SY3570: $i,SY3571: $i] :
( ~ ( in @ SY3570 @ ( relation_field @ SV32 ) )
| ~ ( in @ SY3571 @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV202 @ SY3570 ) @ ( apply @ SV202 @ SY3571 ) ) @ SV59 )
| ( in @ ( ordered_pair @ SY3570 @ SY3571 ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3312: $i] :
( ! [SY3313: $i] :
~ ( in @ ( ordered_pair @ SY3312 @ SY3313 ) @ SV32 )
| ( in @ SY3312 @ ( relation_field @ SV32 ) ) )
| ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV32 )
| ( in @ SY3315 @ ( relation_field @ SV32 ) ) ) )
| ~ ! [SY3576: $i,SY3577: $i] :
( ~ ( in @ ( ordered_pair @ SY3576 @ SY3577 ) @ SV32 )
| ( in @ ( ordered_pair @ ( apply @ SV202 @ SY3576 ) @ ( apply @ SV202 @ SY3577 ) ) @ SV59 ) ) ) ) )
= $true )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1797]) ).
thf(1841,plain,
! [SV59: $i,SV32: $i,SV254: $i] :
( ( ( ~ ( function @ SV254 )
| ~ ( relation @ SV254 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SV254 )
| ( ( relation_dom @ SV254 )
= ( relation_field @ SV32 ) ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1798]) ).
thf(1842,plain,
! [SV59: $i,SV32: $i,SV255: $i] :
( ( ( ~ ( function @ SV255 )
| ~ ( relation @ SV255 )
| ~ ( relation_isomorphism @ SV32 @ SV59 @ SV255 )
| ( ( relation_rng @ SV255 )
= ( relation_field @ SV59 ) ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1799]) ).
thf(1843,plain,
! [SV59: $i,SV32: $i,SV238: $i] :
( ( ( function @ SV238 )
= $false )
| ( ( ~ ( relation @ SV238 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV32 @ SV59 @ SV238 )
| ( one_to_one @ SV238 ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1800]) ).
thf(1844,plain,
! [SV5: $i,SV100: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_C @ SV100 @ SV5 ) @ SV100 )
| ~ ( in @ ( sK4_SY3086 @ SV100 @ SV5 ) @ SV100 ) ) )
= $true )
| ( ( is_transitive_in @ SV5 @ SV100 )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1801]) ).
thf(1845,plain,
! [SV5: $i,SV100: $i] :
( ( ( in @ ( sK5_SY3088 @ SV100 @ SV5 ) @ SV100 )
= $true )
| ( ( is_transitive_in @ SV5 @ SV100 )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1802]) ).
thf(1846,plain,
! [SV5: $i,SV175: $i,SV159: $i,SV101: $i,SV183: $i] :
( ( ( in @ SV183 @ SV101 )
= $false )
| ( ( in @ SV159 @ SV101 )
= $false )
| ( ( in @ SV175 @ SV101 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV159 @ SV175 ) @ SV5 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV175 @ SV183 ) @ SV5 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV159 @ SV183 ) @ SV5 )
= $true )
| ( ( is_transitive_in @ SV5 @ SV101 )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1803]) ).
thf(1847,plain,
! [SV244: $i,SV7: $i,SV46: $i,SV160: $i] :
( ( ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ SV244 ) @ SV7 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV244 @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV46 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV160 ) )
= $true )
| ( ( SV160
= ( relation_composition @ SV7 @ SV46 ) )
= $true )
| ( ( relation @ SV160 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1804]) ).
thf(1848,plain,
! [SV7: $i,SV46: $i,SV160: $i] :
( ( ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK9_SY3093 @ SV160 @ SV46 @ SV7 ) ) @ SV7 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV160 )
= $true )
| ( ( SV160
= ( relation_composition @ SV7 @ SV46 ) )
= $true )
| ( ( relation @ SV160 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1805]) ).
thf(1849,plain,
! [SV7: $i,SV46: $i,SV160: $i] :
( ( ( in @ ( ordered_pair @ ( sK9_SY3093 @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV46 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV160 )
= $true )
| ( ( SV160
= ( relation_composition @ SV7 @ SV46 ) )
= $true )
| ( ( relation @ SV160 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1806]) ).
thf(1850,plain,
! [SV161: $i,SV46: $i,SV248: $i,SV7: $i,SV245: $i] :
( ( ( ! [SY3593: $i] :
( ~ ( in @ ( ordered_pair @ SV245 @ SY3593 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SY3593 @ SV248 ) @ SV46 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV245 @ SV248 ) @ SV161 )
= $true )
| ( ( SV161
= ( relation_composition @ SV7 @ SV46 ) )
= $false )
| ( ( relation @ SV161 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1807]) ).
thf(1851,plain,
! [SV7: $i,SV46: $i,SV161: $i,SV249: $i,SV246: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV246 @ SV249 ) @ SV161 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV246 @ ( sK6_F @ SV249 @ SV246 @ SV161 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SV249 @ SV246 @ SV161 @ SV46 @ SV7 ) @ SV249 ) @ SV46 ) ) )
= $true )
| ( ( SV161
= ( relation_composition @ SV7 @ SV46 ) )
= $false )
| ( ( relation @ SV161 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1808]) ).
thf(1852,plain,
! [SV83: $i,SV67: $i,SV11: $i,SV221: $i,SV209: $i,SV186: $i] :
( ( ( SV186
= ( ordered_pair @ SV209 @ SV221 ) )
= $false )
| ( ( in @ SV209 @ SV11 )
= $false )
| ( ( in @ SV221 @ SV67 )
= $false )
| ( ( in @ SV186 @ SV83 )
= $true )
| ( ( SV83
= ( cartesian_product2 @ SV11 @ SV67 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1812]) ).
thf(1853,plain,
! [SV11: $i,SV67: $i,SV83: $i,SV187: $i] :
( ( ( in @ ( sK26_E @ SV187 @ SV83 @ SV67 @ SV11 ) @ SV11 )
= $true )
| ( ( in @ SV187 @ SV83 )
= $false )
| ( ( SV83
= ( cartesian_product2 @ SV11 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1813]) ).
thf(1854,plain,
! [SV11: $i,SV67: $i,SV83: $i,SV187: $i] :
( ( ( in @ ( sK27_SY3103 @ SV187 @ SV83 @ SV67 @ SV11 ) @ SV67 )
= $true )
| ( ( in @ SV187 @ SV83 )
= $false )
| ( ( SV83
= ( cartesian_product2 @ SV11 @ SV67 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1814]) ).
thf(1855,plain,
! [SV14: $i,SV103: $i] :
( ( ( in @ ( sK14_C @ SV103 @ SV14 ) @ SV103 )
= $true )
| ( ( is_connected_in @ SV14 @ SV103 )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1815]) ).
thf(1856,plain,
! [SV14: $i,SV103: $i] :
( ( ( in @ ( sK15_SY3096 @ SV103 @ SV14 ) @ SV103 )
= $true )
| ( ( is_connected_in @ SV14 @ SV103 )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1816]) ).
thf(1857,plain,
! [SV18: $i,SV133: $i,SV108: $i,SV240: $i] :
( ( ( SV240 = SV108 )
= $false )
| ( ( in @ SV240 @ SV133 )
= $false )
| ( ( SV133
= ( fiber @ SV18 @ SV108 ) )
= $false )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1820]) ).
thf(1858,plain,
! [SV135: $i,SV38: $i,SV235: $i,SV21: $i,SV242: $i] :
( ( ( in @ SV242 @ SV21 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV235 @ SV242 ) @ SV38 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV235 @ SV242 ) @ SV135 )
= $true )
| ( ( SV135
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1823]) ).
thf(1859,plain,
! [SV38: $i,SV21: $i,SV135: $i,SV256: $i,SV250: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV250 @ SV256 ) @ SV135 )
| ( in @ SV256 @ SV21 ) )
= $true )
| ( ( SV135
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1824]) ).
thf(1860,plain,
! [SV21: $i,SV38: $i,SV135: $i,SV257: $i,SV251: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV251 @ SV257 ) @ SV135 )
| ( in @ ( ordered_pair @ SV251 @ SV257 ) @ SV38 ) )
= $true )
| ( ( SV135
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1825]) ).
thf(1861,plain,
! [SV137: $i,SV24: $i,SV243: $i,SV118: $i,SV236: $i] :
( ( ( in @ SV236 @ SV118 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV236 @ SV243 ) @ SV24 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV236 @ SV243 ) @ SV137 )
= $true )
| ( ( SV137
= ( relation_dom_restriction @ SV24 @ SV118 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1827]) ).
thf(1862,plain,
! [SV24: $i,SV118: $i,SV137: $i,SV252: $i] :
( ( ( ! [SY3596: $i] :
~ ( in @ ( ordered_pair @ SV252 @ SY3596 ) @ SV137 ) )
= $true )
| ( ( in @ SV252 @ SV118 )
= $true )
| ( ( SV137
= ( relation_dom_restriction @ SV24 @ SV118 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1828]) ).
thf(1863,plain,
! [SV118: $i,SV24: $i,SV137: $i,SV258: $i,SV253: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV253 @ SV258 ) @ SV137 )
| ( in @ ( ordered_pair @ SV253 @ SV258 ) @ SV24 ) )
= $true )
| ( ( SV137
= ( relation_dom_restriction @ SV24 @ SV118 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(1864,plain,
! [SV27: $i,SV120: $i] :
( ( ( in @ ( sK19_C @ SV120 @ SV27 ) @ SV120 )
= $true )
| ( ( is_antisymmetric_in @ SV27 @ SV120 )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1832]) ).
thf(1865,plain,
! [SV27: $i,SV120: $i] :
( ( ( in @ ( sK20_SY3099 @ SV120 @ SV27 ) @ SV120 )
= $true )
| ( ( is_antisymmetric_in @ SV27 @ SV120 )
= $true )
| ( ( relation @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1833]) ).
thf(1866,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( ~ ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
= $true )
| ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1838]) ).
thf(1867,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) ) )
= $false )
| ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1839]) ).
thf(1868,plain,
! [SV59: $i,SV202: $i,SV32: $i] :
( ( ( ~ ! [SY3570: $i,SY3571: $i] :
( ~ ( in @ SY3570 @ ( relation_field @ SV32 ) )
| ~ ( in @ SY3571 @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV202 @ SY3570 ) @ ( apply @ SV202 @ SY3571 ) ) @ SV59 )
| ( in @ ( ordered_pair @ SY3570 @ SY3571 ) @ SV32 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3312: $i] :
( ! [SY3313: $i] :
~ ( in @ ( ordered_pair @ SY3312 @ SY3313 ) @ SV32 )
| ( in @ SY3312 @ ( relation_field @ SV32 ) ) )
| ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV32 )
| ( in @ SY3315 @ ( relation_field @ SV32 ) ) ) )
| ~ ! [SY3576: $i,SY3577: $i] :
( ~ ( in @ ( ordered_pair @ SY3576 @ SY3577 ) @ SV32 )
| ( in @ ( ordered_pair @ ( apply @ SV202 @ SY3576 ) @ ( apply @ SV202 @ SY3577 ) ) @ SV59 ) ) ) )
= $false )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1840]) ).
thf(1869,plain,
! [SV59: $i,SV32: $i,SV254: $i] :
( ( ( ~ ( function @ SV254 )
| ~ ( relation @ SV254 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV32 @ SV59 @ SV254 )
| ( ( relation_dom @ SV254 )
= ( relation_field @ SV32 ) ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1841]) ).
thf(1870,plain,
! [SV59: $i,SV32: $i,SV255: $i] :
( ( ( ~ ( function @ SV255 )
| ~ ( relation @ SV255 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV32 @ SV59 @ SV255 )
| ( ( relation_rng @ SV255 )
= ( relation_field @ SV59 ) ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1842]) ).
thf(1871,plain,
! [SV59: $i,SV32: $i,SV238: $i] :
( ( ( relation @ SV238 )
= $false )
| ( ( function @ SV238 )
= $false )
| ( ( ~ ( relation_isomorphism @ SV32 @ SV59 @ SV238 )
| ( one_to_one @ SV238 ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1843]) ).
thf(1872,plain,
! [SV5: $i,SV100: $i] :
( ( ( ~ ( in @ ( sK3_C @ SV100 @ SV5 ) @ SV100 )
| ~ ( in @ ( sK4_SY3086 @ SV100 @ SV5 ) @ SV100 ) )
= $false )
| ( ( is_transitive_in @ SV5 @ SV100 )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1844]) ).
thf(1873,plain,
! [SV183: $i,SV101: $i,SV5: $i,SV175: $i,SV159: $i] :
( ( ( in @ ( ordered_pair @ SV159 @ SV175 ) @ SV5 )
= $false )
| ( ( in @ SV175 @ SV101 )
= $false )
| ( ( in @ SV159 @ SV101 )
= $false )
| ( ( in @ SV183 @ SV101 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV175 @ SV183 ) @ SV5 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV159 @ SV183 ) @ SV5 )
= $true )
| ( ( is_transitive_in @ SV5 @ SV101 )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1846]) ).
thf(1874,plain,
! [SV7: $i,SV46: $i,SV160: $i,SV244: $i] :
( ( ( in @ ( ordered_pair @ SV244 @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV46 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ SV244 ) @ SV7 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV160 ) )
= $true )
| ( ( SV160
= ( relation_composition @ SV7 @ SV46 ) )
= $true )
| ( ( relation @ SV160 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1847]) ).
thf(1875,plain,
! [SV161: $i,SV46: $i,SV248: $i,SV7: $i,SV259: $i,SV245: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV245 @ SV259 ) @ SV7 )
| ~ ( in @ ( ordered_pair @ SV259 @ SV248 ) @ SV46 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV245 @ SV248 ) @ SV161 )
= $true )
| ( ( SV161
= ( relation_composition @ SV7 @ SV46 ) )
= $false )
| ( ( relation @ SV161 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1850]) ).
thf(1876,plain,
! [SV7: $i,SV46: $i,SV161: $i,SV249: $i,SV246: $i] :
( ( ( in @ ( ordered_pair @ SV246 @ SV249 ) @ SV161 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV246 @ ( sK6_F @ SV249 @ SV246 @ SV161 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SV249 @ SV246 @ SV161 @ SV46 @ SV7 ) @ SV249 ) @ SV46 ) ) )
= $true )
| ( ( SV161
= ( relation_composition @ SV7 @ SV46 ) )
= $false )
| ( ( relation @ SV161 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1851]) ).
thf(1877,plain,
! [SV135: $i,SV21: $i,SV38: $i,SV242: $i,SV235: $i] :
( ( ( in @ ( ordered_pair @ SV235 @ SV242 ) @ SV38 )
= $false )
| ( ( in @ SV242 @ SV21 )
= $false )
| ( ( in @ ( ordered_pair @ SV235 @ SV242 ) @ SV135 )
= $true )
| ( ( SV135
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1858]) ).
thf(1878,plain,
! [SV38: $i,SV21: $i,SV135: $i,SV256: $i,SV250: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV250 @ SV256 ) @ SV135 ) )
= $true )
| ( ( in @ SV256 @ SV21 )
= $true )
| ( ( SV135
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1859]) ).
thf(1879,plain,
! [SV21: $i,SV38: $i,SV135: $i,SV257: $i,SV251: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV251 @ SV257 ) @ SV135 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV251 @ SV257 ) @ SV38 )
= $true )
| ( ( SV135
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1860]) ).
thf(1880,plain,
! [SV137: $i,SV118: $i,SV24: $i,SV243: $i,SV236: $i] :
( ( ( in @ ( ordered_pair @ SV236 @ SV243 ) @ SV24 )
= $false )
| ( ( in @ SV236 @ SV118 )
= $false )
| ( ( in @ ( ordered_pair @ SV236 @ SV243 ) @ SV137 )
= $true )
| ( ( SV137
= ( relation_dom_restriction @ SV24 @ SV118 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1861]) ).
thf(1881,plain,
! [SV24: $i,SV118: $i,SV137: $i,SV260: $i,SV252: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV252 @ SV260 ) @ SV137 ) )
= $true )
| ( ( in @ SV252 @ SV118 )
= $true )
| ( ( SV137
= ( relation_dom_restriction @ SV24 @ SV118 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(1882,plain,
! [SV118: $i,SV24: $i,SV137: $i,SV258: $i,SV253: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV253 @ SV258 ) @ SV137 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV253 @ SV258 ) @ SV24 )
= $true )
| ( ( SV137
= ( relation_dom_restriction @ SV24 @ SV118 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1863]) ).
thf(1883,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( ~ ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ~ ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
= $true )
| ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1866]) ).
thf(1884,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1867]) ).
thf(1885,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) ) )
= $false )
| ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1867]) ).
thf(1886,plain,
! [SV59: $i,SV202: $i,SV32: $i] :
( ( ( ~ ! [SY3570: $i,SY3571: $i] :
( ~ ( in @ SY3570 @ ( relation_field @ SV32 ) )
| ~ ( in @ SY3571 @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV202 @ SY3570 ) @ ( apply @ SV202 @ SY3571 ) ) @ SV59 )
| ( in @ ( ordered_pair @ SY3570 @ SY3571 ) @ SV32 ) ) )
= $false )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1868]) ).
thf(1887,plain,
! [SV59: $i,SV202: $i,SV32: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY3312: $i] :
( ! [SY3313: $i] :
~ ( in @ ( ordered_pair @ SY3312 @ SY3313 ) @ SV32 )
| ( in @ SY3312 @ ( relation_field @ SV32 ) ) )
| ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV32 )
| ( in @ SY3315 @ ( relation_field @ SV32 ) ) ) )
| ~ ! [SY3576: $i,SY3577: $i] :
( ~ ( in @ ( ordered_pair @ SY3576 @ SY3577 ) @ SV32 )
| ( in @ ( ordered_pair @ ( apply @ SV202 @ SY3576 ) @ ( apply @ SV202 @ SY3577 ) ) @ SV59 ) ) ) )
= $false )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1868]) ).
thf(1888,plain,
! [SV59: $i,SV32: $i,SV254: $i] :
( ( ( ~ ( function @ SV254 ) )
= $true )
| ( ( ~ ( relation @ SV254 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV32 @ SV59 @ SV254 )
| ( ( relation_dom @ SV254 )
= ( relation_field @ SV32 ) ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1869]) ).
thf(1889,plain,
! [SV59: $i,SV32: $i,SV255: $i] :
( ( ( ~ ( function @ SV255 ) )
= $true )
| ( ( ~ ( relation @ SV255 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV32 @ SV59 @ SV255 )
| ( ( relation_rng @ SV255 )
= ( relation_field @ SV59 ) ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1870]) ).
thf(1890,plain,
! [SV238: $i,SV59: $i,SV32: $i] :
( ( ( ~ ( relation_isomorphism @ SV32 @ SV59 @ SV238 ) )
= $true )
| ( ( one_to_one @ SV238 )
= $true )
| ( ( function @ SV238 )
= $false )
| ( ( relation @ SV238 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1871]) ).
thf(1891,plain,
! [SV5: $i,SV100: $i] :
( ( ( ~ ( in @ ( sK3_C @ SV100 @ SV5 ) @ SV100 ) )
= $false )
| ( ( is_transitive_in @ SV5 @ SV100 )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1872]) ).
thf(1892,plain,
! [SV5: $i,SV100: $i] :
( ( ( ~ ( in @ ( sK4_SY3086 @ SV100 @ SV5 ) @ SV100 ) )
= $false )
| ( ( is_transitive_in @ SV5 @ SV100 )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1872]) ).
thf(1893,plain,
! [SV159: $i,SV101: $i,SV5: $i,SV183: $i,SV175: $i] :
( ( ( in @ ( ordered_pair @ SV175 @ SV183 ) @ SV5 )
= $false )
| ( ( in @ SV183 @ SV101 )
= $false )
| ( ( in @ SV159 @ SV101 )
= $false )
| ( ( in @ SV175 @ SV101 )
= $false )
| ( ( in @ ( ordered_pair @ SV159 @ SV175 ) @ SV5 )
= $false )
| ( ( in @ ( ordered_pair @ SV159 @ SV183 ) @ SV5 )
= $true )
| ( ( is_transitive_in @ SV5 @ SV101 )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1873]) ).
thf(1894,plain,
! [SV244: $i,SV7: $i,SV46: $i,SV160: $i] :
( ( ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV160 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK7_D @ SV160 @ SV46 @ SV7 ) @ SV244 ) @ SV7 )
= $false )
| ( ( in @ ( ordered_pair @ SV244 @ ( sK8_SY3089 @ SV160 @ SV46 @ SV7 ) ) @ SV46 )
= $false )
| ( ( SV160
= ( relation_composition @ SV7 @ SV46 ) )
= $true )
| ( ( relation @ SV160 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1874]) ).
thf(1895,plain,
! [SV161: $i,SV46: $i,SV248: $i,SV7: $i,SV259: $i,SV245: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV245 @ SV259 ) @ SV7 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV259 @ SV248 ) @ SV46 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV245 @ SV248 ) @ SV161 )
= $true )
| ( ( SV161
= ( relation_composition @ SV7 @ SV46 ) )
= $false )
| ( ( relation @ SV161 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1875]) ).
thf(1896,plain,
! [SV7: $i,SV46: $i,SV161: $i,SV249: $i,SV246: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV246 @ ( sK6_F @ SV249 @ SV246 @ SV161 @ SV46 @ SV7 ) ) @ SV7 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SV249 @ SV246 @ SV161 @ SV46 @ SV7 ) @ SV249 ) @ SV46 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV246 @ SV249 ) @ SV161 )
= $false )
| ( ( SV161
= ( relation_composition @ SV7 @ SV46 ) )
= $false )
| ( ( relation @ SV161 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1876]) ).
thf(1897,plain,
! [SV38: $i,SV21: $i,SV135: $i,SV256: $i,SV250: $i] :
( ( ( in @ ( ordered_pair @ SV250 @ SV256 ) @ SV135 )
= $false )
| ( ( in @ SV256 @ SV21 )
= $true )
| ( ( SV135
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1878]) ).
thf(1898,plain,
! [SV21: $i,SV38: $i,SV135: $i,SV257: $i,SV251: $i] :
( ( ( in @ ( ordered_pair @ SV251 @ SV257 ) @ SV135 )
= $false )
| ( ( in @ ( ordered_pair @ SV251 @ SV257 ) @ SV38 )
= $true )
| ( ( SV135
= ( relation_rng_restriction @ SV21 @ SV38 ) )
= $false )
| ( ( relation @ SV135 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1879]) ).
thf(1899,plain,
! [SV24: $i,SV118: $i,SV137: $i,SV260: $i,SV252: $i] :
( ( ( in @ ( ordered_pair @ SV252 @ SV260 ) @ SV137 )
= $false )
| ( ( in @ SV252 @ SV118 )
= $true )
| ( ( SV137
= ( relation_dom_restriction @ SV24 @ SV118 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1881]) ).
thf(1900,plain,
! [SV118: $i,SV24: $i,SV137: $i,SV258: $i,SV253: $i] :
( ( ( in @ ( ordered_pair @ SV253 @ SV258 ) @ SV137 )
= $false )
| ( ( in @ ( ordered_pair @ SV253 @ SV258 ) @ SV24 )
= $true )
| ( ( SV137
= ( relation_dom_restriction @ SV24 @ SV118 ) )
= $false )
| ( ( relation @ SV137 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1882]) ).
thf(1901,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( ~ ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) ) )
= $true )
| ( ( ~ ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
= $true )
| ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1883]) ).
thf(1902,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1884]) ).
thf(1903,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
= $true )
| ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1885]) ).
thf(1904,plain,
! [SV59: $i,SV202: $i,SV32: $i] :
( ( ( ! [SY3570: $i,SY3571: $i] :
( ~ ( in @ SY3570 @ ( relation_field @ SV32 ) )
| ~ ( in @ SY3571 @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV202 @ SY3570 ) @ ( apply @ SV202 @ SY3571 ) ) @ SV59 )
| ( in @ ( ordered_pair @ SY3570 @ SY3571 ) @ SV32 ) ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1886]) ).
thf(1905,plain,
! [SV59: $i,SV202: $i,SV32: $i] :
( ( ( ~ ( ~ ~ ( ~ ! [SY3312: $i] :
( ! [SY3313: $i] :
~ ( in @ ( ordered_pair @ SY3312 @ SY3313 ) @ SV32 )
| ( in @ SY3312 @ ( relation_field @ SV32 ) ) )
| ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV32 )
| ( in @ SY3315 @ ( relation_field @ SV32 ) ) ) )
| ~ ! [SY3576: $i,SY3577: $i] :
( ~ ( in @ ( ordered_pair @ SY3576 @ SY3577 ) @ SV32 )
| ( in @ ( ordered_pair @ ( apply @ SV202 @ SY3576 ) @ ( apply @ SV202 @ SY3577 ) ) @ SV59 ) ) ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1887]) ).
thf(1906,plain,
! [SV59: $i,SV32: $i,SV254: $i] :
( ( ( function @ SV254 )
= $false )
| ( ( ~ ( relation @ SV254 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV32 @ SV59 @ SV254 )
| ( ( relation_dom @ SV254 )
= ( relation_field @ SV32 ) ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1888]) ).
thf(1907,plain,
! [SV59: $i,SV32: $i,SV255: $i] :
( ( ( function @ SV255 )
= $false )
| ( ( ~ ( relation @ SV255 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV32 @ SV59 @ SV255 )
| ( ( relation_rng @ SV255 )
= ( relation_field @ SV59 ) ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1889]) ).
thf(1908,plain,
! [SV238: $i,SV59: $i,SV32: $i] :
( ( ( relation_isomorphism @ SV32 @ SV59 @ SV238 )
= $false )
| ( ( one_to_one @ SV238 )
= $true )
| ( ( function @ SV238 )
= $false )
| ( ( relation @ SV238 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1890]) ).
thf(1909,plain,
! [SV5: $i,SV100: $i] :
( ( ( in @ ( sK3_C @ SV100 @ SV5 ) @ SV100 )
= $true )
| ( ( is_transitive_in @ SV5 @ SV100 )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1891]) ).
thf(1910,plain,
! [SV5: $i,SV100: $i] :
( ( ( in @ ( sK4_SY3086 @ SV100 @ SV5 ) @ SV100 )
= $true )
| ( ( is_transitive_in @ SV5 @ SV100 )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1892]) ).
thf(1911,plain,
! [SV161: $i,SV46: $i,SV248: $i,SV7: $i,SV259: $i,SV245: $i] :
( ( ( in @ ( ordered_pair @ SV245 @ SV259 ) @ SV7 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV259 @ SV248 ) @ SV46 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV245 @ SV248 ) @ SV161 )
= $true )
| ( ( SV161
= ( relation_composition @ SV7 @ SV46 ) )
= $false )
| ( ( relation @ SV161 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1895]) ).
thf(1912,plain,
! [SV7: $i,SV46: $i,SV161: $i,SV249: $i,SV246: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV246 @ ( sK6_F @ SV249 @ SV246 @ SV161 @ SV46 @ SV7 ) ) @ SV7 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV246 @ SV249 ) @ SV161 )
= $false )
| ( ( SV161
= ( relation_composition @ SV7 @ SV46 ) )
= $false )
| ( ( relation @ SV161 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1896]) ).
thf(1913,plain,
! [SV7: $i,SV46: $i,SV161: $i,SV246: $i,SV249: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK6_F @ SV249 @ SV246 @ SV161 @ SV46 @ SV7 ) @ SV249 ) @ SV46 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV246 @ SV249 ) @ SV161 )
= $false )
| ( ( SV161
= ( relation_composition @ SV7 @ SV46 ) )
= $false )
| ( ( relation @ SV161 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1896]) ).
thf(1914,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
= $false )
| ( ( ~ ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
= $true )
| ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1901]) ).
thf(1915,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( ~ ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) ) )
= $false )
| ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1902]) ).
thf(1916,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 )
= $true )
| ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1903]) ).
thf(1917,plain,
! [SV59: $i,SV202: $i,SV32: $i,SV261: $i] :
( ( ( ! [SY3598: $i] :
( ~ ( in @ SV261 @ ( relation_field @ SV32 ) )
| ~ ( in @ SY3598 @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV202 @ SV261 ) @ ( apply @ SV202 @ SY3598 ) ) @ SV59 )
| ( in @ ( ordered_pair @ SV261 @ SY3598 ) @ SV32 ) ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1904]) ).
thf(1918,plain,
! [SV59: $i,SV202: $i,SV32: $i] :
( ( ( ~ ~ ( ~ ! [SY3312: $i] :
( ! [SY3313: $i] :
~ ( in @ ( ordered_pair @ SY3312 @ SY3313 ) @ SV32 )
| ( in @ SY3312 @ ( relation_field @ SV32 ) ) )
| ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV32 )
| ( in @ SY3315 @ ( relation_field @ SV32 ) ) ) )
| ~ ! [SY3576: $i,SY3577: $i] :
( ~ ( in @ ( ordered_pair @ SY3576 @ SY3577 ) @ SV32 )
| ( in @ ( ordered_pair @ ( apply @ SV202 @ SY3576 ) @ ( apply @ SV202 @ SY3577 ) ) @ SV59 ) ) )
= $false )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1905]) ).
thf(1919,plain,
! [SV59: $i,SV32: $i,SV254: $i] :
( ( ( relation @ SV254 )
= $false )
| ( ( function @ SV254 )
= $false )
| ( ( ~ ( relation_isomorphism @ SV32 @ SV59 @ SV254 )
| ( ( relation_dom @ SV254 )
= ( relation_field @ SV32 ) ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1906]) ).
thf(1920,plain,
! [SV59: $i,SV32: $i,SV255: $i] :
( ( ( relation @ SV255 )
= $false )
| ( ( function @ SV255 )
= $false )
| ( ( ~ ( relation_isomorphism @ SV32 @ SV59 @ SV255 )
| ( ( relation_rng @ SV255 )
= ( relation_field @ SV59 ) ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1907]) ).
thf(1921,plain,
! [SV161: $i,SV7: $i,SV245: $i,SV46: $i,SV248: $i,SV259: $i] :
( ( ( in @ ( ordered_pair @ SV259 @ SV248 ) @ SV46 )
= $false )
| ( ( in @ ( ordered_pair @ SV245 @ SV259 ) @ SV7 )
= $false )
| ( ( in @ ( ordered_pair @ SV245 @ SV248 ) @ SV161 )
= $true )
| ( ( SV161
= ( relation_composition @ SV7 @ SV46 ) )
= $false )
| ( ( relation @ SV161 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1911]) ).
thf(1922,plain,
! [SV7: $i,SV46: $i,SV161: $i,SV249: $i,SV246: $i] :
( ( ( in @ ( ordered_pair @ SV246 @ ( sK6_F @ SV249 @ SV246 @ SV161 @ SV46 @ SV7 ) ) @ SV7 )
= $true )
| ( ( in @ ( ordered_pair @ SV246 @ SV249 ) @ SV161 )
= $false )
| ( ( SV161
= ( relation_composition @ SV7 @ SV46 ) )
= $false )
| ( ( relation @ SV161 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1912]) ).
thf(1923,plain,
! [SV7: $i,SV46: $i,SV161: $i,SV246: $i,SV249: $i] :
( ( ( in @ ( ordered_pair @ ( sK6_F @ SV249 @ SV246 @ SV161 @ SV46 @ SV7 ) @ SV249 ) @ SV46 )
= $true )
| ( ( in @ ( ordered_pair @ SV246 @ SV249 ) @ SV161 )
= $false )
| ( ( SV161
= ( relation_composition @ SV7 @ SV46 ) )
= $false )
| ( ( relation @ SV161 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1913]) ).
thf(1924,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
= $false )
| ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
= $true )
| ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1914]) ).
thf(1925,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( ~ ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) ) )
= $false )
| ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1915]) ).
thf(1926,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( ~ ( ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) ) )
= $false )
| ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1915]) ).
thf(1927,plain,
! [SV59: $i,SV32: $i,SV174: $i] :
( ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1916]) ).
thf(1928,plain,
! [SV59: $i,SV202: $i,SV262: $i,SV32: $i,SV261: $i] :
( ( ( ~ ( in @ SV261 @ ( relation_field @ SV32 ) )
| ~ ( in @ SV262 @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV202 @ SV261 ) @ ( apply @ SV202 @ SV262 ) ) @ SV59 )
| ( in @ ( ordered_pair @ SV261 @ SV262 ) @ SV32 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(1929,plain,
! [SV202: $i,SV59: $i,SV32: $i] :
( ( ( ~ ~ ( ~ ! [SY3312: $i] :
( ! [SY3313: $i] :
~ ( in @ ( ordered_pair @ SY3312 @ SY3313 ) @ SV32 )
| ( in @ SY3312 @ ( relation_field @ SV32 ) ) )
| ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV32 )
| ( in @ SY3315 @ ( relation_field @ SV32 ) ) ) ) )
= $false )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1918]) ).
thf(1930,plain,
! [SV59: $i,SV202: $i,SV32: $i] :
( ( ( ~ ! [SY3576: $i,SY3577: $i] :
( ~ ( in @ ( ordered_pair @ SY3576 @ SY3577 ) @ SV32 )
| ( in @ ( ordered_pair @ ( apply @ SV202 @ SY3576 ) @ ( apply @ SV202 @ SY3577 ) ) @ SV59 ) ) )
= $false )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1918]) ).
thf(1931,plain,
! [SV254: $i,SV59: $i,SV32: $i] :
( ( ( ~ ( relation_isomorphism @ SV32 @ SV59 @ SV254 ) )
= $true )
| ( ( ( relation_dom @ SV254 )
= ( relation_field @ SV32 ) )
= $true )
| ( ( function @ SV254 )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1919]) ).
thf(1932,plain,
! [SV255: $i,SV59: $i,SV32: $i] :
( ( ( ~ ( relation_isomorphism @ SV32 @ SV59 @ SV255 ) )
= $true )
| ( ( ( relation_rng @ SV255 )
= ( relation_field @ SV59 ) )
= $true )
| ( ( function @ SV255 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1920]) ).
thf(1933,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
= $false )
| ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
= $false )
| ( ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
= $true )
| ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1924]) ).
thf(1934,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
= $true )
| ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1925]) ).
thf(1935,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 ) )
= $true )
| ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1926]) ).
thf(1936,plain,
! [SV59: $i,SV32: $i,SV174: $i] :
( ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) ) )
= $true )
| ( ( ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1927]) ).
thf(1937,plain,
! [SV59: $i,SV202: $i,SV262: $i,SV32: $i,SV261: $i] :
( ( ( ~ ( in @ SV261 @ ( relation_field @ SV32 ) )
| ~ ( in @ SV262 @ ( relation_field @ SV32 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV202 @ SV261 ) @ ( apply @ SV202 @ SV262 ) ) @ SV59 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV261 @ SV262 ) @ SV32 )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1928]) ).
thf(1938,plain,
! [SV202: $i,SV59: $i,SV32: $i] :
( ( ( ~ ( ~ ! [SY3312: $i] :
( ! [SY3313: $i] :
~ ( in @ ( ordered_pair @ SY3312 @ SY3313 ) @ SV32 )
| ( in @ SY3312 @ ( relation_field @ SV32 ) ) )
| ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV32 )
| ( in @ SY3315 @ ( relation_field @ SV32 ) ) ) ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1929]) ).
thf(1939,plain,
! [SV59: $i,SV202: $i,SV32: $i] :
( ( ( ! [SY3576: $i,SY3577: $i] :
( ~ ( in @ ( ordered_pair @ SY3576 @ SY3577 ) @ SV32 )
| ( in @ ( ordered_pair @ ( apply @ SV202 @ SY3576 ) @ ( apply @ SV202 @ SY3577 ) ) @ SV59 ) ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1930]) ).
thf(1940,plain,
! [SV254: $i,SV59: $i,SV32: $i] :
( ( ( relation_isomorphism @ SV32 @ SV59 @ SV254 )
= $false )
| ( ( ( relation_dom @ SV254 )
= ( relation_field @ SV32 ) )
= $true )
| ( ( function @ SV254 )
= $false )
| ( ( relation @ SV254 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1931]) ).
thf(1941,plain,
! [SV255: $i,SV59: $i,SV32: $i] :
( ( ( relation_isomorphism @ SV32 @ SV59 @ SV255 )
= $false )
| ( ( ( relation_rng @ SV255 )
= ( relation_field @ SV59 ) )
= $true )
| ( ( function @ SV255 )
= $false )
| ( ( relation @ SV255 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1932]) ).
thf(1942,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 )
= $false )
| ( ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
= $false )
| ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
= $false )
| ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1933]) ).
thf(1943,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 )
= $true )
| ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1934]) ).
thf(1944,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 )
= $true )
| ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) )
| ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1935]) ).
thf(1945,plain,
! [SV59: $i,SV32: $i,SV174: $i] :
( ( ( ( relation_dom @ SV174 )
= ( relation_field @ SV32 ) )
= $false )
| ( ( ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1936]) ).
thf(1946,plain,
! [SV59: $i,SV202: $i,SV262: $i,SV32: $i,SV261: $i] :
( ( ( ~ ( in @ SV261 @ ( relation_field @ SV32 ) )
| ~ ( in @ SV262 @ ( relation_field @ SV32 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV202 @ SV261 ) @ ( apply @ SV202 @ SV262 ) ) @ SV59 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV261 @ SV262 ) @ SV32 )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1937]) ).
thf(1947,plain,
! [SV202: $i,SV59: $i,SV32: $i] :
( ( ( ~ ! [SY3312: $i] :
( ! [SY3313: $i] :
~ ( in @ ( ordered_pair @ SY3312 @ SY3313 ) @ SV32 )
| ( in @ SY3312 @ ( relation_field @ SV32 ) ) )
| ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV32 )
| ( in @ SY3315 @ ( relation_field @ SV32 ) ) ) )
= $false )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1938]) ).
thf(1948,plain,
! [SV59: $i,SV202: $i,SV32: $i,SV263: $i] :
( ( ( ! [SY3599: $i] :
( ~ ( in @ ( ordered_pair @ SV263 @ SY3599 ) @ SV32 )
| ( in @ ( ordered_pair @ ( apply @ SV202 @ SV263 ) @ ( apply @ SV202 @ SY3599 ) ) @ SV59 ) ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1939]) ).
thf(1949,plain,
! [SV59: $i,SV32: $i,SV174: $i] :
( ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
= $false )
| ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
= $false )
| ( ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 )
= $false )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1942]) ).
thf(1950,plain,
! [SV59: $i,SV32: $i,SV174: $i] :
( ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 )
= $true )
| ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1943]) ).
thf(1951,plain,
! [SV59: $i,SV32: $i,SV174: $i] :
( ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) )
| ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 )
= $true )
| ( ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1944]) ).
thf(1952,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( ( relation_rng @ SV174 )
= ( relation_field @ SV59 ) )
= $false )
| ( ( ( relation_dom @ SV174 )
= ( relation_field @ SV32 ) )
= $false )
| ( ( ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1945]) ).
thf(1953,plain,
! [SV59: $i,SV202: $i,SV262: $i,SV32: $i,SV261: $i] :
( ( ( ~ ( in @ SV261 @ ( relation_field @ SV32 ) ) )
= $true )
| ( ( ~ ( in @ SV262 @ ( relation_field @ SV32 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV202 @ SV261 ) @ ( apply @ SV202 @ SV262 ) ) @ SV59 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV261 @ SV262 ) @ SV32 )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1946]) ).
thf(1954,plain,
! [SV202: $i,SV59: $i,SV32: $i] :
( ( ( ~ ! [SY3312: $i] :
( ! [SY3313: $i] :
~ ( in @ ( ordered_pair @ SY3312 @ SY3313 ) @ SV32 )
| ( in @ SY3312 @ ( relation_field @ SV32 ) ) ) )
= $false )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1947]) ).
thf(1955,plain,
! [SV202: $i,SV59: $i,SV32: $i] :
( ( ( ~ ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV32 )
| ( in @ SY3315 @ ( relation_field @ SV32 ) ) ) )
= $false )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1947]) ).
thf(1956,plain,
! [SV59: $i,SV202: $i,SV32: $i,SV264: $i,SV263: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV263 @ SV264 ) @ SV32 )
| ( in @ ( ordered_pair @ ( apply @ SV202 @ SV263 ) @ ( apply @ SV202 @ SV264 ) ) @ SV59 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1948]) ).
thf(1957,plain,
! [SV59: $i,SV32: $i,SV174: $i] :
( ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) ) )
= $true )
| ( ( ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
= $false )
| ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
= $false )
| ( ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 )
= $false )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1949]) ).
thf(1958,plain,
! [SV59: $i,SV32: $i,SV174: $i] :
( ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) ) )
= $true )
| ( ( ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 )
= $true )
| ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1950]) ).
thf(1959,plain,
! [SV59: $i,SV32: $i,SV174: $i] :
( ( ( ( ( relation_dom @ SV174 )
!= ( relation_field @ SV32 ) ) )
= $true )
| ( ( ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 )
= $true )
| ( ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1951]) ).
thf(1960,plain,
! [SV59: $i,SV32: $i,SV174: $i] :
( ( ( one_to_one @ SV174 )
= $false )
| ( ( ( relation_dom @ SV174 )
= ( relation_field @ SV32 ) )
= $false )
| ( ( ( relation_rng @ SV174 )
= ( relation_field @ SV59 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1952]) ).
thf(1961,plain,
! [SV59: $i,SV202: $i,SV262: $i,SV32: $i,SV261: $i] :
( ( ( in @ SV261 @ ( relation_field @ SV32 ) )
= $false )
| ( ( ~ ( in @ SV262 @ ( relation_field @ SV32 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV202 @ SV261 ) @ ( apply @ SV202 @ SV262 ) ) @ SV59 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV261 @ SV262 ) @ SV32 )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1953]) ).
thf(1962,plain,
! [SV202: $i,SV59: $i,SV32: $i] :
( ( ( ! [SY3312: $i] :
( ! [SY3313: $i] :
~ ( in @ ( ordered_pair @ SY3312 @ SY3313 ) @ SV32 )
| ( in @ SY3312 @ ( relation_field @ SV32 ) ) ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1954]) ).
thf(1963,plain,
! [SV202: $i,SV59: $i,SV32: $i] :
( ( ( ! [SY3314: $i,SY3315: $i] :
( ~ ( in @ ( ordered_pair @ SY3314 @ SY3315 ) @ SV32 )
| ( in @ SY3315 @ ( relation_field @ SV32 ) ) ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1955]) ).
thf(1964,plain,
! [SV59: $i,SV202: $i,SV32: $i,SV264: $i,SV263: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV263 @ SV264 ) @ SV32 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV202 @ SV263 ) @ ( apply @ SV202 @ SV264 ) ) @ SV59 )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1956]) ).
thf(1965,plain,
! [SV59: $i,SV32: $i,SV174: $i] :
( ( ( ( relation_dom @ SV174 )
= ( relation_field @ SV32 ) )
= $false )
| ( ( ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
= $false )
| ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
= $false )
| ( ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 )
= $false )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1957]) ).
thf(1966,plain,
! [SV59: $i,SV32: $i,SV174: $i] :
( ( ( ( relation_dom @ SV174 )
= ( relation_field @ SV32 ) )
= $false )
| ( ( ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 )
= $true )
| ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1958]) ).
thf(1967,plain,
! [SV59: $i,SV32: $i,SV174: $i] :
( ( ( ( relation_dom @ SV174 )
= ( relation_field @ SV32 ) )
= $false )
| ( ( ( ( relation_rng @ SV174 )
!= ( relation_field @ SV59 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 )
= $true )
| ( ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1959]) ).
thf(1968,plain,
! [SV59: $i,SV202: $i,SV261: $i,SV32: $i,SV262: $i] :
( ( ( in @ SV262 @ ( relation_field @ SV32 ) )
= $false )
| ( ( in @ SV261 @ ( relation_field @ SV32 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV202 @ SV261 ) @ ( apply @ SV202 @ SV262 ) ) @ SV59 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV261 @ SV262 ) @ SV32 )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1961]) ).
thf(1969,plain,
! [SV202: $i,SV59: $i,SV32: $i,SV265: $i] :
( ( ( ! [SY3600: $i] :
~ ( in @ ( ordered_pair @ SV265 @ SY3600 ) @ SV32 )
| ( in @ SV265 @ ( relation_field @ SV32 ) ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(1970,plain,
! [SV202: $i,SV59: $i,SV32: $i,SV266: $i] :
( ( ( ! [SY3601: $i] :
( ~ ( in @ ( ordered_pair @ SV266 @ SY3601 ) @ SV32 )
| ( in @ SY3601 @ ( relation_field @ SV32 ) ) ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1963]) ).
thf(1971,plain,
! [SV59: $i,SV202: $i,SV32: $i,SV264: $i,SV263: $i] :
( ( ( in @ ( ordered_pair @ SV263 @ SV264 ) @ SV32 )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV202 @ SV263 ) @ ( apply @ SV202 @ SV264 ) ) @ SV59 )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1964]) ).
thf(1972,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( ( relation_rng @ SV174 )
= ( relation_field @ SV59 ) )
= $false )
| ( ( ( relation_dom @ SV174 )
= ( relation_field @ SV32 ) )
= $false )
| ( ( ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
= $false )
| ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
= $false )
| ( ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 )
= $false )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1965]) ).
thf(1973,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( ( relation_rng @ SV174 )
= ( relation_field @ SV59 ) )
= $false )
| ( ( ( relation_dom @ SV174 )
= ( relation_field @ SV32 ) )
= $false )
| ( ( ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 )
= $true )
| ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1966]) ).
thf(1974,plain,
! [SV32: $i,SV59: $i,SV174: $i] :
( ( ( ( relation_rng @ SV174 )
= ( relation_field @ SV59 ) )
= $false )
| ( ( ( relation_dom @ SV174 )
= ( relation_field @ SV32 ) )
= $false )
| ( ( ~ ( one_to_one @ SV174 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 )
= $true )
| ( ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1967]) ).
thf(1975,plain,
! [SV32: $i,SV59: $i,SV262: $i,SV261: $i,SV202: $i] :
( ( ( in @ ( ordered_pair @ ( apply @ SV202 @ SV261 ) @ ( apply @ SV202 @ SV262 ) ) @ SV59 )
= $false )
| ( ( in @ SV261 @ ( relation_field @ SV32 ) )
= $false )
| ( ( in @ SV262 @ ( relation_field @ SV32 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV261 @ SV262 ) @ SV32 )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1968]) ).
thf(1976,plain,
! [SV202: $i,SV59: $i,SV32: $i,SV265: $i] :
( ( ( ! [SY3600: $i] :
~ ( in @ ( ordered_pair @ SV265 @ SY3600 ) @ SV32 ) )
= $true )
| ( ( in @ SV265 @ ( relation_field @ SV32 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1969]) ).
thf(1977,plain,
! [SV202: $i,SV59: $i,SV32: $i,SV267: $i,SV266: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV266 @ SV267 ) @ SV32 )
| ( in @ SV267 @ ( relation_field @ SV32 ) ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(1978,plain,
! [SV59: $i,SV32: $i,SV174: $i] :
( ( ( one_to_one @ SV174 )
= $false )
| ( ( ( relation_dom @ SV174 )
= ( relation_field @ SV32 ) )
= $false )
| ( ( ( relation_rng @ SV174 )
= ( relation_field @ SV59 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV174 @ ( sK10_D @ SV174 @ SV59 @ SV32 ) ) @ ( apply @ SV174 @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) ) @ SV59 )
= $false )
| ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
= $false )
| ( ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 )
= $false )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1972]) ).
thf(1979,plain,
! [SV59: $i,SV32: $i,SV174: $i] :
( ( ( one_to_one @ SV174 )
= $false )
| ( ( ( relation_dom @ SV174 )
= ( relation_field @ SV32 ) )
= $false )
| ( ( ( relation_rng @ SV174 )
= ( relation_field @ SV59 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 )
= $true )
| ( ( in @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1973]) ).
thf(1980,plain,
! [SV59: $i,SV32: $i,SV174: $i] :
( ( ( one_to_one @ SV174 )
= $false )
| ( ( ( relation_dom @ SV174 )
= ( relation_field @ SV32 ) )
= $false )
| ( ( ( relation_rng @ SV174 )
= ( relation_field @ SV59 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV174 @ SV59 @ SV32 ) @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) ) @ SV32 )
= $true )
| ( ( in @ ( sK11_SY3094 @ SV174 @ SV59 @ SV32 ) @ ( relation_field @ SV32 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV174 )
= $true )
| ( ( function @ SV174 )
= $false )
| ( ( relation @ SV174 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1974]) ).
thf(1981,plain,
! [SV202: $i,SV59: $i,SV32: $i,SV268: $i,SV265: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV265 @ SV268 ) @ SV32 ) )
= $true )
| ( ( in @ SV265 @ ( relation_field @ SV32 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1976]) ).
thf(1982,plain,
! [SV202: $i,SV59: $i,SV32: $i,SV267: $i,SV266: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV266 @ SV267 ) @ SV32 ) )
= $true )
| ( ( in @ SV267 @ ( relation_field @ SV32 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1977]) ).
thf(1983,plain,
! [SV202: $i,SV59: $i,SV32: $i,SV268: $i,SV265: $i] :
( ( ( in @ ( ordered_pair @ SV265 @ SV268 ) @ SV32 )
= $false )
| ( ( in @ SV265 @ ( relation_field @ SV32 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1981]) ).
thf(1984,plain,
! [SV202: $i,SV59: $i,SV32: $i,SV267: $i,SV266: $i] :
( ( ( in @ ( ordered_pair @ SV266 @ SV267 ) @ SV32 )
= $false )
| ( ( in @ SV267 @ ( relation_field @ SV32 ) )
= $true )
| ( ( relation_isomorphism @ SV32 @ SV59 @ SV202 )
= $false )
| ( ( function @ SV202 )
= $false )
| ( ( relation @ SV202 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1982]) ).
thf(1985,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[510,1984,1983,1980,1979,1978,1975,1971,1960,1941,1940,1923,1922,1921,1910,1909,1908,1900,1899,1898,1897,1894,1893,1880,1877,1865,1864,1857,1856,1855,1854,1853,1852,1849,1848,1845,1837,1836,1835,1834,1831,1830,1826,1822,1821,1819,1818,1817,1811,1810,1809,1791,1783,1782,1777,1776,1774,1773,1767,1765,1759,1752,1751,1741,1738,1737,1736,1719,1718,1714,1711,1708,1707,1697,1693,1686,1685,1680,1677,1676,1668,1660,1656,1654,1651,1650,1648,1647,1637,1636,1632,1622,1621,1619,1609,1595,1594,1592,1578,1577,1569,1567,1565,1558,1557,1553,1552,1539,1528,1525,1514,1504,1495,1494,1483,1480,1475,1474,1472,1463,1461,1457,1452,1442,1441,1425,1406,1405,1400,1392,1386,1381,1378,1370,1359,1356,1347,1346,1342,1341,1339,1323,1316,1315,1296,1271,1268,1253,1252,1246,1244,1240,1235,1215,1207,1170,1160,1159,1158,1105,1104,1050,1049,998,919,647,595,549]) ).
thf(1986,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( sK69_B @ A ) @ ( relation_field @ A ) )
& ~ ( in @ ( ordered_pair @ ( sK69_B @ A ) @ ( sK69_B @ A ) ) @ A ) )
| ( reflexive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( reflexive @ A )
| ! [B: $i] :
( ~ ( in @ B @ ( relation_field @ A ) )
| ( in @ ( ordered_pair @ B @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[428]) ).
thf(1987,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( ordered_pair @ ( sK66_B @ A ) @ ( sK67_SY3127 @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK67_SY3127 @ A ) @ ( sK68_SY3129 @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK66_B @ A ) @ ( sK68_SY3129 @ A ) ) @ A ) )
| ( transitive @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( transitive @ A )
| ! [B: $i,C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ B @ C ) @ A )
| ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ ( ordered_pair @ B @ D ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[427]) ).
thf(1988,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( in @ ( ordered_pair @ ( sK64_B @ A ) @ ( sK65_SY3126 @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK65_SY3126 @ A ) @ ( sK64_B @ A ) ) @ A )
& ( ( sK64_B @ A )
!= ( sK65_SY3126 @ A ) ) )
| ( antisymmetric @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( antisymmetric @ A )
| ! [B: $i,C: $i] :
( ~ ( in @ ( ordered_pair @ B @ C ) @ A )
| ~ ( in @ ( ordered_pair @ C @ B ) @ A )
| ( B = C ) ) ) )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(1989,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ( ( sK62_B @ A )
!= ( sK63_SY3125 @ A ) )
& ( in @ ( sK62_B @ A ) @ ( relation_field @ A ) )
& ( in @ ( sK63_SY3125 @ A ) @ ( relation_field @ A ) )
& ~ ( in @ ( ordered_pair @ ( sK62_B @ A ) @ ( sK63_SY3125 @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK63_SY3125 @ A ) @ ( sK62_B @ A ) ) @ A ) )
| ( connected @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ~ ( connected @ A )
| ! [B: $i,C: $i] :
( ( B = C )
| ~ ( in @ B @ ( relation_field @ A ) )
| ~ ( in @ C @ ( relation_field @ A ) )
| ( in @ ( ordered_pair @ B @ C ) @ A )
| ( in @ ( ordered_pair @ C @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[425]) ).
thf(1990,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)],[424]) ).
thf(1991,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)],[423]) ).
thf(1992,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ! [D: $i] :
( ~ ( in @ D @ ( relation_dom @ C ) )
| ~ ( in @ ( ordered_pair @ D @ A ) @ C )
| ~ ( in @ D @ B ) )
| ( in @ A @ ( relation_image @ C @ B ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_image @ C @ B ) )
| ( ( in @ ( sK61_D @ C @ B @ A ) @ ( relation_dom @ C ) )
& ( in @ ( ordered_pair @ ( sK61_D @ C @ B @ A ) @ A ) @ C )
& ( in @ ( sK61_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(1993,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ! [D: $i] :
( ~ ( in @ D @ ( relation_rng @ C ) )
| ~ ( in @ ( ordered_pair @ A @ D ) @ C )
| ~ ( in @ D @ B ) )
| ( in @ A @ ( relation_inverse_image @ C @ B ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ A @ ( relation_inverse_image @ C @ B ) )
| ( ( in @ ( sK60_D @ C @ B @ A ) @ ( relation_rng @ C ) )
& ( in @ ( ordered_pair @ A @ ( sK60_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK60_D @ C @ B @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(1994,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ A @ ( relation_dom @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ B @ ( relation_rng @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(1995,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ B @ A )
| ( ! [SY3124: $i] :
~ ( in @ ( ordered_pair @ ( sK59_D @ C @ B @ A ) @ SY3124 ) @ C )
& ( in @ ( sK59_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 @ ( sK58_E @ D @ C @ B @ A ) ) @ C )
| ~ ( in @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(1996,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( ! [SY3123: $i] :
~ ( in @ ( ordered_pair @ SY3123 @ ( sK57_D @ C @ B @ A ) ) @ C )
& ( in @ ( sK57_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 @ ( sK56_E @ D @ C @ B @ A ) @ D ) @ C )
| ~ ( in @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[418]) ).
thf(1997,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ A @ ( relation_field @ C ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ B @ ( relation_field @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(1998,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ( ordered_pair @ A @ B )
!= ( ordered_pair @ C @ D ) )
| ( A = C ) )
& ! [C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
!= ( ordered_pair @ C @ D ) )
| ( B = D ) ) ) )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(1999,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( in @ ( ordered_pair @ ( sK54_B @ A ) @ ( sK55_SY3122 @ A ) ) @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(2000,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ~ ( relation @ D )
| ~ ( in @ A @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( relation_composition @ ( identity_relation @ C ) @ D ) ) )
& ! [C: $i,D: $i] :
( ~ ( relation @ D )
| ~ ( in @ ( ordered_pair @ A @ B ) @ ( relation_composition @ ( identity_relation @ C ) @ D ) )
| ( in @ A @ C ) )
& ! [C: $i,D: $i] :
( ~ ( relation @ D )
| ~ ( in @ ( ordered_pair @ A @ B ) @ ( relation_composition @ ( identity_relation @ C ) @ D ) )
| ( in @ ( ordered_pair @ A @ B ) @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[414]) ).
thf(2001,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ( B
!= ( apply @ C @ A ) )
| ~ ( in @ A @ ( relation_dom @ C ) )
| ( in @ ( ordered_pair @ A @ B ) @ C ) )
& ! [B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( B
= ( apply @ C @ A ) ) )
& ! [B: $i,C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( in @ A @ ( relation_dom @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(2002,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ( ( ( sK52_C @ B @ A )
!= ( sK53_SY3121 @ B @ A ) )
| ~ ( in @ ( sK52_C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK52_C @ B @ A ) @ ( sK53_SY3121 @ B @ A ) ) @ B ) )
& ( ( ( sK52_C @ B @ A )
= ( sK53_SY3121 @ B @ A ) )
| ( in @ ( ordered_pair @ ( sK52_C @ B @ A ) @ ( sK53_SY3121 @ B @ A ) ) @ B ) )
& ( ( in @ ( sK52_C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK52_C @ B @ A ) @ ( sK53_SY3121 @ B @ A ) ) @ B ) ) )
| ( B
= ( identity_relation @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( B
!= ( identity_relation @ A ) )
| ( ! [C: $i,D: $i] :
( ( C != D )
| ~ ( in @ C @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ B )
| ( C = D ) )
& ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ C @ D ) @ B )
| ( in @ C @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(2003,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK50_D @ C @ B @ A ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ C @ B @ A ) @ ( sK51_SY3120 @ C @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ C @ B @ A ) @ ( sK51_SY3120 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK50_D @ C @ B @ A ) @ B )
| ( in @ ( ordered_pair @ ( sK50_D @ C @ B @ A ) @ ( sK51_SY3120 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK50_D @ C @ B @ A ) @ ( sK51_SY3120 @ C @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK50_D @ C @ B @ A ) @ ( sK51_SY3120 @ C @ B @ A ) ) @ C ) ) )
| ( C
= ( relation_dom_restriction @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ~ ( relation @ C )
| ( C
!= ( relation_dom_restriction @ A @ B ) )
| ( ! [D: $i,E: $i] :
( ~ ( in @ D @ B )
| ~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ( in @ ( ordered_pair @ D @ E ) @ C ) )
& ! [D: $i] :
( ! [E: $i] :
~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ D @ B ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ ( ordered_pair @ D @ E ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(2004,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ~ ( in @ ( sK49_SY3119 @ C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ C @ B @ A ) @ ( sK49_SY3119 @ C @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ C @ B @ A ) @ ( sK49_SY3119 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( sK49_SY3119 @ C @ B @ A ) @ A )
| ( in @ ( ordered_pair @ ( sK48_D @ C @ B @ A ) @ ( sK49_SY3119 @ C @ B @ A ) ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK48_D @ C @ B @ A ) @ ( sK49_SY3119 @ C @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK48_D @ C @ B @ A ) @ ( sK49_SY3119 @ C @ B @ A ) ) @ C ) ) )
| ( C
= ( relation_rng_restriction @ A @ B ) ) )
& ! [C: $i] :
( ~ ( relation @ C )
| ( C
!= ( relation_rng_restriction @ A @ B ) )
| ( ! [D: $i,E: $i] :
( ~ ( in @ E @ A )
| ~ ( in @ ( ordered_pair @ D @ E ) @ B )
| ( in @ ( ordered_pair @ D @ E ) @ C ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ E @ A ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ ( ordered_pair @ D @ E ) @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(2005,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY3117: $i] :
( ~ ( in @ ( ordered_pair @ SY3117 @ ( sK46_D @ C @ B @ A ) ) @ A )
| ~ ( in @ SY3117 @ B ) )
| ~ ( in @ ( sK46_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK47_SY3118 @ C @ B @ A ) @ ( sK46_D @ C @ B @ A ) ) @ A )
& ( in @ ( sK47_SY3118 @ C @ B @ A ) @ B ) )
| ( in @ ( sK46_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( relation_image @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( relation_image @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i] :
( ~ ( in @ ( ordered_pair @ E @ D ) @ A )
| ~ ( in @ E @ B ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( ordered_pair @ ( sK45_E @ D @ C @ B @ A ) @ D ) @ A )
& ( in @ ( sK45_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(2006,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ! [SY3115: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ C @ B @ A ) @ SY3115 ) @ A )
| ~ ( in @ SY3115 @ B ) )
| ~ ( in @ ( sK43_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK43_D @ C @ B @ A ) @ ( sK44_SY3116 @ C @ B @ A ) ) @ A )
& ( in @ ( sK44_SY3116 @ C @ B @ A ) @ B ) )
| ( in @ ( sK43_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( relation_inverse_image @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( relation_inverse_image @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ~ ( in @ E @ B ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( ordered_pair @ D @ ( sK42_E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( sK42_E @ D @ C @ B @ A ) @ B ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(2007,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( A
!= ( ordered_pair @ B @ C ) )
| ( ! [B: $i] :
( ( ( A
= ( ordered_pair @ ( sK40_C @ B @ A ) @ ( sK41_SY3114 @ B @ A ) ) )
& ( B
!= ( sK40_C @ B @ A ) ) )
| ( B
= ( pair_first @ A ) ) )
& ! [B: $i] :
( ( B
!= ( pair_first @ A ) )
| ! [C: $i] :
( ! [D: $i] :
( A
!= ( ordered_pair @ C @ D ) )
| ( B = C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(2008,plain,
( ( ! [A: $i] :
( ( ! [SY3112: $i,SY3113: $i] :
( ( sK39_B @ A )
!= ( ordered_pair @ SY3112 @ SY3113 ) )
& ( in @ ( sK39_B @ A ) @ A ) )
| ( relation @ A ) )
& ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ( B
= ( ordered_pair @ ( sK37_C @ B @ A ) @ ( sK38_SY3111 @ B @ A ) ) )
| ~ ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[406]) ).
thf(2009,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK36_C @ B @ A ) @ B )
& ~ ( in @ ( ordered_pair @ ( sK36_C @ B @ A ) @ ( sK36_C @ B @ A ) ) @ A ) )
| ( is_reflexive_in @ A @ B ) )
& ! [B: $i] :
( ~ ( is_reflexive_in @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ C @ C ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(2010,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i,C: $i] :
( ( ( ( ( sK35_D @ C @ B @ A )
= B )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ C @ B @ A ) @ B ) @ A )
| ~ ( in @ ( sK35_D @ C @ B @ A ) @ C ) )
& ( ( ( sK35_D @ C @ B @ A )
!= B )
| ( in @ ( sK35_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( ordered_pair @ ( sK35_D @ C @ B @ A ) @ B ) @ A )
| ( in @ ( sK35_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( fiber @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( fiber @ A @ B ) )
| ( ! [D: $i] :
( ( D = B )
| ~ ( in @ ( ordered_pair @ D @ B ) @ A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( D != B ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ ( ordered_pair @ D @ B ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(2011,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( A
!= ( ordered_pair @ B @ C ) )
| ( ! [B: $i] :
( ( ( A
= ( ordered_pair @ ( sK33_C @ B @ A ) @ ( sK34_SY3110 @ B @ A ) ) )
& ( B
!= ( sK34_SY3110 @ B @ A ) ) )
| ( B
= ( pair_second @ A ) ) )
& ! [B: $i] :
( ( B
!= ( pair_second @ A ) )
| ! [C: $i,D: $i] :
( ( A
!= ( ordered_pair @ C @ D ) )
| ( B = D ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(2012,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK31_C @ B @ A ) @ ( sK32_SY3109 @ B @ A ) ) @ A )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ B @ A ) @ ( sK32_SY3109 @ B @ A ) ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK31_C @ B @ A ) @ ( sK32_SY3109 @ B @ A ) ) @ A )
| ( in @ ( ordered_pair @ ( sK31_C @ B @ A ) @ ( sK32_SY3109 @ 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)],[402]) ).
thf(2013,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY3104: $i,SY3105: $i] :
( ~ ( in @ SY3104 @ A )
| ~ ( in @ SY3105 @ B )
| ( ( sK28_D @ C @ B @ A )
!= ( ordered_pair @ SY3104 @ SY3105 ) ) )
| ~ ( in @ ( sK28_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK29_SY3106 @ C @ B @ A ) @ A )
& ( in @ ( sK30_SY3108 @ C @ B @ A ) @ B )
& ( ( sK28_D @ C @ B @ A )
= ( ordered_pair @ ( sK29_SY3106 @ C @ B @ A ) @ ( sK30_SY3108 @ C @ B @ A ) ) ) )
| ( in @ ( sK28_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 @ ( sK26_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK27_SY3103 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK26_E @ D @ C @ B @ A ) @ ( sK27_SY3103 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(2014,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( in @ ( ordered_pair @ ( sK24_C @ B @ A ) @ ( sK25_SY3102 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK24_C @ B @ A ) @ ( sK25_SY3102 @ 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)],[400]) ).
thf(2015,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C
!= ( apply @ A @ B ) )
| ( in @ ( ordered_pair @ B @ C ) @ A ) ) )
& ! [B: $i] :
( ~ ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ~ ( in @ ( ordered_pair @ B @ C ) @ A )
| ( C
= ( apply @ A @ B ) ) ) )
& ! [B: $i] :
( ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C
!= ( apply @ A @ B ) )
| ( C = empty_set ) ) )
& ! [B: $i] :
( ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C != empty_set )
| ( C
= ( apply @ A @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[399]) ).
thf(2016,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY3100: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ B @ A ) @ SY3100 ) @ A )
| ~ ( in @ ( sK22_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK22_C @ B @ A ) @ ( sK23_SY3101 @ B @ A ) ) @ A )
| ( in @ ( sK22_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_dom @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_dom @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ C @ ( sK21_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[398]) ).
thf(2017,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK19_C @ B @ A ) @ B )
& ( in @ ( sK20_SY3099 @ B @ A ) @ B )
& ( in @ ( ordered_pair @ ( sK19_C @ B @ A ) @ ( sK20_SY3099 @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK20_SY3099 @ B @ A ) @ ( sK19_C @ B @ A ) ) @ A )
& ( ( sK19_C @ B @ A )
!= ( sK20_SY3099 @ B @ A ) ) )
| ( is_antisymmetric_in @ A @ B ) )
& ! [B: $i] :
( ~ ( is_antisymmetric_in @ A @ B )
| ! [C: $i,D: $i] :
( ~ ( in @ C @ B )
| ~ ( in @ D @ B )
| ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ~ ( in @ ( ordered_pair @ D @ C ) @ A )
| ( C = D ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(2018,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY3097: $i] :
~ ( in @ ( ordered_pair @ SY3097 @ ( sK17_C @ B @ A ) ) @ A )
| ~ ( in @ ( sK17_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK18_SY3098 @ B @ A ) @ ( sK17_C @ B @ A ) ) @ A )
| ( in @ ( sK17_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_rng @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_rng @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ D @ C ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ ( sK16_D @ C @ B @ A ) @ C ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(2019,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[351]) ).
thf(2020,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ( sK14_C @ B @ A )
!= ( sK15_SY3096 @ B @ A ) )
& ( in @ ( sK14_C @ B @ A ) @ B )
& ( in @ ( sK15_SY3096 @ B @ A ) @ B )
& ~ ( in @ ( ordered_pair @ ( sK14_C @ B @ A ) @ ( sK15_SY3096 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK15_SY3096 @ B @ A ) @ ( sK14_C @ B @ A ) ) @ A ) )
| ( is_connected_in @ A @ B ) )
& ! [B: $i] :
( ~ ( is_connected_in @ A @ B )
| ! [C: $i,D: $i] :
( ( C = D )
| ~ ( in @ C @ B )
| ~ ( in @ D @ B )
| ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[395]) ).
thf(2021,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( relation @ B )
| ( ( ~ ( in @ ( ordered_pair @ ( sK12_C @ B @ A ) @ ( sK13_SY3095 @ B @ A ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ B @ A ) @ ( sK12_C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( sK12_C @ B @ A ) @ ( sK13_SY3095 @ B @ A ) ) @ B )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ B @ A ) @ ( sK12_C @ B @ A ) ) @ A ) ) )
| ( B
= ( relation_inverse @ A ) ) )
& ! [B: $i] :
( ~ ( relation @ B )
| ( B
!= ( relation_inverse @ A ) )
| ( ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ C @ D ) @ B )
| ( in @ ( ordered_pair @ D @ C ) @ A ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ D @ C ) @ A )
| ( in @ ( ordered_pair @ C @ D ) @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[394]) ).
thf(2022,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ( ( ~ ( in @ ( sK10_D @ C @ B @ A ) @ ( relation_field @ A ) )
| ~ ( in @ ( sK11_SY3094 @ C @ B @ A ) @ ( relation_field @ A ) )
| ~ ( in @ ( ordered_pair @ ( apply @ C @ ( sK10_D @ C @ B @ A ) ) @ ( apply @ C @ ( sK11_SY3094 @ C @ B @ A ) ) ) @ B )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ ( sK11_SY3094 @ C @ B @ A ) ) @ A ) )
& ( ( in @ ( sK10_D @ C @ B @ A ) @ ( relation_field @ A ) )
| ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ ( sK11_SY3094 @ C @ B @ A ) ) @ A ) )
& ( ( in @ ( sK11_SY3094 @ C @ B @ A ) @ ( relation_field @ A ) )
| ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ ( sK11_SY3094 @ C @ B @ A ) ) @ A ) )
& ( ( in @ ( ordered_pair @ ( apply @ C @ ( sK10_D @ C @ B @ A ) ) @ ( apply @ C @ ( sK11_SY3094 @ C @ B @ A ) ) ) @ B )
| ( in @ ( ordered_pair @ ( sK10_D @ C @ B @ A ) @ ( sK11_SY3094 @ C @ B @ A ) ) @ A ) ) )
| ( ( relation_dom @ C )
!= ( relation_field @ A ) )
| ( ( relation_rng @ C )
!= ( relation_field @ B ) )
| ~ ( one_to_one @ C )
| ( relation_isomorphism @ A @ B @ C ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ( ! [D: $i,E: $i] :
( ~ ( in @ D @ ( relation_field @ A ) )
| ~ ( in @ E @ ( relation_field @ A ) )
| ~ ( in @ ( ordered_pair @ ( apply @ C @ D ) @ ( apply @ C @ E ) ) @ B )
| ( in @ ( ordered_pair @ D @ E ) @ A ) )
& ! [D: $i] :
( ! [E: $i] :
~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ( in @ D @ ( relation_field @ A ) ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ( in @ E @ ( relation_field @ A ) ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ( in @ ( ordered_pair @ ( apply @ C @ D ) @ ( apply @ C @ E ) ) @ B ) ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ( ( relation_dom @ C )
= ( relation_field @ A ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ( ( relation_rng @ C )
= ( relation_field @ B ) ) )
& ! [C: $i] :
( ~ ( function @ C )
| ~ ( relation @ C )
| ~ ( relation_isomorphism @ A @ B @ C )
| ( one_to_one @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(2023,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ! [B: $i] :
( ~ ( relation @ B )
| ( ! [C: $i] :
( ~ ( relation @ C )
| ( ( ! [SY3092: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ C @ B @ A ) @ SY3092 ) @ A )
| ~ ( in @ ( ordered_pair @ SY3092 @ ( sK8_SY3089 @ C @ B @ A ) ) @ B ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ C @ B @ A ) @ ( sK8_SY3089 @ C @ B @ A ) ) @ C ) )
& ( ( ( in @ ( ordered_pair @ ( sK7_D @ C @ B @ A ) @ ( sK9_SY3093 @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK9_SY3093 @ C @ B @ A ) @ ( sK8_SY3089 @ C @ B @ A ) ) @ B ) )
| ( in @ ( ordered_pair @ ( sK7_D @ C @ B @ A ) @ ( sK8_SY3089 @ C @ B @ A ) ) @ C ) ) )
| ( C
= ( relation_composition @ A @ B ) ) )
& ! [C: $i] :
( ~ ( relation @ C )
| ( C
!= ( relation_composition @ A @ B ) )
| ( ! [D: $i,E: $i] :
( ! [F: $i] :
( ~ ( in @ ( ordered_pair @ D @ F ) @ A )
| ~ ( in @ ( ordered_pair @ F @ E ) @ B ) )
| ( in @ ( ordered_pair @ D @ E ) @ C ) )
& ! [D: $i,E: $i] :
( ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( ( in @ ( ordered_pair @ D @ ( sK6_F @ E @ D @ C @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK6_F @ E @ D @ C @ B @ A ) @ E ) @ B ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[392]) ).
thf(2024,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( in @ ( sK3_C @ B @ A ) @ B )
& ( in @ ( sK4_SY3086 @ B @ A ) @ B )
& ( in @ ( sK5_SY3088 @ B @ A ) @ B )
& ( in @ ( ordered_pair @ ( sK3_C @ B @ A ) @ ( sK4_SY3086 @ B @ A ) ) @ A )
& ( in @ ( ordered_pair @ ( sK4_SY3086 @ B @ A ) @ ( sK5_SY3088 @ B @ A ) ) @ A )
& ~ ( in @ ( ordered_pair @ ( sK3_C @ B @ A ) @ ( sK5_SY3088 @ B @ A ) ) @ A ) )
| ( is_transitive_in @ A @ B ) )
& ! [B: $i] :
( ~ ( is_transitive_in @ A @ B )
| ! [C: $i,D: $i,E: $i] :
( ~ ( in @ C @ B )
| ~ ( in @ D @ B )
| ~ ( in @ E @ B )
| ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ~ ( in @ ( ordered_pair @ D @ E ) @ A )
| ( in @ ( ordered_pair @ C @ E ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[391]) ).
thf(2025,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[345]) ).
thf(2026,plain,
( ( ( ( pair_second @ ( ordered_pair @ sK1_A @ sK2_SY3085 ) )
!= sK2_SY3085 ) )
= $true ),
inference(copy,[status(thm)],[390]) ).
thf(2027,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)],[1990]) ).
thf(2028,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)],[1991]) ).
thf(2029,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( in @ ( sK69_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK69_B @ SX0 ) @ ( sK69_B @ SX0 ) ) @ SX0 ) )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ ( relation_field @ SX0 ) )
| ( in @ ( ordered_pair @ SX1 @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1986]) ).
thf(2030,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK14_C @ SX1 @ SX0 )
!= ( sK15_SY3096 @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK15_SY3096 @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK14_C @ SX1 @ SX0 ) @ ( sK15_SY3096 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK15_SY3096 @ SX1 @ SX0 ) @ ( sK14_C @ SX1 @ SX0 ) ) @ SX0 ) )
| ( is_connected_in @ SX0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( is_connected_in @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i] :
( ( SX2 = SX3 )
| ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX3 @ SX1 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2020]) ).
thf(2031,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK39_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK39_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK37_C @ SX1 @ SX0 ) @ ( sK38_SY3111 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2008]) ).
thf(2032,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK64_B @ SX0 ) @ ( sK65_SY3126 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK65_SY3126 @ SX0 ) @ ( sK64_B @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK64_B @ SX0 )
!= ( sK65_SY3126 @ SX0 ) ) ) )
| ( antisymmetric @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX2 @ SX1 ) @ SX0 )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1988]) ).
thf(2033,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i,SX4: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX4 @ SX1 )
| ( ( sK28_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ SX3 @ SX4 ) ) )
| ~ ( in @ ( sK28_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY3106 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK30_SY3108 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( sK28_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ ( sK29_SY3106 @ SX2 @ SX1 @ SX0 ) @ ( sK30_SY3108 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( in @ ( sK28_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 @ ( sK26_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK27_SY3103 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( SX3
!= ( ordered_pair @ ( sK26_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK27_SY3103 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2013]) ).
thf(2034,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK4_SY3086 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ ( sK5_SY3088 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SX1 @ SX0 ) @ ( sK4_SY3086 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( in @ ( ordered_pair @ ( sK4_SY3086 @ SX1 @ SX0 ) @ ( sK5_SY3088 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK3_C @ SX1 @ SX0 ) @ ( sK5_SY3088 @ SX1 @ SX0 ) ) @ SX0 ) )
| ( is_transitive_in @ SX0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( is_transitive_in @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i,SX4: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX3 @ SX1 )
| ~ ( in @ SX4 @ SX1 )
| ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX4 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2024]) ).
thf(2035,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ ( sK46_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ~ ( in @ ( sK46_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SX2 @ SX1 @ SX0 ) @ ( sK46_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK47_SY3118 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( in @ ( sK46_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ( SX2
= ( relation_image @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( relation_image @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX4 @ SX3 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ ( sK45_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2005]) ).
thf(2036,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ ( sK50_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SX2 @ SX1 @ SX0 ) @ ( sK51_SY3120 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SX2 @ SX1 @ SX0 ) @ ( sK51_SY3120 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK50_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK50_D @ SX2 @ SX1 @ SX0 ) @ ( sK51_SY3120 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SX2 @ SX1 @ SX0 ) @ ( sK51_SY3120 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK50_D @ SX2 @ SX1 @ SX0 ) @ ( sK51_SY3120 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) ) ) )
| ( SX2
= ( relation_dom_restriction @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ( SX2
!= ( relation_dom_restriction @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ SX3 @ SX1 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ( in @ SX3 @ SX1 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2003]) ).
thf(2037,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ~ ( in @ ( sK43_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SX2 @ SX1 @ SX0 ) @ ( sK44_SY3116 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK44_SY3116 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( in @ ( sK43_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ( SX2
= ( relation_inverse_image @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( relation_inverse_image @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ~ ( in @ SX4 @ SX1 ) )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ ( ordered_pair @ SX3 @ ( sK42_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK42_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2006]) ).
thf(2038,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SX1 @ SX0 ) @ ( sK25_SY3102 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SX1 @ SX0 ) @ ( sK25_SY3102 @ 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)],[2014]) ).
thf(2039,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ! [SX3: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ ( sK8_SY3089 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ ( sK8_SY3089 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ ( sK9_SY3093 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SX2 @ SX1 @ SX0 ) @ ( sK8_SY3089 @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ ( sK8_SY3089 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) ) )
| ( SX2
= ( relation_composition @ SX0 @ SX1 ) ) )
| ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ( SX2
!= ( relation_composition @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i,SX4: $i] :
( ! [SX5: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX5 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX5 @ SX4 ) @ SX1 ) )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ~ ( ~ ( in @ ( ordered_pair @ SX3 @ ( sK6_F @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SX4 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX4 ) @ SX1 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2023]) ).
thf(2040,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ~ ( ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ ( sK57_D @ SX2 @ SX1 @ SX0 ) ) @ SX2 )
| ~ ( in @ ( sK57_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 @ ( sK56_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX2 )
| ~ ( in @ SX3 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1996]) ).
thf(2041,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ( in @ ( sK11_SY3094 @ SX2 @ SX1 @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SX2 @ ( sK10_D @ SX2 @ SX1 @ SX0 ) ) @ ( apply @ SX2 @ ( sK11_SY3094 @ SX2 @ SX1 @ SX0 ) ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ ( sK11_SY3094 @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ ( relation_field @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ ( sK11_SY3094 @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SX2 @ SX1 @ SX0 ) @ ( relation_field @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ ( sK11_SY3094 @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SX2 @ ( sK10_D @ SX2 @ SX1 @ SX0 ) ) @ ( apply @ SX2 @ ( sK11_SY3094 @ SX2 @ SX1 @ SX0 ) ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ ( sK11_SY3094 @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) ) )
| ( ( relation_dom @ SX2 )
!= ( relation_field @ SX0 ) )
| ( ( relation_rng @ SX2 )
!= ( relation_field @ SX1 ) )
| ~ ( one_to_one @ SX2 )
| ( relation_isomorphism @ SX0 @ SX1 @ SX2 ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( relation_isomorphism @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ SX3 @ ( relation_field @ SX0 ) )
| ~ ( in @ SX4 @ ( relation_field @ SX0 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SX2 @ SX3 ) @ ( apply @ SX2 @ SX4 ) ) @ SX1 )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ( in @ SX3 @ ( relation_field @ SX0 ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ( in @ SX4 @ ( relation_field @ SX0 ) ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX0 )
| ( in @ ( ordered_pair @ ( apply @ SX2 @ SX3 ) @ ( apply @ SX2 @ SX4 ) ) @ SX1 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( relation_isomorphism @ SX0 @ SX1 @ SX2 )
| ( ( relation_dom @ SX2 )
= ( relation_field @ SX0 ) ) )
| ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( relation_isomorphism @ SX0 @ SX1 @ SX2 )
| ( ( relation_rng @ SX2 )
= ( relation_field @ SX1 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( relation_isomorphism @ SX0 @ SX1 @ SX2 )
| ( one_to_one @ SX2 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2022]) ).
thf(2042,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK62_B @ SX0 )
!= ( sK63_SY3125 @ SX0 ) ) )
| ~ ~ ( ~ ( in @ ( sK62_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ( in @ ( sK63_SY3125 @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK62_B @ SX0 ) @ ( sK63_SY3125 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK63_SY3125 @ SX0 ) @ ( sK62_B @ SX0 ) ) @ SX0 ) )
| ( connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( connected @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( SX1 = SX2 )
| ~ ( in @ SX1 @ ( relation_field @ SX0 ) )
| ~ ( in @ SX2 @ ( relation_field @ SX0 ) )
| ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1989]) ).
thf(2043,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ( SX1
!= ( apply @ SX2 @ SX0 ) )
| ~ ( in @ SX0 @ ( relation_dom @ SX2 ) )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( SX1
= ( apply @ SX2 @ SX0 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( function @ SX2 )
| ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX0 @ ( relation_dom @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2001]) ).
thf(2044,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( relation_dom @ SX2 ) )
| ~ ( in @ ( ordered_pair @ SX3 @ SX0 ) @ SX2 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX0 @ ( relation_image @ SX2 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_image @ SX2 @ SX1 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK61_D @ SX2 @ SX1 @ SX0 ) @ ( relation_dom @ SX2 ) )
| ~ ( in @ ( ordered_pair @ ( sK61_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) @ SX2 ) )
| ~ ( in @ ( sK61_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1992]) ).
thf(2045,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i,SX2: $i] :
( SX0
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ( SX0
!= ( ordered_pair @ ( sK40_C @ SX1 @ SX0 ) @ ( sK41_SY3114 @ SX1 @ SX0 ) ) )
| ~ ( ( SX1
!= ( sK40_C @ SX1 @ SX0 ) ) ) )
| ( SX1
= ( pair_first @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( SX1
!= ( pair_first @ SX0 ) )
| ! [SX2: $i] :
( ! [SX3: $i] :
( SX0
!= ( ordered_pair @ SX2 @ SX3 ) )
| ( SX1 = SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2007]) ).
thf(2046,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i,SX2: $i] :
( SX0
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ( SX0
!= ( ordered_pair @ ( sK33_C @ SX1 @ SX0 ) @ ( sK34_SY3110 @ SX1 @ SX0 ) ) )
| ~ ( ( SX1
!= ( sK34_SY3110 @ SX1 @ SX0 ) ) ) )
| ( SX1
= ( pair_second @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( SX1
!= ( pair_second @ SX0 ) )
| ! [SX2: $i,SX3: $i] :
( ( SX0
!= ( ordered_pair @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2011]) ).
thf(2047,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX0 @ ( relation_dom @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX1 @ ( relation_rng @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1994]) ).
thf(2048,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK52_C @ SX1 @ SX0 )
!= ( sK53_SY3121 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK52_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK52_C @ SX1 @ SX0 ) @ ( sK53_SY3121 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK52_C @ SX1 @ SX0 )
= ( sK53_SY3121 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK52_C @ SX1 @ SX0 ) @ ( sK53_SY3121 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK52_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK52_C @ SX1 @ SX0 ) @ ( sK53_SY3121 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( SX2 = SX3 ) )
| ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2002]) ).
thf(2049,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX1 @ SX0 )
| ~ ( ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ ( sK59_D @ SX2 @ SX1 @ SX0 ) @ SX3 ) @ SX2 )
| ~ ( in @ ( sK59_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 @ ( sK58_E @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX2 )
| ~ ( in @ SX3 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1995]) ).
thf(2050,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
| ~ ( in @ ( sK22_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SX1 @ SX0 ) @ ( sK23_SY3101 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK22_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( relation_dom @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( SX1
!= ( relation_dom @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ ( ordered_pair @ SX2 @ ( sK21_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2016]) ).
thf(2051,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SX1 @ SX0 ) @ ( sK32_SY3109 @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ SX1 @ SX0 ) @ ( sK32_SY3109 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK31_C @ SX1 @ SX0 ) @ ( sK32_SY3109 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK31_C @ SX1 @ SX0 ) @ ( sK32_SY3109 @ 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)],[2012]) ).
thf(2052,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK66_B @ SX0 ) @ ( sK67_SY3127 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK67_SY3127 @ SX0 ) @ ( sK68_SY3129 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK66_B @ SX0 ) @ ( sK68_SY3129 @ SX0 ) ) @ SX0 ) )
| ( transitive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( transitive @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX1 @ SX3 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1987]) ).
thf(2053,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SX1 @ SX0 ) @ ( sK13_SY3095 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SX1 @ SX0 ) @ ( sK12_C @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SX1 @ SX0 ) @ ( sK13_SY3095 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ SX1 @ SX0 ) @ ( sK12_C @ SX1 @ SX0 ) ) @ SX0 ) ) )
| ( SX1
= ( relation_inverse @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ( SX1
!= ( relation_inverse @ SX0 ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2021]) ).
thf(2054,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
( ( SX2
!= ( apply @ SX0 @ SX1 ) )
| ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ( SX2
= ( apply @ SX0 @ SX1 ) ) ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
( ( SX2
!= ( apply @ SX0 @ SX1 ) )
| ( SX2 = empty_set ) ) )
| ~ ! [SX1: $i] :
( ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
( ( SX2 != empty_set )
| ( SX2
= ( apply @ SX0 @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2015]) ).
thf(2055,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK20_SY3099 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SX1 @ SX0 ) @ ( sK20_SY3099 @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( in @ ( ordered_pair @ ( sK20_SY3099 @ SX1 @ SX0 ) @ ( sK19_C @ SX1 @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK19_C @ SX1 @ SX0 )
!= ( sK20_SY3099 @ SX1 @ SX0 ) ) ) )
| ( is_antisymmetric_in @ SX0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( is_antisymmetric_in @ SX0 @ SX1 )
| ! [SX2: $i,SX3: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX3 @ SX1 )
| ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( SX2 = SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2017]) ).
thf(2056,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ( ( sK35_D @ SX2 @ SX1 @ SX0 )
= SX1 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) @ SX0 )
| ~ ( in @ ( sK35_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( ( sK35_D @ SX2 @ SX1 @ SX0 )
!= SX1 )
| ( in @ ( sK35_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) @ SX0 )
| ( in @ ( sK35_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( fiber @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( fiber @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ( SX3 = SX1 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX1 ) @ SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( SX3 != SX1 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ ( ordered_pair @ SX3 @ SX1 ) @ SX0 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2010]) ).
thf(2057,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ ( sK49_SY3119 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SX2 @ SX1 @ SX0 ) @ ( sK49_SY3119 @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SX2 @ SX1 @ SX0 ) @ ( sK49_SY3119 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_SY3119 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK48_D @ SX2 @ SX1 @ SX0 ) @ ( sK49_SY3119 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SX2 @ SX1 @ SX0 ) @ ( sK49_SY3119 @ SX2 @ SX1 @ SX0 ) ) @ SX1 )
| ( in @ ( ordered_pair @ ( sK48_D @ SX2 @ SX1 @ SX0 ) @ ( sK49_SY3119 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) ) ) )
| ( SX2
= ( relation_rng_restriction @ SX0 @ SX1 ) ) )
| ~ ! [SX2: $i] :
( ~ ( relation @ SX2 )
| ( SX2
!= ( relation_rng_restriction @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX1 )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ( in @ SX4 @ SX0 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX2 )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2004]) ).
thf(2058,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ SX2 @ ( sK17_C @ SX1 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK18_SY3098 @ SX1 @ SX0 ) @ ( sK17_C @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( relation_rng @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( SX1
!= ( relation_rng @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX2 ) @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ ( ordered_pair @ ( sK16_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2018]) ).
thf(2059,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX0 @ ( relation_field @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX1 @ ( relation_field @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1997]) ).
thf(2060,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( relation @ SX3 )
| ~ ( in @ SX0 @ SX2 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX3 )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( relation_composition @ ( identity_relation @ SX2 ) @ SX3 ) ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( relation @ SX3 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( relation_composition @ ( identity_relation @ SX2 ) @ SX3 ) )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( relation @ SX3 )
| ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( relation_composition @ ( identity_relation @ SX2 ) @ SX3 ) )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2000]) ).
thf(2061,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ( ordered_pair @ SX0 @ SX1 )
!= ( ordered_pair @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( ( ordered_pair @ SX0 @ SX1 )
!= ( ordered_pair @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1998]) ).
thf(2062,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( relation_rng @ SX2 ) )
| ~ ( in @ ( ordered_pair @ SX0 @ SX3 ) @ SX2 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX0 @ ( relation_inverse_image @ SX2 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( in @ SX0 @ ( relation_inverse_image @ SX2 @ SX1 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_D @ SX2 @ SX1 @ SX0 ) @ ( relation_rng @ SX2 ) )
| ~ ( in @ ( ordered_pair @ SX0 @ ( sK60_D @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) )
| ~ ( in @ ( sK60_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1993]) ).
thf(2063,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( in @ ( sK36_C @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SX1 @ SX0 ) @ ( sK36_C @ SX1 @ SX0 ) ) @ SX0 ) )
| ( is_reflexive_in @ SX0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( is_reflexive_in @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ ( ordered_pair @ SX2 @ SX2 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2009]) ).
thf(2064,plain,
! [SV269: $i] :
( ( ~ ( relation @ SV269 )
| ( in @ ( ordered_pair @ ( sK54_B @ SV269 ) @ ( sK55_SY3122 @ SV269 ) ) @ SV269 )
| ( SV269 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1999]) ).
thf(2065,plain,
! [SV270: $i] :
( ( ! [SY3602: $i] :
( ( ordered_pair @ SV270 @ SY3602 )
= ( unordered_pair @ ( unordered_pair @ SV270 @ SY3602 ) @ ( singleton @ SV270 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2019]) ).
thf(2066,plain,
! [SV271: $i] :
( ( ! [SY3603: $i] :
~ ( empty @ ( ordered_pair @ SV271 @ SY3603 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2025]) ).
thf(2067,plain,
( ( ( pair_second @ ( ordered_pair @ sK1_A @ sK2_SY3085 ) )
= sK2_SY3085 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2026]) ).
thf(2068,plain,
! [SV272: $i] :
( ( ! [SY3604: $i] :
~ ( ~ ! [SY3605: $i,SY3606: $i] :
( ~ ( in @ SV272 @ SY3605 )
| ~ ( in @ SY3604 @ SY3606 )
| ( in @ ( ordered_pair @ SV272 @ SY3604 ) @ ( cartesian_product2 @ SY3605 @ SY3606 ) ) )
| ~ ~ ( ~ ! [SY3607: $i] :
( ! [SY3608: $i] :
~ ( in @ ( ordered_pair @ SV272 @ SY3604 ) @ ( cartesian_product2 @ SY3607 @ SY3608 ) )
| ( in @ SV272 @ SY3607 ) )
| ~ ! [SY3609: $i,SY3610: $i] :
( ~ ( in @ ( ordered_pair @ SV272 @ SY3604 ) @ ( cartesian_product2 @ SY3609 @ SY3610 ) )
| ( in @ SY3604 @ SY3610 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2027]) ).
thf(2069,plain,
! [SV273: $i] :
( ( ! [SY3611: $i] :
~ ( ~ ! [SY3612: $i,SY3613: $i] :
( ~ ( in @ SV273 @ SY3612 )
| ~ ( in @ SY3611 @ SY3613 )
| ( in @ ( ordered_pair @ SV273 @ SY3611 ) @ ( cartesian_product2 @ SY3612 @ SY3613 ) ) )
| ~ ~ ( ~ ! [SY3614: $i] :
( ! [SY3615: $i] :
~ ( in @ ( ordered_pair @ SV273 @ SY3611 ) @ ( cartesian_product2 @ SY3614 @ SY3615 ) )
| ( in @ SV273 @ SY3614 ) )
| ~ ! [SY3616: $i,SY3617: $i] :
( ~ ( in @ ( ordered_pair @ SV273 @ SY3611 ) @ ( cartesian_product2 @ SY3616 @ SY3617 ) )
| ( in @ SY3611 @ SY3617 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2070,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( in @ ( sK69_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK69_B @ SX0 ) @ ( sK69_B @ SX0 ) ) @ SX0 ) )
| ( reflexive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ ( relation_field @ SX0 ) )
| ( in @ ( ordered_pair @ SX1 @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2029]) ).
thf(2071,plain,
! [SV274: $i] :
( ( ~ ( relation @ SV274 )
| ~ ( ~ ! [SY3618: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK14_C @ SY3618 @ SV274 )
!= ( sK15_SY3096 @ SY3618 @ SV274 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SY3618 @ SV274 ) @ SY3618 )
| ~ ( in @ ( sK15_SY3096 @ SY3618 @ SV274 ) @ SY3618 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK14_C @ SY3618 @ SV274 ) @ ( sK15_SY3096 @ SY3618 @ SV274 ) ) @ SV274 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK15_SY3096 @ SY3618 @ SV274 ) @ ( sK14_C @ SY3618 @ SV274 ) ) @ SV274 ) )
| ( is_connected_in @ SV274 @ SY3618 ) )
| ~ ! [SY3619: $i] :
( ~ ( is_connected_in @ SV274 @ SY3619 )
| ! [SY3620: $i,SY3621: $i] :
( ( SY3620 = SY3621 )
| ~ ( in @ SY3620 @ SY3619 )
| ~ ( in @ SY3621 @ SY3619 )
| ( in @ ( ordered_pair @ SY3620 @ SY3621 ) @ SV274 )
| ( in @ ( ordered_pair @ SY3621 @ SY3620 ) @ SV274 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2030]) ).
thf(2072,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK39_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK39_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK37_C @ SX1 @ SX0 ) @ ( sK38_SY3111 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2031]) ).
thf(2073,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK64_B @ SX0 ) @ ( sK65_SY3126 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK65_SY3126 @ SX0 ) @ ( sK64_B @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK64_B @ SX0 )
!= ( sK65_SY3126 @ SX0 ) ) ) )
| ( antisymmetric @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX2 @ SX1 ) @ SX0 )
| ( SX1 = SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2032]) ).
thf(2074,plain,
! [SV275: $i] :
( ( ~ ( ~ ! [SY3622: $i,SY3623: $i] :
( ~ ( ~ ( ! [SY3624: $i,SY3625: $i] :
( ~ ( in @ SY3624 @ SV275 )
| ~ ( in @ SY3625 @ SY3622 )
| ( ( sK28_D @ SY3623 @ SY3622 @ SV275 )
!= ( ordered_pair @ SY3624 @ SY3625 ) ) )
| ~ ( in @ ( sK28_D @ SY3623 @ SY3622 @ SV275 ) @ SY3623 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY3106 @ SY3623 @ SY3622 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK30_SY3108 @ SY3623 @ SY3622 @ SV275 ) @ SY3622 ) )
| ( ( sK28_D @ SY3623 @ SY3622 @ SV275 )
!= ( ordered_pair @ ( sK29_SY3106 @ SY3623 @ SY3622 @ SV275 ) @ ( sK30_SY3108 @ SY3623 @ SY3622 @ SV275 ) ) ) )
| ( in @ ( sK28_D @ SY3623 @ SY3622 @ SV275 ) @ SY3623 ) ) )
| ( SY3623
= ( cartesian_product2 @ SV275 @ SY3622 ) ) )
| ~ ! [SY3626: $i,SY3627: $i] :
( ( SY3627
!= ( cartesian_product2 @ SV275 @ SY3626 ) )
| ~ ( ~ ! [SY3628: $i] :
( ! [SY3629: $i,SY3630: $i] :
( ~ ( in @ SY3629 @ SV275 )
| ~ ( in @ SY3630 @ SY3626 )
| ( SY3628
!= ( ordered_pair @ SY3629 @ SY3630 ) ) )
| ( in @ SY3628 @ SY3627 ) )
| ~ ! [SY3631: $i] :
( ~ ( in @ SY3631 @ SY3627 )
| ~ ( ~ ~ ( ~ ( in @ ( sK26_E @ SY3631 @ SY3627 @ SY3626 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK27_SY3103 @ SY3631 @ SY3627 @ SY3626 @ SV275 ) @ SY3626 ) )
| ( SY3631
!= ( ordered_pair @ ( sK26_E @ SY3631 @ SY3627 @ SY3626 @ SV275 ) @ ( sK27_SY3103 @ SY3631 @ SY3627 @ SY3626 @ SV275 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2033]) ).
thf(2075,plain,
! [SV276: $i] :
( ( ~ ( relation @ SV276 )
| ~ ( ~ ! [SY3632: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SY3632 @ SV276 ) @ SY3632 )
| ~ ( in @ ( sK4_SY3086 @ SY3632 @ SV276 ) @ SY3632 ) )
| ~ ( in @ ( sK5_SY3088 @ SY3632 @ SV276 ) @ SY3632 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SY3632 @ SV276 ) @ ( sK4_SY3086 @ SY3632 @ SV276 ) ) @ SV276 ) )
| ~ ( in @ ( ordered_pair @ ( sK4_SY3086 @ SY3632 @ SV276 ) @ ( sK5_SY3088 @ SY3632 @ SV276 ) ) @ SV276 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK3_C @ SY3632 @ SV276 ) @ ( sK5_SY3088 @ SY3632 @ SV276 ) ) @ SV276 ) )
| ( is_transitive_in @ SV276 @ SY3632 ) )
| ~ ! [SY3633: $i] :
( ~ ( is_transitive_in @ SV276 @ SY3633 )
| ! [SY3634: $i,SY3635: $i,SY3636: $i] :
( ~ ( in @ SY3634 @ SY3633 )
| ~ ( in @ SY3635 @ SY3633 )
| ~ ( in @ SY3636 @ SY3633 )
| ~ ( in @ ( ordered_pair @ SY3634 @ SY3635 ) @ SV276 )
| ~ ( in @ ( ordered_pair @ SY3635 @ SY3636 ) @ SV276 )
| ( in @ ( ordered_pair @ SY3634 @ SY3636 ) @ SV276 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2034]) ).
thf(2076,plain,
! [SV277: $i] :
( ( ~ ( relation @ SV277 )
| ~ ( ~ ! [SY3637: $i,SY3638: $i] :
( ~ ( ~ ( ! [SY3639: $i] :
( ~ ( in @ ( ordered_pair @ SY3639 @ ( sK46_D @ SY3638 @ SY3637 @ SV277 ) ) @ SV277 )
| ~ ( in @ SY3639 @ SY3637 ) )
| ~ ( in @ ( sK46_D @ SY3638 @ SY3637 @ SV277 ) @ SY3638 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SY3638 @ SY3637 @ SV277 ) @ ( sK46_D @ SY3638 @ SY3637 @ SV277 ) ) @ SV277 )
| ~ ( in @ ( sK47_SY3118 @ SY3638 @ SY3637 @ SV277 ) @ SY3637 ) )
| ( in @ ( sK46_D @ SY3638 @ SY3637 @ SV277 ) @ SY3638 ) ) )
| ( SY3638
= ( relation_image @ SV277 @ SY3637 ) ) )
| ~ ! [SY3640: $i,SY3641: $i] :
( ( SY3641
!= ( relation_image @ SV277 @ SY3640 ) )
| ~ ( ~ ! [SY3642: $i] :
( ! [SY3643: $i] :
( ~ ( in @ ( ordered_pair @ SY3643 @ SY3642 ) @ SV277 )
| ~ ( in @ SY3643 @ SY3640 ) )
| ( in @ SY3642 @ SY3641 ) )
| ~ ! [SY3644: $i] :
( ~ ( in @ SY3644 @ SY3641 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SY3644 @ SY3641 @ SY3640 @ SV277 ) @ SY3644 ) @ SV277 )
| ~ ( in @ ( sK45_E @ SY3644 @ SY3641 @ SY3640 @ SV277 ) @ SY3640 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2077,plain,
! [SV278: $i] :
( ( ~ ( relation @ SV278 )
| ~ ( ~ ! [SY3645: $i,SY3646: $i] :
( ~ ( relation @ SY3646 )
| ~ ( ~ ( ~ ( in @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ SY3645 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ ( sK51_SY3120 @ SY3646 @ SY3645 @ SV278 ) ) @ SV278 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ ( sK51_SY3120 @ SY3646 @ SY3645 @ SV278 ) ) @ SY3646 ) )
| ~ ~ ( ~ ( ( in @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ SY3645 )
| ( in @ ( ordered_pair @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ ( sK51_SY3120 @ SY3646 @ SY3645 @ SV278 ) ) @ SY3646 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ ( sK51_SY3120 @ SY3646 @ SY3645 @ SV278 ) ) @ SV278 )
| ( in @ ( ordered_pair @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ ( sK51_SY3120 @ SY3646 @ SY3645 @ SV278 ) ) @ SY3646 ) ) ) )
| ( SY3646
= ( relation_dom_restriction @ SV278 @ SY3645 ) ) )
| ~ ! [SY3647: $i,SY3648: $i] :
( ~ ( relation @ SY3648 )
| ( SY3648
!= ( relation_dom_restriction @ SV278 @ SY3647 ) )
| ~ ( ~ ! [SY3649: $i,SY3650: $i] :
( ~ ( in @ SY3649 @ SY3647 )
| ~ ( in @ ( ordered_pair @ SY3649 @ SY3650 ) @ SV278 )
| ( in @ ( ordered_pair @ SY3649 @ SY3650 ) @ SY3648 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3648 )
| ( in @ SX3 @ SY3647 ) )
| ~ ! [SY3653: $i,SY3654: $i] :
( ~ ( in @ ( ordered_pair @ SY3653 @ SY3654 ) @ SY3648 )
| ( in @ ( ordered_pair @ SY3653 @ SY3654 ) @ SV278 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2036]) ).
thf(2078,plain,
! [SV279: $i] :
( ( ~ ( relation @ SV279 )
| ~ ( ~ ! [SY3655: $i,SY3656: $i] :
( ~ ( ~ ( ! [SY3657: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ SY3656 @ SY3655 @ SV279 ) @ SY3657 ) @ SV279 )
| ~ ( in @ SY3657 @ SY3655 ) )
| ~ ( in @ ( sK43_D @ SY3656 @ SY3655 @ SV279 ) @ SY3656 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SY3656 @ SY3655 @ SV279 ) @ ( sK44_SY3116 @ SY3656 @ SY3655 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK44_SY3116 @ SY3656 @ SY3655 @ SV279 ) @ SY3655 ) )
| ( in @ ( sK43_D @ SY3656 @ SY3655 @ SV279 ) @ SY3656 ) ) )
| ( SY3656
= ( relation_inverse_image @ SV279 @ SY3655 ) ) )
| ~ ! [SY3658: $i,SY3659: $i] :
( ( SY3659
!= ( relation_inverse_image @ SV279 @ SY3658 ) )
| ~ ( ~ ! [SY3660: $i] :
( ! [SY3661: $i] :
( ~ ( in @ ( ordered_pair @ SY3660 @ SY3661 ) @ SV279 )
| ~ ( in @ SY3661 @ SY3658 ) )
| ( in @ SY3660 @ SY3659 ) )
| ~ ! [SY3662: $i] :
( ~ ( in @ SY3662 @ SY3659 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3662 @ ( sK42_E @ SY3662 @ SY3659 @ SY3658 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK42_E @ SY3662 @ SY3659 @ SY3658 @ SV279 ) @ SY3658 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2037]) ).
thf(2079,plain,
! [SV280: $i] :
( ( ~ ( relation @ SV280 )
| ~ ( ~ ! [SY3663: $i] :
( ~ ( relation @ SY3663 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3663 @ SV280 ) @ ( sK25_SY3102 @ SY3663 @ SV280 ) ) @ SV280 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3663 @ SV280 ) @ ( sK25_SY3102 @ SY3663 @ SV280 ) ) @ SY3663 ) )
| ( subset @ SV280 @ SY3663 ) )
| ~ ! [SY3664: $i] :
( ~ ( relation @ SY3664 )
| ~ ( subset @ SV280 @ SY3664 )
| ! [SY3665: $i,SY3666: $i] :
( ~ ( in @ ( ordered_pair @ SY3665 @ SY3666 ) @ SV280 )
| ( in @ ( ordered_pair @ SY3665 @ SY3666 ) @ SY3664 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2038]) ).
thf(2080,plain,
! [SV281: $i] :
( ( ~ ( relation @ SV281 )
| ! [SY3667: $i] :
( ~ ( relation @ SY3667 )
| ~ ( ~ ! [SY3668: $i] :
( ~ ( relation @ SY3668 )
| ~ ( ~ ( ! [SY3669: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3668 @ SY3667 @ SV281 ) @ SY3669 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY3669 @ ( sK8_SY3089 @ SY3668 @ SY3667 @ SV281 ) ) @ SY3667 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3668 @ SY3667 @ SV281 ) @ ( sK8_SY3089 @ SY3668 @ SY3667 @ SV281 ) ) @ SY3668 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3668 @ SY3667 @ SV281 ) @ ( sK9_SY3093 @ SY3668 @ SY3667 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SY3668 @ SY3667 @ SV281 ) @ ( sK8_SY3089 @ SY3668 @ SY3667 @ SV281 ) ) @ SY3667 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SY3668 @ SY3667 @ SV281 ) @ ( sK8_SY3089 @ SY3668 @ SY3667 @ SV281 ) ) @ SY3668 ) ) )
| ( SY3668
= ( relation_composition @ SV281 @ SY3667 ) ) )
| ~ ! [SY3670: $i] :
( ~ ( relation @ SY3670 )
| ( SY3670
!= ( relation_composition @ SV281 @ SY3667 ) )
| ~ ( ~ ! [SY3671: $i,SY3672: $i] :
( ! [SY3673: $i] :
( ~ ( in @ ( ordered_pair @ SY3671 @ SY3673 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY3673 @ SY3672 ) @ SY3667 ) )
| ( in @ ( ordered_pair @ SY3671 @ SY3672 ) @ SY3670 ) )
| ~ ! [SY3674: $i,SY3675: $i] :
( ~ ( in @ ( ordered_pair @ SY3674 @ SY3675 ) @ SY3670 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3674 @ ( sK6_F @ SY3675 @ SY3674 @ SY3670 @ SY3667 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY3675 @ SY3674 @ SY3670 @ SY3667 @ SV281 ) @ SY3675 ) @ SY3667 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2039]) ).
thf(2081,plain,
! [SV282: $i] :
( ( ~ ( ~ ! [SY3676: $i,SY3677: $i] :
( ~ ( relation_of2_as_subset @ SY3677 @ SV282 @ SY3676 )
| ~ ( ~ ! [SY3678: $i] :
~ ( in @ ( ordered_pair @ SY3678 @ ( sK57_D @ SY3677 @ SY3676 @ SV282 ) ) @ SY3677 )
| ~ ( in @ ( sK57_D @ SY3677 @ SY3676 @ SV282 ) @ SY3676 ) )
| ( ( relation_rng_as_subset @ SV282 @ SY3676 @ SY3677 )
= SY3676 ) )
| ~ ! [SY3679: $i,SY3680: $i] :
( ~ ( relation_of2_as_subset @ SY3680 @ SV282 @ SY3679 )
| ( ( relation_rng_as_subset @ SV282 @ SY3679 @ SY3680 )
!= SY3679 )
| ! [SY3681: $i] :
( ( in @ ( ordered_pair @ ( sK56_E @ SY3681 @ SY3680 @ SY3679 @ SV282 ) @ SY3681 ) @ SY3680 )
| ~ ( in @ SY3681 @ SY3679 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2040]) ).
thf(2082,plain,
! [SV283: $i] :
( ( ~ ( relation @ SV283 )
| ! [SY3682: $i] :
( ~ ( relation @ SY3682 )
| ~ ( ~ ! [SY3683: $i] :
( ~ ( function @ SY3683 )
| ~ ( relation @ SY3683 )
| ~ ( ~ ( ~ ( in @ ( sK10_D @ SY3683 @ SY3682 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( sK11_SY3094 @ SY3683 @ SY3682 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3683 @ ( sK10_D @ SY3683 @ SY3682 @ SV283 ) ) @ ( apply @ SY3683 @ ( sK11_SY3094 @ SY3683 @ SY3682 @ SV283 ) ) ) @ SY3682 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY3683 @ SY3682 @ SV283 ) @ ( sK11_SY3094 @ SY3683 @ SY3682 @ SV283 ) ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SY3683 @ SY3682 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3683 @ SY3682 @ SV283 ) @ ( sK11_SY3094 @ SY3683 @ SY3682 @ SV283 ) ) @ SV283 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SY3683 @ SY3682 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3683 @ SY3682 @ SV283 ) @ ( sK11_SY3094 @ SY3683 @ SY3682 @ SV283 ) ) @ SV283 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SY3683 @ ( sK10_D @ SY3683 @ SY3682 @ SV283 ) ) @ ( apply @ SY3683 @ ( sK11_SY3094 @ SY3683 @ SY3682 @ SV283 ) ) ) @ SY3682 )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3683 @ SY3682 @ SV283 ) @ ( sK11_SY3094 @ SY3683 @ SY3682 @ SV283 ) ) @ SV283 ) ) ) )
| ( ( relation_dom @ SY3683 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SY3683 )
!= ( relation_field @ SY3682 ) )
| ~ ( one_to_one @ SY3683 )
| ( relation_isomorphism @ SV283 @ SY3682 @ SY3683 ) )
| ~ ~ ( ~ ! [SY3684: $i] :
( ~ ( function @ SY3684 )
| ~ ( relation @ SY3684 )
| ~ ( relation_isomorphism @ SV283 @ SY3682 @ SY3684 )
| ~ ( ~ ! [SY3685: $i,SY3686: $i] :
( ~ ( in @ SY3685 @ ( relation_field @ SV283 ) )
| ~ ( in @ SY3686 @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3684 @ SY3685 ) @ ( apply @ SY3684 @ SY3686 ) ) @ SY3682 )
| ( in @ ( ordered_pair @ SY3685 @ SY3686 ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3687: $i] :
( ! [SY3688: $i] :
~ ( in @ ( ordered_pair @ SY3687 @ SY3688 ) @ SV283 )
| ( in @ SY3687 @ ( relation_field @ SV283 ) ) )
| ~ ! [SY3689: $i,SY3690: $i] :
( ~ ( in @ ( ordered_pair @ SY3689 @ SY3690 ) @ SV283 )
| ( in @ SY3690 @ ( relation_field @ SV283 ) ) ) )
| ~ ! [SY3691: $i,SY3692: $i] :
( ~ ( in @ ( ordered_pair @ SY3691 @ SY3692 ) @ SV283 )
| ( in @ ( ordered_pair @ ( apply @ SY3684 @ SY3691 ) @ ( apply @ SY3684 @ SY3692 ) ) @ SY3682 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3693: $i] :
( ~ ( function @ SY3693 )
| ~ ( relation @ SY3693 )
| ~ ( relation_isomorphism @ SV283 @ SY3682 @ SY3693 )
| ( ( relation_dom @ SY3693 )
= ( relation_field @ SV283 ) ) )
| ~ ! [SY3694: $i] :
( ~ ( function @ SY3694 )
| ~ ( relation @ SY3694 )
| ~ ( relation_isomorphism @ SV283 @ SY3682 @ SY3694 )
| ( ( relation_rng @ SY3694 )
= ( relation_field @ SY3682 ) ) ) )
| ~ ! [SY3695: $i] :
( ~ ( function @ SY3695 )
| ~ ( relation @ SY3695 )
| ~ ( relation_isomorphism @ SV283 @ SY3682 @ SY3695 )
| ( one_to_one @ SY3695 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2041]) ).
thf(2083,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK62_B @ SX0 )
!= ( sK63_SY3125 @ SX0 ) ) )
| ~ ~ ( ~ ( in @ ( sK62_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ( in @ ( sK63_SY3125 @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK62_B @ SX0 ) @ ( sK63_SY3125 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK63_SY3125 @ SX0 ) @ ( sK62_B @ SX0 ) ) @ SX0 ) )
| ( connected @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( connected @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( SX1 = SX2 )
| ~ ( in @ SX1 @ ( relation_field @ SX0 ) )
| ~ ( in @ SX2 @ ( relation_field @ SX0 ) )
| ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2042]) ).
thf(2084,plain,
! [SV284: $i] :
( ( ~ ( ~ ! [SY3696: $i,SY3697: $i] :
( ~ ( function @ SY3697 )
| ~ ( relation @ SY3697 )
| ( SY3696
!= ( apply @ SY3697 @ SV284 ) )
| ~ ( in @ SV284 @ ( relation_dom @ SY3697 ) )
| ( in @ ( ordered_pair @ SV284 @ SY3696 ) @ SY3697 ) )
| ~ ~ ( ~ ! [SY3698: $i,SY3699: $i] :
( ~ ( function @ SY3699 )
| ~ ( relation @ SY3699 )
| ~ ( in @ ( ordered_pair @ SV284 @ SY3698 ) @ SY3699 )
| ( SY3698
= ( apply @ SY3699 @ SV284 ) ) )
| ~ ! [SY3700: $i,SY3701: $i] :
( ~ ( function @ SY3701 )
| ~ ( relation @ SY3701 )
| ~ ( in @ ( ordered_pair @ SV284 @ SY3700 ) @ SY3701 )
| ( in @ SV284 @ ( relation_dom @ SY3701 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2043]) ).
thf(2085,plain,
! [SV285: $i] :
( ( ~ ( ~ ! [SY3702: $i,SY3703: $i] :
( ~ ( relation @ SY3703 )
| ! [SY3704: $i] :
( ~ ( in @ SY3704 @ ( relation_dom @ SY3703 ) )
| ~ ( in @ ( ordered_pair @ SY3704 @ SV285 ) @ SY3703 )
| ~ ( in @ SY3704 @ SY3702 ) )
| ( in @ SV285 @ ( relation_image @ SY3703 @ SY3702 ) ) )
| ~ ! [SY3705: $i,SY3706: $i] :
( ~ ( relation @ SY3706 )
| ~ ( in @ SV285 @ ( relation_image @ SY3706 @ SY3705 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK61_D @ SY3706 @ SY3705 @ SV285 ) @ ( relation_dom @ SY3706 ) )
| ~ ( in @ ( ordered_pair @ ( sK61_D @ SY3706 @ SY3705 @ SV285 ) @ SV285 ) @ SY3706 ) )
| ~ ( in @ ( sK61_D @ SY3706 @ SY3705 @ SV285 ) @ SY3705 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2086,plain,
! [SV286: $i] :
( ( ! [SY3707: $i,SY3708: $i] :
( SV286
!= ( ordered_pair @ SY3707 @ SY3708 ) )
| ~ ( ~ ! [SY3709: $i] :
( ~ ( ( SV286
!= ( ordered_pair @ ( sK40_C @ SY3709 @ SV286 ) @ ( sK41_SY3114 @ SY3709 @ SV286 ) ) )
| ~ ( ( SY3709
!= ( sK40_C @ SY3709 @ SV286 ) ) ) )
| ( SY3709
= ( pair_first @ SV286 ) ) )
| ~ ! [SY3710: $i] :
( ( SY3710
!= ( pair_first @ SV286 ) )
| ! [SY3711: $i] :
( ! [SY3712: $i] :
( SV286
!= ( ordered_pair @ SY3711 @ SY3712 ) )
| ( SY3710 = SY3711 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2045]) ).
thf(2087,plain,
! [SV287: $i] :
( ( ! [SY3713: $i,SY3714: $i] :
( SV287
!= ( ordered_pair @ SY3713 @ SY3714 ) )
| ~ ( ~ ! [SY3715: $i] :
( ~ ( ( SV287
!= ( ordered_pair @ ( sK33_C @ SY3715 @ SV287 ) @ ( sK34_SY3110 @ SY3715 @ SV287 ) ) )
| ~ ( ( SY3715
!= ( sK34_SY3110 @ SY3715 @ SV287 ) ) ) )
| ( SY3715
= ( pair_second @ SV287 ) ) )
| ~ ! [SY3716: $i] :
( ( SY3716
!= ( pair_second @ SV287 ) )
| ! [SY3717: $i,SY3718: $i] :
( ( SV287
!= ( ordered_pair @ SY3717 @ SY3718 ) )
| ( SY3716 = SY3718 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2046]) ).
thf(2088,plain,
! [SV288: $i] :
( ( ~ ( ~ ! [SY3719: $i,SY3720: $i] :
( ~ ( relation @ SY3720 )
| ~ ( in @ ( ordered_pair @ SV288 @ SY3719 ) @ SY3720 )
| ( in @ SV288 @ ( relation_dom @ SY3720 ) ) )
| ~ ! [SY3721: $i,SY3722: $i] :
( ~ ( relation @ SY3722 )
| ~ ( in @ ( ordered_pair @ SV288 @ SY3721 ) @ SY3722 )
| ( in @ SY3721 @ ( relation_rng @ SY3722 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2047]) ).
thf(2089,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK52_C @ SX1 @ SX0 )
!= ( sK53_SY3121 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK52_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK52_C @ SX1 @ SX0 ) @ ( sK53_SY3121 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK52_C @ SX1 @ SX0 )
= ( sK53_SY3121 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK52_C @ SX1 @ SX0 ) @ ( sK53_SY3121 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK52_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK52_C @ SX1 @ SX0 ) @ ( sK53_SY3121 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( SX2 = SX3 ) )
| ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2048]) ).
thf(2090,plain,
! [SV289: $i] :
( ( ~ ( ~ ! [SY3723: $i,SY3724: $i] :
( ~ ( relation_of2_as_subset @ SY3724 @ SY3723 @ SV289 )
| ~ ( ~ ! [SY3725: $i] :
~ ( in @ ( ordered_pair @ ( sK59_D @ SY3724 @ SY3723 @ SV289 ) @ SY3725 ) @ SY3724 )
| ~ ( in @ ( sK59_D @ SY3724 @ SY3723 @ SV289 ) @ SY3723 ) )
| ( ( relation_dom_as_subset @ SY3723 @ SV289 @ SY3724 )
= SY3723 ) )
| ~ ! [SY3726: $i,SY3727: $i] :
( ~ ( relation_of2_as_subset @ SY3727 @ SY3726 @ SV289 )
| ( ( relation_dom_as_subset @ SY3726 @ SV289 @ SY3727 )
!= SY3726 )
| ! [SY3728: $i] :
( ( in @ ( ordered_pair @ SY3728 @ ( sK58_E @ SY3728 @ SY3727 @ SY3726 @ SV289 ) ) @ SY3727 )
| ~ ( in @ SY3728 @ SY3726 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2049]) ).
thf(2091,plain,
! [SV290: $i] :
( ( ~ ( relation @ SV290 )
| ~ ( ~ ! [SY3729: $i] :
( ~ ( ~ ( ! [SY3730: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SY3729 @ SV290 ) @ SY3730 ) @ SV290 )
| ~ ( in @ ( sK22_C @ SY3729 @ SV290 ) @ SY3729 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SY3729 @ SV290 ) @ ( sK23_SY3101 @ SY3729 @ SV290 ) ) @ SV290 )
| ( in @ ( sK22_C @ SY3729 @ SV290 ) @ SY3729 ) ) )
| ( SY3729
= ( relation_dom @ SV290 ) ) )
| ~ ! [SY3731: $i] :
( ( SY3731
!= ( relation_dom @ SV290 ) )
| ~ ( ~ ! [SY3732: $i] :
( ! [SY3733: $i] :
~ ( in @ ( ordered_pair @ SY3732 @ SY3733 ) @ SV290 )
| ( in @ SY3732 @ SY3731 ) )
| ~ ! [SY3734: $i] :
( ~ ( in @ SY3734 @ SY3731 )
| ( in @ ( ordered_pair @ SY3734 @ ( sK21_D @ SY3734 @ SY3731 @ SV290 ) ) @ SV290 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2050]) ).
thf(2092,plain,
! [SV291: $i] :
( ( ~ ( relation @ SV291 )
| ~ ( ~ ! [SY3735: $i] :
( ~ ( relation @ SY3735 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SY3735 @ SV291 ) @ ( sK32_SY3109 @ SY3735 @ SV291 ) ) @ SV291 )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ SY3735 @ SV291 ) @ ( sK32_SY3109 @ SY3735 @ SV291 ) ) @ SY3735 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK31_C @ SY3735 @ SV291 ) @ ( sK32_SY3109 @ SY3735 @ SV291 ) ) @ SV291 )
| ( in @ ( ordered_pair @ ( sK31_C @ SY3735 @ SV291 ) @ ( sK32_SY3109 @ SY3735 @ SV291 ) ) @ SY3735 ) ) )
| ( SV291 = SY3735 ) )
| ~ ! [SY3736: $i] :
( ~ ( relation @ SY3736 )
| ( SV291 != SY3736 )
| ~ ( ~ ! [SY3737: $i,SY3738: $i] :
( ~ ( in @ ( ordered_pair @ SY3737 @ SY3738 ) @ SV291 )
| ( in @ ( ordered_pair @ SY3737 @ SY3738 ) @ SY3736 ) )
| ~ ! [SY3739: $i,SY3740: $i] :
( ~ ( in @ ( ordered_pair @ SY3739 @ SY3740 ) @ SY3736 )
| ( in @ ( ordered_pair @ SY3739 @ SY3740 ) @ SV291 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2051]) ).
thf(2093,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK66_B @ SX0 ) @ ( sK67_SY3127 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK67_SY3127 @ SX0 ) @ ( sK68_SY3129 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK66_B @ SX0 ) @ ( sK68_SY3129 @ SX0 ) ) @ SX0 ) )
| ( transitive @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( transitive @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX1 @ SX3 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2052]) ).
thf(2094,plain,
! [SV292: $i] :
( ( ~ ( relation @ SV292 )
| ~ ( ~ ! [SY3741: $i] :
( ~ ( relation @ SY3741 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SY3741 @ SV292 ) @ ( sK13_SY3095 @ SY3741 @ SV292 ) ) @ SY3741 )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SY3741 @ SV292 ) @ ( sK12_C @ SY3741 @ SV292 ) ) @ SV292 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SY3741 @ SV292 ) @ ( sK13_SY3095 @ SY3741 @ SV292 ) ) @ SY3741 )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ SY3741 @ SV292 ) @ ( sK12_C @ SY3741 @ SV292 ) ) @ SV292 ) ) )
| ( SY3741
= ( relation_inverse @ SV292 ) ) )
| ~ ! [SY3742: $i] :
( ~ ( relation @ SY3742 )
| ( SY3742
!= ( relation_inverse @ SV292 ) )
| ~ ( ~ ! [SY3743: $i,SY3744: $i] :
( ~ ( in @ ( ordered_pair @ SY3743 @ SY3744 ) @ SY3742 )
| ( in @ ( ordered_pair @ SY3744 @ SY3743 ) @ SV292 ) )
| ~ ! [SY3745: $i,SY3746: $i] :
( ~ ( in @ ( ordered_pair @ SY3746 @ SY3745 ) @ SV292 )
| ( in @ ( ordered_pair @ SY3745 @ SY3746 ) @ SY3742 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2053]) ).
thf(2095,plain,
! [SV293: $i] :
( ( ~ ( function @ SV293 )
| ~ ( relation @ SV293 )
| ~ ( ~ ~ ( ~ ! [SY3747: $i] :
( ~ ( in @ SY3747 @ ( relation_dom @ SV293 ) )
| ! [SY3748: $i] :
( ( SY3748
!= ( apply @ SV293 @ SY3747 ) )
| ( in @ ( ordered_pair @ SY3747 @ SY3748 ) @ SV293 ) ) )
| ~ ! [SY3749: $i] :
( ~ ( in @ SY3749 @ ( relation_dom @ SV293 ) )
| ! [SY3750: $i] :
( ~ ( in @ ( ordered_pair @ SY3749 @ SY3750 ) @ SV293 )
| ( SY3750
= ( apply @ SV293 @ SY3749 ) ) ) ) )
| ~ ~ ( ~ ! [SY3751: $i] :
( ( in @ SY3751 @ ( relation_dom @ SV293 ) )
| ! [SY3752: $i] :
( ( SY3752
!= ( apply @ SV293 @ SY3751 ) )
| ( SY3752 = empty_set ) ) )
| ~ ! [SY3753: $i] :
( ( in @ SY3753 @ ( relation_dom @ SV293 ) )
| ! [SY3754: $i] :
( ( SY3754 != empty_set )
| ( SY3754
= ( apply @ SV293 @ SY3753 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2054]) ).
thf(2096,plain,
! [SV294: $i] :
( ( ~ ( relation @ SV294 )
| ~ ( ~ ! [SY3755: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_C @ SY3755 @ SV294 ) @ SY3755 )
| ~ ( in @ ( sK20_SY3099 @ SY3755 @ SV294 ) @ SY3755 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SY3755 @ SV294 ) @ ( sK20_SY3099 @ SY3755 @ SV294 ) ) @ SV294 ) )
| ~ ( in @ ( ordered_pair @ ( sK20_SY3099 @ SY3755 @ SV294 ) @ ( sK19_C @ SY3755 @ SV294 ) ) @ SV294 ) )
| ~ ( ( ( sK19_C @ SY3755 @ SV294 )
!= ( sK20_SY3099 @ SY3755 @ SV294 ) ) ) )
| ( is_antisymmetric_in @ SV294 @ SY3755 ) )
| ~ ! [SY3756: $i] :
( ~ ( is_antisymmetric_in @ SV294 @ SY3756 )
| ! [SY3757: $i,SY3758: $i] :
( ~ ( in @ SY3757 @ SY3756 )
| ~ ( in @ SY3758 @ SY3756 )
| ~ ( in @ ( ordered_pair @ SY3757 @ SY3758 ) @ SV294 )
| ~ ( in @ ( ordered_pair @ SY3758 @ SY3757 ) @ SV294 )
| ( SY3757 = SY3758 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2055]) ).
thf(2097,plain,
! [SV295: $i] :
( ( ~ ( relation @ SV295 )
| ~ ( ~ ! [SY3759: $i,SY3760: $i] :
( ~ ( ~ ( ( ( sK35_D @ SY3760 @ SY3759 @ SV295 )
= SY3759 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SY3760 @ SY3759 @ SV295 ) @ SY3759 ) @ SV295 )
| ~ ( in @ ( sK35_D @ SY3760 @ SY3759 @ SV295 ) @ SY3760 ) )
| ~ ~ ( ~ ( ( ( sK35_D @ SY3760 @ SY3759 @ SV295 )
!= SY3759 )
| ( in @ ( sK35_D @ SY3760 @ SY3759 @ SV295 ) @ SY3760 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SY3760 @ SY3759 @ SV295 ) @ SY3759 ) @ SV295 )
| ( in @ ( sK35_D @ SY3760 @ SY3759 @ SV295 ) @ SY3760 ) ) ) )
| ( SY3760
= ( fiber @ SV295 @ SY3759 ) ) )
| ~ ! [SY3761: $i,SY3762: $i] :
( ( SY3762
!= ( fiber @ SV295 @ SY3761 ) )
| ~ ( ~ ! [SY3763: $i] :
( ( SY3763 = SY3761 )
| ~ ( in @ ( ordered_pair @ SY3763 @ SY3761 ) @ SV295 )
| ( in @ SY3763 @ SY3762 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY3762 )
| ( SX3 != SY3761 ) )
| ~ ! [SY3765: $i] :
( ~ ( in @ SY3765 @ SY3762 )
| ( in @ ( ordered_pair @ SY3765 @ SY3761 ) @ SV295 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2056]) ).
thf(2098,plain,
! [SV296: $i] :
( ( ! [SY3766: $i] :
( ~ ( relation @ SY3766 )
| ~ ( ~ ! [SY3767: $i] :
( ~ ( relation @ SY3767 )
| ~ ( ~ ( ~ ( in @ ( sK49_SY3119 @ SY3767 @ SY3766 @ SV296 ) @ SV296 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SY3767 @ SY3766 @ SV296 ) @ ( sK49_SY3119 @ SY3767 @ SY3766 @ SV296 ) ) @ SY3766 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SY3767 @ SY3766 @ SV296 ) @ ( sK49_SY3119 @ SY3767 @ SY3766 @ SV296 ) ) @ SY3767 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_SY3119 @ SY3767 @ SY3766 @ SV296 ) @ SV296 )
| ( in @ ( ordered_pair @ ( sK48_D @ SY3767 @ SY3766 @ SV296 ) @ ( sK49_SY3119 @ SY3767 @ SY3766 @ SV296 ) ) @ SY3767 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SY3767 @ SY3766 @ SV296 ) @ ( sK49_SY3119 @ SY3767 @ SY3766 @ SV296 ) ) @ SY3766 )
| ( in @ ( ordered_pair @ ( sK48_D @ SY3767 @ SY3766 @ SV296 ) @ ( sK49_SY3119 @ SY3767 @ SY3766 @ SV296 ) ) @ SY3767 ) ) ) )
| ( SY3767
= ( relation_rng_restriction @ SV296 @ SY3766 ) ) )
| ~ ! [SY3768: $i] :
( ~ ( relation @ SY3768 )
| ( SY3768
!= ( relation_rng_restriction @ SV296 @ SY3766 ) )
| ~ ( ~ ! [SY3769: $i,SY3770: $i] :
( ~ ( in @ SY3770 @ SV296 )
| ~ ( in @ ( ordered_pair @ SY3769 @ SY3770 ) @ SY3766 )
| ( in @ ( ordered_pair @ SY3769 @ SY3770 ) @ SY3768 ) )
| ~ ~ ( ~ ! [SY3771: $i,SY3772: $i] :
( ~ ( in @ ( ordered_pair @ SY3771 @ SY3772 ) @ SY3768 )
| ( in @ SY3772 @ SV296 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3768 )
| ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3766 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2057]) ).
thf(2099,plain,
! [SV297: $i] :
( ( ~ ( relation @ SV297 )
| ~ ( ~ ! [SY3775: $i] :
( ~ ( ~ ( ! [SY3776: $i] :
~ ( in @ ( ordered_pair @ SY3776 @ ( sK17_C @ SY3775 @ SV297 ) ) @ SV297 )
| ~ ( in @ ( sK17_C @ SY3775 @ SV297 ) @ SY3775 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK18_SY3098 @ SY3775 @ SV297 ) @ ( sK17_C @ SY3775 @ SV297 ) ) @ SV297 )
| ( in @ ( sK17_C @ SY3775 @ SV297 ) @ SY3775 ) ) )
| ( SY3775
= ( relation_rng @ SV297 ) ) )
| ~ ! [SY3777: $i] :
( ( SY3777
!= ( relation_rng @ SV297 ) )
| ~ ( ~ ! [SY3778: $i] :
( ! [SY3779: $i] :
~ ( in @ ( ordered_pair @ SY3779 @ SY3778 ) @ SV297 )
| ( in @ SY3778 @ SY3777 ) )
| ~ ! [SY3780: $i] :
( ~ ( in @ SY3780 @ SY3777 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3780 @ SY3777 @ SV297 ) @ SY3780 ) @ SV297 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2058]) ).
thf(2100,plain,
! [SV298: $i] :
( ( ~ ( ~ ! [SY3781: $i,SY3782: $i] :
( ~ ( relation @ SY3782 )
| ~ ( in @ ( ordered_pair @ SV298 @ SY3781 ) @ SY3782 )
| ( in @ SV298 @ ( relation_field @ SY3782 ) ) )
| ~ ! [SY3783: $i,SY3784: $i] :
( ~ ( relation @ SY3784 )
| ~ ( in @ ( ordered_pair @ SV298 @ SY3783 ) @ SY3784 )
| ( in @ SY3783 @ ( relation_field @ SY3784 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2059]) ).
thf(2101,plain,
! [SV299: $i] :
( ( ! [SY3785: $i] :
~ ( ~ ! [SY3786: $i,SY3787: $i] :
( ~ ( relation @ SY3787 )
| ~ ( in @ SV299 @ SY3786 )
| ~ ( in @ ( ordered_pair @ SV299 @ SY3785 ) @ SY3787 )
| ( in @ ( ordered_pair @ SV299 @ SY3785 ) @ ( relation_composition @ ( identity_relation @ SY3786 ) @ SY3787 ) ) )
| ~ ~ ( ~ ! [SY3788: $i,SY3789: $i] :
( ~ ( relation @ SY3789 )
| ~ ( in @ ( ordered_pair @ SV299 @ SY3785 ) @ ( relation_composition @ ( identity_relation @ SY3788 ) @ SY3789 ) )
| ( in @ SV299 @ SY3788 ) )
| ~ ! [SY3790: $i,SY3791: $i] :
( ~ ( relation @ SY3791 )
| ~ ( in @ ( ordered_pair @ SV299 @ SY3785 ) @ ( relation_composition @ ( identity_relation @ SY3790 ) @ SY3791 ) )
| ( in @ ( ordered_pair @ SV299 @ SY3785 ) @ SY3791 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(2102,plain,
! [SV300: $i] :
( ( ! [SY3792: $i] :
~ ( ~ ! [SY3793: $i] :
( ! [SY3794: $i] :
( ( ordered_pair @ SV300 @ SY3792 )
!= ( ordered_pair @ SY3793 @ SY3794 ) )
| ( SV300 = SY3793 ) )
| ~ ! [SY3795: $i,SY3796: $i] :
( ( ( ordered_pair @ SV300 @ SY3792 )
!= ( ordered_pair @ SY3795 @ SY3796 ) )
| ( SY3792 = SY3796 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(2103,plain,
! [SV301: $i] :
( ( ~ ( ~ ! [SY3797: $i,SY3798: $i] :
( ~ ( relation @ SY3798 )
| ! [SY3799: $i] :
( ~ ( in @ SY3799 @ ( relation_rng @ SY3798 ) )
| ~ ( in @ ( ordered_pair @ SV301 @ SY3799 ) @ SY3798 )
| ~ ( in @ SY3799 @ SY3797 ) )
| ( in @ SV301 @ ( relation_inverse_image @ SY3798 @ SY3797 ) ) )
| ~ ! [SY3800: $i,SY3801: $i] :
( ~ ( relation @ SY3801 )
| ~ ( in @ SV301 @ ( relation_inverse_image @ SY3801 @ SY3800 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_D @ SY3801 @ SY3800 @ SV301 ) @ ( relation_rng @ SY3801 ) )
| ~ ( in @ ( ordered_pair @ SV301 @ ( sK60_D @ SY3801 @ SY3800 @ SV301 ) ) @ SY3801 ) )
| ~ ( in @ ( sK60_D @ SY3801 @ SY3800 @ SV301 ) @ SY3800 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2062]) ).
thf(2104,plain,
! [SV302: $i] :
( ( ~ ( relation @ SV302 )
| ~ ( ~ ! [SY3802: $i] :
( ~ ( ~ ( in @ ( sK36_C @ SY3802 @ SV302 ) @ SY3802 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SY3802 @ SV302 ) @ ( sK36_C @ SY3802 @ SV302 ) ) @ SV302 ) )
| ( is_reflexive_in @ SV302 @ SY3802 ) )
| ~ ! [SY3803: $i] :
( ~ ( is_reflexive_in @ SV302 @ SY3803 )
| ! [SY3804: $i] :
( ~ ( in @ SY3804 @ SY3803 )
| ( in @ ( ordered_pair @ SY3804 @ SY3804 ) @ SV302 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2063]) ).
thf(2105,plain,
! [SV269: $i] :
( ( ( ~ ( relation @ SV269 ) )
= $true )
| ( ( ( in @ ( ordered_pair @ ( sK54_B @ SV269 ) @ ( sK55_SY3122 @ SV269 ) ) @ SV269 )
| ( SV269 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2064]) ).
thf(2106,plain,
! [SV303: $i,SV270: $i] :
( ( ( ordered_pair @ SV270 @ SV303 )
= ( unordered_pair @ ( unordered_pair @ SV270 @ SV303 ) @ ( singleton @ SV270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2065]) ).
thf(2107,plain,
! [SV304: $i,SV271: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV271 @ SV304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2066]) ).
thf(2108,plain,
! [SV305: $i,SV272: $i] :
( ( ~ ( ~ ! [SY3805: $i,SY3806: $i] :
( ~ ( in @ SV272 @ SY3805 )
| ~ ( in @ SV305 @ SY3806 )
| ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SY3805 @ SY3806 ) ) )
| ~ ~ ( ~ ! [SY3807: $i] :
( ! [SY3808: $i] :
~ ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SY3807 @ SY3808 ) )
| ( in @ SV272 @ SY3807 ) )
| ~ ! [SY3809: $i,SY3810: $i] :
( ~ ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SY3809 @ SY3810 ) )
| ( in @ SV305 @ SY3810 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2068]) ).
thf(2109,plain,
! [SV306: $i,SV273: $i] :
( ( ~ ( ~ ! [SY3811: $i,SY3812: $i] :
( ~ ( in @ SV273 @ SY3811 )
| ~ ( in @ SV306 @ SY3812 )
| ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SY3811 @ SY3812 ) ) )
| ~ ~ ( ~ ! [SY3813: $i] :
( ! [SY3814: $i] :
~ ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SY3813 @ SY3814 ) )
| ( in @ SV273 @ SY3813 ) )
| ~ ! [SY3815: $i,SY3816: $i] :
( ~ ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SY3815 @ SY3816 ) )
| ( in @ SV306 @ SY3816 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2069]) ).
thf(2110,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( in @ ( sK69_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK69_B @ SX0 ) @ ( sK69_B @ SX0 ) ) @ SX0 ) )
| ( reflexive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2070]) ).
thf(2111,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ ( relation_field @ SX0 ) )
| ( in @ ( ordered_pair @ SX1 @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2070]) ).
thf(2112,plain,
! [SV274: $i] :
( ( ( ~ ( relation @ SV274 ) )
= $true )
| ( ( ~ ( ~ ! [SY3618: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK14_C @ SY3618 @ SV274 )
!= ( sK15_SY3096 @ SY3618 @ SV274 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SY3618 @ SV274 ) @ SY3618 )
| ~ ( in @ ( sK15_SY3096 @ SY3618 @ SV274 ) @ SY3618 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK14_C @ SY3618 @ SV274 ) @ ( sK15_SY3096 @ SY3618 @ SV274 ) ) @ SV274 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK15_SY3096 @ SY3618 @ SV274 ) @ ( sK14_C @ SY3618 @ SV274 ) ) @ SV274 ) )
| ( is_connected_in @ SV274 @ SY3618 ) )
| ~ ! [SY3619: $i] :
( ~ ( is_connected_in @ SV274 @ SY3619 )
| ! [SY3620: $i,SY3621: $i] :
( ( SY3620 = SY3621 )
| ~ ( in @ SY3620 @ SY3619 )
| ~ ( in @ SY3621 @ SY3619 )
| ( in @ ( ordered_pair @ SY3620 @ SY3621 ) @ SV274 )
| ( in @ ( ordered_pair @ SY3621 @ SY3620 ) @ SV274 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2071]) ).
thf(2113,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK39_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK39_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2072]) ).
thf(2114,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK37_C @ SX1 @ SX0 ) @ ( sK38_SY3111 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2072]) ).
thf(2115,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK64_B @ SX0 ) @ ( sK65_SY3126 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK65_SY3126 @ SX0 ) @ ( sK64_B @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK64_B @ SX0 )
!= ( sK65_SY3126 @ SX0 ) ) ) )
| ( antisymmetric @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2073]) ).
thf(2116,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX2 @ SX1 ) @ SX0 )
| ( SX1 = SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2073]) ).
thf(2117,plain,
! [SV275: $i] :
( ( ~ ! [SY3622: $i,SY3623: $i] :
( ~ ( ~ ( ! [SY3624: $i,SY3625: $i] :
( ~ ( in @ SY3624 @ SV275 )
| ~ ( in @ SY3625 @ SY3622 )
| ( ( sK28_D @ SY3623 @ SY3622 @ SV275 )
!= ( ordered_pair @ SY3624 @ SY3625 ) ) )
| ~ ( in @ ( sK28_D @ SY3623 @ SY3622 @ SV275 ) @ SY3623 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY3106 @ SY3623 @ SY3622 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK30_SY3108 @ SY3623 @ SY3622 @ SV275 ) @ SY3622 ) )
| ( ( sK28_D @ SY3623 @ SY3622 @ SV275 )
!= ( ordered_pair @ ( sK29_SY3106 @ SY3623 @ SY3622 @ SV275 ) @ ( sK30_SY3108 @ SY3623 @ SY3622 @ SV275 ) ) ) )
| ( in @ ( sK28_D @ SY3623 @ SY3622 @ SV275 ) @ SY3623 ) ) )
| ( SY3623
= ( cartesian_product2 @ SV275 @ SY3622 ) ) )
| ~ ! [SY3626: $i,SY3627: $i] :
( ( SY3627
!= ( cartesian_product2 @ SV275 @ SY3626 ) )
| ~ ( ~ ! [SY3628: $i] :
( ! [SY3629: $i,SY3630: $i] :
( ~ ( in @ SY3629 @ SV275 )
| ~ ( in @ SY3630 @ SY3626 )
| ( SY3628
!= ( ordered_pair @ SY3629 @ SY3630 ) ) )
| ( in @ SY3628 @ SY3627 ) )
| ~ ! [SY3631: $i] :
( ~ ( in @ SY3631 @ SY3627 )
| ~ ( ~ ~ ( ~ ( in @ ( sK26_E @ SY3631 @ SY3627 @ SY3626 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK27_SY3103 @ SY3631 @ SY3627 @ SY3626 @ SV275 ) @ SY3626 ) )
| ( SY3631
!= ( ordered_pair @ ( sK26_E @ SY3631 @ SY3627 @ SY3626 @ SV275 ) @ ( sK27_SY3103 @ SY3631 @ SY3627 @ SY3626 @ SV275 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2074]) ).
thf(2118,plain,
! [SV276: $i] :
( ( ( ~ ( relation @ SV276 ) )
= $true )
| ( ( ~ ( ~ ! [SY3632: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SY3632 @ SV276 ) @ SY3632 )
| ~ ( in @ ( sK4_SY3086 @ SY3632 @ SV276 ) @ SY3632 ) )
| ~ ( in @ ( sK5_SY3088 @ SY3632 @ SV276 ) @ SY3632 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SY3632 @ SV276 ) @ ( sK4_SY3086 @ SY3632 @ SV276 ) ) @ SV276 ) )
| ~ ( in @ ( ordered_pair @ ( sK4_SY3086 @ SY3632 @ SV276 ) @ ( sK5_SY3088 @ SY3632 @ SV276 ) ) @ SV276 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK3_C @ SY3632 @ SV276 ) @ ( sK5_SY3088 @ SY3632 @ SV276 ) ) @ SV276 ) )
| ( is_transitive_in @ SV276 @ SY3632 ) )
| ~ ! [SY3633: $i] :
( ~ ( is_transitive_in @ SV276 @ SY3633 )
| ! [SY3634: $i,SY3635: $i,SY3636: $i] :
( ~ ( in @ SY3634 @ SY3633 )
| ~ ( in @ SY3635 @ SY3633 )
| ~ ( in @ SY3636 @ SY3633 )
| ~ ( in @ ( ordered_pair @ SY3634 @ SY3635 ) @ SV276 )
| ~ ( in @ ( ordered_pair @ SY3635 @ SY3636 ) @ SV276 )
| ( in @ ( ordered_pair @ SY3634 @ SY3636 ) @ SV276 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2075]) ).
thf(2119,plain,
! [SV277: $i] :
( ( ( ~ ( relation @ SV277 ) )
= $true )
| ( ( ~ ( ~ ! [SY3637: $i,SY3638: $i] :
( ~ ( ~ ( ! [SY3639: $i] :
( ~ ( in @ ( ordered_pair @ SY3639 @ ( sK46_D @ SY3638 @ SY3637 @ SV277 ) ) @ SV277 )
| ~ ( in @ SY3639 @ SY3637 ) )
| ~ ( in @ ( sK46_D @ SY3638 @ SY3637 @ SV277 ) @ SY3638 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SY3638 @ SY3637 @ SV277 ) @ ( sK46_D @ SY3638 @ SY3637 @ SV277 ) ) @ SV277 )
| ~ ( in @ ( sK47_SY3118 @ SY3638 @ SY3637 @ SV277 ) @ SY3637 ) )
| ( in @ ( sK46_D @ SY3638 @ SY3637 @ SV277 ) @ SY3638 ) ) )
| ( SY3638
= ( relation_image @ SV277 @ SY3637 ) ) )
| ~ ! [SY3640: $i,SY3641: $i] :
( ( SY3641
!= ( relation_image @ SV277 @ SY3640 ) )
| ~ ( ~ ! [SY3642: $i] :
( ! [SY3643: $i] :
( ~ ( in @ ( ordered_pair @ SY3643 @ SY3642 ) @ SV277 )
| ~ ( in @ SY3643 @ SY3640 ) )
| ( in @ SY3642 @ SY3641 ) )
| ~ ! [SY3644: $i] :
( ~ ( in @ SY3644 @ SY3641 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SY3644 @ SY3641 @ SY3640 @ SV277 ) @ SY3644 ) @ SV277 )
| ~ ( in @ ( sK45_E @ SY3644 @ SY3641 @ SY3640 @ SV277 ) @ SY3640 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2076]) ).
thf(2120,plain,
! [SV278: $i] :
( ( ( ~ ( relation @ SV278 ) )
= $true )
| ( ( ~ ( ~ ! [SY3645: $i,SY3646: $i] :
( ~ ( relation @ SY3646 )
| ~ ( ~ ( ~ ( in @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ SY3645 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ ( sK51_SY3120 @ SY3646 @ SY3645 @ SV278 ) ) @ SV278 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ ( sK51_SY3120 @ SY3646 @ SY3645 @ SV278 ) ) @ SY3646 ) )
| ~ ~ ( ~ ( ( in @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ SY3645 )
| ( in @ ( ordered_pair @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ ( sK51_SY3120 @ SY3646 @ SY3645 @ SV278 ) ) @ SY3646 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ ( sK51_SY3120 @ SY3646 @ SY3645 @ SV278 ) ) @ SV278 )
| ( in @ ( ordered_pair @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ ( sK51_SY3120 @ SY3646 @ SY3645 @ SV278 ) ) @ SY3646 ) ) ) )
| ( SY3646
= ( relation_dom_restriction @ SV278 @ SY3645 ) ) )
| ~ ! [SY3647: $i,SY3648: $i] :
( ~ ( relation @ SY3648 )
| ( SY3648
!= ( relation_dom_restriction @ SV278 @ SY3647 ) )
| ~ ( ~ ! [SY3649: $i,SY3650: $i] :
( ~ ( in @ SY3649 @ SY3647 )
| ~ ( in @ ( ordered_pair @ SY3649 @ SY3650 ) @ SV278 )
| ( in @ ( ordered_pair @ SY3649 @ SY3650 ) @ SY3648 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3648 )
| ( in @ SX3 @ SY3647 ) )
| ~ ! [SY3653: $i,SY3654: $i] :
( ~ ( in @ ( ordered_pair @ SY3653 @ SY3654 ) @ SY3648 )
| ( in @ ( ordered_pair @ SY3653 @ SY3654 ) @ SV278 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2077]) ).
thf(2121,plain,
! [SV279: $i] :
( ( ( ~ ( relation @ SV279 ) )
= $true )
| ( ( ~ ( ~ ! [SY3655: $i,SY3656: $i] :
( ~ ( ~ ( ! [SY3657: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ SY3656 @ SY3655 @ SV279 ) @ SY3657 ) @ SV279 )
| ~ ( in @ SY3657 @ SY3655 ) )
| ~ ( in @ ( sK43_D @ SY3656 @ SY3655 @ SV279 ) @ SY3656 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SY3656 @ SY3655 @ SV279 ) @ ( sK44_SY3116 @ SY3656 @ SY3655 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK44_SY3116 @ SY3656 @ SY3655 @ SV279 ) @ SY3655 ) )
| ( in @ ( sK43_D @ SY3656 @ SY3655 @ SV279 ) @ SY3656 ) ) )
| ( SY3656
= ( relation_inverse_image @ SV279 @ SY3655 ) ) )
| ~ ! [SY3658: $i,SY3659: $i] :
( ( SY3659
!= ( relation_inverse_image @ SV279 @ SY3658 ) )
| ~ ( ~ ! [SY3660: $i] :
( ! [SY3661: $i] :
( ~ ( in @ ( ordered_pair @ SY3660 @ SY3661 ) @ SV279 )
| ~ ( in @ SY3661 @ SY3658 ) )
| ( in @ SY3660 @ SY3659 ) )
| ~ ! [SY3662: $i] :
( ~ ( in @ SY3662 @ SY3659 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3662 @ ( sK42_E @ SY3662 @ SY3659 @ SY3658 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK42_E @ SY3662 @ SY3659 @ SY3658 @ SV279 ) @ SY3658 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2078]) ).
thf(2122,plain,
! [SV280: $i] :
( ( ( ~ ( relation @ SV280 ) )
= $true )
| ( ( ~ ( ~ ! [SY3663: $i] :
( ~ ( relation @ SY3663 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3663 @ SV280 ) @ ( sK25_SY3102 @ SY3663 @ SV280 ) ) @ SV280 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3663 @ SV280 ) @ ( sK25_SY3102 @ SY3663 @ SV280 ) ) @ SY3663 ) )
| ( subset @ SV280 @ SY3663 ) )
| ~ ! [SY3664: $i] :
( ~ ( relation @ SY3664 )
| ~ ( subset @ SV280 @ SY3664 )
| ! [SY3665: $i,SY3666: $i] :
( ~ ( in @ ( ordered_pair @ SY3665 @ SY3666 ) @ SV280 )
| ( in @ ( ordered_pair @ SY3665 @ SY3666 ) @ SY3664 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2079]) ).
thf(2123,plain,
! [SV281: $i] :
( ( ( ~ ( relation @ SV281 ) )
= $true )
| ( ( ! [SY3667: $i] :
( ~ ( relation @ SY3667 )
| ~ ( ~ ! [SY3668: $i] :
( ~ ( relation @ SY3668 )
| ~ ( ~ ( ! [SY3669: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3668 @ SY3667 @ SV281 ) @ SY3669 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY3669 @ ( sK8_SY3089 @ SY3668 @ SY3667 @ SV281 ) ) @ SY3667 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3668 @ SY3667 @ SV281 ) @ ( sK8_SY3089 @ SY3668 @ SY3667 @ SV281 ) ) @ SY3668 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3668 @ SY3667 @ SV281 ) @ ( sK9_SY3093 @ SY3668 @ SY3667 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SY3668 @ SY3667 @ SV281 ) @ ( sK8_SY3089 @ SY3668 @ SY3667 @ SV281 ) ) @ SY3667 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SY3668 @ SY3667 @ SV281 ) @ ( sK8_SY3089 @ SY3668 @ SY3667 @ SV281 ) ) @ SY3668 ) ) )
| ( SY3668
= ( relation_composition @ SV281 @ SY3667 ) ) )
| ~ ! [SY3670: $i] :
( ~ ( relation @ SY3670 )
| ( SY3670
!= ( relation_composition @ SV281 @ SY3667 ) )
| ~ ( ~ ! [SY3671: $i,SY3672: $i] :
( ! [SY3673: $i] :
( ~ ( in @ ( ordered_pair @ SY3671 @ SY3673 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY3673 @ SY3672 ) @ SY3667 ) )
| ( in @ ( ordered_pair @ SY3671 @ SY3672 ) @ SY3670 ) )
| ~ ! [SY3674: $i,SY3675: $i] :
( ~ ( in @ ( ordered_pair @ SY3674 @ SY3675 ) @ SY3670 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3674 @ ( sK6_F @ SY3675 @ SY3674 @ SY3670 @ SY3667 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY3675 @ SY3674 @ SY3670 @ SY3667 @ SV281 ) @ SY3675 ) @ SY3667 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2080]) ).
thf(2124,plain,
! [SV282: $i] :
( ( ~ ! [SY3676: $i,SY3677: $i] :
( ~ ( relation_of2_as_subset @ SY3677 @ SV282 @ SY3676 )
| ~ ( ~ ! [SY3678: $i] :
~ ( in @ ( ordered_pair @ SY3678 @ ( sK57_D @ SY3677 @ SY3676 @ SV282 ) ) @ SY3677 )
| ~ ( in @ ( sK57_D @ SY3677 @ SY3676 @ SV282 ) @ SY3676 ) )
| ( ( relation_rng_as_subset @ SV282 @ SY3676 @ SY3677 )
= SY3676 ) )
| ~ ! [SY3679: $i,SY3680: $i] :
( ~ ( relation_of2_as_subset @ SY3680 @ SV282 @ SY3679 )
| ( ( relation_rng_as_subset @ SV282 @ SY3679 @ SY3680 )
!= SY3679 )
| ! [SY3681: $i] :
( ( in @ ( ordered_pair @ ( sK56_E @ SY3681 @ SY3680 @ SY3679 @ SV282 ) @ SY3681 ) @ SY3680 )
| ~ ( in @ SY3681 @ SY3679 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2081]) ).
thf(2125,plain,
! [SV283: $i] :
( ( ( ~ ( relation @ SV283 ) )
= $true )
| ( ( ! [SY3682: $i] :
( ~ ( relation @ SY3682 )
| ~ ( ~ ! [SY3683: $i] :
( ~ ( function @ SY3683 )
| ~ ( relation @ SY3683 )
| ~ ( ~ ( ~ ( in @ ( sK10_D @ SY3683 @ SY3682 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( sK11_SY3094 @ SY3683 @ SY3682 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3683 @ ( sK10_D @ SY3683 @ SY3682 @ SV283 ) ) @ ( apply @ SY3683 @ ( sK11_SY3094 @ SY3683 @ SY3682 @ SV283 ) ) ) @ SY3682 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY3683 @ SY3682 @ SV283 ) @ ( sK11_SY3094 @ SY3683 @ SY3682 @ SV283 ) ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SY3683 @ SY3682 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3683 @ SY3682 @ SV283 ) @ ( sK11_SY3094 @ SY3683 @ SY3682 @ SV283 ) ) @ SV283 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SY3683 @ SY3682 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3683 @ SY3682 @ SV283 ) @ ( sK11_SY3094 @ SY3683 @ SY3682 @ SV283 ) ) @ SV283 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SY3683 @ ( sK10_D @ SY3683 @ SY3682 @ SV283 ) ) @ ( apply @ SY3683 @ ( sK11_SY3094 @ SY3683 @ SY3682 @ SV283 ) ) ) @ SY3682 )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3683 @ SY3682 @ SV283 ) @ ( sK11_SY3094 @ SY3683 @ SY3682 @ SV283 ) ) @ SV283 ) ) ) )
| ( ( relation_dom @ SY3683 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SY3683 )
!= ( relation_field @ SY3682 ) )
| ~ ( one_to_one @ SY3683 )
| ( relation_isomorphism @ SV283 @ SY3682 @ SY3683 ) )
| ~ ~ ( ~ ! [SY3684: $i] :
( ~ ( function @ SY3684 )
| ~ ( relation @ SY3684 )
| ~ ( relation_isomorphism @ SV283 @ SY3682 @ SY3684 )
| ~ ( ~ ! [SY3685: $i,SY3686: $i] :
( ~ ( in @ SY3685 @ ( relation_field @ SV283 ) )
| ~ ( in @ SY3686 @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3684 @ SY3685 ) @ ( apply @ SY3684 @ SY3686 ) ) @ SY3682 )
| ( in @ ( ordered_pair @ SY3685 @ SY3686 ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3687: $i] :
( ! [SY3688: $i] :
~ ( in @ ( ordered_pair @ SY3687 @ SY3688 ) @ SV283 )
| ( in @ SY3687 @ ( relation_field @ SV283 ) ) )
| ~ ! [SY3689: $i,SY3690: $i] :
( ~ ( in @ ( ordered_pair @ SY3689 @ SY3690 ) @ SV283 )
| ( in @ SY3690 @ ( relation_field @ SV283 ) ) ) )
| ~ ! [SY3691: $i,SY3692: $i] :
( ~ ( in @ ( ordered_pair @ SY3691 @ SY3692 ) @ SV283 )
| ( in @ ( ordered_pair @ ( apply @ SY3684 @ SY3691 ) @ ( apply @ SY3684 @ SY3692 ) ) @ SY3682 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3693: $i] :
( ~ ( function @ SY3693 )
| ~ ( relation @ SY3693 )
| ~ ( relation_isomorphism @ SV283 @ SY3682 @ SY3693 )
| ( ( relation_dom @ SY3693 )
= ( relation_field @ SV283 ) ) )
| ~ ! [SY3694: $i] :
( ~ ( function @ SY3694 )
| ~ ( relation @ SY3694 )
| ~ ( relation_isomorphism @ SV283 @ SY3682 @ SY3694 )
| ( ( relation_rng @ SY3694 )
= ( relation_field @ SY3682 ) ) ) )
| ~ ! [SY3695: $i] :
( ~ ( function @ SY3695 )
| ~ ( relation @ SY3695 )
| ~ ( relation_isomorphism @ SV283 @ SY3682 @ SY3695 )
| ( one_to_one @ SY3695 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2082]) ).
thf(2126,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK62_B @ SX0 )
!= ( sK63_SY3125 @ SX0 ) ) )
| ~ ~ ( ~ ( in @ ( sK62_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ( in @ ( sK63_SY3125 @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK62_B @ SX0 ) @ ( sK63_SY3125 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK63_SY3125 @ SX0 ) @ ( sK62_B @ SX0 ) ) @ SX0 ) )
| ( connected @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2083]) ).
thf(2127,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( connected @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( SX1 = SX2 )
| ~ ( in @ SX1 @ ( relation_field @ SX0 ) )
| ~ ( in @ SX2 @ ( relation_field @ SX0 ) )
| ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2083]) ).
thf(2128,plain,
! [SV284: $i] :
( ( ~ ! [SY3696: $i,SY3697: $i] :
( ~ ( function @ SY3697 )
| ~ ( relation @ SY3697 )
| ( SY3696
!= ( apply @ SY3697 @ SV284 ) )
| ~ ( in @ SV284 @ ( relation_dom @ SY3697 ) )
| ( in @ ( ordered_pair @ SV284 @ SY3696 ) @ SY3697 ) )
| ~ ~ ( ~ ! [SY3698: $i,SY3699: $i] :
( ~ ( function @ SY3699 )
| ~ ( relation @ SY3699 )
| ~ ( in @ ( ordered_pair @ SV284 @ SY3698 ) @ SY3699 )
| ( SY3698
= ( apply @ SY3699 @ SV284 ) ) )
| ~ ! [SY3700: $i,SY3701: $i] :
( ~ ( function @ SY3701 )
| ~ ( relation @ SY3701 )
| ~ ( in @ ( ordered_pair @ SV284 @ SY3700 ) @ SY3701 )
| ( in @ SV284 @ ( relation_dom @ SY3701 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2084]) ).
thf(2129,plain,
! [SV285: $i] :
( ( ~ ! [SY3702: $i,SY3703: $i] :
( ~ ( relation @ SY3703 )
| ! [SY3704: $i] :
( ~ ( in @ SY3704 @ ( relation_dom @ SY3703 ) )
| ~ ( in @ ( ordered_pair @ SY3704 @ SV285 ) @ SY3703 )
| ~ ( in @ SY3704 @ SY3702 ) )
| ( in @ SV285 @ ( relation_image @ SY3703 @ SY3702 ) ) )
| ~ ! [SY3705: $i,SY3706: $i] :
( ~ ( relation @ SY3706 )
| ~ ( in @ SV285 @ ( relation_image @ SY3706 @ SY3705 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK61_D @ SY3706 @ SY3705 @ SV285 ) @ ( relation_dom @ SY3706 ) )
| ~ ( in @ ( ordered_pair @ ( sK61_D @ SY3706 @ SY3705 @ SV285 ) @ SV285 ) @ SY3706 ) )
| ~ ( in @ ( sK61_D @ SY3706 @ SY3705 @ SV285 ) @ SY3705 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2085]) ).
thf(2130,plain,
! [SV286: $i] :
( ( ( ! [SY3707: $i,SY3708: $i] :
( SV286
!= ( ordered_pair @ SY3707 @ SY3708 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3709: $i] :
( ~ ( ( SV286
!= ( ordered_pair @ ( sK40_C @ SY3709 @ SV286 ) @ ( sK41_SY3114 @ SY3709 @ SV286 ) ) )
| ~ ( ( SY3709
!= ( sK40_C @ SY3709 @ SV286 ) ) ) )
| ( SY3709
= ( pair_first @ SV286 ) ) )
| ~ ! [SY3710: $i] :
( ( SY3710
!= ( pair_first @ SV286 ) )
| ! [SY3711: $i] :
( ! [SY3712: $i] :
( SV286
!= ( ordered_pair @ SY3711 @ SY3712 ) )
| ( SY3710 = SY3711 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2086]) ).
thf(2131,plain,
! [SV287: $i] :
( ( ( ! [SY3713: $i,SY3714: $i] :
( SV287
!= ( ordered_pair @ SY3713 @ SY3714 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3715: $i] :
( ~ ( ( SV287
!= ( ordered_pair @ ( sK33_C @ SY3715 @ SV287 ) @ ( sK34_SY3110 @ SY3715 @ SV287 ) ) )
| ~ ( ( SY3715
!= ( sK34_SY3110 @ SY3715 @ SV287 ) ) ) )
| ( SY3715
= ( pair_second @ SV287 ) ) )
| ~ ! [SY3716: $i] :
( ( SY3716
!= ( pair_second @ SV287 ) )
| ! [SY3717: $i,SY3718: $i] :
( ( SV287
!= ( ordered_pair @ SY3717 @ SY3718 ) )
| ( SY3716 = SY3718 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2087]) ).
thf(2132,plain,
! [SV288: $i] :
( ( ~ ! [SY3719: $i,SY3720: $i] :
( ~ ( relation @ SY3720 )
| ~ ( in @ ( ordered_pair @ SV288 @ SY3719 ) @ SY3720 )
| ( in @ SV288 @ ( relation_dom @ SY3720 ) ) )
| ~ ! [SY3721: $i,SY3722: $i] :
( ~ ( relation @ SY3722 )
| ~ ( in @ ( ordered_pair @ SV288 @ SY3721 ) @ SY3722 )
| ( in @ SY3721 @ ( relation_rng @ SY3722 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2088]) ).
thf(2133,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK52_C @ SX1 @ SX0 )
!= ( sK53_SY3121 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK52_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK52_C @ SX1 @ SX0 ) @ ( sK53_SY3121 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK52_C @ SX1 @ SX0 )
= ( sK53_SY3121 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK52_C @ SX1 @ SX0 ) @ ( sK53_SY3121 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK52_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK52_C @ SX1 @ SX0 ) @ ( sK53_SY3121 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2089]) ).
thf(2134,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( SX2 = SX3 ) )
| ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2089]) ).
thf(2135,plain,
! [SV289: $i] :
( ( ~ ! [SY3723: $i,SY3724: $i] :
( ~ ( relation_of2_as_subset @ SY3724 @ SY3723 @ SV289 )
| ~ ( ~ ! [SY3725: $i] :
~ ( in @ ( ordered_pair @ ( sK59_D @ SY3724 @ SY3723 @ SV289 ) @ SY3725 ) @ SY3724 )
| ~ ( in @ ( sK59_D @ SY3724 @ SY3723 @ SV289 ) @ SY3723 ) )
| ( ( relation_dom_as_subset @ SY3723 @ SV289 @ SY3724 )
= SY3723 ) )
| ~ ! [SY3726: $i,SY3727: $i] :
( ~ ( relation_of2_as_subset @ SY3727 @ SY3726 @ SV289 )
| ( ( relation_dom_as_subset @ SY3726 @ SV289 @ SY3727 )
!= SY3726 )
| ! [SY3728: $i] :
( ( in @ ( ordered_pair @ SY3728 @ ( sK58_E @ SY3728 @ SY3727 @ SY3726 @ SV289 ) ) @ SY3727 )
| ~ ( in @ SY3728 @ SY3726 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2090]) ).
thf(2136,plain,
! [SV290: $i] :
( ( ( ~ ( relation @ SV290 ) )
= $true )
| ( ( ~ ( ~ ! [SY3729: $i] :
( ~ ( ~ ( ! [SY3730: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SY3729 @ SV290 ) @ SY3730 ) @ SV290 )
| ~ ( in @ ( sK22_C @ SY3729 @ SV290 ) @ SY3729 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SY3729 @ SV290 ) @ ( sK23_SY3101 @ SY3729 @ SV290 ) ) @ SV290 )
| ( in @ ( sK22_C @ SY3729 @ SV290 ) @ SY3729 ) ) )
| ( SY3729
= ( relation_dom @ SV290 ) ) )
| ~ ! [SY3731: $i] :
( ( SY3731
!= ( relation_dom @ SV290 ) )
| ~ ( ~ ! [SY3732: $i] :
( ! [SY3733: $i] :
~ ( in @ ( ordered_pair @ SY3732 @ SY3733 ) @ SV290 )
| ( in @ SY3732 @ SY3731 ) )
| ~ ! [SY3734: $i] :
( ~ ( in @ SY3734 @ SY3731 )
| ( in @ ( ordered_pair @ SY3734 @ ( sK21_D @ SY3734 @ SY3731 @ SV290 ) ) @ SV290 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2091]) ).
thf(2137,plain,
! [SV291: $i] :
( ( ( ~ ( relation @ SV291 ) )
= $true )
| ( ( ~ ( ~ ! [SY3735: $i] :
( ~ ( relation @ SY3735 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SY3735 @ SV291 ) @ ( sK32_SY3109 @ SY3735 @ SV291 ) ) @ SV291 )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ SY3735 @ SV291 ) @ ( sK32_SY3109 @ SY3735 @ SV291 ) ) @ SY3735 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK31_C @ SY3735 @ SV291 ) @ ( sK32_SY3109 @ SY3735 @ SV291 ) ) @ SV291 )
| ( in @ ( ordered_pair @ ( sK31_C @ SY3735 @ SV291 ) @ ( sK32_SY3109 @ SY3735 @ SV291 ) ) @ SY3735 ) ) )
| ( SV291 = SY3735 ) )
| ~ ! [SY3736: $i] :
( ~ ( relation @ SY3736 )
| ( SV291 != SY3736 )
| ~ ( ~ ! [SY3737: $i,SY3738: $i] :
( ~ ( in @ ( ordered_pair @ SY3737 @ SY3738 ) @ SV291 )
| ( in @ ( ordered_pair @ SY3737 @ SY3738 ) @ SY3736 ) )
| ~ ! [SY3739: $i,SY3740: $i] :
( ~ ( in @ ( ordered_pair @ SY3739 @ SY3740 ) @ SY3736 )
| ( in @ ( ordered_pair @ SY3739 @ SY3740 ) @ SV291 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2092]) ).
thf(2138,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK66_B @ SX0 ) @ ( sK67_SY3127 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK67_SY3127 @ SX0 ) @ ( sK68_SY3129 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK66_B @ SX0 ) @ ( sK68_SY3129 @ SX0 ) ) @ SX0 ) )
| ( transitive @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2093]) ).
thf(2139,plain,
( ( ~ ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( transitive @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX1 @ SX3 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2093]) ).
thf(2140,plain,
! [SV292: $i] :
( ( ( ~ ( relation @ SV292 ) )
= $true )
| ( ( ~ ( ~ ! [SY3741: $i] :
( ~ ( relation @ SY3741 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SY3741 @ SV292 ) @ ( sK13_SY3095 @ SY3741 @ SV292 ) ) @ SY3741 )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SY3741 @ SV292 ) @ ( sK12_C @ SY3741 @ SV292 ) ) @ SV292 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SY3741 @ SV292 ) @ ( sK13_SY3095 @ SY3741 @ SV292 ) ) @ SY3741 )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ SY3741 @ SV292 ) @ ( sK12_C @ SY3741 @ SV292 ) ) @ SV292 ) ) )
| ( SY3741
= ( relation_inverse @ SV292 ) ) )
| ~ ! [SY3742: $i] :
( ~ ( relation @ SY3742 )
| ( SY3742
!= ( relation_inverse @ SV292 ) )
| ~ ( ~ ! [SY3743: $i,SY3744: $i] :
( ~ ( in @ ( ordered_pair @ SY3743 @ SY3744 ) @ SY3742 )
| ( in @ ( ordered_pair @ SY3744 @ SY3743 ) @ SV292 ) )
| ~ ! [SY3745: $i,SY3746: $i] :
( ~ ( in @ ( ordered_pair @ SY3746 @ SY3745 ) @ SV292 )
| ( in @ ( ordered_pair @ SY3745 @ SY3746 ) @ SY3742 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2094]) ).
thf(2141,plain,
! [SV293: $i] :
( ( ( ~ ( function @ SV293 )
| ~ ( relation @ SV293 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY3747: $i] :
( ~ ( in @ SY3747 @ ( relation_dom @ SV293 ) )
| ! [SY3748: $i] :
( ( SY3748
!= ( apply @ SV293 @ SY3747 ) )
| ( in @ ( ordered_pair @ SY3747 @ SY3748 ) @ SV293 ) ) )
| ~ ! [SY3749: $i] :
( ~ ( in @ SY3749 @ ( relation_dom @ SV293 ) )
| ! [SY3750: $i] :
( ~ ( in @ ( ordered_pair @ SY3749 @ SY3750 ) @ SV293 )
| ( SY3750
= ( apply @ SV293 @ SY3749 ) ) ) ) )
| ~ ~ ( ~ ! [SY3751: $i] :
( ( in @ SY3751 @ ( relation_dom @ SV293 ) )
| ! [SY3752: $i] :
( ( SY3752
!= ( apply @ SV293 @ SY3751 ) )
| ( SY3752 = empty_set ) ) )
| ~ ! [SY3753: $i] :
( ( in @ SY3753 @ ( relation_dom @ SV293 ) )
| ! [SY3754: $i] :
( ( SY3754 != empty_set )
| ( SY3754
= ( apply @ SV293 @ SY3753 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2095]) ).
thf(2142,plain,
! [SV294: $i] :
( ( ( ~ ( relation @ SV294 ) )
= $true )
| ( ( ~ ( ~ ! [SY3755: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_C @ SY3755 @ SV294 ) @ SY3755 )
| ~ ( in @ ( sK20_SY3099 @ SY3755 @ SV294 ) @ SY3755 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SY3755 @ SV294 ) @ ( sK20_SY3099 @ SY3755 @ SV294 ) ) @ SV294 ) )
| ~ ( in @ ( ordered_pair @ ( sK20_SY3099 @ SY3755 @ SV294 ) @ ( sK19_C @ SY3755 @ SV294 ) ) @ SV294 ) )
| ~ ( ( ( sK19_C @ SY3755 @ SV294 )
!= ( sK20_SY3099 @ SY3755 @ SV294 ) ) ) )
| ( is_antisymmetric_in @ SV294 @ SY3755 ) )
| ~ ! [SY3756: $i] :
( ~ ( is_antisymmetric_in @ SV294 @ SY3756 )
| ! [SY3757: $i,SY3758: $i] :
( ~ ( in @ SY3757 @ SY3756 )
| ~ ( in @ SY3758 @ SY3756 )
| ~ ( in @ ( ordered_pair @ SY3757 @ SY3758 ) @ SV294 )
| ~ ( in @ ( ordered_pair @ SY3758 @ SY3757 ) @ SV294 )
| ( SY3757 = SY3758 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2096]) ).
thf(2143,plain,
! [SV295: $i] :
( ( ( ~ ( relation @ SV295 ) )
= $true )
| ( ( ~ ( ~ ! [SY3759: $i,SY3760: $i] :
( ~ ( ~ ( ( ( sK35_D @ SY3760 @ SY3759 @ SV295 )
= SY3759 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SY3760 @ SY3759 @ SV295 ) @ SY3759 ) @ SV295 )
| ~ ( in @ ( sK35_D @ SY3760 @ SY3759 @ SV295 ) @ SY3760 ) )
| ~ ~ ( ~ ( ( ( sK35_D @ SY3760 @ SY3759 @ SV295 )
!= SY3759 )
| ( in @ ( sK35_D @ SY3760 @ SY3759 @ SV295 ) @ SY3760 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SY3760 @ SY3759 @ SV295 ) @ SY3759 ) @ SV295 )
| ( in @ ( sK35_D @ SY3760 @ SY3759 @ SV295 ) @ SY3760 ) ) ) )
| ( SY3760
= ( fiber @ SV295 @ SY3759 ) ) )
| ~ ! [SY3761: $i,SY3762: $i] :
( ( SY3762
!= ( fiber @ SV295 @ SY3761 ) )
| ~ ( ~ ! [SY3763: $i] :
( ( SY3763 = SY3761 )
| ~ ( in @ ( ordered_pair @ SY3763 @ SY3761 ) @ SV295 )
| ( in @ SY3763 @ SY3762 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY3762 )
| ( SX3 != SY3761 ) )
| ~ ! [SY3765: $i] :
( ~ ( in @ SY3765 @ SY3762 )
| ( in @ ( ordered_pair @ SY3765 @ SY3761 ) @ SV295 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2097]) ).
thf(2144,plain,
! [SV296: $i,SV307: $i] :
( ( ~ ( relation @ SV307 )
| ~ ( ~ ! [SY3817: $i] :
( ~ ( relation @ SY3817 )
| ~ ( ~ ( ~ ( in @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) @ SV296 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SY3817 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) ) @ SV307 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SY3817 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) ) @ SY3817 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) @ SV296 )
| ( in @ ( ordered_pair @ ( sK48_D @ SY3817 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) ) @ SY3817 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SY3817 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) ) @ SV307 )
| ( in @ ( ordered_pair @ ( sK48_D @ SY3817 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) ) @ SY3817 ) ) ) )
| ( SY3817
= ( relation_rng_restriction @ SV296 @ SV307 ) ) )
| ~ ! [SY3818: $i] :
( ~ ( relation @ SY3818 )
| ( SY3818
!= ( relation_rng_restriction @ SV296 @ SV307 ) )
| ~ ( ~ ! [SY3819: $i,SY3820: $i] :
( ~ ( in @ SY3820 @ SV296 )
| ~ ( in @ ( ordered_pair @ SY3819 @ SY3820 ) @ SV307 )
| ( in @ ( ordered_pair @ SY3819 @ SY3820 ) @ SY3818 ) )
| ~ ~ ( ~ ! [SY3771: $i,SY3772: $i] :
( ~ ( in @ ( ordered_pair @ SY3771 @ SY3772 ) @ SY3818 )
| ( in @ SY3772 @ SV296 ) )
| ~ ! [SY3823: $i,SY3824: $i] :
( ~ ( in @ ( ordered_pair @ SY3823 @ SY3824 ) @ SY3818 )
| ( in @ ( ordered_pair @ SY3823 @ SY3824 ) @ SV307 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2098]) ).
thf(2145,plain,
! [SV297: $i] :
( ( ( ~ ( relation @ SV297 ) )
= $true )
| ( ( ~ ( ~ ! [SY3775: $i] :
( ~ ( ~ ( ! [SY3776: $i] :
~ ( in @ ( ordered_pair @ SY3776 @ ( sK17_C @ SY3775 @ SV297 ) ) @ SV297 )
| ~ ( in @ ( sK17_C @ SY3775 @ SV297 ) @ SY3775 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK18_SY3098 @ SY3775 @ SV297 ) @ ( sK17_C @ SY3775 @ SV297 ) ) @ SV297 )
| ( in @ ( sK17_C @ SY3775 @ SV297 ) @ SY3775 ) ) )
| ( SY3775
= ( relation_rng @ SV297 ) ) )
| ~ ! [SY3777: $i] :
( ( SY3777
!= ( relation_rng @ SV297 ) )
| ~ ( ~ ! [SY3778: $i] :
( ! [SY3779: $i] :
~ ( in @ ( ordered_pair @ SY3779 @ SY3778 ) @ SV297 )
| ( in @ SY3778 @ SY3777 ) )
| ~ ! [SY3780: $i] :
( ~ ( in @ SY3780 @ SY3777 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3780 @ SY3777 @ SV297 ) @ SY3780 ) @ SV297 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2099]) ).
thf(2146,plain,
! [SV298: $i] :
( ( ~ ! [SY3781: $i,SY3782: $i] :
( ~ ( relation @ SY3782 )
| ~ ( in @ ( ordered_pair @ SV298 @ SY3781 ) @ SY3782 )
| ( in @ SV298 @ ( relation_field @ SY3782 ) ) )
| ~ ! [SY3783: $i,SY3784: $i] :
( ~ ( relation @ SY3784 )
| ~ ( in @ ( ordered_pair @ SV298 @ SY3783 ) @ SY3784 )
| ( in @ SY3783 @ ( relation_field @ SY3784 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2100]) ).
thf(2147,plain,
! [SV308: $i,SV299: $i] :
( ( ~ ( ~ ! [SY3825: $i,SY3826: $i] :
( ~ ( relation @ SY3826 )
| ~ ( in @ SV299 @ SY3825 )
| ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ SY3826 )
| ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SY3825 ) @ SY3826 ) ) )
| ~ ~ ( ~ ! [SY3827: $i,SY3828: $i] :
( ~ ( relation @ SY3828 )
| ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SY3827 ) @ SY3828 ) )
| ( in @ SV299 @ SY3827 ) )
| ~ ! [SY3829: $i,SY3830: $i] :
( ~ ( relation @ SY3830 )
| ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SY3829 ) @ SY3830 ) )
| ( in @ ( ordered_pair @ SV299 @ SV308 ) @ SY3830 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2101]) ).
thf(2148,plain,
! [SV309: $i,SV300: $i] :
( ( ~ ( ~ ! [SY3831: $i] :
( ! [SY3832: $i] :
( ( ordered_pair @ SV300 @ SV309 )
!= ( ordered_pair @ SY3831 @ SY3832 ) )
| ( SV300 = SY3831 ) )
| ~ ! [SY3833: $i,SY3834: $i] :
( ( ( ordered_pair @ SV300 @ SV309 )
!= ( ordered_pair @ SY3833 @ SY3834 ) )
| ( SV309 = SY3834 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2102]) ).
thf(2149,plain,
! [SV301: $i] :
( ( ~ ! [SY3797: $i,SY3798: $i] :
( ~ ( relation @ SY3798 )
| ! [SY3799: $i] :
( ~ ( in @ SY3799 @ ( relation_rng @ SY3798 ) )
| ~ ( in @ ( ordered_pair @ SV301 @ SY3799 ) @ SY3798 )
| ~ ( in @ SY3799 @ SY3797 ) )
| ( in @ SV301 @ ( relation_inverse_image @ SY3798 @ SY3797 ) ) )
| ~ ! [SY3800: $i,SY3801: $i] :
( ~ ( relation @ SY3801 )
| ~ ( in @ SV301 @ ( relation_inverse_image @ SY3801 @ SY3800 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_D @ SY3801 @ SY3800 @ SV301 ) @ ( relation_rng @ SY3801 ) )
| ~ ( in @ ( ordered_pair @ SV301 @ ( sK60_D @ SY3801 @ SY3800 @ SV301 ) ) @ SY3801 ) )
| ~ ( in @ ( sK60_D @ SY3801 @ SY3800 @ SV301 ) @ SY3800 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2103]) ).
thf(2150,plain,
! [SV302: $i] :
( ( ( ~ ( relation @ SV302 ) )
= $true )
| ( ( ~ ( ~ ! [SY3802: $i] :
( ~ ( ~ ( in @ ( sK36_C @ SY3802 @ SV302 ) @ SY3802 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SY3802 @ SV302 ) @ ( sK36_C @ SY3802 @ SV302 ) ) @ SV302 ) )
| ( is_reflexive_in @ SV302 @ SY3802 ) )
| ~ ! [SY3803: $i] :
( ~ ( is_reflexive_in @ SV302 @ SY3803 )
| ! [SY3804: $i] :
( ~ ( in @ SY3804 @ SY3803 )
| ( in @ ( ordered_pair @ SY3804 @ SY3804 ) @ SV302 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2104]) ).
thf(2151,plain,
! [SV269: $i] :
( ( ( relation @ SV269 )
= $false )
| ( ( ( in @ ( ordered_pair @ ( sK54_B @ SV269 ) @ ( sK55_SY3122 @ SV269 ) ) @ SV269 )
| ( SV269 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2105]) ).
thf(2152,plain,
! [SV304: $i,SV271: $i] :
( ( empty @ ( ordered_pair @ SV271 @ SV304 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2107]) ).
thf(2153,plain,
! [SV305: $i,SV272: $i] :
( ( ~ ! [SY3805: $i,SY3806: $i] :
( ~ ( in @ SV272 @ SY3805 )
| ~ ( in @ SV305 @ SY3806 )
| ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SY3805 @ SY3806 ) ) )
| ~ ~ ( ~ ! [SY3807: $i] :
( ! [SY3808: $i] :
~ ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SY3807 @ SY3808 ) )
| ( in @ SV272 @ SY3807 ) )
| ~ ! [SY3809: $i,SY3810: $i] :
( ~ ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SY3809 @ SY3810 ) )
| ( in @ SV305 @ SY3810 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2108]) ).
thf(2154,plain,
! [SV306: $i,SV273: $i] :
( ( ~ ! [SY3811: $i,SY3812: $i] :
( ~ ( in @ SV273 @ SY3811 )
| ~ ( in @ SV306 @ SY3812 )
| ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SY3811 @ SY3812 ) ) )
| ~ ~ ( ~ ! [SY3813: $i] :
( ! [SY3814: $i] :
~ ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SY3813 @ SY3814 ) )
| ( in @ SV273 @ SY3813 ) )
| ~ ! [SY3815: $i,SY3816: $i] :
( ~ ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SY3815 @ SY3816 ) )
| ( in @ SV306 @ SY3816 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2109]) ).
thf(2155,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( in @ ( sK69_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK69_B @ SX0 ) @ ( sK69_B @ SX0 ) ) @ SX0 ) )
| ( reflexive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2110]) ).
thf(2156,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( reflexive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ ( relation_field @ SX0 ) )
| ( in @ ( ordered_pair @ SX1 @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2111]) ).
thf(2157,plain,
! [SV274: $i] :
( ( ( relation @ SV274 )
= $false )
| ( ( ~ ( ~ ! [SY3618: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK14_C @ SY3618 @ SV274 )
!= ( sK15_SY3096 @ SY3618 @ SV274 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SY3618 @ SV274 ) @ SY3618 )
| ~ ( in @ ( sK15_SY3096 @ SY3618 @ SV274 ) @ SY3618 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK14_C @ SY3618 @ SV274 ) @ ( sK15_SY3096 @ SY3618 @ SV274 ) ) @ SV274 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK15_SY3096 @ SY3618 @ SV274 ) @ ( sK14_C @ SY3618 @ SV274 ) ) @ SV274 ) )
| ( is_connected_in @ SV274 @ SY3618 ) )
| ~ ! [SY3619: $i] :
( ~ ( is_connected_in @ SV274 @ SY3619 )
| ! [SY3620: $i,SY3621: $i] :
( ( SY3620 = SY3621 )
| ~ ( in @ SY3620 @ SY3619 )
| ~ ( in @ SY3621 @ SY3619 )
| ( in @ ( ordered_pair @ SY3620 @ SY3621 ) @ SV274 )
| ( in @ ( ordered_pair @ SY3621 @ SY3620 ) @ SV274 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2112]) ).
thf(2158,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( sK39_B @ SX0 )
!= ( ordered_pair @ SX1 @ SX2 ) )
| ~ ( in @ ( sK39_B @ SX0 ) @ SX0 ) )
| ( relation @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2113]) ).
thf(2159,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ( SX1
= ( ordered_pair @ ( sK37_C @ SX1 @ SX0 ) @ ( sK38_SY3111 @ SX1 @ SX0 ) ) )
| ~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2114]) ).
thf(2160,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK64_B @ SX0 ) @ ( sK65_SY3126 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK65_SY3126 @ SX0 ) @ ( sK64_B @ SX0 ) ) @ SX0 ) )
| ~ ( ( ( sK64_B @ SX0 )
!= ( sK65_SY3126 @ SX0 ) ) ) )
| ( antisymmetric @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2115]) ).
thf(2161,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( antisymmetric @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX2 @ SX1 ) @ SX0 )
| ( SX1 = SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2116]) ).
thf(2162,plain,
! [SV275: $i] :
( ( ~ ! [SY3622: $i,SY3623: $i] :
( ~ ( ~ ( ! [SY3624: $i,SY3625: $i] :
( ~ ( in @ SY3624 @ SV275 )
| ~ ( in @ SY3625 @ SY3622 )
| ( ( sK28_D @ SY3623 @ SY3622 @ SV275 )
!= ( ordered_pair @ SY3624 @ SY3625 ) ) )
| ~ ( in @ ( sK28_D @ SY3623 @ SY3622 @ SV275 ) @ SY3623 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY3106 @ SY3623 @ SY3622 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK30_SY3108 @ SY3623 @ SY3622 @ SV275 ) @ SY3622 ) )
| ( ( sK28_D @ SY3623 @ SY3622 @ SV275 )
!= ( ordered_pair @ ( sK29_SY3106 @ SY3623 @ SY3622 @ SV275 ) @ ( sK30_SY3108 @ SY3623 @ SY3622 @ SV275 ) ) ) )
| ( in @ ( sK28_D @ SY3623 @ SY3622 @ SV275 ) @ SY3623 ) ) )
| ( SY3623
= ( cartesian_product2 @ SV275 @ SY3622 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2117]) ).
thf(2163,plain,
! [SV275: $i] :
( ( ~ ! [SY3626: $i,SY3627: $i] :
( ( SY3627
!= ( cartesian_product2 @ SV275 @ SY3626 ) )
| ~ ( ~ ! [SY3628: $i] :
( ! [SY3629: $i,SY3630: $i] :
( ~ ( in @ SY3629 @ SV275 )
| ~ ( in @ SY3630 @ SY3626 )
| ( SY3628
!= ( ordered_pair @ SY3629 @ SY3630 ) ) )
| ( in @ SY3628 @ SY3627 ) )
| ~ ! [SY3631: $i] :
( ~ ( in @ SY3631 @ SY3627 )
| ~ ( ~ ~ ( ~ ( in @ ( sK26_E @ SY3631 @ SY3627 @ SY3626 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK27_SY3103 @ SY3631 @ SY3627 @ SY3626 @ SV275 ) @ SY3626 ) )
| ( SY3631
!= ( ordered_pair @ ( sK26_E @ SY3631 @ SY3627 @ SY3626 @ SV275 ) @ ( sK27_SY3103 @ SY3631 @ SY3627 @ SY3626 @ SV275 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2117]) ).
thf(2164,plain,
! [SV276: $i] :
( ( ( relation @ SV276 )
= $false )
| ( ( ~ ( ~ ! [SY3632: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SY3632 @ SV276 ) @ SY3632 )
| ~ ( in @ ( sK4_SY3086 @ SY3632 @ SV276 ) @ SY3632 ) )
| ~ ( in @ ( sK5_SY3088 @ SY3632 @ SV276 ) @ SY3632 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SY3632 @ SV276 ) @ ( sK4_SY3086 @ SY3632 @ SV276 ) ) @ SV276 ) )
| ~ ( in @ ( ordered_pair @ ( sK4_SY3086 @ SY3632 @ SV276 ) @ ( sK5_SY3088 @ SY3632 @ SV276 ) ) @ SV276 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK3_C @ SY3632 @ SV276 ) @ ( sK5_SY3088 @ SY3632 @ SV276 ) ) @ SV276 ) )
| ( is_transitive_in @ SV276 @ SY3632 ) )
| ~ ! [SY3633: $i] :
( ~ ( is_transitive_in @ SV276 @ SY3633 )
| ! [SY3634: $i,SY3635: $i,SY3636: $i] :
( ~ ( in @ SY3634 @ SY3633 )
| ~ ( in @ SY3635 @ SY3633 )
| ~ ( in @ SY3636 @ SY3633 )
| ~ ( in @ ( ordered_pair @ SY3634 @ SY3635 ) @ SV276 )
| ~ ( in @ ( ordered_pair @ SY3635 @ SY3636 ) @ SV276 )
| ( in @ ( ordered_pair @ SY3634 @ SY3636 ) @ SV276 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2118]) ).
thf(2165,plain,
! [SV277: $i] :
( ( ( relation @ SV277 )
= $false )
| ( ( ~ ( ~ ! [SY3637: $i,SY3638: $i] :
( ~ ( ~ ( ! [SY3639: $i] :
( ~ ( in @ ( ordered_pair @ SY3639 @ ( sK46_D @ SY3638 @ SY3637 @ SV277 ) ) @ SV277 )
| ~ ( in @ SY3639 @ SY3637 ) )
| ~ ( in @ ( sK46_D @ SY3638 @ SY3637 @ SV277 ) @ SY3638 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SY3638 @ SY3637 @ SV277 ) @ ( sK46_D @ SY3638 @ SY3637 @ SV277 ) ) @ SV277 )
| ~ ( in @ ( sK47_SY3118 @ SY3638 @ SY3637 @ SV277 ) @ SY3637 ) )
| ( in @ ( sK46_D @ SY3638 @ SY3637 @ SV277 ) @ SY3638 ) ) )
| ( SY3638
= ( relation_image @ SV277 @ SY3637 ) ) )
| ~ ! [SY3640: $i,SY3641: $i] :
( ( SY3641
!= ( relation_image @ SV277 @ SY3640 ) )
| ~ ( ~ ! [SY3642: $i] :
( ! [SY3643: $i] :
( ~ ( in @ ( ordered_pair @ SY3643 @ SY3642 ) @ SV277 )
| ~ ( in @ SY3643 @ SY3640 ) )
| ( in @ SY3642 @ SY3641 ) )
| ~ ! [SY3644: $i] :
( ~ ( in @ SY3644 @ SY3641 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SY3644 @ SY3641 @ SY3640 @ SV277 ) @ SY3644 ) @ SV277 )
| ~ ( in @ ( sK45_E @ SY3644 @ SY3641 @ SY3640 @ SV277 ) @ SY3640 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2119]) ).
thf(2166,plain,
! [SV278: $i] :
( ( ( relation @ SV278 )
= $false )
| ( ( ~ ( ~ ! [SY3645: $i,SY3646: $i] :
( ~ ( relation @ SY3646 )
| ~ ( ~ ( ~ ( in @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ SY3645 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ ( sK51_SY3120 @ SY3646 @ SY3645 @ SV278 ) ) @ SV278 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ ( sK51_SY3120 @ SY3646 @ SY3645 @ SV278 ) ) @ SY3646 ) )
| ~ ~ ( ~ ( ( in @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ SY3645 )
| ( in @ ( ordered_pair @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ ( sK51_SY3120 @ SY3646 @ SY3645 @ SV278 ) ) @ SY3646 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ ( sK51_SY3120 @ SY3646 @ SY3645 @ SV278 ) ) @ SV278 )
| ( in @ ( ordered_pair @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ ( sK51_SY3120 @ SY3646 @ SY3645 @ SV278 ) ) @ SY3646 ) ) ) )
| ( SY3646
= ( relation_dom_restriction @ SV278 @ SY3645 ) ) )
| ~ ! [SY3647: $i,SY3648: $i] :
( ~ ( relation @ SY3648 )
| ( SY3648
!= ( relation_dom_restriction @ SV278 @ SY3647 ) )
| ~ ( ~ ! [SY3649: $i,SY3650: $i] :
( ~ ( in @ SY3649 @ SY3647 )
| ~ ( in @ ( ordered_pair @ SY3649 @ SY3650 ) @ SV278 )
| ( in @ ( ordered_pair @ SY3649 @ SY3650 ) @ SY3648 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3648 )
| ( in @ SX3 @ SY3647 ) )
| ~ ! [SY3653: $i,SY3654: $i] :
( ~ ( in @ ( ordered_pair @ SY3653 @ SY3654 ) @ SY3648 )
| ( in @ ( ordered_pair @ SY3653 @ SY3654 ) @ SV278 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2120]) ).
thf(2167,plain,
! [SV279: $i] :
( ( ( relation @ SV279 )
= $false )
| ( ( ~ ( ~ ! [SY3655: $i,SY3656: $i] :
( ~ ( ~ ( ! [SY3657: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ SY3656 @ SY3655 @ SV279 ) @ SY3657 ) @ SV279 )
| ~ ( in @ SY3657 @ SY3655 ) )
| ~ ( in @ ( sK43_D @ SY3656 @ SY3655 @ SV279 ) @ SY3656 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SY3656 @ SY3655 @ SV279 ) @ ( sK44_SY3116 @ SY3656 @ SY3655 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK44_SY3116 @ SY3656 @ SY3655 @ SV279 ) @ SY3655 ) )
| ( in @ ( sK43_D @ SY3656 @ SY3655 @ SV279 ) @ SY3656 ) ) )
| ( SY3656
= ( relation_inverse_image @ SV279 @ SY3655 ) ) )
| ~ ! [SY3658: $i,SY3659: $i] :
( ( SY3659
!= ( relation_inverse_image @ SV279 @ SY3658 ) )
| ~ ( ~ ! [SY3660: $i] :
( ! [SY3661: $i] :
( ~ ( in @ ( ordered_pair @ SY3660 @ SY3661 ) @ SV279 )
| ~ ( in @ SY3661 @ SY3658 ) )
| ( in @ SY3660 @ SY3659 ) )
| ~ ! [SY3662: $i] :
( ~ ( in @ SY3662 @ SY3659 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3662 @ ( sK42_E @ SY3662 @ SY3659 @ SY3658 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK42_E @ SY3662 @ SY3659 @ SY3658 @ SV279 ) @ SY3658 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2121]) ).
thf(2168,plain,
! [SV280: $i] :
( ( ( relation @ SV280 )
= $false )
| ( ( ~ ( ~ ! [SY3663: $i] :
( ~ ( relation @ SY3663 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3663 @ SV280 ) @ ( sK25_SY3102 @ SY3663 @ SV280 ) ) @ SV280 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3663 @ SV280 ) @ ( sK25_SY3102 @ SY3663 @ SV280 ) ) @ SY3663 ) )
| ( subset @ SV280 @ SY3663 ) )
| ~ ! [SY3664: $i] :
( ~ ( relation @ SY3664 )
| ~ ( subset @ SV280 @ SY3664 )
| ! [SY3665: $i,SY3666: $i] :
( ~ ( in @ ( ordered_pair @ SY3665 @ SY3666 ) @ SV280 )
| ( in @ ( ordered_pair @ SY3665 @ SY3666 ) @ SY3664 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2122]) ).
thf(2169,plain,
! [SV281: $i] :
( ( ( relation @ SV281 )
= $false )
| ( ( ! [SY3667: $i] :
( ~ ( relation @ SY3667 )
| ~ ( ~ ! [SY3668: $i] :
( ~ ( relation @ SY3668 )
| ~ ( ~ ( ! [SY3669: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3668 @ SY3667 @ SV281 ) @ SY3669 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY3669 @ ( sK8_SY3089 @ SY3668 @ SY3667 @ SV281 ) ) @ SY3667 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3668 @ SY3667 @ SV281 ) @ ( sK8_SY3089 @ SY3668 @ SY3667 @ SV281 ) ) @ SY3668 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3668 @ SY3667 @ SV281 ) @ ( sK9_SY3093 @ SY3668 @ SY3667 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SY3668 @ SY3667 @ SV281 ) @ ( sK8_SY3089 @ SY3668 @ SY3667 @ SV281 ) ) @ SY3667 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SY3668 @ SY3667 @ SV281 ) @ ( sK8_SY3089 @ SY3668 @ SY3667 @ SV281 ) ) @ SY3668 ) ) )
| ( SY3668
= ( relation_composition @ SV281 @ SY3667 ) ) )
| ~ ! [SY3670: $i] :
( ~ ( relation @ SY3670 )
| ( SY3670
!= ( relation_composition @ SV281 @ SY3667 ) )
| ~ ( ~ ! [SY3671: $i,SY3672: $i] :
( ! [SY3673: $i] :
( ~ ( in @ ( ordered_pair @ SY3671 @ SY3673 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY3673 @ SY3672 ) @ SY3667 ) )
| ( in @ ( ordered_pair @ SY3671 @ SY3672 ) @ SY3670 ) )
| ~ ! [SY3674: $i,SY3675: $i] :
( ~ ( in @ ( ordered_pair @ SY3674 @ SY3675 ) @ SY3670 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3674 @ ( sK6_F @ SY3675 @ SY3674 @ SY3670 @ SY3667 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY3675 @ SY3674 @ SY3670 @ SY3667 @ SV281 ) @ SY3675 ) @ SY3667 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2123]) ).
thf(2170,plain,
! [SV282: $i] :
( ( ~ ! [SY3676: $i,SY3677: $i] :
( ~ ( relation_of2_as_subset @ SY3677 @ SV282 @ SY3676 )
| ~ ( ~ ! [SY3678: $i] :
~ ( in @ ( ordered_pair @ SY3678 @ ( sK57_D @ SY3677 @ SY3676 @ SV282 ) ) @ SY3677 )
| ~ ( in @ ( sK57_D @ SY3677 @ SY3676 @ SV282 ) @ SY3676 ) )
| ( ( relation_rng_as_subset @ SV282 @ SY3676 @ SY3677 )
= SY3676 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2124]) ).
thf(2171,plain,
! [SV282: $i] :
( ( ~ ! [SY3679: $i,SY3680: $i] :
( ~ ( relation_of2_as_subset @ SY3680 @ SV282 @ SY3679 )
| ( ( relation_rng_as_subset @ SV282 @ SY3679 @ SY3680 )
!= SY3679 )
| ! [SY3681: $i] :
( ( in @ ( ordered_pair @ ( sK56_E @ SY3681 @ SY3680 @ SY3679 @ SV282 ) @ SY3681 ) @ SY3680 )
| ~ ( in @ SY3681 @ SY3679 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2124]) ).
thf(2172,plain,
! [SV283: $i] :
( ( ( relation @ SV283 )
= $false )
| ( ( ! [SY3682: $i] :
( ~ ( relation @ SY3682 )
| ~ ( ~ ! [SY3683: $i] :
( ~ ( function @ SY3683 )
| ~ ( relation @ SY3683 )
| ~ ( ~ ( ~ ( in @ ( sK10_D @ SY3683 @ SY3682 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( sK11_SY3094 @ SY3683 @ SY3682 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3683 @ ( sK10_D @ SY3683 @ SY3682 @ SV283 ) ) @ ( apply @ SY3683 @ ( sK11_SY3094 @ SY3683 @ SY3682 @ SV283 ) ) ) @ SY3682 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY3683 @ SY3682 @ SV283 ) @ ( sK11_SY3094 @ SY3683 @ SY3682 @ SV283 ) ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SY3683 @ SY3682 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3683 @ SY3682 @ SV283 ) @ ( sK11_SY3094 @ SY3683 @ SY3682 @ SV283 ) ) @ SV283 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SY3683 @ SY3682 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3683 @ SY3682 @ SV283 ) @ ( sK11_SY3094 @ SY3683 @ SY3682 @ SV283 ) ) @ SV283 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SY3683 @ ( sK10_D @ SY3683 @ SY3682 @ SV283 ) ) @ ( apply @ SY3683 @ ( sK11_SY3094 @ SY3683 @ SY3682 @ SV283 ) ) ) @ SY3682 )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3683 @ SY3682 @ SV283 ) @ ( sK11_SY3094 @ SY3683 @ SY3682 @ SV283 ) ) @ SV283 ) ) ) )
| ( ( relation_dom @ SY3683 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SY3683 )
!= ( relation_field @ SY3682 ) )
| ~ ( one_to_one @ SY3683 )
| ( relation_isomorphism @ SV283 @ SY3682 @ SY3683 ) )
| ~ ~ ( ~ ! [SY3684: $i] :
( ~ ( function @ SY3684 )
| ~ ( relation @ SY3684 )
| ~ ( relation_isomorphism @ SV283 @ SY3682 @ SY3684 )
| ~ ( ~ ! [SY3685: $i,SY3686: $i] :
( ~ ( in @ SY3685 @ ( relation_field @ SV283 ) )
| ~ ( in @ SY3686 @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3684 @ SY3685 ) @ ( apply @ SY3684 @ SY3686 ) ) @ SY3682 )
| ( in @ ( ordered_pair @ SY3685 @ SY3686 ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3687: $i] :
( ! [SY3688: $i] :
~ ( in @ ( ordered_pair @ SY3687 @ SY3688 ) @ SV283 )
| ( in @ SY3687 @ ( relation_field @ SV283 ) ) )
| ~ ! [SY3689: $i,SY3690: $i] :
( ~ ( in @ ( ordered_pair @ SY3689 @ SY3690 ) @ SV283 )
| ( in @ SY3690 @ ( relation_field @ SV283 ) ) ) )
| ~ ! [SY3691: $i,SY3692: $i] :
( ~ ( in @ ( ordered_pair @ SY3691 @ SY3692 ) @ SV283 )
| ( in @ ( ordered_pair @ ( apply @ SY3684 @ SY3691 ) @ ( apply @ SY3684 @ SY3692 ) ) @ SY3682 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3693: $i] :
( ~ ( function @ SY3693 )
| ~ ( relation @ SY3693 )
| ~ ( relation_isomorphism @ SV283 @ SY3682 @ SY3693 )
| ( ( relation_dom @ SY3693 )
= ( relation_field @ SV283 ) ) )
| ~ ! [SY3694: $i] :
( ~ ( function @ SY3694 )
| ~ ( relation @ SY3694 )
| ~ ( relation_isomorphism @ SV283 @ SY3682 @ SY3694 )
| ( ( relation_rng @ SY3694 )
= ( relation_field @ SY3682 ) ) ) )
| ~ ! [SY3695: $i] :
( ~ ( function @ SY3695 )
| ~ ( relation @ SY3695 )
| ~ ( relation_isomorphism @ SV283 @ SY3682 @ SY3695 )
| ( one_to_one @ SY3695 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2125]) ).
thf(2173,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK62_B @ SX0 )
!= ( sK63_SY3125 @ SX0 ) ) )
| ~ ~ ( ~ ( in @ ( sK62_B @ SX0 ) @ ( relation_field @ SX0 ) )
| ~ ( in @ ( sK63_SY3125 @ SX0 ) @ ( relation_field @ SX0 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK62_B @ SX0 ) @ ( sK63_SY3125 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK63_SY3125 @ SX0 ) @ ( sK62_B @ SX0 ) ) @ SX0 ) )
| ( connected @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2126]) ).
thf(2174,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( connected @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( SX1 = SX2 )
| ~ ( in @ SX1 @ ( relation_field @ SX0 ) )
| ~ ( in @ SX2 @ ( relation_field @ SX0 ) )
| ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2127]) ).
thf(2175,plain,
! [SV284: $i] :
( ( ~ ! [SY3696: $i,SY3697: $i] :
( ~ ( function @ SY3697 )
| ~ ( relation @ SY3697 )
| ( SY3696
!= ( apply @ SY3697 @ SV284 ) )
| ~ ( in @ SV284 @ ( relation_dom @ SY3697 ) )
| ( in @ ( ordered_pair @ SV284 @ SY3696 ) @ SY3697 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2128]) ).
thf(2176,plain,
! [SV284: $i] :
( ( ~ ~ ( ~ ! [SY3698: $i,SY3699: $i] :
( ~ ( function @ SY3699 )
| ~ ( relation @ SY3699 )
| ~ ( in @ ( ordered_pair @ SV284 @ SY3698 ) @ SY3699 )
| ( SY3698
= ( apply @ SY3699 @ SV284 ) ) )
| ~ ! [SY3700: $i,SY3701: $i] :
( ~ ( function @ SY3701 )
| ~ ( relation @ SY3701 )
| ~ ( in @ ( ordered_pair @ SV284 @ SY3700 ) @ SY3701 )
| ( in @ SV284 @ ( relation_dom @ SY3701 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2128]) ).
thf(2177,plain,
! [SV285: $i] :
( ( ~ ! [SY3702: $i,SY3703: $i] :
( ~ ( relation @ SY3703 )
| ! [SY3704: $i] :
( ~ ( in @ SY3704 @ ( relation_dom @ SY3703 ) )
| ~ ( in @ ( ordered_pair @ SY3704 @ SV285 ) @ SY3703 )
| ~ ( in @ SY3704 @ SY3702 ) )
| ( in @ SV285 @ ( relation_image @ SY3703 @ SY3702 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2129]) ).
thf(2178,plain,
! [SV285: $i] :
( ( ~ ! [SY3705: $i,SY3706: $i] :
( ~ ( relation @ SY3706 )
| ~ ( in @ SV285 @ ( relation_image @ SY3706 @ SY3705 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK61_D @ SY3706 @ SY3705 @ SV285 ) @ ( relation_dom @ SY3706 ) )
| ~ ( in @ ( ordered_pair @ ( sK61_D @ SY3706 @ SY3705 @ SV285 ) @ SV285 ) @ SY3706 ) )
| ~ ( in @ ( sK61_D @ SY3706 @ SY3705 @ SV285 ) @ SY3705 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2129]) ).
thf(2179,plain,
! [SV310: $i,SV286: $i] :
( ( ( ! [SY3835: $i] :
( SV286
!= ( ordered_pair @ SV310 @ SY3835 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3709: $i] :
( ~ ( ( SV286
!= ( ordered_pair @ ( sK40_C @ SY3709 @ SV286 ) @ ( sK41_SY3114 @ SY3709 @ SV286 ) ) )
| ~ ( ( SY3709
!= ( sK40_C @ SY3709 @ SV286 ) ) ) )
| ( SY3709
= ( pair_first @ SV286 ) ) )
| ~ ! [SY3710: $i] :
( ( SY3710
!= ( pair_first @ SV286 ) )
| ! [SY3711: $i] :
( ! [SY3712: $i] :
( SV286
!= ( ordered_pair @ SY3711 @ SY3712 ) )
| ( SY3710 = SY3711 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2130]) ).
thf(2180,plain,
! [SV311: $i,SV287: $i] :
( ( ( ! [SY3836: $i] :
( SV287
!= ( ordered_pair @ SV311 @ SY3836 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3715: $i] :
( ~ ( ( SV287
!= ( ordered_pair @ ( sK33_C @ SY3715 @ SV287 ) @ ( sK34_SY3110 @ SY3715 @ SV287 ) ) )
| ~ ( ( SY3715
!= ( sK34_SY3110 @ SY3715 @ SV287 ) ) ) )
| ( SY3715
= ( pair_second @ SV287 ) ) )
| ~ ! [SY3716: $i] :
( ( SY3716
!= ( pair_second @ SV287 ) )
| ! [SY3717: $i,SY3718: $i] :
( ( SV287
!= ( ordered_pair @ SY3717 @ SY3718 ) )
| ( SY3716 = SY3718 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2131]) ).
thf(2181,plain,
! [SV288: $i] :
( ( ~ ! [SY3719: $i,SY3720: $i] :
( ~ ( relation @ SY3720 )
| ~ ( in @ ( ordered_pair @ SV288 @ SY3719 ) @ SY3720 )
| ( in @ SV288 @ ( relation_dom @ SY3720 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2132]) ).
thf(2182,plain,
! [SV288: $i] :
( ( ~ ! [SY3721: $i,SY3722: $i] :
( ~ ( relation @ SY3722 )
| ~ ( in @ ( ordered_pair @ SV288 @ SY3721 ) @ SY3722 )
| ( in @ SY3721 @ ( relation_rng @ SY3722 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2132]) ).
thf(2183,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ( ( sK52_C @ SX1 @ SX0 )
!= ( sK53_SY3121 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK52_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK52_C @ SX1 @ SX0 ) @ ( sK53_SY3121 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ~ ( ~ ( ( ( sK52_C @ SX1 @ SX0 )
= ( sK53_SY3121 @ SX1 @ SX0 ) )
| ( in @ ( ordered_pair @ ( sK52_C @ SX1 @ SX0 ) @ ( sK53_SY3121 @ SX1 @ SX0 ) ) @ SX1 ) )
| ~ ( ( in @ ( sK52_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( ordered_pair @ ( sK52_C @ SX1 @ SX0 ) @ ( sK53_SY3121 @ SX1 @ SX0 ) ) @ SX1 ) ) ) )
| ( SX1
= ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2133]) ).
thf(2184,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( SX1
!= ( identity_relation @ SX0 ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( SX2 = SX3 ) )
| ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2134]) ).
thf(2185,plain,
! [SV289: $i] :
( ( ~ ! [SY3723: $i,SY3724: $i] :
( ~ ( relation_of2_as_subset @ SY3724 @ SY3723 @ SV289 )
| ~ ( ~ ! [SY3725: $i] :
~ ( in @ ( ordered_pair @ ( sK59_D @ SY3724 @ SY3723 @ SV289 ) @ SY3725 ) @ SY3724 )
| ~ ( in @ ( sK59_D @ SY3724 @ SY3723 @ SV289 ) @ SY3723 ) )
| ( ( relation_dom_as_subset @ SY3723 @ SV289 @ SY3724 )
= SY3723 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2135]) ).
thf(2186,plain,
! [SV289: $i] :
( ( ~ ! [SY3726: $i,SY3727: $i] :
( ~ ( relation_of2_as_subset @ SY3727 @ SY3726 @ SV289 )
| ( ( relation_dom_as_subset @ SY3726 @ SV289 @ SY3727 )
!= SY3726 )
| ! [SY3728: $i] :
( ( in @ ( ordered_pair @ SY3728 @ ( sK58_E @ SY3728 @ SY3727 @ SY3726 @ SV289 ) ) @ SY3727 )
| ~ ( in @ SY3728 @ SY3726 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2135]) ).
thf(2187,plain,
! [SV290: $i] :
( ( ( relation @ SV290 )
= $false )
| ( ( ~ ( ~ ! [SY3729: $i] :
( ~ ( ~ ( ! [SY3730: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SY3729 @ SV290 ) @ SY3730 ) @ SV290 )
| ~ ( in @ ( sK22_C @ SY3729 @ SV290 ) @ SY3729 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SY3729 @ SV290 ) @ ( sK23_SY3101 @ SY3729 @ SV290 ) ) @ SV290 )
| ( in @ ( sK22_C @ SY3729 @ SV290 ) @ SY3729 ) ) )
| ( SY3729
= ( relation_dom @ SV290 ) ) )
| ~ ! [SY3731: $i] :
( ( SY3731
!= ( relation_dom @ SV290 ) )
| ~ ( ~ ! [SY3732: $i] :
( ! [SY3733: $i] :
~ ( in @ ( ordered_pair @ SY3732 @ SY3733 ) @ SV290 )
| ( in @ SY3732 @ SY3731 ) )
| ~ ! [SY3734: $i] :
( ~ ( in @ SY3734 @ SY3731 )
| ( in @ ( ordered_pair @ SY3734 @ ( sK21_D @ SY3734 @ SY3731 @ SV290 ) ) @ SV290 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2136]) ).
thf(2188,plain,
! [SV291: $i] :
( ( ( relation @ SV291 )
= $false )
| ( ( ~ ( ~ ! [SY3735: $i] :
( ~ ( relation @ SY3735 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SY3735 @ SV291 ) @ ( sK32_SY3109 @ SY3735 @ SV291 ) ) @ SV291 )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ SY3735 @ SV291 ) @ ( sK32_SY3109 @ SY3735 @ SV291 ) ) @ SY3735 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK31_C @ SY3735 @ SV291 ) @ ( sK32_SY3109 @ SY3735 @ SV291 ) ) @ SV291 )
| ( in @ ( ordered_pair @ ( sK31_C @ SY3735 @ SV291 ) @ ( sK32_SY3109 @ SY3735 @ SV291 ) ) @ SY3735 ) ) )
| ( SV291 = SY3735 ) )
| ~ ! [SY3736: $i] :
( ~ ( relation @ SY3736 )
| ( SV291 != SY3736 )
| ~ ( ~ ! [SY3737: $i,SY3738: $i] :
( ~ ( in @ ( ordered_pair @ SY3737 @ SY3738 ) @ SV291 )
| ( in @ ( ordered_pair @ SY3737 @ SY3738 ) @ SY3736 ) )
| ~ ! [SY3739: $i,SY3740: $i] :
( ~ ( in @ ( ordered_pair @ SY3739 @ SY3740 ) @ SY3736 )
| ( in @ ( ordered_pair @ SY3739 @ SY3740 ) @ SV291 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2137]) ).
thf(2189,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK66_B @ SX0 ) @ ( sK67_SY3127 @ SX0 ) ) @ SX0 )
| ~ ( in @ ( ordered_pair @ ( sK67_SY3127 @ SX0 ) @ ( sK68_SY3129 @ SX0 ) ) @ SX0 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK66_B @ SX0 ) @ ( sK68_SY3129 @ SX0 ) ) @ SX0 ) )
| ( transitive @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2138]) ).
thf(2190,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( transitive @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ ( ordered_pair @ SX1 @ SX3 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2139]) ).
thf(2191,plain,
! [SV292: $i] :
( ( ( relation @ SV292 )
= $false )
| ( ( ~ ( ~ ! [SY3741: $i] :
( ~ ( relation @ SY3741 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SY3741 @ SV292 ) @ ( sK13_SY3095 @ SY3741 @ SV292 ) ) @ SY3741 )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SY3741 @ SV292 ) @ ( sK12_C @ SY3741 @ SV292 ) ) @ SV292 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SY3741 @ SV292 ) @ ( sK13_SY3095 @ SY3741 @ SV292 ) ) @ SY3741 )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ SY3741 @ SV292 ) @ ( sK12_C @ SY3741 @ SV292 ) ) @ SV292 ) ) )
| ( SY3741
= ( relation_inverse @ SV292 ) ) )
| ~ ! [SY3742: $i] :
( ~ ( relation @ SY3742 )
| ( SY3742
!= ( relation_inverse @ SV292 ) )
| ~ ( ~ ! [SY3743: $i,SY3744: $i] :
( ~ ( in @ ( ordered_pair @ SY3743 @ SY3744 ) @ SY3742 )
| ( in @ ( ordered_pair @ SY3744 @ SY3743 ) @ SV292 ) )
| ~ ! [SY3745: $i,SY3746: $i] :
( ~ ( in @ ( ordered_pair @ SY3746 @ SY3745 ) @ SV292 )
| ( in @ ( ordered_pair @ SY3745 @ SY3746 ) @ SY3742 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2140]) ).
thf(2192,plain,
! [SV293: $i] :
( ( ( ~ ( function @ SV293 ) )
= $true )
| ( ( ~ ( relation @ SV293 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY3747: $i] :
( ~ ( in @ SY3747 @ ( relation_dom @ SV293 ) )
| ! [SY3748: $i] :
( ( SY3748
!= ( apply @ SV293 @ SY3747 ) )
| ( in @ ( ordered_pair @ SY3747 @ SY3748 ) @ SV293 ) ) )
| ~ ! [SY3749: $i] :
( ~ ( in @ SY3749 @ ( relation_dom @ SV293 ) )
| ! [SY3750: $i] :
( ~ ( in @ ( ordered_pair @ SY3749 @ SY3750 ) @ SV293 )
| ( SY3750
= ( apply @ SV293 @ SY3749 ) ) ) ) )
| ~ ~ ( ~ ! [SY3751: $i] :
( ( in @ SY3751 @ ( relation_dom @ SV293 ) )
| ! [SY3752: $i] :
( ( SY3752
!= ( apply @ SV293 @ SY3751 ) )
| ( SY3752 = empty_set ) ) )
| ~ ! [SY3753: $i] :
( ( in @ SY3753 @ ( relation_dom @ SV293 ) )
| ! [SY3754: $i] :
( ( SY3754 != empty_set )
| ( SY3754
= ( apply @ SV293 @ SY3753 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2141]) ).
thf(2193,plain,
! [SV294: $i] :
( ( ( relation @ SV294 )
= $false )
| ( ( ~ ( ~ ! [SY3755: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_C @ SY3755 @ SV294 ) @ SY3755 )
| ~ ( in @ ( sK20_SY3099 @ SY3755 @ SV294 ) @ SY3755 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SY3755 @ SV294 ) @ ( sK20_SY3099 @ SY3755 @ SV294 ) ) @ SV294 ) )
| ~ ( in @ ( ordered_pair @ ( sK20_SY3099 @ SY3755 @ SV294 ) @ ( sK19_C @ SY3755 @ SV294 ) ) @ SV294 ) )
| ~ ( ( ( sK19_C @ SY3755 @ SV294 )
!= ( sK20_SY3099 @ SY3755 @ SV294 ) ) ) )
| ( is_antisymmetric_in @ SV294 @ SY3755 ) )
| ~ ! [SY3756: $i] :
( ~ ( is_antisymmetric_in @ SV294 @ SY3756 )
| ! [SY3757: $i,SY3758: $i] :
( ~ ( in @ SY3757 @ SY3756 )
| ~ ( in @ SY3758 @ SY3756 )
| ~ ( in @ ( ordered_pair @ SY3757 @ SY3758 ) @ SV294 )
| ~ ( in @ ( ordered_pair @ SY3758 @ SY3757 ) @ SV294 )
| ( SY3757 = SY3758 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2142]) ).
thf(2194,plain,
! [SV295: $i] :
( ( ( relation @ SV295 )
= $false )
| ( ( ~ ( ~ ! [SY3759: $i,SY3760: $i] :
( ~ ( ~ ( ( ( sK35_D @ SY3760 @ SY3759 @ SV295 )
= SY3759 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SY3760 @ SY3759 @ SV295 ) @ SY3759 ) @ SV295 )
| ~ ( in @ ( sK35_D @ SY3760 @ SY3759 @ SV295 ) @ SY3760 ) )
| ~ ~ ( ~ ( ( ( sK35_D @ SY3760 @ SY3759 @ SV295 )
!= SY3759 )
| ( in @ ( sK35_D @ SY3760 @ SY3759 @ SV295 ) @ SY3760 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SY3760 @ SY3759 @ SV295 ) @ SY3759 ) @ SV295 )
| ( in @ ( sK35_D @ SY3760 @ SY3759 @ SV295 ) @ SY3760 ) ) ) )
| ( SY3760
= ( fiber @ SV295 @ SY3759 ) ) )
| ~ ! [SY3761: $i,SY3762: $i] :
( ( SY3762
!= ( fiber @ SV295 @ SY3761 ) )
| ~ ( ~ ! [SY3763: $i] :
( ( SY3763 = SY3761 )
| ~ ( in @ ( ordered_pair @ SY3763 @ SY3761 ) @ SV295 )
| ( in @ SY3763 @ SY3762 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY3762 )
| ( SX3 != SY3761 ) )
| ~ ! [SY3765: $i] :
( ~ ( in @ SY3765 @ SY3762 )
| ( in @ ( ordered_pair @ SY3765 @ SY3761 ) @ SV295 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2143]) ).
thf(2195,plain,
! [SV296: $i,SV307: $i] :
( ( ( ~ ( relation @ SV307 ) )
= $true )
| ( ( ~ ( ~ ! [SY3817: $i] :
( ~ ( relation @ SY3817 )
| ~ ( ~ ( ~ ( in @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) @ SV296 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SY3817 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) ) @ SV307 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SY3817 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) ) @ SY3817 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) @ SV296 )
| ( in @ ( ordered_pair @ ( sK48_D @ SY3817 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) ) @ SY3817 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SY3817 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) ) @ SV307 )
| ( in @ ( ordered_pair @ ( sK48_D @ SY3817 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) ) @ SY3817 ) ) ) )
| ( SY3817
= ( relation_rng_restriction @ SV296 @ SV307 ) ) )
| ~ ! [SY3818: $i] :
( ~ ( relation @ SY3818 )
| ( SY3818
!= ( relation_rng_restriction @ SV296 @ SV307 ) )
| ~ ( ~ ! [SY3819: $i,SY3820: $i] :
( ~ ( in @ SY3820 @ SV296 )
| ~ ( in @ ( ordered_pair @ SY3819 @ SY3820 ) @ SV307 )
| ( in @ ( ordered_pair @ SY3819 @ SY3820 ) @ SY3818 ) )
| ~ ~ ( ~ ! [SY3771: $i,SY3772: $i] :
( ~ ( in @ ( ordered_pair @ SY3771 @ SY3772 ) @ SY3818 )
| ( in @ SY3772 @ SV296 ) )
| ~ ! [SY3823: $i,SY3824: $i] :
( ~ ( in @ ( ordered_pair @ SY3823 @ SY3824 ) @ SY3818 )
| ( in @ ( ordered_pair @ SY3823 @ SY3824 ) @ SV307 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2144]) ).
thf(2196,plain,
! [SV297: $i] :
( ( ( relation @ SV297 )
= $false )
| ( ( ~ ( ~ ! [SY3775: $i] :
( ~ ( ~ ( ! [SY3776: $i] :
~ ( in @ ( ordered_pair @ SY3776 @ ( sK17_C @ SY3775 @ SV297 ) ) @ SV297 )
| ~ ( in @ ( sK17_C @ SY3775 @ SV297 ) @ SY3775 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK18_SY3098 @ SY3775 @ SV297 ) @ ( sK17_C @ SY3775 @ SV297 ) ) @ SV297 )
| ( in @ ( sK17_C @ SY3775 @ SV297 ) @ SY3775 ) ) )
| ( SY3775
= ( relation_rng @ SV297 ) ) )
| ~ ! [SY3777: $i] :
( ( SY3777
!= ( relation_rng @ SV297 ) )
| ~ ( ~ ! [SY3778: $i] :
( ! [SY3779: $i] :
~ ( in @ ( ordered_pair @ SY3779 @ SY3778 ) @ SV297 )
| ( in @ SY3778 @ SY3777 ) )
| ~ ! [SY3780: $i] :
( ~ ( in @ SY3780 @ SY3777 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3780 @ SY3777 @ SV297 ) @ SY3780 ) @ SV297 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2145]) ).
thf(2197,plain,
! [SV298: $i] :
( ( ~ ! [SY3781: $i,SY3782: $i] :
( ~ ( relation @ SY3782 )
| ~ ( in @ ( ordered_pair @ SV298 @ SY3781 ) @ SY3782 )
| ( in @ SV298 @ ( relation_field @ SY3782 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2146]) ).
thf(2198,plain,
! [SV298: $i] :
( ( ~ ! [SY3783: $i,SY3784: $i] :
( ~ ( relation @ SY3784 )
| ~ ( in @ ( ordered_pair @ SV298 @ SY3783 ) @ SY3784 )
| ( in @ SY3783 @ ( relation_field @ SY3784 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2146]) ).
thf(2199,plain,
! [SV308: $i,SV299: $i] :
( ( ~ ! [SY3825: $i,SY3826: $i] :
( ~ ( relation @ SY3826 )
| ~ ( in @ SV299 @ SY3825 )
| ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ SY3826 )
| ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SY3825 ) @ SY3826 ) ) )
| ~ ~ ( ~ ! [SY3827: $i,SY3828: $i] :
( ~ ( relation @ SY3828 )
| ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SY3827 ) @ SY3828 ) )
| ( in @ SV299 @ SY3827 ) )
| ~ ! [SY3829: $i,SY3830: $i] :
( ~ ( relation @ SY3830 )
| ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SY3829 ) @ SY3830 ) )
| ( in @ ( ordered_pair @ SV299 @ SV308 ) @ SY3830 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2147]) ).
thf(2200,plain,
! [SV309: $i,SV300: $i] :
( ( ~ ! [SY3831: $i] :
( ! [SY3832: $i] :
( ( ordered_pair @ SV300 @ SV309 )
!= ( ordered_pair @ SY3831 @ SY3832 ) )
| ( SV300 = SY3831 ) )
| ~ ! [SY3833: $i,SY3834: $i] :
( ( ( ordered_pair @ SV300 @ SV309 )
!= ( ordered_pair @ SY3833 @ SY3834 ) )
| ( SV309 = SY3834 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2148]) ).
thf(2201,plain,
! [SV301: $i] :
( ( ~ ! [SY3797: $i,SY3798: $i] :
( ~ ( relation @ SY3798 )
| ! [SY3799: $i] :
( ~ ( in @ SY3799 @ ( relation_rng @ SY3798 ) )
| ~ ( in @ ( ordered_pair @ SV301 @ SY3799 ) @ SY3798 )
| ~ ( in @ SY3799 @ SY3797 ) )
| ( in @ SV301 @ ( relation_inverse_image @ SY3798 @ SY3797 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2149]) ).
thf(2202,plain,
! [SV301: $i] :
( ( ~ ! [SY3800: $i,SY3801: $i] :
( ~ ( relation @ SY3801 )
| ~ ( in @ SV301 @ ( relation_inverse_image @ SY3801 @ SY3800 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_D @ SY3801 @ SY3800 @ SV301 ) @ ( relation_rng @ SY3801 ) )
| ~ ( in @ ( ordered_pair @ SV301 @ ( sK60_D @ SY3801 @ SY3800 @ SV301 ) ) @ SY3801 ) )
| ~ ( in @ ( sK60_D @ SY3801 @ SY3800 @ SV301 ) @ SY3800 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2149]) ).
thf(2203,plain,
! [SV302: $i] :
( ( ( relation @ SV302 )
= $false )
| ( ( ~ ( ~ ! [SY3802: $i] :
( ~ ( ~ ( in @ ( sK36_C @ SY3802 @ SV302 ) @ SY3802 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SY3802 @ SV302 ) @ ( sK36_C @ SY3802 @ SV302 ) ) @ SV302 ) )
| ( is_reflexive_in @ SV302 @ SY3802 ) )
| ~ ! [SY3803: $i] :
( ~ ( is_reflexive_in @ SV302 @ SY3803 )
| ! [SY3804: $i] :
( ~ ( in @ SY3804 @ SY3803 )
| ( in @ ( ordered_pair @ SY3804 @ SY3804 ) @ SV302 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2150]) ).
thf(2204,plain,
! [SV269: $i] :
( ( ( in @ ( ordered_pair @ ( sK54_B @ SV269 ) @ ( sK55_SY3122 @ SV269 ) ) @ SV269 )
= $true )
| ( ( SV269 = empty_set )
= $true )
| ( ( relation @ SV269 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2151]) ).
thf(2205,plain,
! [SV305: $i,SV272: $i] :
( ( ~ ! [SY3805: $i,SY3806: $i] :
( ~ ( in @ SV272 @ SY3805 )
| ~ ( in @ SV305 @ SY3806 )
| ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SY3805 @ SY3806 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2153]) ).
thf(2206,plain,
! [SV305: $i,SV272: $i] :
( ( ~ ~ ( ~ ! [SY3807: $i] :
( ! [SY3808: $i] :
~ ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SY3807 @ SY3808 ) )
| ( in @ SV272 @ SY3807 ) )
| ~ ! [SY3809: $i,SY3810: $i] :
( ~ ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SY3809 @ SY3810 ) )
| ( in @ SV305 @ SY3810 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2153]) ).
thf(2207,plain,
! [SV306: $i,SV273: $i] :
( ( ~ ! [SY3811: $i,SY3812: $i] :
( ~ ( in @ SV273 @ SY3811 )
| ~ ( in @ SV306 @ SY3812 )
| ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SY3811 @ SY3812 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2154]) ).
thf(2208,plain,
! [SV306: $i,SV273: $i] :
( ( ~ ~ ( ~ ! [SY3813: $i] :
( ! [SY3814: $i] :
~ ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SY3813 @ SY3814 ) )
| ( in @ SV273 @ SY3813 ) )
| ~ ! [SY3815: $i,SY3816: $i] :
( ~ ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SY3815 @ SY3816 ) )
| ( in @ SV306 @ SY3816 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2154]) ).
thf(2209,plain,
! [SV312: $i] :
( ( ~ ( relation @ SV312 )
| ~ ( ~ ( in @ ( sK69_B @ SV312 ) @ ( relation_field @ SV312 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK69_B @ SV312 ) @ ( sK69_B @ SV312 ) ) @ SV312 ) )
| ( reflexive @ SV312 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2155]) ).
thf(2210,plain,
! [SV313: $i] :
( ( ~ ( relation @ SV313 )
| ~ ( reflexive @ SV313 )
| ! [SY3837: $i] :
( ~ ( in @ SY3837 @ ( relation_field @ SV313 ) )
| ( in @ ( ordered_pair @ SY3837 @ SY3837 ) @ SV313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2156]) ).
thf(2211,plain,
! [SV274: $i] :
( ( ( ~ ! [SY3618: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK14_C @ SY3618 @ SV274 )
!= ( sK15_SY3096 @ SY3618 @ SV274 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SY3618 @ SV274 ) @ SY3618 )
| ~ ( in @ ( sK15_SY3096 @ SY3618 @ SV274 ) @ SY3618 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK14_C @ SY3618 @ SV274 ) @ ( sK15_SY3096 @ SY3618 @ SV274 ) ) @ SV274 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK15_SY3096 @ SY3618 @ SV274 ) @ ( sK14_C @ SY3618 @ SV274 ) ) @ SV274 ) )
| ( is_connected_in @ SV274 @ SY3618 ) )
| ~ ! [SY3619: $i] :
( ~ ( is_connected_in @ SV274 @ SY3619 )
| ! [SY3620: $i,SY3621: $i] :
( ( SY3620 = SY3621 )
| ~ ( in @ SY3620 @ SY3619 )
| ~ ( in @ SY3621 @ SY3619 )
| ( in @ ( ordered_pair @ SY3620 @ SY3621 ) @ SV274 )
| ( in @ ( ordered_pair @ SY3621 @ SY3620 ) @ SV274 ) ) ) )
= $false )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2157]) ).
thf(2212,plain,
! [SV314: $i] :
( ( ~ ( ~ ! [SY3838: $i,SY3839: $i] :
( ( sK39_B @ SV314 )
!= ( ordered_pair @ SY3838 @ SY3839 ) )
| ~ ( in @ ( sK39_B @ SV314 ) @ SV314 ) )
| ( relation @ SV314 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2158]) ).
thf(2213,plain,
! [SV315: $i] :
( ( ~ ( relation @ SV315 )
| ! [SY3840: $i] :
( ( SY3840
= ( ordered_pair @ ( sK37_C @ SY3840 @ SV315 ) @ ( sK38_SY3111 @ SY3840 @ SV315 ) ) )
| ~ ( in @ SY3840 @ SV315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2159]) ).
thf(2214,plain,
! [SV316: $i] :
( ( ~ ( relation @ SV316 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK64_B @ SV316 ) @ ( sK65_SY3126 @ SV316 ) ) @ SV316 )
| ~ ( in @ ( ordered_pair @ ( sK65_SY3126 @ SV316 ) @ ( sK64_B @ SV316 ) ) @ SV316 ) )
| ~ ( ( ( sK64_B @ SV316 )
!= ( sK65_SY3126 @ SV316 ) ) ) )
| ( antisymmetric @ SV316 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2160]) ).
thf(2215,plain,
! [SV317: $i] :
( ( ~ ( relation @ SV317 )
| ~ ( antisymmetric @ SV317 )
| ! [SY3841: $i,SY3842: $i] :
( ~ ( in @ ( ordered_pair @ SY3841 @ SY3842 ) @ SV317 )
| ~ ( in @ ( ordered_pair @ SY3842 @ SY3841 ) @ SV317 )
| ( SY3841 = SY3842 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2161]) ).
thf(2216,plain,
! [SV275: $i] :
( ( ! [SY3622: $i,SY3623: $i] :
( ~ ( ~ ( ! [SY3624: $i,SY3625: $i] :
( ~ ( in @ SY3624 @ SV275 )
| ~ ( in @ SY3625 @ SY3622 )
| ( ( sK28_D @ SY3623 @ SY3622 @ SV275 )
!= ( ordered_pair @ SY3624 @ SY3625 ) ) )
| ~ ( in @ ( sK28_D @ SY3623 @ SY3622 @ SV275 ) @ SY3623 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY3106 @ SY3623 @ SY3622 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK30_SY3108 @ SY3623 @ SY3622 @ SV275 ) @ SY3622 ) )
| ( ( sK28_D @ SY3623 @ SY3622 @ SV275 )
!= ( ordered_pair @ ( sK29_SY3106 @ SY3623 @ SY3622 @ SV275 ) @ ( sK30_SY3108 @ SY3623 @ SY3622 @ SV275 ) ) ) )
| ( in @ ( sK28_D @ SY3623 @ SY3622 @ SV275 ) @ SY3623 ) ) )
| ( SY3623
= ( cartesian_product2 @ SV275 @ SY3622 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2162]) ).
thf(2217,plain,
! [SV275: $i] :
( ( ! [SY3626: $i,SY3627: $i] :
( ( SY3627
!= ( cartesian_product2 @ SV275 @ SY3626 ) )
| ~ ( ~ ! [SY3628: $i] :
( ! [SY3629: $i,SY3630: $i] :
( ~ ( in @ SY3629 @ SV275 )
| ~ ( in @ SY3630 @ SY3626 )
| ( SY3628
!= ( ordered_pair @ SY3629 @ SY3630 ) ) )
| ( in @ SY3628 @ SY3627 ) )
| ~ ! [SY3631: $i] :
( ~ ( in @ SY3631 @ SY3627 )
| ~ ( ~ ~ ( ~ ( in @ ( sK26_E @ SY3631 @ SY3627 @ SY3626 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK27_SY3103 @ SY3631 @ SY3627 @ SY3626 @ SV275 ) @ SY3626 ) )
| ( SY3631
!= ( ordered_pair @ ( sK26_E @ SY3631 @ SY3627 @ SY3626 @ SV275 ) @ ( sK27_SY3103 @ SY3631 @ SY3627 @ SY3626 @ SV275 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2163]) ).
thf(2218,plain,
! [SV276: $i] :
( ( ( ~ ! [SY3632: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SY3632 @ SV276 ) @ SY3632 )
| ~ ( in @ ( sK4_SY3086 @ SY3632 @ SV276 ) @ SY3632 ) )
| ~ ( in @ ( sK5_SY3088 @ SY3632 @ SV276 ) @ SY3632 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SY3632 @ SV276 ) @ ( sK4_SY3086 @ SY3632 @ SV276 ) ) @ SV276 ) )
| ~ ( in @ ( ordered_pair @ ( sK4_SY3086 @ SY3632 @ SV276 ) @ ( sK5_SY3088 @ SY3632 @ SV276 ) ) @ SV276 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK3_C @ SY3632 @ SV276 ) @ ( sK5_SY3088 @ SY3632 @ SV276 ) ) @ SV276 ) )
| ( is_transitive_in @ SV276 @ SY3632 ) )
| ~ ! [SY3633: $i] :
( ~ ( is_transitive_in @ SV276 @ SY3633 )
| ! [SY3634: $i,SY3635: $i,SY3636: $i] :
( ~ ( in @ SY3634 @ SY3633 )
| ~ ( in @ SY3635 @ SY3633 )
| ~ ( in @ SY3636 @ SY3633 )
| ~ ( in @ ( ordered_pair @ SY3634 @ SY3635 ) @ SV276 )
| ~ ( in @ ( ordered_pair @ SY3635 @ SY3636 ) @ SV276 )
| ( in @ ( ordered_pair @ SY3634 @ SY3636 ) @ SV276 ) ) ) )
= $false )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2164]) ).
thf(2219,plain,
! [SV277: $i] :
( ( ( ~ ! [SY3637: $i,SY3638: $i] :
( ~ ( ~ ( ! [SY3639: $i] :
( ~ ( in @ ( ordered_pair @ SY3639 @ ( sK46_D @ SY3638 @ SY3637 @ SV277 ) ) @ SV277 )
| ~ ( in @ SY3639 @ SY3637 ) )
| ~ ( in @ ( sK46_D @ SY3638 @ SY3637 @ SV277 ) @ SY3638 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SY3638 @ SY3637 @ SV277 ) @ ( sK46_D @ SY3638 @ SY3637 @ SV277 ) ) @ SV277 )
| ~ ( in @ ( sK47_SY3118 @ SY3638 @ SY3637 @ SV277 ) @ SY3637 ) )
| ( in @ ( sK46_D @ SY3638 @ SY3637 @ SV277 ) @ SY3638 ) ) )
| ( SY3638
= ( relation_image @ SV277 @ SY3637 ) ) )
| ~ ! [SY3640: $i,SY3641: $i] :
( ( SY3641
!= ( relation_image @ SV277 @ SY3640 ) )
| ~ ( ~ ! [SY3642: $i] :
( ! [SY3643: $i] :
( ~ ( in @ ( ordered_pair @ SY3643 @ SY3642 ) @ SV277 )
| ~ ( in @ SY3643 @ SY3640 ) )
| ( in @ SY3642 @ SY3641 ) )
| ~ ! [SY3644: $i] :
( ~ ( in @ SY3644 @ SY3641 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SY3644 @ SY3641 @ SY3640 @ SV277 ) @ SY3644 ) @ SV277 )
| ~ ( in @ ( sK45_E @ SY3644 @ SY3641 @ SY3640 @ SV277 ) @ SY3640 ) ) ) ) ) )
= $false )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2165]) ).
thf(2220,plain,
! [SV278: $i] :
( ( ( ~ ! [SY3645: $i,SY3646: $i] :
( ~ ( relation @ SY3646 )
| ~ ( ~ ( ~ ( in @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ SY3645 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ ( sK51_SY3120 @ SY3646 @ SY3645 @ SV278 ) ) @ SV278 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ ( sK51_SY3120 @ SY3646 @ SY3645 @ SV278 ) ) @ SY3646 ) )
| ~ ~ ( ~ ( ( in @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ SY3645 )
| ( in @ ( ordered_pair @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ ( sK51_SY3120 @ SY3646 @ SY3645 @ SV278 ) ) @ SY3646 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ ( sK51_SY3120 @ SY3646 @ SY3645 @ SV278 ) ) @ SV278 )
| ( in @ ( ordered_pair @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ ( sK51_SY3120 @ SY3646 @ SY3645 @ SV278 ) ) @ SY3646 ) ) ) )
| ( SY3646
= ( relation_dom_restriction @ SV278 @ SY3645 ) ) )
| ~ ! [SY3647: $i,SY3648: $i] :
( ~ ( relation @ SY3648 )
| ( SY3648
!= ( relation_dom_restriction @ SV278 @ SY3647 ) )
| ~ ( ~ ! [SY3649: $i,SY3650: $i] :
( ~ ( in @ SY3649 @ SY3647 )
| ~ ( in @ ( ordered_pair @ SY3649 @ SY3650 ) @ SV278 )
| ( in @ ( ordered_pair @ SY3649 @ SY3650 ) @ SY3648 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3648 )
| ( in @ SX3 @ SY3647 ) )
| ~ ! [SY3653: $i,SY3654: $i] :
( ~ ( in @ ( ordered_pair @ SY3653 @ SY3654 ) @ SY3648 )
| ( in @ ( ordered_pair @ SY3653 @ SY3654 ) @ SV278 ) ) ) ) ) )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2166]) ).
thf(2221,plain,
! [SV279: $i] :
( ( ( ~ ! [SY3655: $i,SY3656: $i] :
( ~ ( ~ ( ! [SY3657: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ SY3656 @ SY3655 @ SV279 ) @ SY3657 ) @ SV279 )
| ~ ( in @ SY3657 @ SY3655 ) )
| ~ ( in @ ( sK43_D @ SY3656 @ SY3655 @ SV279 ) @ SY3656 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SY3656 @ SY3655 @ SV279 ) @ ( sK44_SY3116 @ SY3656 @ SY3655 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK44_SY3116 @ SY3656 @ SY3655 @ SV279 ) @ SY3655 ) )
| ( in @ ( sK43_D @ SY3656 @ SY3655 @ SV279 ) @ SY3656 ) ) )
| ( SY3656
= ( relation_inverse_image @ SV279 @ SY3655 ) ) )
| ~ ! [SY3658: $i,SY3659: $i] :
( ( SY3659
!= ( relation_inverse_image @ SV279 @ SY3658 ) )
| ~ ( ~ ! [SY3660: $i] :
( ! [SY3661: $i] :
( ~ ( in @ ( ordered_pair @ SY3660 @ SY3661 ) @ SV279 )
| ~ ( in @ SY3661 @ SY3658 ) )
| ( in @ SY3660 @ SY3659 ) )
| ~ ! [SY3662: $i] :
( ~ ( in @ SY3662 @ SY3659 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3662 @ ( sK42_E @ SY3662 @ SY3659 @ SY3658 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK42_E @ SY3662 @ SY3659 @ SY3658 @ SV279 ) @ SY3658 ) ) ) ) ) )
= $false )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2167]) ).
thf(2222,plain,
! [SV280: $i] :
( ( ( ~ ! [SY3663: $i] :
( ~ ( relation @ SY3663 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3663 @ SV280 ) @ ( sK25_SY3102 @ SY3663 @ SV280 ) ) @ SV280 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3663 @ SV280 ) @ ( sK25_SY3102 @ SY3663 @ SV280 ) ) @ SY3663 ) )
| ( subset @ SV280 @ SY3663 ) )
| ~ ! [SY3664: $i] :
( ~ ( relation @ SY3664 )
| ~ ( subset @ SV280 @ SY3664 )
| ! [SY3665: $i,SY3666: $i] :
( ~ ( in @ ( ordered_pair @ SY3665 @ SY3666 ) @ SV280 )
| ( in @ ( ordered_pair @ SY3665 @ SY3666 ) @ SY3664 ) ) ) )
= $false )
| ( ( relation @ SV280 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2168]) ).
thf(2223,plain,
! [SV281: $i,SV318: $i] :
( ( ( ~ ( relation @ SV318 )
| ~ ( ~ ! [SY3843: $i] :
( ~ ( relation @ SY3843 )
| ~ ( ~ ( ! [SY3844: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3843 @ SV318 @ SV281 ) @ SY3844 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY3844 @ ( sK8_SY3089 @ SY3843 @ SV318 @ SV281 ) ) @ SV318 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3843 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SY3843 @ SV318 @ SV281 ) ) @ SY3843 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3843 @ SV318 @ SV281 ) @ ( sK9_SY3093 @ SY3843 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SY3843 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SY3843 @ SV318 @ SV281 ) ) @ SV318 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SY3843 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SY3843 @ SV318 @ SV281 ) ) @ SY3843 ) ) )
| ( SY3843
= ( relation_composition @ SV281 @ SV318 ) ) )
| ~ ! [SY3845: $i] :
( ~ ( relation @ SY3845 )
| ( SY3845
!= ( relation_composition @ SV281 @ SV318 ) )
| ~ ( ~ ! [SY3846: $i,SY3847: $i] :
( ! [SY3848: $i] :
( ~ ( in @ ( ordered_pair @ SY3846 @ SY3848 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY3848 @ SY3847 ) @ SV318 ) )
| ( in @ ( ordered_pair @ SY3846 @ SY3847 ) @ SY3845 ) )
| ~ ! [SY3849: $i,SY3850: $i] :
( ~ ( in @ ( ordered_pair @ SY3849 @ SY3850 ) @ SY3845 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3849 @ ( sK6_F @ SY3850 @ SY3849 @ SY3845 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY3850 @ SY3849 @ SY3845 @ SV318 @ SV281 ) @ SY3850 ) @ SV318 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2169]) ).
thf(2224,plain,
! [SV282: $i] :
( ( ! [SY3676: $i,SY3677: $i] :
( ~ ( relation_of2_as_subset @ SY3677 @ SV282 @ SY3676 )
| ~ ( ~ ! [SY3678: $i] :
~ ( in @ ( ordered_pair @ SY3678 @ ( sK57_D @ SY3677 @ SY3676 @ SV282 ) ) @ SY3677 )
| ~ ( in @ ( sK57_D @ SY3677 @ SY3676 @ SV282 ) @ SY3676 ) )
| ( ( relation_rng_as_subset @ SV282 @ SY3676 @ SY3677 )
= SY3676 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2170]) ).
thf(2225,plain,
! [SV282: $i] :
( ( ! [SY3679: $i,SY3680: $i] :
( ~ ( relation_of2_as_subset @ SY3680 @ SV282 @ SY3679 )
| ( ( relation_rng_as_subset @ SV282 @ SY3679 @ SY3680 )
!= SY3679 )
| ! [SY3681: $i] :
( ( in @ ( ordered_pair @ ( sK56_E @ SY3681 @ SY3680 @ SY3679 @ SV282 ) @ SY3681 ) @ SY3680 )
| ~ ( in @ SY3681 @ SY3679 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2171]) ).
thf(2226,plain,
! [SV283: $i,SV319: $i] :
( ( ( ~ ( relation @ SV319 )
| ~ ( ~ ! [SY3851: $i] :
( ~ ( function @ SY3851 )
| ~ ( relation @ SY3851 )
| ~ ( ~ ( ~ ( in @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3851 @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) ) @ ( apply @ SY3851 @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) ) @ SV319 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) @ SV283 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SY3851 @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) ) @ ( apply @ SY3851 @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) ) @ SV319 )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) @ SV283 ) ) ) )
| ( ( relation_dom @ SY3851 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SY3851 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SY3851 )
| ( relation_isomorphism @ SV283 @ SV319 @ SY3851 ) )
| ~ ~ ( ~ ! [SY3852: $i] :
( ~ ( function @ SY3852 )
| ~ ( relation @ SY3852 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3852 )
| ~ ( ~ ! [SY3853: $i,SY3854: $i] :
( ~ ( in @ SY3853 @ ( relation_field @ SV283 ) )
| ~ ( in @ SY3854 @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3852 @ SY3853 ) @ ( apply @ SY3852 @ SY3854 ) ) @ SV319 )
| ( in @ ( ordered_pair @ SY3853 @ SY3854 ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3687: $i] :
( ! [SY3688: $i] :
~ ( in @ ( ordered_pair @ SY3687 @ SY3688 ) @ SV283 )
| ( in @ SY3687 @ ( relation_field @ SV283 ) ) )
| ~ ! [SY3689: $i,SY3690: $i] :
( ~ ( in @ ( ordered_pair @ SY3689 @ SY3690 ) @ SV283 )
| ( in @ SY3690 @ ( relation_field @ SV283 ) ) ) )
| ~ ! [SY3859: $i,SY3860: $i] :
( ~ ( in @ ( ordered_pair @ SY3859 @ SY3860 ) @ SV283 )
| ( in @ ( ordered_pair @ ( apply @ SY3852 @ SY3859 ) @ ( apply @ SY3852 @ SY3860 ) ) @ SV319 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3861: $i] :
( ~ ( function @ SY3861 )
| ~ ( relation @ SY3861 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3861 )
| ( ( relation_dom @ SY3861 )
= ( relation_field @ SV283 ) ) )
| ~ ! [SY3862: $i] :
( ~ ( function @ SY3862 )
| ~ ( relation @ SY3862 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3862 )
| ( ( relation_rng @ SY3862 )
= ( relation_field @ SV319 ) ) ) )
| ~ ! [SY3863: $i] :
( ~ ( function @ SY3863 )
| ~ ( relation @ SY3863 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3863 )
| ( one_to_one @ SY3863 ) ) ) ) ) )
= $true )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2172]) ).
thf(2227,plain,
! [SV320: $i] :
( ( ~ ( relation @ SV320 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK62_B @ SV320 )
!= ( sK63_SY3125 @ SV320 ) ) )
| ~ ~ ( ~ ( in @ ( sK62_B @ SV320 ) @ ( relation_field @ SV320 ) )
| ~ ( in @ ( sK63_SY3125 @ SV320 ) @ ( relation_field @ SV320 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK62_B @ SV320 ) @ ( sK63_SY3125 @ SV320 ) ) @ SV320 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK63_SY3125 @ SV320 ) @ ( sK62_B @ SV320 ) ) @ SV320 ) )
| ( connected @ SV320 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2173]) ).
thf(2228,plain,
! [SV321: $i] :
( ( ~ ( relation @ SV321 )
| ~ ( connected @ SV321 )
| ! [SY3864: $i,SY3865: $i] :
( ( SY3864 = SY3865 )
| ~ ( in @ SY3864 @ ( relation_field @ SV321 ) )
| ~ ( in @ SY3865 @ ( relation_field @ SV321 ) )
| ( in @ ( ordered_pair @ SY3864 @ SY3865 ) @ SV321 )
| ( in @ ( ordered_pair @ SY3865 @ SY3864 ) @ SV321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2174]) ).
thf(2229,plain,
! [SV284: $i] :
( ( ! [SY3696: $i,SY3697: $i] :
( ~ ( function @ SY3697 )
| ~ ( relation @ SY3697 )
| ( SY3696
!= ( apply @ SY3697 @ SV284 ) )
| ~ ( in @ SV284 @ ( relation_dom @ SY3697 ) )
| ( in @ ( ordered_pair @ SV284 @ SY3696 ) @ SY3697 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2175]) ).
thf(2230,plain,
! [SV284: $i] :
( ( ~ ( ~ ! [SY3698: $i,SY3699: $i] :
( ~ ( function @ SY3699 )
| ~ ( relation @ SY3699 )
| ~ ( in @ ( ordered_pair @ SV284 @ SY3698 ) @ SY3699 )
| ( SY3698
= ( apply @ SY3699 @ SV284 ) ) )
| ~ ! [SY3700: $i,SY3701: $i] :
( ~ ( function @ SY3701 )
| ~ ( relation @ SY3701 )
| ~ ( in @ ( ordered_pair @ SV284 @ SY3700 ) @ SY3701 )
| ( in @ SV284 @ ( relation_dom @ SY3701 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2176]) ).
thf(2231,plain,
! [SV285: $i] :
( ( ! [SY3702: $i,SY3703: $i] :
( ~ ( relation @ SY3703 )
| ! [SY3704: $i] :
( ~ ( in @ SY3704 @ ( relation_dom @ SY3703 ) )
| ~ ( in @ ( ordered_pair @ SY3704 @ SV285 ) @ SY3703 )
| ~ ( in @ SY3704 @ SY3702 ) )
| ( in @ SV285 @ ( relation_image @ SY3703 @ SY3702 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2177]) ).
thf(2232,plain,
! [SV285: $i] :
( ( ! [SY3705: $i,SY3706: $i] :
( ~ ( relation @ SY3706 )
| ~ ( in @ SV285 @ ( relation_image @ SY3706 @ SY3705 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK61_D @ SY3706 @ SY3705 @ SV285 ) @ ( relation_dom @ SY3706 ) )
| ~ ( in @ ( ordered_pair @ ( sK61_D @ SY3706 @ SY3705 @ SV285 ) @ SV285 ) @ SY3706 ) )
| ~ ( in @ ( sK61_D @ SY3706 @ SY3705 @ SV285 ) @ SY3705 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2178]) ).
thf(2233,plain,
! [SV322: $i,SV310: $i,SV286: $i] :
( ( ( ( SV286
!= ( ordered_pair @ SV310 @ SV322 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3709: $i] :
( ~ ( ( SV286
!= ( ordered_pair @ ( sK40_C @ SY3709 @ SV286 ) @ ( sK41_SY3114 @ SY3709 @ SV286 ) ) )
| ~ ( ( SY3709
!= ( sK40_C @ SY3709 @ SV286 ) ) ) )
| ( SY3709
= ( pair_first @ SV286 ) ) )
| ~ ! [SY3710: $i] :
( ( SY3710
!= ( pair_first @ SV286 ) )
| ! [SY3711: $i] :
( ! [SY3712: $i] :
( SV286
!= ( ordered_pair @ SY3711 @ SY3712 ) )
| ( SY3710 = SY3711 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2179]) ).
thf(2234,plain,
! [SV323: $i,SV311: $i,SV287: $i] :
( ( ( ( SV287
!= ( ordered_pair @ SV311 @ SV323 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3715: $i] :
( ~ ( ( SV287
!= ( ordered_pair @ ( sK33_C @ SY3715 @ SV287 ) @ ( sK34_SY3110 @ SY3715 @ SV287 ) ) )
| ~ ( ( SY3715
!= ( sK34_SY3110 @ SY3715 @ SV287 ) ) ) )
| ( SY3715
= ( pair_second @ SV287 ) ) )
| ~ ! [SY3716: $i] :
( ( SY3716
!= ( pair_second @ SV287 ) )
| ! [SY3717: $i,SY3718: $i] :
( ( SV287
!= ( ordered_pair @ SY3717 @ SY3718 ) )
| ( SY3716 = SY3718 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2180]) ).
thf(2235,plain,
! [SV288: $i] :
( ( ! [SY3719: $i,SY3720: $i] :
( ~ ( relation @ SY3720 )
| ~ ( in @ ( ordered_pair @ SV288 @ SY3719 ) @ SY3720 )
| ( in @ SV288 @ ( relation_dom @ SY3720 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2181]) ).
thf(2236,plain,
! [SV288: $i] :
( ( ! [SY3721: $i,SY3722: $i] :
( ~ ( relation @ SY3722 )
| ~ ( in @ ( ordered_pair @ SV288 @ SY3721 ) @ SY3722 )
| ( in @ SY3721 @ ( relation_rng @ SY3722 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2182]) ).
thf(2237,plain,
! [SV324: $i] :
( ( ! [SY3866: $i] :
( ~ ( relation @ SY3866 )
| ~ ( ~ ( ( ( sK52_C @ SY3866 @ SV324 )
!= ( sK53_SY3121 @ SY3866 @ SV324 ) )
| ~ ( in @ ( sK52_C @ SY3866 @ SV324 ) @ SV324 )
| ~ ( in @ ( ordered_pair @ ( sK52_C @ SY3866 @ SV324 ) @ ( sK53_SY3121 @ SY3866 @ SV324 ) ) @ SY3866 ) )
| ~ ~ ( ~ ( ( ( sK52_C @ SY3866 @ SV324 )
= ( sK53_SY3121 @ SY3866 @ SV324 ) )
| ( in @ ( ordered_pair @ ( sK52_C @ SY3866 @ SV324 ) @ ( sK53_SY3121 @ SY3866 @ SV324 ) ) @ SY3866 ) )
| ~ ( ( in @ ( sK52_C @ SY3866 @ SV324 ) @ SV324 )
| ( in @ ( ordered_pair @ ( sK52_C @ SY3866 @ SV324 ) @ ( sK53_SY3121 @ SY3866 @ SV324 ) ) @ SY3866 ) ) ) )
| ( SY3866
= ( identity_relation @ SV324 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2183]) ).
thf(2238,plain,
! [SV325: $i] :
( ( ! [SY3867: $i] :
( ~ ( relation @ SY3867 )
| ( SY3867
!= ( identity_relation @ SV325 ) )
| ~ ( ~ ! [SY3868: $i,SY3869: $i] :
( ( SY3868 != SY3869 )
| ~ ( in @ SY3868 @ SV325 )
| ( in @ ( ordered_pair @ SY3868 @ SY3869 ) @ SY3867 ) )
| ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SY3867 )
| ( SX2 = SX3 ) )
| ~ ! [SY3872: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SY3872 @ SX3 ) @ SY3867 )
| ( in @ SY3872 @ SV325 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2184]) ).
thf(2239,plain,
! [SV289: $i] :
( ( ! [SY3723: $i,SY3724: $i] :
( ~ ( relation_of2_as_subset @ SY3724 @ SY3723 @ SV289 )
| ~ ( ~ ! [SY3725: $i] :
~ ( in @ ( ordered_pair @ ( sK59_D @ SY3724 @ SY3723 @ SV289 ) @ SY3725 ) @ SY3724 )
| ~ ( in @ ( sK59_D @ SY3724 @ SY3723 @ SV289 ) @ SY3723 ) )
| ( ( relation_dom_as_subset @ SY3723 @ SV289 @ SY3724 )
= SY3723 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2185]) ).
thf(2240,plain,
! [SV289: $i] :
( ( ! [SY3726: $i,SY3727: $i] :
( ~ ( relation_of2_as_subset @ SY3727 @ SY3726 @ SV289 )
| ( ( relation_dom_as_subset @ SY3726 @ SV289 @ SY3727 )
!= SY3726 )
| ! [SY3728: $i] :
( ( in @ ( ordered_pair @ SY3728 @ ( sK58_E @ SY3728 @ SY3727 @ SY3726 @ SV289 ) ) @ SY3727 )
| ~ ( in @ SY3728 @ SY3726 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2186]) ).
thf(2241,plain,
! [SV290: $i] :
( ( ( ~ ! [SY3729: $i] :
( ~ ( ~ ( ! [SY3730: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SY3729 @ SV290 ) @ SY3730 ) @ SV290 )
| ~ ( in @ ( sK22_C @ SY3729 @ SV290 ) @ SY3729 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SY3729 @ SV290 ) @ ( sK23_SY3101 @ SY3729 @ SV290 ) ) @ SV290 )
| ( in @ ( sK22_C @ SY3729 @ SV290 ) @ SY3729 ) ) )
| ( SY3729
= ( relation_dom @ SV290 ) ) )
| ~ ! [SY3731: $i] :
( ( SY3731
!= ( relation_dom @ SV290 ) )
| ~ ( ~ ! [SY3732: $i] :
( ! [SY3733: $i] :
~ ( in @ ( ordered_pair @ SY3732 @ SY3733 ) @ SV290 )
| ( in @ SY3732 @ SY3731 ) )
| ~ ! [SY3734: $i] :
( ~ ( in @ SY3734 @ SY3731 )
| ( in @ ( ordered_pair @ SY3734 @ ( sK21_D @ SY3734 @ SY3731 @ SV290 ) ) @ SV290 ) ) ) ) )
= $false )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2187]) ).
thf(2242,plain,
! [SV291: $i] :
( ( ( ~ ! [SY3735: $i] :
( ~ ( relation @ SY3735 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SY3735 @ SV291 ) @ ( sK32_SY3109 @ SY3735 @ SV291 ) ) @ SV291 )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ SY3735 @ SV291 ) @ ( sK32_SY3109 @ SY3735 @ SV291 ) ) @ SY3735 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK31_C @ SY3735 @ SV291 ) @ ( sK32_SY3109 @ SY3735 @ SV291 ) ) @ SV291 )
| ( in @ ( ordered_pair @ ( sK31_C @ SY3735 @ SV291 ) @ ( sK32_SY3109 @ SY3735 @ SV291 ) ) @ SY3735 ) ) )
| ( SV291 = SY3735 ) )
| ~ ! [SY3736: $i] :
( ~ ( relation @ SY3736 )
| ( SV291 != SY3736 )
| ~ ( ~ ! [SY3737: $i,SY3738: $i] :
( ~ ( in @ ( ordered_pair @ SY3737 @ SY3738 ) @ SV291 )
| ( in @ ( ordered_pair @ SY3737 @ SY3738 ) @ SY3736 ) )
| ~ ! [SY3739: $i,SY3740: $i] :
( ~ ( in @ ( ordered_pair @ SY3739 @ SY3740 ) @ SY3736 )
| ( in @ ( ordered_pair @ SY3739 @ SY3740 ) @ SV291 ) ) ) ) )
= $false )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2188]) ).
thf(2243,plain,
! [SV326: $i] :
( ( ~ ( relation @ SV326 )
| ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK66_B @ SV326 ) @ ( sK67_SY3127 @ SV326 ) ) @ SV326 )
| ~ ( in @ ( ordered_pair @ ( sK67_SY3127 @ SV326 ) @ ( sK68_SY3129 @ SV326 ) ) @ SV326 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK66_B @ SV326 ) @ ( sK68_SY3129 @ SV326 ) ) @ SV326 ) )
| ( transitive @ SV326 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2189]) ).
thf(2244,plain,
! [SV327: $i] :
( ( ~ ( relation @ SV327 )
| ~ ( transitive @ SV327 )
| ! [SY3874: $i,SY3875: $i,SY3876: $i] :
( ~ ( in @ ( ordered_pair @ SY3874 @ SY3875 ) @ SV327 )
| ~ ( in @ ( ordered_pair @ SY3875 @ SY3876 ) @ SV327 )
| ( in @ ( ordered_pair @ SY3874 @ SY3876 ) @ SV327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2190]) ).
thf(2245,plain,
! [SV292: $i] :
( ( ( ~ ! [SY3741: $i] :
( ~ ( relation @ SY3741 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SY3741 @ SV292 ) @ ( sK13_SY3095 @ SY3741 @ SV292 ) ) @ SY3741 )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SY3741 @ SV292 ) @ ( sK12_C @ SY3741 @ SV292 ) ) @ SV292 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SY3741 @ SV292 ) @ ( sK13_SY3095 @ SY3741 @ SV292 ) ) @ SY3741 )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ SY3741 @ SV292 ) @ ( sK12_C @ SY3741 @ SV292 ) ) @ SV292 ) ) )
| ( SY3741
= ( relation_inverse @ SV292 ) ) )
| ~ ! [SY3742: $i] :
( ~ ( relation @ SY3742 )
| ( SY3742
!= ( relation_inverse @ SV292 ) )
| ~ ( ~ ! [SY3743: $i,SY3744: $i] :
( ~ ( in @ ( ordered_pair @ SY3743 @ SY3744 ) @ SY3742 )
| ( in @ ( ordered_pair @ SY3744 @ SY3743 ) @ SV292 ) )
| ~ ! [SY3745: $i,SY3746: $i] :
( ~ ( in @ ( ordered_pair @ SY3746 @ SY3745 ) @ SV292 )
| ( in @ ( ordered_pair @ SY3745 @ SY3746 ) @ SY3742 ) ) ) ) )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2191]) ).
thf(2246,plain,
! [SV293: $i] :
( ( ( function @ SV293 )
= $false )
| ( ( ~ ( relation @ SV293 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY3747: $i] :
( ~ ( in @ SY3747 @ ( relation_dom @ SV293 ) )
| ! [SY3748: $i] :
( ( SY3748
!= ( apply @ SV293 @ SY3747 ) )
| ( in @ ( ordered_pair @ SY3747 @ SY3748 ) @ SV293 ) ) )
| ~ ! [SY3749: $i] :
( ~ ( in @ SY3749 @ ( relation_dom @ SV293 ) )
| ! [SY3750: $i] :
( ~ ( in @ ( ordered_pair @ SY3749 @ SY3750 ) @ SV293 )
| ( SY3750
= ( apply @ SV293 @ SY3749 ) ) ) ) )
| ~ ~ ( ~ ! [SY3751: $i] :
( ( in @ SY3751 @ ( relation_dom @ SV293 ) )
| ! [SY3752: $i] :
( ( SY3752
!= ( apply @ SV293 @ SY3751 ) )
| ( SY3752 = empty_set ) ) )
| ~ ! [SY3753: $i] :
( ( in @ SY3753 @ ( relation_dom @ SV293 ) )
| ! [SY3754: $i] :
( ( SY3754 != empty_set )
| ( SY3754
= ( apply @ SV293 @ SY3753 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2192]) ).
thf(2247,plain,
! [SV294: $i] :
( ( ( ~ ! [SY3755: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_C @ SY3755 @ SV294 ) @ SY3755 )
| ~ ( in @ ( sK20_SY3099 @ SY3755 @ SV294 ) @ SY3755 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SY3755 @ SV294 ) @ ( sK20_SY3099 @ SY3755 @ SV294 ) ) @ SV294 ) )
| ~ ( in @ ( ordered_pair @ ( sK20_SY3099 @ SY3755 @ SV294 ) @ ( sK19_C @ SY3755 @ SV294 ) ) @ SV294 ) )
| ~ ( ( ( sK19_C @ SY3755 @ SV294 )
!= ( sK20_SY3099 @ SY3755 @ SV294 ) ) ) )
| ( is_antisymmetric_in @ SV294 @ SY3755 ) )
| ~ ! [SY3756: $i] :
( ~ ( is_antisymmetric_in @ SV294 @ SY3756 )
| ! [SY3757: $i,SY3758: $i] :
( ~ ( in @ SY3757 @ SY3756 )
| ~ ( in @ SY3758 @ SY3756 )
| ~ ( in @ ( ordered_pair @ SY3757 @ SY3758 ) @ SV294 )
| ~ ( in @ ( ordered_pair @ SY3758 @ SY3757 ) @ SV294 )
| ( SY3757 = SY3758 ) ) ) )
= $false )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2193]) ).
thf(2248,plain,
! [SV295: $i] :
( ( ( ~ ! [SY3759: $i,SY3760: $i] :
( ~ ( ~ ( ( ( sK35_D @ SY3760 @ SY3759 @ SV295 )
= SY3759 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SY3760 @ SY3759 @ SV295 ) @ SY3759 ) @ SV295 )
| ~ ( in @ ( sK35_D @ SY3760 @ SY3759 @ SV295 ) @ SY3760 ) )
| ~ ~ ( ~ ( ( ( sK35_D @ SY3760 @ SY3759 @ SV295 )
!= SY3759 )
| ( in @ ( sK35_D @ SY3760 @ SY3759 @ SV295 ) @ SY3760 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SY3760 @ SY3759 @ SV295 ) @ SY3759 ) @ SV295 )
| ( in @ ( sK35_D @ SY3760 @ SY3759 @ SV295 ) @ SY3760 ) ) ) )
| ( SY3760
= ( fiber @ SV295 @ SY3759 ) ) )
| ~ ! [SY3761: $i,SY3762: $i] :
( ( SY3762
!= ( fiber @ SV295 @ SY3761 ) )
| ~ ( ~ ! [SY3763: $i] :
( ( SY3763 = SY3761 )
| ~ ( in @ ( ordered_pair @ SY3763 @ SY3761 ) @ SV295 )
| ( in @ SY3763 @ SY3762 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY3762 )
| ( SX3 != SY3761 ) )
| ~ ! [SY3765: $i] :
( ~ ( in @ SY3765 @ SY3762 )
| ( in @ ( ordered_pair @ SY3765 @ SY3761 ) @ SV295 ) ) ) ) ) )
= $false )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2194]) ).
thf(2249,plain,
! [SV296: $i,SV307: $i] :
( ( ( relation @ SV307 )
= $false )
| ( ( ~ ( ~ ! [SY3817: $i] :
( ~ ( relation @ SY3817 )
| ~ ( ~ ( ~ ( in @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) @ SV296 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SY3817 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) ) @ SV307 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SY3817 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) ) @ SY3817 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) @ SV296 )
| ( in @ ( ordered_pair @ ( sK48_D @ SY3817 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) ) @ SY3817 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SY3817 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) ) @ SV307 )
| ( in @ ( ordered_pair @ ( sK48_D @ SY3817 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) ) @ SY3817 ) ) ) )
| ( SY3817
= ( relation_rng_restriction @ SV296 @ SV307 ) ) )
| ~ ! [SY3818: $i] :
( ~ ( relation @ SY3818 )
| ( SY3818
!= ( relation_rng_restriction @ SV296 @ SV307 ) )
| ~ ( ~ ! [SY3819: $i,SY3820: $i] :
( ~ ( in @ SY3820 @ SV296 )
| ~ ( in @ ( ordered_pair @ SY3819 @ SY3820 ) @ SV307 )
| ( in @ ( ordered_pair @ SY3819 @ SY3820 ) @ SY3818 ) )
| ~ ~ ( ~ ! [SY3771: $i,SY3772: $i] :
( ~ ( in @ ( ordered_pair @ SY3771 @ SY3772 ) @ SY3818 )
| ( in @ SY3772 @ SV296 ) )
| ~ ! [SY3823: $i,SY3824: $i] :
( ~ ( in @ ( ordered_pair @ SY3823 @ SY3824 ) @ SY3818 )
| ( in @ ( ordered_pair @ SY3823 @ SY3824 ) @ SV307 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2195]) ).
thf(2250,plain,
! [SV297: $i] :
( ( ( ~ ! [SY3775: $i] :
( ~ ( ~ ( ! [SY3776: $i] :
~ ( in @ ( ordered_pair @ SY3776 @ ( sK17_C @ SY3775 @ SV297 ) ) @ SV297 )
| ~ ( in @ ( sK17_C @ SY3775 @ SV297 ) @ SY3775 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK18_SY3098 @ SY3775 @ SV297 ) @ ( sK17_C @ SY3775 @ SV297 ) ) @ SV297 )
| ( in @ ( sK17_C @ SY3775 @ SV297 ) @ SY3775 ) ) )
| ( SY3775
= ( relation_rng @ SV297 ) ) )
| ~ ! [SY3777: $i] :
( ( SY3777
!= ( relation_rng @ SV297 ) )
| ~ ( ~ ! [SY3778: $i] :
( ! [SY3779: $i] :
~ ( in @ ( ordered_pair @ SY3779 @ SY3778 ) @ SV297 )
| ( in @ SY3778 @ SY3777 ) )
| ~ ! [SY3780: $i] :
( ~ ( in @ SY3780 @ SY3777 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3780 @ SY3777 @ SV297 ) @ SY3780 ) @ SV297 ) ) ) ) )
= $false )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2196]) ).
thf(2251,plain,
! [SV298: $i] :
( ( ! [SY3781: $i,SY3782: $i] :
( ~ ( relation @ SY3782 )
| ~ ( in @ ( ordered_pair @ SV298 @ SY3781 ) @ SY3782 )
| ( in @ SV298 @ ( relation_field @ SY3782 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2197]) ).
thf(2252,plain,
! [SV298: $i] :
( ( ! [SY3783: $i,SY3784: $i] :
( ~ ( relation @ SY3784 )
| ~ ( in @ ( ordered_pair @ SV298 @ SY3783 ) @ SY3784 )
| ( in @ SY3783 @ ( relation_field @ SY3784 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2198]) ).
thf(2253,plain,
! [SV308: $i,SV299: $i] :
( ( ~ ! [SY3825: $i,SY3826: $i] :
( ~ ( relation @ SY3826 )
| ~ ( in @ SV299 @ SY3825 )
| ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ SY3826 )
| ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SY3825 ) @ SY3826 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2199]) ).
thf(2254,plain,
! [SV308: $i,SV299: $i] :
( ( ~ ~ ( ~ ! [SY3827: $i,SY3828: $i] :
( ~ ( relation @ SY3828 )
| ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SY3827 ) @ SY3828 ) )
| ( in @ SV299 @ SY3827 ) )
| ~ ! [SY3829: $i,SY3830: $i] :
( ~ ( relation @ SY3830 )
| ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SY3829 ) @ SY3830 ) )
| ( in @ ( ordered_pair @ SV299 @ SV308 ) @ SY3830 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2199]) ).
thf(2255,plain,
! [SV309: $i,SV300: $i] :
( ( ~ ! [SY3831: $i] :
( ! [SY3832: $i] :
( ( ordered_pair @ SV300 @ SV309 )
!= ( ordered_pair @ SY3831 @ SY3832 ) )
| ( SV300 = SY3831 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2200]) ).
thf(2256,plain,
! [SV309: $i,SV300: $i] :
( ( ~ ! [SY3833: $i,SY3834: $i] :
( ( ( ordered_pair @ SV300 @ SV309 )
!= ( ordered_pair @ SY3833 @ SY3834 ) )
| ( SV309 = SY3834 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2200]) ).
thf(2257,plain,
! [SV301: $i] :
( ( ! [SY3797: $i,SY3798: $i] :
( ~ ( relation @ SY3798 )
| ! [SY3799: $i] :
( ~ ( in @ SY3799 @ ( relation_rng @ SY3798 ) )
| ~ ( in @ ( ordered_pair @ SV301 @ SY3799 ) @ SY3798 )
| ~ ( in @ SY3799 @ SY3797 ) )
| ( in @ SV301 @ ( relation_inverse_image @ SY3798 @ SY3797 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2201]) ).
thf(2258,plain,
! [SV301: $i] :
( ( ! [SY3800: $i,SY3801: $i] :
( ~ ( relation @ SY3801 )
| ~ ( in @ SV301 @ ( relation_inverse_image @ SY3801 @ SY3800 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_D @ SY3801 @ SY3800 @ SV301 ) @ ( relation_rng @ SY3801 ) )
| ~ ( in @ ( ordered_pair @ SV301 @ ( sK60_D @ SY3801 @ SY3800 @ SV301 ) ) @ SY3801 ) )
| ~ ( in @ ( sK60_D @ SY3801 @ SY3800 @ SV301 ) @ SY3800 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2202]) ).
thf(2259,plain,
! [SV302: $i] :
( ( ( ~ ! [SY3802: $i] :
( ~ ( ~ ( in @ ( sK36_C @ SY3802 @ SV302 ) @ SY3802 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SY3802 @ SV302 ) @ ( sK36_C @ SY3802 @ SV302 ) ) @ SV302 ) )
| ( is_reflexive_in @ SV302 @ SY3802 ) )
| ~ ! [SY3803: $i] :
( ~ ( is_reflexive_in @ SV302 @ SY3803 )
| ! [SY3804: $i] :
( ~ ( in @ SY3804 @ SY3803 )
| ( in @ ( ordered_pair @ SY3804 @ SY3804 ) @ SV302 ) ) ) )
= $false )
| ( ( relation @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2203]) ).
thf(2260,plain,
! [SV305: $i,SV272: $i] :
( ( ! [SY3805: $i,SY3806: $i] :
( ~ ( in @ SV272 @ SY3805 )
| ~ ( in @ SV305 @ SY3806 )
| ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SY3805 @ SY3806 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2205]) ).
thf(2261,plain,
! [SV305: $i,SV272: $i] :
( ( ~ ( ~ ! [SY3807: $i] :
( ! [SY3808: $i] :
~ ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SY3807 @ SY3808 ) )
| ( in @ SV272 @ SY3807 ) )
| ~ ! [SY3809: $i,SY3810: $i] :
( ~ ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SY3809 @ SY3810 ) )
| ( in @ SV305 @ SY3810 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2206]) ).
thf(2262,plain,
! [SV306: $i,SV273: $i] :
( ( ! [SY3811: $i,SY3812: $i] :
( ~ ( in @ SV273 @ SY3811 )
| ~ ( in @ SV306 @ SY3812 )
| ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SY3811 @ SY3812 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2207]) ).
thf(2263,plain,
! [SV306: $i,SV273: $i] :
( ( ~ ( ~ ! [SY3813: $i] :
( ! [SY3814: $i] :
~ ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SY3813 @ SY3814 ) )
| ( in @ SV273 @ SY3813 ) )
| ~ ! [SY3815: $i,SY3816: $i] :
( ~ ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SY3815 @ SY3816 ) )
| ( in @ SV306 @ SY3816 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2208]) ).
thf(2264,plain,
! [SV312: $i] :
( ( ( ~ ( relation @ SV312 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK69_B @ SV312 ) @ ( relation_field @ SV312 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK69_B @ SV312 ) @ ( sK69_B @ SV312 ) ) @ SV312 ) )
| ( reflexive @ SV312 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2209]) ).
thf(2265,plain,
! [SV313: $i] :
( ( ( ~ ( relation @ SV313 ) )
= $true )
| ( ( ~ ( reflexive @ SV313 )
| ! [SY3837: $i] :
( ~ ( in @ SY3837 @ ( relation_field @ SV313 ) )
| ( in @ ( ordered_pair @ SY3837 @ SY3837 ) @ SV313 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2210]) ).
thf(2266,plain,
! [SV274: $i] :
( ( ( ~ ! [SY3618: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK14_C @ SY3618 @ SV274 )
!= ( sK15_SY3096 @ SY3618 @ SV274 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SY3618 @ SV274 ) @ SY3618 )
| ~ ( in @ ( sK15_SY3096 @ SY3618 @ SV274 ) @ SY3618 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK14_C @ SY3618 @ SV274 ) @ ( sK15_SY3096 @ SY3618 @ SV274 ) ) @ SV274 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK15_SY3096 @ SY3618 @ SV274 ) @ ( sK14_C @ SY3618 @ SV274 ) ) @ SV274 ) )
| ( is_connected_in @ SV274 @ SY3618 ) ) )
= $false )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2211]) ).
thf(2267,plain,
! [SV274: $i] :
( ( ( ~ ! [SY3619: $i] :
( ~ ( is_connected_in @ SV274 @ SY3619 )
| ! [SY3620: $i,SY3621: $i] :
( ( SY3620 = SY3621 )
| ~ ( in @ SY3620 @ SY3619 )
| ~ ( in @ SY3621 @ SY3619 )
| ( in @ ( ordered_pair @ SY3620 @ SY3621 ) @ SV274 )
| ( in @ ( ordered_pair @ SY3621 @ SY3620 ) @ SV274 ) ) ) )
= $false )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2211]) ).
thf(2268,plain,
! [SV314: $i] :
( ( ( ~ ( ~ ! [SY3838: $i,SY3839: $i] :
( ( sK39_B @ SV314 )
!= ( ordered_pair @ SY3838 @ SY3839 ) )
| ~ ( in @ ( sK39_B @ SV314 ) @ SV314 ) ) )
= $true )
| ( ( relation @ SV314 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2212]) ).
thf(2269,plain,
! [SV315: $i] :
( ( ( ~ ( relation @ SV315 ) )
= $true )
| ( ( ! [SY3840: $i] :
( ( SY3840
= ( ordered_pair @ ( sK37_C @ SY3840 @ SV315 ) @ ( sK38_SY3111 @ SY3840 @ SV315 ) ) )
| ~ ( in @ SY3840 @ SV315 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2213]) ).
thf(2270,plain,
! [SV316: $i] :
( ( ( ~ ( relation @ SV316 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK64_B @ SV316 ) @ ( sK65_SY3126 @ SV316 ) ) @ SV316 )
| ~ ( in @ ( ordered_pair @ ( sK65_SY3126 @ SV316 ) @ ( sK64_B @ SV316 ) ) @ SV316 ) )
| ~ ( ( ( sK64_B @ SV316 )
!= ( sK65_SY3126 @ SV316 ) ) ) )
| ( antisymmetric @ SV316 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2214]) ).
thf(2271,plain,
! [SV317: $i] :
( ( ( ~ ( relation @ SV317 ) )
= $true )
| ( ( ~ ( antisymmetric @ SV317 )
| ! [SY3841: $i,SY3842: $i] :
( ~ ( in @ ( ordered_pair @ SY3841 @ SY3842 ) @ SV317 )
| ~ ( in @ ( ordered_pair @ SY3842 @ SY3841 ) @ SV317 )
| ( SY3841 = SY3842 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2215]) ).
thf(2272,plain,
! [SV328: $i,SV275: $i] :
( ( ! [SY3877: $i] :
( ~ ( ~ ( ! [SY3878: $i,SY3879: $i] :
( ~ ( in @ SY3878 @ SV275 )
| ~ ( in @ SY3879 @ SV328 )
| ( ( sK28_D @ SY3877 @ SV328 @ SV275 )
!= ( ordered_pair @ SY3878 @ SY3879 ) ) )
| ~ ( in @ ( sK28_D @ SY3877 @ SV328 @ SV275 ) @ SY3877 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY3106 @ SY3877 @ SV328 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK30_SY3108 @ SY3877 @ SV328 @ SV275 ) @ SV328 ) )
| ( ( sK28_D @ SY3877 @ SV328 @ SV275 )
!= ( ordered_pair @ ( sK29_SY3106 @ SY3877 @ SV328 @ SV275 ) @ ( sK30_SY3108 @ SY3877 @ SV328 @ SV275 ) ) ) )
| ( in @ ( sK28_D @ SY3877 @ SV328 @ SV275 ) @ SY3877 ) ) )
| ( SY3877
= ( cartesian_product2 @ SV275 @ SV328 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2216]) ).
thf(2273,plain,
! [SV329: $i,SV275: $i] :
( ( ! [SY3880: $i] :
( ( SY3880
!= ( cartesian_product2 @ SV275 @ SV329 ) )
| ~ ( ~ ! [SY3881: $i] :
( ! [SY3882: $i,SY3883: $i] :
( ~ ( in @ SY3882 @ SV275 )
| ~ ( in @ SY3883 @ SV329 )
| ( SY3881
!= ( ordered_pair @ SY3882 @ SY3883 ) ) )
| ( in @ SY3881 @ SY3880 ) )
| ~ ! [SY3884: $i] :
( ~ ( in @ SY3884 @ SY3880 )
| ~ ( ~ ~ ( ~ ( in @ ( sK26_E @ SY3884 @ SY3880 @ SV329 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK27_SY3103 @ SY3884 @ SY3880 @ SV329 @ SV275 ) @ SV329 ) )
| ( SY3884
!= ( ordered_pair @ ( sK26_E @ SY3884 @ SY3880 @ SV329 @ SV275 ) @ ( sK27_SY3103 @ SY3884 @ SY3880 @ SV329 @ SV275 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2217]) ).
thf(2274,plain,
! [SV276: $i] :
( ( ( ~ ! [SY3632: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SY3632 @ SV276 ) @ SY3632 )
| ~ ( in @ ( sK4_SY3086 @ SY3632 @ SV276 ) @ SY3632 ) )
| ~ ( in @ ( sK5_SY3088 @ SY3632 @ SV276 ) @ SY3632 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SY3632 @ SV276 ) @ ( sK4_SY3086 @ SY3632 @ SV276 ) ) @ SV276 ) )
| ~ ( in @ ( ordered_pair @ ( sK4_SY3086 @ SY3632 @ SV276 ) @ ( sK5_SY3088 @ SY3632 @ SV276 ) ) @ SV276 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK3_C @ SY3632 @ SV276 ) @ ( sK5_SY3088 @ SY3632 @ SV276 ) ) @ SV276 ) )
| ( is_transitive_in @ SV276 @ SY3632 ) ) )
= $false )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2218]) ).
thf(2275,plain,
! [SV276: $i] :
( ( ( ~ ! [SY3633: $i] :
( ~ ( is_transitive_in @ SV276 @ SY3633 )
| ! [SY3634: $i,SY3635: $i,SY3636: $i] :
( ~ ( in @ SY3634 @ SY3633 )
| ~ ( in @ SY3635 @ SY3633 )
| ~ ( in @ SY3636 @ SY3633 )
| ~ ( in @ ( ordered_pair @ SY3634 @ SY3635 ) @ SV276 )
| ~ ( in @ ( ordered_pair @ SY3635 @ SY3636 ) @ SV276 )
| ( in @ ( ordered_pair @ SY3634 @ SY3636 ) @ SV276 ) ) ) )
= $false )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2218]) ).
thf(2276,plain,
! [SV277: $i] :
( ( ( ~ ! [SY3637: $i,SY3638: $i] :
( ~ ( ~ ( ! [SY3639: $i] :
( ~ ( in @ ( ordered_pair @ SY3639 @ ( sK46_D @ SY3638 @ SY3637 @ SV277 ) ) @ SV277 )
| ~ ( in @ SY3639 @ SY3637 ) )
| ~ ( in @ ( sK46_D @ SY3638 @ SY3637 @ SV277 ) @ SY3638 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SY3638 @ SY3637 @ SV277 ) @ ( sK46_D @ SY3638 @ SY3637 @ SV277 ) ) @ SV277 )
| ~ ( in @ ( sK47_SY3118 @ SY3638 @ SY3637 @ SV277 ) @ SY3637 ) )
| ( in @ ( sK46_D @ SY3638 @ SY3637 @ SV277 ) @ SY3638 ) ) )
| ( SY3638
= ( relation_image @ SV277 @ SY3637 ) ) ) )
= $false )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2219]) ).
thf(2277,plain,
! [SV277: $i] :
( ( ( ~ ! [SY3640: $i,SY3641: $i] :
( ( SY3641
!= ( relation_image @ SV277 @ SY3640 ) )
| ~ ( ~ ! [SY3642: $i] :
( ! [SY3643: $i] :
( ~ ( in @ ( ordered_pair @ SY3643 @ SY3642 ) @ SV277 )
| ~ ( in @ SY3643 @ SY3640 ) )
| ( in @ SY3642 @ SY3641 ) )
| ~ ! [SY3644: $i] :
( ~ ( in @ SY3644 @ SY3641 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SY3644 @ SY3641 @ SY3640 @ SV277 ) @ SY3644 ) @ SV277 )
| ~ ( in @ ( sK45_E @ SY3644 @ SY3641 @ SY3640 @ SV277 ) @ SY3640 ) ) ) ) ) )
= $false )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2219]) ).
thf(2278,plain,
! [SV278: $i] :
( ( ( ~ ! [SY3645: $i,SY3646: $i] :
( ~ ( relation @ SY3646 )
| ~ ( ~ ( ~ ( in @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ SY3645 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ ( sK51_SY3120 @ SY3646 @ SY3645 @ SV278 ) ) @ SV278 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ ( sK51_SY3120 @ SY3646 @ SY3645 @ SV278 ) ) @ SY3646 ) )
| ~ ~ ( ~ ( ( in @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ SY3645 )
| ( in @ ( ordered_pair @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ ( sK51_SY3120 @ SY3646 @ SY3645 @ SV278 ) ) @ SY3646 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ ( sK51_SY3120 @ SY3646 @ SY3645 @ SV278 ) ) @ SV278 )
| ( in @ ( ordered_pair @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ ( sK51_SY3120 @ SY3646 @ SY3645 @ SV278 ) ) @ SY3646 ) ) ) )
| ( SY3646
= ( relation_dom_restriction @ SV278 @ SY3645 ) ) ) )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2220]) ).
thf(2279,plain,
! [SV278: $i] :
( ( ( ~ ! [SY3647: $i,SY3648: $i] :
( ~ ( relation @ SY3648 )
| ( SY3648
!= ( relation_dom_restriction @ SV278 @ SY3647 ) )
| ~ ( ~ ! [SY3649: $i,SY3650: $i] :
( ~ ( in @ SY3649 @ SY3647 )
| ~ ( in @ ( ordered_pair @ SY3649 @ SY3650 ) @ SV278 )
| ( in @ ( ordered_pair @ SY3649 @ SY3650 ) @ SY3648 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3648 )
| ( in @ SX3 @ SY3647 ) )
| ~ ! [SY3653: $i,SY3654: $i] :
( ~ ( in @ ( ordered_pair @ SY3653 @ SY3654 ) @ SY3648 )
| ( in @ ( ordered_pair @ SY3653 @ SY3654 ) @ SV278 ) ) ) ) ) )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2220]) ).
thf(2280,plain,
! [SV279: $i] :
( ( ( ~ ! [SY3655: $i,SY3656: $i] :
( ~ ( ~ ( ! [SY3657: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ SY3656 @ SY3655 @ SV279 ) @ SY3657 ) @ SV279 )
| ~ ( in @ SY3657 @ SY3655 ) )
| ~ ( in @ ( sK43_D @ SY3656 @ SY3655 @ SV279 ) @ SY3656 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SY3656 @ SY3655 @ SV279 ) @ ( sK44_SY3116 @ SY3656 @ SY3655 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK44_SY3116 @ SY3656 @ SY3655 @ SV279 ) @ SY3655 ) )
| ( in @ ( sK43_D @ SY3656 @ SY3655 @ SV279 ) @ SY3656 ) ) )
| ( SY3656
= ( relation_inverse_image @ SV279 @ SY3655 ) ) ) )
= $false )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2221]) ).
thf(2281,plain,
! [SV279: $i] :
( ( ( ~ ! [SY3658: $i,SY3659: $i] :
( ( SY3659
!= ( relation_inverse_image @ SV279 @ SY3658 ) )
| ~ ( ~ ! [SY3660: $i] :
( ! [SY3661: $i] :
( ~ ( in @ ( ordered_pair @ SY3660 @ SY3661 ) @ SV279 )
| ~ ( in @ SY3661 @ SY3658 ) )
| ( in @ SY3660 @ SY3659 ) )
| ~ ! [SY3662: $i] :
( ~ ( in @ SY3662 @ SY3659 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3662 @ ( sK42_E @ SY3662 @ SY3659 @ SY3658 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK42_E @ SY3662 @ SY3659 @ SY3658 @ SV279 ) @ SY3658 ) ) ) ) ) )
= $false )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2221]) ).
thf(2282,plain,
! [SV280: $i] :
( ( ( ~ ! [SY3663: $i] :
( ~ ( relation @ SY3663 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3663 @ SV280 ) @ ( sK25_SY3102 @ SY3663 @ SV280 ) ) @ SV280 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3663 @ SV280 ) @ ( sK25_SY3102 @ SY3663 @ SV280 ) ) @ SY3663 ) )
| ( subset @ SV280 @ SY3663 ) ) )
= $false )
| ( ( relation @ SV280 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2222]) ).
thf(2283,plain,
! [SV280: $i] :
( ( ( ~ ! [SY3664: $i] :
( ~ ( relation @ SY3664 )
| ~ ( subset @ SV280 @ SY3664 )
| ! [SY3665: $i,SY3666: $i] :
( ~ ( in @ ( ordered_pair @ SY3665 @ SY3666 ) @ SV280 )
| ( in @ ( ordered_pair @ SY3665 @ SY3666 ) @ SY3664 ) ) ) )
= $false )
| ( ( relation @ SV280 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2222]) ).
thf(2284,plain,
! [SV281: $i,SV318: $i] :
( ( ( ~ ( relation @ SV318 ) )
= $true )
| ( ( ~ ( ~ ! [SY3843: $i] :
( ~ ( relation @ SY3843 )
| ~ ( ~ ( ! [SY3844: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3843 @ SV318 @ SV281 ) @ SY3844 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY3844 @ ( sK8_SY3089 @ SY3843 @ SV318 @ SV281 ) ) @ SV318 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3843 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SY3843 @ SV318 @ SV281 ) ) @ SY3843 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3843 @ SV318 @ SV281 ) @ ( sK9_SY3093 @ SY3843 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SY3843 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SY3843 @ SV318 @ SV281 ) ) @ SV318 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SY3843 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SY3843 @ SV318 @ SV281 ) ) @ SY3843 ) ) )
| ( SY3843
= ( relation_composition @ SV281 @ SV318 ) ) )
| ~ ! [SY3845: $i] :
( ~ ( relation @ SY3845 )
| ( SY3845
!= ( relation_composition @ SV281 @ SV318 ) )
| ~ ( ~ ! [SY3846: $i,SY3847: $i] :
( ! [SY3848: $i] :
( ~ ( in @ ( ordered_pair @ SY3846 @ SY3848 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY3848 @ SY3847 ) @ SV318 ) )
| ( in @ ( ordered_pair @ SY3846 @ SY3847 ) @ SY3845 ) )
| ~ ! [SY3849: $i,SY3850: $i] :
( ~ ( in @ ( ordered_pair @ SY3849 @ SY3850 ) @ SY3845 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3849 @ ( sK6_F @ SY3850 @ SY3849 @ SY3845 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY3850 @ SY3849 @ SY3845 @ SV318 @ SV281 ) @ SY3850 ) @ SV318 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2223]) ).
thf(2285,plain,
! [SV330: $i,SV282: $i] :
( ( ! [SY3885: $i] :
( ~ ( relation_of2_as_subset @ SY3885 @ SV282 @ SV330 )
| ~ ( ~ ! [SY3886: $i] :
~ ( in @ ( ordered_pair @ SY3886 @ ( sK57_D @ SY3885 @ SV330 @ SV282 ) ) @ SY3885 )
| ~ ( in @ ( sK57_D @ SY3885 @ SV330 @ SV282 ) @ SV330 ) )
| ( ( relation_rng_as_subset @ SV282 @ SV330 @ SY3885 )
= SV330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2224]) ).
thf(2286,plain,
! [SV331: $i,SV282: $i] :
( ( ! [SY3887: $i] :
( ~ ( relation_of2_as_subset @ SY3887 @ SV282 @ SV331 )
| ( ( relation_rng_as_subset @ SV282 @ SV331 @ SY3887 )
!= SV331 )
| ! [SY3888: $i] :
( ( in @ ( ordered_pair @ ( sK56_E @ SY3888 @ SY3887 @ SV331 @ SV282 ) @ SY3888 ) @ SY3887 )
| ~ ( in @ SY3888 @ SV331 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2225]) ).
thf(2287,plain,
! [SV283: $i,SV319: $i] :
( ( ( ~ ( relation @ SV319 ) )
= $true )
| ( ( ~ ( ~ ! [SY3851: $i] :
( ~ ( function @ SY3851 )
| ~ ( relation @ SY3851 )
| ~ ( ~ ( ~ ( in @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3851 @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) ) @ ( apply @ SY3851 @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) ) @ SV319 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) @ SV283 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SY3851 @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) ) @ ( apply @ SY3851 @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) ) @ SV319 )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) @ SV283 ) ) ) )
| ( ( relation_dom @ SY3851 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SY3851 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SY3851 )
| ( relation_isomorphism @ SV283 @ SV319 @ SY3851 ) )
| ~ ~ ( ~ ! [SY3852: $i] :
( ~ ( function @ SY3852 )
| ~ ( relation @ SY3852 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3852 )
| ~ ( ~ ! [SY3853: $i,SY3854: $i] :
( ~ ( in @ SY3853 @ ( relation_field @ SV283 ) )
| ~ ( in @ SY3854 @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3852 @ SY3853 ) @ ( apply @ SY3852 @ SY3854 ) ) @ SV319 )
| ( in @ ( ordered_pair @ SY3853 @ SY3854 ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3687: $i] :
( ! [SY3688: $i] :
~ ( in @ ( ordered_pair @ SY3687 @ SY3688 ) @ SV283 )
| ( in @ SY3687 @ ( relation_field @ SV283 ) ) )
| ~ ! [SY3689: $i,SY3690: $i] :
( ~ ( in @ ( ordered_pair @ SY3689 @ SY3690 ) @ SV283 )
| ( in @ SY3690 @ ( relation_field @ SV283 ) ) ) )
| ~ ! [SY3859: $i,SY3860: $i] :
( ~ ( in @ ( ordered_pair @ SY3859 @ SY3860 ) @ SV283 )
| ( in @ ( ordered_pair @ ( apply @ SY3852 @ SY3859 ) @ ( apply @ SY3852 @ SY3860 ) ) @ SV319 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3861: $i] :
( ~ ( function @ SY3861 )
| ~ ( relation @ SY3861 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3861 )
| ( ( relation_dom @ SY3861 )
= ( relation_field @ SV283 ) ) )
| ~ ! [SY3862: $i] :
( ~ ( function @ SY3862 )
| ~ ( relation @ SY3862 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3862 )
| ( ( relation_rng @ SY3862 )
= ( relation_field @ SV319 ) ) ) )
| ~ ! [SY3863: $i] :
( ~ ( function @ SY3863 )
| ~ ( relation @ SY3863 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3863 )
| ( one_to_one @ SY3863 ) ) ) ) ) )
= $true )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2226]) ).
thf(2288,plain,
! [SV320: $i] :
( ( ( ~ ( relation @ SV320 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK62_B @ SV320 )
!= ( sK63_SY3125 @ SV320 ) ) )
| ~ ~ ( ~ ( in @ ( sK62_B @ SV320 ) @ ( relation_field @ SV320 ) )
| ~ ( in @ ( sK63_SY3125 @ SV320 ) @ ( relation_field @ SV320 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK62_B @ SV320 ) @ ( sK63_SY3125 @ SV320 ) ) @ SV320 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK63_SY3125 @ SV320 ) @ ( sK62_B @ SV320 ) ) @ SV320 ) )
| ( connected @ SV320 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2227]) ).
thf(2289,plain,
! [SV321: $i] :
( ( ( ~ ( relation @ SV321 ) )
= $true )
| ( ( ~ ( connected @ SV321 )
| ! [SY3864: $i,SY3865: $i] :
( ( SY3864 = SY3865 )
| ~ ( in @ SY3864 @ ( relation_field @ SV321 ) )
| ~ ( in @ SY3865 @ ( relation_field @ SV321 ) )
| ( in @ ( ordered_pair @ SY3864 @ SY3865 ) @ SV321 )
| ( in @ ( ordered_pair @ SY3865 @ SY3864 ) @ SV321 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2228]) ).
thf(2290,plain,
! [SV284: $i,SV332: $i] :
( ( ! [SY3889: $i] :
( ~ ( function @ SY3889 )
| ~ ( relation @ SY3889 )
| ( SV332
!= ( apply @ SY3889 @ SV284 ) )
| ~ ( in @ SV284 @ ( relation_dom @ SY3889 ) )
| ( in @ ( ordered_pair @ SV284 @ SV332 ) @ SY3889 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2229]) ).
thf(2291,plain,
! [SV284: $i] :
( ( ~ ! [SY3698: $i,SY3699: $i] :
( ~ ( function @ SY3699 )
| ~ ( relation @ SY3699 )
| ~ ( in @ ( ordered_pair @ SV284 @ SY3698 ) @ SY3699 )
| ( SY3698
= ( apply @ SY3699 @ SV284 ) ) )
| ~ ! [SY3700: $i,SY3701: $i] :
( ~ ( function @ SY3701 )
| ~ ( relation @ SY3701 )
| ~ ( in @ ( ordered_pair @ SV284 @ SY3700 ) @ SY3701 )
| ( in @ SV284 @ ( relation_dom @ SY3701 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2230]) ).
thf(2292,plain,
! [SV333: $i,SV285: $i] :
( ( ! [SY3890: $i] :
( ~ ( relation @ SY3890 )
| ! [SY3891: $i] :
( ~ ( in @ SY3891 @ ( relation_dom @ SY3890 ) )
| ~ ( in @ ( ordered_pair @ SY3891 @ SV285 ) @ SY3890 )
| ~ ( in @ SY3891 @ SV333 ) )
| ( in @ SV285 @ ( relation_image @ SY3890 @ SV333 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2231]) ).
thf(2293,plain,
! [SV334: $i,SV285: $i] :
( ( ! [SY3892: $i] :
( ~ ( relation @ SY3892 )
| ~ ( in @ SV285 @ ( relation_image @ SY3892 @ SV334 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK61_D @ SY3892 @ SV334 @ SV285 ) @ ( relation_dom @ SY3892 ) )
| ~ ( in @ ( ordered_pair @ ( sK61_D @ SY3892 @ SV334 @ SV285 ) @ SV285 ) @ SY3892 ) )
| ~ ( in @ ( sK61_D @ SY3892 @ SV334 @ SV285 ) @ SV334 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2232]) ).
thf(2294,plain,
! [SV322: $i,SV310: $i,SV286: $i] :
( ( ( SV286
= ( ordered_pair @ SV310 @ SV322 ) )
= $false )
| ( ( ~ ( ~ ! [SY3709: $i] :
( ~ ( ( SV286
!= ( ordered_pair @ ( sK40_C @ SY3709 @ SV286 ) @ ( sK41_SY3114 @ SY3709 @ SV286 ) ) )
| ~ ( ( SY3709
!= ( sK40_C @ SY3709 @ SV286 ) ) ) )
| ( SY3709
= ( pair_first @ SV286 ) ) )
| ~ ! [SY3710: $i] :
( ( SY3710
!= ( pair_first @ SV286 ) )
| ! [SY3711: $i] :
( ! [SY3712: $i] :
( SV286
!= ( ordered_pair @ SY3711 @ SY3712 ) )
| ( SY3710 = SY3711 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2233]) ).
thf(2295,plain,
! [SV323: $i,SV311: $i,SV287: $i] :
( ( ( SV287
= ( ordered_pair @ SV311 @ SV323 ) )
= $false )
| ( ( ~ ( ~ ! [SY3715: $i] :
( ~ ( ( SV287
!= ( ordered_pair @ ( sK33_C @ SY3715 @ SV287 ) @ ( sK34_SY3110 @ SY3715 @ SV287 ) ) )
| ~ ( ( SY3715
!= ( sK34_SY3110 @ SY3715 @ SV287 ) ) ) )
| ( SY3715
= ( pair_second @ SV287 ) ) )
| ~ ! [SY3716: $i] :
( ( SY3716
!= ( pair_second @ SV287 ) )
| ! [SY3717: $i,SY3718: $i] :
( ( SV287
!= ( ordered_pair @ SY3717 @ SY3718 ) )
| ( SY3716 = SY3718 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2234]) ).
thf(2296,plain,
! [SV335: $i,SV288: $i] :
( ( ! [SY3893: $i] :
( ~ ( relation @ SY3893 )
| ~ ( in @ ( ordered_pair @ SV288 @ SV335 ) @ SY3893 )
| ( in @ SV288 @ ( relation_dom @ SY3893 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2235]) ).
thf(2297,plain,
! [SV336: $i,SV288: $i] :
( ( ! [SY3894: $i] :
( ~ ( relation @ SY3894 )
| ~ ( in @ ( ordered_pair @ SV288 @ SV336 ) @ SY3894 )
| ( in @ SV336 @ ( relation_rng @ SY3894 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2236]) ).
thf(2298,plain,
! [SV324: $i,SV337: $i] :
( ( ~ ( relation @ SV337 )
| ~ ( ~ ( ( ( sK52_C @ SV337 @ SV324 )
!= ( sK53_SY3121 @ SV337 @ SV324 ) )
| ~ ( in @ ( sK52_C @ SV337 @ SV324 ) @ SV324 )
| ~ ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) )
| ~ ~ ( ~ ( ( ( sK52_C @ SV337 @ SV324 )
= ( sK53_SY3121 @ SV337 @ SV324 ) )
| ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) )
| ~ ( ( in @ ( sK52_C @ SV337 @ SV324 ) @ SV324 )
| ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) ) ) )
| ( SV337
= ( identity_relation @ SV324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2237]) ).
thf(2299,plain,
! [SV325: $i,SV338: $i] :
( ( ~ ( relation @ SV338 )
| ( SV338
!= ( identity_relation @ SV325 ) )
| ~ ( ~ ! [SY3895: $i,SY3896: $i] :
( ( SY3895 != SY3896 )
| ~ ( in @ SY3895 @ SV325 )
| ( in @ ( ordered_pair @ SY3895 @ SY3896 ) @ SV338 ) )
| ~ ~ ( ~ ! [SY3897: $i,SY3898: $i] :
( ~ ( in @ ( ordered_pair @ SY3897 @ SY3898 ) @ SV338 )
| ( SY3897 = SY3898 ) )
| ~ ! [SY3899: $i] :
( ! [SY3900: $i] :
~ ( in @ ( ordered_pair @ SY3899 @ SY3900 ) @ SV338 )
| ( in @ SY3899 @ SV325 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2238]) ).
thf(2300,plain,
! [SV289: $i,SV339: $i] :
( ( ! [SY3901: $i] :
( ~ ( relation_of2_as_subset @ SY3901 @ SV339 @ SV289 )
| ~ ( ~ ! [SY3902: $i] :
~ ( in @ ( ordered_pair @ ( sK59_D @ SY3901 @ SV339 @ SV289 ) @ SY3902 ) @ SY3901 )
| ~ ( in @ ( sK59_D @ SY3901 @ SV339 @ SV289 ) @ SV339 ) )
| ( ( relation_dom_as_subset @ SV339 @ SV289 @ SY3901 )
= SV339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2239]) ).
thf(2301,plain,
! [SV289: $i,SV340: $i] :
( ( ! [SY3903: $i] :
( ~ ( relation_of2_as_subset @ SY3903 @ SV340 @ SV289 )
| ( ( relation_dom_as_subset @ SV340 @ SV289 @ SY3903 )
!= SV340 )
| ! [SY3904: $i] :
( ( in @ ( ordered_pair @ SY3904 @ ( sK58_E @ SY3904 @ SY3903 @ SV340 @ SV289 ) ) @ SY3903 )
| ~ ( in @ SY3904 @ SV340 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2240]) ).
thf(2302,plain,
! [SV290: $i] :
( ( ( ~ ! [SY3729: $i] :
( ~ ( ~ ( ! [SY3730: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SY3729 @ SV290 ) @ SY3730 ) @ SV290 )
| ~ ( in @ ( sK22_C @ SY3729 @ SV290 ) @ SY3729 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SY3729 @ SV290 ) @ ( sK23_SY3101 @ SY3729 @ SV290 ) ) @ SV290 )
| ( in @ ( sK22_C @ SY3729 @ SV290 ) @ SY3729 ) ) )
| ( SY3729
= ( relation_dom @ SV290 ) ) ) )
= $false )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2241]) ).
thf(2303,plain,
! [SV290: $i] :
( ( ( ~ ! [SY3731: $i] :
( ( SY3731
!= ( relation_dom @ SV290 ) )
| ~ ( ~ ! [SY3732: $i] :
( ! [SY3733: $i] :
~ ( in @ ( ordered_pair @ SY3732 @ SY3733 ) @ SV290 )
| ( in @ SY3732 @ SY3731 ) )
| ~ ! [SY3734: $i] :
( ~ ( in @ SY3734 @ SY3731 )
| ( in @ ( ordered_pair @ SY3734 @ ( sK21_D @ SY3734 @ SY3731 @ SV290 ) ) @ SV290 ) ) ) ) )
= $false )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2241]) ).
thf(2304,plain,
! [SV291: $i] :
( ( ( ~ ! [SY3735: $i] :
( ~ ( relation @ SY3735 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SY3735 @ SV291 ) @ ( sK32_SY3109 @ SY3735 @ SV291 ) ) @ SV291 )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ SY3735 @ SV291 ) @ ( sK32_SY3109 @ SY3735 @ SV291 ) ) @ SY3735 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK31_C @ SY3735 @ SV291 ) @ ( sK32_SY3109 @ SY3735 @ SV291 ) ) @ SV291 )
| ( in @ ( ordered_pair @ ( sK31_C @ SY3735 @ SV291 ) @ ( sK32_SY3109 @ SY3735 @ SV291 ) ) @ SY3735 ) ) )
| ( SV291 = SY3735 ) ) )
= $false )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2242]) ).
thf(2305,plain,
! [SV291: $i] :
( ( ( ~ ! [SY3736: $i] :
( ~ ( relation @ SY3736 )
| ( SV291 != SY3736 )
| ~ ( ~ ! [SY3737: $i,SY3738: $i] :
( ~ ( in @ ( ordered_pair @ SY3737 @ SY3738 ) @ SV291 )
| ( in @ ( ordered_pair @ SY3737 @ SY3738 ) @ SY3736 ) )
| ~ ! [SY3739: $i,SY3740: $i] :
( ~ ( in @ ( ordered_pair @ SY3739 @ SY3740 ) @ SY3736 )
| ( in @ ( ordered_pair @ SY3739 @ SY3740 ) @ SV291 ) ) ) ) )
= $false )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2242]) ).
thf(2306,plain,
! [SV326: $i] :
( ( ( ~ ( relation @ SV326 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK66_B @ SV326 ) @ ( sK67_SY3127 @ SV326 ) ) @ SV326 )
| ~ ( in @ ( ordered_pair @ ( sK67_SY3127 @ SV326 ) @ ( sK68_SY3129 @ SV326 ) ) @ SV326 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK66_B @ SV326 ) @ ( sK68_SY3129 @ SV326 ) ) @ SV326 ) )
| ( transitive @ SV326 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2243]) ).
thf(2307,plain,
! [SV327: $i] :
( ( ( ~ ( relation @ SV327 ) )
= $true )
| ( ( ~ ( transitive @ SV327 )
| ! [SY3874: $i,SY3875: $i,SY3876: $i] :
( ~ ( in @ ( ordered_pair @ SY3874 @ SY3875 ) @ SV327 )
| ~ ( in @ ( ordered_pair @ SY3875 @ SY3876 ) @ SV327 )
| ( in @ ( ordered_pair @ SY3874 @ SY3876 ) @ SV327 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2244]) ).
thf(2308,plain,
! [SV292: $i] :
( ( ( ~ ! [SY3741: $i] :
( ~ ( relation @ SY3741 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SY3741 @ SV292 ) @ ( sK13_SY3095 @ SY3741 @ SV292 ) ) @ SY3741 )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SY3741 @ SV292 ) @ ( sK12_C @ SY3741 @ SV292 ) ) @ SV292 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SY3741 @ SV292 ) @ ( sK13_SY3095 @ SY3741 @ SV292 ) ) @ SY3741 )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ SY3741 @ SV292 ) @ ( sK12_C @ SY3741 @ SV292 ) ) @ SV292 ) ) )
| ( SY3741
= ( relation_inverse @ SV292 ) ) ) )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2245]) ).
thf(2309,plain,
! [SV292: $i] :
( ( ( ~ ! [SY3742: $i] :
( ~ ( relation @ SY3742 )
| ( SY3742
!= ( relation_inverse @ SV292 ) )
| ~ ( ~ ! [SY3743: $i,SY3744: $i] :
( ~ ( in @ ( ordered_pair @ SY3743 @ SY3744 ) @ SY3742 )
| ( in @ ( ordered_pair @ SY3744 @ SY3743 ) @ SV292 ) )
| ~ ! [SY3745: $i,SY3746: $i] :
( ~ ( in @ ( ordered_pair @ SY3746 @ SY3745 ) @ SV292 )
| ( in @ ( ordered_pair @ SY3745 @ SY3746 ) @ SY3742 ) ) ) ) )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2245]) ).
thf(2310,plain,
! [SV293: $i] :
( ( ( relation @ SV293 )
= $false )
| ( ( function @ SV293 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY3747: $i] :
( ~ ( in @ SY3747 @ ( relation_dom @ SV293 ) )
| ! [SY3748: $i] :
( ( SY3748
!= ( apply @ SV293 @ SY3747 ) )
| ( in @ ( ordered_pair @ SY3747 @ SY3748 ) @ SV293 ) ) )
| ~ ! [SY3749: $i] :
( ~ ( in @ SY3749 @ ( relation_dom @ SV293 ) )
| ! [SY3750: $i] :
( ~ ( in @ ( ordered_pair @ SY3749 @ SY3750 ) @ SV293 )
| ( SY3750
= ( apply @ SV293 @ SY3749 ) ) ) ) )
| ~ ~ ( ~ ! [SY3751: $i] :
( ( in @ SY3751 @ ( relation_dom @ SV293 ) )
| ! [SY3752: $i] :
( ( SY3752
!= ( apply @ SV293 @ SY3751 ) )
| ( SY3752 = empty_set ) ) )
| ~ ! [SY3753: $i] :
( ( in @ SY3753 @ ( relation_dom @ SV293 ) )
| ! [SY3754: $i] :
( ( SY3754 != empty_set )
| ( SY3754
= ( apply @ SV293 @ SY3753 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2246]) ).
thf(2311,plain,
! [SV294: $i] :
( ( ( ~ ! [SY3755: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_C @ SY3755 @ SV294 ) @ SY3755 )
| ~ ( in @ ( sK20_SY3099 @ SY3755 @ SV294 ) @ SY3755 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SY3755 @ SV294 ) @ ( sK20_SY3099 @ SY3755 @ SV294 ) ) @ SV294 ) )
| ~ ( in @ ( ordered_pair @ ( sK20_SY3099 @ SY3755 @ SV294 ) @ ( sK19_C @ SY3755 @ SV294 ) ) @ SV294 ) )
| ~ ( ( ( sK19_C @ SY3755 @ SV294 )
!= ( sK20_SY3099 @ SY3755 @ SV294 ) ) ) )
| ( is_antisymmetric_in @ SV294 @ SY3755 ) ) )
= $false )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2247]) ).
thf(2312,plain,
! [SV294: $i] :
( ( ( ~ ! [SY3756: $i] :
( ~ ( is_antisymmetric_in @ SV294 @ SY3756 )
| ! [SY3757: $i,SY3758: $i] :
( ~ ( in @ SY3757 @ SY3756 )
| ~ ( in @ SY3758 @ SY3756 )
| ~ ( in @ ( ordered_pair @ SY3757 @ SY3758 ) @ SV294 )
| ~ ( in @ ( ordered_pair @ SY3758 @ SY3757 ) @ SV294 )
| ( SY3757 = SY3758 ) ) ) )
= $false )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2247]) ).
thf(2313,plain,
! [SV295: $i] :
( ( ( ~ ! [SY3759: $i,SY3760: $i] :
( ~ ( ~ ( ( ( sK35_D @ SY3760 @ SY3759 @ SV295 )
= SY3759 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SY3760 @ SY3759 @ SV295 ) @ SY3759 ) @ SV295 )
| ~ ( in @ ( sK35_D @ SY3760 @ SY3759 @ SV295 ) @ SY3760 ) )
| ~ ~ ( ~ ( ( ( sK35_D @ SY3760 @ SY3759 @ SV295 )
!= SY3759 )
| ( in @ ( sK35_D @ SY3760 @ SY3759 @ SV295 ) @ SY3760 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SY3760 @ SY3759 @ SV295 ) @ SY3759 ) @ SV295 )
| ( in @ ( sK35_D @ SY3760 @ SY3759 @ SV295 ) @ SY3760 ) ) ) )
| ( SY3760
= ( fiber @ SV295 @ SY3759 ) ) ) )
= $false )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2248]) ).
thf(2314,plain,
! [SV295: $i] :
( ( ( ~ ! [SY3761: $i,SY3762: $i] :
( ( SY3762
!= ( fiber @ SV295 @ SY3761 ) )
| ~ ( ~ ! [SY3763: $i] :
( ( SY3763 = SY3761 )
| ~ ( in @ ( ordered_pair @ SY3763 @ SY3761 ) @ SV295 )
| ( in @ SY3763 @ SY3762 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY3762 )
| ( SX3 != SY3761 ) )
| ~ ! [SY3765: $i] :
( ~ ( in @ SY3765 @ SY3762 )
| ( in @ ( ordered_pair @ SY3765 @ SY3761 ) @ SV295 ) ) ) ) ) )
= $false )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2248]) ).
thf(2315,plain,
! [SV296: $i,SV307: $i] :
( ( ( ~ ! [SY3817: $i] :
( ~ ( relation @ SY3817 )
| ~ ( ~ ( ~ ( in @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) @ SV296 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SY3817 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) ) @ SV307 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SY3817 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) ) @ SY3817 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) @ SV296 )
| ( in @ ( ordered_pair @ ( sK48_D @ SY3817 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) ) @ SY3817 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SY3817 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) ) @ SV307 )
| ( in @ ( ordered_pair @ ( sK48_D @ SY3817 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) ) @ SY3817 ) ) ) )
| ( SY3817
= ( relation_rng_restriction @ SV296 @ SV307 ) ) )
| ~ ! [SY3818: $i] :
( ~ ( relation @ SY3818 )
| ( SY3818
!= ( relation_rng_restriction @ SV296 @ SV307 ) )
| ~ ( ~ ! [SY3819: $i,SY3820: $i] :
( ~ ( in @ SY3820 @ SV296 )
| ~ ( in @ ( ordered_pair @ SY3819 @ SY3820 ) @ SV307 )
| ( in @ ( ordered_pair @ SY3819 @ SY3820 ) @ SY3818 ) )
| ~ ~ ( ~ ! [SY3771: $i,SY3772: $i] :
( ~ ( in @ ( ordered_pair @ SY3771 @ SY3772 ) @ SY3818 )
| ( in @ SY3772 @ SV296 ) )
| ~ ! [SY3823: $i,SY3824: $i] :
( ~ ( in @ ( ordered_pair @ SY3823 @ SY3824 ) @ SY3818 )
| ( in @ ( ordered_pair @ SY3823 @ SY3824 ) @ SV307 ) ) ) ) ) )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2249]) ).
thf(2316,plain,
! [SV297: $i] :
( ( ( ~ ! [SY3775: $i] :
( ~ ( ~ ( ! [SY3776: $i] :
~ ( in @ ( ordered_pair @ SY3776 @ ( sK17_C @ SY3775 @ SV297 ) ) @ SV297 )
| ~ ( in @ ( sK17_C @ SY3775 @ SV297 ) @ SY3775 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK18_SY3098 @ SY3775 @ SV297 ) @ ( sK17_C @ SY3775 @ SV297 ) ) @ SV297 )
| ( in @ ( sK17_C @ SY3775 @ SV297 ) @ SY3775 ) ) )
| ( SY3775
= ( relation_rng @ SV297 ) ) ) )
= $false )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2250]) ).
thf(2317,plain,
! [SV297: $i] :
( ( ( ~ ! [SY3777: $i] :
( ( SY3777
!= ( relation_rng @ SV297 ) )
| ~ ( ~ ! [SY3778: $i] :
( ! [SY3779: $i] :
~ ( in @ ( ordered_pair @ SY3779 @ SY3778 ) @ SV297 )
| ( in @ SY3778 @ SY3777 ) )
| ~ ! [SY3780: $i] :
( ~ ( in @ SY3780 @ SY3777 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3780 @ SY3777 @ SV297 ) @ SY3780 ) @ SV297 ) ) ) ) )
= $false )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2250]) ).
thf(2318,plain,
! [SV341: $i,SV298: $i] :
( ( ! [SY3905: $i] :
( ~ ( relation @ SY3905 )
| ~ ( in @ ( ordered_pair @ SV298 @ SV341 ) @ SY3905 )
| ( in @ SV298 @ ( relation_field @ SY3905 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2251]) ).
thf(2319,plain,
! [SV342: $i,SV298: $i] :
( ( ! [SY3906: $i] :
( ~ ( relation @ SY3906 )
| ~ ( in @ ( ordered_pair @ SV298 @ SV342 ) @ SY3906 )
| ( in @ SV342 @ ( relation_field @ SY3906 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2252]) ).
thf(2320,plain,
! [SV308: $i,SV299: $i] :
( ( ! [SY3825: $i,SY3826: $i] :
( ~ ( relation @ SY3826 )
| ~ ( in @ SV299 @ SY3825 )
| ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ SY3826 )
| ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SY3825 ) @ SY3826 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2253]) ).
thf(2321,plain,
! [SV308: $i,SV299: $i] :
( ( ~ ( ~ ! [SY3827: $i,SY3828: $i] :
( ~ ( relation @ SY3828 )
| ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SY3827 ) @ SY3828 ) )
| ( in @ SV299 @ SY3827 ) )
| ~ ! [SY3829: $i,SY3830: $i] :
( ~ ( relation @ SY3830 )
| ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SY3829 ) @ SY3830 ) )
| ( in @ ( ordered_pair @ SV299 @ SV308 ) @ SY3830 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2254]) ).
thf(2322,plain,
! [SV309: $i,SV300: $i] :
( ( ! [SY3831: $i] :
( ! [SY3832: $i] :
( ( ordered_pair @ SV300 @ SV309 )
!= ( ordered_pair @ SY3831 @ SY3832 ) )
| ( SV300 = SY3831 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2255]) ).
thf(2323,plain,
! [SV309: $i,SV300: $i] :
( ( ! [SY3833: $i,SY3834: $i] :
( ( ( ordered_pair @ SV300 @ SV309 )
!= ( ordered_pair @ SY3833 @ SY3834 ) )
| ( SV309 = SY3834 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2256]) ).
thf(2324,plain,
! [SV343: $i,SV301: $i] :
( ( ! [SY3907: $i] :
( ~ ( relation @ SY3907 )
| ! [SY3908: $i] :
( ~ ( in @ SY3908 @ ( relation_rng @ SY3907 ) )
| ~ ( in @ ( ordered_pair @ SV301 @ SY3908 ) @ SY3907 )
| ~ ( in @ SY3908 @ SV343 ) )
| ( in @ SV301 @ ( relation_inverse_image @ SY3907 @ SV343 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2257]) ).
thf(2325,plain,
! [SV344: $i,SV301: $i] :
( ( ! [SY3909: $i] :
( ~ ( relation @ SY3909 )
| ~ ( in @ SV301 @ ( relation_inverse_image @ SY3909 @ SV344 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_D @ SY3909 @ SV344 @ SV301 ) @ ( relation_rng @ SY3909 ) )
| ~ ( in @ ( ordered_pair @ SV301 @ ( sK60_D @ SY3909 @ SV344 @ SV301 ) ) @ SY3909 ) )
| ~ ( in @ ( sK60_D @ SY3909 @ SV344 @ SV301 ) @ SV344 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2258]) ).
thf(2326,plain,
! [SV302: $i] :
( ( ( ~ ! [SY3802: $i] :
( ~ ( ~ ( in @ ( sK36_C @ SY3802 @ SV302 ) @ SY3802 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SY3802 @ SV302 ) @ ( sK36_C @ SY3802 @ SV302 ) ) @ SV302 ) )
| ( is_reflexive_in @ SV302 @ SY3802 ) ) )
= $false )
| ( ( relation @ SV302 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2259]) ).
thf(2327,plain,
! [SV302: $i] :
( ( ( ~ ! [SY3803: $i] :
( ~ ( is_reflexive_in @ SV302 @ SY3803 )
| ! [SY3804: $i] :
( ~ ( in @ SY3804 @ SY3803 )
| ( in @ ( ordered_pair @ SY3804 @ SY3804 ) @ SV302 ) ) ) )
= $false )
| ( ( relation @ SV302 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2259]) ).
thf(2328,plain,
! [SV305: $i,SV345: $i,SV272: $i] :
( ( ! [SY3910: $i] :
( ~ ( in @ SV272 @ SV345 )
| ~ ( in @ SV305 @ SY3910 )
| ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SV345 @ SY3910 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2260]) ).
thf(2329,plain,
! [SV305: $i,SV272: $i] :
( ( ~ ! [SY3807: $i] :
( ! [SY3808: $i] :
~ ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SY3807 @ SY3808 ) )
| ( in @ SV272 @ SY3807 ) )
| ~ ! [SY3809: $i,SY3810: $i] :
( ~ ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SY3809 @ SY3810 ) )
| ( in @ SV305 @ SY3810 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2261]) ).
thf(2330,plain,
! [SV306: $i,SV346: $i,SV273: $i] :
( ( ! [SY3911: $i] :
( ~ ( in @ SV273 @ SV346 )
| ~ ( in @ SV306 @ SY3911 )
| ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SV346 @ SY3911 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2262]) ).
thf(2331,plain,
! [SV306: $i,SV273: $i] :
( ( ~ ! [SY3813: $i] :
( ! [SY3814: $i] :
~ ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SY3813 @ SY3814 ) )
| ( in @ SV273 @ SY3813 ) )
| ~ ! [SY3815: $i,SY3816: $i] :
( ~ ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SY3815 @ SY3816 ) )
| ( in @ SV306 @ SY3816 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2263]) ).
thf(2332,plain,
! [SV312: $i] :
( ( ( relation @ SV312 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK69_B @ SV312 ) @ ( relation_field @ SV312 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK69_B @ SV312 ) @ ( sK69_B @ SV312 ) ) @ SV312 ) )
| ( reflexive @ SV312 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2264]) ).
thf(2333,plain,
! [SV313: $i] :
( ( ( relation @ SV313 )
= $false )
| ( ( ~ ( reflexive @ SV313 )
| ! [SY3837: $i] :
( ~ ( in @ SY3837 @ ( relation_field @ SV313 ) )
| ( in @ ( ordered_pair @ SY3837 @ SY3837 ) @ SV313 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2265]) ).
thf(2334,plain,
! [SV274: $i] :
( ( ( ! [SY3618: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK14_C @ SY3618 @ SV274 )
!= ( sK15_SY3096 @ SY3618 @ SV274 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SY3618 @ SV274 ) @ SY3618 )
| ~ ( in @ ( sK15_SY3096 @ SY3618 @ SV274 ) @ SY3618 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK14_C @ SY3618 @ SV274 ) @ ( sK15_SY3096 @ SY3618 @ SV274 ) ) @ SV274 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK15_SY3096 @ SY3618 @ SV274 ) @ ( sK14_C @ SY3618 @ SV274 ) ) @ SV274 ) )
| ( is_connected_in @ SV274 @ SY3618 ) ) )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2266]) ).
thf(2335,plain,
! [SV274: $i] :
( ( ( ! [SY3619: $i] :
( ~ ( is_connected_in @ SV274 @ SY3619 )
| ! [SY3620: $i,SY3621: $i] :
( ( SY3620 = SY3621 )
| ~ ( in @ SY3620 @ SY3619 )
| ~ ( in @ SY3621 @ SY3619 )
| ( in @ ( ordered_pair @ SY3620 @ SY3621 ) @ SV274 )
| ( in @ ( ordered_pair @ SY3621 @ SY3620 ) @ SV274 ) ) ) )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2267]) ).
thf(2336,plain,
! [SV314: $i] :
( ( ( ~ ! [SY3838: $i,SY3839: $i] :
( ( sK39_B @ SV314 )
!= ( ordered_pair @ SY3838 @ SY3839 ) )
| ~ ( in @ ( sK39_B @ SV314 ) @ SV314 ) )
= $false )
| ( ( relation @ SV314 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2268]) ).
thf(2337,plain,
! [SV315: $i] :
( ( ( relation @ SV315 )
= $false )
| ( ( ! [SY3840: $i] :
( ( SY3840
= ( ordered_pair @ ( sK37_C @ SY3840 @ SV315 ) @ ( sK38_SY3111 @ SY3840 @ SV315 ) ) )
| ~ ( in @ SY3840 @ SV315 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2269]) ).
thf(2338,plain,
! [SV316: $i] :
( ( ( relation @ SV316 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK64_B @ SV316 ) @ ( sK65_SY3126 @ SV316 ) ) @ SV316 )
| ~ ( in @ ( ordered_pair @ ( sK65_SY3126 @ SV316 ) @ ( sK64_B @ SV316 ) ) @ SV316 ) )
| ~ ( ( ( sK64_B @ SV316 )
!= ( sK65_SY3126 @ SV316 ) ) ) )
| ( antisymmetric @ SV316 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2270]) ).
thf(2339,plain,
! [SV317: $i] :
( ( ( relation @ SV317 )
= $false )
| ( ( ~ ( antisymmetric @ SV317 )
| ! [SY3841: $i,SY3842: $i] :
( ~ ( in @ ( ordered_pair @ SY3841 @ SY3842 ) @ SV317 )
| ~ ( in @ ( ordered_pair @ SY3842 @ SY3841 ) @ SV317 )
| ( SY3841 = SY3842 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2271]) ).
thf(2340,plain,
! [SV347: $i,SV328: $i,SV275: $i] :
( ( ~ ( ~ ( ! [SY3912: $i,SY3913: $i] :
( ~ ( in @ SY3912 @ SV275 )
| ~ ( in @ SY3913 @ SV328 )
| ( ( sK28_D @ SV347 @ SV328 @ SV275 )
!= ( ordered_pair @ SY3912 @ SY3913 ) ) )
| ~ ( in @ ( sK28_D @ SV347 @ SV328 @ SV275 ) @ SV347 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY3106 @ SV347 @ SV328 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK30_SY3108 @ SV347 @ SV328 @ SV275 ) @ SV328 ) )
| ( ( sK28_D @ SV347 @ SV328 @ SV275 )
!= ( ordered_pair @ ( sK29_SY3106 @ SV347 @ SV328 @ SV275 ) @ ( sK30_SY3108 @ SV347 @ SV328 @ SV275 ) ) ) )
| ( in @ ( sK28_D @ SV347 @ SV328 @ SV275 ) @ SV347 ) ) )
| ( SV347
= ( cartesian_product2 @ SV275 @ SV328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2272]) ).
thf(2341,plain,
! [SV329: $i,SV275: $i,SV348: $i] :
( ( ( SV348
!= ( cartesian_product2 @ SV275 @ SV329 ) )
| ~ ( ~ ! [SY3914: $i] :
( ! [SY3882: $i,SY3883: $i] :
( ~ ( in @ SY3882 @ SV275 )
| ~ ( in @ SY3883 @ SV329 )
| ( SY3914
!= ( ordered_pair @ SY3882 @ SY3883 ) ) )
| ( in @ SY3914 @ SV348 ) )
| ~ ! [SY3917: $i] :
( ~ ( in @ SY3917 @ SV348 )
| ~ ( ~ ~ ( ~ ( in @ ( sK26_E @ SY3917 @ SV348 @ SV329 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK27_SY3103 @ SY3917 @ SV348 @ SV329 @ SV275 ) @ SV329 ) )
| ( SY3917
!= ( ordered_pair @ ( sK26_E @ SY3917 @ SV348 @ SV329 @ SV275 ) @ ( sK27_SY3103 @ SY3917 @ SV348 @ SV329 @ SV275 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2273]) ).
thf(2342,plain,
! [SV276: $i] :
( ( ( ! [SY3632: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SY3632 @ SV276 ) @ SY3632 )
| ~ ( in @ ( sK4_SY3086 @ SY3632 @ SV276 ) @ SY3632 ) )
| ~ ( in @ ( sK5_SY3088 @ SY3632 @ SV276 ) @ SY3632 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SY3632 @ SV276 ) @ ( sK4_SY3086 @ SY3632 @ SV276 ) ) @ SV276 ) )
| ~ ( in @ ( ordered_pair @ ( sK4_SY3086 @ SY3632 @ SV276 ) @ ( sK5_SY3088 @ SY3632 @ SV276 ) ) @ SV276 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK3_C @ SY3632 @ SV276 ) @ ( sK5_SY3088 @ SY3632 @ SV276 ) ) @ SV276 ) )
| ( is_transitive_in @ SV276 @ SY3632 ) ) )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2274]) ).
thf(2343,plain,
! [SV276: $i] :
( ( ( ! [SY3633: $i] :
( ~ ( is_transitive_in @ SV276 @ SY3633 )
| ! [SY3634: $i,SY3635: $i,SY3636: $i] :
( ~ ( in @ SY3634 @ SY3633 )
| ~ ( in @ SY3635 @ SY3633 )
| ~ ( in @ SY3636 @ SY3633 )
| ~ ( in @ ( ordered_pair @ SY3634 @ SY3635 ) @ SV276 )
| ~ ( in @ ( ordered_pair @ SY3635 @ SY3636 ) @ SV276 )
| ( in @ ( ordered_pair @ SY3634 @ SY3636 ) @ SV276 ) ) ) )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2275]) ).
thf(2344,plain,
! [SV277: $i] :
( ( ( ! [SY3637: $i,SY3638: $i] :
( ~ ( ~ ( ! [SY3639: $i] :
( ~ ( in @ ( ordered_pair @ SY3639 @ ( sK46_D @ SY3638 @ SY3637 @ SV277 ) ) @ SV277 )
| ~ ( in @ SY3639 @ SY3637 ) )
| ~ ( in @ ( sK46_D @ SY3638 @ SY3637 @ SV277 ) @ SY3638 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SY3638 @ SY3637 @ SV277 ) @ ( sK46_D @ SY3638 @ SY3637 @ SV277 ) ) @ SV277 )
| ~ ( in @ ( sK47_SY3118 @ SY3638 @ SY3637 @ SV277 ) @ SY3637 ) )
| ( in @ ( sK46_D @ SY3638 @ SY3637 @ SV277 ) @ SY3638 ) ) )
| ( SY3638
= ( relation_image @ SV277 @ SY3637 ) ) ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2276]) ).
thf(2345,plain,
! [SV277: $i] :
( ( ( ! [SY3640: $i,SY3641: $i] :
( ( SY3641
!= ( relation_image @ SV277 @ SY3640 ) )
| ~ ( ~ ! [SY3642: $i] :
( ! [SY3643: $i] :
( ~ ( in @ ( ordered_pair @ SY3643 @ SY3642 ) @ SV277 )
| ~ ( in @ SY3643 @ SY3640 ) )
| ( in @ SY3642 @ SY3641 ) )
| ~ ! [SY3644: $i] :
( ~ ( in @ SY3644 @ SY3641 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SY3644 @ SY3641 @ SY3640 @ SV277 ) @ SY3644 ) @ SV277 )
| ~ ( in @ ( sK45_E @ SY3644 @ SY3641 @ SY3640 @ SV277 ) @ SY3640 ) ) ) ) ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2277]) ).
thf(2346,plain,
! [SV278: $i] :
( ( ( ! [SY3645: $i,SY3646: $i] :
( ~ ( relation @ SY3646 )
| ~ ( ~ ( ~ ( in @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ SY3645 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ ( sK51_SY3120 @ SY3646 @ SY3645 @ SV278 ) ) @ SV278 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ ( sK51_SY3120 @ SY3646 @ SY3645 @ SV278 ) ) @ SY3646 ) )
| ~ ~ ( ~ ( ( in @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ SY3645 )
| ( in @ ( ordered_pair @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ ( sK51_SY3120 @ SY3646 @ SY3645 @ SV278 ) ) @ SY3646 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ ( sK51_SY3120 @ SY3646 @ SY3645 @ SV278 ) ) @ SV278 )
| ( in @ ( ordered_pair @ ( sK50_D @ SY3646 @ SY3645 @ SV278 ) @ ( sK51_SY3120 @ SY3646 @ SY3645 @ SV278 ) ) @ SY3646 ) ) ) )
| ( SY3646
= ( relation_dom_restriction @ SV278 @ SY3645 ) ) ) )
= $true )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2278]) ).
thf(2347,plain,
! [SV278: $i] :
( ( ( ! [SY3647: $i,SY3648: $i] :
( ~ ( relation @ SY3648 )
| ( SY3648
!= ( relation_dom_restriction @ SV278 @ SY3647 ) )
| ~ ( ~ ! [SY3649: $i,SY3650: $i] :
( ~ ( in @ SY3649 @ SY3647 )
| ~ ( in @ ( ordered_pair @ SY3649 @ SY3650 ) @ SV278 )
| ( in @ ( ordered_pair @ SY3649 @ SY3650 ) @ SY3648 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SX3 @ SX4 ) @ SY3648 )
| ( in @ SX3 @ SY3647 ) )
| ~ ! [SY3653: $i,SY3654: $i] :
( ~ ( in @ ( ordered_pair @ SY3653 @ SY3654 ) @ SY3648 )
| ( in @ ( ordered_pair @ SY3653 @ SY3654 ) @ SV278 ) ) ) ) ) )
= $true )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2279]) ).
thf(2348,plain,
! [SV279: $i] :
( ( ( ! [SY3655: $i,SY3656: $i] :
( ~ ( ~ ( ! [SY3657: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ SY3656 @ SY3655 @ SV279 ) @ SY3657 ) @ SV279 )
| ~ ( in @ SY3657 @ SY3655 ) )
| ~ ( in @ ( sK43_D @ SY3656 @ SY3655 @ SV279 ) @ SY3656 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SY3656 @ SY3655 @ SV279 ) @ ( sK44_SY3116 @ SY3656 @ SY3655 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK44_SY3116 @ SY3656 @ SY3655 @ SV279 ) @ SY3655 ) )
| ( in @ ( sK43_D @ SY3656 @ SY3655 @ SV279 ) @ SY3656 ) ) )
| ( SY3656
= ( relation_inverse_image @ SV279 @ SY3655 ) ) ) )
= $true )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2280]) ).
thf(2349,plain,
! [SV279: $i] :
( ( ( ! [SY3658: $i,SY3659: $i] :
( ( SY3659
!= ( relation_inverse_image @ SV279 @ SY3658 ) )
| ~ ( ~ ! [SY3660: $i] :
( ! [SY3661: $i] :
( ~ ( in @ ( ordered_pair @ SY3660 @ SY3661 ) @ SV279 )
| ~ ( in @ SY3661 @ SY3658 ) )
| ( in @ SY3660 @ SY3659 ) )
| ~ ! [SY3662: $i] :
( ~ ( in @ SY3662 @ SY3659 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3662 @ ( sK42_E @ SY3662 @ SY3659 @ SY3658 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK42_E @ SY3662 @ SY3659 @ SY3658 @ SV279 ) @ SY3658 ) ) ) ) ) )
= $true )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2281]) ).
thf(2350,plain,
! [SV280: $i] :
( ( ( ! [SY3663: $i] :
( ~ ( relation @ SY3663 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3663 @ SV280 ) @ ( sK25_SY3102 @ SY3663 @ SV280 ) ) @ SV280 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SY3663 @ SV280 ) @ ( sK25_SY3102 @ SY3663 @ SV280 ) ) @ SY3663 ) )
| ( subset @ SV280 @ SY3663 ) ) )
= $true )
| ( ( relation @ SV280 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2282]) ).
thf(2351,plain,
! [SV280: $i] :
( ( ( ! [SY3664: $i] :
( ~ ( relation @ SY3664 )
| ~ ( subset @ SV280 @ SY3664 )
| ! [SY3665: $i,SY3666: $i] :
( ~ ( in @ ( ordered_pair @ SY3665 @ SY3666 ) @ SV280 )
| ( in @ ( ordered_pair @ SY3665 @ SY3666 ) @ SY3664 ) ) ) )
= $true )
| ( ( relation @ SV280 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2283]) ).
thf(2352,plain,
! [SV281: $i,SV318: $i] :
( ( ( relation @ SV318 )
= $false )
| ( ( ~ ( ~ ! [SY3843: $i] :
( ~ ( relation @ SY3843 )
| ~ ( ~ ( ! [SY3844: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3843 @ SV318 @ SV281 ) @ SY3844 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY3844 @ ( sK8_SY3089 @ SY3843 @ SV318 @ SV281 ) ) @ SV318 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3843 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SY3843 @ SV318 @ SV281 ) ) @ SY3843 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3843 @ SV318 @ SV281 ) @ ( sK9_SY3093 @ SY3843 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SY3843 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SY3843 @ SV318 @ SV281 ) ) @ SV318 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SY3843 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SY3843 @ SV318 @ SV281 ) ) @ SY3843 ) ) )
| ( SY3843
= ( relation_composition @ SV281 @ SV318 ) ) )
| ~ ! [SY3845: $i] :
( ~ ( relation @ SY3845 )
| ( SY3845
!= ( relation_composition @ SV281 @ SV318 ) )
| ~ ( ~ ! [SY3846: $i,SY3847: $i] :
( ! [SY3848: $i] :
( ~ ( in @ ( ordered_pair @ SY3846 @ SY3848 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY3848 @ SY3847 ) @ SV318 ) )
| ( in @ ( ordered_pair @ SY3846 @ SY3847 ) @ SY3845 ) )
| ~ ! [SY3849: $i,SY3850: $i] :
( ~ ( in @ ( ordered_pair @ SY3849 @ SY3850 ) @ SY3845 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3849 @ ( sK6_F @ SY3850 @ SY3849 @ SY3845 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY3850 @ SY3849 @ SY3845 @ SV318 @ SV281 ) @ SY3850 ) @ SV318 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2284]) ).
thf(2353,plain,
! [SV330: $i,SV282: $i,SV349: $i] :
( ( ~ ( relation_of2_as_subset @ SV349 @ SV282 @ SV330 )
| ~ ( ~ ! [SY3918: $i] :
~ ( in @ ( ordered_pair @ SY3918 @ ( sK57_D @ SV349 @ SV330 @ SV282 ) ) @ SV349 )
| ~ ( in @ ( sK57_D @ SV349 @ SV330 @ SV282 ) @ SV330 ) )
| ( ( relation_rng_as_subset @ SV282 @ SV330 @ SV349 )
= SV330 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2285]) ).
thf(2354,plain,
! [SV331: $i,SV282: $i,SV350: $i] :
( ( ~ ( relation_of2_as_subset @ SV350 @ SV282 @ SV331 )
| ( ( relation_rng_as_subset @ SV282 @ SV331 @ SV350 )
!= SV331 )
| ! [SY3919: $i] :
( ( in @ ( ordered_pair @ ( sK56_E @ SY3919 @ SV350 @ SV331 @ SV282 ) @ SY3919 ) @ SV350 )
| ~ ( in @ SY3919 @ SV331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2286]) ).
thf(2355,plain,
! [SV283: $i,SV319: $i] :
( ( ( relation @ SV319 )
= $false )
| ( ( ~ ( ~ ! [SY3851: $i] :
( ~ ( function @ SY3851 )
| ~ ( relation @ SY3851 )
| ~ ( ~ ( ~ ( in @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3851 @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) ) @ ( apply @ SY3851 @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) ) @ SV319 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) @ SV283 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SY3851 @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) ) @ ( apply @ SY3851 @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) ) @ SV319 )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) @ SV283 ) ) ) )
| ( ( relation_dom @ SY3851 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SY3851 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SY3851 )
| ( relation_isomorphism @ SV283 @ SV319 @ SY3851 ) )
| ~ ~ ( ~ ! [SY3852: $i] :
( ~ ( function @ SY3852 )
| ~ ( relation @ SY3852 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3852 )
| ~ ( ~ ! [SY3853: $i,SY3854: $i] :
( ~ ( in @ SY3853 @ ( relation_field @ SV283 ) )
| ~ ( in @ SY3854 @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3852 @ SY3853 ) @ ( apply @ SY3852 @ SY3854 ) ) @ SV319 )
| ( in @ ( ordered_pair @ SY3853 @ SY3854 ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3687: $i] :
( ! [SY3688: $i] :
~ ( in @ ( ordered_pair @ SY3687 @ SY3688 ) @ SV283 )
| ( in @ SY3687 @ ( relation_field @ SV283 ) ) )
| ~ ! [SY3689: $i,SY3690: $i] :
( ~ ( in @ ( ordered_pair @ SY3689 @ SY3690 ) @ SV283 )
| ( in @ SY3690 @ ( relation_field @ SV283 ) ) ) )
| ~ ! [SY3859: $i,SY3860: $i] :
( ~ ( in @ ( ordered_pair @ SY3859 @ SY3860 ) @ SV283 )
| ( in @ ( ordered_pair @ ( apply @ SY3852 @ SY3859 ) @ ( apply @ SY3852 @ SY3860 ) ) @ SV319 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3861: $i] :
( ~ ( function @ SY3861 )
| ~ ( relation @ SY3861 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3861 )
| ( ( relation_dom @ SY3861 )
= ( relation_field @ SV283 ) ) )
| ~ ! [SY3862: $i] :
( ~ ( function @ SY3862 )
| ~ ( relation @ SY3862 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3862 )
| ( ( relation_rng @ SY3862 )
= ( relation_field @ SV319 ) ) ) )
| ~ ! [SY3863: $i] :
( ~ ( function @ SY3863 )
| ~ ( relation @ SY3863 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3863 )
| ( one_to_one @ SY3863 ) ) ) ) ) )
= $true )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2287]) ).
thf(2356,plain,
! [SV320: $i] :
( ( ( relation @ SV320 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK62_B @ SV320 )
!= ( sK63_SY3125 @ SV320 ) ) )
| ~ ~ ( ~ ( in @ ( sK62_B @ SV320 ) @ ( relation_field @ SV320 ) )
| ~ ( in @ ( sK63_SY3125 @ SV320 ) @ ( relation_field @ SV320 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK62_B @ SV320 ) @ ( sK63_SY3125 @ SV320 ) ) @ SV320 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK63_SY3125 @ SV320 ) @ ( sK62_B @ SV320 ) ) @ SV320 ) )
| ( connected @ SV320 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2288]) ).
thf(2357,plain,
! [SV321: $i] :
( ( ( relation @ SV321 )
= $false )
| ( ( ~ ( connected @ SV321 )
| ! [SY3864: $i,SY3865: $i] :
( ( SY3864 = SY3865 )
| ~ ( in @ SY3864 @ ( relation_field @ SV321 ) )
| ~ ( in @ SY3865 @ ( relation_field @ SV321 ) )
| ( in @ ( ordered_pair @ SY3864 @ SY3865 ) @ SV321 )
| ( in @ ( ordered_pair @ SY3865 @ SY3864 ) @ SV321 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2289]) ).
thf(2358,plain,
! [SV284: $i,SV332: $i,SV351: $i] :
( ( ~ ( function @ SV351 )
| ~ ( relation @ SV351 )
| ( SV332
!= ( apply @ SV351 @ SV284 ) )
| ~ ( in @ SV284 @ ( relation_dom @ SV351 ) )
| ( in @ ( ordered_pair @ SV284 @ SV332 ) @ SV351 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2290]) ).
thf(2359,plain,
! [SV284: $i] :
( ( ~ ! [SY3698: $i,SY3699: $i] :
( ~ ( function @ SY3699 )
| ~ ( relation @ SY3699 )
| ~ ( in @ ( ordered_pair @ SV284 @ SY3698 ) @ SY3699 )
| ( SY3698
= ( apply @ SY3699 @ SV284 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2291]) ).
thf(2360,plain,
! [SV284: $i] :
( ( ~ ! [SY3700: $i,SY3701: $i] :
( ~ ( function @ SY3701 )
| ~ ( relation @ SY3701 )
| ~ ( in @ ( ordered_pair @ SV284 @ SY3700 ) @ SY3701 )
| ( in @ SV284 @ ( relation_dom @ SY3701 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2291]) ).
thf(2361,plain,
! [SV333: $i,SV285: $i,SV352: $i] :
( ( ~ ( relation @ SV352 )
| ! [SY3920: $i] :
( ~ ( in @ SY3920 @ ( relation_dom @ SV352 ) )
| ~ ( in @ ( ordered_pair @ SY3920 @ SV285 ) @ SV352 )
| ~ ( in @ SY3920 @ SV333 ) )
| ( in @ SV285 @ ( relation_image @ SV352 @ SV333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2292]) ).
thf(2362,plain,
! [SV334: $i,SV285: $i,SV353: $i] :
( ( ~ ( relation @ SV353 )
| ~ ( in @ SV285 @ ( relation_image @ SV353 @ SV334 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK61_D @ SV353 @ SV334 @ SV285 ) @ ( relation_dom @ SV353 ) )
| ~ ( in @ ( ordered_pair @ ( sK61_D @ SV353 @ SV334 @ SV285 ) @ SV285 ) @ SV353 ) )
| ~ ( in @ ( sK61_D @ SV353 @ SV334 @ SV285 ) @ SV334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2293]) ).
thf(2363,plain,
! [SV322: $i,SV310: $i,SV286: $i] :
( ( ( ~ ! [SY3709: $i] :
( ~ ( ( SV286
!= ( ordered_pair @ ( sK40_C @ SY3709 @ SV286 ) @ ( sK41_SY3114 @ SY3709 @ SV286 ) ) )
| ~ ( ( SY3709
!= ( sK40_C @ SY3709 @ SV286 ) ) ) )
| ( SY3709
= ( pair_first @ SV286 ) ) )
| ~ ! [SY3710: $i] :
( ( SY3710
!= ( pair_first @ SV286 ) )
| ! [SY3711: $i] :
( ! [SY3712: $i] :
( SV286
!= ( ordered_pair @ SY3711 @ SY3712 ) )
| ( SY3710 = SY3711 ) ) ) )
= $false )
| ( ( SV286
= ( ordered_pair @ SV310 @ SV322 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2294]) ).
thf(2364,plain,
! [SV323: $i,SV311: $i,SV287: $i] :
( ( ( ~ ! [SY3715: $i] :
( ~ ( ( SV287
!= ( ordered_pair @ ( sK33_C @ SY3715 @ SV287 ) @ ( sK34_SY3110 @ SY3715 @ SV287 ) ) )
| ~ ( ( SY3715
!= ( sK34_SY3110 @ SY3715 @ SV287 ) ) ) )
| ( SY3715
= ( pair_second @ SV287 ) ) )
| ~ ! [SY3716: $i] :
( ( SY3716
!= ( pair_second @ SV287 ) )
| ! [SY3717: $i,SY3718: $i] :
( ( SV287
!= ( ordered_pair @ SY3717 @ SY3718 ) )
| ( SY3716 = SY3718 ) ) ) )
= $false )
| ( ( SV287
= ( ordered_pair @ SV311 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2295]) ).
thf(2365,plain,
! [SV335: $i,SV288: $i,SV354: $i] :
( ( ~ ( relation @ SV354 )
| ~ ( in @ ( ordered_pair @ SV288 @ SV335 ) @ SV354 )
| ( in @ SV288 @ ( relation_dom @ SV354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2296]) ).
thf(2366,plain,
! [SV336: $i,SV288: $i,SV355: $i] :
( ( ~ ( relation @ SV355 )
| ~ ( in @ ( ordered_pair @ SV288 @ SV336 ) @ SV355 )
| ( in @ SV336 @ ( relation_rng @ SV355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2297]) ).
thf(2367,plain,
! [SV324: $i,SV337: $i] :
( ( ( ~ ( relation @ SV337 ) )
= $true )
| ( ( ~ ( ~ ( ( ( sK52_C @ SV337 @ SV324 )
!= ( sK53_SY3121 @ SV337 @ SV324 ) )
| ~ ( in @ ( sK52_C @ SV337 @ SV324 ) @ SV324 )
| ~ ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) )
| ~ ~ ( ~ ( ( ( sK52_C @ SV337 @ SV324 )
= ( sK53_SY3121 @ SV337 @ SV324 ) )
| ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) )
| ~ ( ( in @ ( sK52_C @ SV337 @ SV324 ) @ SV324 )
| ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) ) ) )
| ( SV337
= ( identity_relation @ SV324 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2298]) ).
thf(2368,plain,
! [SV325: $i,SV338: $i] :
( ( ( ~ ( relation @ SV338 ) )
= $true )
| ( ( ( SV338
!= ( identity_relation @ SV325 ) )
| ~ ( ~ ! [SY3895: $i,SY3896: $i] :
( ( SY3895 != SY3896 )
| ~ ( in @ SY3895 @ SV325 )
| ( in @ ( ordered_pair @ SY3895 @ SY3896 ) @ SV338 ) )
| ~ ~ ( ~ ! [SY3897: $i,SY3898: $i] :
( ~ ( in @ ( ordered_pair @ SY3897 @ SY3898 ) @ SV338 )
| ( SY3897 = SY3898 ) )
| ~ ! [SY3899: $i] :
( ! [SY3900: $i] :
~ ( in @ ( ordered_pair @ SY3899 @ SY3900 ) @ SV338 )
| ( in @ SY3899 @ SV325 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2299]) ).
thf(2369,plain,
! [SV289: $i,SV339: $i,SV356: $i] :
( ( ~ ( relation_of2_as_subset @ SV356 @ SV339 @ SV289 )
| ~ ( ~ ! [SY3921: $i] :
~ ( in @ ( ordered_pair @ ( sK59_D @ SV356 @ SV339 @ SV289 ) @ SY3921 ) @ SV356 )
| ~ ( in @ ( sK59_D @ SV356 @ SV339 @ SV289 ) @ SV339 ) )
| ( ( relation_dom_as_subset @ SV339 @ SV289 @ SV356 )
= SV339 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2300]) ).
thf(2370,plain,
! [SV289: $i,SV340: $i,SV357: $i] :
( ( ~ ( relation_of2_as_subset @ SV357 @ SV340 @ SV289 )
| ( ( relation_dom_as_subset @ SV340 @ SV289 @ SV357 )
!= SV340 )
| ! [SY3922: $i] :
( ( in @ ( ordered_pair @ SY3922 @ ( sK58_E @ SY3922 @ SV357 @ SV340 @ SV289 ) ) @ SV357 )
| ~ ( in @ SY3922 @ SV340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2301]) ).
thf(2371,plain,
! [SV290: $i] :
( ( ( ! [SY3729: $i] :
( ~ ( ~ ( ! [SY3730: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SY3729 @ SV290 ) @ SY3730 ) @ SV290 )
| ~ ( in @ ( sK22_C @ SY3729 @ SV290 ) @ SY3729 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SY3729 @ SV290 ) @ ( sK23_SY3101 @ SY3729 @ SV290 ) ) @ SV290 )
| ( in @ ( sK22_C @ SY3729 @ SV290 ) @ SY3729 ) ) )
| ( SY3729
= ( relation_dom @ SV290 ) ) ) )
= $true )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2302]) ).
thf(2372,plain,
! [SV290: $i] :
( ( ( ! [SY3731: $i] :
( ( SY3731
!= ( relation_dom @ SV290 ) )
| ~ ( ~ ! [SY3732: $i] :
( ! [SY3733: $i] :
~ ( in @ ( ordered_pair @ SY3732 @ SY3733 ) @ SV290 )
| ( in @ SY3732 @ SY3731 ) )
| ~ ! [SY3734: $i] :
( ~ ( in @ SY3734 @ SY3731 )
| ( in @ ( ordered_pair @ SY3734 @ ( sK21_D @ SY3734 @ SY3731 @ SV290 ) ) @ SV290 ) ) ) ) )
= $true )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2303]) ).
thf(2373,plain,
! [SV291: $i] :
( ( ( ! [SY3735: $i] :
( ~ ( relation @ SY3735 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SY3735 @ SV291 ) @ ( sK32_SY3109 @ SY3735 @ SV291 ) ) @ SV291 )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ SY3735 @ SV291 ) @ ( sK32_SY3109 @ SY3735 @ SV291 ) ) @ SY3735 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK31_C @ SY3735 @ SV291 ) @ ( sK32_SY3109 @ SY3735 @ SV291 ) ) @ SV291 )
| ( in @ ( ordered_pair @ ( sK31_C @ SY3735 @ SV291 ) @ ( sK32_SY3109 @ SY3735 @ SV291 ) ) @ SY3735 ) ) )
| ( SV291 = SY3735 ) ) )
= $true )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2304]) ).
thf(2374,plain,
! [SV291: $i] :
( ( ( ! [SY3736: $i] :
( ~ ( relation @ SY3736 )
| ( SV291 != SY3736 )
| ~ ( ~ ! [SY3737: $i,SY3738: $i] :
( ~ ( in @ ( ordered_pair @ SY3737 @ SY3738 ) @ SV291 )
| ( in @ ( ordered_pair @ SY3737 @ SY3738 ) @ SY3736 ) )
| ~ ! [SY3739: $i,SY3740: $i] :
( ~ ( in @ ( ordered_pair @ SY3739 @ SY3740 ) @ SY3736 )
| ( in @ ( ordered_pair @ SY3739 @ SY3740 ) @ SV291 ) ) ) ) )
= $true )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2305]) ).
thf(2375,plain,
! [SV326: $i] :
( ( ( relation @ SV326 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK66_B @ SV326 ) @ ( sK67_SY3127 @ SV326 ) ) @ SV326 )
| ~ ( in @ ( ordered_pair @ ( sK67_SY3127 @ SV326 ) @ ( sK68_SY3129 @ SV326 ) ) @ SV326 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK66_B @ SV326 ) @ ( sK68_SY3129 @ SV326 ) ) @ SV326 ) )
| ( transitive @ SV326 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2306]) ).
thf(2376,plain,
! [SV327: $i] :
( ( ( relation @ SV327 )
= $false )
| ( ( ~ ( transitive @ SV327 )
| ! [SY3874: $i,SY3875: $i,SY3876: $i] :
( ~ ( in @ ( ordered_pair @ SY3874 @ SY3875 ) @ SV327 )
| ~ ( in @ ( ordered_pair @ SY3875 @ SY3876 ) @ SV327 )
| ( in @ ( ordered_pair @ SY3874 @ SY3876 ) @ SV327 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2307]) ).
thf(2377,plain,
! [SV292: $i] :
( ( ( ! [SY3741: $i] :
( ~ ( relation @ SY3741 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SY3741 @ SV292 ) @ ( sK13_SY3095 @ SY3741 @ SV292 ) ) @ SY3741 )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SY3741 @ SV292 ) @ ( sK12_C @ SY3741 @ SV292 ) ) @ SV292 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SY3741 @ SV292 ) @ ( sK13_SY3095 @ SY3741 @ SV292 ) ) @ SY3741 )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ SY3741 @ SV292 ) @ ( sK12_C @ SY3741 @ SV292 ) ) @ SV292 ) ) )
| ( SY3741
= ( relation_inverse @ SV292 ) ) ) )
= $true )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2308]) ).
thf(2378,plain,
! [SV292: $i] :
( ( ( ! [SY3742: $i] :
( ~ ( relation @ SY3742 )
| ( SY3742
!= ( relation_inverse @ SV292 ) )
| ~ ( ~ ! [SY3743: $i,SY3744: $i] :
( ~ ( in @ ( ordered_pair @ SY3743 @ SY3744 ) @ SY3742 )
| ( in @ ( ordered_pair @ SY3744 @ SY3743 ) @ SV292 ) )
| ~ ! [SY3745: $i,SY3746: $i] :
( ~ ( in @ ( ordered_pair @ SY3746 @ SY3745 ) @ SV292 )
| ( in @ ( ordered_pair @ SY3745 @ SY3746 ) @ SY3742 ) ) ) ) )
= $true )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2309]) ).
thf(2379,plain,
! [SV293: $i] :
( ( ( ~ ~ ( ~ ! [SY3747: $i] :
( ~ ( in @ SY3747 @ ( relation_dom @ SV293 ) )
| ! [SY3748: $i] :
( ( SY3748
!= ( apply @ SV293 @ SY3747 ) )
| ( in @ ( ordered_pair @ SY3747 @ SY3748 ) @ SV293 ) ) )
| ~ ! [SY3749: $i] :
( ~ ( in @ SY3749 @ ( relation_dom @ SV293 ) )
| ! [SY3750: $i] :
( ~ ( in @ ( ordered_pair @ SY3749 @ SY3750 ) @ SV293 )
| ( SY3750
= ( apply @ SV293 @ SY3749 ) ) ) ) )
| ~ ~ ( ~ ! [SY3751: $i] :
( ( in @ SY3751 @ ( relation_dom @ SV293 ) )
| ! [SY3752: $i] :
( ( SY3752
!= ( apply @ SV293 @ SY3751 ) )
| ( SY3752 = empty_set ) ) )
| ~ ! [SY3753: $i] :
( ( in @ SY3753 @ ( relation_dom @ SV293 ) )
| ! [SY3754: $i] :
( ( SY3754 != empty_set )
| ( SY3754
= ( apply @ SV293 @ SY3753 ) ) ) ) ) )
= $false )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2310]) ).
thf(2380,plain,
! [SV294: $i] :
( ( ( ! [SY3755: $i] :
( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_C @ SY3755 @ SV294 ) @ SY3755 )
| ~ ( in @ ( sK20_SY3099 @ SY3755 @ SV294 ) @ SY3755 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SY3755 @ SV294 ) @ ( sK20_SY3099 @ SY3755 @ SV294 ) ) @ SV294 ) )
| ~ ( in @ ( ordered_pair @ ( sK20_SY3099 @ SY3755 @ SV294 ) @ ( sK19_C @ SY3755 @ SV294 ) ) @ SV294 ) )
| ~ ( ( ( sK19_C @ SY3755 @ SV294 )
!= ( sK20_SY3099 @ SY3755 @ SV294 ) ) ) )
| ( is_antisymmetric_in @ SV294 @ SY3755 ) ) )
= $true )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2311]) ).
thf(2381,plain,
! [SV294: $i] :
( ( ( ! [SY3756: $i] :
( ~ ( is_antisymmetric_in @ SV294 @ SY3756 )
| ! [SY3757: $i,SY3758: $i] :
( ~ ( in @ SY3757 @ SY3756 )
| ~ ( in @ SY3758 @ SY3756 )
| ~ ( in @ ( ordered_pair @ SY3757 @ SY3758 ) @ SV294 )
| ~ ( in @ ( ordered_pair @ SY3758 @ SY3757 ) @ SV294 )
| ( SY3757 = SY3758 ) ) ) )
= $true )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2312]) ).
thf(2382,plain,
! [SV295: $i] :
( ( ( ! [SY3759: $i,SY3760: $i] :
( ~ ( ~ ( ( ( sK35_D @ SY3760 @ SY3759 @ SV295 )
= SY3759 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SY3760 @ SY3759 @ SV295 ) @ SY3759 ) @ SV295 )
| ~ ( in @ ( sK35_D @ SY3760 @ SY3759 @ SV295 ) @ SY3760 ) )
| ~ ~ ( ~ ( ( ( sK35_D @ SY3760 @ SY3759 @ SV295 )
!= SY3759 )
| ( in @ ( sK35_D @ SY3760 @ SY3759 @ SV295 ) @ SY3760 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SY3760 @ SY3759 @ SV295 ) @ SY3759 ) @ SV295 )
| ( in @ ( sK35_D @ SY3760 @ SY3759 @ SV295 ) @ SY3760 ) ) ) )
| ( SY3760
= ( fiber @ SV295 @ SY3759 ) ) ) )
= $true )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2313]) ).
thf(2383,plain,
! [SV295: $i] :
( ( ( ! [SY3761: $i,SY3762: $i] :
( ( SY3762
!= ( fiber @ SV295 @ SY3761 ) )
| ~ ( ~ ! [SY3763: $i] :
( ( SY3763 = SY3761 )
| ~ ( in @ ( ordered_pair @ SY3763 @ SY3761 ) @ SV295 )
| ( in @ SY3763 @ SY3762 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY3762 )
| ( SX3 != SY3761 ) )
| ~ ! [SY3765: $i] :
( ~ ( in @ SY3765 @ SY3762 )
| ( in @ ( ordered_pair @ SY3765 @ SY3761 ) @ SV295 ) ) ) ) ) )
= $true )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2314]) ).
thf(2384,plain,
! [SV296: $i,SV307: $i] :
( ( ( ~ ! [SY3817: $i] :
( ~ ( relation @ SY3817 )
| ~ ( ~ ( ~ ( in @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) @ SV296 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SY3817 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) ) @ SV307 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SY3817 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) ) @ SY3817 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) @ SV296 )
| ( in @ ( ordered_pair @ ( sK48_D @ SY3817 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) ) @ SY3817 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SY3817 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) ) @ SV307 )
| ( in @ ( ordered_pair @ ( sK48_D @ SY3817 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) ) @ SY3817 ) ) ) )
| ( SY3817
= ( relation_rng_restriction @ SV296 @ SV307 ) ) ) )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2315]) ).
thf(2385,plain,
! [SV307: $i,SV296: $i] :
( ( ( ~ ! [SY3818: $i] :
( ~ ( relation @ SY3818 )
| ( SY3818
!= ( relation_rng_restriction @ SV296 @ SV307 ) )
| ~ ( ~ ! [SY3819: $i,SY3820: $i] :
( ~ ( in @ SY3820 @ SV296 )
| ~ ( in @ ( ordered_pair @ SY3819 @ SY3820 ) @ SV307 )
| ( in @ ( ordered_pair @ SY3819 @ SY3820 ) @ SY3818 ) )
| ~ ~ ( ~ ! [SY3771: $i,SY3772: $i] :
( ~ ( in @ ( ordered_pair @ SY3771 @ SY3772 ) @ SY3818 )
| ( in @ SY3772 @ SV296 ) )
| ~ ! [SY3823: $i,SY3824: $i] :
( ~ ( in @ ( ordered_pair @ SY3823 @ SY3824 ) @ SY3818 )
| ( in @ ( ordered_pair @ SY3823 @ SY3824 ) @ SV307 ) ) ) ) ) )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2315]) ).
thf(2386,plain,
! [SV297: $i] :
( ( ( ! [SY3775: $i] :
( ~ ( ~ ( ! [SY3776: $i] :
~ ( in @ ( ordered_pair @ SY3776 @ ( sK17_C @ SY3775 @ SV297 ) ) @ SV297 )
| ~ ( in @ ( sK17_C @ SY3775 @ SV297 ) @ SY3775 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK18_SY3098 @ SY3775 @ SV297 ) @ ( sK17_C @ SY3775 @ SV297 ) ) @ SV297 )
| ( in @ ( sK17_C @ SY3775 @ SV297 ) @ SY3775 ) ) )
| ( SY3775
= ( relation_rng @ SV297 ) ) ) )
= $true )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2316]) ).
thf(2387,plain,
! [SV297: $i] :
( ( ( ! [SY3777: $i] :
( ( SY3777
!= ( relation_rng @ SV297 ) )
| ~ ( ~ ! [SY3778: $i] :
( ! [SY3779: $i] :
~ ( in @ ( ordered_pair @ SY3779 @ SY3778 ) @ SV297 )
| ( in @ SY3778 @ SY3777 ) )
| ~ ! [SY3780: $i] :
( ~ ( in @ SY3780 @ SY3777 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3780 @ SY3777 @ SV297 ) @ SY3780 ) @ SV297 ) ) ) ) )
= $true )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2317]) ).
thf(2388,plain,
! [SV341: $i,SV298: $i,SV358: $i] :
( ( ~ ( relation @ SV358 )
| ~ ( in @ ( ordered_pair @ SV298 @ SV341 ) @ SV358 )
| ( in @ SV298 @ ( relation_field @ SV358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2318]) ).
thf(2389,plain,
! [SV342: $i,SV298: $i,SV359: $i] :
( ( ~ ( relation @ SV359 )
| ~ ( in @ ( ordered_pair @ SV298 @ SV342 ) @ SV359 )
| ( in @ SV342 @ ( relation_field @ SV359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2319]) ).
thf(2390,plain,
! [SV308: $i,SV360: $i,SV299: $i] :
( ( ! [SY3923: $i] :
( ~ ( relation @ SY3923 )
| ~ ( in @ SV299 @ SV360 )
| ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ SY3923 )
| ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SV360 ) @ SY3923 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2320]) ).
thf(2391,plain,
! [SV308: $i,SV299: $i] :
( ( ~ ! [SY3827: $i,SY3828: $i] :
( ~ ( relation @ SY3828 )
| ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SY3827 ) @ SY3828 ) )
| ( in @ SV299 @ SY3827 ) )
| ~ ! [SY3829: $i,SY3830: $i] :
( ~ ( relation @ SY3830 )
| ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SY3829 ) @ SY3830 ) )
| ( in @ ( ordered_pair @ SV299 @ SV308 ) @ SY3830 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2321]) ).
thf(2392,plain,
! [SV361: $i,SV309: $i,SV300: $i] :
( ( ! [SY3924: $i] :
( ( ordered_pair @ SV300 @ SV309 )
!= ( ordered_pair @ SV361 @ SY3924 ) )
| ( SV300 = SV361 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2322]) ).
thf(2393,plain,
! [SV362: $i,SV309: $i,SV300: $i] :
( ( ! [SY3925: $i] :
( ( ( ordered_pair @ SV300 @ SV309 )
!= ( ordered_pair @ SV362 @ SY3925 ) )
| ( SV309 = SY3925 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2323]) ).
thf(2394,plain,
! [SV343: $i,SV301: $i,SV363: $i] :
( ( ~ ( relation @ SV363 )
| ! [SY3926: $i] :
( ~ ( in @ SY3926 @ ( relation_rng @ SV363 ) )
| ~ ( in @ ( ordered_pair @ SV301 @ SY3926 ) @ SV363 )
| ~ ( in @ SY3926 @ SV343 ) )
| ( in @ SV301 @ ( relation_inverse_image @ SV363 @ SV343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2324]) ).
thf(2395,plain,
! [SV344: $i,SV301: $i,SV364: $i] :
( ( ~ ( relation @ SV364 )
| ~ ( in @ SV301 @ ( relation_inverse_image @ SV364 @ SV344 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_D @ SV364 @ SV344 @ SV301 ) @ ( relation_rng @ SV364 ) )
| ~ ( in @ ( ordered_pair @ SV301 @ ( sK60_D @ SV364 @ SV344 @ SV301 ) ) @ SV364 ) )
| ~ ( in @ ( sK60_D @ SV364 @ SV344 @ SV301 ) @ SV344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2325]) ).
thf(2396,plain,
! [SV302: $i] :
( ( ( ! [SY3802: $i] :
( ~ ( ~ ( in @ ( sK36_C @ SY3802 @ SV302 ) @ SY3802 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SY3802 @ SV302 ) @ ( sK36_C @ SY3802 @ SV302 ) ) @ SV302 ) )
| ( is_reflexive_in @ SV302 @ SY3802 ) ) )
= $true )
| ( ( relation @ SV302 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2326]) ).
thf(2397,plain,
! [SV302: $i] :
( ( ( ! [SY3803: $i] :
( ~ ( is_reflexive_in @ SV302 @ SY3803 )
| ! [SY3804: $i] :
( ~ ( in @ SY3804 @ SY3803 )
| ( in @ ( ordered_pair @ SY3804 @ SY3804 ) @ SV302 ) ) ) )
= $true )
| ( ( relation @ SV302 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2327]) ).
thf(2398,plain,
! [SV365: $i,SV305: $i,SV345: $i,SV272: $i] :
( ( ~ ( in @ SV272 @ SV345 )
| ~ ( in @ SV305 @ SV365 )
| ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SV345 @ SV365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2328]) ).
thf(2399,plain,
! [SV305: $i,SV272: $i] :
( ( ~ ! [SY3807: $i] :
( ! [SY3808: $i] :
~ ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SY3807 @ SY3808 ) )
| ( in @ SV272 @ SY3807 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2329]) ).
thf(2400,plain,
! [SV305: $i,SV272: $i] :
( ( ~ ! [SY3809: $i,SY3810: $i] :
( ~ ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SY3809 @ SY3810 ) )
| ( in @ SV305 @ SY3810 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2329]) ).
thf(2401,plain,
! [SV366: $i,SV306: $i,SV346: $i,SV273: $i] :
( ( ~ ( in @ SV273 @ SV346 )
| ~ ( in @ SV306 @ SV366 )
| ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SV346 @ SV366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2330]) ).
thf(2402,plain,
! [SV306: $i,SV273: $i] :
( ( ~ ! [SY3813: $i] :
( ! [SY3814: $i] :
~ ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SY3813 @ SY3814 ) )
| ( in @ SV273 @ SY3813 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2331]) ).
thf(2403,plain,
! [SV306: $i,SV273: $i] :
( ( ~ ! [SY3815: $i,SY3816: $i] :
( ~ ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SY3815 @ SY3816 ) )
| ( in @ SV306 @ SY3816 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2331]) ).
thf(2404,plain,
! [SV312: $i] :
( ( ( ~ ( ~ ( in @ ( sK69_B @ SV312 ) @ ( relation_field @ SV312 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK69_B @ SV312 ) @ ( sK69_B @ SV312 ) ) @ SV312 ) ) )
= $true )
| ( ( reflexive @ SV312 )
= $true )
| ( ( relation @ SV312 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2332]) ).
thf(2405,plain,
! [SV313: $i] :
( ( ( ~ ( reflexive @ SV313 ) )
= $true )
| ( ( ! [SY3837: $i] :
( ~ ( in @ SY3837 @ ( relation_field @ SV313 ) )
| ( in @ ( ordered_pair @ SY3837 @ SY3837 ) @ SV313 ) ) )
= $true )
| ( ( relation @ SV313 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2333]) ).
thf(2406,plain,
! [SV274: $i,SV367: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK14_C @ SV367 @ SV274 )
!= ( sK15_SY3096 @ SV367 @ SV274 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SV367 @ SV274 ) @ SV367 )
| ~ ( in @ ( sK15_SY3096 @ SV367 @ SV274 ) @ SV367 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK14_C @ SV367 @ SV274 ) @ ( sK15_SY3096 @ SV367 @ SV274 ) ) @ SV274 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK15_SY3096 @ SV367 @ SV274 ) @ ( sK14_C @ SV367 @ SV274 ) ) @ SV274 ) )
| ( is_connected_in @ SV274 @ SV367 ) )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2334]) ).
thf(2407,plain,
! [SV368: $i,SV274: $i] :
( ( ( ~ ( is_connected_in @ SV274 @ SV368 )
| ! [SY3927: $i,SY3928: $i] :
( ( SY3927 = SY3928 )
| ~ ( in @ SY3927 @ SV368 )
| ~ ( in @ SY3928 @ SV368 )
| ( in @ ( ordered_pair @ SY3927 @ SY3928 ) @ SV274 )
| ( in @ ( ordered_pair @ SY3928 @ SY3927 ) @ SV274 ) ) )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2335]) ).
thf(2408,plain,
! [SV314: $i] :
( ( ( ~ ! [SY3838: $i,SY3839: $i] :
( ( sK39_B @ SV314 )
!= ( ordered_pair @ SY3838 @ SY3839 ) ) )
= $false )
| ( ( relation @ SV314 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2336]) ).
thf(2409,plain,
! [SV314: $i] :
( ( ( ~ ( in @ ( sK39_B @ SV314 ) @ SV314 ) )
= $false )
| ( ( relation @ SV314 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2336]) ).
thf(2410,plain,
! [SV315: $i,SV369: $i] :
( ( ( ( SV369
= ( ordered_pair @ ( sK37_C @ SV369 @ SV315 ) @ ( sK38_SY3111 @ SV369 @ SV315 ) ) )
| ~ ( in @ SV369 @ SV315 ) )
= $true )
| ( ( relation @ SV315 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2337]) ).
thf(2411,plain,
! [SV316: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK64_B @ SV316 ) @ ( sK65_SY3126 @ SV316 ) ) @ SV316 )
| ~ ( in @ ( ordered_pair @ ( sK65_SY3126 @ SV316 ) @ ( sK64_B @ SV316 ) ) @ SV316 ) )
| ~ ( ( ( sK64_B @ SV316 )
!= ( sK65_SY3126 @ SV316 ) ) ) ) )
= $true )
| ( ( antisymmetric @ SV316 )
= $true )
| ( ( relation @ SV316 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2338]) ).
thf(2412,plain,
! [SV317: $i] :
( ( ( ~ ( antisymmetric @ SV317 ) )
= $true )
| ( ( ! [SY3841: $i,SY3842: $i] :
( ~ ( in @ ( ordered_pair @ SY3841 @ SY3842 ) @ SV317 )
| ~ ( in @ ( ordered_pair @ SY3842 @ SY3841 ) @ SV317 )
| ( SY3841 = SY3842 ) ) )
= $true )
| ( ( relation @ SV317 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2339]) ).
thf(2413,plain,
! [SV347: $i,SV328: $i,SV275: $i] :
( ( ( ~ ( ~ ( ! [SY3912: $i,SY3913: $i] :
( ~ ( in @ SY3912 @ SV275 )
| ~ ( in @ SY3913 @ SV328 )
| ( ( sK28_D @ SV347 @ SV328 @ SV275 )
!= ( ordered_pair @ SY3912 @ SY3913 ) ) )
| ~ ( in @ ( sK28_D @ SV347 @ SV328 @ SV275 ) @ SV347 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY3106 @ SV347 @ SV328 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK30_SY3108 @ SV347 @ SV328 @ SV275 ) @ SV328 ) )
| ( ( sK28_D @ SV347 @ SV328 @ SV275 )
!= ( ordered_pair @ ( sK29_SY3106 @ SV347 @ SV328 @ SV275 ) @ ( sK30_SY3108 @ SV347 @ SV328 @ SV275 ) ) ) )
| ( in @ ( sK28_D @ SV347 @ SV328 @ SV275 ) @ SV347 ) ) ) )
= $true )
| ( ( SV347
= ( cartesian_product2 @ SV275 @ SV328 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2340]) ).
thf(2414,plain,
! [SV329: $i,SV275: $i,SV348: $i] :
( ( ( ( SV348
!= ( cartesian_product2 @ SV275 @ SV329 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3914: $i] :
( ! [SY3882: $i,SY3883: $i] :
( ~ ( in @ SY3882 @ SV275 )
| ~ ( in @ SY3883 @ SV329 )
| ( SY3914
!= ( ordered_pair @ SY3882 @ SY3883 ) ) )
| ( in @ SY3914 @ SV348 ) )
| ~ ! [SY3917: $i] :
( ~ ( in @ SY3917 @ SV348 )
| ~ ( ~ ~ ( ~ ( in @ ( sK26_E @ SY3917 @ SV348 @ SV329 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK27_SY3103 @ SY3917 @ SV348 @ SV329 @ SV275 ) @ SV329 ) )
| ( SY3917
!= ( ordered_pair @ ( sK26_E @ SY3917 @ SV348 @ SV329 @ SV275 ) @ ( sK27_SY3103 @ SY3917 @ SV348 @ SV329 @ SV275 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2341]) ).
thf(2415,plain,
! [SV276: $i,SV370: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SV370 @ SV276 ) @ SV370 )
| ~ ( in @ ( sK4_SY3086 @ SV370 @ SV276 ) @ SV370 ) )
| ~ ( in @ ( sK5_SY3088 @ SV370 @ SV276 ) @ SV370 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SV370 @ SV276 ) @ ( sK4_SY3086 @ SV370 @ SV276 ) ) @ SV276 ) )
| ~ ( in @ ( ordered_pair @ ( sK4_SY3086 @ SV370 @ SV276 ) @ ( sK5_SY3088 @ SV370 @ SV276 ) ) @ SV276 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK3_C @ SV370 @ SV276 ) @ ( sK5_SY3088 @ SV370 @ SV276 ) ) @ SV276 ) )
| ( is_transitive_in @ SV276 @ SV370 ) )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2342]) ).
thf(2416,plain,
! [SV371: $i,SV276: $i] :
( ( ( ~ ( is_transitive_in @ SV276 @ SV371 )
| ! [SY3929: $i,SY3930: $i,SY3931: $i] :
( ~ ( in @ SY3929 @ SV371 )
| ~ ( in @ SY3930 @ SV371 )
| ~ ( in @ SY3931 @ SV371 )
| ~ ( in @ ( ordered_pair @ SY3929 @ SY3930 ) @ SV276 )
| ~ ( in @ ( ordered_pair @ SY3930 @ SY3931 ) @ SV276 )
| ( in @ ( ordered_pair @ SY3929 @ SY3931 ) @ SV276 ) ) )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2343]) ).
thf(2417,plain,
! [SV277: $i,SV372: $i] :
( ( ( ! [SY3932: $i] :
( ~ ( ~ ( ! [SY3933: $i] :
( ~ ( in @ ( ordered_pair @ SY3933 @ ( sK46_D @ SY3932 @ SV372 @ SV277 ) ) @ SV277 )
| ~ ( in @ SY3933 @ SV372 ) )
| ~ ( in @ ( sK46_D @ SY3932 @ SV372 @ SV277 ) @ SY3932 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SY3932 @ SV372 @ SV277 ) @ ( sK46_D @ SY3932 @ SV372 @ SV277 ) ) @ SV277 )
| ~ ( in @ ( sK47_SY3118 @ SY3932 @ SV372 @ SV277 ) @ SV372 ) )
| ( in @ ( sK46_D @ SY3932 @ SV372 @ SV277 ) @ SY3932 ) ) )
| ( SY3932
= ( relation_image @ SV277 @ SV372 ) ) ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2344]) ).
thf(2418,plain,
! [SV373: $i,SV277: $i] :
( ( ( ! [SY3934: $i] :
( ( SY3934
!= ( relation_image @ SV277 @ SV373 ) )
| ~ ( ~ ! [SY3935: $i] :
( ! [SY3936: $i] :
( ~ ( in @ ( ordered_pair @ SY3936 @ SY3935 ) @ SV277 )
| ~ ( in @ SY3936 @ SV373 ) )
| ( in @ SY3935 @ SY3934 ) )
| ~ ! [SY3937: $i] :
( ~ ( in @ SY3937 @ SY3934 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SY3937 @ SY3934 @ SV373 @ SV277 ) @ SY3937 ) @ SV277 )
| ~ ( in @ ( sK45_E @ SY3937 @ SY3934 @ SV373 @ SV277 ) @ SV373 ) ) ) ) ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2345]) ).
thf(2419,plain,
! [SV278: $i,SV374: $i] :
( ( ( ! [SY3938: $i] :
( ~ ( relation @ SY3938 )
| ~ ( ~ ( ~ ( in @ ( sK50_D @ SY3938 @ SV374 @ SV278 ) @ SV374 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SY3938 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SY3938 @ SV374 @ SV278 ) ) @ SV278 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SY3938 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SY3938 @ SV374 @ SV278 ) ) @ SY3938 ) )
| ~ ~ ( ~ ( ( in @ ( sK50_D @ SY3938 @ SV374 @ SV278 ) @ SV374 )
| ( in @ ( ordered_pair @ ( sK50_D @ SY3938 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SY3938 @ SV374 @ SV278 ) ) @ SY3938 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SY3938 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SY3938 @ SV374 @ SV278 ) ) @ SV278 )
| ( in @ ( ordered_pair @ ( sK50_D @ SY3938 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SY3938 @ SV374 @ SV278 ) ) @ SY3938 ) ) ) )
| ( SY3938
= ( relation_dom_restriction @ SV278 @ SV374 ) ) ) )
= $true )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2346]) ).
thf(2420,plain,
! [SV375: $i,SV278: $i] :
( ( ( ! [SY3939: $i] :
( ~ ( relation @ SY3939 )
| ( SY3939
!= ( relation_dom_restriction @ SV278 @ SV375 ) )
| ~ ( ~ ! [SY3940: $i,SY3941: $i] :
( ~ ( in @ SY3940 @ SV375 )
| ~ ( in @ ( ordered_pair @ SY3940 @ SY3941 ) @ SV278 )
| ( in @ ( ordered_pair @ SY3940 @ SY3941 ) @ SY3939 ) )
| ~ ~ ( ~ ! [SY3942: $i] :
( ! [SX4: $i] :
~ ( in @ ( ordered_pair @ SY3942 @ SX4 ) @ SY3939 )
| ( in @ SY3942 @ SV375 ) )
| ~ ! [SY3653: $i,SY3654: $i] :
( ~ ( in @ ( ordered_pair @ SY3653 @ SY3654 ) @ SY3939 )
| ( in @ ( ordered_pair @ SY3653 @ SY3654 ) @ SV278 ) ) ) ) ) )
= $true )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2347]) ).
thf(2421,plain,
! [SV279: $i,SV376: $i] :
( ( ( ! [SY3946: $i] :
( ~ ( ~ ( ! [SY3947: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ SY3946 @ SV376 @ SV279 ) @ SY3947 ) @ SV279 )
| ~ ( in @ SY3947 @ SV376 ) )
| ~ ( in @ ( sK43_D @ SY3946 @ SV376 @ SV279 ) @ SY3946 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SY3946 @ SV376 @ SV279 ) @ ( sK44_SY3116 @ SY3946 @ SV376 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK44_SY3116 @ SY3946 @ SV376 @ SV279 ) @ SV376 ) )
| ( in @ ( sK43_D @ SY3946 @ SV376 @ SV279 ) @ SY3946 ) ) )
| ( SY3946
= ( relation_inverse_image @ SV279 @ SV376 ) ) ) )
= $true )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2348]) ).
thf(2422,plain,
! [SV377: $i,SV279: $i] :
( ( ( ! [SY3948: $i] :
( ( SY3948
!= ( relation_inverse_image @ SV279 @ SV377 ) )
| ~ ( ~ ! [SY3949: $i] :
( ! [SY3950: $i] :
( ~ ( in @ ( ordered_pair @ SY3949 @ SY3950 ) @ SV279 )
| ~ ( in @ SY3950 @ SV377 ) )
| ( in @ SY3949 @ SY3948 ) )
| ~ ! [SY3951: $i] :
( ~ ( in @ SY3951 @ SY3948 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3951 @ ( sK42_E @ SY3951 @ SY3948 @ SV377 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK42_E @ SY3951 @ SY3948 @ SV377 @ SV279 ) @ SV377 ) ) ) ) ) )
= $true )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2349]) ).
thf(2423,plain,
! [SV280: $i,SV378: $i] :
( ( ( ~ ( relation @ SV378 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV378 @ SV280 ) @ ( sK25_SY3102 @ SV378 @ SV280 ) ) @ SV280 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SV378 @ SV280 ) @ ( sK25_SY3102 @ SV378 @ SV280 ) ) @ SV378 ) )
| ( subset @ SV280 @ SV378 ) )
= $true )
| ( ( relation @ SV280 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2350]) ).
thf(2424,plain,
! [SV280: $i,SV379: $i] :
( ( ( ~ ( relation @ SV379 )
| ~ ( subset @ SV280 @ SV379 )
| ! [SY3952: $i,SY3953: $i] :
( ~ ( in @ ( ordered_pair @ SY3952 @ SY3953 ) @ SV280 )
| ( in @ ( ordered_pair @ SY3952 @ SY3953 ) @ SV379 ) ) )
= $true )
| ( ( relation @ SV280 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2351]) ).
thf(2425,plain,
! [SV281: $i,SV318: $i] :
( ( ( ~ ! [SY3843: $i] :
( ~ ( relation @ SY3843 )
| ~ ( ~ ( ! [SY3844: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3843 @ SV318 @ SV281 ) @ SY3844 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY3844 @ ( sK8_SY3089 @ SY3843 @ SV318 @ SV281 ) ) @ SV318 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3843 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SY3843 @ SV318 @ SV281 ) ) @ SY3843 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3843 @ SV318 @ SV281 ) @ ( sK9_SY3093 @ SY3843 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SY3843 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SY3843 @ SV318 @ SV281 ) ) @ SV318 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SY3843 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SY3843 @ SV318 @ SV281 ) ) @ SY3843 ) ) )
| ( SY3843
= ( relation_composition @ SV281 @ SV318 ) ) )
| ~ ! [SY3845: $i] :
( ~ ( relation @ SY3845 )
| ( SY3845
!= ( relation_composition @ SV281 @ SV318 ) )
| ~ ( ~ ! [SY3846: $i,SY3847: $i] :
( ! [SY3848: $i] :
( ~ ( in @ ( ordered_pair @ SY3846 @ SY3848 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY3848 @ SY3847 ) @ SV318 ) )
| ( in @ ( ordered_pair @ SY3846 @ SY3847 ) @ SY3845 ) )
| ~ ! [SY3849: $i,SY3850: $i] :
( ~ ( in @ ( ordered_pair @ SY3849 @ SY3850 ) @ SY3845 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3849 @ ( sK6_F @ SY3850 @ SY3849 @ SY3845 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY3850 @ SY3849 @ SY3845 @ SV318 @ SV281 ) @ SY3850 ) @ SV318 ) ) ) ) ) )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2352]) ).
thf(2426,plain,
! [SV330: $i,SV282: $i,SV349: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV349 @ SV282 @ SV330 ) )
= $true )
| ( ( ~ ( ~ ! [SY3918: $i] :
~ ( in @ ( ordered_pair @ SY3918 @ ( sK57_D @ SV349 @ SV330 @ SV282 ) ) @ SV349 )
| ~ ( in @ ( sK57_D @ SV349 @ SV330 @ SV282 ) @ SV330 ) )
| ( ( relation_rng_as_subset @ SV282 @ SV330 @ SV349 )
= SV330 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2353]) ).
thf(2427,plain,
! [SV331: $i,SV282: $i,SV350: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV350 @ SV282 @ SV331 ) )
= $true )
| ( ( ( ( relation_rng_as_subset @ SV282 @ SV331 @ SV350 )
!= SV331 )
| ! [SY3919: $i] :
( ( in @ ( ordered_pair @ ( sK56_E @ SY3919 @ SV350 @ SV331 @ SV282 ) @ SY3919 ) @ SV350 )
| ~ ( in @ SY3919 @ SV331 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2354]) ).
thf(2428,plain,
! [SV283: $i,SV319: $i] :
( ( ( ~ ! [SY3851: $i] :
( ~ ( function @ SY3851 )
| ~ ( relation @ SY3851 )
| ~ ( ~ ( ~ ( in @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3851 @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) ) @ ( apply @ SY3851 @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) ) @ SV319 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) @ SV283 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SY3851 @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) ) @ ( apply @ SY3851 @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) ) @ SV319 )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) @ SV283 ) ) ) )
| ( ( relation_dom @ SY3851 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SY3851 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SY3851 )
| ( relation_isomorphism @ SV283 @ SV319 @ SY3851 ) )
| ~ ~ ( ~ ! [SY3852: $i] :
( ~ ( function @ SY3852 )
| ~ ( relation @ SY3852 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3852 )
| ~ ( ~ ! [SY3853: $i,SY3854: $i] :
( ~ ( in @ SY3853 @ ( relation_field @ SV283 ) )
| ~ ( in @ SY3854 @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3852 @ SY3853 ) @ ( apply @ SY3852 @ SY3854 ) ) @ SV319 )
| ( in @ ( ordered_pair @ SY3853 @ SY3854 ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3687: $i] :
( ! [SY3688: $i] :
~ ( in @ ( ordered_pair @ SY3687 @ SY3688 ) @ SV283 )
| ( in @ SY3687 @ ( relation_field @ SV283 ) ) )
| ~ ! [SY3689: $i,SY3690: $i] :
( ~ ( in @ ( ordered_pair @ SY3689 @ SY3690 ) @ SV283 )
| ( in @ SY3690 @ ( relation_field @ SV283 ) ) ) )
| ~ ! [SY3859: $i,SY3860: $i] :
( ~ ( in @ ( ordered_pair @ SY3859 @ SY3860 ) @ SV283 )
| ( in @ ( ordered_pair @ ( apply @ SY3852 @ SY3859 ) @ ( apply @ SY3852 @ SY3860 ) ) @ SV319 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3861: $i] :
( ~ ( function @ SY3861 )
| ~ ( relation @ SY3861 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3861 )
| ( ( relation_dom @ SY3861 )
= ( relation_field @ SV283 ) ) )
| ~ ! [SY3862: $i] :
( ~ ( function @ SY3862 )
| ~ ( relation @ SY3862 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3862 )
| ( ( relation_rng @ SY3862 )
= ( relation_field @ SV319 ) ) ) )
| ~ ! [SY3863: $i] :
( ~ ( function @ SY3863 )
| ~ ( relation @ SY3863 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3863 )
| ( one_to_one @ SY3863 ) ) ) ) )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2355]) ).
thf(2429,plain,
! [SV320: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK62_B @ SV320 )
!= ( sK63_SY3125 @ SV320 ) ) )
| ~ ~ ( ~ ( in @ ( sK62_B @ SV320 ) @ ( relation_field @ SV320 ) )
| ~ ( in @ ( sK63_SY3125 @ SV320 ) @ ( relation_field @ SV320 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK62_B @ SV320 ) @ ( sK63_SY3125 @ SV320 ) ) @ SV320 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK63_SY3125 @ SV320 ) @ ( sK62_B @ SV320 ) ) @ SV320 ) ) )
= $true )
| ( ( connected @ SV320 )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2356]) ).
thf(2430,plain,
! [SV321: $i] :
( ( ( ~ ( connected @ SV321 ) )
= $true )
| ( ( ! [SY3864: $i,SY3865: $i] :
( ( SY3864 = SY3865 )
| ~ ( in @ SY3864 @ ( relation_field @ SV321 ) )
| ~ ( in @ SY3865 @ ( relation_field @ SV321 ) )
| ( in @ ( ordered_pair @ SY3864 @ SY3865 ) @ SV321 )
| ( in @ ( ordered_pair @ SY3865 @ SY3864 ) @ SV321 ) ) )
= $true )
| ( ( relation @ SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2357]) ).
thf(2431,plain,
! [SV284: $i,SV332: $i,SV351: $i] :
( ( ( ~ ( function @ SV351 )
| ~ ( relation @ SV351 ) )
= $true )
| ( ( ( SV332
!= ( apply @ SV351 @ SV284 ) )
| ~ ( in @ SV284 @ ( relation_dom @ SV351 ) )
| ( in @ ( ordered_pair @ SV284 @ SV332 ) @ SV351 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2358]) ).
thf(2432,plain,
! [SV284: $i] :
( ( ! [SY3698: $i,SY3699: $i] :
( ~ ( function @ SY3699 )
| ~ ( relation @ SY3699 )
| ~ ( in @ ( ordered_pair @ SV284 @ SY3698 ) @ SY3699 )
| ( SY3698
= ( apply @ SY3699 @ SV284 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2359]) ).
thf(2433,plain,
! [SV284: $i] :
( ( ! [SY3700: $i,SY3701: $i] :
( ~ ( function @ SY3701 )
| ~ ( relation @ SY3701 )
| ~ ( in @ ( ordered_pair @ SV284 @ SY3700 ) @ SY3701 )
| ( in @ SV284 @ ( relation_dom @ SY3701 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2360]) ).
thf(2434,plain,
! [SV333: $i,SV285: $i,SV352: $i] :
( ( ( ~ ( relation @ SV352 ) )
= $true )
| ( ( ! [SY3920: $i] :
( ~ ( in @ SY3920 @ ( relation_dom @ SV352 ) )
| ~ ( in @ ( ordered_pair @ SY3920 @ SV285 ) @ SV352 )
| ~ ( in @ SY3920 @ SV333 ) )
| ( in @ SV285 @ ( relation_image @ SV352 @ SV333 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2361]) ).
thf(2435,plain,
! [SV334: $i,SV285: $i,SV353: $i] :
( ( ( ~ ( relation @ SV353 ) )
= $true )
| ( ( ~ ( in @ SV285 @ ( relation_image @ SV353 @ SV334 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK61_D @ SV353 @ SV334 @ SV285 ) @ ( relation_dom @ SV353 ) )
| ~ ( in @ ( ordered_pair @ ( sK61_D @ SV353 @ SV334 @ SV285 ) @ SV285 ) @ SV353 ) )
| ~ ( in @ ( sK61_D @ SV353 @ SV334 @ SV285 ) @ SV334 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2362]) ).
thf(2436,plain,
! [SV322: $i,SV310: $i,SV286: $i] :
( ( ( ~ ! [SY3709: $i] :
( ~ ( ( SV286
!= ( ordered_pair @ ( sK40_C @ SY3709 @ SV286 ) @ ( sK41_SY3114 @ SY3709 @ SV286 ) ) )
| ~ ( ( SY3709
!= ( sK40_C @ SY3709 @ SV286 ) ) ) )
| ( SY3709
= ( pair_first @ SV286 ) ) ) )
= $false )
| ( ( SV286
= ( ordered_pair @ SV310 @ SV322 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2363]) ).
thf(2437,plain,
! [SV322: $i,SV310: $i,SV286: $i] :
( ( ( ~ ! [SY3710: $i] :
( ( SY3710
!= ( pair_first @ SV286 ) )
| ! [SY3711: $i] :
( ! [SY3712: $i] :
( SV286
!= ( ordered_pair @ SY3711 @ SY3712 ) )
| ( SY3710 = SY3711 ) ) ) )
= $false )
| ( ( SV286
= ( ordered_pair @ SV310 @ SV322 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2363]) ).
thf(2438,plain,
! [SV323: $i,SV311: $i,SV287: $i] :
( ( ( ~ ! [SY3715: $i] :
( ~ ( ( SV287
!= ( ordered_pair @ ( sK33_C @ SY3715 @ SV287 ) @ ( sK34_SY3110 @ SY3715 @ SV287 ) ) )
| ~ ( ( SY3715
!= ( sK34_SY3110 @ SY3715 @ SV287 ) ) ) )
| ( SY3715
= ( pair_second @ SV287 ) ) ) )
= $false )
| ( ( SV287
= ( ordered_pair @ SV311 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2364]) ).
thf(2439,plain,
! [SV323: $i,SV311: $i,SV287: $i] :
( ( ( ~ ! [SY3716: $i] :
( ( SY3716
!= ( pair_second @ SV287 ) )
| ! [SY3717: $i,SY3718: $i] :
( ( SV287
!= ( ordered_pair @ SY3717 @ SY3718 ) )
| ( SY3716 = SY3718 ) ) ) )
= $false )
| ( ( SV287
= ( ordered_pair @ SV311 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2364]) ).
thf(2440,plain,
! [SV335: $i,SV288: $i,SV354: $i] :
( ( ( ~ ( relation @ SV354 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV288 @ SV335 ) @ SV354 )
| ( in @ SV288 @ ( relation_dom @ SV354 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2365]) ).
thf(2441,plain,
! [SV336: $i,SV288: $i,SV355: $i] :
( ( ( ~ ( relation @ SV355 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV288 @ SV336 ) @ SV355 )
| ( in @ SV336 @ ( relation_rng @ SV355 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2366]) ).
thf(2442,plain,
! [SV324: $i,SV337: $i] :
( ( ( relation @ SV337 )
= $false )
| ( ( ~ ( ~ ( ( ( sK52_C @ SV337 @ SV324 )
!= ( sK53_SY3121 @ SV337 @ SV324 ) )
| ~ ( in @ ( sK52_C @ SV337 @ SV324 ) @ SV324 )
| ~ ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) )
| ~ ~ ( ~ ( ( ( sK52_C @ SV337 @ SV324 )
= ( sK53_SY3121 @ SV337 @ SV324 ) )
| ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) )
| ~ ( ( in @ ( sK52_C @ SV337 @ SV324 ) @ SV324 )
| ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) ) ) )
| ( SV337
= ( identity_relation @ SV324 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2367]) ).
thf(2443,plain,
! [SV325: $i,SV338: $i] :
( ( ( relation @ SV338 )
= $false )
| ( ( ( SV338
!= ( identity_relation @ SV325 ) )
| ~ ( ~ ! [SY3895: $i,SY3896: $i] :
( ( SY3895 != SY3896 )
| ~ ( in @ SY3895 @ SV325 )
| ( in @ ( ordered_pair @ SY3895 @ SY3896 ) @ SV338 ) )
| ~ ~ ( ~ ! [SY3897: $i,SY3898: $i] :
( ~ ( in @ ( ordered_pair @ SY3897 @ SY3898 ) @ SV338 )
| ( SY3897 = SY3898 ) )
| ~ ! [SY3899: $i] :
( ! [SY3900: $i] :
~ ( in @ ( ordered_pair @ SY3899 @ SY3900 ) @ SV338 )
| ( in @ SY3899 @ SV325 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2368]) ).
thf(2444,plain,
! [SV289: $i,SV339: $i,SV356: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV356 @ SV339 @ SV289 ) )
= $true )
| ( ( ~ ( ~ ! [SY3921: $i] :
~ ( in @ ( ordered_pair @ ( sK59_D @ SV356 @ SV339 @ SV289 ) @ SY3921 ) @ SV356 )
| ~ ( in @ ( sK59_D @ SV356 @ SV339 @ SV289 ) @ SV339 ) )
| ( ( relation_dom_as_subset @ SV339 @ SV289 @ SV356 )
= SV339 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2369]) ).
thf(2445,plain,
! [SV289: $i,SV340: $i,SV357: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV357 @ SV340 @ SV289 ) )
= $true )
| ( ( ( ( relation_dom_as_subset @ SV340 @ SV289 @ SV357 )
!= SV340 )
| ! [SY3922: $i] :
( ( in @ ( ordered_pair @ SY3922 @ ( sK58_E @ SY3922 @ SV357 @ SV340 @ SV289 ) ) @ SV357 )
| ~ ( in @ SY3922 @ SV340 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2370]) ).
thf(2446,plain,
! [SV290: $i,SV380: $i] :
( ( ( ~ ( ~ ( ! [SY3954: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SV380 @ SV290 ) @ SY3954 ) @ SV290 )
| ~ ( in @ ( sK22_C @ SV380 @ SV290 ) @ SV380 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SV380 @ SV290 ) @ ( sK23_SY3101 @ SV380 @ SV290 ) ) @ SV290 )
| ( in @ ( sK22_C @ SV380 @ SV290 ) @ SV380 ) ) )
| ( SV380
= ( relation_dom @ SV290 ) ) )
= $true )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2371]) ).
thf(2447,plain,
! [SV290: $i,SV381: $i] :
( ( ( ( SV381
!= ( relation_dom @ SV290 ) )
| ~ ( ~ ! [SY3955: $i] :
( ! [SY3733: $i] :
~ ( in @ ( ordered_pair @ SY3955 @ SY3733 ) @ SV290 )
| ( in @ SY3955 @ SV381 ) )
| ~ ! [SY3957: $i] :
( ~ ( in @ SY3957 @ SV381 )
| ( in @ ( ordered_pair @ SY3957 @ ( sK21_D @ SY3957 @ SV381 @ SV290 ) ) @ SV290 ) ) ) )
= $true )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2372]) ).
thf(2448,plain,
! [SV291: $i,SV382: $i] :
( ( ( ~ ( relation @ SV382 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV291 )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV382 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV291 )
| ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV382 ) ) )
| ( SV291 = SV382 ) )
= $true )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2373]) ).
thf(2449,plain,
! [SV291: $i,SV383: $i] :
( ( ( ~ ( relation @ SV383 )
| ( SV291 != SV383 )
| ~ ( ~ ! [SY3958: $i,SY3959: $i] :
( ~ ( in @ ( ordered_pair @ SY3958 @ SY3959 ) @ SV291 )
| ( in @ ( ordered_pair @ SY3958 @ SY3959 ) @ SV383 ) )
| ~ ! [SY3960: $i,SY3961: $i] :
( ~ ( in @ ( ordered_pair @ SY3960 @ SY3961 ) @ SV383 )
| ( in @ ( ordered_pair @ SY3960 @ SY3961 ) @ SV291 ) ) ) )
= $true )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2374]) ).
thf(2450,plain,
! [SV326: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK66_B @ SV326 ) @ ( sK67_SY3127 @ SV326 ) ) @ SV326 )
| ~ ( in @ ( ordered_pair @ ( sK67_SY3127 @ SV326 ) @ ( sK68_SY3129 @ SV326 ) ) @ SV326 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK66_B @ SV326 ) @ ( sK68_SY3129 @ SV326 ) ) @ SV326 ) ) )
= $true )
| ( ( transitive @ SV326 )
= $true )
| ( ( relation @ SV326 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2375]) ).
thf(2451,plain,
! [SV327: $i] :
( ( ( ~ ( transitive @ SV327 ) )
= $true )
| ( ( ! [SY3874: $i,SY3875: $i,SY3876: $i] :
( ~ ( in @ ( ordered_pair @ SY3874 @ SY3875 ) @ SV327 )
| ~ ( in @ ( ordered_pair @ SY3875 @ SY3876 ) @ SV327 )
| ( in @ ( ordered_pair @ SY3874 @ SY3876 ) @ SV327 ) ) )
= $true )
| ( ( relation @ SV327 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2376]) ).
thf(2452,plain,
! [SV292: $i,SV384: $i] :
( ( ( ~ ( relation @ SV384 )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SV384 @ SV292 ) @ ( sK13_SY3095 @ SV384 @ SV292 ) ) @ SV384 )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV384 @ SV292 ) @ ( sK12_C @ SV384 @ SV292 ) ) @ SV292 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SV384 @ SV292 ) @ ( sK13_SY3095 @ SV384 @ SV292 ) ) @ SV384 )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV384 @ SV292 ) @ ( sK12_C @ SV384 @ SV292 ) ) @ SV292 ) ) )
| ( SV384
= ( relation_inverse @ SV292 ) ) )
= $true )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2377]) ).
thf(2453,plain,
! [SV292: $i,SV385: $i] :
( ( ( ~ ( relation @ SV385 )
| ( SV385
!= ( relation_inverse @ SV292 ) )
| ~ ( ~ ! [SY3962: $i,SY3963: $i] :
( ~ ( in @ ( ordered_pair @ SY3962 @ SY3963 ) @ SV385 )
| ( in @ ( ordered_pair @ SY3963 @ SY3962 ) @ SV292 ) )
| ~ ! [SY3964: $i,SY3965: $i] :
( ~ ( in @ ( ordered_pair @ SY3965 @ SY3964 ) @ SV292 )
| ( in @ ( ordered_pair @ SY3964 @ SY3965 ) @ SV385 ) ) ) )
= $true )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2378]) ).
thf(2454,plain,
! [SV293: $i] :
( ( ( ~ ~ ( ~ ! [SY3747: $i] :
( ~ ( in @ SY3747 @ ( relation_dom @ SV293 ) )
| ! [SY3748: $i] :
( ( SY3748
!= ( apply @ SV293 @ SY3747 ) )
| ( in @ ( ordered_pair @ SY3747 @ SY3748 ) @ SV293 ) ) )
| ~ ! [SY3749: $i] :
( ~ ( in @ SY3749 @ ( relation_dom @ SV293 ) )
| ! [SY3750: $i] :
( ~ ( in @ ( ordered_pair @ SY3749 @ SY3750 ) @ SV293 )
| ( SY3750
= ( apply @ SV293 @ SY3749 ) ) ) ) ) )
= $false )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2379]) ).
thf(2455,plain,
! [SV293: $i] :
( ( ( ~ ~ ( ~ ! [SY3751: $i] :
( ( in @ SY3751 @ ( relation_dom @ SV293 ) )
| ! [SY3752: $i] :
( ( SY3752
!= ( apply @ SV293 @ SY3751 ) )
| ( SY3752 = empty_set ) ) )
| ~ ! [SY3753: $i] :
( ( in @ SY3753 @ ( relation_dom @ SV293 ) )
| ! [SY3754: $i] :
( ( SY3754 != empty_set )
| ( SY3754
= ( apply @ SV293 @ SY3753 ) ) ) ) ) )
= $false )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2379]) ).
thf(2456,plain,
! [SV294: $i,SV386: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_C @ SV386 @ SV294 ) @ SV386 )
| ~ ( in @ ( sK20_SY3099 @ SV386 @ SV294 ) @ SV386 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SV386 @ SV294 ) @ ( sK20_SY3099 @ SV386 @ SV294 ) ) @ SV294 ) )
| ~ ( in @ ( ordered_pair @ ( sK20_SY3099 @ SV386 @ SV294 ) @ ( sK19_C @ SV386 @ SV294 ) ) @ SV294 ) )
| ~ ( ( ( sK19_C @ SV386 @ SV294 )
!= ( sK20_SY3099 @ SV386 @ SV294 ) ) ) )
| ( is_antisymmetric_in @ SV294 @ SV386 ) )
= $true )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2380]) ).
thf(2457,plain,
! [SV387: $i,SV294: $i] :
( ( ( ~ ( is_antisymmetric_in @ SV294 @ SV387 )
| ! [SY3966: $i,SY3967: $i] :
( ~ ( in @ SY3966 @ SV387 )
| ~ ( in @ SY3967 @ SV387 )
| ~ ( in @ ( ordered_pair @ SY3966 @ SY3967 ) @ SV294 )
| ~ ( in @ ( ordered_pair @ SY3967 @ SY3966 ) @ SV294 )
| ( SY3966 = SY3967 ) ) )
= $true )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2381]) ).
thf(2458,plain,
! [SV295: $i,SV388: $i] :
( ( ( ! [SY3968: $i] :
( ~ ( ~ ( ( ( sK35_D @ SY3968 @ SV388 @ SV295 )
= SV388 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SY3968 @ SV388 @ SV295 ) @ SV388 ) @ SV295 )
| ~ ( in @ ( sK35_D @ SY3968 @ SV388 @ SV295 ) @ SY3968 ) )
| ~ ~ ( ~ ( ( ( sK35_D @ SY3968 @ SV388 @ SV295 )
!= SV388 )
| ( in @ ( sK35_D @ SY3968 @ SV388 @ SV295 ) @ SY3968 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SY3968 @ SV388 @ SV295 ) @ SV388 ) @ SV295 )
| ( in @ ( sK35_D @ SY3968 @ SV388 @ SV295 ) @ SY3968 ) ) ) )
| ( SY3968
= ( fiber @ SV295 @ SV388 ) ) ) )
= $true )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2382]) ).
thf(2459,plain,
! [SV389: $i,SV295: $i] :
( ( ( ! [SY3969: $i] :
( ( SY3969
!= ( fiber @ SV295 @ SV389 ) )
| ~ ( ~ ! [SY3970: $i] :
( ( SY3970 = SV389 )
| ~ ( in @ ( ordered_pair @ SY3970 @ SV389 ) @ SV295 )
| ( in @ SY3970 @ SY3969 ) )
| ~ ~ ( ~ ! [SY3971: $i] :
( ~ ( in @ SY3971 @ SY3969 )
| ( SY3971 != SV389 ) )
| ~ ! [SY3972: $i] :
( ~ ( in @ SY3972 @ SY3969 )
| ( in @ ( ordered_pair @ SY3972 @ SV389 ) @ SV295 ) ) ) ) ) )
= $true )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2383]) ).
thf(2460,plain,
! [SV296: $i,SV307: $i] :
( ( ( ! [SY3817: $i] :
( ~ ( relation @ SY3817 )
| ~ ( ~ ( ~ ( in @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) @ SV296 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SY3817 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) ) @ SV307 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SY3817 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) ) @ SY3817 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) @ SV296 )
| ( in @ ( ordered_pair @ ( sK48_D @ SY3817 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) ) @ SY3817 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SY3817 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) ) @ SV307 )
| ( in @ ( ordered_pair @ ( sK48_D @ SY3817 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SY3817 @ SV307 @ SV296 ) ) @ SY3817 ) ) ) )
| ( SY3817
= ( relation_rng_restriction @ SV296 @ SV307 ) ) ) )
= $true )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2384]) ).
thf(2461,plain,
! [SV307: $i,SV296: $i] :
( ( ( ! [SY3818: $i] :
( ~ ( relation @ SY3818 )
| ( SY3818
!= ( relation_rng_restriction @ SV296 @ SV307 ) )
| ~ ( ~ ! [SY3819: $i,SY3820: $i] :
( ~ ( in @ SY3820 @ SV296 )
| ~ ( in @ ( ordered_pair @ SY3819 @ SY3820 ) @ SV307 )
| ( in @ ( ordered_pair @ SY3819 @ SY3820 ) @ SY3818 ) )
| ~ ~ ( ~ ! [SY3771: $i,SY3772: $i] :
( ~ ( in @ ( ordered_pair @ SY3771 @ SY3772 ) @ SY3818 )
| ( in @ SY3772 @ SV296 ) )
| ~ ! [SY3823: $i,SY3824: $i] :
( ~ ( in @ ( ordered_pair @ SY3823 @ SY3824 ) @ SY3818 )
| ( in @ ( ordered_pair @ SY3823 @ SY3824 ) @ SV307 ) ) ) ) ) )
= $true )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2385]) ).
thf(2462,plain,
! [SV297: $i,SV390: $i] :
( ( ( ~ ( ~ ( ! [SY3973: $i] :
~ ( in @ ( ordered_pair @ SY3973 @ ( sK17_C @ SV390 @ SV297 ) ) @ SV297 )
| ~ ( in @ ( sK17_C @ SV390 @ SV297 ) @ SV390 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK18_SY3098 @ SV390 @ SV297 ) @ ( sK17_C @ SV390 @ SV297 ) ) @ SV297 )
| ( in @ ( sK17_C @ SV390 @ SV297 ) @ SV390 ) ) )
| ( SV390
= ( relation_rng @ SV297 ) ) )
= $true )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2386]) ).
thf(2463,plain,
! [SV297: $i,SV391: $i] :
( ( ( ( SV391
!= ( relation_rng @ SV297 ) )
| ~ ( ~ ! [SY3974: $i] :
( ! [SY3779: $i] :
~ ( in @ ( ordered_pair @ SY3779 @ SY3974 ) @ SV297 )
| ( in @ SY3974 @ SV391 ) )
| ~ ! [SY3976: $i] :
( ~ ( in @ SY3976 @ SV391 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3976 @ SV391 @ SV297 ) @ SY3976 ) @ SV297 ) ) ) )
= $true )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2387]) ).
thf(2464,plain,
! [SV341: $i,SV298: $i,SV358: $i] :
( ( ( ~ ( relation @ SV358 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV298 @ SV341 ) @ SV358 )
| ( in @ SV298 @ ( relation_field @ SV358 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2388]) ).
thf(2465,plain,
! [SV342: $i,SV298: $i,SV359: $i] :
( ( ( ~ ( relation @ SV359 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV298 @ SV342 ) @ SV359 )
| ( in @ SV342 @ ( relation_field @ SV359 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2389]) ).
thf(2466,plain,
! [SV308: $i,SV360: $i,SV299: $i,SV392: $i] :
( ( ~ ( relation @ SV392 )
| ~ ( in @ SV299 @ SV360 )
| ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ SV392 )
| ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SV360 ) @ SV392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2390]) ).
thf(2467,plain,
! [SV308: $i,SV299: $i] :
( ( ~ ! [SY3827: $i,SY3828: $i] :
( ~ ( relation @ SY3828 )
| ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SY3827 ) @ SY3828 ) )
| ( in @ SV299 @ SY3827 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2391]) ).
thf(2468,plain,
! [SV308: $i,SV299: $i] :
( ( ~ ! [SY3829: $i,SY3830: $i] :
( ~ ( relation @ SY3830 )
| ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SY3829 ) @ SY3830 ) )
| ( in @ ( ordered_pair @ SV299 @ SV308 ) @ SY3830 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2391]) ).
thf(2469,plain,
! [SV361: $i,SV309: $i,SV300: $i] :
( ( ( ! [SY3924: $i] :
( ( ordered_pair @ SV300 @ SV309 )
!= ( ordered_pair @ SV361 @ SY3924 ) ) )
= $true )
| ( ( SV300 = SV361 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2392]) ).
thf(2470,plain,
! [SV393: $i,SV362: $i,SV309: $i,SV300: $i] :
( ( ( ( ordered_pair @ SV300 @ SV309 )
!= ( ordered_pair @ SV362 @ SV393 ) )
| ( SV309 = SV393 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2393]) ).
thf(2471,plain,
! [SV343: $i,SV301: $i,SV363: $i] :
( ( ( ~ ( relation @ SV363 ) )
= $true )
| ( ( ! [SY3926: $i] :
( ~ ( in @ SY3926 @ ( relation_rng @ SV363 ) )
| ~ ( in @ ( ordered_pair @ SV301 @ SY3926 ) @ SV363 )
| ~ ( in @ SY3926 @ SV343 ) )
| ( in @ SV301 @ ( relation_inverse_image @ SV363 @ SV343 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2394]) ).
thf(2472,plain,
! [SV344: $i,SV301: $i,SV364: $i] :
( ( ( ~ ( relation @ SV364 ) )
= $true )
| ( ( ~ ( in @ SV301 @ ( relation_inverse_image @ SV364 @ SV344 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_D @ SV364 @ SV344 @ SV301 ) @ ( relation_rng @ SV364 ) )
| ~ ( in @ ( ordered_pair @ SV301 @ ( sK60_D @ SV364 @ SV344 @ SV301 ) ) @ SV364 ) )
| ~ ( in @ ( sK60_D @ SV364 @ SV344 @ SV301 ) @ SV344 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2395]) ).
thf(2473,plain,
! [SV302: $i,SV394: $i] :
( ( ( ~ ( ~ ( in @ ( sK36_C @ SV394 @ SV302 ) @ SV394 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SV394 @ SV302 ) @ ( sK36_C @ SV394 @ SV302 ) ) @ SV302 ) )
| ( is_reflexive_in @ SV302 @ SV394 ) )
= $true )
| ( ( relation @ SV302 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2396]) ).
thf(2474,plain,
! [SV395: $i,SV302: $i] :
( ( ( ~ ( is_reflexive_in @ SV302 @ SV395 )
| ! [SY3977: $i] :
( ~ ( in @ SY3977 @ SV395 )
| ( in @ ( ordered_pair @ SY3977 @ SY3977 ) @ SV302 ) ) )
= $true )
| ( ( relation @ SV302 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2397]) ).
thf(2475,plain,
! [SV365: $i,SV305: $i,SV345: $i,SV272: $i] :
( ( ( ~ ( in @ SV272 @ SV345 )
| ~ ( in @ SV305 @ SV365 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SV345 @ SV365 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2398]) ).
thf(2476,plain,
! [SV305: $i,SV272: $i] :
( ( ! [SY3807: $i] :
( ! [SY3808: $i] :
~ ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SY3807 @ SY3808 ) )
| ( in @ SV272 @ SY3807 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2399]) ).
thf(2477,plain,
! [SV305: $i,SV272: $i] :
( ( ! [SY3809: $i,SY3810: $i] :
( ~ ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SY3809 @ SY3810 ) )
| ( in @ SV305 @ SY3810 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2400]) ).
thf(2478,plain,
! [SV366: $i,SV306: $i,SV346: $i,SV273: $i] :
( ( ( ~ ( in @ SV273 @ SV346 )
| ~ ( in @ SV306 @ SV366 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SV346 @ SV366 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2401]) ).
thf(2479,plain,
! [SV306: $i,SV273: $i] :
( ( ! [SY3813: $i] :
( ! [SY3814: $i] :
~ ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SY3813 @ SY3814 ) )
| ( in @ SV273 @ SY3813 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2402]) ).
thf(2480,plain,
! [SV306: $i,SV273: $i] :
( ( ! [SY3815: $i,SY3816: $i] :
( ~ ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SY3815 @ SY3816 ) )
| ( in @ SV306 @ SY3816 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2403]) ).
thf(2481,plain,
! [SV312: $i] :
( ( ( ~ ( in @ ( sK69_B @ SV312 ) @ ( relation_field @ SV312 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK69_B @ SV312 ) @ ( sK69_B @ SV312 ) ) @ SV312 ) )
= $false )
| ( ( reflexive @ SV312 )
= $true )
| ( ( relation @ SV312 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2404]) ).
thf(2482,plain,
! [SV313: $i] :
( ( ( reflexive @ SV313 )
= $false )
| ( ( ! [SY3837: $i] :
( ~ ( in @ SY3837 @ ( relation_field @ SV313 ) )
| ( in @ ( ordered_pair @ SY3837 @ SY3837 ) @ SV313 ) ) )
= $true )
| ( ( relation @ SV313 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2405]) ).
thf(2483,plain,
! [SV274: $i,SV367: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( ( sK14_C @ SV367 @ SV274 )
!= ( sK15_SY3096 @ SV367 @ SV274 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SV367 @ SV274 ) @ SV367 )
| ~ ( in @ ( sK15_SY3096 @ SV367 @ SV274 ) @ SV367 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK14_C @ SV367 @ SV274 ) @ ( sK15_SY3096 @ SV367 @ SV274 ) ) @ SV274 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK15_SY3096 @ SV367 @ SV274 ) @ ( sK14_C @ SV367 @ SV274 ) ) @ SV274 ) ) )
= $true )
| ( ( is_connected_in @ SV274 @ SV367 )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2406]) ).
thf(2484,plain,
! [SV368: $i,SV274: $i] :
( ( ( ~ ( is_connected_in @ SV274 @ SV368 ) )
= $true )
| ( ( ! [SY3927: $i,SY3928: $i] :
( ( SY3927 = SY3928 )
| ~ ( in @ SY3927 @ SV368 )
| ~ ( in @ SY3928 @ SV368 )
| ( in @ ( ordered_pair @ SY3927 @ SY3928 ) @ SV274 )
| ( in @ ( ordered_pair @ SY3928 @ SY3927 ) @ SV274 ) ) )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2407]) ).
thf(2485,plain,
! [SV314: $i] :
( ( ( ! [SY3838: $i,SY3839: $i] :
( ( sK39_B @ SV314 )
!= ( ordered_pair @ SY3838 @ SY3839 ) ) )
= $true )
| ( ( relation @ SV314 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2408]) ).
thf(2486,plain,
! [SV314: $i] :
( ( ( in @ ( sK39_B @ SV314 ) @ SV314 )
= $true )
| ( ( relation @ SV314 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2409]) ).
thf(2487,plain,
! [SV315: $i,SV369: $i] :
( ( ( SV369
= ( ordered_pair @ ( sK37_C @ SV369 @ SV315 ) @ ( sK38_SY3111 @ SV369 @ SV315 ) ) )
= $true )
| ( ( ~ ( in @ SV369 @ SV315 ) )
= $true )
| ( ( relation @ SV315 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2410]) ).
thf(2488,plain,
! [SV316: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK64_B @ SV316 ) @ ( sK65_SY3126 @ SV316 ) ) @ SV316 )
| ~ ( in @ ( ordered_pair @ ( sK65_SY3126 @ SV316 ) @ ( sK64_B @ SV316 ) ) @ SV316 ) )
| ~ ( ( ( sK64_B @ SV316 )
!= ( sK65_SY3126 @ SV316 ) ) ) )
= $false )
| ( ( antisymmetric @ SV316 )
= $true )
| ( ( relation @ SV316 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2411]) ).
thf(2489,plain,
! [SV317: $i] :
( ( ( antisymmetric @ SV317 )
= $false )
| ( ( ! [SY3841: $i,SY3842: $i] :
( ~ ( in @ ( ordered_pair @ SY3841 @ SY3842 ) @ SV317 )
| ~ ( in @ ( ordered_pair @ SY3842 @ SY3841 ) @ SV317 )
| ( SY3841 = SY3842 ) ) )
= $true )
| ( ( relation @ SV317 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2412]) ).
thf(2490,plain,
! [SV347: $i,SV328: $i,SV275: $i] :
( ( ( ~ ( ! [SY3912: $i,SY3913: $i] :
( ~ ( in @ SY3912 @ SV275 )
| ~ ( in @ SY3913 @ SV328 )
| ( ( sK28_D @ SV347 @ SV328 @ SV275 )
!= ( ordered_pair @ SY3912 @ SY3913 ) ) )
| ~ ( in @ ( sK28_D @ SV347 @ SV328 @ SV275 ) @ SV347 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY3106 @ SV347 @ SV328 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK30_SY3108 @ SV347 @ SV328 @ SV275 ) @ SV328 ) )
| ( ( sK28_D @ SV347 @ SV328 @ SV275 )
!= ( ordered_pair @ ( sK29_SY3106 @ SV347 @ SV328 @ SV275 ) @ ( sK30_SY3108 @ SV347 @ SV328 @ SV275 ) ) ) )
| ( in @ ( sK28_D @ SV347 @ SV328 @ SV275 ) @ SV347 ) ) )
= $false )
| ( ( SV347
= ( cartesian_product2 @ SV275 @ SV328 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2413]) ).
thf(2491,plain,
! [SV329: $i,SV275: $i,SV348: $i] :
( ( ( SV348
= ( cartesian_product2 @ SV275 @ SV329 ) )
= $false )
| ( ( ~ ( ~ ! [SY3914: $i] :
( ! [SY3882: $i,SY3883: $i] :
( ~ ( in @ SY3882 @ SV275 )
| ~ ( in @ SY3883 @ SV329 )
| ( SY3914
!= ( ordered_pair @ SY3882 @ SY3883 ) ) )
| ( in @ SY3914 @ SV348 ) )
| ~ ! [SY3917: $i] :
( ~ ( in @ SY3917 @ SV348 )
| ~ ( ~ ~ ( ~ ( in @ ( sK26_E @ SY3917 @ SV348 @ SV329 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK27_SY3103 @ SY3917 @ SV348 @ SV329 @ SV275 ) @ SV329 ) )
| ( SY3917
!= ( ordered_pair @ ( sK26_E @ SY3917 @ SV348 @ SV329 @ SV275 ) @ ( sK27_SY3103 @ SY3917 @ SV348 @ SV329 @ SV275 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2414]) ).
thf(2492,plain,
! [SV276: $i,SV370: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SV370 @ SV276 ) @ SV370 )
| ~ ( in @ ( sK4_SY3086 @ SV370 @ SV276 ) @ SV370 ) )
| ~ ( in @ ( sK5_SY3088 @ SV370 @ SV276 ) @ SV370 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SV370 @ SV276 ) @ ( sK4_SY3086 @ SV370 @ SV276 ) ) @ SV276 ) )
| ~ ( in @ ( ordered_pair @ ( sK4_SY3086 @ SV370 @ SV276 ) @ ( sK5_SY3088 @ SV370 @ SV276 ) ) @ SV276 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK3_C @ SV370 @ SV276 ) @ ( sK5_SY3088 @ SV370 @ SV276 ) ) @ SV276 ) ) )
= $true )
| ( ( is_transitive_in @ SV276 @ SV370 )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2415]) ).
thf(2493,plain,
! [SV371: $i,SV276: $i] :
( ( ( ~ ( is_transitive_in @ SV276 @ SV371 ) )
= $true )
| ( ( ! [SY3929: $i,SY3930: $i,SY3931: $i] :
( ~ ( in @ SY3929 @ SV371 )
| ~ ( in @ SY3930 @ SV371 )
| ~ ( in @ SY3931 @ SV371 )
| ~ ( in @ ( ordered_pair @ SY3929 @ SY3930 ) @ SV276 )
| ~ ( in @ ( ordered_pair @ SY3930 @ SY3931 ) @ SV276 )
| ( in @ ( ordered_pair @ SY3929 @ SY3931 ) @ SV276 ) ) )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2416]) ).
thf(2494,plain,
! [SV277: $i,SV372: $i,SV396: $i] :
( ( ( ~ ( ~ ( ! [SY3978: $i] :
( ~ ( in @ ( ordered_pair @ SY3978 @ ( sK46_D @ SV396 @ SV372 @ SV277 ) ) @ SV277 )
| ~ ( in @ SY3978 @ SV372 ) )
| ~ ( in @ ( sK46_D @ SV396 @ SV372 @ SV277 ) @ SV396 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SV396 @ SV372 @ SV277 ) @ ( sK46_D @ SV396 @ SV372 @ SV277 ) ) @ SV277 )
| ~ ( in @ ( sK47_SY3118 @ SV396 @ SV372 @ SV277 ) @ SV372 ) )
| ( in @ ( sK46_D @ SV396 @ SV372 @ SV277 ) @ SV396 ) ) )
| ( SV396
= ( relation_image @ SV277 @ SV372 ) ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2417]) ).
thf(2495,plain,
! [SV373: $i,SV277: $i,SV397: $i] :
( ( ( ( SV397
!= ( relation_image @ SV277 @ SV373 ) )
| ~ ( ~ ! [SY3979: $i] :
( ! [SY3936: $i] :
( ~ ( in @ ( ordered_pair @ SY3936 @ SY3979 ) @ SV277 )
| ~ ( in @ SY3936 @ SV373 ) )
| ( in @ SY3979 @ SV397 ) )
| ~ ! [SY3981: $i] :
( ~ ( in @ SY3981 @ SV397 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SY3981 @ SV397 @ SV373 @ SV277 ) @ SY3981 ) @ SV277 )
| ~ ( in @ ( sK45_E @ SY3981 @ SV397 @ SV373 @ SV277 ) @ SV373 ) ) ) ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2418]) ).
thf(2496,plain,
! [SV278: $i,SV374: $i,SV398: $i] :
( ( ( ~ ( relation @ SV398 )
| ~ ( ~ ( ~ ( in @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ SV374 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV278 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) )
| ~ ~ ( ~ ( ( in @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ SV374 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV278 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) ) ) )
| ( SV398
= ( relation_dom_restriction @ SV278 @ SV374 ) ) )
= $true )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2419]) ).
thf(2497,plain,
! [SV375: $i,SV278: $i,SV399: $i] :
( ( ( ~ ( relation @ SV399 )
| ( SV399
!= ( relation_dom_restriction @ SV278 @ SV375 ) )
| ~ ( ~ ! [SY3982: $i,SY3983: $i] :
( ~ ( in @ SY3982 @ SV375 )
| ~ ( in @ ( ordered_pair @ SY3982 @ SY3983 ) @ SV278 )
| ( in @ ( ordered_pair @ SY3982 @ SY3983 ) @ SV399 ) )
| ~ ~ ( ~ ! [SY3984: $i] :
( ! [SY3985: $i] :
~ ( in @ ( ordered_pair @ SY3984 @ SY3985 ) @ SV399 )
| ( in @ SY3984 @ SV375 ) )
| ~ ! [SY3986: $i,SY3987: $i] :
( ~ ( in @ ( ordered_pair @ SY3986 @ SY3987 ) @ SV399 )
| ( in @ ( ordered_pair @ SY3986 @ SY3987 ) @ SV278 ) ) ) ) )
= $true )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2420]) ).
thf(2498,plain,
! [SV279: $i,SV376: $i,SV400: $i] :
( ( ( ~ ( ~ ( ! [SY3988: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SY3988 ) @ SV279 )
| ~ ( in @ SY3988 @ SV376 ) )
| ~ ( in @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SV400 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ ( sK44_SY3116 @ SV400 @ SV376 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK44_SY3116 @ SV400 @ SV376 @ SV279 ) @ SV376 ) )
| ( in @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SV400 ) ) )
| ( SV400
= ( relation_inverse_image @ SV279 @ SV376 ) ) )
= $true )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2421]) ).
thf(2499,plain,
! [SV377: $i,SV279: $i,SV401: $i] :
( ( ( ( SV401
!= ( relation_inverse_image @ SV279 @ SV377 ) )
| ~ ( ~ ! [SY3989: $i] :
( ! [SY3950: $i] :
( ~ ( in @ ( ordered_pair @ SY3989 @ SY3950 ) @ SV279 )
| ~ ( in @ SY3950 @ SV377 ) )
| ( in @ SY3989 @ SV401 ) )
| ~ ! [SY3991: $i] :
( ~ ( in @ SY3991 @ SV401 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3991 @ ( sK42_E @ SY3991 @ SV401 @ SV377 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK42_E @ SY3991 @ SV401 @ SV377 @ SV279 ) @ SV377 ) ) ) ) )
= $true )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2422]) ).
thf(2500,plain,
! [SV280: $i,SV378: $i] :
( ( ( ~ ( relation @ SV378 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV378 @ SV280 ) @ ( sK25_SY3102 @ SV378 @ SV280 ) ) @ SV280 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SV378 @ SV280 ) @ ( sK25_SY3102 @ SV378 @ SV280 ) ) @ SV378 ) )
| ( subset @ SV280 @ SV378 ) )
= $true )
| ( ( relation @ SV280 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2423]) ).
thf(2501,plain,
! [SV280: $i,SV379: $i] :
( ( ( ~ ( relation @ SV379 ) )
= $true )
| ( ( ~ ( subset @ SV280 @ SV379 )
| ! [SY3952: $i,SY3953: $i] :
( ~ ( in @ ( ordered_pair @ SY3952 @ SY3953 ) @ SV280 )
| ( in @ ( ordered_pair @ SY3952 @ SY3953 ) @ SV379 ) ) )
= $true )
| ( ( relation @ SV280 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2424]) ).
thf(2502,plain,
! [SV281: $i,SV318: $i] :
( ( ( ~ ! [SY3843: $i] :
( ~ ( relation @ SY3843 )
| ~ ( ~ ( ! [SY3844: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3843 @ SV318 @ SV281 ) @ SY3844 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY3844 @ ( sK8_SY3089 @ SY3843 @ SV318 @ SV281 ) ) @ SV318 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3843 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SY3843 @ SV318 @ SV281 ) ) @ SY3843 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3843 @ SV318 @ SV281 ) @ ( sK9_SY3093 @ SY3843 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SY3843 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SY3843 @ SV318 @ SV281 ) ) @ SV318 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SY3843 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SY3843 @ SV318 @ SV281 ) ) @ SY3843 ) ) )
| ( SY3843
= ( relation_composition @ SV281 @ SV318 ) ) ) )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2425]) ).
thf(2503,plain,
! [SV318: $i,SV281: $i] :
( ( ( ~ ! [SY3845: $i] :
( ~ ( relation @ SY3845 )
| ( SY3845
!= ( relation_composition @ SV281 @ SV318 ) )
| ~ ( ~ ! [SY3846: $i,SY3847: $i] :
( ! [SY3848: $i] :
( ~ ( in @ ( ordered_pair @ SY3846 @ SY3848 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY3848 @ SY3847 ) @ SV318 ) )
| ( in @ ( ordered_pair @ SY3846 @ SY3847 ) @ SY3845 ) )
| ~ ! [SY3849: $i,SY3850: $i] :
( ~ ( in @ ( ordered_pair @ SY3849 @ SY3850 ) @ SY3845 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3849 @ ( sK6_F @ SY3850 @ SY3849 @ SY3845 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY3850 @ SY3849 @ SY3845 @ SV318 @ SV281 ) @ SY3850 ) @ SV318 ) ) ) ) ) )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2425]) ).
thf(2504,plain,
! [SV330: $i,SV282: $i,SV349: $i] :
( ( ( relation_of2_as_subset @ SV349 @ SV282 @ SV330 )
= $false )
| ( ( ~ ( ~ ! [SY3918: $i] :
~ ( in @ ( ordered_pair @ SY3918 @ ( sK57_D @ SV349 @ SV330 @ SV282 ) ) @ SV349 )
| ~ ( in @ ( sK57_D @ SV349 @ SV330 @ SV282 ) @ SV330 ) )
| ( ( relation_rng_as_subset @ SV282 @ SV330 @ SV349 )
= SV330 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2426]) ).
thf(2505,plain,
! [SV331: $i,SV282: $i,SV350: $i] :
( ( ( relation_of2_as_subset @ SV350 @ SV282 @ SV331 )
= $false )
| ( ( ( ( relation_rng_as_subset @ SV282 @ SV331 @ SV350 )
!= SV331 )
| ! [SY3919: $i] :
( ( in @ ( ordered_pair @ ( sK56_E @ SY3919 @ SV350 @ SV331 @ SV282 ) @ SY3919 ) @ SV350 )
| ~ ( in @ SY3919 @ SV331 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2427]) ).
thf(2506,plain,
! [SV283: $i,SV319: $i] :
( ( ( ~ ! [SY3851: $i] :
( ~ ( function @ SY3851 )
| ~ ( relation @ SY3851 )
| ~ ( ~ ( ~ ( in @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3851 @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) ) @ ( apply @ SY3851 @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) ) @ SV319 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) @ SV283 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SY3851 @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) ) @ ( apply @ SY3851 @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) ) @ SV319 )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) @ SV283 ) ) ) )
| ( ( relation_dom @ SY3851 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SY3851 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SY3851 )
| ( relation_isomorphism @ SV283 @ SV319 @ SY3851 ) ) )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2428]) ).
thf(2507,plain,
! [SV319: $i,SV283: $i] :
( ( ( ~ ~ ( ~ ! [SY3852: $i] :
( ~ ( function @ SY3852 )
| ~ ( relation @ SY3852 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3852 )
| ~ ( ~ ! [SY3853: $i,SY3854: $i] :
( ~ ( in @ SY3853 @ ( relation_field @ SV283 ) )
| ~ ( in @ SY3854 @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3852 @ SY3853 ) @ ( apply @ SY3852 @ SY3854 ) ) @ SV319 )
| ( in @ ( ordered_pair @ SY3853 @ SY3854 ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3687: $i] :
( ! [SY3688: $i] :
~ ( in @ ( ordered_pair @ SY3687 @ SY3688 ) @ SV283 )
| ( in @ SY3687 @ ( relation_field @ SV283 ) ) )
| ~ ! [SY3689: $i,SY3690: $i] :
( ~ ( in @ ( ordered_pair @ SY3689 @ SY3690 ) @ SV283 )
| ( in @ SY3690 @ ( relation_field @ SV283 ) ) ) )
| ~ ! [SY3859: $i,SY3860: $i] :
( ~ ( in @ ( ordered_pair @ SY3859 @ SY3860 ) @ SV283 )
| ( in @ ( ordered_pair @ ( apply @ SY3852 @ SY3859 ) @ ( apply @ SY3852 @ SY3860 ) ) @ SV319 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3861: $i] :
( ~ ( function @ SY3861 )
| ~ ( relation @ SY3861 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3861 )
| ( ( relation_dom @ SY3861 )
= ( relation_field @ SV283 ) ) )
| ~ ! [SY3862: $i] :
( ~ ( function @ SY3862 )
| ~ ( relation @ SY3862 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3862 )
| ( ( relation_rng @ SY3862 )
= ( relation_field @ SV319 ) ) ) )
| ~ ! [SY3863: $i] :
( ~ ( function @ SY3863 )
| ~ ( relation @ SY3863 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3863 )
| ( one_to_one @ SY3863 ) ) ) ) )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2428]) ).
thf(2508,plain,
! [SV320: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK62_B @ SV320 )
!= ( sK63_SY3125 @ SV320 ) ) )
| ~ ~ ( ~ ( in @ ( sK62_B @ SV320 ) @ ( relation_field @ SV320 ) )
| ~ ( in @ ( sK63_SY3125 @ SV320 ) @ ( relation_field @ SV320 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK62_B @ SV320 ) @ ( sK63_SY3125 @ SV320 ) ) @ SV320 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK63_SY3125 @ SV320 ) @ ( sK62_B @ SV320 ) ) @ SV320 ) )
= $false )
| ( ( connected @ SV320 )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2429]) ).
thf(2509,plain,
! [SV321: $i] :
( ( ( connected @ SV321 )
= $false )
| ( ( ! [SY3864: $i,SY3865: $i] :
( ( SY3864 = SY3865 )
| ~ ( in @ SY3864 @ ( relation_field @ SV321 ) )
| ~ ( in @ SY3865 @ ( relation_field @ SV321 ) )
| ( in @ ( ordered_pair @ SY3864 @ SY3865 ) @ SV321 )
| ( in @ ( ordered_pair @ SY3865 @ SY3864 ) @ SV321 ) ) )
= $true )
| ( ( relation @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2430]) ).
thf(2510,plain,
! [SV284: $i,SV332: $i,SV351: $i] :
( ( ( ~ ( function @ SV351 ) )
= $true )
| ( ( ~ ( relation @ SV351 ) )
= $true )
| ( ( ( SV332
!= ( apply @ SV351 @ SV284 ) )
| ~ ( in @ SV284 @ ( relation_dom @ SV351 ) )
| ( in @ ( ordered_pair @ SV284 @ SV332 ) @ SV351 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2431]) ).
thf(2511,plain,
! [SV402: $i,SV284: $i] :
( ( ! [SY3992: $i] :
( ~ ( function @ SY3992 )
| ~ ( relation @ SY3992 )
| ~ ( in @ ( ordered_pair @ SV284 @ SV402 ) @ SY3992 )
| ( SV402
= ( apply @ SY3992 @ SV284 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2432]) ).
thf(2512,plain,
! [SV403: $i,SV284: $i] :
( ( ! [SY3993: $i] :
( ~ ( function @ SY3993 )
| ~ ( relation @ SY3993 )
| ~ ( in @ ( ordered_pair @ SV284 @ SV403 ) @ SY3993 )
| ( in @ SV284 @ ( relation_dom @ SY3993 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2433]) ).
thf(2513,plain,
! [SV333: $i,SV285: $i,SV352: $i] :
( ( ( relation @ SV352 )
= $false )
| ( ( ! [SY3920: $i] :
( ~ ( in @ SY3920 @ ( relation_dom @ SV352 ) )
| ~ ( in @ ( ordered_pair @ SY3920 @ SV285 ) @ SV352 )
| ~ ( in @ SY3920 @ SV333 ) )
| ( in @ SV285 @ ( relation_image @ SV352 @ SV333 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2434]) ).
thf(2514,plain,
! [SV334: $i,SV285: $i,SV353: $i] :
( ( ( relation @ SV353 )
= $false )
| ( ( ~ ( in @ SV285 @ ( relation_image @ SV353 @ SV334 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK61_D @ SV353 @ SV334 @ SV285 ) @ ( relation_dom @ SV353 ) )
| ~ ( in @ ( ordered_pair @ ( sK61_D @ SV353 @ SV334 @ SV285 ) @ SV285 ) @ SV353 ) )
| ~ ( in @ ( sK61_D @ SV353 @ SV334 @ SV285 ) @ SV334 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2435]) ).
thf(2515,plain,
! [SV322: $i,SV310: $i,SV286: $i] :
( ( ( ! [SY3709: $i] :
( ~ ( ( SV286
!= ( ordered_pair @ ( sK40_C @ SY3709 @ SV286 ) @ ( sK41_SY3114 @ SY3709 @ SV286 ) ) )
| ~ ( ( SY3709
!= ( sK40_C @ SY3709 @ SV286 ) ) ) )
| ( SY3709
= ( pair_first @ SV286 ) ) ) )
= $true )
| ( ( SV286
= ( ordered_pair @ SV310 @ SV322 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2436]) ).
thf(2516,plain,
! [SV322: $i,SV310: $i,SV286: $i] :
( ( ( ! [SY3710: $i] :
( ( SY3710
!= ( pair_first @ SV286 ) )
| ! [SY3711: $i] :
( ! [SY3712: $i] :
( SV286
!= ( ordered_pair @ SY3711 @ SY3712 ) )
| ( SY3710 = SY3711 ) ) ) )
= $true )
| ( ( SV286
= ( ordered_pair @ SV310 @ SV322 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2437]) ).
thf(2517,plain,
! [SV323: $i,SV311: $i,SV287: $i] :
( ( ( ! [SY3715: $i] :
( ~ ( ( SV287
!= ( ordered_pair @ ( sK33_C @ SY3715 @ SV287 ) @ ( sK34_SY3110 @ SY3715 @ SV287 ) ) )
| ~ ( ( SY3715
!= ( sK34_SY3110 @ SY3715 @ SV287 ) ) ) )
| ( SY3715
= ( pair_second @ SV287 ) ) ) )
= $true )
| ( ( SV287
= ( ordered_pair @ SV311 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2438]) ).
thf(2518,plain,
! [SV323: $i,SV311: $i,SV287: $i] :
( ( ( ! [SY3716: $i] :
( ( SY3716
!= ( pair_second @ SV287 ) )
| ! [SY3717: $i,SY3718: $i] :
( ( SV287
!= ( ordered_pair @ SY3717 @ SY3718 ) )
| ( SY3716 = SY3718 ) ) ) )
= $true )
| ( ( SV287
= ( ordered_pair @ SV311 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2439]) ).
thf(2519,plain,
! [SV335: $i,SV288: $i,SV354: $i] :
( ( ( relation @ SV354 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV288 @ SV335 ) @ SV354 )
| ( in @ SV288 @ ( relation_dom @ SV354 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2440]) ).
thf(2520,plain,
! [SV336: $i,SV288: $i,SV355: $i] :
( ( ( relation @ SV355 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV288 @ SV336 ) @ SV355 )
| ( in @ SV336 @ ( relation_rng @ SV355 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2441]) ).
thf(2521,plain,
! [SV324: $i,SV337: $i] :
( ( ( ~ ( ~ ( ( ( sK52_C @ SV337 @ SV324 )
!= ( sK53_SY3121 @ SV337 @ SV324 ) )
| ~ ( in @ ( sK52_C @ SV337 @ SV324 ) @ SV324 )
| ~ ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) )
| ~ ~ ( ~ ( ( ( sK52_C @ SV337 @ SV324 )
= ( sK53_SY3121 @ SV337 @ SV324 ) )
| ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) )
| ~ ( ( in @ ( sK52_C @ SV337 @ SV324 ) @ SV324 )
| ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) ) ) ) )
= $true )
| ( ( SV337
= ( identity_relation @ SV324 ) )
= $true )
| ( ( relation @ SV337 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2442]) ).
thf(2522,plain,
! [SV325: $i,SV338: $i] :
( ( ( ( SV338
!= ( identity_relation @ SV325 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3895: $i,SY3896: $i] :
( ( SY3895 != SY3896 )
| ~ ( in @ SY3895 @ SV325 )
| ( in @ ( ordered_pair @ SY3895 @ SY3896 ) @ SV338 ) )
| ~ ~ ( ~ ! [SY3897: $i,SY3898: $i] :
( ~ ( in @ ( ordered_pair @ SY3897 @ SY3898 ) @ SV338 )
| ( SY3897 = SY3898 ) )
| ~ ! [SY3899: $i] :
( ! [SY3900: $i] :
~ ( in @ ( ordered_pair @ SY3899 @ SY3900 ) @ SV338 )
| ( in @ SY3899 @ SV325 ) ) ) ) )
= $true )
| ( ( relation @ SV338 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2443]) ).
thf(2523,plain,
! [SV289: $i,SV339: $i,SV356: $i] :
( ( ( relation_of2_as_subset @ SV356 @ SV339 @ SV289 )
= $false )
| ( ( ~ ( ~ ! [SY3921: $i] :
~ ( in @ ( ordered_pair @ ( sK59_D @ SV356 @ SV339 @ SV289 ) @ SY3921 ) @ SV356 )
| ~ ( in @ ( sK59_D @ SV356 @ SV339 @ SV289 ) @ SV339 ) )
| ( ( relation_dom_as_subset @ SV339 @ SV289 @ SV356 )
= SV339 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2444]) ).
thf(2524,plain,
! [SV289: $i,SV340: $i,SV357: $i] :
( ( ( relation_of2_as_subset @ SV357 @ SV340 @ SV289 )
= $false )
| ( ( ( ( relation_dom_as_subset @ SV340 @ SV289 @ SV357 )
!= SV340 )
| ! [SY3922: $i] :
( ( in @ ( ordered_pair @ SY3922 @ ( sK58_E @ SY3922 @ SV357 @ SV340 @ SV289 ) ) @ SV357 )
| ~ ( in @ SY3922 @ SV340 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2445]) ).
thf(2525,plain,
! [SV290: $i,SV380: $i] :
( ( ( ~ ( ~ ( ! [SY3954: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SV380 @ SV290 ) @ SY3954 ) @ SV290 )
| ~ ( in @ ( sK22_C @ SV380 @ SV290 ) @ SV380 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SV380 @ SV290 ) @ ( sK23_SY3101 @ SV380 @ SV290 ) ) @ SV290 )
| ( in @ ( sK22_C @ SV380 @ SV290 ) @ SV380 ) ) ) )
= $true )
| ( ( SV380
= ( relation_dom @ SV290 ) )
= $true )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2446]) ).
thf(2526,plain,
! [SV290: $i,SV381: $i] :
( ( ( ( SV381
!= ( relation_dom @ SV290 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3955: $i] :
( ! [SY3733: $i] :
~ ( in @ ( ordered_pair @ SY3955 @ SY3733 ) @ SV290 )
| ( in @ SY3955 @ SV381 ) )
| ~ ! [SY3957: $i] :
( ~ ( in @ SY3957 @ SV381 )
| ( in @ ( ordered_pair @ SY3957 @ ( sK21_D @ SY3957 @ SV381 @ SV290 ) ) @ SV290 ) ) ) )
= $true )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2447]) ).
thf(2527,plain,
! [SV291: $i,SV382: $i] :
( ( ( ~ ( relation @ SV382 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV291 )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV382 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV291 )
| ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV382 ) ) )
| ( SV291 = SV382 ) )
= $true )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2448]) ).
thf(2528,plain,
! [SV291: $i,SV383: $i] :
( ( ( ~ ( relation @ SV383 ) )
= $true )
| ( ( ( SV291 != SV383 )
| ~ ( ~ ! [SY3958: $i,SY3959: $i] :
( ~ ( in @ ( ordered_pair @ SY3958 @ SY3959 ) @ SV291 )
| ( in @ ( ordered_pair @ SY3958 @ SY3959 ) @ SV383 ) )
| ~ ! [SY3960: $i,SY3961: $i] :
( ~ ( in @ ( ordered_pair @ SY3960 @ SY3961 ) @ SV383 )
| ( in @ ( ordered_pair @ SY3960 @ SY3961 ) @ SV291 ) ) ) )
= $true )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2449]) ).
thf(2529,plain,
! [SV326: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK66_B @ SV326 ) @ ( sK67_SY3127 @ SV326 ) ) @ SV326 )
| ~ ( in @ ( ordered_pair @ ( sK67_SY3127 @ SV326 ) @ ( sK68_SY3129 @ SV326 ) ) @ SV326 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK66_B @ SV326 ) @ ( sK68_SY3129 @ SV326 ) ) @ SV326 ) )
= $false )
| ( ( transitive @ SV326 )
= $true )
| ( ( relation @ SV326 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2450]) ).
thf(2530,plain,
! [SV327: $i] :
( ( ( transitive @ SV327 )
= $false )
| ( ( ! [SY3874: $i,SY3875: $i,SY3876: $i] :
( ~ ( in @ ( ordered_pair @ SY3874 @ SY3875 ) @ SV327 )
| ~ ( in @ ( ordered_pair @ SY3875 @ SY3876 ) @ SV327 )
| ( in @ ( ordered_pair @ SY3874 @ SY3876 ) @ SV327 ) ) )
= $true )
| ( ( relation @ SV327 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2451]) ).
thf(2531,plain,
! [SV292: $i,SV384: $i] :
( ( ( ~ ( relation @ SV384 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SV384 @ SV292 ) @ ( sK13_SY3095 @ SV384 @ SV292 ) ) @ SV384 )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV384 @ SV292 ) @ ( sK12_C @ SV384 @ SV292 ) ) @ SV292 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SV384 @ SV292 ) @ ( sK13_SY3095 @ SV384 @ SV292 ) ) @ SV384 )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV384 @ SV292 ) @ ( sK12_C @ SV384 @ SV292 ) ) @ SV292 ) ) )
| ( SV384
= ( relation_inverse @ SV292 ) ) )
= $true )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2452]) ).
thf(2532,plain,
! [SV292: $i,SV385: $i] :
( ( ( ~ ( relation @ SV385 ) )
= $true )
| ( ( ( SV385
!= ( relation_inverse @ SV292 ) )
| ~ ( ~ ! [SY3962: $i,SY3963: $i] :
( ~ ( in @ ( ordered_pair @ SY3962 @ SY3963 ) @ SV385 )
| ( in @ ( ordered_pair @ SY3963 @ SY3962 ) @ SV292 ) )
| ~ ! [SY3964: $i,SY3965: $i] :
( ~ ( in @ ( ordered_pair @ SY3965 @ SY3964 ) @ SV292 )
| ( in @ ( ordered_pair @ SY3964 @ SY3965 ) @ SV385 ) ) ) )
= $true )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2453]) ).
thf(2533,plain,
! [SV293: $i] :
( ( ( ~ ( ~ ! [SY3747: $i] :
( ~ ( in @ SY3747 @ ( relation_dom @ SV293 ) )
| ! [SY3748: $i] :
( ( SY3748
!= ( apply @ SV293 @ SY3747 ) )
| ( in @ ( ordered_pair @ SY3747 @ SY3748 ) @ SV293 ) ) )
| ~ ! [SY3749: $i] :
( ~ ( in @ SY3749 @ ( relation_dom @ SV293 ) )
| ! [SY3750: $i] :
( ~ ( in @ ( ordered_pair @ SY3749 @ SY3750 ) @ SV293 )
| ( SY3750
= ( apply @ SV293 @ SY3749 ) ) ) ) ) )
= $true )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2454]) ).
thf(2534,plain,
! [SV293: $i] :
( ( ( ~ ( ~ ! [SY3751: $i] :
( ( in @ SY3751 @ ( relation_dom @ SV293 ) )
| ! [SY3752: $i] :
( ( SY3752
!= ( apply @ SV293 @ SY3751 ) )
| ( SY3752 = empty_set ) ) )
| ~ ! [SY3753: $i] :
( ( in @ SY3753 @ ( relation_dom @ SV293 ) )
| ! [SY3754: $i] :
( ( SY3754 != empty_set )
| ( SY3754
= ( apply @ SV293 @ SY3753 ) ) ) ) ) )
= $true )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2455]) ).
thf(2535,plain,
! [SV294: $i,SV386: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_C @ SV386 @ SV294 ) @ SV386 )
| ~ ( in @ ( sK20_SY3099 @ SV386 @ SV294 ) @ SV386 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SV386 @ SV294 ) @ ( sK20_SY3099 @ SV386 @ SV294 ) ) @ SV294 ) )
| ~ ( in @ ( ordered_pair @ ( sK20_SY3099 @ SV386 @ SV294 ) @ ( sK19_C @ SV386 @ SV294 ) ) @ SV294 ) )
| ~ ( ( ( sK19_C @ SV386 @ SV294 )
!= ( sK20_SY3099 @ SV386 @ SV294 ) ) ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV294 @ SV386 )
= $true )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2456]) ).
thf(2536,plain,
! [SV387: $i,SV294: $i] :
( ( ( ~ ( is_antisymmetric_in @ SV294 @ SV387 ) )
= $true )
| ( ( ! [SY3966: $i,SY3967: $i] :
( ~ ( in @ SY3966 @ SV387 )
| ~ ( in @ SY3967 @ SV387 )
| ~ ( in @ ( ordered_pair @ SY3966 @ SY3967 ) @ SV294 )
| ~ ( in @ ( ordered_pair @ SY3967 @ SY3966 ) @ SV294 )
| ( SY3966 = SY3967 ) ) )
= $true )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2457]) ).
thf(2537,plain,
! [SV295: $i,SV388: $i,SV404: $i] :
( ( ( ~ ( ~ ( ( ( sK35_D @ SV404 @ SV388 @ SV295 )
= SV388 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV388 ) @ SV295 )
| ~ ( in @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV404 ) )
| ~ ~ ( ~ ( ( ( sK35_D @ SV404 @ SV388 @ SV295 )
!= SV388 )
| ( in @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV404 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV388 ) @ SV295 )
| ( in @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV404 ) ) ) )
| ( SV404
= ( fiber @ SV295 @ SV388 ) ) )
= $true )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2458]) ).
thf(2538,plain,
! [SV389: $i,SV295: $i,SV405: $i] :
( ( ( ( SV405
!= ( fiber @ SV295 @ SV389 ) )
| ~ ( ~ ! [SY3994: $i] :
( ( SY3994 = SV389 )
| ~ ( in @ ( ordered_pair @ SY3994 @ SV389 ) @ SV295 )
| ( in @ SY3994 @ SV405 ) )
| ~ ~ ( ~ ! [SY3995: $i] :
( ~ ( in @ SY3995 @ SV405 )
| ( SY3995 != SV389 ) )
| ~ ! [SY3996: $i] :
( ~ ( in @ SY3996 @ SV405 )
| ( in @ ( ordered_pair @ SY3996 @ SV389 ) @ SV295 ) ) ) ) )
= $true )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2459]) ).
thf(2539,plain,
! [SV296: $i,SV307: $i,SV406: $i] :
( ( ( ~ ( relation @ SV406 )
| ~ ( ~ ( ~ ( in @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) @ SV296 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV307 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) @ SV296 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV307 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) ) ) )
| ( SV406
= ( relation_rng_restriction @ SV296 @ SV307 ) ) )
= $true )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2460]) ).
thf(2540,plain,
! [SV307: $i,SV296: $i,SV407: $i] :
( ( ( ~ ( relation @ SV407 )
| ( SV407
!= ( relation_rng_restriction @ SV296 @ SV307 ) )
| ~ ( ~ ! [SY3997: $i,SY3998: $i] :
( ~ ( in @ SY3998 @ SV296 )
| ~ ( in @ ( ordered_pair @ SY3997 @ SY3998 ) @ SV307 )
| ( in @ ( ordered_pair @ SY3997 @ SY3998 ) @ SV407 ) )
| ~ ~ ( ~ ! [SY3999: $i,SY4000: $i] :
( ~ ( in @ ( ordered_pair @ SY3999 @ SY4000 ) @ SV407 )
| ( in @ SY4000 @ SV296 ) )
| ~ ! [SY4001: $i,SY4002: $i] :
( ~ ( in @ ( ordered_pair @ SY4001 @ SY4002 ) @ SV407 )
| ( in @ ( ordered_pair @ SY4001 @ SY4002 ) @ SV307 ) ) ) ) )
= $true )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2461]) ).
thf(2541,plain,
! [SV297: $i,SV390: $i] :
( ( ( ~ ( ~ ( ! [SY3973: $i] :
~ ( in @ ( ordered_pair @ SY3973 @ ( sK17_C @ SV390 @ SV297 ) ) @ SV297 )
| ~ ( in @ ( sK17_C @ SV390 @ SV297 ) @ SV390 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK18_SY3098 @ SV390 @ SV297 ) @ ( sK17_C @ SV390 @ SV297 ) ) @ SV297 )
| ( in @ ( sK17_C @ SV390 @ SV297 ) @ SV390 ) ) ) )
= $true )
| ( ( SV390
= ( relation_rng @ SV297 ) )
= $true )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2462]) ).
thf(2542,plain,
! [SV297: $i,SV391: $i] :
( ( ( ( SV391
!= ( relation_rng @ SV297 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3974: $i] :
( ! [SY3779: $i] :
~ ( in @ ( ordered_pair @ SY3779 @ SY3974 ) @ SV297 )
| ( in @ SY3974 @ SV391 ) )
| ~ ! [SY3976: $i] :
( ~ ( in @ SY3976 @ SV391 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3976 @ SV391 @ SV297 ) @ SY3976 ) @ SV297 ) ) ) )
= $true )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2463]) ).
thf(2543,plain,
! [SV341: $i,SV298: $i,SV358: $i] :
( ( ( relation @ SV358 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV298 @ SV341 ) @ SV358 )
| ( in @ SV298 @ ( relation_field @ SV358 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2464]) ).
thf(2544,plain,
! [SV342: $i,SV298: $i,SV359: $i] :
( ( ( relation @ SV359 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV298 @ SV342 ) @ SV359 )
| ( in @ SV342 @ ( relation_field @ SV359 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2465]) ).
thf(2545,plain,
! [SV308: $i,SV360: $i,SV299: $i,SV392: $i] :
( ( ( ~ ( relation @ SV392 ) )
= $true )
| ( ( ~ ( in @ SV299 @ SV360 )
| ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ SV392 )
| ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SV360 ) @ SV392 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2466]) ).
thf(2546,plain,
! [SV308: $i,SV299: $i] :
( ( ! [SY3827: $i,SY3828: $i] :
( ~ ( relation @ SY3828 )
| ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SY3827 ) @ SY3828 ) )
| ( in @ SV299 @ SY3827 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2467]) ).
thf(2547,plain,
! [SV308: $i,SV299: $i] :
( ( ! [SY3829: $i,SY3830: $i] :
( ~ ( relation @ SY3830 )
| ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SY3829 ) @ SY3830 ) )
| ( in @ ( ordered_pair @ SV299 @ SV308 ) @ SY3830 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2468]) ).
thf(2548,plain,
! [SV408: $i,SV361: $i,SV309: $i,SV300: $i] :
( ( ( ( ( ordered_pair @ SV300 @ SV309 )
!= ( ordered_pair @ SV361 @ SV408 ) ) )
= $true )
| ( ( SV300 = SV361 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2469]) ).
thf(2549,plain,
! [SV393: $i,SV362: $i,SV309: $i,SV300: $i] :
( ( ( ( ( ordered_pair @ SV300 @ SV309 )
!= ( ordered_pair @ SV362 @ SV393 ) ) )
= $true )
| ( ( SV309 = SV393 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2470]) ).
thf(2550,plain,
! [SV343: $i,SV301: $i,SV363: $i] :
( ( ( relation @ SV363 )
= $false )
| ( ( ! [SY3926: $i] :
( ~ ( in @ SY3926 @ ( relation_rng @ SV363 ) )
| ~ ( in @ ( ordered_pair @ SV301 @ SY3926 ) @ SV363 )
| ~ ( in @ SY3926 @ SV343 ) )
| ( in @ SV301 @ ( relation_inverse_image @ SV363 @ SV343 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2471]) ).
thf(2551,plain,
! [SV344: $i,SV301: $i,SV364: $i] :
( ( ( relation @ SV364 )
= $false )
| ( ( ~ ( in @ SV301 @ ( relation_inverse_image @ SV364 @ SV344 ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK60_D @ SV364 @ SV344 @ SV301 ) @ ( relation_rng @ SV364 ) )
| ~ ( in @ ( ordered_pair @ SV301 @ ( sK60_D @ SV364 @ SV344 @ SV301 ) ) @ SV364 ) )
| ~ ( in @ ( sK60_D @ SV364 @ SV344 @ SV301 ) @ SV344 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2472]) ).
thf(2552,plain,
! [SV302: $i,SV394: $i] :
( ( ( ~ ( ~ ( in @ ( sK36_C @ SV394 @ SV302 ) @ SV394 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SV394 @ SV302 ) @ ( sK36_C @ SV394 @ SV302 ) ) @ SV302 ) ) )
= $true )
| ( ( is_reflexive_in @ SV302 @ SV394 )
= $true )
| ( ( relation @ SV302 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2473]) ).
thf(2553,plain,
! [SV395: $i,SV302: $i] :
( ( ( ~ ( is_reflexive_in @ SV302 @ SV395 ) )
= $true )
| ( ( ! [SY3977: $i] :
( ~ ( in @ SY3977 @ SV395 )
| ( in @ ( ordered_pair @ SY3977 @ SY3977 ) @ SV302 ) ) )
= $true )
| ( ( relation @ SV302 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2474]) ).
thf(2554,plain,
! [SV365: $i,SV305: $i,SV345: $i,SV272: $i] :
( ( ( ~ ( in @ SV272 @ SV345 ) )
= $true )
| ( ( ~ ( in @ SV305 @ SV365 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SV345 @ SV365 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2475]) ).
thf(2555,plain,
! [SV409: $i,SV305: $i,SV272: $i] :
( ( ! [SY4003: $i] :
~ ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SV409 @ SY4003 ) )
| ( in @ SV272 @ SV409 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2476]) ).
thf(2556,plain,
! [SV410: $i,SV305: $i,SV272: $i] :
( ( ! [SY4004: $i] :
( ~ ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SV410 @ SY4004 ) )
| ( in @ SV305 @ SY4004 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2477]) ).
thf(2557,plain,
! [SV366: $i,SV306: $i,SV346: $i,SV273: $i] :
( ( ( ~ ( in @ SV273 @ SV346 ) )
= $true )
| ( ( ~ ( in @ SV306 @ SV366 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SV346 @ SV366 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2478]) ).
thf(2558,plain,
! [SV411: $i,SV306: $i,SV273: $i] :
( ( ! [SY4005: $i] :
~ ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SV411 @ SY4005 ) )
| ( in @ SV273 @ SV411 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2479]) ).
thf(2559,plain,
! [SV412: $i,SV306: $i,SV273: $i] :
( ( ! [SY4006: $i] :
( ~ ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SV412 @ SY4006 ) )
| ( in @ SV306 @ SY4006 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2480]) ).
thf(2560,plain,
! [SV312: $i] :
( ( ( ~ ( in @ ( sK69_B @ SV312 ) @ ( relation_field @ SV312 ) ) )
= $false )
| ( ( reflexive @ SV312 )
= $true )
| ( ( relation @ SV312 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2481]) ).
thf(2561,plain,
! [SV312: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK69_B @ SV312 ) @ ( sK69_B @ SV312 ) ) @ SV312 ) )
= $false )
| ( ( reflexive @ SV312 )
= $true )
| ( ( relation @ SV312 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2481]) ).
thf(2562,plain,
! [SV313: $i,SV413: $i] :
( ( ( ~ ( in @ SV413 @ ( relation_field @ SV313 ) )
| ( in @ ( ordered_pair @ SV413 @ SV413 ) @ SV313 ) )
= $true )
| ( ( reflexive @ SV313 )
= $false )
| ( ( relation @ SV313 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2482]) ).
thf(2563,plain,
! [SV274: $i,SV367: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK14_C @ SV367 @ SV274 )
!= ( sK15_SY3096 @ SV367 @ SV274 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SV367 @ SV274 ) @ SV367 )
| ~ ( in @ ( sK15_SY3096 @ SV367 @ SV274 ) @ SV367 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK14_C @ SV367 @ SV274 ) @ ( sK15_SY3096 @ SV367 @ SV274 ) ) @ SV274 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK15_SY3096 @ SV367 @ SV274 ) @ ( sK14_C @ SV367 @ SV274 ) ) @ SV274 ) )
= $false )
| ( ( is_connected_in @ SV274 @ SV367 )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2483]) ).
thf(2564,plain,
! [SV368: $i,SV274: $i] :
( ( ( is_connected_in @ SV274 @ SV368 )
= $false )
| ( ( ! [SY3927: $i,SY3928: $i] :
( ( SY3927 = SY3928 )
| ~ ( in @ SY3927 @ SV368 )
| ~ ( in @ SY3928 @ SV368 )
| ( in @ ( ordered_pair @ SY3927 @ SY3928 ) @ SV274 )
| ( in @ ( ordered_pair @ SY3928 @ SY3927 ) @ SV274 ) ) )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2484]) ).
thf(2565,plain,
! [SV414: $i,SV314: $i] :
( ( ( ! [SY4007: $i] :
( ( sK39_B @ SV314 )
!= ( ordered_pair @ SV414 @ SY4007 ) ) )
= $true )
| ( ( relation @ SV314 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2485]) ).
thf(2566,plain,
! [SV315: $i,SV369: $i] :
( ( ( in @ SV369 @ SV315 )
= $false )
| ( ( SV369
= ( ordered_pair @ ( sK37_C @ SV369 @ SV315 ) @ ( sK38_SY3111 @ SV369 @ SV315 ) ) )
= $true )
| ( ( relation @ SV315 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2487]) ).
thf(2567,plain,
! [SV316: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK64_B @ SV316 ) @ ( sK65_SY3126 @ SV316 ) ) @ SV316 )
| ~ ( in @ ( ordered_pair @ ( sK65_SY3126 @ SV316 ) @ ( sK64_B @ SV316 ) ) @ SV316 ) ) )
= $false )
| ( ( antisymmetric @ SV316 )
= $true )
| ( ( relation @ SV316 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2488]) ).
thf(2568,plain,
! [SV316: $i] :
( ( ( ~ ( ( ( sK64_B @ SV316 )
!= ( sK65_SY3126 @ SV316 ) ) ) )
= $false )
| ( ( antisymmetric @ SV316 )
= $true )
| ( ( relation @ SV316 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2488]) ).
thf(2569,plain,
! [SV317: $i,SV415: $i] :
( ( ( ! [SY4008: $i] :
( ~ ( in @ ( ordered_pair @ SV415 @ SY4008 ) @ SV317 )
| ~ ( in @ ( ordered_pair @ SY4008 @ SV415 ) @ SV317 )
| ( SV415 = SY4008 ) ) )
= $true )
| ( ( antisymmetric @ SV317 )
= $false )
| ( ( relation @ SV317 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2489]) ).
thf(2570,plain,
! [SV347: $i,SV328: $i,SV275: $i] :
( ( ( ~ ( ! [SY3912: $i,SY3913: $i] :
( ~ ( in @ SY3912 @ SV275 )
| ~ ( in @ SY3913 @ SV328 )
| ( ( sK28_D @ SV347 @ SV328 @ SV275 )
!= ( ordered_pair @ SY3912 @ SY3913 ) ) )
| ~ ( in @ ( sK28_D @ SV347 @ SV328 @ SV275 ) @ SV347 ) ) )
= $false )
| ( ( SV347
= ( cartesian_product2 @ SV275 @ SV328 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2490]) ).
thf(2571,plain,
! [SV275: $i,SV328: $i,SV347: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY3106 @ SV347 @ SV328 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK30_SY3108 @ SV347 @ SV328 @ SV275 ) @ SV328 ) )
| ( ( sK28_D @ SV347 @ SV328 @ SV275 )
!= ( ordered_pair @ ( sK29_SY3106 @ SV347 @ SV328 @ SV275 ) @ ( sK30_SY3108 @ SV347 @ SV328 @ SV275 ) ) ) )
| ( in @ ( sK28_D @ SV347 @ SV328 @ SV275 ) @ SV347 ) ) )
= $false )
| ( ( SV347
= ( cartesian_product2 @ SV275 @ SV328 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2490]) ).
thf(2572,plain,
! [SV348: $i,SV329: $i,SV275: $i] :
( ( ( ~ ! [SY3914: $i] :
( ! [SY3882: $i,SY3883: $i] :
( ~ ( in @ SY3882 @ SV275 )
| ~ ( in @ SY3883 @ SV329 )
| ( SY3914
!= ( ordered_pair @ SY3882 @ SY3883 ) ) )
| ( in @ SY3914 @ SV348 ) )
| ~ ! [SY3917: $i] :
( ~ ( in @ SY3917 @ SV348 )
| ~ ( ~ ~ ( ~ ( in @ ( sK26_E @ SY3917 @ SV348 @ SV329 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK27_SY3103 @ SY3917 @ SV348 @ SV329 @ SV275 ) @ SV329 ) )
| ( SY3917
!= ( ordered_pair @ ( sK26_E @ SY3917 @ SV348 @ SV329 @ SV275 ) @ ( sK27_SY3103 @ SY3917 @ SV348 @ SV329 @ SV275 ) ) ) ) ) )
= $false )
| ( ( SV348
= ( cartesian_product2 @ SV275 @ SV329 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2491]) ).
thf(2573,plain,
! [SV276: $i,SV370: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SV370 @ SV276 ) @ SV370 )
| ~ ( in @ ( sK4_SY3086 @ SV370 @ SV276 ) @ SV370 ) )
| ~ ( in @ ( sK5_SY3088 @ SV370 @ SV276 ) @ SV370 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SV370 @ SV276 ) @ ( sK4_SY3086 @ SV370 @ SV276 ) ) @ SV276 ) )
| ~ ( in @ ( ordered_pair @ ( sK4_SY3086 @ SV370 @ SV276 ) @ ( sK5_SY3088 @ SV370 @ SV276 ) ) @ SV276 ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK3_C @ SV370 @ SV276 ) @ ( sK5_SY3088 @ SV370 @ SV276 ) ) @ SV276 ) )
= $false )
| ( ( is_transitive_in @ SV276 @ SV370 )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2492]) ).
thf(2574,plain,
! [SV371: $i,SV276: $i] :
( ( ( is_transitive_in @ SV276 @ SV371 )
= $false )
| ( ( ! [SY3929: $i,SY3930: $i,SY3931: $i] :
( ~ ( in @ SY3929 @ SV371 )
| ~ ( in @ SY3930 @ SV371 )
| ~ ( in @ SY3931 @ SV371 )
| ~ ( in @ ( ordered_pair @ SY3929 @ SY3930 ) @ SV276 )
| ~ ( in @ ( ordered_pair @ SY3930 @ SY3931 ) @ SV276 )
| ( in @ ( ordered_pair @ SY3929 @ SY3931 ) @ SV276 ) ) )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2493]) ).
thf(2575,plain,
! [SV277: $i,SV372: $i,SV396: $i] :
( ( ( ~ ( ~ ( ! [SY3978: $i] :
( ~ ( in @ ( ordered_pair @ SY3978 @ ( sK46_D @ SV396 @ SV372 @ SV277 ) ) @ SV277 )
| ~ ( in @ SY3978 @ SV372 ) )
| ~ ( in @ ( sK46_D @ SV396 @ SV372 @ SV277 ) @ SV396 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SV396 @ SV372 @ SV277 ) @ ( sK46_D @ SV396 @ SV372 @ SV277 ) ) @ SV277 )
| ~ ( in @ ( sK47_SY3118 @ SV396 @ SV372 @ SV277 ) @ SV372 ) )
| ( in @ ( sK46_D @ SV396 @ SV372 @ SV277 ) @ SV396 ) ) ) )
= $true )
| ( ( SV396
= ( relation_image @ SV277 @ SV372 ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2494]) ).
thf(2576,plain,
! [SV373: $i,SV277: $i,SV397: $i] :
( ( ( ( SV397
!= ( relation_image @ SV277 @ SV373 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3979: $i] :
( ! [SY3936: $i] :
( ~ ( in @ ( ordered_pair @ SY3936 @ SY3979 ) @ SV277 )
| ~ ( in @ SY3936 @ SV373 ) )
| ( in @ SY3979 @ SV397 ) )
| ~ ! [SY3981: $i] :
( ~ ( in @ SY3981 @ SV397 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SY3981 @ SV397 @ SV373 @ SV277 ) @ SY3981 ) @ SV277 )
| ~ ( in @ ( sK45_E @ SY3981 @ SV397 @ SV373 @ SV277 ) @ SV373 ) ) ) ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2495]) ).
thf(2577,plain,
! [SV278: $i,SV374: $i,SV398: $i] :
( ( ( ~ ( relation @ SV398 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ SV374 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV278 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) )
| ~ ~ ( ~ ( ( in @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ SV374 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV278 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) ) ) )
| ( SV398
= ( relation_dom_restriction @ SV278 @ SV374 ) ) )
= $true )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2496]) ).
thf(2578,plain,
! [SV375: $i,SV278: $i,SV399: $i] :
( ( ( ~ ( relation @ SV399 ) )
= $true )
| ( ( ( SV399
!= ( relation_dom_restriction @ SV278 @ SV375 ) )
| ~ ( ~ ! [SY3982: $i,SY3983: $i] :
( ~ ( in @ SY3982 @ SV375 )
| ~ ( in @ ( ordered_pair @ SY3982 @ SY3983 ) @ SV278 )
| ( in @ ( ordered_pair @ SY3982 @ SY3983 ) @ SV399 ) )
| ~ ~ ( ~ ! [SY3984: $i] :
( ! [SY3985: $i] :
~ ( in @ ( ordered_pair @ SY3984 @ SY3985 ) @ SV399 )
| ( in @ SY3984 @ SV375 ) )
| ~ ! [SY3986: $i,SY3987: $i] :
( ~ ( in @ ( ordered_pair @ SY3986 @ SY3987 ) @ SV399 )
| ( in @ ( ordered_pair @ SY3986 @ SY3987 ) @ SV278 ) ) ) ) )
= $true )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2497]) ).
thf(2579,plain,
! [SV279: $i,SV376: $i,SV400: $i] :
( ( ( ~ ( ~ ( ! [SY3988: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SY3988 ) @ SV279 )
| ~ ( in @ SY3988 @ SV376 ) )
| ~ ( in @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SV400 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ ( sK44_SY3116 @ SV400 @ SV376 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK44_SY3116 @ SV400 @ SV376 @ SV279 ) @ SV376 ) )
| ( in @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SV400 ) ) ) )
= $true )
| ( ( SV400
= ( relation_inverse_image @ SV279 @ SV376 ) )
= $true )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2498]) ).
thf(2580,plain,
! [SV377: $i,SV279: $i,SV401: $i] :
( ( ( ( SV401
!= ( relation_inverse_image @ SV279 @ SV377 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3989: $i] :
( ! [SY3950: $i] :
( ~ ( in @ ( ordered_pair @ SY3989 @ SY3950 ) @ SV279 )
| ~ ( in @ SY3950 @ SV377 ) )
| ( in @ SY3989 @ SV401 ) )
| ~ ! [SY3991: $i] :
( ~ ( in @ SY3991 @ SV401 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3991 @ ( sK42_E @ SY3991 @ SV401 @ SV377 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK42_E @ SY3991 @ SV401 @ SV377 @ SV279 ) @ SV377 ) ) ) ) )
= $true )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2499]) ).
thf(2581,plain,
! [SV280: $i,SV378: $i] :
( ( ( relation @ SV378 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV378 @ SV280 ) @ ( sK25_SY3102 @ SV378 @ SV280 ) ) @ SV280 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SV378 @ SV280 ) @ ( sK25_SY3102 @ SV378 @ SV280 ) ) @ SV378 ) )
| ( subset @ SV280 @ SV378 ) )
= $true )
| ( ( relation @ SV280 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2500]) ).
thf(2582,plain,
! [SV280: $i,SV379: $i] :
( ( ( relation @ SV379 )
= $false )
| ( ( ~ ( subset @ SV280 @ SV379 )
| ! [SY3952: $i,SY3953: $i] :
( ~ ( in @ ( ordered_pair @ SY3952 @ SY3953 ) @ SV280 )
| ( in @ ( ordered_pair @ SY3952 @ SY3953 ) @ SV379 ) ) )
= $true )
| ( ( relation @ SV280 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2501]) ).
thf(2583,plain,
! [SV281: $i,SV318: $i] :
( ( ( ! [SY3843: $i] :
( ~ ( relation @ SY3843 )
| ~ ( ~ ( ! [SY3844: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3843 @ SV318 @ SV281 ) @ SY3844 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY3844 @ ( sK8_SY3089 @ SY3843 @ SV318 @ SV281 ) ) @ SV318 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3843 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SY3843 @ SV318 @ SV281 ) ) @ SY3843 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SY3843 @ SV318 @ SV281 ) @ ( sK9_SY3093 @ SY3843 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SY3843 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SY3843 @ SV318 @ SV281 ) ) @ SV318 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SY3843 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SY3843 @ SV318 @ SV281 ) ) @ SY3843 ) ) )
| ( SY3843
= ( relation_composition @ SV281 @ SV318 ) ) ) )
= $true )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2502]) ).
thf(2584,plain,
! [SV318: $i,SV281: $i] :
( ( ( ! [SY3845: $i] :
( ~ ( relation @ SY3845 )
| ( SY3845
!= ( relation_composition @ SV281 @ SV318 ) )
| ~ ( ~ ! [SY3846: $i,SY3847: $i] :
( ! [SY3848: $i] :
( ~ ( in @ ( ordered_pair @ SY3846 @ SY3848 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY3848 @ SY3847 ) @ SV318 ) )
| ( in @ ( ordered_pair @ SY3846 @ SY3847 ) @ SY3845 ) )
| ~ ! [SY3849: $i,SY3850: $i] :
( ~ ( in @ ( ordered_pair @ SY3849 @ SY3850 ) @ SY3845 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3849 @ ( sK6_F @ SY3850 @ SY3849 @ SY3845 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY3850 @ SY3849 @ SY3845 @ SV318 @ SV281 ) @ SY3850 ) @ SV318 ) ) ) ) ) )
= $true )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2503]) ).
thf(2585,plain,
! [SV282: $i,SV330: $i,SV349: $i] :
( ( ( ~ ( ~ ! [SY3918: $i] :
~ ( in @ ( ordered_pair @ SY3918 @ ( sK57_D @ SV349 @ SV330 @ SV282 ) ) @ SV349 )
| ~ ( in @ ( sK57_D @ SV349 @ SV330 @ SV282 ) @ SV330 ) ) )
= $true )
| ( ( ( relation_rng_as_subset @ SV282 @ SV330 @ SV349 )
= SV330 )
= $true )
| ( ( relation_of2_as_subset @ SV349 @ SV282 @ SV330 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2504]) ).
thf(2586,plain,
! [SV350: $i,SV331: $i,SV282: $i] :
( ( ( ( ( relation_rng_as_subset @ SV282 @ SV331 @ SV350 )
!= SV331 ) )
= $true )
| ( ( ! [SY3919: $i] :
( ( in @ ( ordered_pair @ ( sK56_E @ SY3919 @ SV350 @ SV331 @ SV282 ) @ SY3919 ) @ SV350 )
| ~ ( in @ SY3919 @ SV331 ) ) )
= $true )
| ( ( relation_of2_as_subset @ SV350 @ SV282 @ SV331 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2505]) ).
thf(2587,plain,
! [SV283: $i,SV319: $i] :
( ( ( ! [SY3851: $i] :
( ~ ( function @ SY3851 )
| ~ ( relation @ SY3851 )
| ~ ( ~ ( ~ ( in @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3851 @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) ) @ ( apply @ SY3851 @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) ) @ SV319 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) @ SV283 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SY3851 @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) ) @ ( apply @ SY3851 @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) ) @ SV319 )
| ( in @ ( ordered_pair @ ( sK10_D @ SY3851 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SY3851 @ SV319 @ SV283 ) ) @ SV283 ) ) ) )
| ( ( relation_dom @ SY3851 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SY3851 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SY3851 )
| ( relation_isomorphism @ SV283 @ SV319 @ SY3851 ) ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2506]) ).
thf(2588,plain,
! [SV319: $i,SV283: $i] :
( ( ( ~ ( ~ ! [SY3852: $i] :
( ~ ( function @ SY3852 )
| ~ ( relation @ SY3852 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3852 )
| ~ ( ~ ! [SY3853: $i,SY3854: $i] :
( ~ ( in @ SY3853 @ ( relation_field @ SV283 ) )
| ~ ( in @ SY3854 @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3852 @ SY3853 ) @ ( apply @ SY3852 @ SY3854 ) ) @ SV319 )
| ( in @ ( ordered_pair @ SY3853 @ SY3854 ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3687: $i] :
( ! [SY3688: $i] :
~ ( in @ ( ordered_pair @ SY3687 @ SY3688 ) @ SV283 )
| ( in @ SY3687 @ ( relation_field @ SV283 ) ) )
| ~ ! [SY3689: $i,SY3690: $i] :
( ~ ( in @ ( ordered_pair @ SY3689 @ SY3690 ) @ SV283 )
| ( in @ SY3690 @ ( relation_field @ SV283 ) ) ) )
| ~ ! [SY3859: $i,SY3860: $i] :
( ~ ( in @ ( ordered_pair @ SY3859 @ SY3860 ) @ SV283 )
| ( in @ ( ordered_pair @ ( apply @ SY3852 @ SY3859 ) @ ( apply @ SY3852 @ SY3860 ) ) @ SV319 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3861: $i] :
( ~ ( function @ SY3861 )
| ~ ( relation @ SY3861 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3861 )
| ( ( relation_dom @ SY3861 )
= ( relation_field @ SV283 ) ) )
| ~ ! [SY3862: $i] :
( ~ ( function @ SY3862 )
| ~ ( relation @ SY3862 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3862 )
| ( ( relation_rng @ SY3862 )
= ( relation_field @ SV319 ) ) ) )
| ~ ! [SY3863: $i] :
( ~ ( function @ SY3863 )
| ~ ( relation @ SY3863 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3863 )
| ( one_to_one @ SY3863 ) ) ) ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2507]) ).
thf(2589,plain,
! [SV320: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK62_B @ SV320 )
!= ( sK63_SY3125 @ SV320 ) ) )
| ~ ~ ( ~ ( in @ ( sK62_B @ SV320 ) @ ( relation_field @ SV320 ) )
| ~ ( in @ ( sK63_SY3125 @ SV320 ) @ ( relation_field @ SV320 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK62_B @ SV320 ) @ ( sK63_SY3125 @ SV320 ) ) @ SV320 ) ) )
= $false )
| ( ( connected @ SV320 )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2508]) ).
thf(2590,plain,
! [SV320: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK63_SY3125 @ SV320 ) @ ( sK62_B @ SV320 ) ) @ SV320 ) )
= $false )
| ( ( connected @ SV320 )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2508]) ).
thf(2591,plain,
! [SV321: $i,SV416: $i] :
( ( ( ! [SY4009: $i] :
( ( SV416 = SY4009 )
| ~ ( in @ SV416 @ ( relation_field @ SV321 ) )
| ~ ( in @ SY4009 @ ( relation_field @ SV321 ) )
| ( in @ ( ordered_pair @ SV416 @ SY4009 ) @ SV321 )
| ( in @ ( ordered_pair @ SY4009 @ SV416 ) @ SV321 ) ) )
= $true )
| ( ( connected @ SV321 )
= $false )
| ( ( relation @ SV321 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2509]) ).
thf(2592,plain,
! [SV284: $i,SV332: $i,SV351: $i] :
( ( ( function @ SV351 )
= $false )
| ( ( ~ ( relation @ SV351 ) )
= $true )
| ( ( ( SV332
!= ( apply @ SV351 @ SV284 ) )
| ~ ( in @ SV284 @ ( relation_dom @ SV351 ) )
| ( in @ ( ordered_pair @ SV284 @ SV332 ) @ SV351 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2510]) ).
thf(2593,plain,
! [SV402: $i,SV284: $i,SV417: $i] :
( ( ~ ( function @ SV417 )
| ~ ( relation @ SV417 )
| ~ ( in @ ( ordered_pair @ SV284 @ SV402 ) @ SV417 )
| ( SV402
= ( apply @ SV417 @ SV284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2511]) ).
thf(2594,plain,
! [SV403: $i,SV284: $i,SV418: $i] :
( ( ~ ( function @ SV418 )
| ~ ( relation @ SV418 )
| ~ ( in @ ( ordered_pair @ SV284 @ SV403 ) @ SV418 )
| ( in @ SV284 @ ( relation_dom @ SV418 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2512]) ).
thf(2595,plain,
! [SV333: $i,SV285: $i,SV352: $i] :
( ( ( ! [SY3920: $i] :
( ~ ( in @ SY3920 @ ( relation_dom @ SV352 ) )
| ~ ( in @ ( ordered_pair @ SY3920 @ SV285 ) @ SV352 )
| ~ ( in @ SY3920 @ SV333 ) ) )
= $true )
| ( ( in @ SV285 @ ( relation_image @ SV352 @ SV333 ) )
= $true )
| ( ( relation @ SV352 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2513]) ).
thf(2596,plain,
! [SV334: $i,SV353: $i,SV285: $i] :
( ( ( ~ ( in @ SV285 @ ( relation_image @ SV353 @ SV334 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK61_D @ SV353 @ SV334 @ SV285 ) @ ( relation_dom @ SV353 ) )
| ~ ( in @ ( ordered_pair @ ( sK61_D @ SV353 @ SV334 @ SV285 ) @ SV285 ) @ SV353 ) )
| ~ ( in @ ( sK61_D @ SV353 @ SV334 @ SV285 ) @ SV334 ) ) )
= $true )
| ( ( relation @ SV353 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2514]) ).
thf(2597,plain,
! [SV322: $i,SV310: $i,SV419: $i,SV286: $i] :
( ( ( ~ ( ( SV286
!= ( ordered_pair @ ( sK40_C @ SV419 @ SV286 ) @ ( sK41_SY3114 @ SV419 @ SV286 ) ) )
| ~ ( ( SV419
!= ( sK40_C @ SV419 @ SV286 ) ) ) )
| ( SV419
= ( pair_first @ SV286 ) ) )
= $true )
| ( ( SV286
= ( ordered_pair @ SV310 @ SV322 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2515]) ).
thf(2598,plain,
! [SV322: $i,SV310: $i,SV286: $i,SV420: $i] :
( ( ( ( SV420
!= ( pair_first @ SV286 ) )
| ! [SY4010: $i] :
( ! [SY3712: $i] :
( SV286
!= ( ordered_pair @ SY4010 @ SY3712 ) )
| ( SV420 = SY4010 ) ) )
= $true )
| ( ( SV286
= ( ordered_pair @ SV310 @ SV322 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2516]) ).
thf(2599,plain,
! [SV323: $i,SV311: $i,SV421: $i,SV287: $i] :
( ( ( ~ ( ( SV287
!= ( ordered_pair @ ( sK33_C @ SV421 @ SV287 ) @ ( sK34_SY3110 @ SV421 @ SV287 ) ) )
| ~ ( ( SV421
!= ( sK34_SY3110 @ SV421 @ SV287 ) ) ) )
| ( SV421
= ( pair_second @ SV287 ) ) )
= $true )
| ( ( SV287
= ( ordered_pair @ SV311 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2517]) ).
thf(2600,plain,
! [SV323: $i,SV311: $i,SV287: $i,SV422: $i] :
( ( ( ( SV422
!= ( pair_second @ SV287 ) )
| ! [SY4012: $i,SY4013: $i] :
( ( SV287
!= ( ordered_pair @ SY4012 @ SY4013 ) )
| ( SV422 = SY4013 ) ) )
= $true )
| ( ( SV287
= ( ordered_pair @ SV311 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2518]) ).
thf(2601,plain,
! [SV354: $i,SV335: $i,SV288: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV288 @ SV335 ) @ SV354 ) )
= $true )
| ( ( in @ SV288 @ ( relation_dom @ SV354 ) )
= $true )
| ( ( relation @ SV354 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2519]) ).
thf(2602,plain,
! [SV355: $i,SV336: $i,SV288: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV288 @ SV336 ) @ SV355 ) )
= $true )
| ( ( in @ SV336 @ ( relation_rng @ SV355 ) )
= $true )
| ( ( relation @ SV355 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2520]) ).
thf(2603,plain,
! [SV324: $i,SV337: $i] :
( ( ( ~ ( ( ( sK52_C @ SV337 @ SV324 )
!= ( sK53_SY3121 @ SV337 @ SV324 ) )
| ~ ( in @ ( sK52_C @ SV337 @ SV324 ) @ SV324 )
| ~ ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) )
| ~ ~ ( ~ ( ( ( sK52_C @ SV337 @ SV324 )
= ( sK53_SY3121 @ SV337 @ SV324 ) )
| ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) )
| ~ ( ( in @ ( sK52_C @ SV337 @ SV324 ) @ SV324 )
| ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) ) ) )
= $false )
| ( ( SV337
= ( identity_relation @ SV324 ) )
= $true )
| ( ( relation @ SV337 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2521]) ).
thf(2604,plain,
! [SV325: $i,SV338: $i] :
( ( ( SV338
= ( identity_relation @ SV325 ) )
= $false )
| ( ( ~ ( ~ ! [SY3895: $i,SY3896: $i] :
( ( SY3895 != SY3896 )
| ~ ( in @ SY3895 @ SV325 )
| ( in @ ( ordered_pair @ SY3895 @ SY3896 ) @ SV338 ) )
| ~ ~ ( ~ ! [SY3897: $i,SY3898: $i] :
( ~ ( in @ ( ordered_pair @ SY3897 @ SY3898 ) @ SV338 )
| ( SY3897 = SY3898 ) )
| ~ ! [SY3899: $i] :
( ! [SY3900: $i] :
~ ( in @ ( ordered_pair @ SY3899 @ SY3900 ) @ SV338 )
| ( in @ SY3899 @ SV325 ) ) ) ) )
= $true )
| ( ( relation @ SV338 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2522]) ).
thf(2605,plain,
! [SV289: $i,SV339: $i,SV356: $i] :
( ( ( ~ ( ~ ! [SY3921: $i] :
~ ( in @ ( ordered_pair @ ( sK59_D @ SV356 @ SV339 @ SV289 ) @ SY3921 ) @ SV356 )
| ~ ( in @ ( sK59_D @ SV356 @ SV339 @ SV289 ) @ SV339 ) ) )
= $true )
| ( ( ( relation_dom_as_subset @ SV339 @ SV289 @ SV356 )
= SV339 )
= $true )
| ( ( relation_of2_as_subset @ SV356 @ SV339 @ SV289 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2523]) ).
thf(2606,plain,
! [SV357: $i,SV289: $i,SV340: $i] :
( ( ( ( ( relation_dom_as_subset @ SV340 @ SV289 @ SV357 )
!= SV340 ) )
= $true )
| ( ( ! [SY3922: $i] :
( ( in @ ( ordered_pair @ SY3922 @ ( sK58_E @ SY3922 @ SV357 @ SV340 @ SV289 ) ) @ SV357 )
| ~ ( in @ SY3922 @ SV340 ) ) )
= $true )
| ( ( relation_of2_as_subset @ SV357 @ SV340 @ SV289 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2524]) ).
thf(2607,plain,
! [SV290: $i,SV380: $i] :
( ( ( ~ ( ! [SY3954: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SV380 @ SV290 ) @ SY3954 ) @ SV290 )
| ~ ( in @ ( sK22_C @ SV380 @ SV290 ) @ SV380 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SV380 @ SV290 ) @ ( sK23_SY3101 @ SV380 @ SV290 ) ) @ SV290 )
| ( in @ ( sK22_C @ SV380 @ SV290 ) @ SV380 ) ) )
= $false )
| ( ( SV380
= ( relation_dom @ SV290 ) )
= $true )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2525]) ).
thf(2608,plain,
! [SV290: $i,SV381: $i] :
( ( ( SV381
= ( relation_dom @ SV290 ) )
= $false )
| ( ( ~ ( ~ ! [SY3955: $i] :
( ! [SY3733: $i] :
~ ( in @ ( ordered_pair @ SY3955 @ SY3733 ) @ SV290 )
| ( in @ SY3955 @ SV381 ) )
| ~ ! [SY3957: $i] :
( ~ ( in @ SY3957 @ SV381 )
| ( in @ ( ordered_pair @ SY3957 @ ( sK21_D @ SY3957 @ SV381 @ SV290 ) ) @ SV290 ) ) ) )
= $true )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2526]) ).
thf(2609,plain,
! [SV291: $i,SV382: $i] :
( ( ( relation @ SV382 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV291 )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV382 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV291 )
| ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV382 ) ) )
| ( SV291 = SV382 ) )
= $true )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2527]) ).
thf(2610,plain,
! [SV291: $i,SV383: $i] :
( ( ( relation @ SV383 )
= $false )
| ( ( ( SV291 != SV383 )
| ~ ( ~ ! [SY3958: $i,SY3959: $i] :
( ~ ( in @ ( ordered_pair @ SY3958 @ SY3959 ) @ SV291 )
| ( in @ ( ordered_pair @ SY3958 @ SY3959 ) @ SV383 ) )
| ~ ! [SY3960: $i,SY3961: $i] :
( ~ ( in @ ( ordered_pair @ SY3960 @ SY3961 ) @ SV383 )
| ( in @ ( ordered_pair @ SY3960 @ SY3961 ) @ SV291 ) ) ) )
= $true )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2528]) ).
thf(2611,plain,
! [SV326: $i] :
( ( ( ~ ~ ( ~ ( in @ ( ordered_pair @ ( sK66_B @ SV326 ) @ ( sK67_SY3127 @ SV326 ) ) @ SV326 )
| ~ ( in @ ( ordered_pair @ ( sK67_SY3127 @ SV326 ) @ ( sK68_SY3129 @ SV326 ) ) @ SV326 ) ) )
= $false )
| ( ( transitive @ SV326 )
= $true )
| ( ( relation @ SV326 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2529]) ).
thf(2612,plain,
! [SV326: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK66_B @ SV326 ) @ ( sK68_SY3129 @ SV326 ) ) @ SV326 ) )
= $false )
| ( ( transitive @ SV326 )
= $true )
| ( ( relation @ SV326 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2529]) ).
thf(2613,plain,
! [SV327: $i,SV423: $i] :
( ( ( ! [SY4014: $i,SY4015: $i] :
( ~ ( in @ ( ordered_pair @ SV423 @ SY4014 ) @ SV327 )
| ~ ( in @ ( ordered_pair @ SY4014 @ SY4015 ) @ SV327 )
| ( in @ ( ordered_pair @ SV423 @ SY4015 ) @ SV327 ) ) )
= $true )
| ( ( transitive @ SV327 )
= $false )
| ( ( relation @ SV327 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2530]) ).
thf(2614,plain,
! [SV292: $i,SV384: $i] :
( ( ( relation @ SV384 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SV384 @ SV292 ) @ ( sK13_SY3095 @ SV384 @ SV292 ) ) @ SV384 )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV384 @ SV292 ) @ ( sK12_C @ SV384 @ SV292 ) ) @ SV292 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SV384 @ SV292 ) @ ( sK13_SY3095 @ SV384 @ SV292 ) ) @ SV384 )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV384 @ SV292 ) @ ( sK12_C @ SV384 @ SV292 ) ) @ SV292 ) ) )
| ( SV384
= ( relation_inverse @ SV292 ) ) )
= $true )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2531]) ).
thf(2615,plain,
! [SV292: $i,SV385: $i] :
( ( ( relation @ SV385 )
= $false )
| ( ( ( SV385
!= ( relation_inverse @ SV292 ) )
| ~ ( ~ ! [SY3962: $i,SY3963: $i] :
( ~ ( in @ ( ordered_pair @ SY3962 @ SY3963 ) @ SV385 )
| ( in @ ( ordered_pair @ SY3963 @ SY3962 ) @ SV292 ) )
| ~ ! [SY3964: $i,SY3965: $i] :
( ~ ( in @ ( ordered_pair @ SY3965 @ SY3964 ) @ SV292 )
| ( in @ ( ordered_pair @ SY3964 @ SY3965 ) @ SV385 ) ) ) )
= $true )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2532]) ).
thf(2616,plain,
! [SV293: $i] :
( ( ( ~ ! [SY3747: $i] :
( ~ ( in @ SY3747 @ ( relation_dom @ SV293 ) )
| ! [SY3748: $i] :
( ( SY3748
!= ( apply @ SV293 @ SY3747 ) )
| ( in @ ( ordered_pair @ SY3747 @ SY3748 ) @ SV293 ) ) )
| ~ ! [SY3749: $i] :
( ~ ( in @ SY3749 @ ( relation_dom @ SV293 ) )
| ! [SY3750: $i] :
( ~ ( in @ ( ordered_pair @ SY3749 @ SY3750 ) @ SV293 )
| ( SY3750
= ( apply @ SV293 @ SY3749 ) ) ) ) )
= $false )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2533]) ).
thf(2617,plain,
! [SV293: $i] :
( ( ( ~ ! [SY3751: $i] :
( ( in @ SY3751 @ ( relation_dom @ SV293 ) )
| ! [SY3752: $i] :
( ( SY3752
!= ( apply @ SV293 @ SY3751 ) )
| ( SY3752 = empty_set ) ) )
| ~ ! [SY3753: $i] :
( ( in @ SY3753 @ ( relation_dom @ SV293 ) )
| ! [SY3754: $i] :
( ( SY3754 != empty_set )
| ( SY3754
= ( apply @ SV293 @ SY3753 ) ) ) ) )
= $false )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2534]) ).
thf(2618,plain,
! [SV294: $i,SV386: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_C @ SV386 @ SV294 ) @ SV386 )
| ~ ( in @ ( sK20_SY3099 @ SV386 @ SV294 ) @ SV386 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SV386 @ SV294 ) @ ( sK20_SY3099 @ SV386 @ SV294 ) ) @ SV294 ) )
| ~ ( in @ ( ordered_pair @ ( sK20_SY3099 @ SV386 @ SV294 ) @ ( sK19_C @ SV386 @ SV294 ) ) @ SV294 ) )
| ~ ( ( ( sK19_C @ SV386 @ SV294 )
!= ( sK20_SY3099 @ SV386 @ SV294 ) ) ) )
= $false )
| ( ( is_antisymmetric_in @ SV294 @ SV386 )
= $true )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2535]) ).
thf(2619,plain,
! [SV387: $i,SV294: $i] :
( ( ( is_antisymmetric_in @ SV294 @ SV387 )
= $false )
| ( ( ! [SY3966: $i,SY3967: $i] :
( ~ ( in @ SY3966 @ SV387 )
| ~ ( in @ SY3967 @ SV387 )
| ~ ( in @ ( ordered_pair @ SY3966 @ SY3967 ) @ SV294 )
| ~ ( in @ ( ordered_pair @ SY3967 @ SY3966 ) @ SV294 )
| ( SY3966 = SY3967 ) ) )
= $true )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2536]) ).
thf(2620,plain,
! [SV295: $i,SV388: $i,SV404: $i] :
( ( ( ~ ( ~ ( ( ( sK35_D @ SV404 @ SV388 @ SV295 )
= SV388 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV388 ) @ SV295 )
| ~ ( in @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV404 ) )
| ~ ~ ( ~ ( ( ( sK35_D @ SV404 @ SV388 @ SV295 )
!= SV388 )
| ( in @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV404 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV388 ) @ SV295 )
| ( in @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV404 ) ) ) ) )
= $true )
| ( ( SV404
= ( fiber @ SV295 @ SV388 ) )
= $true )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2537]) ).
thf(2621,plain,
! [SV389: $i,SV295: $i,SV405: $i] :
( ( ( ( SV405
!= ( fiber @ SV295 @ SV389 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3994: $i] :
( ( SY3994 = SV389 )
| ~ ( in @ ( ordered_pair @ SY3994 @ SV389 ) @ SV295 )
| ( in @ SY3994 @ SV405 ) )
| ~ ~ ( ~ ! [SY3995: $i] :
( ~ ( in @ SY3995 @ SV405 )
| ( SY3995 != SV389 ) )
| ~ ! [SY3996: $i] :
( ~ ( in @ SY3996 @ SV405 )
| ( in @ ( ordered_pair @ SY3996 @ SV389 ) @ SV295 ) ) ) ) )
= $true )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2538]) ).
thf(2622,plain,
! [SV296: $i,SV307: $i,SV406: $i] :
( ( ( ~ ( relation @ SV406 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) @ SV296 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV307 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) @ SV296 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV307 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) ) ) )
| ( SV406
= ( relation_rng_restriction @ SV296 @ SV307 ) ) )
= $true )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2539]) ).
thf(2623,plain,
! [SV307: $i,SV296: $i,SV407: $i] :
( ( ( ~ ( relation @ SV407 ) )
= $true )
| ( ( ( SV407
!= ( relation_rng_restriction @ SV296 @ SV307 ) )
| ~ ( ~ ! [SY3997: $i,SY3998: $i] :
( ~ ( in @ SY3998 @ SV296 )
| ~ ( in @ ( ordered_pair @ SY3997 @ SY3998 ) @ SV307 )
| ( in @ ( ordered_pair @ SY3997 @ SY3998 ) @ SV407 ) )
| ~ ~ ( ~ ! [SY3999: $i,SY4000: $i] :
( ~ ( in @ ( ordered_pair @ SY3999 @ SY4000 ) @ SV407 )
| ( in @ SY4000 @ SV296 ) )
| ~ ! [SY4001: $i,SY4002: $i] :
( ~ ( in @ ( ordered_pair @ SY4001 @ SY4002 ) @ SV407 )
| ( in @ ( ordered_pair @ SY4001 @ SY4002 ) @ SV307 ) ) ) ) )
= $true )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2540]) ).
thf(2624,plain,
! [SV297: $i,SV390: $i] :
( ( ( ~ ( ! [SY3973: $i] :
~ ( in @ ( ordered_pair @ SY3973 @ ( sK17_C @ SV390 @ SV297 ) ) @ SV297 )
| ~ ( in @ ( sK17_C @ SV390 @ SV297 ) @ SV390 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK18_SY3098 @ SV390 @ SV297 ) @ ( sK17_C @ SV390 @ SV297 ) ) @ SV297 )
| ( in @ ( sK17_C @ SV390 @ SV297 ) @ SV390 ) ) )
= $false )
| ( ( SV390
= ( relation_rng @ SV297 ) )
= $true )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2541]) ).
thf(2625,plain,
! [SV297: $i,SV391: $i] :
( ( ( SV391
= ( relation_rng @ SV297 ) )
= $false )
| ( ( ~ ( ~ ! [SY3974: $i] :
( ! [SY3779: $i] :
~ ( in @ ( ordered_pair @ SY3779 @ SY3974 ) @ SV297 )
| ( in @ SY3974 @ SV391 ) )
| ~ ! [SY3976: $i] :
( ~ ( in @ SY3976 @ SV391 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3976 @ SV391 @ SV297 ) @ SY3976 ) @ SV297 ) ) ) )
= $true )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2542]) ).
thf(2626,plain,
! [SV358: $i,SV341: $i,SV298: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV298 @ SV341 ) @ SV358 ) )
= $true )
| ( ( in @ SV298 @ ( relation_field @ SV358 ) )
= $true )
| ( ( relation @ SV358 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2543]) ).
thf(2627,plain,
! [SV359: $i,SV342: $i,SV298: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV298 @ SV342 ) @ SV359 ) )
= $true )
| ( ( in @ SV342 @ ( relation_field @ SV359 ) )
= $true )
| ( ( relation @ SV359 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2544]) ).
thf(2628,plain,
! [SV308: $i,SV360: $i,SV299: $i,SV392: $i] :
( ( ( relation @ SV392 )
= $false )
| ( ( ~ ( in @ SV299 @ SV360 )
| ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ SV392 )
| ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SV360 ) @ SV392 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2545]) ).
thf(2629,plain,
! [SV424: $i,SV308: $i,SV299: $i] :
( ( ! [SY4016: $i] :
( ~ ( relation @ SY4016 )
| ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SV424 ) @ SY4016 ) )
| ( in @ SV299 @ SV424 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2546]) ).
thf(2630,plain,
! [SV425: $i,SV308: $i,SV299: $i] :
( ( ! [SY4017: $i] :
( ~ ( relation @ SY4017 )
| ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SV425 ) @ SY4017 ) )
| ( in @ ( ordered_pair @ SV299 @ SV308 ) @ SY4017 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2547]) ).
thf(2631,plain,
! [SV408: $i,SV361: $i,SV309: $i,SV300: $i] :
( ( ( ( ordered_pair @ SV300 @ SV309 )
= ( ordered_pair @ SV361 @ SV408 ) )
= $false )
| ( ( SV300 = SV361 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2548]) ).
thf(2632,plain,
! [SV393: $i,SV362: $i,SV309: $i,SV300: $i] :
( ( ( ( ordered_pair @ SV300 @ SV309 )
= ( ordered_pair @ SV362 @ SV393 ) )
= $false )
| ( ( SV309 = SV393 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2549]) ).
thf(2633,plain,
! [SV343: $i,SV301: $i,SV363: $i] :
( ( ( ! [SY3926: $i] :
( ~ ( in @ SY3926 @ ( relation_rng @ SV363 ) )
| ~ ( in @ ( ordered_pair @ SV301 @ SY3926 ) @ SV363 )
| ~ ( in @ SY3926 @ SV343 ) ) )
= $true )
| ( ( in @ SV301 @ ( relation_inverse_image @ SV363 @ SV343 ) )
= $true )
| ( ( relation @ SV363 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2550]) ).
thf(2634,plain,
! [SV344: $i,SV364: $i,SV301: $i] :
( ( ( ~ ( in @ SV301 @ ( relation_inverse_image @ SV364 @ SV344 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK60_D @ SV364 @ SV344 @ SV301 ) @ ( relation_rng @ SV364 ) )
| ~ ( in @ ( ordered_pair @ SV301 @ ( sK60_D @ SV364 @ SV344 @ SV301 ) ) @ SV364 ) )
| ~ ( in @ ( sK60_D @ SV364 @ SV344 @ SV301 ) @ SV344 ) ) )
= $true )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2551]) ).
thf(2635,plain,
! [SV302: $i,SV394: $i] :
( ( ( ~ ( in @ ( sK36_C @ SV394 @ SV302 ) @ SV394 )
| ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SV394 @ SV302 ) @ ( sK36_C @ SV394 @ SV302 ) ) @ SV302 ) )
= $false )
| ( ( is_reflexive_in @ SV302 @ SV394 )
= $true )
| ( ( relation @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2552]) ).
thf(2636,plain,
! [SV395: $i,SV302: $i] :
( ( ( is_reflexive_in @ SV302 @ SV395 )
= $false )
| ( ( ! [SY3977: $i] :
( ~ ( in @ SY3977 @ SV395 )
| ( in @ ( ordered_pair @ SY3977 @ SY3977 ) @ SV302 ) ) )
= $true )
| ( ( relation @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2553]) ).
thf(2637,plain,
! [SV365: $i,SV305: $i,SV345: $i,SV272: $i] :
( ( ( in @ SV272 @ SV345 )
= $false )
| ( ( ~ ( in @ SV305 @ SV365 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SV345 @ SV365 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2554]) ).
thf(2638,plain,
! [SV409: $i,SV305: $i,SV272: $i] :
( ( ( ! [SY4003: $i] :
~ ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SV409 @ SY4003 ) ) )
= $true )
| ( ( in @ SV272 @ SV409 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2555]) ).
thf(2639,plain,
! [SV426: $i,SV410: $i,SV305: $i,SV272: $i] :
( ( ~ ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SV410 @ SV426 ) )
| ( in @ SV305 @ SV426 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2556]) ).
thf(2640,plain,
! [SV366: $i,SV306: $i,SV346: $i,SV273: $i] :
( ( ( in @ SV273 @ SV346 )
= $false )
| ( ( ~ ( in @ SV306 @ SV366 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SV346 @ SV366 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2557]) ).
thf(2641,plain,
! [SV411: $i,SV306: $i,SV273: $i] :
( ( ( ! [SY4005: $i] :
~ ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SV411 @ SY4005 ) ) )
= $true )
| ( ( in @ SV273 @ SV411 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2558]) ).
thf(2642,plain,
! [SV427: $i,SV412: $i,SV306: $i,SV273: $i] :
( ( ~ ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SV412 @ SV427 ) )
| ( in @ SV306 @ SV427 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2559]) ).
thf(2643,plain,
! [SV312: $i] :
( ( ( in @ ( sK69_B @ SV312 ) @ ( relation_field @ SV312 ) )
= $true )
| ( ( reflexive @ SV312 )
= $true )
| ( ( relation @ SV312 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2560]) ).
thf(2644,plain,
! [SV312: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK69_B @ SV312 ) @ ( sK69_B @ SV312 ) ) @ SV312 ) )
= $true )
| ( ( reflexive @ SV312 )
= $true )
| ( ( relation @ SV312 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2561]) ).
thf(2645,plain,
! [SV313: $i,SV413: $i] :
( ( ( ~ ( in @ SV413 @ ( relation_field @ SV313 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV413 @ SV413 ) @ SV313 )
= $true )
| ( ( reflexive @ SV313 )
= $false )
| ( ( relation @ SV313 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2562]) ).
thf(2646,plain,
! [SV274: $i,SV367: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( ( sK14_C @ SV367 @ SV274 )
!= ( sK15_SY3096 @ SV367 @ SV274 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SV367 @ SV274 ) @ SV367 )
| ~ ( in @ ( sK15_SY3096 @ SV367 @ SV274 ) @ SV367 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK14_C @ SV367 @ SV274 ) @ ( sK15_SY3096 @ SV367 @ SV274 ) ) @ SV274 ) ) )
= $false )
| ( ( is_connected_in @ SV274 @ SV367 )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2563]) ).
thf(2647,plain,
! [SV274: $i,SV367: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK15_SY3096 @ SV367 @ SV274 ) @ ( sK14_C @ SV367 @ SV274 ) ) @ SV274 ) )
= $false )
| ( ( is_connected_in @ SV274 @ SV367 )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2563]) ).
thf(2648,plain,
! [SV274: $i,SV368: $i,SV428: $i] :
( ( ( ! [SY4018: $i] :
( ( SV428 = SY4018 )
| ~ ( in @ SV428 @ SV368 )
| ~ ( in @ SY4018 @ SV368 )
| ( in @ ( ordered_pair @ SV428 @ SY4018 ) @ SV274 )
| ( in @ ( ordered_pair @ SY4018 @ SV428 ) @ SV274 ) ) )
= $true )
| ( ( is_connected_in @ SV274 @ SV368 )
= $false )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2564]) ).
thf(2649,plain,
! [SV429: $i,SV414: $i,SV314: $i] :
( ( ( ( ( sK39_B @ SV314 )
!= ( ordered_pair @ SV414 @ SV429 ) ) )
= $true )
| ( ( relation @ SV314 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2565]) ).
thf(2650,plain,
! [SV316: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK64_B @ SV316 ) @ ( sK65_SY3126 @ SV316 ) ) @ SV316 )
| ~ ( in @ ( ordered_pair @ ( sK65_SY3126 @ SV316 ) @ ( sK64_B @ SV316 ) ) @ SV316 ) ) )
= $true )
| ( ( antisymmetric @ SV316 )
= $true )
| ( ( relation @ SV316 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2567]) ).
thf(2651,plain,
! [SV316: $i] :
( ( ( ( ( sK64_B @ SV316 )
!= ( sK65_SY3126 @ SV316 ) ) )
= $true )
| ( ( antisymmetric @ SV316 )
= $true )
| ( ( relation @ SV316 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2568]) ).
thf(2652,plain,
! [SV317: $i,SV430: $i,SV415: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV415 @ SV430 ) @ SV317 )
| ~ ( in @ ( ordered_pair @ SV430 @ SV415 ) @ SV317 )
| ( SV415 = SV430 ) )
= $true )
| ( ( antisymmetric @ SV317 )
= $false )
| ( ( relation @ SV317 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2569]) ).
thf(2653,plain,
! [SV347: $i,SV328: $i,SV275: $i] :
( ( ( ! [SY3912: $i,SY3913: $i] :
( ~ ( in @ SY3912 @ SV275 )
| ~ ( in @ SY3913 @ SV328 )
| ( ( sK28_D @ SV347 @ SV328 @ SV275 )
!= ( ordered_pair @ SY3912 @ SY3913 ) ) )
| ~ ( in @ ( sK28_D @ SV347 @ SV328 @ SV275 ) @ SV347 ) )
= $true )
| ( ( SV347
= ( cartesian_product2 @ SV275 @ SV328 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2570]) ).
thf(2654,plain,
! [SV275: $i,SV328: $i,SV347: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY3106 @ SV347 @ SV328 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK30_SY3108 @ SV347 @ SV328 @ SV275 ) @ SV328 ) )
| ( ( sK28_D @ SV347 @ SV328 @ SV275 )
!= ( ordered_pair @ ( sK29_SY3106 @ SV347 @ SV328 @ SV275 ) @ ( sK30_SY3108 @ SV347 @ SV328 @ SV275 ) ) ) )
| ( in @ ( sK28_D @ SV347 @ SV328 @ SV275 ) @ SV347 ) )
= $true )
| ( ( SV347
= ( cartesian_product2 @ SV275 @ SV328 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2571]) ).
thf(2655,plain,
! [SV348: $i,SV329: $i,SV275: $i] :
( ( ( ~ ! [SY3914: $i] :
( ! [SY3882: $i,SY3883: $i] :
( ~ ( in @ SY3882 @ SV275 )
| ~ ( in @ SY3883 @ SV329 )
| ( SY3914
!= ( ordered_pair @ SY3882 @ SY3883 ) ) )
| ( in @ SY3914 @ SV348 ) ) )
= $false )
| ( ( SV348
= ( cartesian_product2 @ SV275 @ SV329 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2572]) ).
thf(2656,plain,
! [SV275: $i,SV329: $i,SV348: $i] :
( ( ( ~ ! [SY3917: $i] :
( ~ ( in @ SY3917 @ SV348 )
| ~ ( ~ ~ ( ~ ( in @ ( sK26_E @ SY3917 @ SV348 @ SV329 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK27_SY3103 @ SY3917 @ SV348 @ SV329 @ SV275 ) @ SV329 ) )
| ( SY3917
!= ( ordered_pair @ ( sK26_E @ SY3917 @ SV348 @ SV329 @ SV275 ) @ ( sK27_SY3103 @ SY3917 @ SV348 @ SV329 @ SV275 ) ) ) ) ) )
= $false )
| ( ( SV348
= ( cartesian_product2 @ SV275 @ SV329 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2572]) ).
thf(2657,plain,
! [SV276: $i,SV370: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SV370 @ SV276 ) @ SV370 )
| ~ ( in @ ( sK4_SY3086 @ SV370 @ SV276 ) @ SV370 ) )
| ~ ( in @ ( sK5_SY3088 @ SV370 @ SV276 ) @ SV370 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SV370 @ SV276 ) @ ( sK4_SY3086 @ SV370 @ SV276 ) ) @ SV276 ) )
| ~ ( in @ ( ordered_pair @ ( sK4_SY3086 @ SV370 @ SV276 ) @ ( sK5_SY3088 @ SV370 @ SV276 ) ) @ SV276 ) ) )
= $false )
| ( ( is_transitive_in @ SV276 @ SV370 )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2573]) ).
thf(2658,plain,
! [SV276: $i,SV370: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK3_C @ SV370 @ SV276 ) @ ( sK5_SY3088 @ SV370 @ SV276 ) ) @ SV276 ) )
= $false )
| ( ( is_transitive_in @ SV276 @ SV370 )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2573]) ).
thf(2659,plain,
! [SV276: $i,SV371: $i,SV431: $i] :
( ( ( ! [SY4019: $i,SY4020: $i] :
( ~ ( in @ SV431 @ SV371 )
| ~ ( in @ SY4019 @ SV371 )
| ~ ( in @ SY4020 @ SV371 )
| ~ ( in @ ( ordered_pair @ SV431 @ SY4019 ) @ SV276 )
| ~ ( in @ ( ordered_pair @ SY4019 @ SY4020 ) @ SV276 )
| ( in @ ( ordered_pair @ SV431 @ SY4020 ) @ SV276 ) ) )
= $true )
| ( ( is_transitive_in @ SV276 @ SV371 )
= $false )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2574]) ).
thf(2660,plain,
! [SV277: $i,SV372: $i,SV396: $i] :
( ( ( ~ ( ! [SY3978: $i] :
( ~ ( in @ ( ordered_pair @ SY3978 @ ( sK46_D @ SV396 @ SV372 @ SV277 ) ) @ SV277 )
| ~ ( in @ SY3978 @ SV372 ) )
| ~ ( in @ ( sK46_D @ SV396 @ SV372 @ SV277 ) @ SV396 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SV396 @ SV372 @ SV277 ) @ ( sK46_D @ SV396 @ SV372 @ SV277 ) ) @ SV277 )
| ~ ( in @ ( sK47_SY3118 @ SV396 @ SV372 @ SV277 ) @ SV372 ) )
| ( in @ ( sK46_D @ SV396 @ SV372 @ SV277 ) @ SV396 ) ) )
= $false )
| ( ( SV396
= ( relation_image @ SV277 @ SV372 ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2575]) ).
thf(2661,plain,
! [SV373: $i,SV277: $i,SV397: $i] :
( ( ( SV397
= ( relation_image @ SV277 @ SV373 ) )
= $false )
| ( ( ~ ( ~ ! [SY3979: $i] :
( ! [SY3936: $i] :
( ~ ( in @ ( ordered_pair @ SY3936 @ SY3979 ) @ SV277 )
| ~ ( in @ SY3936 @ SV373 ) )
| ( in @ SY3979 @ SV397 ) )
| ~ ! [SY3981: $i] :
( ~ ( in @ SY3981 @ SV397 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SY3981 @ SV397 @ SV373 @ SV277 ) @ SY3981 ) @ SV277 )
| ~ ( in @ ( sK45_E @ SY3981 @ SV397 @ SV373 @ SV277 ) @ SV373 ) ) ) ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2576]) ).
thf(2662,plain,
! [SV278: $i,SV374: $i,SV398: $i] :
( ( ( relation @ SV398 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ SV374 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV278 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) )
| ~ ~ ( ~ ( ( in @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ SV374 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV278 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) ) ) )
| ( SV398
= ( relation_dom_restriction @ SV278 @ SV374 ) ) )
= $true )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2577]) ).
thf(2663,plain,
! [SV375: $i,SV278: $i,SV399: $i] :
( ( ( relation @ SV399 )
= $false )
| ( ( ( SV399
!= ( relation_dom_restriction @ SV278 @ SV375 ) )
| ~ ( ~ ! [SY3982: $i,SY3983: $i] :
( ~ ( in @ SY3982 @ SV375 )
| ~ ( in @ ( ordered_pair @ SY3982 @ SY3983 ) @ SV278 )
| ( in @ ( ordered_pair @ SY3982 @ SY3983 ) @ SV399 ) )
| ~ ~ ( ~ ! [SY3984: $i] :
( ! [SY3985: $i] :
~ ( in @ ( ordered_pair @ SY3984 @ SY3985 ) @ SV399 )
| ( in @ SY3984 @ SV375 ) )
| ~ ! [SY3986: $i,SY3987: $i] :
( ~ ( in @ ( ordered_pair @ SY3986 @ SY3987 ) @ SV399 )
| ( in @ ( ordered_pair @ SY3986 @ SY3987 ) @ SV278 ) ) ) ) )
= $true )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2578]) ).
thf(2664,plain,
! [SV279: $i,SV376: $i,SV400: $i] :
( ( ( ~ ( ! [SY3988: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SY3988 ) @ SV279 )
| ~ ( in @ SY3988 @ SV376 ) )
| ~ ( in @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SV400 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ ( sK44_SY3116 @ SV400 @ SV376 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK44_SY3116 @ SV400 @ SV376 @ SV279 ) @ SV376 ) )
| ( in @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SV400 ) ) )
= $false )
| ( ( SV400
= ( relation_inverse_image @ SV279 @ SV376 ) )
= $true )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2579]) ).
thf(2665,plain,
! [SV377: $i,SV279: $i,SV401: $i] :
( ( ( SV401
= ( relation_inverse_image @ SV279 @ SV377 ) )
= $false )
| ( ( ~ ( ~ ! [SY3989: $i] :
( ! [SY3950: $i] :
( ~ ( in @ ( ordered_pair @ SY3989 @ SY3950 ) @ SV279 )
| ~ ( in @ SY3950 @ SV377 ) )
| ( in @ SY3989 @ SV401 ) )
| ~ ! [SY3991: $i] :
( ~ ( in @ SY3991 @ SV401 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3991 @ ( sK42_E @ SY3991 @ SV401 @ SV377 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK42_E @ SY3991 @ SV401 @ SV377 @ SV279 ) @ SV377 ) ) ) ) )
= $true )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2580]) ).
thf(2666,plain,
! [SV280: $i,SV378: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV378 @ SV280 ) @ ( sK25_SY3102 @ SV378 @ SV280 ) ) @ SV280 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SV378 @ SV280 ) @ ( sK25_SY3102 @ SV378 @ SV280 ) ) @ SV378 ) ) )
= $true )
| ( ( subset @ SV280 @ SV378 )
= $true )
| ( ( relation @ SV378 )
= $false )
| ( ( relation @ SV280 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2581]) ).
thf(2667,plain,
! [SV379: $i,SV280: $i] :
( ( ( ~ ( subset @ SV280 @ SV379 ) )
= $true )
| ( ( ! [SY3952: $i,SY3953: $i] :
( ~ ( in @ ( ordered_pair @ SY3952 @ SY3953 ) @ SV280 )
| ( in @ ( ordered_pair @ SY3952 @ SY3953 ) @ SV379 ) ) )
= $true )
| ( ( relation @ SV379 )
= $false )
| ( ( relation @ SV280 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2582]) ).
thf(2668,plain,
! [SV281: $i,SV318: $i,SV432: $i] :
( ( ( ~ ( relation @ SV432 )
| ~ ( ~ ( ! [SY4021: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ SY4021 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY4021 @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV318 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV432 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK9_SY3093 @ SV432 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV318 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV432 ) ) )
| ( SV432
= ( relation_composition @ SV281 @ SV318 ) ) )
= $true )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2583]) ).
thf(2669,plain,
! [SV318: $i,SV281: $i,SV433: $i] :
( ( ( ~ ( relation @ SV433 )
| ( SV433
!= ( relation_composition @ SV281 @ SV318 ) )
| ~ ( ~ ! [SY4022: $i,SY4023: $i] :
( ! [SY3848: $i] :
( ~ ( in @ ( ordered_pair @ SY4022 @ SY3848 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY3848 @ SY4023 ) @ SV318 ) )
| ( in @ ( ordered_pair @ SY4022 @ SY4023 ) @ SV433 ) )
| ~ ! [SY4025: $i,SY4026: $i] :
( ~ ( in @ ( ordered_pair @ SY4025 @ SY4026 ) @ SV433 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4025 @ ( sK6_F @ SY4026 @ SY4025 @ SV433 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY4026 @ SY4025 @ SV433 @ SV318 @ SV281 ) @ SY4026 ) @ SV318 ) ) ) ) )
= $true )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2584]) ).
thf(2670,plain,
! [SV282: $i,SV330: $i,SV349: $i] :
( ( ( ~ ! [SY3918: $i] :
~ ( in @ ( ordered_pair @ SY3918 @ ( sK57_D @ SV349 @ SV330 @ SV282 ) ) @ SV349 )
| ~ ( in @ ( sK57_D @ SV349 @ SV330 @ SV282 ) @ SV330 ) )
= $false )
| ( ( ( relation_rng_as_subset @ SV282 @ SV330 @ SV349 )
= SV330 )
= $true )
| ( ( relation_of2_as_subset @ SV349 @ SV282 @ SV330 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2585]) ).
thf(2671,plain,
! [SV350: $i,SV331: $i,SV282: $i] :
( ( ( ( relation_rng_as_subset @ SV282 @ SV331 @ SV350 )
= SV331 )
= $false )
| ( ( ! [SY3919: $i] :
( ( in @ ( ordered_pair @ ( sK56_E @ SY3919 @ SV350 @ SV331 @ SV282 ) @ SY3919 ) @ SV350 )
| ~ ( in @ SY3919 @ SV331 ) ) )
= $true )
| ( ( relation_of2_as_subset @ SV350 @ SV282 @ SV331 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2586]) ).
thf(2672,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( ~ ( function @ SV434 )
| ~ ( relation @ SV434 )
| ~ ( ~ ( ~ ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) ) ) )
| ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 )
| ( relation_isomorphism @ SV283 @ SV319 @ SV434 ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2587]) ).
thf(2673,plain,
! [SV319: $i,SV283: $i] :
( ( ( ~ ! [SY3852: $i] :
( ~ ( function @ SY3852 )
| ~ ( relation @ SY3852 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3852 )
| ~ ( ~ ! [SY3853: $i,SY3854: $i] :
( ~ ( in @ SY3853 @ ( relation_field @ SV283 ) )
| ~ ( in @ SY3854 @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3852 @ SY3853 ) @ ( apply @ SY3852 @ SY3854 ) ) @ SV319 )
| ( in @ ( ordered_pair @ SY3853 @ SY3854 ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3687: $i] :
( ! [SY3688: $i] :
~ ( in @ ( ordered_pair @ SY3687 @ SY3688 ) @ SV283 )
| ( in @ SY3687 @ ( relation_field @ SV283 ) ) )
| ~ ! [SY3689: $i,SY3690: $i] :
( ~ ( in @ ( ordered_pair @ SY3689 @ SY3690 ) @ SV283 )
| ( in @ SY3690 @ ( relation_field @ SV283 ) ) ) )
| ~ ! [SY3859: $i,SY3860: $i] :
( ~ ( in @ ( ordered_pair @ SY3859 @ SY3860 ) @ SV283 )
| ( in @ ( ordered_pair @ ( apply @ SY3852 @ SY3859 ) @ ( apply @ SY3852 @ SY3860 ) ) @ SV319 ) ) ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3861: $i] :
( ~ ( function @ SY3861 )
| ~ ( relation @ SY3861 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3861 )
| ( ( relation_dom @ SY3861 )
= ( relation_field @ SV283 ) ) )
| ~ ! [SY3862: $i] :
( ~ ( function @ SY3862 )
| ~ ( relation @ SY3862 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3862 )
| ( ( relation_rng @ SY3862 )
= ( relation_field @ SV319 ) ) ) )
| ~ ! [SY3863: $i] :
( ~ ( function @ SY3863 )
| ~ ( relation @ SY3863 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3863 )
| ( one_to_one @ SY3863 ) ) ) )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2588]) ).
thf(2674,plain,
! [SV320: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK62_B @ SV320 )
!= ( sK63_SY3125 @ SV320 ) ) )
| ~ ~ ( ~ ( in @ ( sK62_B @ SV320 ) @ ( relation_field @ SV320 ) )
| ~ ( in @ ( sK63_SY3125 @ SV320 ) @ ( relation_field @ SV320 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK62_B @ SV320 ) @ ( sK63_SY3125 @ SV320 ) ) @ SV320 ) ) )
= $true )
| ( ( connected @ SV320 )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2589]) ).
thf(2675,plain,
! [SV320: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK63_SY3125 @ SV320 ) @ ( sK62_B @ SV320 ) ) @ SV320 ) )
= $true )
| ( ( connected @ SV320 )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2590]) ).
thf(2676,plain,
! [SV321: $i,SV435: $i,SV416: $i] :
( ( ( ( SV416 = SV435 )
| ~ ( in @ SV416 @ ( relation_field @ SV321 ) )
| ~ ( in @ SV435 @ ( relation_field @ SV321 ) )
| ( in @ ( ordered_pair @ SV416 @ SV435 ) @ SV321 )
| ( in @ ( ordered_pair @ SV435 @ SV416 ) @ SV321 ) )
= $true )
| ( ( connected @ SV321 )
= $false )
| ( ( relation @ SV321 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2591]) ).
thf(2677,plain,
! [SV284: $i,SV332: $i,SV351: $i] :
( ( ( relation @ SV351 )
= $false )
| ( ( function @ SV351 )
= $false )
| ( ( ( SV332
!= ( apply @ SV351 @ SV284 ) )
| ~ ( in @ SV284 @ ( relation_dom @ SV351 ) )
| ( in @ ( ordered_pair @ SV284 @ SV332 ) @ SV351 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2592]) ).
thf(2678,plain,
! [SV402: $i,SV284: $i,SV417: $i] :
( ( ( ~ ( function @ SV417 )
| ~ ( relation @ SV417 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV284 @ SV402 ) @ SV417 )
| ( SV402
= ( apply @ SV417 @ SV284 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2593]) ).
thf(2679,plain,
! [SV403: $i,SV284: $i,SV418: $i] :
( ( ( ~ ( function @ SV418 )
| ~ ( relation @ SV418 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV284 @ SV403 ) @ SV418 )
| ( in @ SV284 @ ( relation_dom @ SV418 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2594]) ).
thf(2680,plain,
! [SV333: $i,SV285: $i,SV352: $i,SV436: $i] :
( ( ( ~ ( in @ SV436 @ ( relation_dom @ SV352 ) )
| ~ ( in @ ( ordered_pair @ SV436 @ SV285 ) @ SV352 )
| ~ ( in @ SV436 @ SV333 ) )
= $true )
| ( ( in @ SV285 @ ( relation_image @ SV352 @ SV333 ) )
= $true )
| ( ( relation @ SV352 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2595]) ).
thf(2681,plain,
! [SV334: $i,SV353: $i,SV285: $i] :
( ( ( in @ SV285 @ ( relation_image @ SV353 @ SV334 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK61_D @ SV353 @ SV334 @ SV285 ) @ ( relation_dom @ SV353 ) )
| ~ ( in @ ( ordered_pair @ ( sK61_D @ SV353 @ SV334 @ SV285 ) @ SV285 ) @ SV353 ) )
| ~ ( in @ ( sK61_D @ SV353 @ SV334 @ SV285 ) @ SV334 ) ) )
= $true )
| ( ( relation @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2596]) ).
thf(2682,plain,
! [SV322: $i,SV310: $i,SV419: $i,SV286: $i] :
( ( ( ~ ( ( SV286
!= ( ordered_pair @ ( sK40_C @ SV419 @ SV286 ) @ ( sK41_SY3114 @ SV419 @ SV286 ) ) )
| ~ ( ( SV419
!= ( sK40_C @ SV419 @ SV286 ) ) ) ) )
= $true )
| ( ( SV419
= ( pair_first @ SV286 ) )
= $true )
| ( ( SV286
= ( ordered_pair @ SV310 @ SV322 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2597]) ).
thf(2683,plain,
! [SV322: $i,SV310: $i,SV286: $i,SV420: $i] :
( ( ( ( SV420
!= ( pair_first @ SV286 ) ) )
= $true )
| ( ( ! [SY4010: $i] :
( ! [SY3712: $i] :
( SV286
!= ( ordered_pair @ SY4010 @ SY3712 ) )
| ( SV420 = SY4010 ) ) )
= $true )
| ( ( SV286
= ( ordered_pair @ SV310 @ SV322 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2598]) ).
thf(2684,plain,
! [SV323: $i,SV311: $i,SV421: $i,SV287: $i] :
( ( ( ~ ( ( SV287
!= ( ordered_pair @ ( sK33_C @ SV421 @ SV287 ) @ ( sK34_SY3110 @ SV421 @ SV287 ) ) )
| ~ ( ( SV421
!= ( sK34_SY3110 @ SV421 @ SV287 ) ) ) ) )
= $true )
| ( ( SV421
= ( pair_second @ SV287 ) )
= $true )
| ( ( SV287
= ( ordered_pair @ SV311 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2599]) ).
thf(2685,plain,
! [SV323: $i,SV311: $i,SV287: $i,SV422: $i] :
( ( ( ( SV422
!= ( pair_second @ SV287 ) ) )
= $true )
| ( ( ! [SY4012: $i,SY4013: $i] :
( ( SV287
!= ( ordered_pair @ SY4012 @ SY4013 ) )
| ( SV422 = SY4013 ) ) )
= $true )
| ( ( SV287
= ( ordered_pair @ SV311 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2600]) ).
thf(2686,plain,
! [SV354: $i,SV335: $i,SV288: $i] :
( ( ( in @ ( ordered_pair @ SV288 @ SV335 ) @ SV354 )
= $false )
| ( ( in @ SV288 @ ( relation_dom @ SV354 ) )
= $true )
| ( ( relation @ SV354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2601]) ).
thf(2687,plain,
! [SV355: $i,SV336: $i,SV288: $i] :
( ( ( in @ ( ordered_pair @ SV288 @ SV336 ) @ SV355 )
= $false )
| ( ( in @ SV336 @ ( relation_rng @ SV355 ) )
= $true )
| ( ( relation @ SV355 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2602]) ).
thf(2688,plain,
! [SV324: $i,SV337: $i] :
( ( ( ~ ( ( ( sK52_C @ SV337 @ SV324 )
!= ( sK53_SY3121 @ SV337 @ SV324 ) )
| ~ ( in @ ( sK52_C @ SV337 @ SV324 ) @ SV324 )
| ~ ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) ) )
= $false )
| ( ( SV337
= ( identity_relation @ SV324 ) )
= $true )
| ( ( relation @ SV337 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2603]) ).
thf(2689,plain,
! [SV324: $i,SV337: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK52_C @ SV337 @ SV324 )
= ( sK53_SY3121 @ SV337 @ SV324 ) )
| ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) )
| ~ ( ( in @ ( sK52_C @ SV337 @ SV324 ) @ SV324 )
| ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) ) ) )
= $false )
| ( ( SV337
= ( identity_relation @ SV324 ) )
= $true )
| ( ( relation @ SV337 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2603]) ).
thf(2690,plain,
! [SV338: $i,SV325: $i] :
( ( ( ~ ! [SY3895: $i,SY3896: $i] :
( ( SY3895 != SY3896 )
| ~ ( in @ SY3895 @ SV325 )
| ( in @ ( ordered_pair @ SY3895 @ SY3896 ) @ SV338 ) )
| ~ ~ ( ~ ! [SY3897: $i,SY3898: $i] :
( ~ ( in @ ( ordered_pair @ SY3897 @ SY3898 ) @ SV338 )
| ( SY3897 = SY3898 ) )
| ~ ! [SY3899: $i] :
( ! [SY3900: $i] :
~ ( in @ ( ordered_pair @ SY3899 @ SY3900 ) @ SV338 )
| ( in @ SY3899 @ SV325 ) ) ) )
= $false )
| ( ( SV338
= ( identity_relation @ SV325 ) )
= $false )
| ( ( relation @ SV338 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2604]) ).
thf(2691,plain,
! [SV289: $i,SV339: $i,SV356: $i] :
( ( ( ~ ! [SY3921: $i] :
~ ( in @ ( ordered_pair @ ( sK59_D @ SV356 @ SV339 @ SV289 ) @ SY3921 ) @ SV356 )
| ~ ( in @ ( sK59_D @ SV356 @ SV339 @ SV289 ) @ SV339 ) )
= $false )
| ( ( ( relation_dom_as_subset @ SV339 @ SV289 @ SV356 )
= SV339 )
= $true )
| ( ( relation_of2_as_subset @ SV356 @ SV339 @ SV289 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2605]) ).
thf(2692,plain,
! [SV357: $i,SV289: $i,SV340: $i] :
( ( ( ( relation_dom_as_subset @ SV340 @ SV289 @ SV357 )
= SV340 )
= $false )
| ( ( ! [SY3922: $i] :
( ( in @ ( ordered_pair @ SY3922 @ ( sK58_E @ SY3922 @ SV357 @ SV340 @ SV289 ) ) @ SV357 )
| ~ ( in @ SY3922 @ SV340 ) ) )
= $true )
| ( ( relation_of2_as_subset @ SV357 @ SV340 @ SV289 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2606]) ).
thf(2693,plain,
! [SV290: $i,SV380: $i] :
( ( ( ~ ( ! [SY3954: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SV380 @ SV290 ) @ SY3954 ) @ SV290 )
| ~ ( in @ ( sK22_C @ SV380 @ SV290 ) @ SV380 ) ) )
= $false )
| ( ( SV380
= ( relation_dom @ SV290 ) )
= $true )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2607]) ).
thf(2694,plain,
! [SV290: $i,SV380: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK22_C @ SV380 @ SV290 ) @ ( sK23_SY3101 @ SV380 @ SV290 ) ) @ SV290 )
| ( in @ ( sK22_C @ SV380 @ SV290 ) @ SV380 ) ) )
= $false )
| ( ( SV380
= ( relation_dom @ SV290 ) )
= $true )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2607]) ).
thf(2695,plain,
! [SV381: $i,SV290: $i] :
( ( ( ~ ! [SY3955: $i] :
( ! [SY3733: $i] :
~ ( in @ ( ordered_pair @ SY3955 @ SY3733 ) @ SV290 )
| ( in @ SY3955 @ SV381 ) )
| ~ ! [SY3957: $i] :
( ~ ( in @ SY3957 @ SV381 )
| ( in @ ( ordered_pair @ SY3957 @ ( sK21_D @ SY3957 @ SV381 @ SV290 ) ) @ SV290 ) ) )
= $false )
| ( ( SV381
= ( relation_dom @ SV290 ) )
= $false )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2608]) ).
thf(2696,plain,
! [SV291: $i,SV382: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV291 )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV382 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV291 )
| ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV382 ) ) ) )
= $true )
| ( ( SV291 = SV382 )
= $true )
| ( ( relation @ SV382 )
= $false )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2609]) ).
thf(2697,plain,
! [SV383: $i,SV291: $i] :
( ( ( ( SV291 != SV383 ) )
= $true )
| ( ( ~ ( ~ ! [SY3958: $i,SY3959: $i] :
( ~ ( in @ ( ordered_pair @ SY3958 @ SY3959 ) @ SV291 )
| ( in @ ( ordered_pair @ SY3958 @ SY3959 ) @ SV383 ) )
| ~ ! [SY3960: $i,SY3961: $i] :
( ~ ( in @ ( ordered_pair @ SY3960 @ SY3961 ) @ SV383 )
| ( in @ ( ordered_pair @ SY3960 @ SY3961 ) @ SV291 ) ) ) )
= $true )
| ( ( relation @ SV383 )
= $false )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2610]) ).
thf(2698,plain,
! [SV326: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK66_B @ SV326 ) @ ( sK67_SY3127 @ SV326 ) ) @ SV326 )
| ~ ( in @ ( ordered_pair @ ( sK67_SY3127 @ SV326 ) @ ( sK68_SY3129 @ SV326 ) ) @ SV326 ) ) )
= $true )
| ( ( transitive @ SV326 )
= $true )
| ( ( relation @ SV326 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2611]) ).
thf(2699,plain,
! [SV326: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK66_B @ SV326 ) @ ( sK68_SY3129 @ SV326 ) ) @ SV326 ) )
= $true )
| ( ( transitive @ SV326 )
= $true )
| ( ( relation @ SV326 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2612]) ).
thf(2700,plain,
! [SV327: $i,SV437: $i,SV423: $i] :
( ( ( ! [SY4027: $i] :
( ~ ( in @ ( ordered_pair @ SV423 @ SV437 ) @ SV327 )
| ~ ( in @ ( ordered_pair @ SV437 @ SY4027 ) @ SV327 )
| ( in @ ( ordered_pair @ SV423 @ SY4027 ) @ SV327 ) ) )
= $true )
| ( ( transitive @ SV327 )
= $false )
| ( ( relation @ SV327 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2613]) ).
thf(2701,plain,
! [SV292: $i,SV384: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SV384 @ SV292 ) @ ( sK13_SY3095 @ SV384 @ SV292 ) ) @ SV384 )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV384 @ SV292 ) @ ( sK12_C @ SV384 @ SV292 ) ) @ SV292 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SV384 @ SV292 ) @ ( sK13_SY3095 @ SV384 @ SV292 ) ) @ SV384 )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV384 @ SV292 ) @ ( sK12_C @ SV384 @ SV292 ) ) @ SV292 ) ) ) )
= $true )
| ( ( SV384
= ( relation_inverse @ SV292 ) )
= $true )
| ( ( relation @ SV384 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2614]) ).
thf(2702,plain,
! [SV292: $i,SV385: $i] :
( ( ( ( SV385
!= ( relation_inverse @ SV292 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3962: $i,SY3963: $i] :
( ~ ( in @ ( ordered_pair @ SY3962 @ SY3963 ) @ SV385 )
| ( in @ ( ordered_pair @ SY3963 @ SY3962 ) @ SV292 ) )
| ~ ! [SY3964: $i,SY3965: $i] :
( ~ ( in @ ( ordered_pair @ SY3965 @ SY3964 ) @ SV292 )
| ( in @ ( ordered_pair @ SY3964 @ SY3965 ) @ SV385 ) ) ) )
= $true )
| ( ( relation @ SV385 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2615]) ).
thf(2703,plain,
! [SV293: $i] :
( ( ( ~ ! [SY3747: $i] :
( ~ ( in @ SY3747 @ ( relation_dom @ SV293 ) )
| ! [SY3748: $i] :
( ( SY3748
!= ( apply @ SV293 @ SY3747 ) )
| ( in @ ( ordered_pair @ SY3747 @ SY3748 ) @ SV293 ) ) ) )
= $false )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2616]) ).
thf(2704,plain,
! [SV293: $i] :
( ( ( ~ ! [SY3749: $i] :
( ~ ( in @ SY3749 @ ( relation_dom @ SV293 ) )
| ! [SY3750: $i] :
( ~ ( in @ ( ordered_pair @ SY3749 @ SY3750 ) @ SV293 )
| ( SY3750
= ( apply @ SV293 @ SY3749 ) ) ) ) )
= $false )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2616]) ).
thf(2705,plain,
! [SV293: $i] :
( ( ( ~ ! [SY3751: $i] :
( ( in @ SY3751 @ ( relation_dom @ SV293 ) )
| ! [SY3752: $i] :
( ( SY3752
!= ( apply @ SV293 @ SY3751 ) )
| ( SY3752 = empty_set ) ) ) )
= $false )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2617]) ).
thf(2706,plain,
! [SV293: $i] :
( ( ( ~ ! [SY3753: $i] :
( ( in @ SY3753 @ ( relation_dom @ SV293 ) )
| ! [SY3754: $i] :
( ( SY3754 != empty_set )
| ( SY3754
= ( apply @ SV293 @ SY3753 ) ) ) ) )
= $false )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2617]) ).
thf(2707,plain,
! [SV294: $i,SV386: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_C @ SV386 @ SV294 ) @ SV386 )
| ~ ( in @ ( sK20_SY3099 @ SV386 @ SV294 ) @ SV386 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SV386 @ SV294 ) @ ( sK20_SY3099 @ SV386 @ SV294 ) ) @ SV294 ) )
| ~ ( in @ ( ordered_pair @ ( sK20_SY3099 @ SV386 @ SV294 ) @ ( sK19_C @ SV386 @ SV294 ) ) @ SV294 ) ) )
= $false )
| ( ( is_antisymmetric_in @ SV294 @ SV386 )
= $true )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2618]) ).
thf(2708,plain,
! [SV294: $i,SV386: $i] :
( ( ( ~ ( ( ( sK19_C @ SV386 @ SV294 )
!= ( sK20_SY3099 @ SV386 @ SV294 ) ) ) )
= $false )
| ( ( is_antisymmetric_in @ SV294 @ SV386 )
= $true )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2618]) ).
thf(2709,plain,
! [SV294: $i,SV387: $i,SV438: $i] :
( ( ( ! [SY4028: $i] :
( ~ ( in @ SV438 @ SV387 )
| ~ ( in @ SY4028 @ SV387 )
| ~ ( in @ ( ordered_pair @ SV438 @ SY4028 ) @ SV294 )
| ~ ( in @ ( ordered_pair @ SY4028 @ SV438 ) @ SV294 )
| ( SV438 = SY4028 ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV294 @ SV387 )
= $false )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2619]) ).
thf(2710,plain,
! [SV295: $i,SV388: $i,SV404: $i] :
( ( ( ~ ( ( ( sK35_D @ SV404 @ SV388 @ SV295 )
= SV388 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV388 ) @ SV295 )
| ~ ( in @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV404 ) )
| ~ ~ ( ~ ( ( ( sK35_D @ SV404 @ SV388 @ SV295 )
!= SV388 )
| ( in @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV404 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV388 ) @ SV295 )
| ( in @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV404 ) ) ) )
= $false )
| ( ( SV404
= ( fiber @ SV295 @ SV388 ) )
= $true )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2620]) ).
thf(2711,plain,
! [SV389: $i,SV295: $i,SV405: $i] :
( ( ( SV405
= ( fiber @ SV295 @ SV389 ) )
= $false )
| ( ( ~ ( ~ ! [SY3994: $i] :
( ( SY3994 = SV389 )
| ~ ( in @ ( ordered_pair @ SY3994 @ SV389 ) @ SV295 )
| ( in @ SY3994 @ SV405 ) )
| ~ ~ ( ~ ! [SY3995: $i] :
( ~ ( in @ SY3995 @ SV405 )
| ( SY3995 != SV389 ) )
| ~ ! [SY3996: $i] :
( ~ ( in @ SY3996 @ SV405 )
| ( in @ ( ordered_pair @ SY3996 @ SV389 ) @ SV295 ) ) ) ) )
= $true )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2621]) ).
thf(2712,plain,
! [SV296: $i,SV307: $i,SV406: $i] :
( ( ( relation @ SV406 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) @ SV296 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV307 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) @ SV296 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV307 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) ) ) )
| ( SV406
= ( relation_rng_restriction @ SV296 @ SV307 ) ) )
= $true )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2622]) ).
thf(2713,plain,
! [SV307: $i,SV296: $i,SV407: $i] :
( ( ( relation @ SV407 )
= $false )
| ( ( ( SV407
!= ( relation_rng_restriction @ SV296 @ SV307 ) )
| ~ ( ~ ! [SY3997: $i,SY3998: $i] :
( ~ ( in @ SY3998 @ SV296 )
| ~ ( in @ ( ordered_pair @ SY3997 @ SY3998 ) @ SV307 )
| ( in @ ( ordered_pair @ SY3997 @ SY3998 ) @ SV407 ) )
| ~ ~ ( ~ ! [SY3999: $i,SY4000: $i] :
( ~ ( in @ ( ordered_pair @ SY3999 @ SY4000 ) @ SV407 )
| ( in @ SY4000 @ SV296 ) )
| ~ ! [SY4001: $i,SY4002: $i] :
( ~ ( in @ ( ordered_pair @ SY4001 @ SY4002 ) @ SV407 )
| ( in @ ( ordered_pair @ SY4001 @ SY4002 ) @ SV307 ) ) ) ) )
= $true )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2623]) ).
thf(2714,plain,
! [SV297: $i,SV390: $i] :
( ( ( ~ ( ! [SY3973: $i] :
~ ( in @ ( ordered_pair @ SY3973 @ ( sK17_C @ SV390 @ SV297 ) ) @ SV297 )
| ~ ( in @ ( sK17_C @ SV390 @ SV297 ) @ SV390 ) ) )
= $false )
| ( ( SV390
= ( relation_rng @ SV297 ) )
= $true )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2624]) ).
thf(2715,plain,
! [SV297: $i,SV390: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK18_SY3098 @ SV390 @ SV297 ) @ ( sK17_C @ SV390 @ SV297 ) ) @ SV297 )
| ( in @ ( sK17_C @ SV390 @ SV297 ) @ SV390 ) ) )
= $false )
| ( ( SV390
= ( relation_rng @ SV297 ) )
= $true )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2624]) ).
thf(2716,plain,
! [SV391: $i,SV297: $i] :
( ( ( ~ ! [SY3974: $i] :
( ! [SY3779: $i] :
~ ( in @ ( ordered_pair @ SY3779 @ SY3974 ) @ SV297 )
| ( in @ SY3974 @ SV391 ) )
| ~ ! [SY3976: $i] :
( ~ ( in @ SY3976 @ SV391 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3976 @ SV391 @ SV297 ) @ SY3976 ) @ SV297 ) ) )
= $false )
| ( ( SV391
= ( relation_rng @ SV297 ) )
= $false )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2625]) ).
thf(2717,plain,
! [SV358: $i,SV341: $i,SV298: $i] :
( ( ( in @ ( ordered_pair @ SV298 @ SV341 ) @ SV358 )
= $false )
| ( ( in @ SV298 @ ( relation_field @ SV358 ) )
= $true )
| ( ( relation @ SV358 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2626]) ).
thf(2718,plain,
! [SV359: $i,SV342: $i,SV298: $i] :
( ( ( in @ ( ordered_pair @ SV298 @ SV342 ) @ SV359 )
= $false )
| ( ( in @ SV342 @ ( relation_field @ SV359 ) )
= $true )
| ( ( relation @ SV359 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2627]) ).
thf(2719,plain,
! [SV392: $i,SV308: $i,SV360: $i,SV299: $i] :
( ( ( ~ ( in @ SV299 @ SV360 )
| ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ SV392 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SV360 ) @ SV392 ) )
= $true )
| ( ( relation @ SV392 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2628]) ).
thf(2720,plain,
! [SV424: $i,SV308: $i,SV299: $i,SV439: $i] :
( ( ~ ( relation @ SV439 )
| ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SV424 ) @ SV439 ) )
| ( in @ SV299 @ SV424 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2629]) ).
thf(2721,plain,
! [SV425: $i,SV308: $i,SV299: $i,SV440: $i] :
( ( ~ ( relation @ SV440 )
| ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SV425 ) @ SV440 ) )
| ( in @ ( ordered_pair @ SV299 @ SV308 ) @ SV440 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2630]) ).
thf(2722,plain,
! [SV343: $i,SV301: $i,SV363: $i,SV441: $i] :
( ( ( ~ ( in @ SV441 @ ( relation_rng @ SV363 ) )
| ~ ( in @ ( ordered_pair @ SV301 @ SV441 ) @ SV363 )
| ~ ( in @ SV441 @ SV343 ) )
= $true )
| ( ( in @ SV301 @ ( relation_inverse_image @ SV363 @ SV343 ) )
= $true )
| ( ( relation @ SV363 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2633]) ).
thf(2723,plain,
! [SV344: $i,SV364: $i,SV301: $i] :
( ( ( in @ SV301 @ ( relation_inverse_image @ SV364 @ SV344 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK60_D @ SV364 @ SV344 @ SV301 ) @ ( relation_rng @ SV364 ) )
| ~ ( in @ ( ordered_pair @ SV301 @ ( sK60_D @ SV364 @ SV344 @ SV301 ) ) @ SV364 ) )
| ~ ( in @ ( sK60_D @ SV364 @ SV344 @ SV301 ) @ SV344 ) ) )
= $true )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2634]) ).
thf(2724,plain,
! [SV302: $i,SV394: $i] :
( ( ( ~ ( in @ ( sK36_C @ SV394 @ SV302 ) @ SV394 ) )
= $false )
| ( ( is_reflexive_in @ SV302 @ SV394 )
= $true )
| ( ( relation @ SV302 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2635]) ).
thf(2725,plain,
! [SV302: $i,SV394: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK36_C @ SV394 @ SV302 ) @ ( sK36_C @ SV394 @ SV302 ) ) @ SV302 ) )
= $false )
| ( ( is_reflexive_in @ SV302 @ SV394 )
= $true )
| ( ( relation @ SV302 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2635]) ).
thf(2726,plain,
! [SV302: $i,SV395: $i,SV442: $i] :
( ( ( ~ ( in @ SV442 @ SV395 )
| ( in @ ( ordered_pair @ SV442 @ SV442 ) @ SV302 ) )
= $true )
| ( ( is_reflexive_in @ SV302 @ SV395 )
= $false )
| ( ( relation @ SV302 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2636]) ).
thf(2727,plain,
! [SV345: $i,SV272: $i,SV365: $i,SV305: $i] :
( ( ( in @ SV305 @ SV365 )
= $false )
| ( ( in @ SV272 @ SV345 )
= $false )
| ( ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SV345 @ SV365 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2637]) ).
thf(2728,plain,
! [SV443: $i,SV409: $i,SV305: $i,SV272: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SV409 @ SV443 ) ) )
= $true )
| ( ( in @ SV272 @ SV409 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2638]) ).
thf(2729,plain,
! [SV426: $i,SV410: $i,SV305: $i,SV272: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SV410 @ SV426 ) ) )
= $true )
| ( ( in @ SV305 @ SV426 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2639]) ).
thf(2730,plain,
! [SV346: $i,SV273: $i,SV366: $i,SV306: $i] :
( ( ( in @ SV306 @ SV366 )
= $false )
| ( ( in @ SV273 @ SV346 )
= $false )
| ( ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SV346 @ SV366 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2640]) ).
thf(2731,plain,
! [SV444: $i,SV411: $i,SV306: $i,SV273: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SV411 @ SV444 ) ) )
= $true )
| ( ( in @ SV273 @ SV411 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2641]) ).
thf(2732,plain,
! [SV427: $i,SV412: $i,SV306: $i,SV273: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SV412 @ SV427 ) ) )
= $true )
| ( ( in @ SV306 @ SV427 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2642]) ).
thf(2733,plain,
! [SV312: $i] :
( ( ( in @ ( ordered_pair @ ( sK69_B @ SV312 ) @ ( sK69_B @ SV312 ) ) @ SV312 )
= $false )
| ( ( reflexive @ SV312 )
= $true )
| ( ( relation @ SV312 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2644]) ).
thf(2734,plain,
! [SV313: $i,SV413: $i] :
( ( ( in @ SV413 @ ( relation_field @ SV313 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV413 @ SV413 ) @ SV313 )
= $true )
| ( ( reflexive @ SV313 )
= $false )
| ( ( relation @ SV313 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2645]) ).
thf(2735,plain,
! [SV274: $i,SV367: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( ( sK14_C @ SV367 @ SV274 )
!= ( sK15_SY3096 @ SV367 @ SV274 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SV367 @ SV274 ) @ SV367 )
| ~ ( in @ ( sK15_SY3096 @ SV367 @ SV274 ) @ SV367 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK14_C @ SV367 @ SV274 ) @ ( sK15_SY3096 @ SV367 @ SV274 ) ) @ SV274 ) ) )
= $true )
| ( ( is_connected_in @ SV274 @ SV367 )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2646]) ).
thf(2736,plain,
! [SV274: $i,SV367: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK15_SY3096 @ SV367 @ SV274 ) @ ( sK14_C @ SV367 @ SV274 ) ) @ SV274 ) )
= $true )
| ( ( is_connected_in @ SV274 @ SV367 )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2647]) ).
thf(2737,plain,
! [SV274: $i,SV368: $i,SV445: $i,SV428: $i] :
( ( ( ( SV428 = SV445 )
| ~ ( in @ SV428 @ SV368 )
| ~ ( in @ SV445 @ SV368 )
| ( in @ ( ordered_pair @ SV428 @ SV445 ) @ SV274 )
| ( in @ ( ordered_pair @ SV445 @ SV428 ) @ SV274 ) )
= $true )
| ( ( is_connected_in @ SV274 @ SV368 )
= $false )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2648]) ).
thf(2738,plain,
! [SV429: $i,SV414: $i,SV314: $i] :
( ( ( ( sK39_B @ SV314 )
= ( ordered_pair @ SV414 @ SV429 ) )
= $false )
| ( ( relation @ SV314 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2649]) ).
thf(2739,plain,
! [SV316: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK64_B @ SV316 ) @ ( sK65_SY3126 @ SV316 ) ) @ SV316 )
| ~ ( in @ ( ordered_pair @ ( sK65_SY3126 @ SV316 ) @ ( sK64_B @ SV316 ) ) @ SV316 ) )
= $false )
| ( ( antisymmetric @ SV316 )
= $true )
| ( ( relation @ SV316 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2650]) ).
thf(2740,plain,
! [SV316: $i] :
( ( ( ( sK64_B @ SV316 )
= ( sK65_SY3126 @ SV316 ) )
= $false )
| ( ( antisymmetric @ SV316 )
= $true )
| ( ( relation @ SV316 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2651]) ).
thf(2741,plain,
! [SV317: $i,SV430: $i,SV415: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV415 @ SV430 ) @ SV317 )
| ~ ( in @ ( ordered_pair @ SV430 @ SV415 ) @ SV317 ) )
= $true )
| ( ( SV415 = SV430 )
= $true )
| ( ( antisymmetric @ SV317 )
= $false )
| ( ( relation @ SV317 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2652]) ).
thf(2742,plain,
! [SV347: $i,SV328: $i,SV275: $i] :
( ( ( ! [SY3912: $i,SY3913: $i] :
( ~ ( in @ SY3912 @ SV275 )
| ~ ( in @ SY3913 @ SV328 )
| ( ( sK28_D @ SV347 @ SV328 @ SV275 )
!= ( ordered_pair @ SY3912 @ SY3913 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK28_D @ SV347 @ SV328 @ SV275 ) @ SV347 ) )
= $true )
| ( ( SV347
= ( cartesian_product2 @ SV275 @ SV328 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2653]) ).
thf(2743,plain,
! [SV275: $i,SV328: $i,SV347: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK29_SY3106 @ SV347 @ SV328 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK30_SY3108 @ SV347 @ SV328 @ SV275 ) @ SV328 ) )
| ( ( sK28_D @ SV347 @ SV328 @ SV275 )
!= ( ordered_pair @ ( sK29_SY3106 @ SV347 @ SV328 @ SV275 ) @ ( sK30_SY3108 @ SV347 @ SV328 @ SV275 ) ) ) ) )
= $true )
| ( ( in @ ( sK28_D @ SV347 @ SV328 @ SV275 ) @ SV347 )
= $true )
| ( ( SV347
= ( cartesian_product2 @ SV275 @ SV328 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2654]) ).
thf(2744,plain,
! [SV348: $i,SV329: $i,SV275: $i] :
( ( ( ! [SY3914: $i] :
( ! [SY3882: $i,SY3883: $i] :
( ~ ( in @ SY3882 @ SV275 )
| ~ ( in @ SY3883 @ SV329 )
| ( SY3914
!= ( ordered_pair @ SY3882 @ SY3883 ) ) )
| ( in @ SY3914 @ SV348 ) ) )
= $true )
| ( ( SV348
= ( cartesian_product2 @ SV275 @ SV329 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2655]) ).
thf(2745,plain,
! [SV275: $i,SV329: $i,SV348: $i] :
( ( ( ! [SY3917: $i] :
( ~ ( in @ SY3917 @ SV348 )
| ~ ( ~ ~ ( ~ ( in @ ( sK26_E @ SY3917 @ SV348 @ SV329 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK27_SY3103 @ SY3917 @ SV348 @ SV329 @ SV275 ) @ SV329 ) )
| ( SY3917
!= ( ordered_pair @ ( sK26_E @ SY3917 @ SV348 @ SV329 @ SV275 ) @ ( sK27_SY3103 @ SY3917 @ SV348 @ SV329 @ SV275 ) ) ) ) ) )
= $true )
| ( ( SV348
= ( cartesian_product2 @ SV275 @ SV329 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2656]) ).
thf(2746,plain,
! [SV276: $i,SV370: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SV370 @ SV276 ) @ SV370 )
| ~ ( in @ ( sK4_SY3086 @ SV370 @ SV276 ) @ SV370 ) )
| ~ ( in @ ( sK5_SY3088 @ SV370 @ SV276 ) @ SV370 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SV370 @ SV276 ) @ ( sK4_SY3086 @ SV370 @ SV276 ) ) @ SV276 ) )
| ~ ( in @ ( ordered_pair @ ( sK4_SY3086 @ SV370 @ SV276 ) @ ( sK5_SY3088 @ SV370 @ SV276 ) ) @ SV276 ) ) )
= $true )
| ( ( is_transitive_in @ SV276 @ SV370 )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2657]) ).
thf(2747,plain,
! [SV276: $i,SV370: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK3_C @ SV370 @ SV276 ) @ ( sK5_SY3088 @ SV370 @ SV276 ) ) @ SV276 ) )
= $true )
| ( ( is_transitive_in @ SV276 @ SV370 )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2658]) ).
thf(2748,plain,
! [SV276: $i,SV446: $i,SV371: $i,SV431: $i] :
( ( ( ! [SY4029: $i] :
( ~ ( in @ SV431 @ SV371 )
| ~ ( in @ SV446 @ SV371 )
| ~ ( in @ SY4029 @ SV371 )
| ~ ( in @ ( ordered_pair @ SV431 @ SV446 ) @ SV276 )
| ~ ( in @ ( ordered_pair @ SV446 @ SY4029 ) @ SV276 )
| ( in @ ( ordered_pair @ SV431 @ SY4029 ) @ SV276 ) ) )
= $true )
| ( ( is_transitive_in @ SV276 @ SV371 )
= $false )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2659]) ).
thf(2749,plain,
! [SV277: $i,SV372: $i,SV396: $i] :
( ( ( ~ ( ! [SY3978: $i] :
( ~ ( in @ ( ordered_pair @ SY3978 @ ( sK46_D @ SV396 @ SV372 @ SV277 ) ) @ SV277 )
| ~ ( in @ SY3978 @ SV372 ) )
| ~ ( in @ ( sK46_D @ SV396 @ SV372 @ SV277 ) @ SV396 ) ) )
= $false )
| ( ( SV396
= ( relation_image @ SV277 @ SV372 ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2660]) ).
thf(2750,plain,
! [SV277: $i,SV372: $i,SV396: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SV396 @ SV372 @ SV277 ) @ ( sK46_D @ SV396 @ SV372 @ SV277 ) ) @ SV277 )
| ~ ( in @ ( sK47_SY3118 @ SV396 @ SV372 @ SV277 ) @ SV372 ) )
| ( in @ ( sK46_D @ SV396 @ SV372 @ SV277 ) @ SV396 ) ) )
= $false )
| ( ( SV396
= ( relation_image @ SV277 @ SV372 ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2660]) ).
thf(2751,plain,
! [SV397: $i,SV373: $i,SV277: $i] :
( ( ( ~ ! [SY3979: $i] :
( ! [SY3936: $i] :
( ~ ( in @ ( ordered_pair @ SY3936 @ SY3979 ) @ SV277 )
| ~ ( in @ SY3936 @ SV373 ) )
| ( in @ SY3979 @ SV397 ) )
| ~ ! [SY3981: $i] :
( ~ ( in @ SY3981 @ SV397 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SY3981 @ SV397 @ SV373 @ SV277 ) @ SY3981 ) @ SV277 )
| ~ ( in @ ( sK45_E @ SY3981 @ SV397 @ SV373 @ SV277 ) @ SV373 ) ) ) )
= $false )
| ( ( SV397
= ( relation_image @ SV277 @ SV373 ) )
= $false )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2661]) ).
thf(2752,plain,
! [SV278: $i,SV374: $i,SV398: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ SV374 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV278 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) )
| ~ ~ ( ~ ( ( in @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ SV374 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV278 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) ) ) ) )
= $true )
| ( ( SV398
= ( relation_dom_restriction @ SV278 @ SV374 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2662]) ).
thf(2753,plain,
! [SV375: $i,SV278: $i,SV399: $i] :
( ( ( ( SV399
!= ( relation_dom_restriction @ SV278 @ SV375 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3982: $i,SY3983: $i] :
( ~ ( in @ SY3982 @ SV375 )
| ~ ( in @ ( ordered_pair @ SY3982 @ SY3983 ) @ SV278 )
| ( in @ ( ordered_pair @ SY3982 @ SY3983 ) @ SV399 ) )
| ~ ~ ( ~ ! [SY3984: $i] :
( ! [SY3985: $i] :
~ ( in @ ( ordered_pair @ SY3984 @ SY3985 ) @ SV399 )
| ( in @ SY3984 @ SV375 ) )
| ~ ! [SY3986: $i,SY3987: $i] :
( ~ ( in @ ( ordered_pair @ SY3986 @ SY3987 ) @ SV399 )
| ( in @ ( ordered_pair @ SY3986 @ SY3987 ) @ SV278 ) ) ) ) )
= $true )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2663]) ).
thf(2754,plain,
! [SV279: $i,SV376: $i,SV400: $i] :
( ( ( ~ ( ! [SY3988: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SY3988 ) @ SV279 )
| ~ ( in @ SY3988 @ SV376 ) )
| ~ ( in @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SV400 ) ) )
= $false )
| ( ( SV400
= ( relation_inverse_image @ SV279 @ SV376 ) )
= $true )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2664]) ).
thf(2755,plain,
! [SV279: $i,SV376: $i,SV400: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ ( sK44_SY3116 @ SV400 @ SV376 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK44_SY3116 @ SV400 @ SV376 @ SV279 ) @ SV376 ) )
| ( in @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SV400 ) ) )
= $false )
| ( ( SV400
= ( relation_inverse_image @ SV279 @ SV376 ) )
= $true )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2664]) ).
thf(2756,plain,
! [SV401: $i,SV377: $i,SV279: $i] :
( ( ( ~ ! [SY3989: $i] :
( ! [SY3950: $i] :
( ~ ( in @ ( ordered_pair @ SY3989 @ SY3950 ) @ SV279 )
| ~ ( in @ SY3950 @ SV377 ) )
| ( in @ SY3989 @ SV401 ) )
| ~ ! [SY3991: $i] :
( ~ ( in @ SY3991 @ SV401 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3991 @ ( sK42_E @ SY3991 @ SV401 @ SV377 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK42_E @ SY3991 @ SV401 @ SV377 @ SV279 ) @ SV377 ) ) ) )
= $false )
| ( ( SV401
= ( relation_inverse_image @ SV279 @ SV377 ) )
= $false )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2665]) ).
thf(2757,plain,
! [SV280: $i,SV378: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV378 @ SV280 ) @ ( sK25_SY3102 @ SV378 @ SV280 ) ) @ SV280 )
| ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SV378 @ SV280 ) @ ( sK25_SY3102 @ SV378 @ SV280 ) ) @ SV378 ) )
= $false )
| ( ( subset @ SV280 @ SV378 )
= $true )
| ( ( relation @ SV378 )
= $false )
| ( ( relation @ SV280 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2666]) ).
thf(2758,plain,
! [SV379: $i,SV280: $i] :
( ( ( subset @ SV280 @ SV379 )
= $false )
| ( ( ! [SY3952: $i,SY3953: $i] :
( ~ ( in @ ( ordered_pair @ SY3952 @ SY3953 ) @ SV280 )
| ( in @ ( ordered_pair @ SY3952 @ SY3953 ) @ SV379 ) ) )
= $true )
| ( ( relation @ SV379 )
= $false )
| ( ( relation @ SV280 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2667]) ).
thf(2759,plain,
! [SV281: $i,SV318: $i,SV432: $i] :
( ( ( ~ ( relation @ SV432 ) )
= $true )
| ( ( ~ ( ~ ( ! [SY4021: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ SY4021 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY4021 @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV318 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV432 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK9_SY3093 @ SV432 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV318 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV432 ) ) )
| ( SV432
= ( relation_composition @ SV281 @ SV318 ) ) )
= $true )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2668]) ).
thf(2760,plain,
! [SV318: $i,SV281: $i,SV433: $i] :
( ( ( ~ ( relation @ SV433 ) )
= $true )
| ( ( ( SV433
!= ( relation_composition @ SV281 @ SV318 ) )
| ~ ( ~ ! [SY4022: $i,SY4023: $i] :
( ! [SY3848: $i] :
( ~ ( in @ ( ordered_pair @ SY4022 @ SY3848 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY3848 @ SY4023 ) @ SV318 ) )
| ( in @ ( ordered_pair @ SY4022 @ SY4023 ) @ SV433 ) )
| ~ ! [SY4025: $i,SY4026: $i] :
( ~ ( in @ ( ordered_pair @ SY4025 @ SY4026 ) @ SV433 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4025 @ ( sK6_F @ SY4026 @ SY4025 @ SV433 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY4026 @ SY4025 @ SV433 @ SV318 @ SV281 ) @ SY4026 ) @ SV318 ) ) ) ) )
= $true )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2669]) ).
thf(2761,plain,
! [SV282: $i,SV330: $i,SV349: $i] :
( ( ( ~ ! [SY3918: $i] :
~ ( in @ ( ordered_pair @ SY3918 @ ( sK57_D @ SV349 @ SV330 @ SV282 ) ) @ SV349 ) )
= $false )
| ( ( ( relation_rng_as_subset @ SV282 @ SV330 @ SV349 )
= SV330 )
= $true )
| ( ( relation_of2_as_subset @ SV349 @ SV282 @ SV330 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2670]) ).
thf(2762,plain,
! [SV282: $i,SV330: $i,SV349: $i] :
( ( ( ~ ( in @ ( sK57_D @ SV349 @ SV330 @ SV282 ) @ SV330 ) )
= $false )
| ( ( ( relation_rng_as_subset @ SV282 @ SV330 @ SV349 )
= SV330 )
= $true )
| ( ( relation_of2_as_subset @ SV349 @ SV282 @ SV330 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2670]) ).
thf(2763,plain,
! [SV282: $i,SV331: $i,SV350: $i,SV447: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK56_E @ SV447 @ SV350 @ SV331 @ SV282 ) @ SV447 ) @ SV350 )
| ~ ( in @ SV447 @ SV331 ) )
= $true )
| ( ( ( relation_rng_as_subset @ SV282 @ SV331 @ SV350 )
= SV331 )
= $false )
| ( ( relation_of2_as_subset @ SV350 @ SV282 @ SV331 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2671]) ).
thf(2764,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( ~ ( function @ SV434 )
| ~ ( relation @ SV434 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) ) ) )
| ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 )
| ( relation_isomorphism @ SV283 @ SV319 @ SV434 ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2672]) ).
thf(2765,plain,
! [SV319: $i,SV283: $i] :
( ( ( ~ ! [SY3852: $i] :
( ~ ( function @ SY3852 )
| ~ ( relation @ SY3852 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3852 )
| ~ ( ~ ! [SY3853: $i,SY3854: $i] :
( ~ ( in @ SY3853 @ ( relation_field @ SV283 ) )
| ~ ( in @ SY3854 @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3852 @ SY3853 ) @ ( apply @ SY3852 @ SY3854 ) ) @ SV319 )
| ( in @ ( ordered_pair @ SY3853 @ SY3854 ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3687: $i] :
( ! [SY3688: $i] :
~ ( in @ ( ordered_pair @ SY3687 @ SY3688 ) @ SV283 )
| ( in @ SY3687 @ ( relation_field @ SV283 ) ) )
| ~ ! [SY3689: $i,SY3690: $i] :
( ~ ( in @ ( ordered_pair @ SY3689 @ SY3690 ) @ SV283 )
| ( in @ SY3690 @ ( relation_field @ SV283 ) ) ) )
| ~ ! [SY3859: $i,SY3860: $i] :
( ~ ( in @ ( ordered_pair @ SY3859 @ SY3860 ) @ SV283 )
| ( in @ ( ordered_pair @ ( apply @ SY3852 @ SY3859 ) @ ( apply @ SY3852 @ SY3860 ) ) @ SV319 ) ) ) ) ) )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2673]) ).
thf(2766,plain,
! [SV319: $i,SV283: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY3861: $i] :
( ~ ( function @ SY3861 )
| ~ ( relation @ SY3861 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3861 )
| ( ( relation_dom @ SY3861 )
= ( relation_field @ SV283 ) ) )
| ~ ! [SY3862: $i] :
( ~ ( function @ SY3862 )
| ~ ( relation @ SY3862 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3862 )
| ( ( relation_rng @ SY3862 )
= ( relation_field @ SV319 ) ) ) )
| ~ ! [SY3863: $i] :
( ~ ( function @ SY3863 )
| ~ ( relation @ SY3863 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3863 )
| ( one_to_one @ SY3863 ) ) ) )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2673]) ).
thf(2767,plain,
! [SV320: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK62_B @ SV320 )
!= ( sK63_SY3125 @ SV320 ) ) )
| ~ ~ ( ~ ( in @ ( sK62_B @ SV320 ) @ ( relation_field @ SV320 ) )
| ~ ( in @ ( sK63_SY3125 @ SV320 ) @ ( relation_field @ SV320 ) ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK62_B @ SV320 ) @ ( sK63_SY3125 @ SV320 ) ) @ SV320 ) )
= $false )
| ( ( connected @ SV320 )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2674]) ).
thf(2768,plain,
! [SV320: $i] :
( ( ( in @ ( ordered_pair @ ( sK63_SY3125 @ SV320 ) @ ( sK62_B @ SV320 ) ) @ SV320 )
= $false )
| ( ( connected @ SV320 )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2675]) ).
thf(2769,plain,
! [SV321: $i,SV435: $i,SV416: $i] :
( ( ( ( SV416 = SV435 )
| ~ ( in @ SV416 @ ( relation_field @ SV321 ) )
| ~ ( in @ SV435 @ ( relation_field @ SV321 ) )
| ( in @ ( ordered_pair @ SV416 @ SV435 ) @ SV321 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV435 @ SV416 ) @ SV321 )
= $true )
| ( ( connected @ SV321 )
= $false )
| ( ( relation @ SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2676]) ).
thf(2770,plain,
! [SV284: $i,SV351: $i,SV332: $i] :
( ( ( ( SV332
!= ( apply @ SV351 @ SV284 ) )
| ~ ( in @ SV284 @ ( relation_dom @ SV351 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV284 @ SV332 ) @ SV351 )
= $true )
| ( ( function @ SV351 )
= $false )
| ( ( relation @ SV351 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2677]) ).
thf(2771,plain,
! [SV402: $i,SV284: $i,SV417: $i] :
( ( ( ~ ( function @ SV417 ) )
= $true )
| ( ( ~ ( relation @ SV417 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV284 @ SV402 ) @ SV417 )
| ( SV402
= ( apply @ SV417 @ SV284 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2678]) ).
thf(2772,plain,
! [SV403: $i,SV284: $i,SV418: $i] :
( ( ( ~ ( function @ SV418 ) )
= $true )
| ( ( ~ ( relation @ SV418 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV284 @ SV403 ) @ SV418 )
| ( in @ SV284 @ ( relation_dom @ SV418 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2679]) ).
thf(2773,plain,
! [SV333: $i,SV285: $i,SV352: $i,SV436: $i] :
( ( ( ~ ( in @ SV436 @ ( relation_dom @ SV352 ) )
| ~ ( in @ ( ordered_pair @ SV436 @ SV285 ) @ SV352 ) )
= $true )
| ( ( ~ ( in @ SV436 @ SV333 ) )
= $true )
| ( ( in @ SV285 @ ( relation_image @ SV352 @ SV333 ) )
= $true )
| ( ( relation @ SV352 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2680]) ).
thf(2774,plain,
! [SV285: $i,SV334: $i,SV353: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK61_D @ SV353 @ SV334 @ SV285 ) @ ( relation_dom @ SV353 ) )
| ~ ( in @ ( ordered_pair @ ( sK61_D @ SV353 @ SV334 @ SV285 ) @ SV285 ) @ SV353 ) )
| ~ ( in @ ( sK61_D @ SV353 @ SV334 @ SV285 ) @ SV334 ) )
= $false )
| ( ( in @ SV285 @ ( relation_image @ SV353 @ SV334 ) )
= $false )
| ( ( relation @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2681]) ).
thf(2775,plain,
! [SV322: $i,SV310: $i,SV419: $i,SV286: $i] :
( ( ( ( SV286
!= ( ordered_pair @ ( sK40_C @ SV419 @ SV286 ) @ ( sK41_SY3114 @ SV419 @ SV286 ) ) )
| ~ ( ( SV419
!= ( sK40_C @ SV419 @ SV286 ) ) ) )
= $false )
| ( ( SV419
= ( pair_first @ SV286 ) )
= $true )
| ( ( SV286
= ( ordered_pair @ SV310 @ SV322 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2682]) ).
thf(2776,plain,
! [SV322: $i,SV310: $i,SV286: $i,SV420: $i] :
( ( ( SV420
= ( pair_first @ SV286 ) )
= $false )
| ( ( ! [SY4010: $i] :
( ! [SY3712: $i] :
( SV286
!= ( ordered_pair @ SY4010 @ SY3712 ) )
| ( SV420 = SY4010 ) ) )
= $true )
| ( ( SV286
= ( ordered_pair @ SV310 @ SV322 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2683]) ).
thf(2777,plain,
! [SV323: $i,SV311: $i,SV421: $i,SV287: $i] :
( ( ( ( SV287
!= ( ordered_pair @ ( sK33_C @ SV421 @ SV287 ) @ ( sK34_SY3110 @ SV421 @ SV287 ) ) )
| ~ ( ( SV421
!= ( sK34_SY3110 @ SV421 @ SV287 ) ) ) )
= $false )
| ( ( SV421
= ( pair_second @ SV287 ) )
= $true )
| ( ( SV287
= ( ordered_pair @ SV311 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2684]) ).
thf(2778,plain,
! [SV323: $i,SV311: $i,SV287: $i,SV422: $i] :
( ( ( SV422
= ( pair_second @ SV287 ) )
= $false )
| ( ( ! [SY4012: $i,SY4013: $i] :
( ( SV287
!= ( ordered_pair @ SY4012 @ SY4013 ) )
| ( SV422 = SY4013 ) ) )
= $true )
| ( ( SV287
= ( ordered_pair @ SV311 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2685]) ).
thf(2779,plain,
! [SV324: $i,SV337: $i] :
( ( ( ( ( sK52_C @ SV337 @ SV324 )
!= ( sK53_SY3121 @ SV337 @ SV324 ) )
| ~ ( in @ ( sK52_C @ SV337 @ SV324 ) @ SV324 )
| ~ ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) )
= $true )
| ( ( SV337
= ( identity_relation @ SV324 ) )
= $true )
| ( ( relation @ SV337 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2688]) ).
thf(2780,plain,
! [SV324: $i,SV337: $i] :
( ( ( ~ ( ~ ( ( ( sK52_C @ SV337 @ SV324 )
= ( sK53_SY3121 @ SV337 @ SV324 ) )
| ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) )
| ~ ( ( in @ ( sK52_C @ SV337 @ SV324 ) @ SV324 )
| ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) ) ) )
= $true )
| ( ( SV337
= ( identity_relation @ SV324 ) )
= $true )
| ( ( relation @ SV337 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2689]) ).
thf(2781,plain,
! [SV338: $i,SV325: $i] :
( ( ( ~ ! [SY3895: $i,SY3896: $i] :
( ( SY3895 != SY3896 )
| ~ ( in @ SY3895 @ SV325 )
| ( in @ ( ordered_pair @ SY3895 @ SY3896 ) @ SV338 ) ) )
= $false )
| ( ( SV338
= ( identity_relation @ SV325 ) )
= $false )
| ( ( relation @ SV338 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2690]) ).
thf(2782,plain,
! [SV325: $i,SV338: $i] :
( ( ( ~ ~ ( ~ ! [SY3897: $i,SY3898: $i] :
( ~ ( in @ ( ordered_pair @ SY3897 @ SY3898 ) @ SV338 )
| ( SY3897 = SY3898 ) )
| ~ ! [SY3899: $i] :
( ! [SY3900: $i] :
~ ( in @ ( ordered_pair @ SY3899 @ SY3900 ) @ SV338 )
| ( in @ SY3899 @ SV325 ) ) ) )
= $false )
| ( ( SV338
= ( identity_relation @ SV325 ) )
= $false )
| ( ( relation @ SV338 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2690]) ).
thf(2783,plain,
! [SV289: $i,SV339: $i,SV356: $i] :
( ( ( ~ ! [SY3921: $i] :
~ ( in @ ( ordered_pair @ ( sK59_D @ SV356 @ SV339 @ SV289 ) @ SY3921 ) @ SV356 ) )
= $false )
| ( ( ( relation_dom_as_subset @ SV339 @ SV289 @ SV356 )
= SV339 )
= $true )
| ( ( relation_of2_as_subset @ SV356 @ SV339 @ SV289 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2691]) ).
thf(2784,plain,
! [SV289: $i,SV339: $i,SV356: $i] :
( ( ( ~ ( in @ ( sK59_D @ SV356 @ SV339 @ SV289 ) @ SV339 ) )
= $false )
| ( ( ( relation_dom_as_subset @ SV339 @ SV289 @ SV356 )
= SV339 )
= $true )
| ( ( relation_of2_as_subset @ SV356 @ SV339 @ SV289 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2691]) ).
thf(2785,plain,
! [SV289: $i,SV340: $i,SV357: $i,SV448: $i] :
( ( ( ( in @ ( ordered_pair @ SV448 @ ( sK58_E @ SV448 @ SV357 @ SV340 @ SV289 ) ) @ SV357 )
| ~ ( in @ SV448 @ SV340 ) )
= $true )
| ( ( ( relation_dom_as_subset @ SV340 @ SV289 @ SV357 )
= SV340 )
= $false )
| ( ( relation_of2_as_subset @ SV357 @ SV340 @ SV289 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2692]) ).
thf(2786,plain,
! [SV290: $i,SV380: $i] :
( ( ( ! [SY3954: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SV380 @ SV290 ) @ SY3954 ) @ SV290 )
| ~ ( in @ ( sK22_C @ SV380 @ SV290 ) @ SV380 ) )
= $true )
| ( ( SV380
= ( relation_dom @ SV290 ) )
= $true )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2693]) ).
thf(2787,plain,
! [SV290: $i,SV380: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK22_C @ SV380 @ SV290 ) @ ( sK23_SY3101 @ SV380 @ SV290 ) ) @ SV290 )
| ( in @ ( sK22_C @ SV380 @ SV290 ) @ SV380 ) )
= $true )
| ( ( SV380
= ( relation_dom @ SV290 ) )
= $true )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2694]) ).
thf(2788,plain,
! [SV381: $i,SV290: $i] :
( ( ( ~ ! [SY3955: $i] :
( ! [SY3733: $i] :
~ ( in @ ( ordered_pair @ SY3955 @ SY3733 ) @ SV290 )
| ( in @ SY3955 @ SV381 ) ) )
= $false )
| ( ( SV381
= ( relation_dom @ SV290 ) )
= $false )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2695]) ).
thf(2789,plain,
! [SV290: $i,SV381: $i] :
( ( ( ~ ! [SY3957: $i] :
( ~ ( in @ SY3957 @ SV381 )
| ( in @ ( ordered_pair @ SY3957 @ ( sK21_D @ SY3957 @ SV381 @ SV290 ) ) @ SV290 ) ) )
= $false )
| ( ( SV381
= ( relation_dom @ SV290 ) )
= $false )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2695]) ).
thf(2790,plain,
! [SV291: $i,SV382: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV291 )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV382 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV291 )
| ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV382 ) ) )
= $false )
| ( ( SV291 = SV382 )
= $true )
| ( ( relation @ SV382 )
= $false )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2696]) ).
thf(2791,plain,
! [SV383: $i,SV291: $i] :
( ( ( SV291 = SV383 )
= $false )
| ( ( ~ ( ~ ! [SY3958: $i,SY3959: $i] :
( ~ ( in @ ( ordered_pair @ SY3958 @ SY3959 ) @ SV291 )
| ( in @ ( ordered_pair @ SY3958 @ SY3959 ) @ SV383 ) )
| ~ ! [SY3960: $i,SY3961: $i] :
( ~ ( in @ ( ordered_pair @ SY3960 @ SY3961 ) @ SV383 )
| ( in @ ( ordered_pair @ SY3960 @ SY3961 ) @ SV291 ) ) ) )
= $true )
| ( ( relation @ SV383 )
= $false )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2697]) ).
thf(2792,plain,
! [SV326: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK66_B @ SV326 ) @ ( sK67_SY3127 @ SV326 ) ) @ SV326 )
| ~ ( in @ ( ordered_pair @ ( sK67_SY3127 @ SV326 ) @ ( sK68_SY3129 @ SV326 ) ) @ SV326 ) )
= $false )
| ( ( transitive @ SV326 )
= $true )
| ( ( relation @ SV326 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2698]) ).
thf(2793,plain,
! [SV326: $i] :
( ( ( in @ ( ordered_pair @ ( sK66_B @ SV326 ) @ ( sK68_SY3129 @ SV326 ) ) @ SV326 )
= $false )
| ( ( transitive @ SV326 )
= $true )
| ( ( relation @ SV326 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2699]) ).
thf(2794,plain,
! [SV449: $i,SV327: $i,SV437: $i,SV423: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV423 @ SV437 ) @ SV327 )
| ~ ( in @ ( ordered_pair @ SV437 @ SV449 ) @ SV327 )
| ( in @ ( ordered_pair @ SV423 @ SV449 ) @ SV327 ) )
= $true )
| ( ( transitive @ SV327 )
= $false )
| ( ( relation @ SV327 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2700]) ).
thf(2795,plain,
! [SV292: $i,SV384: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SV384 @ SV292 ) @ ( sK13_SY3095 @ SV384 @ SV292 ) ) @ SV384 )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV384 @ SV292 ) @ ( sK12_C @ SV384 @ SV292 ) ) @ SV292 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SV384 @ SV292 ) @ ( sK13_SY3095 @ SV384 @ SV292 ) ) @ SV384 )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV384 @ SV292 ) @ ( sK12_C @ SV384 @ SV292 ) ) @ SV292 ) ) )
= $false )
| ( ( SV384
= ( relation_inverse @ SV292 ) )
= $true )
| ( ( relation @ SV384 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2701]) ).
thf(2796,plain,
! [SV292: $i,SV385: $i] :
( ( ( SV385
= ( relation_inverse @ SV292 ) )
= $false )
| ( ( ~ ( ~ ! [SY3962: $i,SY3963: $i] :
( ~ ( in @ ( ordered_pair @ SY3962 @ SY3963 ) @ SV385 )
| ( in @ ( ordered_pair @ SY3963 @ SY3962 ) @ SV292 ) )
| ~ ! [SY3964: $i,SY3965: $i] :
( ~ ( in @ ( ordered_pair @ SY3965 @ SY3964 ) @ SV292 )
| ( in @ ( ordered_pair @ SY3964 @ SY3965 ) @ SV385 ) ) ) )
= $true )
| ( ( relation @ SV385 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2702]) ).
thf(2797,plain,
! [SV293: $i] :
( ( ( ! [SY3747: $i] :
( ~ ( in @ SY3747 @ ( relation_dom @ SV293 ) )
| ! [SY3748: $i] :
( ( SY3748
!= ( apply @ SV293 @ SY3747 ) )
| ( in @ ( ordered_pair @ SY3747 @ SY3748 ) @ SV293 ) ) ) )
= $true )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2703]) ).
thf(2798,plain,
! [SV293: $i] :
( ( ( ! [SY3749: $i] :
( ~ ( in @ SY3749 @ ( relation_dom @ SV293 ) )
| ! [SY3750: $i] :
( ~ ( in @ ( ordered_pair @ SY3749 @ SY3750 ) @ SV293 )
| ( SY3750
= ( apply @ SV293 @ SY3749 ) ) ) ) )
= $true )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2704]) ).
thf(2799,plain,
! [SV293: $i] :
( ( ( ! [SY3751: $i] :
( ( in @ SY3751 @ ( relation_dom @ SV293 ) )
| ! [SY3752: $i] :
( ( SY3752
!= ( apply @ SV293 @ SY3751 ) )
| ( SY3752 = empty_set ) ) ) )
= $true )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2705]) ).
thf(2800,plain,
! [SV293: $i] :
( ( ( ! [SY3753: $i] :
( ( in @ SY3753 @ ( relation_dom @ SV293 ) )
| ! [SY3754: $i] :
( ( SY3754 != empty_set )
| ( SY3754
= ( apply @ SV293 @ SY3753 ) ) ) ) )
= $true )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2706]) ).
thf(2801,plain,
! [SV294: $i,SV386: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_C @ SV386 @ SV294 ) @ SV386 )
| ~ ( in @ ( sK20_SY3099 @ SV386 @ SV294 ) @ SV386 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SV386 @ SV294 ) @ ( sK20_SY3099 @ SV386 @ SV294 ) ) @ SV294 ) )
| ~ ( in @ ( ordered_pair @ ( sK20_SY3099 @ SV386 @ SV294 ) @ ( sK19_C @ SV386 @ SV294 ) ) @ SV294 ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV294 @ SV386 )
= $true )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2707]) ).
thf(2802,plain,
! [SV294: $i,SV386: $i] :
( ( ( ( ( sK19_C @ SV386 @ SV294 )
!= ( sK20_SY3099 @ SV386 @ SV294 ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV294 @ SV386 )
= $true )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2708]) ).
thf(2803,plain,
! [SV294: $i,SV450: $i,SV387: $i,SV438: $i] :
( ( ( ~ ( in @ SV438 @ SV387 )
| ~ ( in @ SV450 @ SV387 )
| ~ ( in @ ( ordered_pair @ SV438 @ SV450 ) @ SV294 )
| ~ ( in @ ( ordered_pair @ SV450 @ SV438 ) @ SV294 )
| ( SV438 = SV450 ) )
= $true )
| ( ( is_antisymmetric_in @ SV294 @ SV387 )
= $false )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2709]) ).
thf(2804,plain,
! [SV295: $i,SV388: $i,SV404: $i] :
( ( ( ~ ( ( ( sK35_D @ SV404 @ SV388 @ SV295 )
= SV388 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV388 ) @ SV295 )
| ~ ( in @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV404 ) ) )
= $false )
| ( ( SV404
= ( fiber @ SV295 @ SV388 ) )
= $true )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2710]) ).
thf(2805,plain,
! [SV295: $i,SV388: $i,SV404: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK35_D @ SV404 @ SV388 @ SV295 )
!= SV388 )
| ( in @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV404 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV388 ) @ SV295 )
| ( in @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV404 ) ) ) )
= $false )
| ( ( SV404
= ( fiber @ SV295 @ SV388 ) )
= $true )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2710]) ).
thf(2806,plain,
! [SV405: $i,SV295: $i,SV389: $i] :
( ( ( ~ ! [SY3994: $i] :
( ( SY3994 = SV389 )
| ~ ( in @ ( ordered_pair @ SY3994 @ SV389 ) @ SV295 )
| ( in @ SY3994 @ SV405 ) )
| ~ ~ ( ~ ! [SY3995: $i] :
( ~ ( in @ SY3995 @ SV405 )
| ( SY3995 != SV389 ) )
| ~ ! [SY3996: $i] :
( ~ ( in @ SY3996 @ SV405 )
| ( in @ ( ordered_pair @ SY3996 @ SV389 ) @ SV295 ) ) ) )
= $false )
| ( ( SV405
= ( fiber @ SV295 @ SV389 ) )
= $false )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2711]) ).
thf(2807,plain,
! [SV296: $i,SV307: $i,SV406: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) @ SV296 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV307 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) @ SV296 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV307 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) ) ) ) )
= $true )
| ( ( SV406
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $true )
| ( ( relation @ SV406 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2712]) ).
thf(2808,plain,
! [SV307: $i,SV296: $i,SV407: $i] :
( ( ( ( SV407
!= ( relation_rng_restriction @ SV296 @ SV307 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY3997: $i,SY3998: $i] :
( ~ ( in @ SY3998 @ SV296 )
| ~ ( in @ ( ordered_pair @ SY3997 @ SY3998 ) @ SV307 )
| ( in @ ( ordered_pair @ SY3997 @ SY3998 ) @ SV407 ) )
| ~ ~ ( ~ ! [SY3999: $i,SY4000: $i] :
( ~ ( in @ ( ordered_pair @ SY3999 @ SY4000 ) @ SV407 )
| ( in @ SY4000 @ SV296 ) )
| ~ ! [SY4001: $i,SY4002: $i] :
( ~ ( in @ ( ordered_pair @ SY4001 @ SY4002 ) @ SV407 )
| ( in @ ( ordered_pair @ SY4001 @ SY4002 ) @ SV307 ) ) ) ) )
= $true )
| ( ( relation @ SV407 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2713]) ).
thf(2809,plain,
! [SV297: $i,SV390: $i] :
( ( ( ! [SY3973: $i] :
~ ( in @ ( ordered_pair @ SY3973 @ ( sK17_C @ SV390 @ SV297 ) ) @ SV297 )
| ~ ( in @ ( sK17_C @ SV390 @ SV297 ) @ SV390 ) )
= $true )
| ( ( SV390
= ( relation_rng @ SV297 ) )
= $true )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2714]) ).
thf(2810,plain,
! [SV297: $i,SV390: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK18_SY3098 @ SV390 @ SV297 ) @ ( sK17_C @ SV390 @ SV297 ) ) @ SV297 )
| ( in @ ( sK17_C @ SV390 @ SV297 ) @ SV390 ) )
= $true )
| ( ( SV390
= ( relation_rng @ SV297 ) )
= $true )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2715]) ).
thf(2811,plain,
! [SV391: $i,SV297: $i] :
( ( ( ~ ! [SY3974: $i] :
( ! [SY3779: $i] :
~ ( in @ ( ordered_pair @ SY3779 @ SY3974 ) @ SV297 )
| ( in @ SY3974 @ SV391 ) ) )
= $false )
| ( ( SV391
= ( relation_rng @ SV297 ) )
= $false )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2716]) ).
thf(2812,plain,
! [SV297: $i,SV391: $i] :
( ( ( ~ ! [SY3976: $i] :
( ~ ( in @ SY3976 @ SV391 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3976 @ SV391 @ SV297 ) @ SY3976 ) @ SV297 ) ) )
= $false )
| ( ( SV391
= ( relation_rng @ SV297 ) )
= $false )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2716]) ).
thf(2813,plain,
! [SV392: $i,SV308: $i,SV360: $i,SV299: $i] :
( ( ( ~ ( in @ SV299 @ SV360 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ SV392 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SV360 ) @ SV392 ) )
= $true )
| ( ( relation @ SV392 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2719]) ).
thf(2814,plain,
! [SV424: $i,SV308: $i,SV299: $i,SV439: $i] :
( ( ( ~ ( relation @ SV439 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SV424 ) @ SV439 ) )
| ( in @ SV299 @ SV424 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2720]) ).
thf(2815,plain,
! [SV425: $i,SV308: $i,SV299: $i,SV440: $i] :
( ( ( ~ ( relation @ SV440 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SV425 ) @ SV440 ) )
| ( in @ ( ordered_pair @ SV299 @ SV308 ) @ SV440 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2721]) ).
thf(2816,plain,
! [SV343: $i,SV301: $i,SV363: $i,SV441: $i] :
( ( ( ~ ( in @ SV441 @ ( relation_rng @ SV363 ) )
| ~ ( in @ ( ordered_pair @ SV301 @ SV441 ) @ SV363 ) )
= $true )
| ( ( ~ ( in @ SV441 @ SV343 ) )
= $true )
| ( ( in @ SV301 @ ( relation_inverse_image @ SV363 @ SV343 ) )
= $true )
| ( ( relation @ SV363 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2722]) ).
thf(2817,plain,
! [SV301: $i,SV344: $i,SV364: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK60_D @ SV364 @ SV344 @ SV301 ) @ ( relation_rng @ SV364 ) )
| ~ ( in @ ( ordered_pair @ SV301 @ ( sK60_D @ SV364 @ SV344 @ SV301 ) ) @ SV364 ) )
| ~ ( in @ ( sK60_D @ SV364 @ SV344 @ SV301 ) @ SV344 ) )
= $false )
| ( ( in @ SV301 @ ( relation_inverse_image @ SV364 @ SV344 ) )
= $false )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2723]) ).
thf(2818,plain,
! [SV302: $i,SV394: $i] :
( ( ( in @ ( sK36_C @ SV394 @ SV302 ) @ SV394 )
= $true )
| ( ( is_reflexive_in @ SV302 @ SV394 )
= $true )
| ( ( relation @ SV302 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2724]) ).
thf(2819,plain,
! [SV302: $i,SV394: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK36_C @ SV394 @ SV302 ) @ ( sK36_C @ SV394 @ SV302 ) ) @ SV302 ) )
= $true )
| ( ( is_reflexive_in @ SV302 @ SV394 )
= $true )
| ( ( relation @ SV302 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2725]) ).
thf(2820,plain,
! [SV302: $i,SV395: $i,SV442: $i] :
( ( ( ~ ( in @ SV442 @ SV395 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV442 @ SV442 ) @ SV302 )
= $true )
| ( ( is_reflexive_in @ SV302 @ SV395 )
= $false )
| ( ( relation @ SV302 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2726]) ).
thf(2821,plain,
! [SV443: $i,SV409: $i,SV305: $i,SV272: $i] :
( ( ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SV409 @ SV443 ) )
= $false )
| ( ( in @ SV272 @ SV409 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2728]) ).
thf(2822,plain,
! [SV426: $i,SV410: $i,SV305: $i,SV272: $i] :
( ( ( in @ ( ordered_pair @ SV272 @ SV305 ) @ ( cartesian_product2 @ SV410 @ SV426 ) )
= $false )
| ( ( in @ SV305 @ SV426 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2729]) ).
thf(2823,plain,
! [SV444: $i,SV411: $i,SV306: $i,SV273: $i] :
( ( ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SV411 @ SV444 ) )
= $false )
| ( ( in @ SV273 @ SV411 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2731]) ).
thf(2824,plain,
! [SV427: $i,SV412: $i,SV306: $i,SV273: $i] :
( ( ( in @ ( ordered_pair @ SV273 @ SV306 ) @ ( cartesian_product2 @ SV412 @ SV427 ) )
= $false )
| ( ( in @ SV306 @ SV427 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2732]) ).
thf(2825,plain,
! [SV274: $i,SV367: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK14_C @ SV367 @ SV274 )
!= ( sK15_SY3096 @ SV367 @ SV274 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SV367 @ SV274 ) @ SV367 )
| ~ ( in @ ( sK15_SY3096 @ SV367 @ SV274 ) @ SV367 ) ) )
| ~ ~ ( in @ ( ordered_pair @ ( sK14_C @ SV367 @ SV274 ) @ ( sK15_SY3096 @ SV367 @ SV274 ) ) @ SV274 ) )
= $false )
| ( ( is_connected_in @ SV274 @ SV367 )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2735]) ).
thf(2826,plain,
! [SV274: $i,SV367: $i] :
( ( ( in @ ( ordered_pair @ ( sK15_SY3096 @ SV367 @ SV274 ) @ ( sK14_C @ SV367 @ SV274 ) ) @ SV274 )
= $false )
| ( ( is_connected_in @ SV274 @ SV367 )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2736]) ).
thf(2827,plain,
! [SV274: $i,SV368: $i,SV445: $i,SV428: $i] :
( ( ( ( SV428 = SV445 )
| ~ ( in @ SV428 @ SV368 )
| ~ ( in @ SV445 @ SV368 )
| ( in @ ( ordered_pair @ SV428 @ SV445 ) @ SV274 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV445 @ SV428 ) @ SV274 )
= $true )
| ( ( is_connected_in @ SV274 @ SV368 )
= $false )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2737]) ).
thf(2828,plain,
! [SV316: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK64_B @ SV316 ) @ ( sK65_SY3126 @ SV316 ) ) @ SV316 ) )
= $false )
| ( ( antisymmetric @ SV316 )
= $true )
| ( ( relation @ SV316 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2739]) ).
thf(2829,plain,
! [SV316: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK65_SY3126 @ SV316 ) @ ( sK64_B @ SV316 ) ) @ SV316 ) )
= $false )
| ( ( antisymmetric @ SV316 )
= $true )
| ( ( relation @ SV316 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2739]) ).
thf(2830,plain,
! [SV317: $i,SV430: $i,SV415: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV415 @ SV430 ) @ SV317 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV430 @ SV415 ) @ SV317 ) )
= $true )
| ( ( SV415 = SV430 )
= $true )
| ( ( antisymmetric @ SV317 )
= $false )
| ( ( relation @ SV317 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2741]) ).
thf(2831,plain,
! [SV347: $i,SV328: $i,SV275: $i,SV451: $i] :
( ( ( ! [SY4030: $i] :
( ~ ( in @ SV451 @ SV275 )
| ~ ( in @ SY4030 @ SV328 )
| ( ( sK28_D @ SV347 @ SV328 @ SV275 )
!= ( ordered_pair @ SV451 @ SY4030 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK28_D @ SV347 @ SV328 @ SV275 ) @ SV347 ) )
= $true )
| ( ( SV347
= ( cartesian_product2 @ SV275 @ SV328 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2742]) ).
thf(2832,plain,
! [SV275: $i,SV328: $i,SV347: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK29_SY3106 @ SV347 @ SV328 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK30_SY3108 @ SV347 @ SV328 @ SV275 ) @ SV328 ) )
| ( ( sK28_D @ SV347 @ SV328 @ SV275 )
!= ( ordered_pair @ ( sK29_SY3106 @ SV347 @ SV328 @ SV275 ) @ ( sK30_SY3108 @ SV347 @ SV328 @ SV275 ) ) ) )
= $false )
| ( ( in @ ( sK28_D @ SV347 @ SV328 @ SV275 ) @ SV347 )
= $true )
| ( ( SV347
= ( cartesian_product2 @ SV275 @ SV328 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2743]) ).
thf(2833,plain,
! [SV348: $i,SV452: $i,SV329: $i,SV275: $i] :
( ( ( ! [SY4031: $i,SY4032: $i] :
( ~ ( in @ SY4031 @ SV275 )
| ~ ( in @ SY4032 @ SV329 )
| ( SV452
!= ( ordered_pair @ SY4031 @ SY4032 ) ) )
| ( in @ SV452 @ SV348 ) )
= $true )
| ( ( SV348
= ( cartesian_product2 @ SV275 @ SV329 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2744]) ).
thf(2834,plain,
! [SV275: $i,SV329: $i,SV348: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV348 )
| ~ ( ~ ~ ( ~ ( in @ ( sK26_E @ SV453 @ SV348 @ SV329 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK27_SY3103 @ SV453 @ SV348 @ SV329 @ SV275 ) @ SV329 ) )
| ( SV453
!= ( ordered_pair @ ( sK26_E @ SV453 @ SV348 @ SV329 @ SV275 ) @ ( sK27_SY3103 @ SV453 @ SV348 @ SV329 @ SV275 ) ) ) ) )
= $true )
| ( ( SV348
= ( cartesian_product2 @ SV275 @ SV329 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2745]) ).
thf(2835,plain,
! [SV276: $i,SV370: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SV370 @ SV276 ) @ SV370 )
| ~ ( in @ ( sK4_SY3086 @ SV370 @ SV276 ) @ SV370 ) )
| ~ ( in @ ( sK5_SY3088 @ SV370 @ SV276 ) @ SV370 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SV370 @ SV276 ) @ ( sK4_SY3086 @ SV370 @ SV276 ) ) @ SV276 ) )
| ~ ( in @ ( ordered_pair @ ( sK4_SY3086 @ SV370 @ SV276 ) @ ( sK5_SY3088 @ SV370 @ SV276 ) ) @ SV276 ) )
= $false )
| ( ( is_transitive_in @ SV276 @ SV370 )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2746]) ).
thf(2836,plain,
! [SV276: $i,SV370: $i] :
( ( ( in @ ( ordered_pair @ ( sK3_C @ SV370 @ SV276 ) @ ( sK5_SY3088 @ SV370 @ SV276 ) ) @ SV276 )
= $false )
| ( ( is_transitive_in @ SV276 @ SV370 )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2747]) ).
thf(2837,plain,
! [SV276: $i,SV454: $i,SV446: $i,SV371: $i,SV431: $i] :
( ( ( ~ ( in @ SV431 @ SV371 )
| ~ ( in @ SV446 @ SV371 )
| ~ ( in @ SV454 @ SV371 )
| ~ ( in @ ( ordered_pair @ SV431 @ SV446 ) @ SV276 )
| ~ ( in @ ( ordered_pair @ SV446 @ SV454 ) @ SV276 )
| ( in @ ( ordered_pair @ SV431 @ SV454 ) @ SV276 ) )
= $true )
| ( ( is_transitive_in @ SV276 @ SV371 )
= $false )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2748]) ).
thf(2838,plain,
! [SV277: $i,SV372: $i,SV396: $i] :
( ( ( ! [SY3978: $i] :
( ~ ( in @ ( ordered_pair @ SY3978 @ ( sK46_D @ SV396 @ SV372 @ SV277 ) ) @ SV277 )
| ~ ( in @ SY3978 @ SV372 ) )
| ~ ( in @ ( sK46_D @ SV396 @ SV372 @ SV277 ) @ SV396 ) )
= $true )
| ( ( SV396
= ( relation_image @ SV277 @ SV372 ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2749]) ).
thf(2839,plain,
! [SV277: $i,SV372: $i,SV396: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SV396 @ SV372 @ SV277 ) @ ( sK46_D @ SV396 @ SV372 @ SV277 ) ) @ SV277 )
| ~ ( in @ ( sK47_SY3118 @ SV396 @ SV372 @ SV277 ) @ SV372 ) )
| ( in @ ( sK46_D @ SV396 @ SV372 @ SV277 ) @ SV396 ) )
= $true )
| ( ( SV396
= ( relation_image @ SV277 @ SV372 ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2750]) ).
thf(2840,plain,
! [SV397: $i,SV373: $i,SV277: $i] :
( ( ( ~ ! [SY3979: $i] :
( ! [SY3936: $i] :
( ~ ( in @ ( ordered_pair @ SY3936 @ SY3979 ) @ SV277 )
| ~ ( in @ SY3936 @ SV373 ) )
| ( in @ SY3979 @ SV397 ) ) )
= $false )
| ( ( SV397
= ( relation_image @ SV277 @ SV373 ) )
= $false )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2751]) ).
thf(2841,plain,
! [SV277: $i,SV373: $i,SV397: $i] :
( ( ( ~ ! [SY3981: $i] :
( ~ ( in @ SY3981 @ SV397 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SY3981 @ SV397 @ SV373 @ SV277 ) @ SY3981 ) @ SV277 )
| ~ ( in @ ( sK45_E @ SY3981 @ SV397 @ SV373 @ SV277 ) @ SV373 ) ) ) )
= $false )
| ( ( SV397
= ( relation_image @ SV277 @ SV373 ) )
= $false )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2751]) ).
thf(2842,plain,
! [SV278: $i,SV374: $i,SV398: $i] :
( ( ( ~ ( ~ ( in @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ SV374 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV278 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) )
| ~ ~ ( ~ ( ( in @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ SV374 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV278 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) ) ) )
= $false )
| ( ( SV398
= ( relation_dom_restriction @ SV278 @ SV374 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2752]) ).
thf(2843,plain,
! [SV375: $i,SV278: $i,SV399: $i] :
( ( ( SV399
= ( relation_dom_restriction @ SV278 @ SV375 ) )
= $false )
| ( ( ~ ( ~ ! [SY3982: $i,SY3983: $i] :
( ~ ( in @ SY3982 @ SV375 )
| ~ ( in @ ( ordered_pair @ SY3982 @ SY3983 ) @ SV278 )
| ( in @ ( ordered_pair @ SY3982 @ SY3983 ) @ SV399 ) )
| ~ ~ ( ~ ! [SY3984: $i] :
( ! [SY3985: $i] :
~ ( in @ ( ordered_pair @ SY3984 @ SY3985 ) @ SV399 )
| ( in @ SY3984 @ SV375 ) )
| ~ ! [SY3986: $i,SY3987: $i] :
( ~ ( in @ ( ordered_pair @ SY3986 @ SY3987 ) @ SV399 )
| ( in @ ( ordered_pair @ SY3986 @ SY3987 ) @ SV278 ) ) ) ) )
= $true )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2753]) ).
thf(2844,plain,
! [SV279: $i,SV376: $i,SV400: $i] :
( ( ( ! [SY3988: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SY3988 ) @ SV279 )
| ~ ( in @ SY3988 @ SV376 ) )
| ~ ( in @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SV400 ) )
= $true )
| ( ( SV400
= ( relation_inverse_image @ SV279 @ SV376 ) )
= $true )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2754]) ).
thf(2845,plain,
! [SV279: $i,SV376: $i,SV400: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ ( sK44_SY3116 @ SV400 @ SV376 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK44_SY3116 @ SV400 @ SV376 @ SV279 ) @ SV376 ) )
| ( in @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SV400 ) )
= $true )
| ( ( SV400
= ( relation_inverse_image @ SV279 @ SV376 ) )
= $true )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2755]) ).
thf(2846,plain,
! [SV401: $i,SV377: $i,SV279: $i] :
( ( ( ~ ! [SY3989: $i] :
( ! [SY3950: $i] :
( ~ ( in @ ( ordered_pair @ SY3989 @ SY3950 ) @ SV279 )
| ~ ( in @ SY3950 @ SV377 ) )
| ( in @ SY3989 @ SV401 ) ) )
= $false )
| ( ( SV401
= ( relation_inverse_image @ SV279 @ SV377 ) )
= $false )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2756]) ).
thf(2847,plain,
! [SV279: $i,SV377: $i,SV401: $i] :
( ( ( ~ ! [SY3991: $i] :
( ~ ( in @ SY3991 @ SV401 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3991 @ ( sK42_E @ SY3991 @ SV401 @ SV377 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK42_E @ SY3991 @ SV401 @ SV377 @ SV279 ) @ SV377 ) ) ) )
= $false )
| ( ( SV401
= ( relation_inverse_image @ SV279 @ SV377 ) )
= $false )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2756]) ).
thf(2848,plain,
! [SV280: $i,SV378: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV378 @ SV280 ) @ ( sK25_SY3102 @ SV378 @ SV280 ) ) @ SV280 ) )
= $false )
| ( ( subset @ SV280 @ SV378 )
= $true )
| ( ( relation @ SV378 )
= $false )
| ( ( relation @ SV280 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2757]) ).
thf(2849,plain,
! [SV280: $i,SV378: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK24_C @ SV378 @ SV280 ) @ ( sK25_SY3102 @ SV378 @ SV280 ) ) @ SV378 ) )
= $false )
| ( ( subset @ SV280 @ SV378 )
= $true )
| ( ( relation @ SV378 )
= $false )
| ( ( relation @ SV280 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2757]) ).
thf(2850,plain,
! [SV379: $i,SV280: $i,SV455: $i] :
( ( ( ! [SY4033: $i] :
( ~ ( in @ ( ordered_pair @ SV455 @ SY4033 ) @ SV280 )
| ( in @ ( ordered_pair @ SV455 @ SY4033 ) @ SV379 ) ) )
= $true )
| ( ( subset @ SV280 @ SV379 )
= $false )
| ( ( relation @ SV379 )
= $false )
| ( ( relation @ SV280 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2758]) ).
thf(2851,plain,
! [SV281: $i,SV318: $i,SV432: $i] :
( ( ( relation @ SV432 )
= $false )
| ( ( ~ ( ~ ( ! [SY4021: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ SY4021 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY4021 @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV318 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV432 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK9_SY3093 @ SV432 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV318 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV432 ) ) )
| ( SV432
= ( relation_composition @ SV281 @ SV318 ) ) )
= $true )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2759]) ).
thf(2852,plain,
! [SV318: $i,SV281: $i,SV433: $i] :
( ( ( relation @ SV433 )
= $false )
| ( ( ( SV433
!= ( relation_composition @ SV281 @ SV318 ) )
| ~ ( ~ ! [SY4022: $i,SY4023: $i] :
( ! [SY3848: $i] :
( ~ ( in @ ( ordered_pair @ SY4022 @ SY3848 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY3848 @ SY4023 ) @ SV318 ) )
| ( in @ ( ordered_pair @ SY4022 @ SY4023 ) @ SV433 ) )
| ~ ! [SY4025: $i,SY4026: $i] :
( ~ ( in @ ( ordered_pair @ SY4025 @ SY4026 ) @ SV433 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4025 @ ( sK6_F @ SY4026 @ SY4025 @ SV433 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY4026 @ SY4025 @ SV433 @ SV318 @ SV281 ) @ SY4026 ) @ SV318 ) ) ) ) )
= $true )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2760]) ).
thf(2853,plain,
! [SV282: $i,SV330: $i,SV349: $i] :
( ( ( ! [SY3918: $i] :
~ ( in @ ( ordered_pair @ SY3918 @ ( sK57_D @ SV349 @ SV330 @ SV282 ) ) @ SV349 ) )
= $true )
| ( ( ( relation_rng_as_subset @ SV282 @ SV330 @ SV349 )
= SV330 )
= $true )
| ( ( relation_of2_as_subset @ SV349 @ SV282 @ SV330 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2761]) ).
thf(2854,plain,
! [SV282: $i,SV330: $i,SV349: $i] :
( ( ( in @ ( sK57_D @ SV349 @ SV330 @ SV282 ) @ SV330 )
= $true )
| ( ( ( relation_rng_as_subset @ SV282 @ SV330 @ SV349 )
= SV330 )
= $true )
| ( ( relation_of2_as_subset @ SV349 @ SV282 @ SV330 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2762]) ).
thf(2855,plain,
! [SV282: $i,SV331: $i,SV350: $i,SV447: $i] :
( ( ( in @ ( ordered_pair @ ( sK56_E @ SV447 @ SV350 @ SV331 @ SV282 ) @ SV447 ) @ SV350 )
= $true )
| ( ( ~ ( in @ SV447 @ SV331 ) )
= $true )
| ( ( ( relation_rng_as_subset @ SV282 @ SV331 @ SV350 )
= SV331 )
= $false )
| ( ( relation_of2_as_subset @ SV350 @ SV282 @ SV331 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2763]) ).
thf(2856,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( ~ ( function @ SV434 ) )
= $true )
| ( ( ~ ( relation @ SV434 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) ) ) )
| ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 )
| ( relation_isomorphism @ SV283 @ SV319 @ SV434 ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2764]) ).
thf(2857,plain,
! [SV319: $i,SV283: $i] :
( ( ( ! [SY3852: $i] :
( ~ ( function @ SY3852 )
| ~ ( relation @ SY3852 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3852 )
| ~ ( ~ ! [SY3853: $i,SY3854: $i] :
( ~ ( in @ SY3853 @ ( relation_field @ SV283 ) )
| ~ ( in @ SY3854 @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SY3852 @ SY3853 ) @ ( apply @ SY3852 @ SY3854 ) ) @ SV319 )
| ( in @ ( ordered_pair @ SY3853 @ SY3854 ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3687: $i] :
( ! [SY3688: $i] :
~ ( in @ ( ordered_pair @ SY3687 @ SY3688 ) @ SV283 )
| ( in @ SY3687 @ ( relation_field @ SV283 ) ) )
| ~ ! [SY3689: $i,SY3690: $i] :
( ~ ( in @ ( ordered_pair @ SY3689 @ SY3690 ) @ SV283 )
| ( in @ SY3690 @ ( relation_field @ SV283 ) ) ) )
| ~ ! [SY3859: $i,SY3860: $i] :
( ~ ( in @ ( ordered_pair @ SY3859 @ SY3860 ) @ SV283 )
| ( in @ ( ordered_pair @ ( apply @ SY3852 @ SY3859 ) @ ( apply @ SY3852 @ SY3860 ) ) @ SV319 ) ) ) ) ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2765]) ).
thf(2858,plain,
! [SV319: $i,SV283: $i] :
( ( ( ~ ( ~ ~ ( ~ ! [SY3861: $i] :
( ~ ( function @ SY3861 )
| ~ ( relation @ SY3861 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3861 )
| ( ( relation_dom @ SY3861 )
= ( relation_field @ SV283 ) ) )
| ~ ! [SY3862: $i] :
( ~ ( function @ SY3862 )
| ~ ( relation @ SY3862 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3862 )
| ( ( relation_rng @ SY3862 )
= ( relation_field @ SV319 ) ) ) )
| ~ ! [SY3863: $i] :
( ~ ( function @ SY3863 )
| ~ ( relation @ SY3863 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3863 )
| ( one_to_one @ SY3863 ) ) ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2766]) ).
thf(2859,plain,
! [SV320: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK62_B @ SV320 )
!= ( sK63_SY3125 @ SV320 ) ) )
| ~ ~ ( ~ ( in @ ( sK62_B @ SV320 ) @ ( relation_field @ SV320 ) )
| ~ ( in @ ( sK63_SY3125 @ SV320 ) @ ( relation_field @ SV320 ) ) ) ) )
= $false )
| ( ( connected @ SV320 )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2767]) ).
thf(2860,plain,
! [SV320: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK62_B @ SV320 ) @ ( sK63_SY3125 @ SV320 ) ) @ SV320 ) )
= $false )
| ( ( connected @ SV320 )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2767]) ).
thf(2861,plain,
! [SV321: $i,SV435: $i,SV416: $i] :
( ( ( ( SV416 = SV435 )
| ~ ( in @ SV416 @ ( relation_field @ SV321 ) )
| ~ ( in @ SV435 @ ( relation_field @ SV321 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV416 @ SV435 ) @ SV321 )
= $true )
| ( ( in @ ( ordered_pair @ SV435 @ SV416 ) @ SV321 )
= $true )
| ( ( connected @ SV321 )
= $false )
| ( ( relation @ SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2769]) ).
thf(2862,plain,
! [SV284: $i,SV351: $i,SV332: $i] :
( ( ( ( SV332
!= ( apply @ SV351 @ SV284 ) ) )
= $true )
| ( ( ~ ( in @ SV284 @ ( relation_dom @ SV351 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV284 @ SV332 ) @ SV351 )
= $true )
| ( ( function @ SV351 )
= $false )
| ( ( relation @ SV351 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2770]) ).
thf(2863,plain,
! [SV402: $i,SV284: $i,SV417: $i] :
( ( ( function @ SV417 )
= $false )
| ( ( ~ ( relation @ SV417 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV284 @ SV402 ) @ SV417 )
| ( SV402
= ( apply @ SV417 @ SV284 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2771]) ).
thf(2864,plain,
! [SV403: $i,SV284: $i,SV418: $i] :
( ( ( function @ SV418 )
= $false )
| ( ( ~ ( relation @ SV418 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV284 @ SV403 ) @ SV418 )
| ( in @ SV284 @ ( relation_dom @ SV418 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2772]) ).
thf(2865,plain,
! [SV333: $i,SV285: $i,SV352: $i,SV436: $i] :
( ( ( ~ ( in @ SV436 @ ( relation_dom @ SV352 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV436 @ SV285 ) @ SV352 ) )
= $true )
| ( ( ~ ( in @ SV436 @ SV333 ) )
= $true )
| ( ( in @ SV285 @ ( relation_image @ SV352 @ SV333 ) )
= $true )
| ( ( relation @ SV352 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2773]) ).
thf(2866,plain,
! [SV285: $i,SV334: $i,SV353: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK61_D @ SV353 @ SV334 @ SV285 ) @ ( relation_dom @ SV353 ) )
| ~ ( in @ ( ordered_pair @ ( sK61_D @ SV353 @ SV334 @ SV285 ) @ SV285 ) @ SV353 ) ) )
= $false )
| ( ( in @ SV285 @ ( relation_image @ SV353 @ SV334 ) )
= $false )
| ( ( relation @ SV353 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2774]) ).
thf(2867,plain,
! [SV285: $i,SV334: $i,SV353: $i] :
( ( ( ~ ( in @ ( sK61_D @ SV353 @ SV334 @ SV285 ) @ SV334 ) )
= $false )
| ( ( in @ SV285 @ ( relation_image @ SV353 @ SV334 ) )
= $false )
| ( ( relation @ SV353 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2774]) ).
thf(2868,plain,
! [SV322: $i,SV310: $i,SV419: $i,SV286: $i] :
( ( ( ( SV286
!= ( ordered_pair @ ( sK40_C @ SV419 @ SV286 ) @ ( sK41_SY3114 @ SV419 @ SV286 ) ) ) )
= $false )
| ( ( SV419
= ( pair_first @ SV286 ) )
= $true )
| ( ( SV286
= ( ordered_pair @ SV310 @ SV322 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2775]) ).
thf(2869,plain,
! [SV322: $i,SV310: $i,SV286: $i,SV419: $i] :
( ( ( ~ ( ( SV419
!= ( sK40_C @ SV419 @ SV286 ) ) ) )
= $false )
| ( ( SV419
= ( pair_first @ SV286 ) )
= $true )
| ( ( SV286
= ( ordered_pair @ SV310 @ SV322 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2775]) ).
thf(2870,plain,
! [SV322: $i,SV310: $i,SV420: $i,SV456: $i,SV286: $i] :
( ( ( ! [SY4034: $i] :
( SV286
!= ( ordered_pair @ SV456 @ SY4034 ) )
| ( SV420 = SV456 ) )
= $true )
| ( ( SV420
= ( pair_first @ SV286 ) )
= $false )
| ( ( SV286
= ( ordered_pair @ SV310 @ SV322 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2776]) ).
thf(2871,plain,
! [SV323: $i,SV311: $i,SV421: $i,SV287: $i] :
( ( ( ( SV287
!= ( ordered_pair @ ( sK33_C @ SV421 @ SV287 ) @ ( sK34_SY3110 @ SV421 @ SV287 ) ) ) )
= $false )
| ( ( SV421
= ( pair_second @ SV287 ) )
= $true )
| ( ( SV287
= ( ordered_pair @ SV311 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2777]) ).
thf(2872,plain,
! [SV323: $i,SV311: $i,SV287: $i,SV421: $i] :
( ( ( ~ ( ( SV421
!= ( sK34_SY3110 @ SV421 @ SV287 ) ) ) )
= $false )
| ( ( SV421
= ( pair_second @ SV287 ) )
= $true )
| ( ( SV287
= ( ordered_pair @ SV311 @ SV323 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2777]) ).
thf(2873,plain,
! [SV323: $i,SV311: $i,SV422: $i,SV457: $i,SV287: $i] :
( ( ( ! [SY4035: $i] :
( ( SV287
!= ( ordered_pair @ SV457 @ SY4035 ) )
| ( SV422 = SY4035 ) ) )
= $true )
| ( ( SV422
= ( pair_second @ SV287 ) )
= $false )
| ( ( SV287
= ( ordered_pair @ SV311 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2778]) ).
thf(2874,plain,
! [SV324: $i,SV337: $i] :
( ( ( ( ( sK52_C @ SV337 @ SV324 )
!= ( sK53_SY3121 @ SV337 @ SV324 ) )
| ~ ( in @ ( sK52_C @ SV337 @ SV324 ) @ SV324 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) )
= $true )
| ( ( SV337
= ( identity_relation @ SV324 ) )
= $true )
| ( ( relation @ SV337 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2779]) ).
thf(2875,plain,
! [SV324: $i,SV337: $i] :
( ( ( ~ ( ( ( sK52_C @ SV337 @ SV324 )
= ( sK53_SY3121 @ SV337 @ SV324 ) )
| ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) )
| ~ ( ( in @ ( sK52_C @ SV337 @ SV324 ) @ SV324 )
| ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) ) )
= $false )
| ( ( SV337
= ( identity_relation @ SV324 ) )
= $true )
| ( ( relation @ SV337 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2780]) ).
thf(2876,plain,
! [SV338: $i,SV325: $i] :
( ( ( ! [SY3895: $i,SY3896: $i] :
( ( SY3895 != SY3896 )
| ~ ( in @ SY3895 @ SV325 )
| ( in @ ( ordered_pair @ SY3895 @ SY3896 ) @ SV338 ) ) )
= $true )
| ( ( SV338
= ( identity_relation @ SV325 ) )
= $false )
| ( ( relation @ SV338 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2781]) ).
thf(2877,plain,
! [SV325: $i,SV338: $i] :
( ( ( ~ ( ~ ! [SY3897: $i,SY3898: $i] :
( ~ ( in @ ( ordered_pair @ SY3897 @ SY3898 ) @ SV338 )
| ( SY3897 = SY3898 ) )
| ~ ! [SY3899: $i] :
( ! [SY3900: $i] :
~ ( in @ ( ordered_pair @ SY3899 @ SY3900 ) @ SV338 )
| ( in @ SY3899 @ SV325 ) ) ) )
= $true )
| ( ( SV338
= ( identity_relation @ SV325 ) )
= $false )
| ( ( relation @ SV338 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2782]) ).
thf(2878,plain,
! [SV289: $i,SV339: $i,SV356: $i] :
( ( ( ! [SY3921: $i] :
~ ( in @ ( ordered_pair @ ( sK59_D @ SV356 @ SV339 @ SV289 ) @ SY3921 ) @ SV356 ) )
= $true )
| ( ( ( relation_dom_as_subset @ SV339 @ SV289 @ SV356 )
= SV339 )
= $true )
| ( ( relation_of2_as_subset @ SV356 @ SV339 @ SV289 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2783]) ).
thf(2879,plain,
! [SV289: $i,SV339: $i,SV356: $i] :
( ( ( in @ ( sK59_D @ SV356 @ SV339 @ SV289 ) @ SV339 )
= $true )
| ( ( ( relation_dom_as_subset @ SV339 @ SV289 @ SV356 )
= SV339 )
= $true )
| ( ( relation_of2_as_subset @ SV356 @ SV339 @ SV289 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2784]) ).
thf(2880,plain,
! [SV289: $i,SV340: $i,SV357: $i,SV448: $i] :
( ( ( in @ ( ordered_pair @ SV448 @ ( sK58_E @ SV448 @ SV357 @ SV340 @ SV289 ) ) @ SV357 )
= $true )
| ( ( ~ ( in @ SV448 @ SV340 ) )
= $true )
| ( ( ( relation_dom_as_subset @ SV340 @ SV289 @ SV357 )
= SV340 )
= $false )
| ( ( relation_of2_as_subset @ SV357 @ SV340 @ SV289 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2785]) ).
thf(2881,plain,
! [SV290: $i,SV380: $i] :
( ( ( ! [SY3954: $i] :
~ ( in @ ( ordered_pair @ ( sK22_C @ SV380 @ SV290 ) @ SY3954 ) @ SV290 ) )
= $true )
| ( ( ~ ( in @ ( sK22_C @ SV380 @ SV290 ) @ SV380 ) )
= $true )
| ( ( SV380
= ( relation_dom @ SV290 ) )
= $true )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2786]) ).
thf(2882,plain,
! [SV290: $i,SV380: $i] :
( ( ( in @ ( ordered_pair @ ( sK22_C @ SV380 @ SV290 ) @ ( sK23_SY3101 @ SV380 @ SV290 ) ) @ SV290 )
= $true )
| ( ( in @ ( sK22_C @ SV380 @ SV290 ) @ SV380 )
= $true )
| ( ( SV380
= ( relation_dom @ SV290 ) )
= $true )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2787]) ).
thf(2883,plain,
! [SV381: $i,SV290: $i] :
( ( ( ! [SY3955: $i] :
( ! [SY3733: $i] :
~ ( in @ ( ordered_pair @ SY3955 @ SY3733 ) @ SV290 )
| ( in @ SY3955 @ SV381 ) ) )
= $true )
| ( ( SV381
= ( relation_dom @ SV290 ) )
= $false )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2788]) ).
thf(2884,plain,
! [SV290: $i,SV381: $i] :
( ( ( ! [SY3957: $i] :
( ~ ( in @ SY3957 @ SV381 )
| ( in @ ( ordered_pair @ SY3957 @ ( sK21_D @ SY3957 @ SV381 @ SV290 ) ) @ SV290 ) ) )
= $true )
| ( ( SV381
= ( relation_dom @ SV290 ) )
= $false )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2789]) ).
thf(2885,plain,
! [SV291: $i,SV382: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV291 )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV382 ) ) )
= $false )
| ( ( SV291 = SV382 )
= $true )
| ( ( relation @ SV382 )
= $false )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2790]) ).
thf(2886,plain,
! [SV291: $i,SV382: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV291 )
| ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV382 ) ) )
= $false )
| ( ( SV291 = SV382 )
= $true )
| ( ( relation @ SV382 )
= $false )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2790]) ).
thf(2887,plain,
! [SV383: $i,SV291: $i] :
( ( ( ~ ! [SY3958: $i,SY3959: $i] :
( ~ ( in @ ( ordered_pair @ SY3958 @ SY3959 ) @ SV291 )
| ( in @ ( ordered_pair @ SY3958 @ SY3959 ) @ SV383 ) )
| ~ ! [SY3960: $i,SY3961: $i] :
( ~ ( in @ ( ordered_pair @ SY3960 @ SY3961 ) @ SV383 )
| ( in @ ( ordered_pair @ SY3960 @ SY3961 ) @ SV291 ) ) )
= $false )
| ( ( SV291 = SV383 )
= $false )
| ( ( relation @ SV383 )
= $false )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2791]) ).
thf(2888,plain,
! [SV326: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK66_B @ SV326 ) @ ( sK67_SY3127 @ SV326 ) ) @ SV326 ) )
= $false )
| ( ( transitive @ SV326 )
= $true )
| ( ( relation @ SV326 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2792]) ).
thf(2889,plain,
! [SV326: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK67_SY3127 @ SV326 ) @ ( sK68_SY3129 @ SV326 ) ) @ SV326 ) )
= $false )
| ( ( transitive @ SV326 )
= $true )
| ( ( relation @ SV326 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2792]) ).
thf(2890,plain,
! [SV449: $i,SV327: $i,SV437: $i,SV423: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV423 @ SV437 ) @ SV327 )
| ~ ( in @ ( ordered_pair @ SV437 @ SV449 ) @ SV327 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV423 @ SV449 ) @ SV327 )
= $true )
| ( ( transitive @ SV327 )
= $false )
| ( ( relation @ SV327 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2794]) ).
thf(2891,plain,
! [SV292: $i,SV384: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SV384 @ SV292 ) @ ( sK13_SY3095 @ SV384 @ SV292 ) ) @ SV384 )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV384 @ SV292 ) @ ( sK12_C @ SV384 @ SV292 ) ) @ SV292 ) ) )
= $false )
| ( ( SV384
= ( relation_inverse @ SV292 ) )
= $true )
| ( ( relation @ SV384 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2795]) ).
thf(2892,plain,
! [SV292: $i,SV384: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SV384 @ SV292 ) @ ( sK13_SY3095 @ SV384 @ SV292 ) ) @ SV384 )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV384 @ SV292 ) @ ( sK12_C @ SV384 @ SV292 ) ) @ SV292 ) ) )
= $false )
| ( ( SV384
= ( relation_inverse @ SV292 ) )
= $true )
| ( ( relation @ SV384 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2795]) ).
thf(2893,plain,
! [SV292: $i,SV385: $i] :
( ( ( ~ ! [SY3962: $i,SY3963: $i] :
( ~ ( in @ ( ordered_pair @ SY3962 @ SY3963 ) @ SV385 )
| ( in @ ( ordered_pair @ SY3963 @ SY3962 ) @ SV292 ) )
| ~ ! [SY3964: $i,SY3965: $i] :
( ~ ( in @ ( ordered_pair @ SY3965 @ SY3964 ) @ SV292 )
| ( in @ ( ordered_pair @ SY3964 @ SY3965 ) @ SV385 ) ) )
= $false )
| ( ( SV385
= ( relation_inverse @ SV292 ) )
= $false )
| ( ( relation @ SV385 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2796]) ).
thf(2894,plain,
! [SV293: $i,SV458: $i] :
( ( ( ~ ( in @ SV458 @ ( relation_dom @ SV293 ) )
| ! [SY4036: $i] :
( ( SY4036
!= ( apply @ SV293 @ SV458 ) )
| ( in @ ( ordered_pair @ SV458 @ SY4036 ) @ SV293 ) ) )
= $true )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2797]) ).
thf(2895,plain,
! [SV293: $i,SV459: $i] :
( ( ( ~ ( in @ SV459 @ ( relation_dom @ SV293 ) )
| ! [SY4037: $i] :
( ~ ( in @ ( ordered_pair @ SV459 @ SY4037 ) @ SV293 )
| ( SY4037
= ( apply @ SV293 @ SV459 ) ) ) )
= $true )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2798]) ).
thf(2896,plain,
! [SV293: $i,SV460: $i] :
( ( ( ( in @ SV460 @ ( relation_dom @ SV293 ) )
| ! [SY4038: $i] :
( ( SY4038
!= ( apply @ SV293 @ SV460 ) )
| ( SY4038 = empty_set ) ) )
= $true )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2799]) ).
thf(2897,plain,
! [SV293: $i,SV461: $i] :
( ( ( ( in @ SV461 @ ( relation_dom @ SV293 ) )
| ! [SY4039: $i] :
( ( SY4039 != empty_set )
| ( SY4039
= ( apply @ SV293 @ SV461 ) ) ) )
= $true )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2800]) ).
thf(2898,plain,
! [SV294: $i,SV386: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_C @ SV386 @ SV294 ) @ SV386 )
| ~ ( in @ ( sK20_SY3099 @ SV386 @ SV294 ) @ SV386 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SV386 @ SV294 ) @ ( sK20_SY3099 @ SV386 @ SV294 ) ) @ SV294 ) )
| ~ ( in @ ( ordered_pair @ ( sK20_SY3099 @ SV386 @ SV294 ) @ ( sK19_C @ SV386 @ SV294 ) ) @ SV294 ) )
= $false )
| ( ( is_antisymmetric_in @ SV294 @ SV386 )
= $true )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2801]) ).
thf(2899,plain,
! [SV294: $i,SV386: $i] :
( ( ( ( sK19_C @ SV386 @ SV294 )
= ( sK20_SY3099 @ SV386 @ SV294 ) )
= $false )
| ( ( is_antisymmetric_in @ SV294 @ SV386 )
= $true )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2802]) ).
thf(2900,plain,
! [SV294: $i,SV450: $i,SV387: $i,SV438: $i] :
( ( ( ~ ( in @ SV438 @ SV387 )
| ~ ( in @ SV450 @ SV387 )
| ~ ( in @ ( ordered_pair @ SV438 @ SV450 ) @ SV294 )
| ~ ( in @ ( ordered_pair @ SV450 @ SV438 ) @ SV294 ) )
= $true )
| ( ( SV438 = SV450 )
= $true )
| ( ( is_antisymmetric_in @ SV294 @ SV387 )
= $false )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2803]) ).
thf(2901,plain,
! [SV295: $i,SV388: $i,SV404: $i] :
( ( ( ( ( sK35_D @ SV404 @ SV388 @ SV295 )
= SV388 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV388 ) @ SV295 )
| ~ ( in @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV404 ) )
= $true )
| ( ( SV404
= ( fiber @ SV295 @ SV388 ) )
= $true )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2804]) ).
thf(2902,plain,
! [SV295: $i,SV388: $i,SV404: $i] :
( ( ( ~ ( ~ ( ( ( sK35_D @ SV404 @ SV388 @ SV295 )
!= SV388 )
| ( in @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV404 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV388 ) @ SV295 )
| ( in @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV404 ) ) ) )
= $true )
| ( ( SV404
= ( fiber @ SV295 @ SV388 ) )
= $true )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2805]) ).
thf(2903,plain,
! [SV405: $i,SV295: $i,SV389: $i] :
( ( ( ~ ! [SY3994: $i] :
( ( SY3994 = SV389 )
| ~ ( in @ ( ordered_pair @ SY3994 @ SV389 ) @ SV295 )
| ( in @ SY3994 @ SV405 ) ) )
= $false )
| ( ( SV405
= ( fiber @ SV295 @ SV389 ) )
= $false )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2806]) ).
thf(2904,plain,
! [SV295: $i,SV389: $i,SV405: $i] :
( ( ( ~ ~ ( ~ ! [SY3995: $i] :
( ~ ( in @ SY3995 @ SV405 )
| ( SY3995 != SV389 ) )
| ~ ! [SY3996: $i] :
( ~ ( in @ SY3996 @ SV405 )
| ( in @ ( ordered_pair @ SY3996 @ SV389 ) @ SV295 ) ) ) )
= $false )
| ( ( SV405
= ( fiber @ SV295 @ SV389 ) )
= $false )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2806]) ).
thf(2905,plain,
! [SV296: $i,SV307: $i,SV406: $i] :
( ( ( ~ ( ~ ( in @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) @ SV296 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV307 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) )
| ~ ~ ( ~ ( ( in @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) @ SV296 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV307 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) ) ) )
= $false )
| ( ( SV406
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $true )
| ( ( relation @ SV406 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2807]) ).
thf(2906,plain,
! [SV307: $i,SV296: $i,SV407: $i] :
( ( ( SV407
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $false )
| ( ( ~ ( ~ ! [SY3997: $i,SY3998: $i] :
( ~ ( in @ SY3998 @ SV296 )
| ~ ( in @ ( ordered_pair @ SY3997 @ SY3998 ) @ SV307 )
| ( in @ ( ordered_pair @ SY3997 @ SY3998 ) @ SV407 ) )
| ~ ~ ( ~ ! [SY3999: $i,SY4000: $i] :
( ~ ( in @ ( ordered_pair @ SY3999 @ SY4000 ) @ SV407 )
| ( in @ SY4000 @ SV296 ) )
| ~ ! [SY4001: $i,SY4002: $i] :
( ~ ( in @ ( ordered_pair @ SY4001 @ SY4002 ) @ SV407 )
| ( in @ ( ordered_pair @ SY4001 @ SY4002 ) @ SV307 ) ) ) ) )
= $true )
| ( ( relation @ SV407 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2808]) ).
thf(2907,plain,
! [SV297: $i,SV390: $i] :
( ( ( ! [SY3973: $i] :
~ ( in @ ( ordered_pair @ SY3973 @ ( sK17_C @ SV390 @ SV297 ) ) @ SV297 ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV390 @ SV297 ) @ SV390 ) )
= $true )
| ( ( SV390
= ( relation_rng @ SV297 ) )
= $true )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2809]) ).
thf(2908,plain,
! [SV297: $i,SV390: $i] :
( ( ( in @ ( ordered_pair @ ( sK18_SY3098 @ SV390 @ SV297 ) @ ( sK17_C @ SV390 @ SV297 ) ) @ SV297 )
= $true )
| ( ( in @ ( sK17_C @ SV390 @ SV297 ) @ SV390 )
= $true )
| ( ( SV390
= ( relation_rng @ SV297 ) )
= $true )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2810]) ).
thf(2909,plain,
! [SV391: $i,SV297: $i] :
( ( ( ! [SY3974: $i] :
( ! [SY3779: $i] :
~ ( in @ ( ordered_pair @ SY3779 @ SY3974 ) @ SV297 )
| ( in @ SY3974 @ SV391 ) ) )
= $true )
| ( ( SV391
= ( relation_rng @ SV297 ) )
= $false )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2811]) ).
thf(2910,plain,
! [SV297: $i,SV391: $i] :
( ( ( ! [SY3976: $i] :
( ~ ( in @ SY3976 @ SV391 )
| ( in @ ( ordered_pair @ ( sK16_D @ SY3976 @ SV391 @ SV297 ) @ SY3976 ) @ SV297 ) ) )
= $true )
| ( ( SV391
= ( relation_rng @ SV297 ) )
= $false )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2812]) ).
thf(2911,plain,
! [SV392: $i,SV308: $i,SV360: $i,SV299: $i] :
( ( ( in @ SV299 @ SV360 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ SV392 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SV360 ) @ SV392 ) )
= $true )
| ( ( relation @ SV392 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2813]) ).
thf(2912,plain,
! [SV424: $i,SV308: $i,SV299: $i,SV439: $i] :
( ( ( relation @ SV439 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SV424 ) @ SV439 ) )
| ( in @ SV299 @ SV424 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2814]) ).
thf(2913,plain,
! [SV425: $i,SV308: $i,SV299: $i,SV440: $i] :
( ( ( relation @ SV440 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SV425 ) @ SV440 ) )
| ( in @ ( ordered_pair @ SV299 @ SV308 ) @ SV440 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2815]) ).
thf(2914,plain,
! [SV343: $i,SV301: $i,SV363: $i,SV441: $i] :
( ( ( ~ ( in @ SV441 @ ( relation_rng @ SV363 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV301 @ SV441 ) @ SV363 ) )
= $true )
| ( ( ~ ( in @ SV441 @ SV343 ) )
= $true )
| ( ( in @ SV301 @ ( relation_inverse_image @ SV363 @ SV343 ) )
= $true )
| ( ( relation @ SV363 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2816]) ).
thf(2915,plain,
! [SV301: $i,SV344: $i,SV364: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK60_D @ SV364 @ SV344 @ SV301 ) @ ( relation_rng @ SV364 ) )
| ~ ( in @ ( ordered_pair @ SV301 @ ( sK60_D @ SV364 @ SV344 @ SV301 ) ) @ SV364 ) ) )
= $false )
| ( ( in @ SV301 @ ( relation_inverse_image @ SV364 @ SV344 ) )
= $false )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2817]) ).
thf(2916,plain,
! [SV301: $i,SV344: $i,SV364: $i] :
( ( ( ~ ( in @ ( sK60_D @ SV364 @ SV344 @ SV301 ) @ SV344 ) )
= $false )
| ( ( in @ SV301 @ ( relation_inverse_image @ SV364 @ SV344 ) )
= $false )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2817]) ).
thf(2917,plain,
! [SV302: $i,SV394: $i] :
( ( ( in @ ( ordered_pair @ ( sK36_C @ SV394 @ SV302 ) @ ( sK36_C @ SV394 @ SV302 ) ) @ SV302 )
= $false )
| ( ( is_reflexive_in @ SV302 @ SV394 )
= $true )
| ( ( relation @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2819]) ).
thf(2918,plain,
! [SV302: $i,SV395: $i,SV442: $i] :
( ( ( in @ SV442 @ SV395 )
= $false )
| ( ( in @ ( ordered_pair @ SV442 @ SV442 ) @ SV302 )
= $true )
| ( ( is_reflexive_in @ SV302 @ SV395 )
= $false )
| ( ( relation @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2820]) ).
thf(2919,plain,
! [SV274: $i,SV367: $i] :
( ( ( ~ ~ ( ~ ( ( ( sK14_C @ SV367 @ SV274 )
!= ( sK15_SY3096 @ SV367 @ SV274 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SV367 @ SV274 ) @ SV367 )
| ~ ( in @ ( sK15_SY3096 @ SV367 @ SV274 ) @ SV367 ) ) ) )
= $false )
| ( ( is_connected_in @ SV274 @ SV367 )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2825]) ).
thf(2920,plain,
! [SV274: $i,SV367: $i] :
( ( ( ~ ~ ( in @ ( ordered_pair @ ( sK14_C @ SV367 @ SV274 ) @ ( sK15_SY3096 @ SV367 @ SV274 ) ) @ SV274 ) )
= $false )
| ( ( is_connected_in @ SV274 @ SV367 )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2825]) ).
thf(2921,plain,
! [SV274: $i,SV368: $i,SV445: $i,SV428: $i] :
( ( ( ( SV428 = SV445 )
| ~ ( in @ SV428 @ SV368 )
| ~ ( in @ SV445 @ SV368 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV428 @ SV445 ) @ SV274 )
= $true )
| ( ( in @ ( ordered_pair @ SV445 @ SV428 ) @ SV274 )
= $true )
| ( ( is_connected_in @ SV274 @ SV368 )
= $false )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2827]) ).
thf(2922,plain,
! [SV316: $i] :
( ( ( in @ ( ordered_pair @ ( sK64_B @ SV316 ) @ ( sK65_SY3126 @ SV316 ) ) @ SV316 )
= $true )
| ( ( antisymmetric @ SV316 )
= $true )
| ( ( relation @ SV316 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2828]) ).
thf(2923,plain,
! [SV316: $i] :
( ( ( in @ ( ordered_pair @ ( sK65_SY3126 @ SV316 ) @ ( sK64_B @ SV316 ) ) @ SV316 )
= $true )
| ( ( antisymmetric @ SV316 )
= $true )
| ( ( relation @ SV316 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2829]) ).
thf(2924,plain,
! [SV317: $i,SV430: $i,SV415: $i] :
( ( ( in @ ( ordered_pair @ SV415 @ SV430 ) @ SV317 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV430 @ SV415 ) @ SV317 ) )
= $true )
| ( ( SV415 = SV430 )
= $true )
| ( ( antisymmetric @ SV317 )
= $false )
| ( ( relation @ SV317 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2830]) ).
thf(2925,plain,
! [SV347: $i,SV328: $i,SV462: $i,SV275: $i,SV451: $i] :
( ( ( ~ ( in @ SV451 @ SV275 )
| ~ ( in @ SV462 @ SV328 )
| ( ( sK28_D @ SV347 @ SV328 @ SV275 )
!= ( ordered_pair @ SV451 @ SV462 ) ) )
= $true )
| ( ( ~ ( in @ ( sK28_D @ SV347 @ SV328 @ SV275 ) @ SV347 ) )
= $true )
| ( ( SV347
= ( cartesian_product2 @ SV275 @ SV328 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2831]) ).
thf(2926,plain,
! [SV275: $i,SV328: $i,SV347: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK29_SY3106 @ SV347 @ SV328 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK30_SY3108 @ SV347 @ SV328 @ SV275 ) @ SV328 ) ) )
= $false )
| ( ( in @ ( sK28_D @ SV347 @ SV328 @ SV275 ) @ SV347 )
= $true )
| ( ( SV347
= ( cartesian_product2 @ SV275 @ SV328 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2832]) ).
thf(2927,plain,
! [SV275: $i,SV328: $i,SV347: $i] :
( ( ( ( ( sK28_D @ SV347 @ SV328 @ SV275 )
!= ( ordered_pair @ ( sK29_SY3106 @ SV347 @ SV328 @ SV275 ) @ ( sK30_SY3108 @ SV347 @ SV328 @ SV275 ) ) ) )
= $false )
| ( ( in @ ( sK28_D @ SV347 @ SV328 @ SV275 ) @ SV347 )
= $true )
| ( ( SV347
= ( cartesian_product2 @ SV275 @ SV328 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2832]) ).
thf(2928,plain,
! [SV348: $i,SV452: $i,SV329: $i,SV275: $i] :
( ( ( ! [SY4031: $i,SY4032: $i] :
( ~ ( in @ SY4031 @ SV275 )
| ~ ( in @ SY4032 @ SV329 )
| ( SV452
!= ( ordered_pair @ SY4031 @ SY4032 ) ) ) )
= $true )
| ( ( in @ SV452 @ SV348 )
= $true )
| ( ( SV348
= ( cartesian_product2 @ SV275 @ SV329 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2833]) ).
thf(2929,plain,
! [SV275: $i,SV329: $i,SV348: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV348 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK26_E @ SV453 @ SV348 @ SV329 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK27_SY3103 @ SV453 @ SV348 @ SV329 @ SV275 ) @ SV329 ) )
| ( SV453
!= ( ordered_pair @ ( sK26_E @ SV453 @ SV348 @ SV329 @ SV275 ) @ ( sK27_SY3103 @ SV453 @ SV348 @ SV329 @ SV275 ) ) ) ) )
= $true )
| ( ( SV348
= ( cartesian_product2 @ SV275 @ SV329 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2834]) ).
thf(2930,plain,
! [SV276: $i,SV370: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SV370 @ SV276 ) @ SV370 )
| ~ ( in @ ( sK4_SY3086 @ SV370 @ SV276 ) @ SV370 ) )
| ~ ( in @ ( sK5_SY3088 @ SV370 @ SV276 ) @ SV370 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SV370 @ SV276 ) @ ( sK4_SY3086 @ SV370 @ SV276 ) ) @ SV276 ) ) )
= $false )
| ( ( is_transitive_in @ SV276 @ SV370 )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2835]) ).
thf(2931,plain,
! [SV276: $i,SV370: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK4_SY3086 @ SV370 @ SV276 ) @ ( sK5_SY3088 @ SV370 @ SV276 ) ) @ SV276 ) )
= $false )
| ( ( is_transitive_in @ SV276 @ SV370 )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2835]) ).
thf(2932,plain,
! [SV276: $i,SV454: $i,SV446: $i,SV371: $i,SV431: $i] :
( ( ( ~ ( in @ SV431 @ SV371 )
| ~ ( in @ SV446 @ SV371 )
| ~ ( in @ SV454 @ SV371 )
| ~ ( in @ ( ordered_pair @ SV431 @ SV446 ) @ SV276 )
| ~ ( in @ ( ordered_pair @ SV446 @ SV454 ) @ SV276 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV431 @ SV454 ) @ SV276 )
= $true )
| ( ( is_transitive_in @ SV276 @ SV371 )
= $false )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2837]) ).
thf(2933,plain,
! [SV277: $i,SV372: $i,SV396: $i] :
( ( ( ! [SY3978: $i] :
( ~ ( in @ ( ordered_pair @ SY3978 @ ( sK46_D @ SV396 @ SV372 @ SV277 ) ) @ SV277 )
| ~ ( in @ SY3978 @ SV372 ) ) )
= $true )
| ( ( ~ ( in @ ( sK46_D @ SV396 @ SV372 @ SV277 ) @ SV396 ) )
= $true )
| ( ( SV396
= ( relation_image @ SV277 @ SV372 ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2838]) ).
thf(2934,plain,
! [SV277: $i,SV372: $i,SV396: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SV396 @ SV372 @ SV277 ) @ ( sK46_D @ SV396 @ SV372 @ SV277 ) ) @ SV277 )
| ~ ( in @ ( sK47_SY3118 @ SV396 @ SV372 @ SV277 ) @ SV372 ) ) )
= $true )
| ( ( in @ ( sK46_D @ SV396 @ SV372 @ SV277 ) @ SV396 )
= $true )
| ( ( SV396
= ( relation_image @ SV277 @ SV372 ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2839]) ).
thf(2935,plain,
! [SV397: $i,SV373: $i,SV277: $i] :
( ( ( ! [SY3979: $i] :
( ! [SY3936: $i] :
( ~ ( in @ ( ordered_pair @ SY3936 @ SY3979 ) @ SV277 )
| ~ ( in @ SY3936 @ SV373 ) )
| ( in @ SY3979 @ SV397 ) ) )
= $true )
| ( ( SV397
= ( relation_image @ SV277 @ SV373 ) )
= $false )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2840]) ).
thf(2936,plain,
! [SV277: $i,SV373: $i,SV397: $i] :
( ( ( ! [SY3981: $i] :
( ~ ( in @ SY3981 @ SV397 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SY3981 @ SV397 @ SV373 @ SV277 ) @ SY3981 ) @ SV277 )
| ~ ( in @ ( sK45_E @ SY3981 @ SV397 @ SV373 @ SV277 ) @ SV373 ) ) ) )
= $true )
| ( ( SV397
= ( relation_image @ SV277 @ SV373 ) )
= $false )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2841]) ).
thf(2937,plain,
! [SV278: $i,SV374: $i,SV398: $i] :
( ( ( ~ ( ~ ( in @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ SV374 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV278 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) ) )
= $false )
| ( ( SV398
= ( relation_dom_restriction @ SV278 @ SV374 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2842]) ).
thf(2938,plain,
! [SV278: $i,SV374: $i,SV398: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ SV374 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV278 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) ) ) )
= $false )
| ( ( SV398
= ( relation_dom_restriction @ SV278 @ SV374 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2842]) ).
thf(2939,plain,
! [SV399: $i,SV278: $i,SV375: $i] :
( ( ( ~ ! [SY3982: $i,SY3983: $i] :
( ~ ( in @ SY3982 @ SV375 )
| ~ ( in @ ( ordered_pair @ SY3982 @ SY3983 ) @ SV278 )
| ( in @ ( ordered_pair @ SY3982 @ SY3983 ) @ SV399 ) )
| ~ ~ ( ~ ! [SY3984: $i] :
( ! [SY3985: $i] :
~ ( in @ ( ordered_pair @ SY3984 @ SY3985 ) @ SV399 )
| ( in @ SY3984 @ SV375 ) )
| ~ ! [SY3986: $i,SY3987: $i] :
( ~ ( in @ ( ordered_pair @ SY3986 @ SY3987 ) @ SV399 )
| ( in @ ( ordered_pair @ SY3986 @ SY3987 ) @ SV278 ) ) ) )
= $false )
| ( ( SV399
= ( relation_dom_restriction @ SV278 @ SV375 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2843]) ).
thf(2940,plain,
! [SV279: $i,SV376: $i,SV400: $i] :
( ( ( ! [SY3988: $i] :
( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SY3988 ) @ SV279 )
| ~ ( in @ SY3988 @ SV376 ) ) )
= $true )
| ( ( ~ ( in @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SV400 ) )
= $true )
| ( ( SV400
= ( relation_inverse_image @ SV279 @ SV376 ) )
= $true )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2844]) ).
thf(2941,plain,
! [SV279: $i,SV376: $i,SV400: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ ( sK44_SY3116 @ SV400 @ SV376 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK44_SY3116 @ SV400 @ SV376 @ SV279 ) @ SV376 ) ) )
= $true )
| ( ( in @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SV400 )
= $true )
| ( ( SV400
= ( relation_inverse_image @ SV279 @ SV376 ) )
= $true )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2845]) ).
thf(2942,plain,
! [SV401: $i,SV377: $i,SV279: $i] :
( ( ( ! [SY3989: $i] :
( ! [SY3950: $i] :
( ~ ( in @ ( ordered_pair @ SY3989 @ SY3950 ) @ SV279 )
| ~ ( in @ SY3950 @ SV377 ) )
| ( in @ SY3989 @ SV401 ) ) )
= $true )
| ( ( SV401
= ( relation_inverse_image @ SV279 @ SV377 ) )
= $false )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2846]) ).
thf(2943,plain,
! [SV279: $i,SV377: $i,SV401: $i] :
( ( ( ! [SY3991: $i] :
( ~ ( in @ SY3991 @ SV401 )
| ~ ( ~ ( in @ ( ordered_pair @ SY3991 @ ( sK42_E @ SY3991 @ SV401 @ SV377 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK42_E @ SY3991 @ SV401 @ SV377 @ SV279 ) @ SV377 ) ) ) )
= $true )
| ( ( SV401
= ( relation_inverse_image @ SV279 @ SV377 ) )
= $false )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2847]) ).
thf(2944,plain,
! [SV280: $i,SV378: $i] :
( ( ( in @ ( ordered_pair @ ( sK24_C @ SV378 @ SV280 ) @ ( sK25_SY3102 @ SV378 @ SV280 ) ) @ SV280 )
= $true )
| ( ( subset @ SV280 @ SV378 )
= $true )
| ( ( relation @ SV378 )
= $false )
| ( ( relation @ SV280 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2848]) ).
thf(2945,plain,
! [SV280: $i,SV378: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK24_C @ SV378 @ SV280 ) @ ( sK25_SY3102 @ SV378 @ SV280 ) ) @ SV378 ) )
= $true )
| ( ( subset @ SV280 @ SV378 )
= $true )
| ( ( relation @ SV378 )
= $false )
| ( ( relation @ SV280 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2849]) ).
thf(2946,plain,
! [SV379: $i,SV280: $i,SV463: $i,SV455: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV455 @ SV463 ) @ SV280 )
| ( in @ ( ordered_pair @ SV455 @ SV463 ) @ SV379 ) )
= $true )
| ( ( subset @ SV280 @ SV379 )
= $false )
| ( ( relation @ SV379 )
= $false )
| ( ( relation @ SV280 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2850]) ).
thf(2947,plain,
! [SV281: $i,SV318: $i,SV432: $i] :
( ( ( ~ ( ~ ( ! [SY4021: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ SY4021 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY4021 @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV318 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV432 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK9_SY3093 @ SV432 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV318 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV432 ) ) ) )
= $true )
| ( ( SV432
= ( relation_composition @ SV281 @ SV318 ) )
= $true )
| ( ( relation @ SV432 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2851]) ).
thf(2948,plain,
! [SV318: $i,SV281: $i,SV433: $i] :
( ( ( ( SV433
!= ( relation_composition @ SV281 @ SV318 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY4022: $i,SY4023: $i] :
( ! [SY3848: $i] :
( ~ ( in @ ( ordered_pair @ SY4022 @ SY3848 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY3848 @ SY4023 ) @ SV318 ) )
| ( in @ ( ordered_pair @ SY4022 @ SY4023 ) @ SV433 ) )
| ~ ! [SY4025: $i,SY4026: $i] :
( ~ ( in @ ( ordered_pair @ SY4025 @ SY4026 ) @ SV433 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4025 @ ( sK6_F @ SY4026 @ SY4025 @ SV433 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY4026 @ SY4025 @ SV433 @ SV318 @ SV281 ) @ SY4026 ) @ SV318 ) ) ) ) )
= $true )
| ( ( relation @ SV433 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2852]) ).
thf(2949,plain,
! [SV282: $i,SV330: $i,SV349: $i,SV464: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV464 @ ( sK57_D @ SV349 @ SV330 @ SV282 ) ) @ SV349 ) )
= $true )
| ( ( ( relation_rng_as_subset @ SV282 @ SV330 @ SV349 )
= SV330 )
= $true )
| ( ( relation_of2_as_subset @ SV349 @ SV282 @ SV330 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2853]) ).
thf(2950,plain,
! [SV282: $i,SV350: $i,SV331: $i,SV447: $i] :
( ( ( in @ SV447 @ SV331 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK56_E @ SV447 @ SV350 @ SV331 @ SV282 ) @ SV447 ) @ SV350 )
= $true )
| ( ( ( relation_rng_as_subset @ SV282 @ SV331 @ SV350 )
= SV331 )
= $false )
| ( ( relation_of2_as_subset @ SV350 @ SV282 @ SV331 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2855]) ).
thf(2951,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( function @ SV434 )
= $false )
| ( ( ~ ( relation @ SV434 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) ) ) )
| ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 )
| ( relation_isomorphism @ SV283 @ SV319 @ SV434 ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2856]) ).
thf(2952,plain,
! [SV319: $i,SV283: $i,SV465: $i] :
( ( ( ~ ( function @ SV465 )
| ~ ( relation @ SV465 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
| ~ ( ~ ! [SY4040: $i,SY4041: $i] :
( ~ ( in @ SY4040 @ ( relation_field @ SV283 ) )
| ~ ( in @ SY4041 @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV465 @ SY4040 ) @ ( apply @ SV465 @ SY4041 ) ) @ SV319 )
| ( in @ ( ordered_pair @ SY4040 @ SY4041 ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3687: $i] :
( ! [SY3688: $i] :
~ ( in @ ( ordered_pair @ SY3687 @ SY3688 ) @ SV283 )
| ( in @ SY3687 @ ( relation_field @ SV283 ) ) )
| ~ ! [SY3689: $i,SY3690: $i] :
( ~ ( in @ ( ordered_pair @ SY3689 @ SY3690 ) @ SV283 )
| ( in @ SY3690 @ ( relation_field @ SV283 ) ) ) )
| ~ ! [SY4046: $i,SY4047: $i] :
( ~ ( in @ ( ordered_pair @ SY4046 @ SY4047 ) @ SV283 )
| ( in @ ( ordered_pair @ ( apply @ SV465 @ SY4046 ) @ ( apply @ SV465 @ SY4047 ) ) @ SV319 ) ) ) ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2857]) ).
thf(2953,plain,
! [SV319: $i,SV283: $i] :
( ( ( ~ ~ ( ~ ! [SY3861: $i] :
( ~ ( function @ SY3861 )
| ~ ( relation @ SY3861 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3861 )
| ( ( relation_dom @ SY3861 )
= ( relation_field @ SV283 ) ) )
| ~ ! [SY3862: $i] :
( ~ ( function @ SY3862 )
| ~ ( relation @ SY3862 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3862 )
| ( ( relation_rng @ SY3862 )
= ( relation_field @ SV319 ) ) ) )
| ~ ! [SY3863: $i] :
( ~ ( function @ SY3863 )
| ~ ( relation @ SY3863 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3863 )
| ( one_to_one @ SY3863 ) ) )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2858]) ).
thf(2954,plain,
! [SV320: $i] :
( ( ( ~ ( ~ ( ( ( sK62_B @ SV320 )
!= ( sK63_SY3125 @ SV320 ) ) )
| ~ ~ ( ~ ( in @ ( sK62_B @ SV320 ) @ ( relation_field @ SV320 ) )
| ~ ( in @ ( sK63_SY3125 @ SV320 ) @ ( relation_field @ SV320 ) ) ) ) )
= $true )
| ( ( connected @ SV320 )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2859]) ).
thf(2955,plain,
! [SV320: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK62_B @ SV320 ) @ ( sK63_SY3125 @ SV320 ) ) @ SV320 ) )
= $true )
| ( ( connected @ SV320 )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2860]) ).
thf(2956,plain,
! [SV321: $i,SV435: $i,SV416: $i] :
( ( ( SV416 = SV435 )
= $true )
| ( ( ~ ( in @ SV416 @ ( relation_field @ SV321 ) )
| ~ ( in @ SV435 @ ( relation_field @ SV321 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV416 @ SV435 ) @ SV321 )
= $true )
| ( ( in @ ( ordered_pair @ SV435 @ SV416 ) @ SV321 )
= $true )
| ( ( connected @ SV321 )
= $false )
| ( ( relation @ SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2861]) ).
thf(2957,plain,
! [SV284: $i,SV351: $i,SV332: $i] :
( ( ( SV332
= ( apply @ SV351 @ SV284 ) )
= $false )
| ( ( ~ ( in @ SV284 @ ( relation_dom @ SV351 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV284 @ SV332 ) @ SV351 )
= $true )
| ( ( function @ SV351 )
= $false )
| ( ( relation @ SV351 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2862]) ).
thf(2958,plain,
! [SV402: $i,SV284: $i,SV417: $i] :
( ( ( relation @ SV417 )
= $false )
| ( ( function @ SV417 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV284 @ SV402 ) @ SV417 )
| ( SV402
= ( apply @ SV417 @ SV284 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2863]) ).
thf(2959,plain,
! [SV403: $i,SV284: $i,SV418: $i] :
( ( ( relation @ SV418 )
= $false )
| ( ( function @ SV418 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV284 @ SV403 ) @ SV418 )
| ( in @ SV284 @ ( relation_dom @ SV418 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2864]) ).
thf(2960,plain,
! [SV333: $i,SV285: $i,SV352: $i,SV436: $i] :
( ( ( in @ SV436 @ ( relation_dom @ SV352 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV436 @ SV285 ) @ SV352 ) )
= $true )
| ( ( ~ ( in @ SV436 @ SV333 ) )
= $true )
| ( ( in @ SV285 @ ( relation_image @ SV352 @ SV333 ) )
= $true )
| ( ( relation @ SV352 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2865]) ).
thf(2961,plain,
! [SV285: $i,SV334: $i,SV353: $i] :
( ( ( ~ ( ~ ( in @ ( sK61_D @ SV353 @ SV334 @ SV285 ) @ ( relation_dom @ SV353 ) )
| ~ ( in @ ( ordered_pair @ ( sK61_D @ SV353 @ SV334 @ SV285 ) @ SV285 ) @ SV353 ) ) )
= $true )
| ( ( in @ SV285 @ ( relation_image @ SV353 @ SV334 ) )
= $false )
| ( ( relation @ SV353 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2866]) ).
thf(2962,plain,
! [SV285: $i,SV334: $i,SV353: $i] :
( ( ( in @ ( sK61_D @ SV353 @ SV334 @ SV285 ) @ SV334 )
= $true )
| ( ( in @ SV285 @ ( relation_image @ SV353 @ SV334 ) )
= $false )
| ( ( relation @ SV353 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2867]) ).
thf(2963,plain,
! [SV322: $i,SV310: $i,SV419: $i,SV286: $i] :
( ( ( SV286
= ( ordered_pair @ ( sK40_C @ SV419 @ SV286 ) @ ( sK41_SY3114 @ SV419 @ SV286 ) ) )
= $true )
| ( ( SV419
= ( pair_first @ SV286 ) )
= $true )
| ( ( SV286
= ( ordered_pair @ SV310 @ SV322 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2868]) ).
thf(2964,plain,
! [SV322: $i,SV310: $i,SV286: $i,SV419: $i] :
( ( ( ( SV419
!= ( sK40_C @ SV419 @ SV286 ) ) )
= $true )
| ( ( SV419
= ( pair_first @ SV286 ) )
= $true )
| ( ( SV286
= ( ordered_pair @ SV310 @ SV322 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2869]) ).
thf(2965,plain,
! [SV322: $i,SV310: $i,SV420: $i,SV456: $i,SV286: $i] :
( ( ( ! [SY4034: $i] :
( SV286
!= ( ordered_pair @ SV456 @ SY4034 ) ) )
= $true )
| ( ( SV420 = SV456 )
= $true )
| ( ( SV420
= ( pair_first @ SV286 ) )
= $false )
| ( ( SV286
= ( ordered_pair @ SV310 @ SV322 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2870]) ).
thf(2966,plain,
! [SV323: $i,SV311: $i,SV421: $i,SV287: $i] :
( ( ( SV287
= ( ordered_pair @ ( sK33_C @ SV421 @ SV287 ) @ ( sK34_SY3110 @ SV421 @ SV287 ) ) )
= $true )
| ( ( SV421
= ( pair_second @ SV287 ) )
= $true )
| ( ( SV287
= ( ordered_pair @ SV311 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2871]) ).
thf(2967,plain,
! [SV323: $i,SV311: $i,SV287: $i,SV421: $i] :
( ( ( ( SV421
!= ( sK34_SY3110 @ SV421 @ SV287 ) ) )
= $true )
| ( ( SV421
= ( pair_second @ SV287 ) )
= $true )
| ( ( SV287
= ( ordered_pair @ SV311 @ SV323 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2872]) ).
thf(2968,plain,
! [SV323: $i,SV311: $i,SV422: $i,SV466: $i,SV457: $i,SV287: $i] :
( ( ( ( SV287
!= ( ordered_pair @ SV457 @ SV466 ) )
| ( SV422 = SV466 ) )
= $true )
| ( ( SV422
= ( pair_second @ SV287 ) )
= $false )
| ( ( SV287
= ( ordered_pair @ SV311 @ SV323 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2873]) ).
thf(2969,plain,
! [SV324: $i,SV337: $i] :
( ( ( ( ( sK52_C @ SV337 @ SV324 )
!= ( sK53_SY3121 @ SV337 @ SV324 ) ) )
= $true )
| ( ( ~ ( in @ ( sK52_C @ SV337 @ SV324 ) @ SV324 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) )
= $true )
| ( ( SV337
= ( identity_relation @ SV324 ) )
= $true )
| ( ( relation @ SV337 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2874]) ).
thf(2970,plain,
! [SV324: $i,SV337: $i] :
( ( ( ~ ( ( ( sK52_C @ SV337 @ SV324 )
= ( sK53_SY3121 @ SV337 @ SV324 ) )
| ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) ) )
= $false )
| ( ( SV337
= ( identity_relation @ SV324 ) )
= $true )
| ( ( relation @ SV337 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2875]) ).
thf(2971,plain,
! [SV324: $i,SV337: $i] :
( ( ( ~ ( ( in @ ( sK52_C @ SV337 @ SV324 ) @ SV324 )
| ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) ) )
= $false )
| ( ( SV337
= ( identity_relation @ SV324 ) )
= $true )
| ( ( relation @ SV337 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2875]) ).
thf(2972,plain,
! [SV338: $i,SV325: $i,SV467: $i] :
( ( ( ! [SY4048: $i] :
( ( SV467 != SY4048 )
| ~ ( in @ SV467 @ SV325 )
| ( in @ ( ordered_pair @ SV467 @ SY4048 ) @ SV338 ) ) )
= $true )
| ( ( SV338
= ( identity_relation @ SV325 ) )
= $false )
| ( ( relation @ SV338 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2876]) ).
thf(2973,plain,
! [SV325: $i,SV338: $i] :
( ( ( ~ ! [SY3897: $i,SY3898: $i] :
( ~ ( in @ ( ordered_pair @ SY3897 @ SY3898 ) @ SV338 )
| ( SY3897 = SY3898 ) )
| ~ ! [SY3899: $i] :
( ! [SY3900: $i] :
~ ( in @ ( ordered_pair @ SY3899 @ SY3900 ) @ SV338 )
| ( in @ SY3899 @ SV325 ) ) )
= $false )
| ( ( SV338
= ( identity_relation @ SV325 ) )
= $false )
| ( ( relation @ SV338 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2877]) ).
thf(2974,plain,
! [SV468: $i,SV289: $i,SV339: $i,SV356: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK59_D @ SV356 @ SV339 @ SV289 ) @ SV468 ) @ SV356 ) )
= $true )
| ( ( ( relation_dom_as_subset @ SV339 @ SV289 @ SV356 )
= SV339 )
= $true )
| ( ( relation_of2_as_subset @ SV356 @ SV339 @ SV289 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2878]) ).
thf(2975,plain,
! [SV289: $i,SV357: $i,SV340: $i,SV448: $i] :
( ( ( in @ SV448 @ SV340 )
= $false )
| ( ( in @ ( ordered_pair @ SV448 @ ( sK58_E @ SV448 @ SV357 @ SV340 @ SV289 ) ) @ SV357 )
= $true )
| ( ( ( relation_dom_as_subset @ SV340 @ SV289 @ SV357 )
= SV340 )
= $false )
| ( ( relation_of2_as_subset @ SV357 @ SV340 @ SV289 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2880]) ).
thf(2976,plain,
! [SV469: $i,SV290: $i,SV380: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK22_C @ SV380 @ SV290 ) @ SV469 ) @ SV290 ) )
= $true )
| ( ( ~ ( in @ ( sK22_C @ SV380 @ SV290 ) @ SV380 ) )
= $true )
| ( ( SV380
= ( relation_dom @ SV290 ) )
= $true )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2881]) ).
thf(2977,plain,
! [SV381: $i,SV290: $i,SV470: $i] :
( ( ( ! [SY4049: $i] :
~ ( in @ ( ordered_pair @ SV470 @ SY4049 ) @ SV290 )
| ( in @ SV470 @ SV381 ) )
= $true )
| ( ( SV381
= ( relation_dom @ SV290 ) )
= $false )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2883]) ).
thf(2978,plain,
! [SV290: $i,SV381: $i,SV471: $i] :
( ( ( ~ ( in @ SV471 @ SV381 )
| ( in @ ( ordered_pair @ SV471 @ ( sK21_D @ SV471 @ SV381 @ SV290 ) ) @ SV290 ) )
= $true )
| ( ( SV381
= ( relation_dom @ SV290 ) )
= $false )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2884]) ).
thf(2979,plain,
! [SV291: $i,SV382: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV291 )
| ~ ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV382 ) )
= $true )
| ( ( SV291 = SV382 )
= $true )
| ( ( relation @ SV382 )
= $false )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2885]) ).
thf(2980,plain,
! [SV291: $i,SV382: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV291 )
| ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV382 ) )
= $true )
| ( ( SV291 = SV382 )
= $true )
| ( ( relation @ SV382 )
= $false )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2886]) ).
thf(2981,plain,
! [SV383: $i,SV291: $i] :
( ( ( ~ ! [SY3958: $i,SY3959: $i] :
( ~ ( in @ ( ordered_pair @ SY3958 @ SY3959 ) @ SV291 )
| ( in @ ( ordered_pair @ SY3958 @ SY3959 ) @ SV383 ) ) )
= $false )
| ( ( SV291 = SV383 )
= $false )
| ( ( relation @ SV383 )
= $false )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2887]) ).
thf(2982,plain,
! [SV291: $i,SV383: $i] :
( ( ( ~ ! [SY3960: $i,SY3961: $i] :
( ~ ( in @ ( ordered_pair @ SY3960 @ SY3961 ) @ SV383 )
| ( in @ ( ordered_pair @ SY3960 @ SY3961 ) @ SV291 ) ) )
= $false )
| ( ( SV291 = SV383 )
= $false )
| ( ( relation @ SV383 )
= $false )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2887]) ).
thf(2983,plain,
! [SV326: $i] :
( ( ( in @ ( ordered_pair @ ( sK66_B @ SV326 ) @ ( sK67_SY3127 @ SV326 ) ) @ SV326 )
= $true )
| ( ( transitive @ SV326 )
= $true )
| ( ( relation @ SV326 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2888]) ).
thf(2984,plain,
! [SV326: $i] :
( ( ( in @ ( ordered_pair @ ( sK67_SY3127 @ SV326 ) @ ( sK68_SY3129 @ SV326 ) ) @ SV326 )
= $true )
| ( ( transitive @ SV326 )
= $true )
| ( ( relation @ SV326 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2889]) ).
thf(2985,plain,
! [SV449: $i,SV327: $i,SV437: $i,SV423: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV423 @ SV437 ) @ SV327 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV437 @ SV449 ) @ SV327 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV423 @ SV449 ) @ SV327 )
= $true )
| ( ( transitive @ SV327 )
= $false )
| ( ( relation @ SV327 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2890]) ).
thf(2986,plain,
! [SV292: $i,SV384: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SV384 @ SV292 ) @ ( sK13_SY3095 @ SV384 @ SV292 ) ) @ SV384 )
| ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV384 @ SV292 ) @ ( sK12_C @ SV384 @ SV292 ) ) @ SV292 ) )
= $true )
| ( ( SV384
= ( relation_inverse @ SV292 ) )
= $true )
| ( ( relation @ SV384 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2891]) ).
thf(2987,plain,
! [SV292: $i,SV384: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK12_C @ SV384 @ SV292 ) @ ( sK13_SY3095 @ SV384 @ SV292 ) ) @ SV384 )
| ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV384 @ SV292 ) @ ( sK12_C @ SV384 @ SV292 ) ) @ SV292 ) )
= $true )
| ( ( SV384
= ( relation_inverse @ SV292 ) )
= $true )
| ( ( relation @ SV384 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2892]) ).
thf(2988,plain,
! [SV292: $i,SV385: $i] :
( ( ( ~ ! [SY3962: $i,SY3963: $i] :
( ~ ( in @ ( ordered_pair @ SY3962 @ SY3963 ) @ SV385 )
| ( in @ ( ordered_pair @ SY3963 @ SY3962 ) @ SV292 ) ) )
= $false )
| ( ( SV385
= ( relation_inverse @ SV292 ) )
= $false )
| ( ( relation @ SV385 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2893]) ).
thf(2989,plain,
! [SV385: $i,SV292: $i] :
( ( ( ~ ! [SY3964: $i,SY3965: $i] :
( ~ ( in @ ( ordered_pair @ SY3965 @ SY3964 ) @ SV292 )
| ( in @ ( ordered_pair @ SY3964 @ SY3965 ) @ SV385 ) ) )
= $false )
| ( ( SV385
= ( relation_inverse @ SV292 ) )
= $false )
| ( ( relation @ SV385 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2893]) ).
thf(2990,plain,
! [SV293: $i,SV458: $i] :
( ( ( ~ ( in @ SV458 @ ( relation_dom @ SV293 ) ) )
= $true )
| ( ( ! [SY4036: $i] :
( ( SY4036
!= ( apply @ SV293 @ SV458 ) )
| ( in @ ( ordered_pair @ SV458 @ SY4036 ) @ SV293 ) ) )
= $true )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2894]) ).
thf(2991,plain,
! [SV293: $i,SV459: $i] :
( ( ( ~ ( in @ SV459 @ ( relation_dom @ SV293 ) ) )
= $true )
| ( ( ! [SY4037: $i] :
( ~ ( in @ ( ordered_pair @ SV459 @ SY4037 ) @ SV293 )
| ( SY4037
= ( apply @ SV293 @ SV459 ) ) ) )
= $true )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2895]) ).
thf(2992,plain,
! [SV293: $i,SV460: $i] :
( ( ( in @ SV460 @ ( relation_dom @ SV293 ) )
= $true )
| ( ( ! [SY4038: $i] :
( ( SY4038
!= ( apply @ SV293 @ SV460 ) )
| ( SY4038 = empty_set ) ) )
= $true )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2896]) ).
thf(2993,plain,
! [SV293: $i,SV461: $i] :
( ( ( in @ SV461 @ ( relation_dom @ SV293 ) )
= $true )
| ( ( ! [SY4039: $i] :
( ( SY4039 != empty_set )
| ( SY4039
= ( apply @ SV293 @ SV461 ) ) ) )
= $true )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2897]) ).
thf(2994,plain,
! [SV294: $i,SV386: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK19_C @ SV386 @ SV294 ) @ SV386 )
| ~ ( in @ ( sK20_SY3099 @ SV386 @ SV294 ) @ SV386 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SV386 @ SV294 ) @ ( sK20_SY3099 @ SV386 @ SV294 ) ) @ SV294 ) ) )
= $false )
| ( ( is_antisymmetric_in @ SV294 @ SV386 )
= $true )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2898]) ).
thf(2995,plain,
! [SV294: $i,SV386: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK20_SY3099 @ SV386 @ SV294 ) @ ( sK19_C @ SV386 @ SV294 ) ) @ SV294 ) )
= $false )
| ( ( is_antisymmetric_in @ SV294 @ SV386 )
= $true )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2898]) ).
thf(2996,plain,
! [SV294: $i,SV450: $i,SV387: $i,SV438: $i] :
( ( ( ~ ( in @ SV438 @ SV387 )
| ~ ( in @ SV450 @ SV387 )
| ~ ( in @ ( ordered_pair @ SV438 @ SV450 ) @ SV294 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV450 @ SV438 ) @ SV294 ) )
= $true )
| ( ( SV438 = SV450 )
= $true )
| ( ( is_antisymmetric_in @ SV294 @ SV387 )
= $false )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2900]) ).
thf(2997,plain,
! [SV295: $i,SV388: $i,SV404: $i] :
( ( ( ( ( sK35_D @ SV404 @ SV388 @ SV295 )
= SV388 )
| ~ ( in @ ( ordered_pair @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV388 ) @ SV295 ) )
= $true )
| ( ( ~ ( in @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV404 ) )
= $true )
| ( ( SV404
= ( fiber @ SV295 @ SV388 ) )
= $true )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2901]) ).
thf(2998,plain,
! [SV295: $i,SV388: $i,SV404: $i] :
( ( ( ~ ( ( ( sK35_D @ SV404 @ SV388 @ SV295 )
!= SV388 )
| ( in @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV404 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV388 ) @ SV295 )
| ( in @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV404 ) ) )
= $false )
| ( ( SV404
= ( fiber @ SV295 @ SV388 ) )
= $true )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2902]) ).
thf(2999,plain,
! [SV405: $i,SV295: $i,SV389: $i] :
( ( ( ! [SY3994: $i] :
( ( SY3994 = SV389 )
| ~ ( in @ ( ordered_pair @ SY3994 @ SV389 ) @ SV295 )
| ( in @ SY3994 @ SV405 ) ) )
= $true )
| ( ( SV405
= ( fiber @ SV295 @ SV389 ) )
= $false )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2903]) ).
thf(3000,plain,
! [SV295: $i,SV389: $i,SV405: $i] :
( ( ( ~ ( ~ ! [SY3995: $i] :
( ~ ( in @ SY3995 @ SV405 )
| ( SY3995 != SV389 ) )
| ~ ! [SY3996: $i] :
( ~ ( in @ SY3996 @ SV405 )
| ( in @ ( ordered_pair @ SY3996 @ SV389 ) @ SV295 ) ) ) )
= $true )
| ( ( SV405
= ( fiber @ SV295 @ SV389 ) )
= $false )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2904]) ).
thf(3001,plain,
! [SV296: $i,SV307: $i,SV406: $i] :
( ( ( ~ ( ~ ( in @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) @ SV296 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV307 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) ) )
= $false )
| ( ( SV406
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $true )
| ( ( relation @ SV406 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2905]) ).
thf(3002,plain,
! [SV296: $i,SV307: $i,SV406: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) @ SV296 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV307 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) ) ) )
= $false )
| ( ( SV406
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $true )
| ( ( relation @ SV406 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2905]) ).
thf(3003,plain,
! [SV407: $i,SV307: $i,SV296: $i] :
( ( ( ~ ! [SY3997: $i,SY3998: $i] :
( ~ ( in @ SY3998 @ SV296 )
| ~ ( in @ ( ordered_pair @ SY3997 @ SY3998 ) @ SV307 )
| ( in @ ( ordered_pair @ SY3997 @ SY3998 ) @ SV407 ) )
| ~ ~ ( ~ ! [SY3999: $i,SY4000: $i] :
( ~ ( in @ ( ordered_pair @ SY3999 @ SY4000 ) @ SV407 )
| ( in @ SY4000 @ SV296 ) )
| ~ ! [SY4001: $i,SY4002: $i] :
( ~ ( in @ ( ordered_pair @ SY4001 @ SY4002 ) @ SV407 )
| ( in @ ( ordered_pair @ SY4001 @ SY4002 ) @ SV307 ) ) ) )
= $false )
| ( ( SV407
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $false )
| ( ( relation @ SV407 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2906]) ).
thf(3004,plain,
! [SV297: $i,SV390: $i,SV472: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV472 @ ( sK17_C @ SV390 @ SV297 ) ) @ SV297 ) )
= $true )
| ( ( ~ ( in @ ( sK17_C @ SV390 @ SV297 ) @ SV390 ) )
= $true )
| ( ( SV390
= ( relation_rng @ SV297 ) )
= $true )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2907]) ).
thf(3005,plain,
! [SV391: $i,SV297: $i,SV473: $i] :
( ( ( ! [SY4050: $i] :
~ ( in @ ( ordered_pair @ SY4050 @ SV473 ) @ SV297 )
| ( in @ SV473 @ SV391 ) )
= $true )
| ( ( SV391
= ( relation_rng @ SV297 ) )
= $false )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2909]) ).
thf(3006,plain,
! [SV297: $i,SV391: $i,SV474: $i] :
( ( ( ~ ( in @ SV474 @ SV391 )
| ( in @ ( ordered_pair @ ( sK16_D @ SV474 @ SV391 @ SV297 ) @ SV474 ) @ SV297 ) )
= $true )
| ( ( SV391
= ( relation_rng @ SV297 ) )
= $false )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2910]) ).
thf(3007,plain,
! [SV360: $i,SV392: $i,SV308: $i,SV299: $i] :
( ( ( in @ ( ordered_pair @ SV299 @ SV308 ) @ SV392 )
= $false )
| ( ( in @ SV299 @ SV360 )
= $false )
| ( ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SV360 ) @ SV392 ) )
= $true )
| ( ( relation @ SV392 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2911]) ).
thf(3008,plain,
! [SV439: $i,SV424: $i,SV308: $i,SV299: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SV424 ) @ SV439 ) ) )
= $true )
| ( ( in @ SV299 @ SV424 )
= $true )
| ( ( relation @ SV439 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2912]) ).
thf(3009,plain,
! [SV440: $i,SV425: $i,SV308: $i,SV299: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SV425 ) @ SV440 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV299 @ SV308 ) @ SV440 )
= $true )
| ( ( relation @ SV440 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2913]) ).
thf(3010,plain,
! [SV343: $i,SV301: $i,SV363: $i,SV441: $i] :
( ( ( in @ SV441 @ ( relation_rng @ SV363 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV301 @ SV441 ) @ SV363 ) )
= $true )
| ( ( ~ ( in @ SV441 @ SV343 ) )
= $true )
| ( ( in @ SV301 @ ( relation_inverse_image @ SV363 @ SV343 ) )
= $true )
| ( ( relation @ SV363 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2914]) ).
thf(3011,plain,
! [SV301: $i,SV344: $i,SV364: $i] :
( ( ( ~ ( ~ ( in @ ( sK60_D @ SV364 @ SV344 @ SV301 ) @ ( relation_rng @ SV364 ) )
| ~ ( in @ ( ordered_pair @ SV301 @ ( sK60_D @ SV364 @ SV344 @ SV301 ) ) @ SV364 ) ) )
= $true )
| ( ( in @ SV301 @ ( relation_inverse_image @ SV364 @ SV344 ) )
= $false )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2915]) ).
thf(3012,plain,
! [SV301: $i,SV344: $i,SV364: $i] :
( ( ( in @ ( sK60_D @ SV364 @ SV344 @ SV301 ) @ SV344 )
= $true )
| ( ( in @ SV301 @ ( relation_inverse_image @ SV364 @ SV344 ) )
= $false )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2916]) ).
thf(3013,plain,
! [SV274: $i,SV367: $i] :
( ( ( ~ ( ~ ( ( ( sK14_C @ SV367 @ SV274 )
!= ( sK15_SY3096 @ SV367 @ SV274 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SV367 @ SV274 ) @ SV367 )
| ~ ( in @ ( sK15_SY3096 @ SV367 @ SV274 ) @ SV367 ) ) ) )
= $true )
| ( ( is_connected_in @ SV274 @ SV367 )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2919]) ).
thf(3014,plain,
! [SV274: $i,SV367: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK14_C @ SV367 @ SV274 ) @ ( sK15_SY3096 @ SV367 @ SV274 ) ) @ SV274 ) )
= $true )
| ( ( is_connected_in @ SV274 @ SV367 )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2920]) ).
thf(3015,plain,
! [SV274: $i,SV368: $i,SV445: $i,SV428: $i] :
( ( ( SV428 = SV445 )
= $true )
| ( ( ~ ( in @ SV428 @ SV368 )
| ~ ( in @ SV445 @ SV368 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV428 @ SV445 ) @ SV274 )
= $true )
| ( ( in @ ( ordered_pair @ SV445 @ SV428 ) @ SV274 )
= $true )
| ( ( is_connected_in @ SV274 @ SV368 )
= $false )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2921]) ).
thf(3016,plain,
! [SV317: $i,SV415: $i,SV430: $i] :
( ( ( in @ ( ordered_pair @ SV430 @ SV415 ) @ SV317 )
= $false )
| ( ( in @ ( ordered_pair @ SV415 @ SV430 ) @ SV317 )
= $false )
| ( ( SV415 = SV430 )
= $true )
| ( ( antisymmetric @ SV317 )
= $false )
| ( ( relation @ SV317 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2924]) ).
thf(3017,plain,
! [SV347: $i,SV328: $i,SV462: $i,SV275: $i,SV451: $i] :
( ( ( ~ ( in @ SV451 @ SV275 )
| ~ ( in @ SV462 @ SV328 ) )
= $true )
| ( ( ( ( sK28_D @ SV347 @ SV328 @ SV275 )
!= ( ordered_pair @ SV451 @ SV462 ) ) )
= $true )
| ( ( ~ ( in @ ( sK28_D @ SV347 @ SV328 @ SV275 ) @ SV347 ) )
= $true )
| ( ( SV347
= ( cartesian_product2 @ SV275 @ SV328 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2925]) ).
thf(3018,plain,
! [SV275: $i,SV328: $i,SV347: $i] :
( ( ( ~ ( ~ ( in @ ( sK29_SY3106 @ SV347 @ SV328 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK30_SY3108 @ SV347 @ SV328 @ SV275 ) @ SV328 ) ) )
= $true )
| ( ( in @ ( sK28_D @ SV347 @ SV328 @ SV275 ) @ SV347 )
= $true )
| ( ( SV347
= ( cartesian_product2 @ SV275 @ SV328 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2926]) ).
thf(3019,plain,
! [SV275: $i,SV328: $i,SV347: $i] :
( ( ( ( sK28_D @ SV347 @ SV328 @ SV275 )
= ( ordered_pair @ ( sK29_SY3106 @ SV347 @ SV328 @ SV275 ) @ ( sK30_SY3108 @ SV347 @ SV328 @ SV275 ) ) )
= $true )
| ( ( in @ ( sK28_D @ SV347 @ SV328 @ SV275 ) @ SV347 )
= $true )
| ( ( SV347
= ( cartesian_product2 @ SV275 @ SV328 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2927]) ).
thf(3020,plain,
! [SV348: $i,SV452: $i,SV329: $i,SV275: $i,SV475: $i] :
( ( ( ! [SY4051: $i] :
( ~ ( in @ SV475 @ SV275 )
| ~ ( in @ SY4051 @ SV329 )
| ( SV452
!= ( ordered_pair @ SV475 @ SY4051 ) ) ) )
= $true )
| ( ( in @ SV452 @ SV348 )
= $true )
| ( ( SV348
= ( cartesian_product2 @ SV275 @ SV329 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2928]) ).
thf(3021,plain,
! [SV275: $i,SV329: $i,SV348: $i,SV453: $i] :
( ( ( in @ SV453 @ SV348 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK26_E @ SV453 @ SV348 @ SV329 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK27_SY3103 @ SV453 @ SV348 @ SV329 @ SV275 ) @ SV329 ) )
| ( SV453
!= ( ordered_pair @ ( sK26_E @ SV453 @ SV348 @ SV329 @ SV275 ) @ ( sK27_SY3103 @ SV453 @ SV348 @ SV329 @ SV275 ) ) ) ) )
= $true )
| ( ( SV348
= ( cartesian_product2 @ SV275 @ SV329 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2929]) ).
thf(3022,plain,
! [SV276: $i,SV370: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SV370 @ SV276 ) @ SV370 )
| ~ ( in @ ( sK4_SY3086 @ SV370 @ SV276 ) @ SV370 ) )
| ~ ( in @ ( sK5_SY3088 @ SV370 @ SV276 ) @ SV370 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SV370 @ SV276 ) @ ( sK4_SY3086 @ SV370 @ SV276 ) ) @ SV276 ) ) )
= $true )
| ( ( is_transitive_in @ SV276 @ SV370 )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2930]) ).
thf(3023,plain,
! [SV276: $i,SV370: $i] :
( ( ( in @ ( ordered_pair @ ( sK4_SY3086 @ SV370 @ SV276 ) @ ( sK5_SY3088 @ SV370 @ SV276 ) ) @ SV276 )
= $true )
| ( ( is_transitive_in @ SV276 @ SV370 )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2931]) ).
thf(3024,plain,
! [SV276: $i,SV454: $i,SV446: $i,SV371: $i,SV431: $i] :
( ( ( ~ ( in @ SV431 @ SV371 )
| ~ ( in @ SV446 @ SV371 )
| ~ ( in @ SV454 @ SV371 )
| ~ ( in @ ( ordered_pair @ SV431 @ SV446 ) @ SV276 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV446 @ SV454 ) @ SV276 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV431 @ SV454 ) @ SV276 )
= $true )
| ( ( is_transitive_in @ SV276 @ SV371 )
= $false )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2932]) ).
thf(3025,plain,
! [SV277: $i,SV372: $i,SV396: $i,SV476: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV476 @ ( sK46_D @ SV396 @ SV372 @ SV277 ) ) @ SV277 )
| ~ ( in @ SV476 @ SV372 ) )
= $true )
| ( ( ~ ( in @ ( sK46_D @ SV396 @ SV372 @ SV277 ) @ SV396 ) )
= $true )
| ( ( SV396
= ( relation_image @ SV277 @ SV372 ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2933]) ).
thf(3026,plain,
! [SV277: $i,SV372: $i,SV396: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SV396 @ SV372 @ SV277 ) @ ( sK46_D @ SV396 @ SV372 @ SV277 ) ) @ SV277 )
| ~ ( in @ ( sK47_SY3118 @ SV396 @ SV372 @ SV277 ) @ SV372 ) )
= $false )
| ( ( in @ ( sK46_D @ SV396 @ SV372 @ SV277 ) @ SV396 )
= $true )
| ( ( SV396
= ( relation_image @ SV277 @ SV372 ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2934]) ).
thf(3027,plain,
! [SV397: $i,SV373: $i,SV277: $i,SV477: $i] :
( ( ( ! [SY4052: $i] :
( ~ ( in @ ( ordered_pair @ SY4052 @ SV477 ) @ SV277 )
| ~ ( in @ SY4052 @ SV373 ) )
| ( in @ SV477 @ SV397 ) )
= $true )
| ( ( SV397
= ( relation_image @ SV277 @ SV373 ) )
= $false )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2935]) ).
thf(3028,plain,
! [SV277: $i,SV373: $i,SV397: $i,SV478: $i] :
( ( ( ~ ( in @ SV478 @ SV397 )
| ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SV478 @ SV397 @ SV373 @ SV277 ) @ SV478 ) @ SV277 )
| ~ ( in @ ( sK45_E @ SV478 @ SV397 @ SV373 @ SV277 ) @ SV373 ) ) )
= $true )
| ( ( SV397
= ( relation_image @ SV277 @ SV373 ) )
= $false )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2936]) ).
thf(3029,plain,
! [SV278: $i,SV374: $i,SV398: $i] :
( ( ( ~ ( in @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ SV374 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV278 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) )
= $true )
| ( ( SV398
= ( relation_dom_restriction @ SV278 @ SV374 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2937]) ).
thf(3030,plain,
! [SV278: $i,SV374: $i,SV398: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ SV374 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV278 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) ) ) )
= $true )
| ( ( SV398
= ( relation_dom_restriction @ SV278 @ SV374 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2938]) ).
thf(3031,plain,
! [SV399: $i,SV278: $i,SV375: $i] :
( ( ( ~ ! [SY3982: $i,SY3983: $i] :
( ~ ( in @ SY3982 @ SV375 )
| ~ ( in @ ( ordered_pair @ SY3982 @ SY3983 ) @ SV278 )
| ( in @ ( ordered_pair @ SY3982 @ SY3983 ) @ SV399 ) ) )
= $false )
| ( ( SV399
= ( relation_dom_restriction @ SV278 @ SV375 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2939]) ).
thf(3032,plain,
! [SV278: $i,SV375: $i,SV399: $i] :
( ( ( ~ ~ ( ~ ! [SY3984: $i] :
( ! [SY3985: $i] :
~ ( in @ ( ordered_pair @ SY3984 @ SY3985 ) @ SV399 )
| ( in @ SY3984 @ SV375 ) )
| ~ ! [SY3986: $i,SY3987: $i] :
( ~ ( in @ ( ordered_pair @ SY3986 @ SY3987 ) @ SV399 )
| ( in @ ( ordered_pair @ SY3986 @ SY3987 ) @ SV278 ) ) ) )
= $false )
| ( ( SV399
= ( relation_dom_restriction @ SV278 @ SV375 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2939]) ).
thf(3033,plain,
! [SV479: $i,SV279: $i,SV376: $i,SV400: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SV479 ) @ SV279 )
| ~ ( in @ SV479 @ SV376 ) )
= $true )
| ( ( ~ ( in @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SV400 ) )
= $true )
| ( ( SV400
= ( relation_inverse_image @ SV279 @ SV376 ) )
= $true )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2940]) ).
thf(3034,plain,
! [SV279: $i,SV376: $i,SV400: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ ( sK44_SY3116 @ SV400 @ SV376 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK44_SY3116 @ SV400 @ SV376 @ SV279 ) @ SV376 ) )
= $false )
| ( ( in @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SV400 )
= $true )
| ( ( SV400
= ( relation_inverse_image @ SV279 @ SV376 ) )
= $true )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2941]) ).
thf(3035,plain,
! [SV401: $i,SV377: $i,SV279: $i,SV480: $i] :
( ( ( ! [SY4053: $i] :
( ~ ( in @ ( ordered_pair @ SV480 @ SY4053 ) @ SV279 )
| ~ ( in @ SY4053 @ SV377 ) )
| ( in @ SV480 @ SV401 ) )
= $true )
| ( ( SV401
= ( relation_inverse_image @ SV279 @ SV377 ) )
= $false )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2942]) ).
thf(3036,plain,
! [SV279: $i,SV377: $i,SV401: $i,SV481: $i] :
( ( ( ~ ( in @ SV481 @ SV401 )
| ~ ( ~ ( in @ ( ordered_pair @ SV481 @ ( sK42_E @ SV481 @ SV401 @ SV377 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK42_E @ SV481 @ SV401 @ SV377 @ SV279 ) @ SV377 ) ) )
= $true )
| ( ( SV401
= ( relation_inverse_image @ SV279 @ SV377 ) )
= $false )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2943]) ).
thf(3037,plain,
! [SV280: $i,SV378: $i] :
( ( ( in @ ( ordered_pair @ ( sK24_C @ SV378 @ SV280 ) @ ( sK25_SY3102 @ SV378 @ SV280 ) ) @ SV378 )
= $false )
| ( ( subset @ SV280 @ SV378 )
= $true )
| ( ( relation @ SV378 )
= $false )
| ( ( relation @ SV280 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2945]) ).
thf(3038,plain,
! [SV379: $i,SV280: $i,SV463: $i,SV455: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV455 @ SV463 ) @ SV280 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV455 @ SV463 ) @ SV379 )
= $true )
| ( ( subset @ SV280 @ SV379 )
= $false )
| ( ( relation @ SV379 )
= $false )
| ( ( relation @ SV280 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2946]) ).
thf(3039,plain,
! [SV281: $i,SV318: $i,SV432: $i] :
( ( ( ~ ( ! [SY4021: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ SY4021 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY4021 @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV318 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV432 ) )
| ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK9_SY3093 @ SV432 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV318 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV432 ) ) )
= $false )
| ( ( SV432
= ( relation_composition @ SV281 @ SV318 ) )
= $true )
| ( ( relation @ SV432 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2947]) ).
thf(3040,plain,
! [SV318: $i,SV281: $i,SV433: $i] :
( ( ( SV433
= ( relation_composition @ SV281 @ SV318 ) )
= $false )
| ( ( ~ ( ~ ! [SY4022: $i,SY4023: $i] :
( ! [SY3848: $i] :
( ~ ( in @ ( ordered_pair @ SY4022 @ SY3848 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY3848 @ SY4023 ) @ SV318 ) )
| ( in @ ( ordered_pair @ SY4022 @ SY4023 ) @ SV433 ) )
| ~ ! [SY4025: $i,SY4026: $i] :
( ~ ( in @ ( ordered_pair @ SY4025 @ SY4026 ) @ SV433 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4025 @ ( sK6_F @ SY4026 @ SY4025 @ SV433 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY4026 @ SY4025 @ SV433 @ SV318 @ SV281 ) @ SY4026 ) @ SV318 ) ) ) ) )
= $true )
| ( ( relation @ SV433 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2948]) ).
thf(3041,plain,
! [SV282: $i,SV330: $i,SV349: $i,SV464: $i] :
( ( ( in @ ( ordered_pair @ SV464 @ ( sK57_D @ SV349 @ SV330 @ SV282 ) ) @ SV349 )
= $false )
| ( ( ( relation_rng_as_subset @ SV282 @ SV330 @ SV349 )
= SV330 )
= $true )
| ( ( relation_of2_as_subset @ SV349 @ SV282 @ SV330 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2949]) ).
thf(3042,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( relation @ SV434 )
= $false )
| ( ( function @ SV434 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) ) ) )
| ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 )
| ( relation_isomorphism @ SV283 @ SV319 @ SV434 ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2951]) ).
thf(3043,plain,
! [SV319: $i,SV283: $i,SV465: $i] :
( ( ( ~ ( function @ SV465 )
| ~ ( relation @ SV465 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
| ~ ( ~ ! [SY4040: $i,SY4041: $i] :
( ~ ( in @ SY4040 @ ( relation_field @ SV283 ) )
| ~ ( in @ SY4041 @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV465 @ SY4040 ) @ ( apply @ SV465 @ SY4041 ) ) @ SV319 )
| ( in @ ( ordered_pair @ SY4040 @ SY4041 ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3687: $i] :
( ! [SY3688: $i] :
~ ( in @ ( ordered_pair @ SY3687 @ SY3688 ) @ SV283 )
| ( in @ SY3687 @ ( relation_field @ SV283 ) ) )
| ~ ! [SY3689: $i,SY3690: $i] :
( ~ ( in @ ( ordered_pair @ SY3689 @ SY3690 ) @ SV283 )
| ( in @ SY3690 @ ( relation_field @ SV283 ) ) ) )
| ~ ! [SY4046: $i,SY4047: $i] :
( ~ ( in @ ( ordered_pair @ SY4046 @ SY4047 ) @ SV283 )
| ( in @ ( ordered_pair @ ( apply @ SV465 @ SY4046 ) @ ( apply @ SV465 @ SY4047 ) ) @ SV319 ) ) ) ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2952]) ).
thf(3044,plain,
! [SV319: $i,SV283: $i] :
( ( ( ~ ~ ( ~ ! [SY3861: $i] :
( ~ ( function @ SY3861 )
| ~ ( relation @ SY3861 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3861 )
| ( ( relation_dom @ SY3861 )
= ( relation_field @ SV283 ) ) )
| ~ ! [SY3862: $i] :
( ~ ( function @ SY3862 )
| ~ ( relation @ SY3862 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3862 )
| ( ( relation_rng @ SY3862 )
= ( relation_field @ SV319 ) ) ) ) )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2953]) ).
thf(3045,plain,
! [SV319: $i,SV283: $i] :
( ( ( ~ ! [SY3863: $i] :
( ~ ( function @ SY3863 )
| ~ ( relation @ SY3863 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3863 )
| ( one_to_one @ SY3863 ) ) )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2953]) ).
thf(3046,plain,
! [SV320: $i] :
( ( ( ~ ( ( ( sK62_B @ SV320 )
!= ( sK63_SY3125 @ SV320 ) ) )
| ~ ~ ( ~ ( in @ ( sK62_B @ SV320 ) @ ( relation_field @ SV320 ) )
| ~ ( in @ ( sK63_SY3125 @ SV320 ) @ ( relation_field @ SV320 ) ) ) )
= $false )
| ( ( connected @ SV320 )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2954]) ).
thf(3047,plain,
! [SV320: $i] :
( ( ( in @ ( ordered_pair @ ( sK62_B @ SV320 ) @ ( sK63_SY3125 @ SV320 ) ) @ SV320 )
= $false )
| ( ( connected @ SV320 )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2955]) ).
thf(3048,plain,
! [SV435: $i,SV321: $i,SV416: $i] :
( ( ( ~ ( in @ SV416 @ ( relation_field @ SV321 ) ) )
= $true )
| ( ( ~ ( in @ SV435 @ ( relation_field @ SV321 ) ) )
= $true )
| ( ( SV416 = SV435 )
= $true )
| ( ( in @ ( ordered_pair @ SV416 @ SV435 ) @ SV321 )
= $true )
| ( ( in @ ( ordered_pair @ SV435 @ SV416 ) @ SV321 )
= $true )
| ( ( connected @ SV321 )
= $false )
| ( ( relation @ SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2956]) ).
thf(3049,plain,
! [SV332: $i,SV351: $i,SV284: $i] :
( ( ( in @ SV284 @ ( relation_dom @ SV351 ) )
= $false )
| ( ( SV332
= ( apply @ SV351 @ SV284 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV284 @ SV332 ) @ SV351 )
= $true )
| ( ( function @ SV351 )
= $false )
| ( ( relation @ SV351 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2957]) ).
thf(3050,plain,
! [SV417: $i,SV402: $i,SV284: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV284 @ SV402 ) @ SV417 ) )
= $true )
| ( ( SV402
= ( apply @ SV417 @ SV284 ) )
= $true )
| ( ( function @ SV417 )
= $false )
| ( ( relation @ SV417 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2958]) ).
thf(3051,plain,
! [SV418: $i,SV403: $i,SV284: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV284 @ SV403 ) @ SV418 ) )
= $true )
| ( ( in @ SV284 @ ( relation_dom @ SV418 ) )
= $true )
| ( ( function @ SV418 )
= $false )
| ( ( relation @ SV418 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2959]) ).
thf(3052,plain,
! [SV333: $i,SV352: $i,SV285: $i,SV436: $i] :
( ( ( in @ ( ordered_pair @ SV436 @ SV285 ) @ SV352 )
= $false )
| ( ( in @ SV436 @ ( relation_dom @ SV352 ) )
= $false )
| ( ( ~ ( in @ SV436 @ SV333 ) )
= $true )
| ( ( in @ SV285 @ ( relation_image @ SV352 @ SV333 ) )
= $true )
| ( ( relation @ SV352 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2960]) ).
thf(3053,plain,
! [SV285: $i,SV334: $i,SV353: $i] :
( ( ( ~ ( in @ ( sK61_D @ SV353 @ SV334 @ SV285 ) @ ( relation_dom @ SV353 ) )
| ~ ( in @ ( ordered_pair @ ( sK61_D @ SV353 @ SV334 @ SV285 ) @ SV285 ) @ SV353 ) )
= $false )
| ( ( in @ SV285 @ ( relation_image @ SV353 @ SV334 ) )
= $false )
| ( ( relation @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2961]) ).
thf(3054,plain,
! [SV322: $i,SV310: $i,SV286: $i,SV419: $i] :
( ( ( SV419
= ( sK40_C @ SV419 @ SV286 ) )
= $false )
| ( ( SV419
= ( pair_first @ SV286 ) )
= $true )
| ( ( SV286
= ( ordered_pair @ SV310 @ SV322 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2964]) ).
thf(3055,plain,
! [SV322: $i,SV310: $i,SV420: $i,SV482: $i,SV456: $i,SV286: $i] :
( ( ( ( SV286
!= ( ordered_pair @ SV456 @ SV482 ) ) )
= $true )
| ( ( SV420 = SV456 )
= $true )
| ( ( SV420
= ( pair_first @ SV286 ) )
= $false )
| ( ( SV286
= ( ordered_pair @ SV310 @ SV322 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2965]) ).
thf(3056,plain,
! [SV323: $i,SV311: $i,SV287: $i,SV421: $i] :
( ( ( SV421
= ( sK34_SY3110 @ SV421 @ SV287 ) )
= $false )
| ( ( SV421
= ( pair_second @ SV287 ) )
= $true )
| ( ( SV287
= ( ordered_pair @ SV311 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2967]) ).
thf(3057,plain,
! [SV323: $i,SV311: $i,SV422: $i,SV466: $i,SV457: $i,SV287: $i] :
( ( ( ( SV287
!= ( ordered_pair @ SV457 @ SV466 ) ) )
= $true )
| ( ( SV422 = SV466 )
= $true )
| ( ( SV422
= ( pair_second @ SV287 ) )
= $false )
| ( ( SV287
= ( ordered_pair @ SV311 @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2968]) ).
thf(3058,plain,
! [SV324: $i,SV337: $i] :
( ( ( ( sK52_C @ SV337 @ SV324 )
= ( sK53_SY3121 @ SV337 @ SV324 ) )
= $false )
| ( ( ~ ( in @ ( sK52_C @ SV337 @ SV324 ) @ SV324 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) )
= $true )
| ( ( SV337
= ( identity_relation @ SV324 ) )
= $true )
| ( ( relation @ SV337 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2969]) ).
thf(3059,plain,
! [SV324: $i,SV337: $i] :
( ( ( ( ( sK52_C @ SV337 @ SV324 )
= ( sK53_SY3121 @ SV337 @ SV324 ) )
| ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) )
= $true )
| ( ( SV337
= ( identity_relation @ SV324 ) )
= $true )
| ( ( relation @ SV337 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2970]) ).
thf(3060,plain,
! [SV324: $i,SV337: $i] :
( ( ( ( in @ ( sK52_C @ SV337 @ SV324 ) @ SV324 )
| ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) )
= $true )
| ( ( SV337
= ( identity_relation @ SV324 ) )
= $true )
| ( ( relation @ SV337 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2971]) ).
thf(3061,plain,
! [SV338: $i,SV325: $i,SV483: $i,SV467: $i] :
( ( ( ( SV467 != SV483 )
| ~ ( in @ SV467 @ SV325 )
| ( in @ ( ordered_pair @ SV467 @ SV483 ) @ SV338 ) )
= $true )
| ( ( SV338
= ( identity_relation @ SV325 ) )
= $false )
| ( ( relation @ SV338 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2972]) ).
thf(3062,plain,
! [SV325: $i,SV338: $i] :
( ( ( ~ ! [SY3897: $i,SY3898: $i] :
( ~ ( in @ ( ordered_pair @ SY3897 @ SY3898 ) @ SV338 )
| ( SY3897 = SY3898 ) ) )
= $false )
| ( ( SV338
= ( identity_relation @ SV325 ) )
= $false )
| ( ( relation @ SV338 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2973]) ).
thf(3063,plain,
! [SV325: $i,SV338: $i] :
( ( ( ~ ! [SY3899: $i] :
( ! [SY3900: $i] :
~ ( in @ ( ordered_pair @ SY3899 @ SY3900 ) @ SV338 )
| ( in @ SY3899 @ SV325 ) ) )
= $false )
| ( ( SV338
= ( identity_relation @ SV325 ) )
= $false )
| ( ( relation @ SV338 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2973]) ).
thf(3064,plain,
! [SV468: $i,SV289: $i,SV339: $i,SV356: $i] :
( ( ( in @ ( ordered_pair @ ( sK59_D @ SV356 @ SV339 @ SV289 ) @ SV468 ) @ SV356 )
= $false )
| ( ( ( relation_dom_as_subset @ SV339 @ SV289 @ SV356 )
= SV339 )
= $true )
| ( ( relation_of2_as_subset @ SV356 @ SV339 @ SV289 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2974]) ).
thf(3065,plain,
! [SV469: $i,SV290: $i,SV380: $i] :
( ( ( in @ ( ordered_pair @ ( sK22_C @ SV380 @ SV290 ) @ SV469 ) @ SV290 )
= $false )
| ( ( ~ ( in @ ( sK22_C @ SV380 @ SV290 ) @ SV380 ) )
= $true )
| ( ( SV380
= ( relation_dom @ SV290 ) )
= $true )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2976]) ).
thf(3066,plain,
! [SV381: $i,SV290: $i,SV470: $i] :
( ( ( ! [SY4049: $i] :
~ ( in @ ( ordered_pair @ SV470 @ SY4049 ) @ SV290 ) )
= $true )
| ( ( in @ SV470 @ SV381 )
= $true )
| ( ( SV381
= ( relation_dom @ SV290 ) )
= $false )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2977]) ).
thf(3067,plain,
! [SV290: $i,SV381: $i,SV471: $i] :
( ( ( ~ ( in @ SV471 @ SV381 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV471 @ ( sK21_D @ SV471 @ SV381 @ SV290 ) ) @ SV290 )
= $true )
| ( ( SV381
= ( relation_dom @ SV290 ) )
= $false )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2978]) ).
thf(3068,plain,
! [SV291: $i,SV382: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV291 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV382 ) )
= $true )
| ( ( SV291 = SV382 )
= $true )
| ( ( relation @ SV382 )
= $false )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2979]) ).
thf(3069,plain,
! [SV291: $i,SV382: $i] :
( ( ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV291 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV382 )
= $true )
| ( ( SV291 = SV382 )
= $true )
| ( ( relation @ SV382 )
= $false )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2980]) ).
thf(3070,plain,
! [SV383: $i,SV291: $i] :
( ( ( ! [SY3958: $i,SY3959: $i] :
( ~ ( in @ ( ordered_pair @ SY3958 @ SY3959 ) @ SV291 )
| ( in @ ( ordered_pair @ SY3958 @ SY3959 ) @ SV383 ) ) )
= $true )
| ( ( SV291 = SV383 )
= $false )
| ( ( relation @ SV383 )
= $false )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2981]) ).
thf(3071,plain,
! [SV291: $i,SV383: $i] :
( ( ( ! [SY3960: $i,SY3961: $i] :
( ~ ( in @ ( ordered_pair @ SY3960 @ SY3961 ) @ SV383 )
| ( in @ ( ordered_pair @ SY3960 @ SY3961 ) @ SV291 ) ) )
= $true )
| ( ( SV291 = SV383 )
= $false )
| ( ( relation @ SV383 )
= $false )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2982]) ).
thf(3072,plain,
! [SV449: $i,SV327: $i,SV437: $i,SV423: $i] :
( ( ( in @ ( ordered_pair @ SV423 @ SV437 ) @ SV327 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV437 @ SV449 ) @ SV327 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV423 @ SV449 ) @ SV327 )
= $true )
| ( ( transitive @ SV327 )
= $false )
| ( ( relation @ SV327 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2985]) ).
thf(3073,plain,
! [SV292: $i,SV384: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SV384 @ SV292 ) @ ( sK13_SY3095 @ SV384 @ SV292 ) ) @ SV384 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV384 @ SV292 ) @ ( sK12_C @ SV384 @ SV292 ) ) @ SV292 ) )
= $true )
| ( ( SV384
= ( relation_inverse @ SV292 ) )
= $true )
| ( ( relation @ SV384 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2986]) ).
thf(3074,plain,
! [SV292: $i,SV384: $i] :
( ( ( in @ ( ordered_pair @ ( sK12_C @ SV384 @ SV292 ) @ ( sK13_SY3095 @ SV384 @ SV292 ) ) @ SV384 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV384 @ SV292 ) @ ( sK12_C @ SV384 @ SV292 ) ) @ SV292 )
= $true )
| ( ( SV384
= ( relation_inverse @ SV292 ) )
= $true )
| ( ( relation @ SV384 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2987]) ).
thf(3075,plain,
! [SV292: $i,SV385: $i] :
( ( ( ! [SY3962: $i,SY3963: $i] :
( ~ ( in @ ( ordered_pair @ SY3962 @ SY3963 ) @ SV385 )
| ( in @ ( ordered_pair @ SY3963 @ SY3962 ) @ SV292 ) ) )
= $true )
| ( ( SV385
= ( relation_inverse @ SV292 ) )
= $false )
| ( ( relation @ SV385 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2988]) ).
thf(3076,plain,
! [SV385: $i,SV292: $i] :
( ( ( ! [SY3964: $i,SY3965: $i] :
( ~ ( in @ ( ordered_pair @ SY3965 @ SY3964 ) @ SV292 )
| ( in @ ( ordered_pair @ SY3964 @ SY3965 ) @ SV385 ) ) )
= $true )
| ( ( SV385
= ( relation_inverse @ SV292 ) )
= $false )
| ( ( relation @ SV385 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2989]) ).
thf(3077,plain,
! [SV293: $i,SV458: $i] :
( ( ( in @ SV458 @ ( relation_dom @ SV293 ) )
= $false )
| ( ( ! [SY4036: $i] :
( ( SY4036
!= ( apply @ SV293 @ SV458 ) )
| ( in @ ( ordered_pair @ SV458 @ SY4036 ) @ SV293 ) ) )
= $true )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2990]) ).
thf(3078,plain,
! [SV293: $i,SV459: $i] :
( ( ( in @ SV459 @ ( relation_dom @ SV293 ) )
= $false )
| ( ( ! [SY4037: $i] :
( ~ ( in @ ( ordered_pair @ SV459 @ SY4037 ) @ SV293 )
| ( SY4037
= ( apply @ SV293 @ SV459 ) ) ) )
= $true )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2991]) ).
thf(3079,plain,
! [SV460: $i,SV293: $i,SV484: $i] :
( ( ( ( SV484
!= ( apply @ SV293 @ SV460 ) )
| ( SV484 = empty_set ) )
= $true )
| ( ( in @ SV460 @ ( relation_dom @ SV293 ) )
= $true )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2992]) ).
thf(3080,plain,
! [SV461: $i,SV293: $i,SV485: $i] :
( ( ( ( SV485 != empty_set )
| ( SV485
= ( apply @ SV293 @ SV461 ) ) )
= $true )
| ( ( in @ SV461 @ ( relation_dom @ SV293 ) )
= $true )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2993]) ).
thf(3081,plain,
! [SV294: $i,SV386: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK19_C @ SV386 @ SV294 ) @ SV386 )
| ~ ( in @ ( sK20_SY3099 @ SV386 @ SV294 ) @ SV386 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SV386 @ SV294 ) @ ( sK20_SY3099 @ SV386 @ SV294 ) ) @ SV294 ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV294 @ SV386 )
= $true )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2994]) ).
thf(3082,plain,
! [SV294: $i,SV386: $i] :
( ( ( in @ ( ordered_pair @ ( sK20_SY3099 @ SV386 @ SV294 ) @ ( sK19_C @ SV386 @ SV294 ) ) @ SV294 )
= $true )
| ( ( is_antisymmetric_in @ SV294 @ SV386 )
= $true )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2995]) ).
thf(3083,plain,
! [SV294: $i,SV450: $i,SV387: $i,SV438: $i] :
( ( ( ~ ( in @ SV438 @ SV387 )
| ~ ( in @ SV450 @ SV387 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV438 @ SV450 ) @ SV294 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV450 @ SV438 ) @ SV294 ) )
= $true )
| ( ( SV438 = SV450 )
= $true )
| ( ( is_antisymmetric_in @ SV294 @ SV387 )
= $false )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2996]) ).
thf(3084,plain,
! [SV295: $i,SV388: $i,SV404: $i] :
( ( ( ( sK35_D @ SV404 @ SV388 @ SV295 )
= SV388 )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV388 ) @ SV295 ) )
= $true )
| ( ( ~ ( in @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV404 ) )
= $true )
| ( ( SV404
= ( fiber @ SV295 @ SV388 ) )
= $true )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2997]) ).
thf(3085,plain,
! [SV295: $i,SV388: $i,SV404: $i] :
( ( ( ~ ( ( ( sK35_D @ SV404 @ SV388 @ SV295 )
!= SV388 )
| ( in @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV404 ) ) )
= $false )
| ( ( SV404
= ( fiber @ SV295 @ SV388 ) )
= $true )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2998]) ).
thf(3086,plain,
! [SV295: $i,SV388: $i,SV404: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV388 ) @ SV295 )
| ( in @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV404 ) ) )
= $false )
| ( ( SV404
= ( fiber @ SV295 @ SV388 ) )
= $true )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2998]) ).
thf(3087,plain,
! [SV405: $i,SV295: $i,SV389: $i,SV486: $i] :
( ( ( ( SV486 = SV389 )
| ~ ( in @ ( ordered_pair @ SV486 @ SV389 ) @ SV295 )
| ( in @ SV486 @ SV405 ) )
= $true )
| ( ( SV405
= ( fiber @ SV295 @ SV389 ) )
= $false )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2999]) ).
thf(3088,plain,
! [SV295: $i,SV389: $i,SV405: $i] :
( ( ( ~ ! [SY3995: $i] :
( ~ ( in @ SY3995 @ SV405 )
| ( SY3995 != SV389 ) )
| ~ ! [SY3996: $i] :
( ~ ( in @ SY3996 @ SV405 )
| ( in @ ( ordered_pair @ SY3996 @ SV389 ) @ SV295 ) ) )
= $false )
| ( ( SV405
= ( fiber @ SV295 @ SV389 ) )
= $false )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3000]) ).
thf(3089,plain,
! [SV296: $i,SV307: $i,SV406: $i] :
( ( ( ~ ( in @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) @ SV296 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV307 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) )
= $true )
| ( ( SV406
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $true )
| ( ( relation @ SV406 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3001]) ).
thf(3090,plain,
! [SV296: $i,SV307: $i,SV406: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) @ SV296 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV307 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) ) ) )
= $true )
| ( ( SV406
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $true )
| ( ( relation @ SV406 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3002]) ).
thf(3091,plain,
! [SV407: $i,SV307: $i,SV296: $i] :
( ( ( ~ ! [SY3997: $i,SY3998: $i] :
( ~ ( in @ SY3998 @ SV296 )
| ~ ( in @ ( ordered_pair @ SY3997 @ SY3998 ) @ SV307 )
| ( in @ ( ordered_pair @ SY3997 @ SY3998 ) @ SV407 ) ) )
= $false )
| ( ( SV407
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $false )
| ( ( relation @ SV407 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3003]) ).
thf(3092,plain,
! [SV307: $i,SV296: $i,SV407: $i] :
( ( ( ~ ~ ( ~ ! [SY3999: $i,SY4000: $i] :
( ~ ( in @ ( ordered_pair @ SY3999 @ SY4000 ) @ SV407 )
| ( in @ SY4000 @ SV296 ) )
| ~ ! [SY4001: $i,SY4002: $i] :
( ~ ( in @ ( ordered_pair @ SY4001 @ SY4002 ) @ SV407 )
| ( in @ ( ordered_pair @ SY4001 @ SY4002 ) @ SV307 ) ) ) )
= $false )
| ( ( SV407
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $false )
| ( ( relation @ SV407 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3003]) ).
thf(3093,plain,
! [SV297: $i,SV390: $i,SV472: $i] :
( ( ( in @ ( ordered_pair @ SV472 @ ( sK17_C @ SV390 @ SV297 ) ) @ SV297 )
= $false )
| ( ( ~ ( in @ ( sK17_C @ SV390 @ SV297 ) @ SV390 ) )
= $true )
| ( ( SV390
= ( relation_rng @ SV297 ) )
= $true )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3004]) ).
thf(3094,plain,
! [SV391: $i,SV297: $i,SV473: $i] :
( ( ( ! [SY4050: $i] :
~ ( in @ ( ordered_pair @ SY4050 @ SV473 ) @ SV297 ) )
= $true )
| ( ( in @ SV473 @ SV391 )
= $true )
| ( ( SV391
= ( relation_rng @ SV297 ) )
= $false )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3005]) ).
thf(3095,plain,
! [SV297: $i,SV391: $i,SV474: $i] :
( ( ( ~ ( in @ SV474 @ SV391 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK16_D @ SV474 @ SV391 @ SV297 ) @ SV474 ) @ SV297 )
= $true )
| ( ( SV391
= ( relation_rng @ SV297 ) )
= $false )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3006]) ).
thf(3096,plain,
! [SV439: $i,SV424: $i,SV308: $i,SV299: $i] :
( ( ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SV424 ) @ SV439 ) )
= $false )
| ( ( in @ SV299 @ SV424 )
= $true )
| ( ( relation @ SV439 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3008]) ).
thf(3097,plain,
! [SV440: $i,SV425: $i,SV308: $i,SV299: $i] :
( ( ( in @ ( ordered_pair @ SV299 @ SV308 ) @ ( relation_composition @ ( identity_relation @ SV425 ) @ SV440 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV299 @ SV308 ) @ SV440 )
= $true )
| ( ( relation @ SV440 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3009]) ).
thf(3098,plain,
! [SV343: $i,SV363: $i,SV441: $i,SV301: $i] :
( ( ( in @ ( ordered_pair @ SV301 @ SV441 ) @ SV363 )
= $false )
| ( ( in @ SV441 @ ( relation_rng @ SV363 ) )
= $false )
| ( ( ~ ( in @ SV441 @ SV343 ) )
= $true )
| ( ( in @ SV301 @ ( relation_inverse_image @ SV363 @ SV343 ) )
= $true )
| ( ( relation @ SV363 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3010]) ).
thf(3099,plain,
! [SV301: $i,SV344: $i,SV364: $i] :
( ( ( ~ ( in @ ( sK60_D @ SV364 @ SV344 @ SV301 ) @ ( relation_rng @ SV364 ) )
| ~ ( in @ ( ordered_pair @ SV301 @ ( sK60_D @ SV364 @ SV344 @ SV301 ) ) @ SV364 ) )
= $false )
| ( ( in @ SV301 @ ( relation_inverse_image @ SV364 @ SV344 ) )
= $false )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3011]) ).
thf(3100,plain,
! [SV274: $i,SV367: $i] :
( ( ( ~ ( ( ( sK14_C @ SV367 @ SV274 )
!= ( sK15_SY3096 @ SV367 @ SV274 ) ) )
| ~ ~ ( ~ ( in @ ( sK14_C @ SV367 @ SV274 ) @ SV367 )
| ~ ( in @ ( sK15_SY3096 @ SV367 @ SV274 ) @ SV367 ) ) )
= $false )
| ( ( is_connected_in @ SV274 @ SV367 )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3013]) ).
thf(3101,plain,
! [SV274: $i,SV367: $i] :
( ( ( in @ ( ordered_pair @ ( sK14_C @ SV367 @ SV274 ) @ ( sK15_SY3096 @ SV367 @ SV274 ) ) @ SV274 )
= $false )
| ( ( is_connected_in @ SV274 @ SV367 )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3014]) ).
thf(3102,plain,
! [SV274: $i,SV445: $i,SV368: $i,SV428: $i] :
( ( ( ~ ( in @ SV428 @ SV368 ) )
= $true )
| ( ( ~ ( in @ SV445 @ SV368 ) )
= $true )
| ( ( SV428 = SV445 )
= $true )
| ( ( in @ ( ordered_pair @ SV428 @ SV445 ) @ SV274 )
= $true )
| ( ( in @ ( ordered_pair @ SV445 @ SV428 ) @ SV274 )
= $true )
| ( ( is_connected_in @ SV274 @ SV368 )
= $false )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3015]) ).
thf(3103,plain,
! [SV347: $i,SV328: $i,SV462: $i,SV275: $i,SV451: $i] :
( ( ( ~ ( in @ SV451 @ SV275 ) )
= $true )
| ( ( ~ ( in @ SV462 @ SV328 ) )
= $true )
| ( ( ( ( sK28_D @ SV347 @ SV328 @ SV275 )
!= ( ordered_pair @ SV451 @ SV462 ) ) )
= $true )
| ( ( ~ ( in @ ( sK28_D @ SV347 @ SV328 @ SV275 ) @ SV347 ) )
= $true )
| ( ( SV347
= ( cartesian_product2 @ SV275 @ SV328 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3017]) ).
thf(3104,plain,
! [SV275: $i,SV328: $i,SV347: $i] :
( ( ( ~ ( in @ ( sK29_SY3106 @ SV347 @ SV328 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK30_SY3108 @ SV347 @ SV328 @ SV275 ) @ SV328 ) )
= $false )
| ( ( in @ ( sK28_D @ SV347 @ SV328 @ SV275 ) @ SV347 )
= $true )
| ( ( SV347
= ( cartesian_product2 @ SV275 @ SV328 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3018]) ).
thf(3105,plain,
! [SV348: $i,SV452: $i,SV329: $i,SV487: $i,SV275: $i,SV475: $i] :
( ( ( ~ ( in @ SV475 @ SV275 )
| ~ ( in @ SV487 @ SV329 )
| ( SV452
!= ( ordered_pair @ SV475 @ SV487 ) ) )
= $true )
| ( ( in @ SV452 @ SV348 )
= $true )
| ( ( SV348
= ( cartesian_product2 @ SV275 @ SV329 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3020]) ).
thf(3106,plain,
! [SV275: $i,SV329: $i,SV348: $i,SV453: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK26_E @ SV453 @ SV348 @ SV329 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK27_SY3103 @ SV453 @ SV348 @ SV329 @ SV275 ) @ SV329 ) )
| ( SV453
!= ( ordered_pair @ ( sK26_E @ SV453 @ SV348 @ SV329 @ SV275 ) @ ( sK27_SY3103 @ SV453 @ SV348 @ SV329 @ SV275 ) ) ) )
= $false )
| ( ( in @ SV453 @ SV348 )
= $false )
| ( ( SV348
= ( cartesian_product2 @ SV275 @ SV329 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3021]) ).
thf(3107,plain,
! [SV276: $i,SV370: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SV370 @ SV276 ) @ SV370 )
| ~ ( in @ ( sK4_SY3086 @ SV370 @ SV276 ) @ SV370 ) )
| ~ ( in @ ( sK5_SY3088 @ SV370 @ SV276 ) @ SV370 ) )
| ~ ( in @ ( ordered_pair @ ( sK3_C @ SV370 @ SV276 ) @ ( sK4_SY3086 @ SV370 @ SV276 ) ) @ SV276 ) )
= $false )
| ( ( is_transitive_in @ SV276 @ SV370 )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3022]) ).
thf(3108,plain,
! [SV276: $i,SV454: $i,SV446: $i,SV371: $i,SV431: $i] :
( ( ( ~ ( in @ SV431 @ SV371 )
| ~ ( in @ SV446 @ SV371 )
| ~ ( in @ SV454 @ SV371 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV431 @ SV446 ) @ SV276 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV446 @ SV454 ) @ SV276 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV431 @ SV454 ) @ SV276 )
= $true )
| ( ( is_transitive_in @ SV276 @ SV371 )
= $false )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3024]) ).
thf(3109,plain,
! [SV277: $i,SV372: $i,SV396: $i,SV476: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV476 @ ( sK46_D @ SV396 @ SV372 @ SV277 ) ) @ SV277 ) )
= $true )
| ( ( ~ ( in @ SV476 @ SV372 ) )
= $true )
| ( ( ~ ( in @ ( sK46_D @ SV396 @ SV372 @ SV277 ) @ SV396 ) )
= $true )
| ( ( SV396
= ( relation_image @ SV277 @ SV372 ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3025]) ).
thf(3110,plain,
! [SV277: $i,SV372: $i,SV396: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK47_SY3118 @ SV396 @ SV372 @ SV277 ) @ ( sK46_D @ SV396 @ SV372 @ SV277 ) ) @ SV277 ) )
= $false )
| ( ( in @ ( sK46_D @ SV396 @ SV372 @ SV277 ) @ SV396 )
= $true )
| ( ( SV396
= ( relation_image @ SV277 @ SV372 ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3026]) ).
thf(3111,plain,
! [SV277: $i,SV372: $i,SV396: $i] :
( ( ( ~ ( in @ ( sK47_SY3118 @ SV396 @ SV372 @ SV277 ) @ SV372 ) )
= $false )
| ( ( in @ ( sK46_D @ SV396 @ SV372 @ SV277 ) @ SV396 )
= $true )
| ( ( SV396
= ( relation_image @ SV277 @ SV372 ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3026]) ).
thf(3112,plain,
! [SV397: $i,SV373: $i,SV277: $i,SV477: $i] :
( ( ( ! [SY4052: $i] :
( ~ ( in @ ( ordered_pair @ SY4052 @ SV477 ) @ SV277 )
| ~ ( in @ SY4052 @ SV373 ) ) )
= $true )
| ( ( in @ SV477 @ SV397 )
= $true )
| ( ( SV397
= ( relation_image @ SV277 @ SV373 ) )
= $false )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3027]) ).
thf(3113,plain,
! [SV277: $i,SV373: $i,SV397: $i,SV478: $i] :
( ( ( ~ ( in @ SV478 @ SV397 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SV478 @ SV397 @ SV373 @ SV277 ) @ SV478 ) @ SV277 )
| ~ ( in @ ( sK45_E @ SV478 @ SV397 @ SV373 @ SV277 ) @ SV373 ) ) )
= $true )
| ( ( SV397
= ( relation_image @ SV277 @ SV373 ) )
= $false )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3028]) ).
thf(3114,plain,
! [SV278: $i,SV374: $i,SV398: $i] :
( ( ( ~ ( in @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ SV374 )
| ~ ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV278 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) )
= $true )
| ( ( SV398
= ( relation_dom_restriction @ SV278 @ SV374 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3029]) ).
thf(3115,plain,
! [SV278: $i,SV374: $i,SV398: $i] :
( ( ( ~ ( ( in @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ SV374 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV278 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) ) )
= $false )
| ( ( SV398
= ( relation_dom_restriction @ SV278 @ SV374 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3030]) ).
thf(3116,plain,
! [SV399: $i,SV278: $i,SV375: $i] :
( ( ( ! [SY3982: $i,SY3983: $i] :
( ~ ( in @ SY3982 @ SV375 )
| ~ ( in @ ( ordered_pair @ SY3982 @ SY3983 ) @ SV278 )
| ( in @ ( ordered_pair @ SY3982 @ SY3983 ) @ SV399 ) ) )
= $true )
| ( ( SV399
= ( relation_dom_restriction @ SV278 @ SV375 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3031]) ).
thf(3117,plain,
! [SV278: $i,SV375: $i,SV399: $i] :
( ( ( ~ ( ~ ! [SY3984: $i] :
( ! [SY3985: $i] :
~ ( in @ ( ordered_pair @ SY3984 @ SY3985 ) @ SV399 )
| ( in @ SY3984 @ SV375 ) )
| ~ ! [SY3986: $i,SY3987: $i] :
( ~ ( in @ ( ordered_pair @ SY3986 @ SY3987 ) @ SV399 )
| ( in @ ( ordered_pair @ SY3986 @ SY3987 ) @ SV278 ) ) ) )
= $true )
| ( ( SV399
= ( relation_dom_restriction @ SV278 @ SV375 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3032]) ).
thf(3118,plain,
! [SV479: $i,SV279: $i,SV376: $i,SV400: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SV479 ) @ SV279 ) )
= $true )
| ( ( ~ ( in @ SV479 @ SV376 ) )
= $true )
| ( ( ~ ( in @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SV400 ) )
= $true )
| ( ( SV400
= ( relation_inverse_image @ SV279 @ SV376 ) )
= $true )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3033]) ).
thf(3119,plain,
! [SV279: $i,SV376: $i,SV400: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ ( sK44_SY3116 @ SV400 @ SV376 @ SV279 ) ) @ SV279 ) )
= $false )
| ( ( in @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SV400 )
= $true )
| ( ( SV400
= ( relation_inverse_image @ SV279 @ SV376 ) )
= $true )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3034]) ).
thf(3120,plain,
! [SV279: $i,SV376: $i,SV400: $i] :
( ( ( ~ ( in @ ( sK44_SY3116 @ SV400 @ SV376 @ SV279 ) @ SV376 ) )
= $false )
| ( ( in @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SV400 )
= $true )
| ( ( SV400
= ( relation_inverse_image @ SV279 @ SV376 ) )
= $true )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3034]) ).
thf(3121,plain,
! [SV401: $i,SV377: $i,SV279: $i,SV480: $i] :
( ( ( ! [SY4053: $i] :
( ~ ( in @ ( ordered_pair @ SV480 @ SY4053 ) @ SV279 )
| ~ ( in @ SY4053 @ SV377 ) ) )
= $true )
| ( ( in @ SV480 @ SV401 )
= $true )
| ( ( SV401
= ( relation_inverse_image @ SV279 @ SV377 ) )
= $false )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3035]) ).
thf(3122,plain,
! [SV279: $i,SV377: $i,SV401: $i,SV481: $i] :
( ( ( ~ ( in @ SV481 @ SV401 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV481 @ ( sK42_E @ SV481 @ SV401 @ SV377 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK42_E @ SV481 @ SV401 @ SV377 @ SV279 ) @ SV377 ) ) )
= $true )
| ( ( SV401
= ( relation_inverse_image @ SV279 @ SV377 ) )
= $false )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3036]) ).
thf(3123,plain,
! [SV379: $i,SV280: $i,SV463: $i,SV455: $i] :
( ( ( in @ ( ordered_pair @ SV455 @ SV463 ) @ SV280 )
= $false )
| ( ( in @ ( ordered_pair @ SV455 @ SV463 ) @ SV379 )
= $true )
| ( ( subset @ SV280 @ SV379 )
= $false )
| ( ( relation @ SV379 )
= $false )
| ( ( relation @ SV280 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3038]) ).
thf(3124,plain,
! [SV281: $i,SV318: $i,SV432: $i] :
( ( ( ~ ( ! [SY4021: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ SY4021 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY4021 @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV318 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV432 ) ) )
= $false )
| ( ( SV432
= ( relation_composition @ SV281 @ SV318 ) )
= $true )
| ( ( relation @ SV432 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3039]) ).
thf(3125,plain,
! [SV281: $i,SV318: $i,SV432: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK9_SY3093 @ SV432 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV318 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV432 ) ) )
= $false )
| ( ( SV432
= ( relation_composition @ SV281 @ SV318 ) )
= $true )
| ( ( relation @ SV432 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3039]) ).
thf(3126,plain,
! [SV433: $i,SV318: $i,SV281: $i] :
( ( ( ~ ! [SY4022: $i,SY4023: $i] :
( ! [SY3848: $i] :
( ~ ( in @ ( ordered_pair @ SY4022 @ SY3848 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY3848 @ SY4023 ) @ SV318 ) )
| ( in @ ( ordered_pair @ SY4022 @ SY4023 ) @ SV433 ) )
| ~ ! [SY4025: $i,SY4026: $i] :
( ~ ( in @ ( ordered_pair @ SY4025 @ SY4026 ) @ SV433 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4025 @ ( sK6_F @ SY4026 @ SY4025 @ SV433 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY4026 @ SY4025 @ SV433 @ SV318 @ SV281 ) @ SY4026 ) @ SV318 ) ) ) )
= $false )
| ( ( SV433
= ( relation_composition @ SV281 @ SV318 ) )
= $false )
| ( ( relation @ SV433 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3040]) ).
thf(3127,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) ) ) )
| ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3042]) ).
thf(3128,plain,
! [SV319: $i,SV283: $i,SV465: $i] :
( ( ( ~ ( function @ SV465 ) )
= $true )
| ( ( ~ ( relation @ SV465 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
| ~ ( ~ ! [SY4040: $i,SY4041: $i] :
( ~ ( in @ SY4040 @ ( relation_field @ SV283 ) )
| ~ ( in @ SY4041 @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV465 @ SY4040 ) @ ( apply @ SV465 @ SY4041 ) ) @ SV319 )
| ( in @ ( ordered_pair @ SY4040 @ SY4041 ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3687: $i] :
( ! [SY3688: $i] :
~ ( in @ ( ordered_pair @ SY3687 @ SY3688 ) @ SV283 )
| ( in @ SY3687 @ ( relation_field @ SV283 ) ) )
| ~ ! [SY3689: $i,SY3690: $i] :
( ~ ( in @ ( ordered_pair @ SY3689 @ SY3690 ) @ SV283 )
| ( in @ SY3690 @ ( relation_field @ SV283 ) ) ) )
| ~ ! [SY4046: $i,SY4047: $i] :
( ~ ( in @ ( ordered_pair @ SY4046 @ SY4047 ) @ SV283 )
| ( in @ ( ordered_pair @ ( apply @ SV465 @ SY4046 ) @ ( apply @ SV465 @ SY4047 ) ) @ SV319 ) ) ) ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3043]) ).
thf(3129,plain,
! [SV319: $i,SV283: $i] :
( ( ( ~ ( ~ ! [SY3861: $i] :
( ~ ( function @ SY3861 )
| ~ ( relation @ SY3861 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3861 )
| ( ( relation_dom @ SY3861 )
= ( relation_field @ SV283 ) ) )
| ~ ! [SY3862: $i] :
( ~ ( function @ SY3862 )
| ~ ( relation @ SY3862 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3862 )
| ( ( relation_rng @ SY3862 )
= ( relation_field @ SV319 ) ) ) ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3044]) ).
thf(3130,plain,
! [SV319: $i,SV283: $i] :
( ( ( ! [SY3863: $i] :
( ~ ( function @ SY3863 )
| ~ ( relation @ SY3863 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3863 )
| ( one_to_one @ SY3863 ) ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3045]) ).
thf(3131,plain,
! [SV320: $i] :
( ( ( ~ ( ( ( sK62_B @ SV320 )
!= ( sK63_SY3125 @ SV320 ) ) ) )
= $false )
| ( ( connected @ SV320 )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3046]) ).
thf(3132,plain,
! [SV320: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK62_B @ SV320 ) @ ( relation_field @ SV320 ) )
| ~ ( in @ ( sK63_SY3125 @ SV320 ) @ ( relation_field @ SV320 ) ) ) )
= $false )
| ( ( connected @ SV320 )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3046]) ).
thf(3133,plain,
! [SV435: $i,SV321: $i,SV416: $i] :
( ( ( in @ SV416 @ ( relation_field @ SV321 ) )
= $false )
| ( ( ~ ( in @ SV435 @ ( relation_field @ SV321 ) ) )
= $true )
| ( ( SV416 = SV435 )
= $true )
| ( ( in @ ( ordered_pair @ SV416 @ SV435 ) @ SV321 )
= $true )
| ( ( in @ ( ordered_pair @ SV435 @ SV416 ) @ SV321 )
= $true )
| ( ( connected @ SV321 )
= $false )
| ( ( relation @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3048]) ).
thf(3134,plain,
! [SV417: $i,SV402: $i,SV284: $i] :
( ( ( in @ ( ordered_pair @ SV284 @ SV402 ) @ SV417 )
= $false )
| ( ( SV402
= ( apply @ SV417 @ SV284 ) )
= $true )
| ( ( function @ SV417 )
= $false )
| ( ( relation @ SV417 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3050]) ).
thf(3135,plain,
! [SV418: $i,SV403: $i,SV284: $i] :
( ( ( in @ ( ordered_pair @ SV284 @ SV403 ) @ SV418 )
= $false )
| ( ( in @ SV284 @ ( relation_dom @ SV418 ) )
= $true )
| ( ( function @ SV418 )
= $false )
| ( ( relation @ SV418 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3051]) ).
thf(3136,plain,
! [SV285: $i,SV352: $i,SV333: $i,SV436: $i] :
( ( ( in @ SV436 @ SV333 )
= $false )
| ( ( in @ SV436 @ ( relation_dom @ SV352 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV436 @ SV285 ) @ SV352 )
= $false )
| ( ( in @ SV285 @ ( relation_image @ SV352 @ SV333 ) )
= $true )
| ( ( relation @ SV352 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3052]) ).
thf(3137,plain,
! [SV285: $i,SV334: $i,SV353: $i] :
( ( ( ~ ( in @ ( sK61_D @ SV353 @ SV334 @ SV285 ) @ ( relation_dom @ SV353 ) ) )
= $false )
| ( ( in @ SV285 @ ( relation_image @ SV353 @ SV334 ) )
= $false )
| ( ( relation @ SV353 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3053]) ).
thf(3138,plain,
! [SV285: $i,SV334: $i,SV353: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK61_D @ SV353 @ SV334 @ SV285 ) @ SV285 ) @ SV353 ) )
= $false )
| ( ( in @ SV285 @ ( relation_image @ SV353 @ SV334 ) )
= $false )
| ( ( relation @ SV353 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3053]) ).
thf(3139,plain,
! [SV322: $i,SV310: $i,SV420: $i,SV482: $i,SV456: $i,SV286: $i] :
( ( ( SV286
= ( ordered_pair @ SV456 @ SV482 ) )
= $false )
| ( ( SV420 = SV456 )
= $true )
| ( ( SV420
= ( pair_first @ SV286 ) )
= $false )
| ( ( SV286
= ( ordered_pair @ SV310 @ SV322 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3055]) ).
thf(3140,plain,
! [SV323: $i,SV311: $i,SV422: $i,SV466: $i,SV457: $i,SV287: $i] :
( ( ( SV287
= ( ordered_pair @ SV457 @ SV466 ) )
= $false )
| ( ( SV422 = SV466 )
= $true )
| ( ( SV422
= ( pair_second @ SV287 ) )
= $false )
| ( ( SV287
= ( ordered_pair @ SV311 @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3057]) ).
thf(3141,plain,
! [SV324: $i,SV337: $i] :
( ( ( in @ ( sK52_C @ SV337 @ SV324 ) @ SV324 )
= $false )
| ( ( ( sK52_C @ SV337 @ SV324 )
= ( sK53_SY3121 @ SV337 @ SV324 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 ) )
= $true )
| ( ( SV337
= ( identity_relation @ SV324 ) )
= $true )
| ( ( relation @ SV337 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3058]) ).
thf(3142,plain,
! [SV324: $i,SV337: $i] :
( ( ( ( sK52_C @ SV337 @ SV324 )
= ( sK53_SY3121 @ SV337 @ SV324 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 )
= $true )
| ( ( SV337
= ( identity_relation @ SV324 ) )
= $true )
| ( ( relation @ SV337 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3059]) ).
thf(3143,plain,
! [SV324: $i,SV337: $i] :
( ( ( in @ ( sK52_C @ SV337 @ SV324 ) @ SV324 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 )
= $true )
| ( ( SV337
= ( identity_relation @ SV324 ) )
= $true )
| ( ( relation @ SV337 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3060]) ).
thf(3144,plain,
! [SV338: $i,SV325: $i,SV483: $i,SV467: $i] :
( ( ( ( SV467 != SV483 )
| ~ ( in @ SV467 @ SV325 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV467 @ SV483 ) @ SV338 )
= $true )
| ( ( SV338
= ( identity_relation @ SV325 ) )
= $false )
| ( ( relation @ SV338 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3061]) ).
thf(3145,plain,
! [SV325: $i,SV338: $i] :
( ( ( ! [SY3897: $i,SY3898: $i] :
( ~ ( in @ ( ordered_pair @ SY3897 @ SY3898 ) @ SV338 )
| ( SY3897 = SY3898 ) ) )
= $true )
| ( ( SV338
= ( identity_relation @ SV325 ) )
= $false )
| ( ( relation @ SV338 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3062]) ).
thf(3146,plain,
! [SV325: $i,SV338: $i] :
( ( ( ! [SY3899: $i] :
( ! [SY3900: $i] :
~ ( in @ ( ordered_pair @ SY3899 @ SY3900 ) @ SV338 )
| ( in @ SY3899 @ SV325 ) ) )
= $true )
| ( ( SV338
= ( identity_relation @ SV325 ) )
= $false )
| ( ( relation @ SV338 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3063]) ).
thf(3147,plain,
! [SV469: $i,SV290: $i,SV380: $i] :
( ( ( in @ ( sK22_C @ SV380 @ SV290 ) @ SV380 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK22_C @ SV380 @ SV290 ) @ SV469 ) @ SV290 )
= $false )
| ( ( SV380
= ( relation_dom @ SV290 ) )
= $true )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3065]) ).
thf(3148,plain,
! [SV381: $i,SV290: $i,SV488: $i,SV470: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV470 @ SV488 ) @ SV290 ) )
= $true )
| ( ( in @ SV470 @ SV381 )
= $true )
| ( ( SV381
= ( relation_dom @ SV290 ) )
= $false )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3066]) ).
thf(3149,plain,
! [SV290: $i,SV381: $i,SV471: $i] :
( ( ( in @ SV471 @ SV381 )
= $false )
| ( ( in @ ( ordered_pair @ SV471 @ ( sK21_D @ SV471 @ SV381 @ SV290 ) ) @ SV290 )
= $true )
| ( ( SV381
= ( relation_dom @ SV290 ) )
= $false )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3067]) ).
thf(3150,plain,
! [SV291: $i,SV382: $i] :
( ( ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV291 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV382 ) )
= $true )
| ( ( SV291 = SV382 )
= $true )
| ( ( relation @ SV382 )
= $false )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3068]) ).
thf(3151,plain,
! [SV383: $i,SV291: $i,SV489: $i] :
( ( ( ! [SY4054: $i] :
( ~ ( in @ ( ordered_pair @ SV489 @ SY4054 ) @ SV291 )
| ( in @ ( ordered_pair @ SV489 @ SY4054 ) @ SV383 ) ) )
= $true )
| ( ( SV291 = SV383 )
= $false )
| ( ( relation @ SV383 )
= $false )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3070]) ).
thf(3152,plain,
! [SV291: $i,SV383: $i,SV490: $i] :
( ( ( ! [SY4055: $i] :
( ~ ( in @ ( ordered_pair @ SV490 @ SY4055 ) @ SV383 )
| ( in @ ( ordered_pair @ SV490 @ SY4055 ) @ SV291 ) ) )
= $true )
| ( ( SV291 = SV383 )
= $false )
| ( ( relation @ SV383 )
= $false )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3071]) ).
thf(3153,plain,
! [SV423: $i,SV327: $i,SV449: $i,SV437: $i] :
( ( ( in @ ( ordered_pair @ SV437 @ SV449 ) @ SV327 )
= $false )
| ( ( in @ ( ordered_pair @ SV423 @ SV437 ) @ SV327 )
= $false )
| ( ( in @ ( ordered_pair @ SV423 @ SV449 ) @ SV327 )
= $true )
| ( ( transitive @ SV327 )
= $false )
| ( ( relation @ SV327 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3072]) ).
thf(3154,plain,
! [SV292: $i,SV384: $i] :
( ( ( in @ ( ordered_pair @ ( sK12_C @ SV384 @ SV292 ) @ ( sK13_SY3095 @ SV384 @ SV292 ) ) @ SV384 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV384 @ SV292 ) @ ( sK12_C @ SV384 @ SV292 ) ) @ SV292 ) )
= $true )
| ( ( SV384
= ( relation_inverse @ SV292 ) )
= $true )
| ( ( relation @ SV384 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3073]) ).
thf(3155,plain,
! [SV292: $i,SV385: $i,SV491: $i] :
( ( ( ! [SY4056: $i] :
( ~ ( in @ ( ordered_pair @ SV491 @ SY4056 ) @ SV385 )
| ( in @ ( ordered_pair @ SY4056 @ SV491 ) @ SV292 ) ) )
= $true )
| ( ( SV385
= ( relation_inverse @ SV292 ) )
= $false )
| ( ( relation @ SV385 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3075]) ).
thf(3156,plain,
! [SV385: $i,SV292: $i,SV492: $i] :
( ( ( ! [SY4057: $i] :
( ~ ( in @ ( ordered_pair @ SY4057 @ SV492 ) @ SV292 )
| ( in @ ( ordered_pair @ SV492 @ SY4057 ) @ SV385 ) ) )
= $true )
| ( ( SV385
= ( relation_inverse @ SV292 ) )
= $false )
| ( ( relation @ SV385 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3076]) ).
thf(3157,plain,
! [SV458: $i,SV293: $i,SV493: $i] :
( ( ( ( SV493
!= ( apply @ SV293 @ SV458 ) )
| ( in @ ( ordered_pair @ SV458 @ SV493 ) @ SV293 ) )
= $true )
| ( ( in @ SV458 @ ( relation_dom @ SV293 ) )
= $false )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3077]) ).
thf(3158,plain,
! [SV293: $i,SV494: $i,SV459: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV459 @ SV494 ) @ SV293 )
| ( SV494
= ( apply @ SV293 @ SV459 ) ) )
= $true )
| ( ( in @ SV459 @ ( relation_dom @ SV293 ) )
= $false )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3078]) ).
thf(3159,plain,
! [SV460: $i,SV293: $i,SV484: $i] :
( ( ( ( SV484
!= ( apply @ SV293 @ SV460 ) ) )
= $true )
| ( ( SV484 = empty_set )
= $true )
| ( ( in @ SV460 @ ( relation_dom @ SV293 ) )
= $true )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3079]) ).
thf(3160,plain,
! [SV461: $i,SV293: $i,SV485: $i] :
( ( ( ( SV485 != empty_set ) )
= $true )
| ( ( SV485
= ( apply @ SV293 @ SV461 ) )
= $true )
| ( ( in @ SV461 @ ( relation_dom @ SV293 ) )
= $true )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3080]) ).
thf(3161,plain,
! [SV294: $i,SV386: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK19_C @ SV386 @ SV294 ) @ SV386 )
| ~ ( in @ ( sK20_SY3099 @ SV386 @ SV294 ) @ SV386 ) )
| ~ ( in @ ( ordered_pair @ ( sK19_C @ SV386 @ SV294 ) @ ( sK20_SY3099 @ SV386 @ SV294 ) ) @ SV294 ) )
= $false )
| ( ( is_antisymmetric_in @ SV294 @ SV386 )
= $true )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3081]) ).
thf(3162,plain,
! [SV294: $i,SV450: $i,SV387: $i,SV438: $i] :
( ( ( ~ ( in @ SV438 @ SV387 ) )
= $true )
| ( ( ~ ( in @ SV450 @ SV387 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV438 @ SV450 ) @ SV294 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV450 @ SV438 ) @ SV294 ) )
= $true )
| ( ( SV438 = SV450 )
= $true )
| ( ( is_antisymmetric_in @ SV294 @ SV387 )
= $false )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3083]) ).
thf(3163,plain,
! [SV295: $i,SV388: $i,SV404: $i] :
( ( ( in @ ( ordered_pair @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV388 ) @ SV295 )
= $false )
| ( ( ( sK35_D @ SV404 @ SV388 @ SV295 )
= SV388 )
= $true )
| ( ( ~ ( in @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV404 ) )
= $true )
| ( ( SV404
= ( fiber @ SV295 @ SV388 ) )
= $true )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3084]) ).
thf(3164,plain,
! [SV295: $i,SV388: $i,SV404: $i] :
( ( ( ( ( sK35_D @ SV404 @ SV388 @ SV295 )
!= SV388 )
| ( in @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV404 ) )
= $true )
| ( ( SV404
= ( fiber @ SV295 @ SV388 ) )
= $true )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3085]) ).
thf(3165,plain,
! [SV295: $i,SV388: $i,SV404: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV388 ) @ SV295 )
| ( in @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV404 ) )
= $true )
| ( ( SV404
= ( fiber @ SV295 @ SV388 ) )
= $true )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3086]) ).
thf(3166,plain,
! [SV405: $i,SV295: $i,SV389: $i,SV486: $i] :
( ( ( ( SV486 = SV389 )
| ~ ( in @ ( ordered_pair @ SV486 @ SV389 ) @ SV295 ) )
= $true )
| ( ( in @ SV486 @ SV405 )
= $true )
| ( ( SV405
= ( fiber @ SV295 @ SV389 ) )
= $false )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3087]) ).
thf(3167,plain,
! [SV295: $i,SV389: $i,SV405: $i] :
( ( ( ~ ! [SY3995: $i] :
( ~ ( in @ SY3995 @ SV405 )
| ( SY3995 != SV389 ) ) )
= $false )
| ( ( SV405
= ( fiber @ SV295 @ SV389 ) )
= $false )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3088]) ).
thf(3168,plain,
! [SV295: $i,SV389: $i,SV405: $i] :
( ( ( ~ ! [SY3996: $i] :
( ~ ( in @ SY3996 @ SV405 )
| ( in @ ( ordered_pair @ SY3996 @ SV389 ) @ SV295 ) ) )
= $false )
| ( ( SV405
= ( fiber @ SV295 @ SV389 ) )
= $false )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3088]) ).
thf(3169,plain,
! [SV296: $i,SV307: $i,SV406: $i] :
( ( ( ~ ( in @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) @ SV296 )
| ~ ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV307 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) )
= $true )
| ( ( SV406
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $true )
| ( ( relation @ SV406 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3089]) ).
thf(3170,plain,
! [SV296: $i,SV307: $i,SV406: $i] :
( ( ( ~ ( ( in @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) @ SV296 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV307 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) ) )
= $false )
| ( ( SV406
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $true )
| ( ( relation @ SV406 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3090]) ).
thf(3171,plain,
! [SV407: $i,SV307: $i,SV296: $i] :
( ( ( ! [SY3997: $i,SY3998: $i] :
( ~ ( in @ SY3998 @ SV296 )
| ~ ( in @ ( ordered_pair @ SY3997 @ SY3998 ) @ SV307 )
| ( in @ ( ordered_pair @ SY3997 @ SY3998 ) @ SV407 ) ) )
= $true )
| ( ( SV407
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $false )
| ( ( relation @ SV407 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3091]) ).
thf(3172,plain,
! [SV307: $i,SV296: $i,SV407: $i] :
( ( ( ~ ( ~ ! [SY3999: $i,SY4000: $i] :
( ~ ( in @ ( ordered_pair @ SY3999 @ SY4000 ) @ SV407 )
| ( in @ SY4000 @ SV296 ) )
| ~ ! [SY4001: $i,SY4002: $i] :
( ~ ( in @ ( ordered_pair @ SY4001 @ SY4002 ) @ SV407 )
| ( in @ ( ordered_pair @ SY4001 @ SY4002 ) @ SV307 ) ) ) )
= $true )
| ( ( SV407
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $false )
| ( ( relation @ SV407 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3092]) ).
thf(3173,plain,
! [SV472: $i,SV297: $i,SV390: $i] :
( ( ( in @ ( sK17_C @ SV390 @ SV297 ) @ SV390 )
= $false )
| ( ( in @ ( ordered_pair @ SV472 @ ( sK17_C @ SV390 @ SV297 ) ) @ SV297 )
= $false )
| ( ( SV390
= ( relation_rng @ SV297 ) )
= $true )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3093]) ).
thf(3174,plain,
! [SV391: $i,SV297: $i,SV473: $i,SV495: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV495 @ SV473 ) @ SV297 ) )
= $true )
| ( ( in @ SV473 @ SV391 )
= $true )
| ( ( SV391
= ( relation_rng @ SV297 ) )
= $false )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3094]) ).
thf(3175,plain,
! [SV297: $i,SV391: $i,SV474: $i] :
( ( ( in @ SV474 @ SV391 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK16_D @ SV474 @ SV391 @ SV297 ) @ SV474 ) @ SV297 )
= $true )
| ( ( SV391
= ( relation_rng @ SV297 ) )
= $false )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3095]) ).
thf(3176,plain,
! [SV301: $i,SV363: $i,SV343: $i,SV441: $i] :
( ( ( in @ SV441 @ SV343 )
= $false )
| ( ( in @ SV441 @ ( relation_rng @ SV363 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV301 @ SV441 ) @ SV363 )
= $false )
| ( ( in @ SV301 @ ( relation_inverse_image @ SV363 @ SV343 ) )
= $true )
| ( ( relation @ SV363 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3098]) ).
thf(3177,plain,
! [SV301: $i,SV344: $i,SV364: $i] :
( ( ( ~ ( in @ ( sK60_D @ SV364 @ SV344 @ SV301 ) @ ( relation_rng @ SV364 ) ) )
= $false )
| ( ( in @ SV301 @ ( relation_inverse_image @ SV364 @ SV344 ) )
= $false )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3099]) ).
thf(3178,plain,
! [SV344: $i,SV364: $i,SV301: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV301 @ ( sK60_D @ SV364 @ SV344 @ SV301 ) ) @ SV364 ) )
= $false )
| ( ( in @ SV301 @ ( relation_inverse_image @ SV364 @ SV344 ) )
= $false )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3099]) ).
thf(3179,plain,
! [SV274: $i,SV367: $i] :
( ( ( ~ ( ( ( sK14_C @ SV367 @ SV274 )
!= ( sK15_SY3096 @ SV367 @ SV274 ) ) ) )
= $false )
| ( ( is_connected_in @ SV274 @ SV367 )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3100]) ).
thf(3180,plain,
! [SV274: $i,SV367: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK14_C @ SV367 @ SV274 ) @ SV367 )
| ~ ( in @ ( sK15_SY3096 @ SV367 @ SV274 ) @ SV367 ) ) )
= $false )
| ( ( is_connected_in @ SV274 @ SV367 )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3100]) ).
thf(3181,plain,
! [SV274: $i,SV445: $i,SV368: $i,SV428: $i] :
( ( ( in @ SV428 @ SV368 )
= $false )
| ( ( ~ ( in @ SV445 @ SV368 ) )
= $true )
| ( ( SV428 = SV445 )
= $true )
| ( ( in @ ( ordered_pair @ SV428 @ SV445 ) @ SV274 )
= $true )
| ( ( in @ ( ordered_pair @ SV445 @ SV428 ) @ SV274 )
= $true )
| ( ( is_connected_in @ SV274 @ SV368 )
= $false )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3102]) ).
thf(3182,plain,
! [SV347: $i,SV328: $i,SV462: $i,SV275: $i,SV451: $i] :
( ( ( in @ SV451 @ SV275 )
= $false )
| ( ( ~ ( in @ SV462 @ SV328 ) )
= $true )
| ( ( ( ( sK28_D @ SV347 @ SV328 @ SV275 )
!= ( ordered_pair @ SV451 @ SV462 ) ) )
= $true )
| ( ( ~ ( in @ ( sK28_D @ SV347 @ SV328 @ SV275 ) @ SV347 ) )
= $true )
| ( ( SV347
= ( cartesian_product2 @ SV275 @ SV328 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3103]) ).
thf(3183,plain,
! [SV275: $i,SV328: $i,SV347: $i] :
( ( ( ~ ( in @ ( sK29_SY3106 @ SV347 @ SV328 @ SV275 ) @ SV275 ) )
= $false )
| ( ( in @ ( sK28_D @ SV347 @ SV328 @ SV275 ) @ SV347 )
= $true )
| ( ( SV347
= ( cartesian_product2 @ SV275 @ SV328 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3104]) ).
thf(3184,plain,
! [SV275: $i,SV328: $i,SV347: $i] :
( ( ( ~ ( in @ ( sK30_SY3108 @ SV347 @ SV328 @ SV275 ) @ SV328 ) )
= $false )
| ( ( in @ ( sK28_D @ SV347 @ SV328 @ SV275 ) @ SV347 )
= $true )
| ( ( SV347
= ( cartesian_product2 @ SV275 @ SV328 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3104]) ).
thf(3185,plain,
! [SV348: $i,SV452: $i,SV329: $i,SV487: $i,SV275: $i,SV475: $i] :
( ( ( ~ ( in @ SV475 @ SV275 )
| ~ ( in @ SV487 @ SV329 ) )
= $true )
| ( ( ( SV452
!= ( ordered_pair @ SV475 @ SV487 ) ) )
= $true )
| ( ( in @ SV452 @ SV348 )
= $true )
| ( ( SV348
= ( cartesian_product2 @ SV275 @ SV329 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3105]) ).
thf(3186,plain,
! [SV275: $i,SV329: $i,SV348: $i,SV453: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK26_E @ SV453 @ SV348 @ SV329 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK27_SY3103 @ SV453 @ SV348 @ SV329 @ SV275 ) @ SV329 ) ) )
= $false )
| ( ( in @ SV453 @ SV348 )
= $false )
| ( ( SV348
= ( cartesian_product2 @ SV275 @ SV329 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3106]) ).
thf(3187,plain,
! [SV275: $i,SV329: $i,SV348: $i,SV453: $i] :
( ( ( ( SV453
!= ( ordered_pair @ ( sK26_E @ SV453 @ SV348 @ SV329 @ SV275 ) @ ( sK27_SY3103 @ SV453 @ SV348 @ SV329 @ SV275 ) ) ) )
= $false )
| ( ( in @ SV453 @ SV348 )
= $false )
| ( ( SV348
= ( cartesian_product2 @ SV275 @ SV329 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3106]) ).
thf(3188,plain,
! [SV276: $i,SV370: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SV370 @ SV276 ) @ SV370 )
| ~ ( in @ ( sK4_SY3086 @ SV370 @ SV276 ) @ SV370 ) )
| ~ ( in @ ( sK5_SY3088 @ SV370 @ SV276 ) @ SV370 ) ) )
= $false )
| ( ( is_transitive_in @ SV276 @ SV370 )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3107]) ).
thf(3189,plain,
! [SV276: $i,SV370: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK3_C @ SV370 @ SV276 ) @ ( sK4_SY3086 @ SV370 @ SV276 ) ) @ SV276 ) )
= $false )
| ( ( is_transitive_in @ SV276 @ SV370 )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3107]) ).
thf(3190,plain,
! [SV276: $i,SV454: $i,SV446: $i,SV371: $i,SV431: $i] :
( ( ( ~ ( in @ SV431 @ SV371 )
| ~ ( in @ SV446 @ SV371 ) )
= $true )
| ( ( ~ ( in @ SV454 @ SV371 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV431 @ SV446 ) @ SV276 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV446 @ SV454 ) @ SV276 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV431 @ SV454 ) @ SV276 )
= $true )
| ( ( is_transitive_in @ SV276 @ SV371 )
= $false )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3108]) ).
thf(3191,plain,
! [SV277: $i,SV372: $i,SV396: $i,SV476: $i] :
( ( ( in @ ( ordered_pair @ SV476 @ ( sK46_D @ SV396 @ SV372 @ SV277 ) ) @ SV277 )
= $false )
| ( ( ~ ( in @ SV476 @ SV372 ) )
= $true )
| ( ( ~ ( in @ ( sK46_D @ SV396 @ SV372 @ SV277 ) @ SV396 ) )
= $true )
| ( ( SV396
= ( relation_image @ SV277 @ SV372 ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3109]) ).
thf(3192,plain,
! [SV277: $i,SV372: $i,SV396: $i] :
( ( ( in @ ( ordered_pair @ ( sK47_SY3118 @ SV396 @ SV372 @ SV277 ) @ ( sK46_D @ SV396 @ SV372 @ SV277 ) ) @ SV277 )
= $true )
| ( ( in @ ( sK46_D @ SV396 @ SV372 @ SV277 ) @ SV396 )
= $true )
| ( ( SV396
= ( relation_image @ SV277 @ SV372 ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3110]) ).
thf(3193,plain,
! [SV277: $i,SV372: $i,SV396: $i] :
( ( ( in @ ( sK47_SY3118 @ SV396 @ SV372 @ SV277 ) @ SV372 )
= $true )
| ( ( in @ ( sK46_D @ SV396 @ SV372 @ SV277 ) @ SV396 )
= $true )
| ( ( SV396
= ( relation_image @ SV277 @ SV372 ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3111]) ).
thf(3194,plain,
! [SV397: $i,SV373: $i,SV277: $i,SV477: $i,SV496: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV496 @ SV477 ) @ SV277 )
| ~ ( in @ SV496 @ SV373 ) )
= $true )
| ( ( in @ SV477 @ SV397 )
= $true )
| ( ( SV397
= ( relation_image @ SV277 @ SV373 ) )
= $false )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3112]) ).
thf(3195,plain,
! [SV277: $i,SV373: $i,SV397: $i,SV478: $i] :
( ( ( in @ SV478 @ SV397 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SV478 @ SV397 @ SV373 @ SV277 ) @ SV478 ) @ SV277 )
| ~ ( in @ ( sK45_E @ SV478 @ SV397 @ SV373 @ SV277 ) @ SV373 ) ) )
= $true )
| ( ( SV397
= ( relation_image @ SV277 @ SV373 ) )
= $false )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3113]) ).
thf(3196,plain,
! [SV278: $i,SV374: $i,SV398: $i] :
( ( ( ~ ( in @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ SV374 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV278 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) )
= $true )
| ( ( SV398
= ( relation_dom_restriction @ SV278 @ SV374 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3114]) ).
thf(3197,plain,
! [SV278: $i,SV374: $i,SV398: $i] :
( ( ( ~ ( ( in @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ SV374 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) ) )
= $false )
| ( ( SV398
= ( relation_dom_restriction @ SV278 @ SV374 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3115]) ).
thf(3198,plain,
! [SV278: $i,SV374: $i,SV398: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV278 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) ) )
= $false )
| ( ( SV398
= ( relation_dom_restriction @ SV278 @ SV374 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3115]) ).
thf(3199,plain,
! [SV399: $i,SV278: $i,SV375: $i,SV497: $i] :
( ( ( ! [SY4058: $i] :
( ~ ( in @ SV497 @ SV375 )
| ~ ( in @ ( ordered_pair @ SV497 @ SY4058 ) @ SV278 )
| ( in @ ( ordered_pair @ SV497 @ SY4058 ) @ SV399 ) ) )
= $true )
| ( ( SV399
= ( relation_dom_restriction @ SV278 @ SV375 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3116]) ).
thf(3200,plain,
! [SV278: $i,SV375: $i,SV399: $i] :
( ( ( ~ ! [SY3984: $i] :
( ! [SY3985: $i] :
~ ( in @ ( ordered_pair @ SY3984 @ SY3985 ) @ SV399 )
| ( in @ SY3984 @ SV375 ) )
| ~ ! [SY3986: $i,SY3987: $i] :
( ~ ( in @ ( ordered_pair @ SY3986 @ SY3987 ) @ SV399 )
| ( in @ ( ordered_pair @ SY3986 @ SY3987 ) @ SV278 ) ) )
= $false )
| ( ( SV399
= ( relation_dom_restriction @ SV278 @ SV375 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3117]) ).
thf(3201,plain,
! [SV479: $i,SV279: $i,SV376: $i,SV400: $i] :
( ( ( in @ ( ordered_pair @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SV479 ) @ SV279 )
= $false )
| ( ( ~ ( in @ SV479 @ SV376 ) )
= $true )
| ( ( ~ ( in @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SV400 ) )
= $true )
| ( ( SV400
= ( relation_inverse_image @ SV279 @ SV376 ) )
= $true )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3118]) ).
thf(3202,plain,
! [SV279: $i,SV376: $i,SV400: $i] :
( ( ( in @ ( ordered_pair @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ ( sK44_SY3116 @ SV400 @ SV376 @ SV279 ) ) @ SV279 )
= $true )
| ( ( in @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SV400 )
= $true )
| ( ( SV400
= ( relation_inverse_image @ SV279 @ SV376 ) )
= $true )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3119]) ).
thf(3203,plain,
! [SV279: $i,SV376: $i,SV400: $i] :
( ( ( in @ ( sK44_SY3116 @ SV400 @ SV376 @ SV279 ) @ SV376 )
= $true )
| ( ( in @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SV400 )
= $true )
| ( ( SV400
= ( relation_inverse_image @ SV279 @ SV376 ) )
= $true )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3120]) ).
thf(3204,plain,
! [SV401: $i,SV377: $i,SV279: $i,SV498: $i,SV480: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV480 @ SV498 ) @ SV279 )
| ~ ( in @ SV498 @ SV377 ) )
= $true )
| ( ( in @ SV480 @ SV401 )
= $true )
| ( ( SV401
= ( relation_inverse_image @ SV279 @ SV377 ) )
= $false )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3121]) ).
thf(3205,plain,
! [SV279: $i,SV377: $i,SV401: $i,SV481: $i] :
( ( ( in @ SV481 @ SV401 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV481 @ ( sK42_E @ SV481 @ SV401 @ SV377 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK42_E @ SV481 @ SV401 @ SV377 @ SV279 ) @ SV377 ) ) )
= $true )
| ( ( SV401
= ( relation_inverse_image @ SV279 @ SV377 ) )
= $false )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3122]) ).
thf(3206,plain,
! [SV281: $i,SV318: $i,SV432: $i] :
( ( ( ! [SY4021: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ SY4021 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY4021 @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV318 ) )
| ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV432 ) )
= $true )
| ( ( SV432
= ( relation_composition @ SV281 @ SV318 ) )
= $true )
| ( ( relation @ SV432 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3124]) ).
thf(3207,plain,
! [SV281: $i,SV318: $i,SV432: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK9_SY3093 @ SV432 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV318 ) )
| ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV432 ) )
= $true )
| ( ( SV432
= ( relation_composition @ SV281 @ SV318 ) )
= $true )
| ( ( relation @ SV432 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3125]) ).
thf(3208,plain,
! [SV433: $i,SV318: $i,SV281: $i] :
( ( ( ~ ! [SY4022: $i,SY4023: $i] :
( ! [SY3848: $i] :
( ~ ( in @ ( ordered_pair @ SY4022 @ SY3848 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY3848 @ SY4023 ) @ SV318 ) )
| ( in @ ( ordered_pair @ SY4022 @ SY4023 ) @ SV433 ) ) )
= $false )
| ( ( SV433
= ( relation_composition @ SV281 @ SV318 ) )
= $false )
| ( ( relation @ SV433 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3126]) ).
thf(3209,plain,
! [SV281: $i,SV318: $i,SV433: $i] :
( ( ( ~ ! [SY4025: $i,SY4026: $i] :
( ~ ( in @ ( ordered_pair @ SY4025 @ SY4026 ) @ SV433 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4025 @ ( sK6_F @ SY4026 @ SY4025 @ SV433 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY4026 @ SY4025 @ SV433 @ SV318 @ SV281 ) @ SY4026 ) @ SV318 ) ) ) )
= $false )
| ( ( SV433
= ( relation_composition @ SV281 @ SV318 ) )
= $false )
| ( ( relation @ SV433 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3126]) ).
thf(3210,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3127]) ).
thf(3211,plain,
! [SV319: $i,SV283: $i,SV465: $i] :
( ( ( function @ SV465 )
= $false )
| ( ( ~ ( relation @ SV465 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
| ~ ( ~ ! [SY4040: $i,SY4041: $i] :
( ~ ( in @ SY4040 @ ( relation_field @ SV283 ) )
| ~ ( in @ SY4041 @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV465 @ SY4040 ) @ ( apply @ SV465 @ SY4041 ) ) @ SV319 )
| ( in @ ( ordered_pair @ SY4040 @ SY4041 ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3687: $i] :
( ! [SY3688: $i] :
~ ( in @ ( ordered_pair @ SY3687 @ SY3688 ) @ SV283 )
| ( in @ SY3687 @ ( relation_field @ SV283 ) ) )
| ~ ! [SY3689: $i,SY3690: $i] :
( ~ ( in @ ( ordered_pair @ SY3689 @ SY3690 ) @ SV283 )
| ( in @ SY3690 @ ( relation_field @ SV283 ) ) ) )
| ~ ! [SY4046: $i,SY4047: $i] :
( ~ ( in @ ( ordered_pair @ SY4046 @ SY4047 ) @ SV283 )
| ( in @ ( ordered_pair @ ( apply @ SV465 @ SY4046 ) @ ( apply @ SV465 @ SY4047 ) ) @ SV319 ) ) ) ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3128]) ).
thf(3212,plain,
! [SV319: $i,SV283: $i] :
( ( ( ~ ! [SY3861: $i] :
( ~ ( function @ SY3861 )
| ~ ( relation @ SY3861 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3861 )
| ( ( relation_dom @ SY3861 )
= ( relation_field @ SV283 ) ) )
| ~ ! [SY3862: $i] :
( ~ ( function @ SY3862 )
| ~ ( relation @ SY3862 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3862 )
| ( ( relation_rng @ SY3862 )
= ( relation_field @ SV319 ) ) ) )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3129]) ).
thf(3213,plain,
! [SV319: $i,SV283: $i,SV499: $i] :
( ( ( ~ ( function @ SV499 )
| ~ ( relation @ SV499 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SV499 )
| ( one_to_one @ SV499 ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3130]) ).
thf(3214,plain,
! [SV320: $i] :
( ( ( ( ( sK62_B @ SV320 )
!= ( sK63_SY3125 @ SV320 ) ) )
= $true )
| ( ( connected @ SV320 )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3131]) ).
thf(3215,plain,
! [SV320: $i] :
( ( ( ~ ( ~ ( in @ ( sK62_B @ SV320 ) @ ( relation_field @ SV320 ) )
| ~ ( in @ ( sK63_SY3125 @ SV320 ) @ ( relation_field @ SV320 ) ) ) )
= $true )
| ( ( connected @ SV320 )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3132]) ).
thf(3216,plain,
! [SV416: $i,SV321: $i,SV435: $i] :
( ( ( in @ SV435 @ ( relation_field @ SV321 ) )
= $false )
| ( ( in @ SV416 @ ( relation_field @ SV321 ) )
= $false )
| ( ( SV416 = SV435 )
= $true )
| ( ( in @ ( ordered_pair @ SV416 @ SV435 ) @ SV321 )
= $true )
| ( ( in @ ( ordered_pair @ SV435 @ SV416 ) @ SV321 )
= $true )
| ( ( connected @ SV321 )
= $false )
| ( ( relation @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3133]) ).
thf(3217,plain,
! [SV285: $i,SV334: $i,SV353: $i] :
( ( ( in @ ( sK61_D @ SV353 @ SV334 @ SV285 ) @ ( relation_dom @ SV353 ) )
= $true )
| ( ( in @ SV285 @ ( relation_image @ SV353 @ SV334 ) )
= $false )
| ( ( relation @ SV353 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3137]) ).
thf(3218,plain,
! [SV285: $i,SV334: $i,SV353: $i] :
( ( ( in @ ( ordered_pair @ ( sK61_D @ SV353 @ SV334 @ SV285 ) @ SV285 ) @ SV353 )
= $true )
| ( ( in @ SV285 @ ( relation_image @ SV353 @ SV334 ) )
= $false )
| ( ( relation @ SV353 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3138]) ).
thf(3219,plain,
! [SV324: $i,SV337: $i] :
( ( ( in @ ( ordered_pair @ ( sK52_C @ SV337 @ SV324 ) @ ( sK53_SY3121 @ SV337 @ SV324 ) ) @ SV337 )
= $false )
| ( ( ( sK52_C @ SV337 @ SV324 )
= ( sK53_SY3121 @ SV337 @ SV324 ) )
= $false )
| ( ( in @ ( sK52_C @ SV337 @ SV324 ) @ SV324 )
= $false )
| ( ( SV337
= ( identity_relation @ SV324 ) )
= $true )
| ( ( relation @ SV337 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3141]) ).
thf(3220,plain,
! [SV338: $i,SV325: $i,SV483: $i,SV467: $i] :
( ( ( ( SV467 != SV483 ) )
= $true )
| ( ( ~ ( in @ SV467 @ SV325 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV467 @ SV483 ) @ SV338 )
= $true )
| ( ( SV338
= ( identity_relation @ SV325 ) )
= $false )
| ( ( relation @ SV338 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3144]) ).
thf(3221,plain,
! [SV325: $i,SV338: $i,SV500: $i] :
( ( ( ! [SY4059: $i] :
( ~ ( in @ ( ordered_pair @ SV500 @ SY4059 ) @ SV338 )
| ( SV500 = SY4059 ) ) )
= $true )
| ( ( SV338
= ( identity_relation @ SV325 ) )
= $false )
| ( ( relation @ SV338 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3145]) ).
thf(3222,plain,
! [SV325: $i,SV338: $i,SV501: $i] :
( ( ( ! [SY4060: $i] :
~ ( in @ ( ordered_pair @ SV501 @ SY4060 ) @ SV338 )
| ( in @ SV501 @ SV325 ) )
= $true )
| ( ( SV338
= ( identity_relation @ SV325 ) )
= $false )
| ( ( relation @ SV338 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3146]) ).
thf(3223,plain,
! [SV381: $i,SV290: $i,SV488: $i,SV470: $i] :
( ( ( in @ ( ordered_pair @ SV470 @ SV488 ) @ SV290 )
= $false )
| ( ( in @ SV470 @ SV381 )
= $true )
| ( ( SV381
= ( relation_dom @ SV290 ) )
= $false )
| ( ( relation @ SV290 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3148]) ).
thf(3224,plain,
! [SV291: $i,SV382: $i] :
( ( ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV382 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK31_C @ SV382 @ SV291 ) @ ( sK32_SY3109 @ SV382 @ SV291 ) ) @ SV291 )
= $false )
| ( ( SV291 = SV382 )
= $true )
| ( ( relation @ SV382 )
= $false )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3150]) ).
thf(3225,plain,
! [SV383: $i,SV291: $i,SV502: $i,SV489: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV489 @ SV502 ) @ SV291 )
| ( in @ ( ordered_pair @ SV489 @ SV502 ) @ SV383 ) )
= $true )
| ( ( SV291 = SV383 )
= $false )
| ( ( relation @ SV383 )
= $false )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3151]) ).
thf(3226,plain,
! [SV291: $i,SV383: $i,SV503: $i,SV490: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV490 @ SV503 ) @ SV383 )
| ( in @ ( ordered_pair @ SV490 @ SV503 ) @ SV291 ) )
= $true )
| ( ( SV291 = SV383 )
= $false )
| ( ( relation @ SV383 )
= $false )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3152]) ).
thf(3227,plain,
! [SV292: $i,SV384: $i] :
( ( ( in @ ( ordered_pair @ ( sK13_SY3095 @ SV384 @ SV292 ) @ ( sK12_C @ SV384 @ SV292 ) ) @ SV292 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK12_C @ SV384 @ SV292 ) @ ( sK13_SY3095 @ SV384 @ SV292 ) ) @ SV384 )
= $false )
| ( ( SV384
= ( relation_inverse @ SV292 ) )
= $true )
| ( ( relation @ SV384 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3154]) ).
thf(3228,plain,
! [SV292: $i,SV385: $i,SV504: $i,SV491: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV491 @ SV504 ) @ SV385 )
| ( in @ ( ordered_pair @ SV504 @ SV491 ) @ SV292 ) )
= $true )
| ( ( SV385
= ( relation_inverse @ SV292 ) )
= $false )
| ( ( relation @ SV385 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3155]) ).
thf(3229,plain,
! [SV385: $i,SV292: $i,SV492: $i,SV505: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV505 @ SV492 ) @ SV292 )
| ( in @ ( ordered_pair @ SV492 @ SV505 ) @ SV385 ) )
= $true )
| ( ( SV385
= ( relation_inverse @ SV292 ) )
= $false )
| ( ( relation @ SV385 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3156]) ).
thf(3230,plain,
! [SV458: $i,SV293: $i,SV493: $i] :
( ( ( ( SV493
!= ( apply @ SV293 @ SV458 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV458 @ SV493 ) @ SV293 )
= $true )
| ( ( in @ SV458 @ ( relation_dom @ SV293 ) )
= $false )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3157]) ).
thf(3231,plain,
! [SV293: $i,SV494: $i,SV459: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV459 @ SV494 ) @ SV293 ) )
= $true )
| ( ( SV494
= ( apply @ SV293 @ SV459 ) )
= $true )
| ( ( in @ SV459 @ ( relation_dom @ SV293 ) )
= $false )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3158]) ).
thf(3232,plain,
! [SV460: $i,SV293: $i,SV484: $i] :
( ( ( SV484
= ( apply @ SV293 @ SV460 ) )
= $false )
| ( ( SV484 = empty_set )
= $true )
| ( ( in @ SV460 @ ( relation_dom @ SV293 ) )
= $true )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3159]) ).
thf(3233,plain,
! [SV461: $i,SV293: $i,SV485: $i] :
( ( ( SV485 = empty_set )
= $false )
| ( ( SV485
= ( apply @ SV293 @ SV461 ) )
= $true )
| ( ( in @ SV461 @ ( relation_dom @ SV293 ) )
= $true )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3160]) ).
thf(3234,plain,
! [SV294: $i,SV386: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK19_C @ SV386 @ SV294 ) @ SV386 )
| ~ ( in @ ( sK20_SY3099 @ SV386 @ SV294 ) @ SV386 ) ) )
= $false )
| ( ( is_antisymmetric_in @ SV294 @ SV386 )
= $true )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3161]) ).
thf(3235,plain,
! [SV294: $i,SV386: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK19_C @ SV386 @ SV294 ) @ ( sK20_SY3099 @ SV386 @ SV294 ) ) @ SV294 ) )
= $false )
| ( ( is_antisymmetric_in @ SV294 @ SV386 )
= $true )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3161]) ).
thf(3236,plain,
! [SV294: $i,SV450: $i,SV387: $i,SV438: $i] :
( ( ( in @ SV438 @ SV387 )
= $false )
| ( ( ~ ( in @ SV450 @ SV387 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV438 @ SV450 ) @ SV294 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV450 @ SV438 ) @ SV294 ) )
= $true )
| ( ( SV438 = SV450 )
= $true )
| ( ( is_antisymmetric_in @ SV294 @ SV387 )
= $false )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3162]) ).
thf(3237,plain,
! [SV295: $i,SV388: $i,SV404: $i] :
( ( ( in @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV404 )
= $false )
| ( ( ( sK35_D @ SV404 @ SV388 @ SV295 )
= SV388 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV388 ) @ SV295 )
= $false )
| ( ( SV404
= ( fiber @ SV295 @ SV388 ) )
= $true )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3163]) ).
thf(3238,plain,
! [SV295: $i,SV388: $i,SV404: $i] :
( ( ( ( ( sK35_D @ SV404 @ SV388 @ SV295 )
!= SV388 ) )
= $true )
| ( ( in @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV404 )
= $true )
| ( ( SV404
= ( fiber @ SV295 @ SV388 ) )
= $true )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3164]) ).
thf(3239,plain,
! [SV295: $i,SV388: $i,SV404: $i] :
( ( ( in @ ( ordered_pair @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV388 ) @ SV295 )
= $true )
| ( ( in @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV404 )
= $true )
| ( ( SV404
= ( fiber @ SV295 @ SV388 ) )
= $true )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3165]) ).
thf(3240,plain,
! [SV405: $i,SV295: $i,SV389: $i,SV486: $i] :
( ( ( SV486 = SV389 )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV486 @ SV389 ) @ SV295 ) )
= $true )
| ( ( in @ SV486 @ SV405 )
= $true )
| ( ( SV405
= ( fiber @ SV295 @ SV389 ) )
= $false )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3166]) ).
thf(3241,plain,
! [SV295: $i,SV389: $i,SV405: $i] :
( ( ( ! [SY3995: $i] :
( ~ ( in @ SY3995 @ SV405 )
| ( SY3995 != SV389 ) ) )
= $true )
| ( ( SV405
= ( fiber @ SV295 @ SV389 ) )
= $false )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3167]) ).
thf(3242,plain,
! [SV295: $i,SV389: $i,SV405: $i] :
( ( ( ! [SY3996: $i] :
( ~ ( in @ SY3996 @ SV405 )
| ( in @ ( ordered_pair @ SY3996 @ SV389 ) @ SV295 ) ) )
= $true )
| ( ( SV405
= ( fiber @ SV295 @ SV389 ) )
= $false )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3168]) ).
thf(3243,plain,
! [SV296: $i,SV307: $i,SV406: $i] :
( ( ( ~ ( in @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) @ SV296 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV307 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) )
= $true )
| ( ( SV406
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $true )
| ( ( relation @ SV406 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3169]) ).
thf(3244,plain,
! [SV296: $i,SV307: $i,SV406: $i] :
( ( ( ~ ( ( in @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) @ SV296 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) ) )
= $false )
| ( ( SV406
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $true )
| ( ( relation @ SV406 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3170]) ).
thf(3245,plain,
! [SV296: $i,SV307: $i,SV406: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV307 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) ) )
= $false )
| ( ( SV406
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $true )
| ( ( relation @ SV406 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3170]) ).
thf(3246,plain,
! [SV407: $i,SV307: $i,SV506: $i,SV296: $i] :
( ( ( ! [SY4061: $i] :
( ~ ( in @ SY4061 @ SV296 )
| ~ ( in @ ( ordered_pair @ SV506 @ SY4061 ) @ SV307 )
| ( in @ ( ordered_pair @ SV506 @ SY4061 ) @ SV407 ) ) )
= $true )
| ( ( SV407
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $false )
| ( ( relation @ SV407 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3171]) ).
thf(3247,plain,
! [SV307: $i,SV296: $i,SV407: $i] :
( ( ( ~ ! [SY3999: $i,SY4000: $i] :
( ~ ( in @ ( ordered_pair @ SY3999 @ SY4000 ) @ SV407 )
| ( in @ SY4000 @ SV296 ) )
| ~ ! [SY4001: $i,SY4002: $i] :
( ~ ( in @ ( ordered_pair @ SY4001 @ SY4002 ) @ SV407 )
| ( in @ ( ordered_pair @ SY4001 @ SY4002 ) @ SV307 ) ) )
= $false )
| ( ( SV407
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $false )
| ( ( relation @ SV407 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3172]) ).
thf(3248,plain,
! [SV391: $i,SV297: $i,SV473: $i,SV495: $i] :
( ( ( in @ ( ordered_pair @ SV495 @ SV473 ) @ SV297 )
= $false )
| ( ( in @ SV473 @ SV391 )
= $true )
| ( ( SV391
= ( relation_rng @ SV297 ) )
= $false )
| ( ( relation @ SV297 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3174]) ).
thf(3249,plain,
! [SV301: $i,SV344: $i,SV364: $i] :
( ( ( in @ ( sK60_D @ SV364 @ SV344 @ SV301 ) @ ( relation_rng @ SV364 ) )
= $true )
| ( ( in @ SV301 @ ( relation_inverse_image @ SV364 @ SV344 ) )
= $false )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3177]) ).
thf(3250,plain,
! [SV344: $i,SV364: $i,SV301: $i] :
( ( ( in @ ( ordered_pair @ SV301 @ ( sK60_D @ SV364 @ SV344 @ SV301 ) ) @ SV364 )
= $true )
| ( ( in @ SV301 @ ( relation_inverse_image @ SV364 @ SV344 ) )
= $false )
| ( ( relation @ SV364 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3178]) ).
thf(3251,plain,
! [SV274: $i,SV367: $i] :
( ( ( ( ( sK14_C @ SV367 @ SV274 )
!= ( sK15_SY3096 @ SV367 @ SV274 ) ) )
= $true )
| ( ( is_connected_in @ SV274 @ SV367 )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3179]) ).
thf(3252,plain,
! [SV274: $i,SV367: $i] :
( ( ( ~ ( ~ ( in @ ( sK14_C @ SV367 @ SV274 ) @ SV367 )
| ~ ( in @ ( sK15_SY3096 @ SV367 @ SV274 ) @ SV367 ) ) )
= $true )
| ( ( is_connected_in @ SV274 @ SV367 )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3180]) ).
thf(3253,plain,
! [SV274: $i,SV428: $i,SV368: $i,SV445: $i] :
( ( ( in @ SV445 @ SV368 )
= $false )
| ( ( in @ SV428 @ SV368 )
= $false )
| ( ( SV428 = SV445 )
= $true )
| ( ( in @ ( ordered_pair @ SV428 @ SV445 ) @ SV274 )
= $true )
| ( ( in @ ( ordered_pair @ SV445 @ SV428 ) @ SV274 )
= $true )
| ( ( is_connected_in @ SV274 @ SV368 )
= $false )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3181]) ).
thf(3254,plain,
! [SV347: $i,SV275: $i,SV451: $i,SV328: $i,SV462: $i] :
( ( ( in @ SV462 @ SV328 )
= $false )
| ( ( in @ SV451 @ SV275 )
= $false )
| ( ( ( ( sK28_D @ SV347 @ SV328 @ SV275 )
!= ( ordered_pair @ SV451 @ SV462 ) ) )
= $true )
| ( ( ~ ( in @ ( sK28_D @ SV347 @ SV328 @ SV275 ) @ SV347 ) )
= $true )
| ( ( SV347
= ( cartesian_product2 @ SV275 @ SV328 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3182]) ).
thf(3255,plain,
! [SV275: $i,SV328: $i,SV347: $i] :
( ( ( in @ ( sK29_SY3106 @ SV347 @ SV328 @ SV275 ) @ SV275 )
= $true )
| ( ( in @ ( sK28_D @ SV347 @ SV328 @ SV275 ) @ SV347 )
= $true )
| ( ( SV347
= ( cartesian_product2 @ SV275 @ SV328 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3183]) ).
thf(3256,plain,
! [SV275: $i,SV328: $i,SV347: $i] :
( ( ( in @ ( sK30_SY3108 @ SV347 @ SV328 @ SV275 ) @ SV328 )
= $true )
| ( ( in @ ( sK28_D @ SV347 @ SV328 @ SV275 ) @ SV347 )
= $true )
| ( ( SV347
= ( cartesian_product2 @ SV275 @ SV328 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3184]) ).
thf(3257,plain,
! [SV348: $i,SV452: $i,SV329: $i,SV487: $i,SV275: $i,SV475: $i] :
( ( ( ~ ( in @ SV475 @ SV275 ) )
= $true )
| ( ( ~ ( in @ SV487 @ SV329 ) )
= $true )
| ( ( ( SV452
!= ( ordered_pair @ SV475 @ SV487 ) ) )
= $true )
| ( ( in @ SV452 @ SV348 )
= $true )
| ( ( SV348
= ( cartesian_product2 @ SV275 @ SV329 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3185]) ).
thf(3258,plain,
! [SV275: $i,SV329: $i,SV348: $i,SV453: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_E @ SV453 @ SV348 @ SV329 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK27_SY3103 @ SV453 @ SV348 @ SV329 @ SV275 ) @ SV329 ) ) )
= $true )
| ( ( in @ SV453 @ SV348 )
= $false )
| ( ( SV348
= ( cartesian_product2 @ SV275 @ SV329 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3186]) ).
thf(3259,plain,
! [SV275: $i,SV329: $i,SV348: $i,SV453: $i] :
( ( ( SV453
= ( ordered_pair @ ( sK26_E @ SV453 @ SV348 @ SV329 @ SV275 ) @ ( sK27_SY3103 @ SV453 @ SV348 @ SV329 @ SV275 ) ) )
= $true )
| ( ( in @ SV453 @ SV348 )
= $false )
| ( ( SV348
= ( cartesian_product2 @ SV275 @ SV329 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3187]) ).
thf(3260,plain,
! [SV276: $i,SV370: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK3_C @ SV370 @ SV276 ) @ SV370 )
| ~ ( in @ ( sK4_SY3086 @ SV370 @ SV276 ) @ SV370 ) )
| ~ ( in @ ( sK5_SY3088 @ SV370 @ SV276 ) @ SV370 ) ) )
= $true )
| ( ( is_transitive_in @ SV276 @ SV370 )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3188]) ).
thf(3261,plain,
! [SV276: $i,SV370: $i] :
( ( ( in @ ( ordered_pair @ ( sK3_C @ SV370 @ SV276 ) @ ( sK4_SY3086 @ SV370 @ SV276 ) ) @ SV276 )
= $true )
| ( ( is_transitive_in @ SV276 @ SV370 )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3189]) ).
thf(3262,plain,
! [SV276: $i,SV454: $i,SV446: $i,SV371: $i,SV431: $i] :
( ( ( ~ ( in @ SV431 @ SV371 ) )
= $true )
| ( ( ~ ( in @ SV446 @ SV371 ) )
= $true )
| ( ( ~ ( in @ SV454 @ SV371 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV431 @ SV446 ) @ SV276 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV446 @ SV454 ) @ SV276 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV431 @ SV454 ) @ SV276 )
= $true )
| ( ( is_transitive_in @ SV276 @ SV371 )
= $false )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3190]) ).
thf(3263,plain,
! [SV277: $i,SV396: $i,SV372: $i,SV476: $i] :
( ( ( in @ SV476 @ SV372 )
= $false )
| ( ( in @ ( ordered_pair @ SV476 @ ( sK46_D @ SV396 @ SV372 @ SV277 ) ) @ SV277 )
= $false )
| ( ( ~ ( in @ ( sK46_D @ SV396 @ SV372 @ SV277 ) @ SV396 ) )
= $true )
| ( ( SV396
= ( relation_image @ SV277 @ SV372 ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3191]) ).
thf(3264,plain,
! [SV397: $i,SV373: $i,SV277: $i,SV477: $i,SV496: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV496 @ SV477 ) @ SV277 ) )
= $true )
| ( ( ~ ( in @ SV496 @ SV373 ) )
= $true )
| ( ( in @ SV477 @ SV397 )
= $true )
| ( ( SV397
= ( relation_image @ SV277 @ SV373 ) )
= $false )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3194]) ).
thf(3265,plain,
! [SV277: $i,SV373: $i,SV397: $i,SV478: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SV478 @ SV397 @ SV373 @ SV277 ) @ SV478 ) @ SV277 )
| ~ ( in @ ( sK45_E @ SV478 @ SV397 @ SV373 @ SV277 ) @ SV373 ) )
= $false )
| ( ( in @ SV478 @ SV397 )
= $false )
| ( ( SV397
= ( relation_image @ SV277 @ SV373 ) )
= $false )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3195]) ).
thf(3266,plain,
! [SV278: $i,SV374: $i,SV398: $i] :
( ( ( in @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ SV374 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV278 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) )
= $true )
| ( ( SV398
= ( relation_dom_restriction @ SV278 @ SV374 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3196]) ).
thf(3267,plain,
! [SV278: $i,SV374: $i,SV398: $i] :
( ( ( ( in @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ SV374 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) )
= $true )
| ( ( SV398
= ( relation_dom_restriction @ SV278 @ SV374 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3197]) ).
thf(3268,plain,
! [SV278: $i,SV374: $i,SV398: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV278 )
| ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) )
= $true )
| ( ( SV398
= ( relation_dom_restriction @ SV278 @ SV374 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3198]) ).
thf(3269,plain,
! [SV399: $i,SV278: $i,SV507: $i,SV375: $i,SV497: $i] :
( ( ( ~ ( in @ SV497 @ SV375 )
| ~ ( in @ ( ordered_pair @ SV497 @ SV507 ) @ SV278 )
| ( in @ ( ordered_pair @ SV497 @ SV507 ) @ SV399 ) )
= $true )
| ( ( SV399
= ( relation_dom_restriction @ SV278 @ SV375 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3199]) ).
thf(3270,plain,
! [SV278: $i,SV375: $i,SV399: $i] :
( ( ( ~ ! [SY3984: $i] :
( ! [SY3985: $i] :
~ ( in @ ( ordered_pair @ SY3984 @ SY3985 ) @ SV399 )
| ( in @ SY3984 @ SV375 ) ) )
= $false )
| ( ( SV399
= ( relation_dom_restriction @ SV278 @ SV375 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3200]) ).
thf(3271,plain,
! [SV375: $i,SV278: $i,SV399: $i] :
( ( ( ~ ! [SY3986: $i,SY3987: $i] :
( ~ ( in @ ( ordered_pair @ SY3986 @ SY3987 ) @ SV399 )
| ( in @ ( ordered_pair @ SY3986 @ SY3987 ) @ SV278 ) ) )
= $false )
| ( ( SV399
= ( relation_dom_restriction @ SV278 @ SV375 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3200]) ).
thf(3272,plain,
! [SV279: $i,SV400: $i,SV376: $i,SV479: $i] :
( ( ( in @ SV479 @ SV376 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SV479 ) @ SV279 )
= $false )
| ( ( ~ ( in @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SV400 ) )
= $true )
| ( ( SV400
= ( relation_inverse_image @ SV279 @ SV376 ) )
= $true )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3201]) ).
thf(3273,plain,
! [SV401: $i,SV377: $i,SV279: $i,SV498: $i,SV480: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV480 @ SV498 ) @ SV279 ) )
= $true )
| ( ( ~ ( in @ SV498 @ SV377 ) )
= $true )
| ( ( in @ SV480 @ SV401 )
= $true )
| ( ( SV401
= ( relation_inverse_image @ SV279 @ SV377 ) )
= $false )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3204]) ).
thf(3274,plain,
! [SV279: $i,SV377: $i,SV401: $i,SV481: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV481 @ ( sK42_E @ SV481 @ SV401 @ SV377 @ SV279 ) ) @ SV279 )
| ~ ( in @ ( sK42_E @ SV481 @ SV401 @ SV377 @ SV279 ) @ SV377 ) )
= $false )
| ( ( in @ SV481 @ SV401 )
= $false )
| ( ( SV401
= ( relation_inverse_image @ SV279 @ SV377 ) )
= $false )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3205]) ).
thf(3275,plain,
! [SV281: $i,SV318: $i,SV432: $i] :
( ( ( ! [SY4021: $i] :
( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ SY4021 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY4021 @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV318 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV432 ) )
= $true )
| ( ( SV432
= ( relation_composition @ SV281 @ SV318 ) )
= $true )
| ( ( relation @ SV432 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3206]) ).
thf(3276,plain,
! [SV281: $i,SV318: $i,SV432: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK9_SY3093 @ SV432 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV318 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV432 )
= $true )
| ( ( SV432
= ( relation_composition @ SV281 @ SV318 ) )
= $true )
| ( ( relation @ SV432 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3207]) ).
thf(3277,plain,
! [SV433: $i,SV318: $i,SV281: $i] :
( ( ( ! [SY4022: $i,SY4023: $i] :
( ! [SY3848: $i] :
( ~ ( in @ ( ordered_pair @ SY4022 @ SY3848 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY3848 @ SY4023 ) @ SV318 ) )
| ( in @ ( ordered_pair @ SY4022 @ SY4023 ) @ SV433 ) ) )
= $true )
| ( ( SV433
= ( relation_composition @ SV281 @ SV318 ) )
= $false )
| ( ( relation @ SV433 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3208]) ).
thf(3278,plain,
! [SV281: $i,SV318: $i,SV433: $i] :
( ( ( ! [SY4025: $i,SY4026: $i] :
( ~ ( in @ ( ordered_pair @ SY4025 @ SY4026 ) @ SV433 )
| ~ ( ~ ( in @ ( ordered_pair @ SY4025 @ ( sK6_F @ SY4026 @ SY4025 @ SV433 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY4026 @ SY4025 @ SV433 @ SV318 @ SV281 ) @ SY4026 ) @ SV318 ) ) ) )
= $true )
| ( ( SV433
= ( relation_composition @ SV281 @ SV318 ) )
= $false )
| ( ( relation @ SV433 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3209]) ).
thf(3279,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3210]) ).
thf(3280,plain,
! [SV319: $i,SV283: $i,SV465: $i] :
( ( ( relation @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( ~ ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
| ~ ( ~ ! [SY4040: $i,SY4041: $i] :
( ~ ( in @ SY4040 @ ( relation_field @ SV283 ) )
| ~ ( in @ SY4041 @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV465 @ SY4040 ) @ ( apply @ SV465 @ SY4041 ) ) @ SV319 )
| ( in @ ( ordered_pair @ SY4040 @ SY4041 ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3687: $i] :
( ! [SY3688: $i] :
~ ( in @ ( ordered_pair @ SY3687 @ SY3688 ) @ SV283 )
| ( in @ SY3687 @ ( relation_field @ SV283 ) ) )
| ~ ! [SY3689: $i,SY3690: $i] :
( ~ ( in @ ( ordered_pair @ SY3689 @ SY3690 ) @ SV283 )
| ( in @ SY3690 @ ( relation_field @ SV283 ) ) ) )
| ~ ! [SY4046: $i,SY4047: $i] :
( ~ ( in @ ( ordered_pair @ SY4046 @ SY4047 ) @ SV283 )
| ( in @ ( ordered_pair @ ( apply @ SV465 @ SY4046 ) @ ( apply @ SV465 @ SY4047 ) ) @ SV319 ) ) ) ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3211]) ).
thf(3281,plain,
! [SV319: $i,SV283: $i] :
( ( ( ~ ! [SY3861: $i] :
( ~ ( function @ SY3861 )
| ~ ( relation @ SY3861 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3861 )
| ( ( relation_dom @ SY3861 )
= ( relation_field @ SV283 ) ) ) )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3212]) ).
thf(3282,plain,
! [SV319: $i,SV283: $i] :
( ( ( ~ ! [SY3862: $i] :
( ~ ( function @ SY3862 )
| ~ ( relation @ SY3862 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3862 )
| ( ( relation_rng @ SY3862 )
= ( relation_field @ SV319 ) ) ) )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3212]) ).
thf(3283,plain,
! [SV319: $i,SV283: $i,SV499: $i] :
( ( ( ~ ( function @ SV499 )
| ~ ( relation @ SV499 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV283 @ SV319 @ SV499 )
| ( one_to_one @ SV499 ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3213]) ).
thf(3284,plain,
! [SV320: $i] :
( ( ( ( sK62_B @ SV320 )
= ( sK63_SY3125 @ SV320 ) )
= $false )
| ( ( connected @ SV320 )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3214]) ).
thf(3285,plain,
! [SV320: $i] :
( ( ( ~ ( in @ ( sK62_B @ SV320 ) @ ( relation_field @ SV320 ) )
| ~ ( in @ ( sK63_SY3125 @ SV320 ) @ ( relation_field @ SV320 ) ) )
= $false )
| ( ( connected @ SV320 )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3215]) ).
thf(3286,plain,
! [SV338: $i,SV325: $i,SV483: $i,SV467: $i] :
( ( ( SV467 = SV483 )
= $false )
| ( ( ~ ( in @ SV467 @ SV325 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV467 @ SV483 ) @ SV338 )
= $true )
| ( ( SV338
= ( identity_relation @ SV325 ) )
= $false )
| ( ( relation @ SV338 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3220]) ).
thf(3287,plain,
! [SV325: $i,SV338: $i,SV508: $i,SV500: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV500 @ SV508 ) @ SV338 )
| ( SV500 = SV508 ) )
= $true )
| ( ( SV338
= ( identity_relation @ SV325 ) )
= $false )
| ( ( relation @ SV338 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3221]) ).
thf(3288,plain,
! [SV325: $i,SV338: $i,SV501: $i] :
( ( ( ! [SY4060: $i] :
~ ( in @ ( ordered_pair @ SV501 @ SY4060 ) @ SV338 ) )
= $true )
| ( ( in @ SV501 @ SV325 )
= $true )
| ( ( SV338
= ( identity_relation @ SV325 ) )
= $false )
| ( ( relation @ SV338 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3222]) ).
thf(3289,plain,
! [SV383: $i,SV291: $i,SV502: $i,SV489: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV489 @ SV502 ) @ SV291 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV489 @ SV502 ) @ SV383 )
= $true )
| ( ( SV291 = SV383 )
= $false )
| ( ( relation @ SV383 )
= $false )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3225]) ).
thf(3290,plain,
! [SV291: $i,SV383: $i,SV503: $i,SV490: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV490 @ SV503 ) @ SV383 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV490 @ SV503 ) @ SV291 )
= $true )
| ( ( SV291 = SV383 )
= $false )
| ( ( relation @ SV383 )
= $false )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3226]) ).
thf(3291,plain,
! [SV292: $i,SV385: $i,SV504: $i,SV491: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV491 @ SV504 ) @ SV385 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV504 @ SV491 ) @ SV292 )
= $true )
| ( ( SV385
= ( relation_inverse @ SV292 ) )
= $false )
| ( ( relation @ SV385 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3228]) ).
thf(3292,plain,
! [SV385: $i,SV292: $i,SV492: $i,SV505: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV505 @ SV492 ) @ SV292 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV492 @ SV505 ) @ SV385 )
= $true )
| ( ( SV385
= ( relation_inverse @ SV292 ) )
= $false )
| ( ( relation @ SV385 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3229]) ).
thf(3293,plain,
! [SV458: $i,SV293: $i,SV493: $i] :
( ( ( SV493
= ( apply @ SV293 @ SV458 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV458 @ SV493 ) @ SV293 )
= $true )
| ( ( in @ SV458 @ ( relation_dom @ SV293 ) )
= $false )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3230]) ).
thf(3294,plain,
! [SV293: $i,SV494: $i,SV459: $i] :
( ( ( in @ ( ordered_pair @ SV459 @ SV494 ) @ SV293 )
= $false )
| ( ( SV494
= ( apply @ SV293 @ SV459 ) )
= $true )
| ( ( in @ SV459 @ ( relation_dom @ SV293 ) )
= $false )
| ( ( function @ SV293 )
= $false )
| ( ( relation @ SV293 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3231]) ).
thf(3295,plain,
! [SV294: $i,SV386: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_C @ SV386 @ SV294 ) @ SV386 )
| ~ ( in @ ( sK20_SY3099 @ SV386 @ SV294 ) @ SV386 ) ) )
= $true )
| ( ( is_antisymmetric_in @ SV294 @ SV386 )
= $true )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3234]) ).
thf(3296,plain,
! [SV294: $i,SV386: $i] :
( ( ( in @ ( ordered_pair @ ( sK19_C @ SV386 @ SV294 ) @ ( sK20_SY3099 @ SV386 @ SV294 ) ) @ SV294 )
= $true )
| ( ( is_antisymmetric_in @ SV294 @ SV386 )
= $true )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3235]) ).
thf(3297,plain,
! [SV294: $i,SV438: $i,SV387: $i,SV450: $i] :
( ( ( in @ SV450 @ SV387 )
= $false )
| ( ( in @ SV438 @ SV387 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV438 @ SV450 ) @ SV294 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV450 @ SV438 ) @ SV294 ) )
= $true )
| ( ( SV438 = SV450 )
= $true )
| ( ( is_antisymmetric_in @ SV294 @ SV387 )
= $false )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3236]) ).
thf(3298,plain,
! [SV295: $i,SV388: $i,SV404: $i] :
( ( ( ( sK35_D @ SV404 @ SV388 @ SV295 )
= SV388 )
= $false )
| ( ( in @ ( sK35_D @ SV404 @ SV388 @ SV295 ) @ SV404 )
= $true )
| ( ( SV404
= ( fiber @ SV295 @ SV388 ) )
= $true )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3238]) ).
thf(3299,plain,
! [SV405: $i,SV295: $i,SV389: $i,SV486: $i] :
( ( ( in @ ( ordered_pair @ SV486 @ SV389 ) @ SV295 )
= $false )
| ( ( SV486 = SV389 )
= $true )
| ( ( in @ SV486 @ SV405 )
= $true )
| ( ( SV405
= ( fiber @ SV295 @ SV389 ) )
= $false )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3240]) ).
thf(3300,plain,
! [SV295: $i,SV389: $i,SV405: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV405 )
| ( SV509 != SV389 ) )
= $true )
| ( ( SV405
= ( fiber @ SV295 @ SV389 ) )
= $false )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3241]) ).
thf(3301,plain,
! [SV295: $i,SV389: $i,SV405: $i,SV510: $i] :
( ( ( ~ ( in @ SV510 @ SV405 )
| ( in @ ( ordered_pair @ SV510 @ SV389 ) @ SV295 ) )
= $true )
| ( ( SV405
= ( fiber @ SV295 @ SV389 ) )
= $false )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3242]) ).
thf(3302,plain,
! [SV296: $i,SV307: $i,SV406: $i] :
( ( ( in @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) @ SV296 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV307 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) )
= $true )
| ( ( SV406
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $true )
| ( ( relation @ SV406 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3243]) ).
thf(3303,plain,
! [SV296: $i,SV307: $i,SV406: $i] :
( ( ( ( in @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) @ SV296 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) )
= $true )
| ( ( SV406
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $true )
| ( ( relation @ SV406 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3244]) ).
thf(3304,plain,
! [SV296: $i,SV307: $i,SV406: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV307 )
| ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) )
= $true )
| ( ( SV406
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $true )
| ( ( relation @ SV406 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3245]) ).
thf(3305,plain,
! [SV407: $i,SV307: $i,SV506: $i,SV296: $i,SV511: $i] :
( ( ( ~ ( in @ SV511 @ SV296 )
| ~ ( in @ ( ordered_pair @ SV506 @ SV511 ) @ SV307 )
| ( in @ ( ordered_pair @ SV506 @ SV511 ) @ SV407 ) )
= $true )
| ( ( SV407
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $false )
| ( ( relation @ SV407 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3246]) ).
thf(3306,plain,
! [SV307: $i,SV296: $i,SV407: $i] :
( ( ( ~ ! [SY3999: $i,SY4000: $i] :
( ~ ( in @ ( ordered_pair @ SY3999 @ SY4000 ) @ SV407 )
| ( in @ SY4000 @ SV296 ) ) )
= $false )
| ( ( SV407
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $false )
| ( ( relation @ SV407 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3247]) ).
thf(3307,plain,
! [SV296: $i,SV307: $i,SV407: $i] :
( ( ( ~ ! [SY4001: $i,SY4002: $i] :
( ~ ( in @ ( ordered_pair @ SY4001 @ SY4002 ) @ SV407 )
| ( in @ ( ordered_pair @ SY4001 @ SY4002 ) @ SV307 ) ) )
= $false )
| ( ( SV407
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $false )
| ( ( relation @ SV407 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3247]) ).
thf(3308,plain,
! [SV274: $i,SV367: $i] :
( ( ( ( sK14_C @ SV367 @ SV274 )
= ( sK15_SY3096 @ SV367 @ SV274 ) )
= $false )
| ( ( is_connected_in @ SV274 @ SV367 )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3251]) ).
thf(3309,plain,
! [SV274: $i,SV367: $i] :
( ( ( ~ ( in @ ( sK14_C @ SV367 @ SV274 ) @ SV367 )
| ~ ( in @ ( sK15_SY3096 @ SV367 @ SV274 ) @ SV367 ) )
= $false )
| ( ( is_connected_in @ SV274 @ SV367 )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3252]) ).
thf(3310,plain,
! [SV462: $i,SV451: $i,SV275: $i,SV328: $i,SV347: $i] :
( ( ( ( sK28_D @ SV347 @ SV328 @ SV275 )
= ( ordered_pair @ SV451 @ SV462 ) )
= $false )
| ( ( in @ SV451 @ SV275 )
= $false )
| ( ( in @ SV462 @ SV328 )
= $false )
| ( ( ~ ( in @ ( sK28_D @ SV347 @ SV328 @ SV275 ) @ SV347 ) )
= $true )
| ( ( SV347
= ( cartesian_product2 @ SV275 @ SV328 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3254]) ).
thf(3311,plain,
! [SV348: $i,SV452: $i,SV329: $i,SV487: $i,SV275: $i,SV475: $i] :
( ( ( in @ SV475 @ SV275 )
= $false )
| ( ( ~ ( in @ SV487 @ SV329 ) )
= $true )
| ( ( ( SV452
!= ( ordered_pair @ SV475 @ SV487 ) ) )
= $true )
| ( ( in @ SV452 @ SV348 )
= $true )
| ( ( SV348
= ( cartesian_product2 @ SV275 @ SV329 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3257]) ).
thf(3312,plain,
! [SV275: $i,SV329: $i,SV348: $i,SV453: $i] :
( ( ( ~ ( in @ ( sK26_E @ SV453 @ SV348 @ SV329 @ SV275 ) @ SV275 )
| ~ ( in @ ( sK27_SY3103 @ SV453 @ SV348 @ SV329 @ SV275 ) @ SV329 ) )
= $false )
| ( ( in @ SV453 @ SV348 )
= $false )
| ( ( SV348
= ( cartesian_product2 @ SV275 @ SV329 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3258]) ).
thf(3313,plain,
! [SV276: $i,SV370: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK3_C @ SV370 @ SV276 ) @ SV370 )
| ~ ( in @ ( sK4_SY3086 @ SV370 @ SV276 ) @ SV370 ) )
| ~ ( in @ ( sK5_SY3088 @ SV370 @ SV276 ) @ SV370 ) )
= $false )
| ( ( is_transitive_in @ SV276 @ SV370 )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3260]) ).
thf(3314,plain,
! [SV276: $i,SV454: $i,SV446: $i,SV371: $i,SV431: $i] :
( ( ( in @ SV431 @ SV371 )
= $false )
| ( ( ~ ( in @ SV446 @ SV371 ) )
= $true )
| ( ( ~ ( in @ SV454 @ SV371 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV431 @ SV446 ) @ SV276 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV446 @ SV454 ) @ SV276 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV431 @ SV454 ) @ SV276 )
= $true )
| ( ( is_transitive_in @ SV276 @ SV371 )
= $false )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3262]) ).
thf(3315,plain,
! [SV476: $i,SV277: $i,SV372: $i,SV396: $i] :
( ( ( in @ ( sK46_D @ SV396 @ SV372 @ SV277 ) @ SV396 )
= $false )
| ( ( in @ ( ordered_pair @ SV476 @ ( sK46_D @ SV396 @ SV372 @ SV277 ) ) @ SV277 )
= $false )
| ( ( in @ SV476 @ SV372 )
= $false )
| ( ( SV396
= ( relation_image @ SV277 @ SV372 ) )
= $true )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3263]) ).
thf(3316,plain,
! [SV397: $i,SV373: $i,SV277: $i,SV477: $i,SV496: $i] :
( ( ( in @ ( ordered_pair @ SV496 @ SV477 ) @ SV277 )
= $false )
| ( ( ~ ( in @ SV496 @ SV373 ) )
= $true )
| ( ( in @ SV477 @ SV397 )
= $true )
| ( ( SV397
= ( relation_image @ SV277 @ SV373 ) )
= $false )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3264]) ).
thf(3317,plain,
! [SV277: $i,SV373: $i,SV397: $i,SV478: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK45_E @ SV478 @ SV397 @ SV373 @ SV277 ) @ SV478 ) @ SV277 ) )
= $false )
| ( ( in @ SV478 @ SV397 )
= $false )
| ( ( SV397
= ( relation_image @ SV277 @ SV373 ) )
= $false )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3265]) ).
thf(3318,plain,
! [SV277: $i,SV373: $i,SV397: $i,SV478: $i] :
( ( ( ~ ( in @ ( sK45_E @ SV478 @ SV397 @ SV373 @ SV277 ) @ SV373 ) )
= $false )
| ( ( in @ SV478 @ SV397 )
= $false )
| ( ( SV397
= ( relation_image @ SV277 @ SV373 ) )
= $false )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3265]) ).
thf(3319,plain,
! [SV278: $i,SV374: $i,SV398: $i] :
( ( ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV278 )
= $false )
| ( ( in @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ SV374 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 ) )
= $true )
| ( ( SV398
= ( relation_dom_restriction @ SV278 @ SV374 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3266]) ).
thf(3320,plain,
! [SV278: $i,SV374: $i,SV398: $i] :
( ( ( in @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ SV374 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 )
= $true )
| ( ( SV398
= ( relation_dom_restriction @ SV278 @ SV374 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3267]) ).
thf(3321,plain,
! [SV278: $i,SV374: $i,SV398: $i] :
( ( ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV278 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 )
= $true )
| ( ( SV398
= ( relation_dom_restriction @ SV278 @ SV374 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3268]) ).
thf(3322,plain,
! [SV399: $i,SV278: $i,SV507: $i,SV375: $i,SV497: $i] :
( ( ( ~ ( in @ SV497 @ SV375 )
| ~ ( in @ ( ordered_pair @ SV497 @ SV507 ) @ SV278 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV497 @ SV507 ) @ SV399 )
= $true )
| ( ( SV399
= ( relation_dom_restriction @ SV278 @ SV375 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3269]) ).
thf(3323,plain,
! [SV278: $i,SV375: $i,SV399: $i] :
( ( ( ! [SY3984: $i] :
( ! [SY3985: $i] :
~ ( in @ ( ordered_pair @ SY3984 @ SY3985 ) @ SV399 )
| ( in @ SY3984 @ SV375 ) ) )
= $true )
| ( ( SV399
= ( relation_dom_restriction @ SV278 @ SV375 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3270]) ).
thf(3324,plain,
! [SV375: $i,SV278: $i,SV399: $i] :
( ( ( ! [SY3986: $i,SY3987: $i] :
( ~ ( in @ ( ordered_pair @ SY3986 @ SY3987 ) @ SV399 )
| ( in @ ( ordered_pair @ SY3986 @ SY3987 ) @ SV278 ) ) )
= $true )
| ( ( SV399
= ( relation_dom_restriction @ SV278 @ SV375 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3271]) ).
thf(3325,plain,
! [SV479: $i,SV279: $i,SV376: $i,SV400: $i] :
( ( ( in @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SV400 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK43_D @ SV400 @ SV376 @ SV279 ) @ SV479 ) @ SV279 )
= $false )
| ( ( in @ SV479 @ SV376 )
= $false )
| ( ( SV400
= ( relation_inverse_image @ SV279 @ SV376 ) )
= $true )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3272]) ).
thf(3326,plain,
! [SV401: $i,SV377: $i,SV279: $i,SV498: $i,SV480: $i] :
( ( ( in @ ( ordered_pair @ SV480 @ SV498 ) @ SV279 )
= $false )
| ( ( ~ ( in @ SV498 @ SV377 ) )
= $true )
| ( ( in @ SV480 @ SV401 )
= $true )
| ( ( SV401
= ( relation_inverse_image @ SV279 @ SV377 ) )
= $false )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3273]) ).
thf(3327,plain,
! [SV279: $i,SV377: $i,SV401: $i,SV481: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV481 @ ( sK42_E @ SV481 @ SV401 @ SV377 @ SV279 ) ) @ SV279 ) )
= $false )
| ( ( in @ SV481 @ SV401 )
= $false )
| ( ( SV401
= ( relation_inverse_image @ SV279 @ SV377 ) )
= $false )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3274]) ).
thf(3328,plain,
! [SV279: $i,SV377: $i,SV401: $i,SV481: $i] :
( ( ( ~ ( in @ ( sK42_E @ SV481 @ SV401 @ SV377 @ SV279 ) @ SV377 ) )
= $false )
| ( ( in @ SV481 @ SV401 )
= $false )
| ( ( SV401
= ( relation_inverse_image @ SV279 @ SV377 ) )
= $false )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3274]) ).
thf(3329,plain,
! [SV512: $i,SV281: $i,SV318: $i,SV432: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ SV512 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SV512 @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV318 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV432 ) )
= $true )
| ( ( SV432
= ( relation_composition @ SV281 @ SV318 ) )
= $true )
| ( ( relation @ SV432 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3275]) ).
thf(3330,plain,
! [SV281: $i,SV318: $i,SV432: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK9_SY3093 @ SV432 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV318 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV432 )
= $true )
| ( ( SV432
= ( relation_composition @ SV281 @ SV318 ) )
= $true )
| ( ( relation @ SV432 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3276]) ).
thf(3331,plain,
! [SV433: $i,SV318: $i,SV281: $i,SV513: $i] :
( ( ( ! [SY4062: $i] :
( ! [SY4063: $i] :
( ~ ( in @ ( ordered_pair @ SV513 @ SY4063 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY4063 @ SY4062 ) @ SV318 ) )
| ( in @ ( ordered_pair @ SV513 @ SY4062 ) @ SV433 ) ) )
= $true )
| ( ( SV433
= ( relation_composition @ SV281 @ SV318 ) )
= $false )
| ( ( relation @ SV433 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3277]) ).
thf(3332,plain,
! [SV281: $i,SV318: $i,SV433: $i,SV514: $i] :
( ( ( ! [SY4064: $i] :
( ~ ( in @ ( ordered_pair @ SV514 @ SY4064 ) @ SV433 )
| ~ ( ~ ( in @ ( ordered_pair @ SV514 @ ( sK6_F @ SY4064 @ SV514 @ SV433 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SY4064 @ SV514 @ SV433 @ SV318 @ SV281 ) @ SY4064 ) @ SV318 ) ) ) )
= $true )
| ( ( SV433
= ( relation_composition @ SV281 @ SV318 ) )
= $false )
| ( ( relation @ SV433 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3278]) ).
thf(3333,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) ) )
= $false )
| ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3279]) ).
thf(3334,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3279]) ).
thf(3335,plain,
! [SV465: $i,SV319: $i,SV283: $i] :
( ( ( ~ ( relation_isomorphism @ SV283 @ SV319 @ SV465 ) )
= $true )
| ( ( ~ ( ~ ! [SY4040: $i,SY4041: $i] :
( ~ ( in @ SY4040 @ ( relation_field @ SV283 ) )
| ~ ( in @ SY4041 @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV465 @ SY4040 ) @ ( apply @ SV465 @ SY4041 ) ) @ SV319 )
| ( in @ ( ordered_pair @ SY4040 @ SY4041 ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3687: $i] :
( ! [SY3688: $i] :
~ ( in @ ( ordered_pair @ SY3687 @ SY3688 ) @ SV283 )
| ( in @ SY3687 @ ( relation_field @ SV283 ) ) )
| ~ ! [SY3689: $i,SY3690: $i] :
( ~ ( in @ ( ordered_pair @ SY3689 @ SY3690 ) @ SV283 )
| ( in @ SY3690 @ ( relation_field @ SV283 ) ) ) )
| ~ ! [SY4046: $i,SY4047: $i] :
( ~ ( in @ ( ordered_pair @ SY4046 @ SY4047 ) @ SV283 )
| ( in @ ( ordered_pair @ ( apply @ SV465 @ SY4046 ) @ ( apply @ SV465 @ SY4047 ) ) @ SV319 ) ) ) ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3280]) ).
thf(3336,plain,
! [SV319: $i,SV283: $i] :
( ( ( ! [SY3861: $i] :
( ~ ( function @ SY3861 )
| ~ ( relation @ SY3861 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3861 )
| ( ( relation_dom @ SY3861 )
= ( relation_field @ SV283 ) ) ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3281]) ).
thf(3337,plain,
! [SV319: $i,SV283: $i] :
( ( ( ! [SY3862: $i] :
( ~ ( function @ SY3862 )
| ~ ( relation @ SY3862 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SY3862 )
| ( ( relation_rng @ SY3862 )
= ( relation_field @ SV319 ) ) ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3282]) ).
thf(3338,plain,
! [SV319: $i,SV283: $i,SV499: $i] :
( ( ( ~ ( function @ SV499 ) )
= $true )
| ( ( ~ ( relation @ SV499 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV283 @ SV319 @ SV499 )
| ( one_to_one @ SV499 ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3283]) ).
thf(3339,plain,
! [SV320: $i] :
( ( ( ~ ( in @ ( sK62_B @ SV320 ) @ ( relation_field @ SV320 ) ) )
= $false )
| ( ( connected @ SV320 )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3285]) ).
thf(3340,plain,
! [SV320: $i] :
( ( ( ~ ( in @ ( sK63_SY3125 @ SV320 ) @ ( relation_field @ SV320 ) ) )
= $false )
| ( ( connected @ SV320 )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3285]) ).
thf(3341,plain,
! [SV338: $i,SV483: $i,SV325: $i,SV467: $i] :
( ( ( in @ SV467 @ SV325 )
= $false )
| ( ( SV467 = SV483 )
= $false )
| ( ( in @ ( ordered_pair @ SV467 @ SV483 ) @ SV338 )
= $true )
| ( ( SV338
= ( identity_relation @ SV325 ) )
= $false )
| ( ( relation @ SV338 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3286]) ).
thf(3342,plain,
! [SV325: $i,SV338: $i,SV508: $i,SV500: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV500 @ SV508 ) @ SV338 ) )
= $true )
| ( ( SV500 = SV508 )
= $true )
| ( ( SV338
= ( identity_relation @ SV325 ) )
= $false )
| ( ( relation @ SV338 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3287]) ).
thf(3343,plain,
! [SV325: $i,SV338: $i,SV515: $i,SV501: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV501 @ SV515 ) @ SV338 ) )
= $true )
| ( ( in @ SV501 @ SV325 )
= $true )
| ( ( SV338
= ( identity_relation @ SV325 ) )
= $false )
| ( ( relation @ SV338 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3288]) ).
thf(3344,plain,
! [SV383: $i,SV291: $i,SV502: $i,SV489: $i] :
( ( ( in @ ( ordered_pair @ SV489 @ SV502 ) @ SV291 )
= $false )
| ( ( in @ ( ordered_pair @ SV489 @ SV502 ) @ SV383 )
= $true )
| ( ( SV291 = SV383 )
= $false )
| ( ( relation @ SV383 )
= $false )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3289]) ).
thf(3345,plain,
! [SV291: $i,SV383: $i,SV503: $i,SV490: $i] :
( ( ( in @ ( ordered_pair @ SV490 @ SV503 ) @ SV383 )
= $false )
| ( ( in @ ( ordered_pair @ SV490 @ SV503 ) @ SV291 )
= $true )
| ( ( SV291 = SV383 )
= $false )
| ( ( relation @ SV383 )
= $false )
| ( ( relation @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3290]) ).
thf(3346,plain,
! [SV292: $i,SV385: $i,SV504: $i,SV491: $i] :
( ( ( in @ ( ordered_pair @ SV491 @ SV504 ) @ SV385 )
= $false )
| ( ( in @ ( ordered_pair @ SV504 @ SV491 ) @ SV292 )
= $true )
| ( ( SV385
= ( relation_inverse @ SV292 ) )
= $false )
| ( ( relation @ SV385 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3291]) ).
thf(3347,plain,
! [SV385: $i,SV292: $i,SV492: $i,SV505: $i] :
( ( ( in @ ( ordered_pair @ SV505 @ SV492 ) @ SV292 )
= $false )
| ( ( in @ ( ordered_pair @ SV492 @ SV505 ) @ SV385 )
= $true )
| ( ( SV385
= ( relation_inverse @ SV292 ) )
= $false )
| ( ( relation @ SV385 )
= $false )
| ( ( relation @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3292]) ).
thf(3348,plain,
! [SV294: $i,SV386: $i] :
( ( ( ~ ( in @ ( sK19_C @ SV386 @ SV294 ) @ SV386 )
| ~ ( in @ ( sK20_SY3099 @ SV386 @ SV294 ) @ SV386 ) )
= $false )
| ( ( is_antisymmetric_in @ SV294 @ SV386 )
= $true )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3295]) ).
thf(3349,plain,
! [SV387: $i,SV294: $i,SV450: $i,SV438: $i] :
( ( ( in @ ( ordered_pair @ SV438 @ SV450 ) @ SV294 )
= $false )
| ( ( in @ SV438 @ SV387 )
= $false )
| ( ( in @ SV450 @ SV387 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV450 @ SV438 ) @ SV294 ) )
= $true )
| ( ( SV438 = SV450 )
= $true )
| ( ( is_antisymmetric_in @ SV294 @ SV387 )
= $false )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3297]) ).
thf(3350,plain,
! [SV295: $i,SV389: $i,SV405: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV405 ) )
= $true )
| ( ( ( SV509 != SV389 ) )
= $true )
| ( ( SV405
= ( fiber @ SV295 @ SV389 ) )
= $false )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3300]) ).
thf(3351,plain,
! [SV295: $i,SV389: $i,SV405: $i,SV510: $i] :
( ( ( ~ ( in @ SV510 @ SV405 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV510 @ SV389 ) @ SV295 )
= $true )
| ( ( SV405
= ( fiber @ SV295 @ SV389 ) )
= $false )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3301]) ).
thf(3352,plain,
! [SV296: $i,SV307: $i,SV406: $i] :
( ( ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV307 )
= $false )
| ( ( in @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) @ SV296 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 ) )
= $true )
| ( ( SV406
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $true )
| ( ( relation @ SV406 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3302]) ).
thf(3353,plain,
! [SV296: $i,SV307: $i,SV406: $i] :
( ( ( in @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) @ SV296 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 )
= $true )
| ( ( SV406
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $true )
| ( ( relation @ SV406 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3303]) ).
thf(3354,plain,
! [SV296: $i,SV307: $i,SV406: $i] :
( ( ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV307 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 )
= $true )
| ( ( SV406
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $true )
| ( ( relation @ SV406 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3304]) ).
thf(3355,plain,
! [SV407: $i,SV307: $i,SV506: $i,SV296: $i,SV511: $i] :
( ( ( ~ ( in @ SV511 @ SV296 )
| ~ ( in @ ( ordered_pair @ SV506 @ SV511 ) @ SV307 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV506 @ SV511 ) @ SV407 )
= $true )
| ( ( SV407
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $false )
| ( ( relation @ SV407 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3305]) ).
thf(3356,plain,
! [SV307: $i,SV296: $i,SV407: $i] :
( ( ( ! [SY3999: $i,SY4000: $i] :
( ~ ( in @ ( ordered_pair @ SY3999 @ SY4000 ) @ SV407 )
| ( in @ SY4000 @ SV296 ) ) )
= $true )
| ( ( SV407
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $false )
| ( ( relation @ SV407 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3306]) ).
thf(3357,plain,
! [SV296: $i,SV307: $i,SV407: $i] :
( ( ( ! [SY4001: $i,SY4002: $i] :
( ~ ( in @ ( ordered_pair @ SY4001 @ SY4002 ) @ SV407 )
| ( in @ ( ordered_pair @ SY4001 @ SY4002 ) @ SV307 ) ) )
= $true )
| ( ( SV407
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $false )
| ( ( relation @ SV407 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3307]) ).
thf(3358,plain,
! [SV274: $i,SV367: $i] :
( ( ( ~ ( in @ ( sK14_C @ SV367 @ SV274 ) @ SV367 ) )
= $false )
| ( ( is_connected_in @ SV274 @ SV367 )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3309]) ).
thf(3359,plain,
! [SV274: $i,SV367: $i] :
( ( ( ~ ( in @ ( sK15_SY3096 @ SV367 @ SV274 ) @ SV367 ) )
= $false )
| ( ( is_connected_in @ SV274 @ SV367 )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3309]) ).
thf(3360,plain,
! [SV451: $i,SV462: $i,SV275: $i,SV328: $i,SV347: $i] :
( ( ( in @ ( sK28_D @ SV347 @ SV328 @ SV275 ) @ SV347 )
= $false )
| ( ( in @ SV462 @ SV328 )
= $false )
| ( ( in @ SV451 @ SV275 )
= $false )
| ( ( ( sK28_D @ SV347 @ SV328 @ SV275 )
= ( ordered_pair @ SV451 @ SV462 ) )
= $false )
| ( ( SV347
= ( cartesian_product2 @ SV275 @ SV328 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3310]) ).
thf(3361,plain,
! [SV348: $i,SV452: $i,SV275: $i,SV475: $i,SV329: $i,SV487: $i] :
( ( ( in @ SV487 @ SV329 )
= $false )
| ( ( in @ SV475 @ SV275 )
= $false )
| ( ( ( SV452
!= ( ordered_pair @ SV475 @ SV487 ) ) )
= $true )
| ( ( in @ SV452 @ SV348 )
= $true )
| ( ( SV348
= ( cartesian_product2 @ SV275 @ SV329 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3311]) ).
thf(3362,plain,
! [SV275: $i,SV329: $i,SV348: $i,SV453: $i] :
( ( ( ~ ( in @ ( sK26_E @ SV453 @ SV348 @ SV329 @ SV275 ) @ SV275 ) )
= $false )
| ( ( in @ SV453 @ SV348 )
= $false )
| ( ( SV348
= ( cartesian_product2 @ SV275 @ SV329 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3312]) ).
thf(3363,plain,
! [SV275: $i,SV329: $i,SV348: $i,SV453: $i] :
( ( ( ~ ( in @ ( sK27_SY3103 @ SV453 @ SV348 @ SV329 @ SV275 ) @ SV329 ) )
= $false )
| ( ( in @ SV453 @ SV348 )
= $false )
| ( ( SV348
= ( cartesian_product2 @ SV275 @ SV329 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3312]) ).
thf(3364,plain,
! [SV276: $i,SV370: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK3_C @ SV370 @ SV276 ) @ SV370 )
| ~ ( in @ ( sK4_SY3086 @ SV370 @ SV276 ) @ SV370 ) ) )
= $false )
| ( ( is_transitive_in @ SV276 @ SV370 )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3313]) ).
thf(3365,plain,
! [SV276: $i,SV370: $i] :
( ( ( ~ ( in @ ( sK5_SY3088 @ SV370 @ SV276 ) @ SV370 ) )
= $false )
| ( ( is_transitive_in @ SV276 @ SV370 )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3313]) ).
thf(3366,plain,
! [SV276: $i,SV454: $i,SV431: $i,SV371: $i,SV446: $i] :
( ( ( in @ SV446 @ SV371 )
= $false )
| ( ( in @ SV431 @ SV371 )
= $false )
| ( ( ~ ( in @ SV454 @ SV371 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV431 @ SV446 ) @ SV276 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV446 @ SV454 ) @ SV276 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV431 @ SV454 ) @ SV276 )
= $true )
| ( ( is_transitive_in @ SV276 @ SV371 )
= $false )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3314]) ).
thf(3367,plain,
! [SV397: $i,SV277: $i,SV477: $i,SV373: $i,SV496: $i] :
( ( ( in @ SV496 @ SV373 )
= $false )
| ( ( in @ ( ordered_pair @ SV496 @ SV477 ) @ SV277 )
= $false )
| ( ( in @ SV477 @ SV397 )
= $true )
| ( ( SV397
= ( relation_image @ SV277 @ SV373 ) )
= $false )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3316]) ).
thf(3368,plain,
! [SV277: $i,SV373: $i,SV397: $i,SV478: $i] :
( ( ( in @ ( ordered_pair @ ( sK45_E @ SV478 @ SV397 @ SV373 @ SV277 ) @ SV478 ) @ SV277 )
= $true )
| ( ( in @ SV478 @ SV397 )
= $false )
| ( ( SV397
= ( relation_image @ SV277 @ SV373 ) )
= $false )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3317]) ).
thf(3369,plain,
! [SV277: $i,SV373: $i,SV397: $i,SV478: $i] :
( ( ( in @ ( sK45_E @ SV478 @ SV397 @ SV373 @ SV277 ) @ SV373 )
= $true )
| ( ( in @ SV478 @ SV397 )
= $false )
| ( ( SV397
= ( relation_image @ SV277 @ SV373 ) )
= $false )
| ( ( relation @ SV277 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3318]) ).
thf(3370,plain,
! [SV278: $i,SV374: $i,SV398: $i] :
( ( ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV398 )
= $false )
| ( ( in @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ SV374 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK50_D @ SV398 @ SV374 @ SV278 ) @ ( sK51_SY3120 @ SV398 @ SV374 @ SV278 ) ) @ SV278 )
= $false )
| ( ( SV398
= ( relation_dom_restriction @ SV278 @ SV374 ) )
= $true )
| ( ( relation @ SV398 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3319]) ).
thf(3371,plain,
! [SV399: $i,SV278: $i,SV507: $i,SV375: $i,SV497: $i] :
( ( ( ~ ( in @ SV497 @ SV375 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV497 @ SV507 ) @ SV278 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV497 @ SV507 ) @ SV399 )
= $true )
| ( ( SV399
= ( relation_dom_restriction @ SV278 @ SV375 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3322]) ).
thf(3372,plain,
! [SV278: $i,SV375: $i,SV399: $i,SV516: $i] :
( ( ( ! [SY4065: $i] :
~ ( in @ ( ordered_pair @ SV516 @ SY4065 ) @ SV399 )
| ( in @ SV516 @ SV375 ) )
= $true )
| ( ( SV399
= ( relation_dom_restriction @ SV278 @ SV375 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3323]) ).
thf(3373,plain,
! [SV375: $i,SV278: $i,SV399: $i,SV517: $i] :
( ( ( ! [SY4066: $i] :
( ~ ( in @ ( ordered_pair @ SV517 @ SY4066 ) @ SV399 )
| ( in @ ( ordered_pair @ SV517 @ SY4066 ) @ SV278 ) ) )
= $true )
| ( ( SV399
= ( relation_dom_restriction @ SV278 @ SV375 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3324]) ).
thf(3374,plain,
! [SV401: $i,SV279: $i,SV480: $i,SV377: $i,SV498: $i] :
( ( ( in @ SV498 @ SV377 )
= $false )
| ( ( in @ ( ordered_pair @ SV480 @ SV498 ) @ SV279 )
= $false )
| ( ( in @ SV480 @ SV401 )
= $true )
| ( ( SV401
= ( relation_inverse_image @ SV279 @ SV377 ) )
= $false )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3326]) ).
thf(3375,plain,
! [SV279: $i,SV377: $i,SV401: $i,SV481: $i] :
( ( ( in @ ( ordered_pair @ SV481 @ ( sK42_E @ SV481 @ SV401 @ SV377 @ SV279 ) ) @ SV279 )
= $true )
| ( ( in @ SV481 @ SV401 )
= $false )
| ( ( SV401
= ( relation_inverse_image @ SV279 @ SV377 ) )
= $false )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3327]) ).
thf(3376,plain,
! [SV279: $i,SV377: $i,SV401: $i,SV481: $i] :
( ( ( in @ ( sK42_E @ SV481 @ SV401 @ SV377 @ SV279 ) @ SV377 )
= $true )
| ( ( in @ SV481 @ SV401 )
= $false )
| ( ( SV401
= ( relation_inverse_image @ SV279 @ SV377 ) )
= $false )
| ( ( relation @ SV279 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3328]) ).
thf(3377,plain,
! [SV512: $i,SV281: $i,SV318: $i,SV432: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ SV512 ) @ SV281 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV512 @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV318 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV432 ) )
= $true )
| ( ( SV432
= ( relation_composition @ SV281 @ SV318 ) )
= $true )
| ( ( relation @ SV432 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3329]) ).
thf(3378,plain,
! [SV281: $i,SV318: $i,SV432: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK9_SY3093 @ SV432 @ SV318 @ SV281 ) ) @ SV281 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV432 )
= $true )
| ( ( SV432
= ( relation_composition @ SV281 @ SV318 ) )
= $true )
| ( ( relation @ SV432 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3330]) ).
thf(3379,plain,
! [SV281: $i,SV318: $i,SV432: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK9_SY3093 @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV318 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV432 )
= $true )
| ( ( SV432
= ( relation_composition @ SV281 @ SV318 ) )
= $true )
| ( ( relation @ SV432 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3330]) ).
thf(3380,plain,
! [SV433: $i,SV318: $i,SV518: $i,SV281: $i,SV513: $i] :
( ( ( ! [SY4067: $i] :
( ~ ( in @ ( ordered_pair @ SV513 @ SY4067 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY4067 @ SV518 ) @ SV318 ) )
| ( in @ ( ordered_pair @ SV513 @ SV518 ) @ SV433 ) )
= $true )
| ( ( SV433
= ( relation_composition @ SV281 @ SV318 ) )
= $false )
| ( ( relation @ SV433 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3331]) ).
thf(3381,plain,
! [SV281: $i,SV318: $i,SV433: $i,SV519: $i,SV514: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV514 @ SV519 ) @ SV433 )
| ~ ( ~ ( in @ ( ordered_pair @ SV514 @ ( sK6_F @ SV519 @ SV514 @ SV433 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SV519 @ SV514 @ SV433 @ SV318 @ SV281 ) @ SV519 ) @ SV318 ) ) )
= $true )
| ( ( SV433
= ( relation_composition @ SV281 @ SV318 ) )
= $false )
| ( ( relation @ SV433 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3332]) ).
thf(3382,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( ~ ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
| ~ ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
= $true )
| ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3333]) ).
thf(3383,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3334]) ).
thf(3384,plain,
! [SV465: $i,SV319: $i,SV283: $i] :
( ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( ~ ( ~ ! [SY4040: $i,SY4041: $i] :
( ~ ( in @ SY4040 @ ( relation_field @ SV283 ) )
| ~ ( in @ SY4041 @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV465 @ SY4040 ) @ ( apply @ SV465 @ SY4041 ) ) @ SV319 )
| ( in @ ( ordered_pair @ SY4040 @ SY4041 ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3687: $i] :
( ! [SY3688: $i] :
~ ( in @ ( ordered_pair @ SY3687 @ SY3688 ) @ SV283 )
| ( in @ SY3687 @ ( relation_field @ SV283 ) ) )
| ~ ! [SY3689: $i,SY3690: $i] :
( ~ ( in @ ( ordered_pair @ SY3689 @ SY3690 ) @ SV283 )
| ( in @ SY3690 @ ( relation_field @ SV283 ) ) ) )
| ~ ! [SY4046: $i,SY4047: $i] :
( ~ ( in @ ( ordered_pair @ SY4046 @ SY4047 ) @ SV283 )
| ( in @ ( ordered_pair @ ( apply @ SV465 @ SY4046 ) @ ( apply @ SV465 @ SY4047 ) ) @ SV319 ) ) ) ) )
= $true )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3335]) ).
thf(3385,plain,
! [SV319: $i,SV283: $i,SV520: $i] :
( ( ( ~ ( function @ SV520 )
| ~ ( relation @ SV520 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SV520 )
| ( ( relation_dom @ SV520 )
= ( relation_field @ SV283 ) ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3336]) ).
thf(3386,plain,
! [SV319: $i,SV283: $i,SV521: $i] :
( ( ( ~ ( function @ SV521 )
| ~ ( relation @ SV521 )
| ~ ( relation_isomorphism @ SV283 @ SV319 @ SV521 )
| ( ( relation_rng @ SV521 )
= ( relation_field @ SV319 ) ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3337]) ).
thf(3387,plain,
! [SV319: $i,SV283: $i,SV499: $i] :
( ( ( function @ SV499 )
= $false )
| ( ( ~ ( relation @ SV499 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV283 @ SV319 @ SV499 )
| ( one_to_one @ SV499 ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3338]) ).
thf(3388,plain,
! [SV320: $i] :
( ( ( in @ ( sK62_B @ SV320 ) @ ( relation_field @ SV320 ) )
= $true )
| ( ( connected @ SV320 )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3339]) ).
thf(3389,plain,
! [SV320: $i] :
( ( ( in @ ( sK63_SY3125 @ SV320 ) @ ( relation_field @ SV320 ) )
= $true )
| ( ( connected @ SV320 )
= $true )
| ( ( relation @ SV320 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3340]) ).
thf(3390,plain,
! [SV325: $i,SV338: $i,SV508: $i,SV500: $i] :
( ( ( in @ ( ordered_pair @ SV500 @ SV508 ) @ SV338 )
= $false )
| ( ( SV500 = SV508 )
= $true )
| ( ( SV338
= ( identity_relation @ SV325 ) )
= $false )
| ( ( relation @ SV338 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3342]) ).
thf(3391,plain,
! [SV325: $i,SV338: $i,SV515: $i,SV501: $i] :
( ( ( in @ ( ordered_pair @ SV501 @ SV515 ) @ SV338 )
= $false )
| ( ( in @ SV501 @ SV325 )
= $true )
| ( ( SV338
= ( identity_relation @ SV325 ) )
= $false )
| ( ( relation @ SV338 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3343]) ).
thf(3392,plain,
! [SV294: $i,SV386: $i] :
( ( ( ~ ( in @ ( sK19_C @ SV386 @ SV294 ) @ SV386 ) )
= $false )
| ( ( is_antisymmetric_in @ SV294 @ SV386 )
= $true )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3348]) ).
thf(3393,plain,
! [SV294: $i,SV386: $i] :
( ( ( ~ ( in @ ( sK20_SY3099 @ SV386 @ SV294 ) @ SV386 ) )
= $false )
| ( ( is_antisymmetric_in @ SV294 @ SV386 )
= $true )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3348]) ).
thf(3394,plain,
! [SV387: $i,SV294: $i,SV438: $i,SV450: $i] :
( ( ( in @ ( ordered_pair @ SV450 @ SV438 ) @ SV294 )
= $false )
| ( ( in @ SV450 @ SV387 )
= $false )
| ( ( in @ SV438 @ SV387 )
= $false )
| ( ( in @ ( ordered_pair @ SV438 @ SV450 ) @ SV294 )
= $false )
| ( ( SV438 = SV450 )
= $true )
| ( ( is_antisymmetric_in @ SV294 @ SV387 )
= $false )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3349]) ).
thf(3395,plain,
! [SV295: $i,SV389: $i,SV405: $i,SV509: $i] :
( ( ( in @ SV509 @ SV405 )
= $false )
| ( ( ( SV509 != SV389 ) )
= $true )
| ( ( SV405
= ( fiber @ SV295 @ SV389 ) )
= $false )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3350]) ).
thf(3396,plain,
! [SV295: $i,SV389: $i,SV405: $i,SV510: $i] :
( ( ( in @ SV510 @ SV405 )
= $false )
| ( ( in @ ( ordered_pair @ SV510 @ SV389 ) @ SV295 )
= $true )
| ( ( SV405
= ( fiber @ SV295 @ SV389 ) )
= $false )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3351]) ).
thf(3397,plain,
! [SV296: $i,SV307: $i,SV406: $i] :
( ( ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV406 )
= $false )
| ( ( in @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) @ SV296 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK48_D @ SV406 @ SV307 @ SV296 ) @ ( sK49_SY3119 @ SV406 @ SV307 @ SV296 ) ) @ SV307 )
= $false )
| ( ( SV406
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $true )
| ( ( relation @ SV406 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3352]) ).
thf(3398,plain,
! [SV407: $i,SV307: $i,SV506: $i,SV296: $i,SV511: $i] :
( ( ( ~ ( in @ SV511 @ SV296 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV506 @ SV511 ) @ SV307 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV506 @ SV511 ) @ SV407 )
= $true )
| ( ( SV407
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $false )
| ( ( relation @ SV407 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3355]) ).
thf(3399,plain,
! [SV307: $i,SV296: $i,SV407: $i,SV522: $i] :
( ( ( ! [SY4068: $i] :
( ~ ( in @ ( ordered_pair @ SV522 @ SY4068 ) @ SV407 )
| ( in @ SY4068 @ SV296 ) ) )
= $true )
| ( ( SV407
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $false )
| ( ( relation @ SV407 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3356]) ).
thf(3400,plain,
! [SV296: $i,SV307: $i,SV407: $i,SV523: $i] :
( ( ( ! [SY4069: $i] :
( ~ ( in @ ( ordered_pair @ SV523 @ SY4069 ) @ SV407 )
| ( in @ ( ordered_pair @ SV523 @ SY4069 ) @ SV307 ) ) )
= $true )
| ( ( SV407
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $false )
| ( ( relation @ SV407 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3357]) ).
thf(3401,plain,
! [SV274: $i,SV367: $i] :
( ( ( in @ ( sK14_C @ SV367 @ SV274 ) @ SV367 )
= $true )
| ( ( is_connected_in @ SV274 @ SV367 )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3358]) ).
thf(3402,plain,
! [SV274: $i,SV367: $i] :
( ( ( in @ ( sK15_SY3096 @ SV367 @ SV274 ) @ SV367 )
= $true )
| ( ( is_connected_in @ SV274 @ SV367 )
= $true )
| ( ( relation @ SV274 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3359]) ).
thf(3403,plain,
! [SV348: $i,SV329: $i,SV275: $i,SV487: $i,SV475: $i,SV452: $i] :
( ( ( SV452
= ( ordered_pair @ SV475 @ SV487 ) )
= $false )
| ( ( in @ SV475 @ SV275 )
= $false )
| ( ( in @ SV487 @ SV329 )
= $false )
| ( ( in @ SV452 @ SV348 )
= $true )
| ( ( SV348
= ( cartesian_product2 @ SV275 @ SV329 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3361]) ).
thf(3404,plain,
! [SV275: $i,SV329: $i,SV348: $i,SV453: $i] :
( ( ( in @ ( sK26_E @ SV453 @ SV348 @ SV329 @ SV275 ) @ SV275 )
= $true )
| ( ( in @ SV453 @ SV348 )
= $false )
| ( ( SV348
= ( cartesian_product2 @ SV275 @ SV329 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3362]) ).
thf(3405,plain,
! [SV275: $i,SV329: $i,SV348: $i,SV453: $i] :
( ( ( in @ ( sK27_SY3103 @ SV453 @ SV348 @ SV329 @ SV275 ) @ SV329 )
= $true )
| ( ( in @ SV453 @ SV348 )
= $false )
| ( ( SV348
= ( cartesian_product2 @ SV275 @ SV329 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3363]) ).
thf(3406,plain,
! [SV276: $i,SV370: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_C @ SV370 @ SV276 ) @ SV370 )
| ~ ( in @ ( sK4_SY3086 @ SV370 @ SV276 ) @ SV370 ) ) )
= $true )
| ( ( is_transitive_in @ SV276 @ SV370 )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3364]) ).
thf(3407,plain,
! [SV276: $i,SV370: $i] :
( ( ( in @ ( sK5_SY3088 @ SV370 @ SV276 ) @ SV370 )
= $true )
| ( ( is_transitive_in @ SV276 @ SV370 )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3365]) ).
thf(3408,plain,
! [SV276: $i,SV446: $i,SV431: $i,SV371: $i,SV454: $i] :
( ( ( in @ SV454 @ SV371 )
= $false )
| ( ( in @ SV431 @ SV371 )
= $false )
| ( ( in @ SV446 @ SV371 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV431 @ SV446 ) @ SV276 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV446 @ SV454 ) @ SV276 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV431 @ SV454 ) @ SV276 )
= $true )
| ( ( is_transitive_in @ SV276 @ SV371 )
= $false )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3366]) ).
thf(3409,plain,
! [SV399: $i,SV278: $i,SV507: $i,SV375: $i,SV497: $i] :
( ( ( in @ SV497 @ SV375 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV497 @ SV507 ) @ SV278 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV497 @ SV507 ) @ SV399 )
= $true )
| ( ( SV399
= ( relation_dom_restriction @ SV278 @ SV375 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3371]) ).
thf(3410,plain,
! [SV278: $i,SV375: $i,SV399: $i,SV516: $i] :
( ( ( ! [SY4065: $i] :
~ ( in @ ( ordered_pair @ SV516 @ SY4065 ) @ SV399 ) )
= $true )
| ( ( in @ SV516 @ SV375 )
= $true )
| ( ( SV399
= ( relation_dom_restriction @ SV278 @ SV375 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3372]) ).
thf(3411,plain,
! [SV375: $i,SV278: $i,SV399: $i,SV524: $i,SV517: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV517 @ SV524 ) @ SV399 )
| ( in @ ( ordered_pair @ SV517 @ SV524 ) @ SV278 ) )
= $true )
| ( ( SV399
= ( relation_dom_restriction @ SV278 @ SV375 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3373]) ).
thf(3412,plain,
! [SV512: $i,SV281: $i,SV318: $i,SV432: $i] :
( ( ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ SV512 ) @ SV281 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV512 @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV318 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV432 ) )
= $true )
| ( ( SV432
= ( relation_composition @ SV281 @ SV318 ) )
= $true )
| ( ( relation @ SV432 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3377]) ).
thf(3413,plain,
! [SV281: $i,SV318: $i,SV432: $i] :
( ( ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK9_SY3093 @ SV432 @ SV318 @ SV281 ) ) @ SV281 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV432 )
= $true )
| ( ( SV432
= ( relation_composition @ SV281 @ SV318 ) )
= $true )
| ( ( relation @ SV432 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3378]) ).
thf(3414,plain,
! [SV281: $i,SV318: $i,SV432: $i] :
( ( ( in @ ( ordered_pair @ ( sK9_SY3093 @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV318 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV432 )
= $true )
| ( ( SV432
= ( relation_composition @ SV281 @ SV318 ) )
= $true )
| ( ( relation @ SV432 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3379]) ).
thf(3415,plain,
! [SV433: $i,SV318: $i,SV518: $i,SV281: $i,SV513: $i] :
( ( ( ! [SY4067: $i] :
( ~ ( in @ ( ordered_pair @ SV513 @ SY4067 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SY4067 @ SV518 ) @ SV318 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV513 @ SV518 ) @ SV433 )
= $true )
| ( ( SV433
= ( relation_composition @ SV281 @ SV318 ) )
= $false )
| ( ( relation @ SV433 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3380]) ).
thf(3416,plain,
! [SV281: $i,SV318: $i,SV433: $i,SV519: $i,SV514: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV514 @ SV519 ) @ SV433 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV514 @ ( sK6_F @ SV519 @ SV514 @ SV433 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SV519 @ SV514 @ SV433 @ SV318 @ SV281 ) @ SV519 ) @ SV318 ) ) )
= $true )
| ( ( SV433
= ( relation_composition @ SV281 @ SV318 ) )
= $false )
| ( ( relation @ SV433 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3381]) ).
thf(3417,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( ~ ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
= $true )
| ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3382]) ).
thf(3418,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) ) )
| ~ ( ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) ) )
= $false )
| ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3383]) ).
thf(3419,plain,
! [SV319: $i,SV465: $i,SV283: $i] :
( ( ( ~ ! [SY4040: $i,SY4041: $i] :
( ~ ( in @ SY4040 @ ( relation_field @ SV283 ) )
| ~ ( in @ SY4041 @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV465 @ SY4040 ) @ ( apply @ SV465 @ SY4041 ) ) @ SV319 )
| ( in @ ( ordered_pair @ SY4040 @ SY4041 ) @ SV283 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY3687: $i] :
( ! [SY3688: $i] :
~ ( in @ ( ordered_pair @ SY3687 @ SY3688 ) @ SV283 )
| ( in @ SY3687 @ ( relation_field @ SV283 ) ) )
| ~ ! [SY3689: $i,SY3690: $i] :
( ~ ( in @ ( ordered_pair @ SY3689 @ SY3690 ) @ SV283 )
| ( in @ SY3690 @ ( relation_field @ SV283 ) ) ) )
| ~ ! [SY4046: $i,SY4047: $i] :
( ~ ( in @ ( ordered_pair @ SY4046 @ SY4047 ) @ SV283 )
| ( in @ ( ordered_pair @ ( apply @ SV465 @ SY4046 ) @ ( apply @ SV465 @ SY4047 ) ) @ SV319 ) ) ) )
= $false )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3384]) ).
thf(3420,plain,
! [SV319: $i,SV283: $i,SV520: $i] :
( ( ( ~ ( function @ SV520 )
| ~ ( relation @ SV520 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV283 @ SV319 @ SV520 )
| ( ( relation_dom @ SV520 )
= ( relation_field @ SV283 ) ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3385]) ).
thf(3421,plain,
! [SV319: $i,SV283: $i,SV521: $i] :
( ( ( ~ ( function @ SV521 )
| ~ ( relation @ SV521 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV283 @ SV319 @ SV521 )
| ( ( relation_rng @ SV521 )
= ( relation_field @ SV319 ) ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3386]) ).
thf(3422,plain,
! [SV319: $i,SV283: $i,SV499: $i] :
( ( ( relation @ SV499 )
= $false )
| ( ( function @ SV499 )
= $false )
| ( ( ~ ( relation_isomorphism @ SV283 @ SV319 @ SV499 )
| ( one_to_one @ SV499 ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3387]) ).
thf(3423,plain,
! [SV294: $i,SV386: $i] :
( ( ( in @ ( sK19_C @ SV386 @ SV294 ) @ SV386 )
= $true )
| ( ( is_antisymmetric_in @ SV294 @ SV386 )
= $true )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3392]) ).
thf(3424,plain,
! [SV294: $i,SV386: $i] :
( ( ( in @ ( sK20_SY3099 @ SV386 @ SV294 ) @ SV386 )
= $true )
| ( ( is_antisymmetric_in @ SV294 @ SV386 )
= $true )
| ( ( relation @ SV294 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3393]) ).
thf(3425,plain,
! [SV295: $i,SV405: $i,SV389: $i,SV509: $i] :
( ( ( SV509 = SV389 )
= $false )
| ( ( in @ SV509 @ SV405 )
= $false )
| ( ( SV405
= ( fiber @ SV295 @ SV389 ) )
= $false )
| ( ( relation @ SV295 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3395]) ).
thf(3426,plain,
! [SV407: $i,SV307: $i,SV506: $i,SV296: $i,SV511: $i] :
( ( ( in @ SV511 @ SV296 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV506 @ SV511 ) @ SV307 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV506 @ SV511 ) @ SV407 )
= $true )
| ( ( SV407
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $false )
| ( ( relation @ SV407 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3398]) ).
thf(3427,plain,
! [SV307: $i,SV296: $i,SV407: $i,SV525: $i,SV522: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV522 @ SV525 ) @ SV407 )
| ( in @ SV525 @ SV296 ) )
= $true )
| ( ( SV407
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $false )
| ( ( relation @ SV407 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3399]) ).
thf(3428,plain,
! [SV296: $i,SV307: $i,SV407: $i,SV526: $i,SV523: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV523 @ SV526 ) @ SV407 )
| ( in @ ( ordered_pair @ SV523 @ SV526 ) @ SV307 ) )
= $true )
| ( ( SV407
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $false )
| ( ( relation @ SV407 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3400]) ).
thf(3429,plain,
! [SV276: $i,SV370: $i] :
( ( ( ~ ( in @ ( sK3_C @ SV370 @ SV276 ) @ SV370 )
| ~ ( in @ ( sK4_SY3086 @ SV370 @ SV276 ) @ SV370 ) )
= $false )
| ( ( is_transitive_in @ SV276 @ SV370 )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3406]) ).
thf(3430,plain,
! [SV454: $i,SV371: $i,SV276: $i,SV446: $i,SV431: $i] :
( ( ( in @ ( ordered_pair @ SV431 @ SV446 ) @ SV276 )
= $false )
| ( ( in @ SV446 @ SV371 )
= $false )
| ( ( in @ SV431 @ SV371 )
= $false )
| ( ( in @ SV454 @ SV371 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV446 @ SV454 ) @ SV276 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV431 @ SV454 ) @ SV276 )
= $true )
| ( ( is_transitive_in @ SV276 @ SV371 )
= $false )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3408]) ).
thf(3431,plain,
! [SV399: $i,SV375: $i,SV278: $i,SV507: $i,SV497: $i] :
( ( ( in @ ( ordered_pair @ SV497 @ SV507 ) @ SV278 )
= $false )
| ( ( in @ SV497 @ SV375 )
= $false )
| ( ( in @ ( ordered_pair @ SV497 @ SV507 ) @ SV399 )
= $true )
| ( ( SV399
= ( relation_dom_restriction @ SV278 @ SV375 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3409]) ).
thf(3432,plain,
! [SV278: $i,SV375: $i,SV399: $i,SV527: $i,SV516: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV516 @ SV527 ) @ SV399 ) )
= $true )
| ( ( in @ SV516 @ SV375 )
= $true )
| ( ( SV399
= ( relation_dom_restriction @ SV278 @ SV375 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3410]) ).
thf(3433,plain,
! [SV375: $i,SV278: $i,SV399: $i,SV524: $i,SV517: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV517 @ SV524 ) @ SV399 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV517 @ SV524 ) @ SV278 )
= $true )
| ( ( SV399
= ( relation_dom_restriction @ SV278 @ SV375 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3411]) ).
thf(3434,plain,
! [SV281: $i,SV318: $i,SV432: $i,SV512: $i] :
( ( ( in @ ( ordered_pair @ SV512 @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV318 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ SV512 ) @ SV281 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV432 ) )
= $true )
| ( ( SV432
= ( relation_composition @ SV281 @ SV318 ) )
= $true )
| ( ( relation @ SV432 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3412]) ).
thf(3435,plain,
! [SV433: $i,SV318: $i,SV518: $i,SV281: $i,SV528: $i,SV513: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV513 @ SV528 ) @ SV281 )
| ~ ( in @ ( ordered_pair @ SV528 @ SV518 ) @ SV318 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV513 @ SV518 ) @ SV433 )
= $true )
| ( ( SV433
= ( relation_composition @ SV281 @ SV318 ) )
= $false )
| ( ( relation @ SV433 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3415]) ).
thf(3436,plain,
! [SV281: $i,SV318: $i,SV433: $i,SV519: $i,SV514: $i] :
( ( ( in @ ( ordered_pair @ SV514 @ SV519 ) @ SV433 )
= $false )
| ( ( ~ ( ~ ( in @ ( ordered_pair @ SV514 @ ( sK6_F @ SV519 @ SV514 @ SV433 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SV519 @ SV514 @ SV433 @ SV318 @ SV281 ) @ SV519 ) @ SV318 ) ) )
= $true )
| ( ( SV433
= ( relation_composition @ SV281 @ SV318 ) )
= $false )
| ( ( relation @ SV433 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3416]) ).
thf(3437,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( ~ ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ~ ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
= $true )
| ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3417]) ).
thf(3438,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) ) ) )
= $false )
| ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3418]) ).
thf(3439,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) ) )
= $false )
| ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3418]) ).
thf(3440,plain,
! [SV319: $i,SV465: $i,SV283: $i] :
( ( ( ~ ! [SY4040: $i,SY4041: $i] :
( ~ ( in @ SY4040 @ ( relation_field @ SV283 ) )
| ~ ( in @ SY4041 @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV465 @ SY4040 ) @ ( apply @ SV465 @ SY4041 ) ) @ SV319 )
| ( in @ ( ordered_pair @ SY4040 @ SY4041 ) @ SV283 ) ) )
= $false )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3419]) ).
thf(3441,plain,
! [SV319: $i,SV465: $i,SV283: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY3687: $i] :
( ! [SY3688: $i] :
~ ( in @ ( ordered_pair @ SY3687 @ SY3688 ) @ SV283 )
| ( in @ SY3687 @ ( relation_field @ SV283 ) ) )
| ~ ! [SY3689: $i,SY3690: $i] :
( ~ ( in @ ( ordered_pair @ SY3689 @ SY3690 ) @ SV283 )
| ( in @ SY3690 @ ( relation_field @ SV283 ) ) ) )
| ~ ! [SY4046: $i,SY4047: $i] :
( ~ ( in @ ( ordered_pair @ SY4046 @ SY4047 ) @ SV283 )
| ( in @ ( ordered_pair @ ( apply @ SV465 @ SY4046 ) @ ( apply @ SV465 @ SY4047 ) ) @ SV319 ) ) ) )
= $false )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3419]) ).
thf(3442,plain,
! [SV319: $i,SV283: $i,SV520: $i] :
( ( ( ~ ( function @ SV520 ) )
= $true )
| ( ( ~ ( relation @ SV520 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV283 @ SV319 @ SV520 )
| ( ( relation_dom @ SV520 )
= ( relation_field @ SV283 ) ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3420]) ).
thf(3443,plain,
! [SV319: $i,SV283: $i,SV521: $i] :
( ( ( ~ ( function @ SV521 ) )
= $true )
| ( ( ~ ( relation @ SV521 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV283 @ SV319 @ SV521 )
| ( ( relation_rng @ SV521 )
= ( relation_field @ SV319 ) ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3421]) ).
thf(3444,plain,
! [SV499: $i,SV319: $i,SV283: $i] :
( ( ( ~ ( relation_isomorphism @ SV283 @ SV319 @ SV499 ) )
= $true )
| ( ( one_to_one @ SV499 )
= $true )
| ( ( function @ SV499 )
= $false )
| ( ( relation @ SV499 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3422]) ).
thf(3445,plain,
! [SV407: $i,SV296: $i,SV307: $i,SV511: $i,SV506: $i] :
( ( ( in @ ( ordered_pair @ SV506 @ SV511 ) @ SV307 )
= $false )
| ( ( in @ SV511 @ SV296 )
= $false )
| ( ( in @ ( ordered_pair @ SV506 @ SV511 ) @ SV407 )
= $true )
| ( ( SV407
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $false )
| ( ( relation @ SV407 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3426]) ).
thf(3446,plain,
! [SV307: $i,SV296: $i,SV407: $i,SV525: $i,SV522: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV522 @ SV525 ) @ SV407 ) )
= $true )
| ( ( in @ SV525 @ SV296 )
= $true )
| ( ( SV407
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $false )
| ( ( relation @ SV407 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3427]) ).
thf(3447,plain,
! [SV296: $i,SV307: $i,SV407: $i,SV526: $i,SV523: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV523 @ SV526 ) @ SV407 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV523 @ SV526 ) @ SV307 )
= $true )
| ( ( SV407
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $false )
| ( ( relation @ SV407 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3428]) ).
thf(3448,plain,
! [SV276: $i,SV370: $i] :
( ( ( ~ ( in @ ( sK3_C @ SV370 @ SV276 ) @ SV370 ) )
= $false )
| ( ( is_transitive_in @ SV276 @ SV370 )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3429]) ).
thf(3449,plain,
! [SV276: $i,SV370: $i] :
( ( ( ~ ( in @ ( sK4_SY3086 @ SV370 @ SV276 ) @ SV370 ) )
= $false )
| ( ( is_transitive_in @ SV276 @ SV370 )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3429]) ).
thf(3450,plain,
! [SV431: $i,SV371: $i,SV276: $i,SV454: $i,SV446: $i] :
( ( ( in @ ( ordered_pair @ SV446 @ SV454 ) @ SV276 )
= $false )
| ( ( in @ SV454 @ SV371 )
= $false )
| ( ( in @ SV431 @ SV371 )
= $false )
| ( ( in @ SV446 @ SV371 )
= $false )
| ( ( in @ ( ordered_pair @ SV431 @ SV446 ) @ SV276 )
= $false )
| ( ( in @ ( ordered_pair @ SV431 @ SV454 ) @ SV276 )
= $true )
| ( ( is_transitive_in @ SV276 @ SV371 )
= $false )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3430]) ).
thf(3451,plain,
! [SV278: $i,SV375: $i,SV399: $i,SV527: $i,SV516: $i] :
( ( ( in @ ( ordered_pair @ SV516 @ SV527 ) @ SV399 )
= $false )
| ( ( in @ SV516 @ SV375 )
= $true )
| ( ( SV399
= ( relation_dom_restriction @ SV278 @ SV375 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3432]) ).
thf(3452,plain,
! [SV375: $i,SV278: $i,SV399: $i,SV524: $i,SV517: $i] :
( ( ( in @ ( ordered_pair @ SV517 @ SV524 ) @ SV399 )
= $false )
| ( ( in @ ( ordered_pair @ SV517 @ SV524 ) @ SV278 )
= $true )
| ( ( SV399
= ( relation_dom_restriction @ SV278 @ SV375 ) )
= $false )
| ( ( relation @ SV399 )
= $false )
| ( ( relation @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3433]) ).
thf(3453,plain,
! [SV512: $i,SV281: $i,SV318: $i,SV432: $i] :
( ( ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV432 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK7_D @ SV432 @ SV318 @ SV281 ) @ SV512 ) @ SV281 )
= $false )
| ( ( in @ ( ordered_pair @ SV512 @ ( sK8_SY3089 @ SV432 @ SV318 @ SV281 ) ) @ SV318 )
= $false )
| ( ( SV432
= ( relation_composition @ SV281 @ SV318 ) )
= $true )
| ( ( relation @ SV432 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3434]) ).
thf(3454,plain,
! [SV433: $i,SV318: $i,SV518: $i,SV281: $i,SV528: $i,SV513: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV513 @ SV528 ) @ SV281 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV528 @ SV518 ) @ SV318 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV513 @ SV518 ) @ SV433 )
= $true )
| ( ( SV433
= ( relation_composition @ SV281 @ SV318 ) )
= $false )
| ( ( relation @ SV433 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3435]) ).
thf(3455,plain,
! [SV281: $i,SV318: $i,SV433: $i,SV519: $i,SV514: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV514 @ ( sK6_F @ SV519 @ SV514 @ SV433 @ SV318 @ SV281 ) ) @ SV281 )
| ~ ( in @ ( ordered_pair @ ( sK6_F @ SV519 @ SV514 @ SV433 @ SV318 @ SV281 ) @ SV519 ) @ SV318 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV514 @ SV519 ) @ SV433 )
= $false )
| ( ( SV433
= ( relation_composition @ SV281 @ SV318 ) )
= $false )
| ( ( relation @ SV433 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3436]) ).
thf(3456,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( ~ ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) ) )
= $true )
| ( ( ~ ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
= $true )
| ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3437]) ).
thf(3457,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) ) ) )
= $true )
| ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3438]) ).
thf(3458,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
= $true )
| ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3439]) ).
thf(3459,plain,
! [SV319: $i,SV465: $i,SV283: $i] :
( ( ( ! [SY4040: $i,SY4041: $i] :
( ~ ( in @ SY4040 @ ( relation_field @ SV283 ) )
| ~ ( in @ SY4041 @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV465 @ SY4040 ) @ ( apply @ SV465 @ SY4041 ) ) @ SV319 )
| ( in @ ( ordered_pair @ SY4040 @ SY4041 ) @ SV283 ) ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3440]) ).
thf(3460,plain,
! [SV319: $i,SV465: $i,SV283: $i] :
( ( ( ~ ( ~ ~ ( ~ ! [SY3687: $i] :
( ! [SY3688: $i] :
~ ( in @ ( ordered_pair @ SY3687 @ SY3688 ) @ SV283 )
| ( in @ SY3687 @ ( relation_field @ SV283 ) ) )
| ~ ! [SY3689: $i,SY3690: $i] :
( ~ ( in @ ( ordered_pair @ SY3689 @ SY3690 ) @ SV283 )
| ( in @ SY3690 @ ( relation_field @ SV283 ) ) ) )
| ~ ! [SY4046: $i,SY4047: $i] :
( ~ ( in @ ( ordered_pair @ SY4046 @ SY4047 ) @ SV283 )
| ( in @ ( ordered_pair @ ( apply @ SV465 @ SY4046 ) @ ( apply @ SV465 @ SY4047 ) ) @ SV319 ) ) ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3441]) ).
thf(3461,plain,
! [SV319: $i,SV283: $i,SV520: $i] :
( ( ( function @ SV520 )
= $false )
| ( ( ~ ( relation @ SV520 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV283 @ SV319 @ SV520 )
| ( ( relation_dom @ SV520 )
= ( relation_field @ SV283 ) ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3442]) ).
thf(3462,plain,
! [SV319: $i,SV283: $i,SV521: $i] :
( ( ( function @ SV521 )
= $false )
| ( ( ~ ( relation @ SV521 ) )
= $true )
| ( ( ~ ( relation_isomorphism @ SV283 @ SV319 @ SV521 )
| ( ( relation_rng @ SV521 )
= ( relation_field @ SV319 ) ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3443]) ).
thf(3463,plain,
! [SV499: $i,SV319: $i,SV283: $i] :
( ( ( relation_isomorphism @ SV283 @ SV319 @ SV499 )
= $false )
| ( ( one_to_one @ SV499 )
= $true )
| ( ( function @ SV499 )
= $false )
| ( ( relation @ SV499 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3444]) ).
thf(3464,plain,
! [SV307: $i,SV296: $i,SV407: $i,SV525: $i,SV522: $i] :
( ( ( in @ ( ordered_pair @ SV522 @ SV525 ) @ SV407 )
= $false )
| ( ( in @ SV525 @ SV296 )
= $true )
| ( ( SV407
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $false )
| ( ( relation @ SV407 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3446]) ).
thf(3465,plain,
! [SV296: $i,SV307: $i,SV407: $i,SV526: $i,SV523: $i] :
( ( ( in @ ( ordered_pair @ SV523 @ SV526 ) @ SV407 )
= $false )
| ( ( in @ ( ordered_pair @ SV523 @ SV526 ) @ SV307 )
= $true )
| ( ( SV407
= ( relation_rng_restriction @ SV296 @ SV307 ) )
= $false )
| ( ( relation @ SV407 )
= $false )
| ( ( relation @ SV307 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3447]) ).
thf(3466,plain,
! [SV276: $i,SV370: $i] :
( ( ( in @ ( sK3_C @ SV370 @ SV276 ) @ SV370 )
= $true )
| ( ( is_transitive_in @ SV276 @ SV370 )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3448]) ).
thf(3467,plain,
! [SV276: $i,SV370: $i] :
( ( ( in @ ( sK4_SY3086 @ SV370 @ SV276 ) @ SV370 )
= $true )
| ( ( is_transitive_in @ SV276 @ SV370 )
= $true )
| ( ( relation @ SV276 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3449]) ).
thf(3468,plain,
! [SV433: $i,SV318: $i,SV518: $i,SV281: $i,SV528: $i,SV513: $i] :
( ( ( in @ ( ordered_pair @ SV513 @ SV528 ) @ SV281 )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV528 @ SV518 ) @ SV318 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV513 @ SV518 ) @ SV433 )
= $true )
| ( ( SV433
= ( relation_composition @ SV281 @ SV318 ) )
= $false )
| ( ( relation @ SV433 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3454]) ).
thf(3469,plain,
! [SV281: $i,SV318: $i,SV433: $i,SV519: $i,SV514: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV514 @ ( sK6_F @ SV519 @ SV514 @ SV433 @ SV318 @ SV281 ) ) @ SV281 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV514 @ SV519 ) @ SV433 )
= $false )
| ( ( SV433
= ( relation_composition @ SV281 @ SV318 ) )
= $false )
| ( ( relation @ SV433 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3455]) ).
thf(3470,plain,
! [SV281: $i,SV318: $i,SV433: $i,SV514: $i,SV519: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK6_F @ SV519 @ SV514 @ SV433 @ SV318 @ SV281 ) @ SV519 ) @ SV318 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV514 @ SV519 ) @ SV433 )
= $false )
| ( ( SV433
= ( relation_composition @ SV281 @ SV318 ) )
= $false )
| ( ( relation @ SV433 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3455]) ).
thf(3471,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
= $false )
| ( ( ~ ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
= $true )
| ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3456]) ).
thf(3472,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( ~ ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
| ~ ( ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) ) )
= $false )
| ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3457]) ).
thf(3473,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 )
= $true )
| ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3458]) ).
thf(3474,plain,
! [SV319: $i,SV465: $i,SV283: $i,SV529: $i] :
( ( ( ! [SY4070: $i] :
( ~ ( in @ SV529 @ ( relation_field @ SV283 ) )
| ~ ( in @ SY4070 @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV465 @ SV529 ) @ ( apply @ SV465 @ SY4070 ) ) @ SV319 )
| ( in @ ( ordered_pair @ SV529 @ SY4070 ) @ SV283 ) ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3459]) ).
thf(3475,plain,
! [SV319: $i,SV465: $i,SV283: $i] :
( ( ( ~ ~ ( ~ ! [SY3687: $i] :
( ! [SY3688: $i] :
~ ( in @ ( ordered_pair @ SY3687 @ SY3688 ) @ SV283 )
| ( in @ SY3687 @ ( relation_field @ SV283 ) ) )
| ~ ! [SY3689: $i,SY3690: $i] :
( ~ ( in @ ( ordered_pair @ SY3689 @ SY3690 ) @ SV283 )
| ( in @ SY3690 @ ( relation_field @ SV283 ) ) ) )
| ~ ! [SY4046: $i,SY4047: $i] :
( ~ ( in @ ( ordered_pair @ SY4046 @ SY4047 ) @ SV283 )
| ( in @ ( ordered_pair @ ( apply @ SV465 @ SY4046 ) @ ( apply @ SV465 @ SY4047 ) ) @ SV319 ) ) )
= $false )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3460]) ).
thf(3476,plain,
! [SV319: $i,SV283: $i,SV520: $i] :
( ( ( relation @ SV520 )
= $false )
| ( ( function @ SV520 )
= $false )
| ( ( ~ ( relation_isomorphism @ SV283 @ SV319 @ SV520 )
| ( ( relation_dom @ SV520 )
= ( relation_field @ SV283 ) ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3461]) ).
thf(3477,plain,
! [SV319: $i,SV283: $i,SV521: $i] :
( ( ( relation @ SV521 )
= $false )
| ( ( function @ SV521 )
= $false )
| ( ( ~ ( relation_isomorphism @ SV283 @ SV319 @ SV521 )
| ( ( relation_rng @ SV521 )
= ( relation_field @ SV319 ) ) )
= $true )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3462]) ).
thf(3478,plain,
! [SV433: $i,SV281: $i,SV513: $i,SV318: $i,SV518: $i,SV528: $i] :
( ( ( in @ ( ordered_pair @ SV528 @ SV518 ) @ SV318 )
= $false )
| ( ( in @ ( ordered_pair @ SV513 @ SV528 ) @ SV281 )
= $false )
| ( ( in @ ( ordered_pair @ SV513 @ SV518 ) @ SV433 )
= $true )
| ( ( SV433
= ( relation_composition @ SV281 @ SV318 ) )
= $false )
| ( ( relation @ SV433 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3468]) ).
thf(3479,plain,
! [SV281: $i,SV318: $i,SV433: $i,SV519: $i,SV514: $i] :
( ( ( in @ ( ordered_pair @ SV514 @ ( sK6_F @ SV519 @ SV514 @ SV433 @ SV318 @ SV281 ) ) @ SV281 )
= $true )
| ( ( in @ ( ordered_pair @ SV514 @ SV519 ) @ SV433 )
= $false )
| ( ( SV433
= ( relation_composition @ SV281 @ SV318 ) )
= $false )
| ( ( relation @ SV433 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3469]) ).
thf(3480,plain,
! [SV281: $i,SV318: $i,SV433: $i,SV514: $i,SV519: $i] :
( ( ( in @ ( ordered_pair @ ( sK6_F @ SV519 @ SV514 @ SV433 @ SV318 @ SV281 ) @ SV519 ) @ SV318 )
= $true )
| ( ( in @ ( ordered_pair @ SV514 @ SV519 ) @ SV433 )
= $false )
| ( ( SV433
= ( relation_composition @ SV281 @ SV318 ) )
= $false )
| ( ( relation @ SV433 )
= $false )
| ( ( relation @ SV318 )
= $false )
| ( ( relation @ SV281 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3470]) ).
thf(3481,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
= $false )
| ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
= $true )
| ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3471]) ).
thf(3482,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( ~ ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) ) )
= $false )
| ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3472]) ).
thf(3483,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( ~ ( ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) ) )
= $false )
| ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3472]) ).
thf(3484,plain,
! [SV319: $i,SV283: $i,SV434: $i] :
( ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3473]) ).
thf(3485,plain,
! [SV319: $i,SV465: $i,SV530: $i,SV283: $i,SV529: $i] :
( ( ( ~ ( in @ SV529 @ ( relation_field @ SV283 ) )
| ~ ( in @ SV530 @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV465 @ SV529 ) @ ( apply @ SV465 @ SV530 ) ) @ SV319 )
| ( in @ ( ordered_pair @ SV529 @ SV530 ) @ SV283 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3474]) ).
thf(3486,plain,
! [SV465: $i,SV319: $i,SV283: $i] :
( ( ( ~ ~ ( ~ ! [SY3687: $i] :
( ! [SY3688: $i] :
~ ( in @ ( ordered_pair @ SY3687 @ SY3688 ) @ SV283 )
| ( in @ SY3687 @ ( relation_field @ SV283 ) ) )
| ~ ! [SY3689: $i,SY3690: $i] :
( ~ ( in @ ( ordered_pair @ SY3689 @ SY3690 ) @ SV283 )
| ( in @ SY3690 @ ( relation_field @ SV283 ) ) ) ) )
= $false )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3475]) ).
thf(3487,plain,
! [SV319: $i,SV465: $i,SV283: $i] :
( ( ( ~ ! [SY4046: $i,SY4047: $i] :
( ~ ( in @ ( ordered_pair @ SY4046 @ SY4047 ) @ SV283 )
| ( in @ ( ordered_pair @ ( apply @ SV465 @ SY4046 ) @ ( apply @ SV465 @ SY4047 ) ) @ SV319 ) ) )
= $false )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3475]) ).
thf(3488,plain,
! [SV520: $i,SV319: $i,SV283: $i] :
( ( ( ~ ( relation_isomorphism @ SV283 @ SV319 @ SV520 ) )
= $true )
| ( ( ( relation_dom @ SV520 )
= ( relation_field @ SV283 ) )
= $true )
| ( ( function @ SV520 )
= $false )
| ( ( relation @ SV520 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3476]) ).
thf(3489,plain,
! [SV521: $i,SV319: $i,SV283: $i] :
( ( ( ~ ( relation_isomorphism @ SV283 @ SV319 @ SV521 ) )
= $true )
| ( ( ( relation_rng @ SV521 )
= ( relation_field @ SV319 ) )
= $true )
| ( ( function @ SV521 )
= $false )
| ( ( relation @ SV521 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3477]) ).
thf(3490,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
= $false )
| ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
= $false )
| ( ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
= $true )
| ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3481]) ).
thf(3491,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
= $true )
| ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3482]) ).
thf(3492,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
| ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 ) )
= $true )
| ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3483]) ).
thf(3493,plain,
! [SV319: $i,SV283: $i,SV434: $i] :
( ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) ) )
= $true )
| ( ( ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3484]) ).
thf(3494,plain,
! [SV319: $i,SV465: $i,SV530: $i,SV283: $i,SV529: $i] :
( ( ( ~ ( in @ SV529 @ ( relation_field @ SV283 ) )
| ~ ( in @ SV530 @ ( relation_field @ SV283 ) )
| ~ ( in @ ( ordered_pair @ ( apply @ SV465 @ SV529 ) @ ( apply @ SV465 @ SV530 ) ) @ SV319 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV529 @ SV530 ) @ SV283 )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3485]) ).
thf(3495,plain,
! [SV465: $i,SV319: $i,SV283: $i] :
( ( ( ~ ( ~ ! [SY3687: $i] :
( ! [SY3688: $i] :
~ ( in @ ( ordered_pair @ SY3687 @ SY3688 ) @ SV283 )
| ( in @ SY3687 @ ( relation_field @ SV283 ) ) )
| ~ ! [SY3689: $i,SY3690: $i] :
( ~ ( in @ ( ordered_pair @ SY3689 @ SY3690 ) @ SV283 )
| ( in @ SY3690 @ ( relation_field @ SV283 ) ) ) ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3486]) ).
thf(3496,plain,
! [SV319: $i,SV465: $i,SV283: $i] :
( ( ( ! [SY4046: $i,SY4047: $i] :
( ~ ( in @ ( ordered_pair @ SY4046 @ SY4047 ) @ SV283 )
| ( in @ ( ordered_pair @ ( apply @ SV465 @ SY4046 ) @ ( apply @ SV465 @ SY4047 ) ) @ SV319 ) ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3487]) ).
thf(3497,plain,
! [SV520: $i,SV319: $i,SV283: $i] :
( ( ( relation_isomorphism @ SV283 @ SV319 @ SV520 )
= $false )
| ( ( ( relation_dom @ SV520 )
= ( relation_field @ SV283 ) )
= $true )
| ( ( function @ SV520 )
= $false )
| ( ( relation @ SV520 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3488]) ).
thf(3498,plain,
! [SV521: $i,SV319: $i,SV283: $i] :
( ( ( relation_isomorphism @ SV283 @ SV319 @ SV521 )
= $false )
| ( ( ( relation_rng @ SV521 )
= ( relation_field @ SV319 ) )
= $true )
| ( ( function @ SV521 )
= $false )
| ( ( relation @ SV521 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3489]) ).
thf(3499,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 )
= $false )
| ( ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
= $false )
| ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
= $false )
| ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3490]) ).
thf(3500,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 )
= $true )
| ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3491]) ).
thf(3501,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 )
= $true )
| ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) )
| ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3492]) ).
thf(3502,plain,
! [SV319: $i,SV283: $i,SV434: $i] :
( ( ( ( relation_dom @ SV434 )
= ( relation_field @ SV283 ) )
= $false )
| ( ( ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3493]) ).
thf(3503,plain,
! [SV319: $i,SV465: $i,SV530: $i,SV283: $i,SV529: $i] :
( ( ( ~ ( in @ SV529 @ ( relation_field @ SV283 ) )
| ~ ( in @ SV530 @ ( relation_field @ SV283 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV465 @ SV529 ) @ ( apply @ SV465 @ SV530 ) ) @ SV319 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV529 @ SV530 ) @ SV283 )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3494]) ).
thf(3504,plain,
! [SV465: $i,SV319: $i,SV283: $i] :
( ( ( ~ ! [SY3687: $i] :
( ! [SY3688: $i] :
~ ( in @ ( ordered_pair @ SY3687 @ SY3688 ) @ SV283 )
| ( in @ SY3687 @ ( relation_field @ SV283 ) ) )
| ~ ! [SY3689: $i,SY3690: $i] :
( ~ ( in @ ( ordered_pair @ SY3689 @ SY3690 ) @ SV283 )
| ( in @ SY3690 @ ( relation_field @ SV283 ) ) ) )
= $false )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3495]) ).
thf(3505,plain,
! [SV319: $i,SV465: $i,SV283: $i,SV531: $i] :
( ( ( ! [SY4071: $i] :
( ~ ( in @ ( ordered_pair @ SV531 @ SY4071 ) @ SV283 )
| ( in @ ( ordered_pair @ ( apply @ SV465 @ SV531 ) @ ( apply @ SV465 @ SY4071 ) ) @ SV319 ) ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3496]) ).
thf(3506,plain,
! [SV319: $i,SV283: $i,SV434: $i] :
( ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
= $false )
| ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
= $false )
| ( ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 )
= $false )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3499]) ).
thf(3507,plain,
! [SV319: $i,SV283: $i,SV434: $i] :
( ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 )
= $true )
| ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3500]) ).
thf(3508,plain,
! [SV319: $i,SV283: $i,SV434: $i] :
( ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) )
| ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 )
= $true )
| ( ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3501]) ).
thf(3509,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( ( relation_rng @ SV434 )
= ( relation_field @ SV319 ) )
= $false )
| ( ( ( relation_dom @ SV434 )
= ( relation_field @ SV283 ) )
= $false )
| ( ( ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3502]) ).
thf(3510,plain,
! [SV319: $i,SV465: $i,SV530: $i,SV283: $i,SV529: $i] :
( ( ( ~ ( in @ SV529 @ ( relation_field @ SV283 ) ) )
= $true )
| ( ( ~ ( in @ SV530 @ ( relation_field @ SV283 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV465 @ SV529 ) @ ( apply @ SV465 @ SV530 ) ) @ SV319 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV529 @ SV530 ) @ SV283 )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3503]) ).
thf(3511,plain,
! [SV465: $i,SV319: $i,SV283: $i] :
( ( ( ~ ! [SY3687: $i] :
( ! [SY3688: $i] :
~ ( in @ ( ordered_pair @ SY3687 @ SY3688 ) @ SV283 )
| ( in @ SY3687 @ ( relation_field @ SV283 ) ) ) )
= $false )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3504]) ).
thf(3512,plain,
! [SV465: $i,SV319: $i,SV283: $i] :
( ( ( ~ ! [SY3689: $i,SY3690: $i] :
( ~ ( in @ ( ordered_pair @ SY3689 @ SY3690 ) @ SV283 )
| ( in @ SY3690 @ ( relation_field @ SV283 ) ) ) )
= $false )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3504]) ).
thf(3513,plain,
! [SV319: $i,SV465: $i,SV283: $i,SV532: $i,SV531: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV531 @ SV532 ) @ SV283 )
| ( in @ ( ordered_pair @ ( apply @ SV465 @ SV531 ) @ ( apply @ SV465 @ SV532 ) ) @ SV319 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3505]) ).
thf(3514,plain,
! [SV319: $i,SV283: $i,SV434: $i] :
( ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) ) )
= $true )
| ( ( ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
= $false )
| ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
= $false )
| ( ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 )
= $false )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3506]) ).
thf(3515,plain,
! [SV319: $i,SV283: $i,SV434: $i] :
( ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) ) )
= $true )
| ( ( ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 )
= $true )
| ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3507]) ).
thf(3516,plain,
! [SV319: $i,SV283: $i,SV434: $i] :
( ( ( ( ( relation_dom @ SV434 )
!= ( relation_field @ SV283 ) ) )
= $true )
| ( ( ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 )
= $true )
| ( ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3508]) ).
thf(3517,plain,
! [SV319: $i,SV283: $i,SV434: $i] :
( ( ( one_to_one @ SV434 )
= $false )
| ( ( ( relation_dom @ SV434 )
= ( relation_field @ SV283 ) )
= $false )
| ( ( ( relation_rng @ SV434 )
= ( relation_field @ SV319 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3509]) ).
thf(3518,plain,
! [SV319: $i,SV465: $i,SV530: $i,SV283: $i,SV529: $i] :
( ( ( in @ SV529 @ ( relation_field @ SV283 ) )
= $false )
| ( ( ~ ( in @ SV530 @ ( relation_field @ SV283 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV465 @ SV529 ) @ ( apply @ SV465 @ SV530 ) ) @ SV319 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV529 @ SV530 ) @ SV283 )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3510]) ).
thf(3519,plain,
! [SV465: $i,SV319: $i,SV283: $i] :
( ( ( ! [SY3687: $i] :
( ! [SY3688: $i] :
~ ( in @ ( ordered_pair @ SY3687 @ SY3688 ) @ SV283 )
| ( in @ SY3687 @ ( relation_field @ SV283 ) ) ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3511]) ).
thf(3520,plain,
! [SV465: $i,SV319: $i,SV283: $i] :
( ( ( ! [SY3689: $i,SY3690: $i] :
( ~ ( in @ ( ordered_pair @ SY3689 @ SY3690 ) @ SV283 )
| ( in @ SY3690 @ ( relation_field @ SV283 ) ) ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3512]) ).
thf(3521,plain,
! [SV319: $i,SV465: $i,SV283: $i,SV532: $i,SV531: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV531 @ SV532 ) @ SV283 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV465 @ SV531 ) @ ( apply @ SV465 @ SV532 ) ) @ SV319 )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3513]) ).
thf(3522,plain,
! [SV319: $i,SV283: $i,SV434: $i] :
( ( ( ( relation_dom @ SV434 )
= ( relation_field @ SV283 ) )
= $false )
| ( ( ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
= $false )
| ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
= $false )
| ( ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 )
= $false )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3514]) ).
thf(3523,plain,
! [SV319: $i,SV283: $i,SV434: $i] :
( ( ( ( relation_dom @ SV434 )
= ( relation_field @ SV283 ) )
= $false )
| ( ( ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 )
= $true )
| ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3515]) ).
thf(3524,plain,
! [SV319: $i,SV283: $i,SV434: $i] :
( ( ( ( relation_dom @ SV434 )
= ( relation_field @ SV283 ) )
= $false )
| ( ( ( ( relation_rng @ SV434 )
!= ( relation_field @ SV319 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 )
= $true )
| ( ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3516]) ).
thf(3525,plain,
! [SV319: $i,SV465: $i,SV529: $i,SV283: $i,SV530: $i] :
( ( ( in @ SV530 @ ( relation_field @ SV283 ) )
= $false )
| ( ( in @ SV529 @ ( relation_field @ SV283 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ ( apply @ SV465 @ SV529 ) @ ( apply @ SV465 @ SV530 ) ) @ SV319 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV529 @ SV530 ) @ SV283 )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3518]) ).
thf(3526,plain,
! [SV465: $i,SV319: $i,SV283: $i,SV533: $i] :
( ( ( ! [SY4072: $i] :
~ ( in @ ( ordered_pair @ SV533 @ SY4072 ) @ SV283 )
| ( in @ SV533 @ ( relation_field @ SV283 ) ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3519]) ).
thf(3527,plain,
! [SV465: $i,SV319: $i,SV283: $i,SV534: $i] :
( ( ( ! [SY4073: $i] :
( ~ ( in @ ( ordered_pair @ SV534 @ SY4073 ) @ SV283 )
| ( in @ SY4073 @ ( relation_field @ SV283 ) ) ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3520]) ).
thf(3528,plain,
! [SV319: $i,SV465: $i,SV283: $i,SV532: $i,SV531: $i] :
( ( ( in @ ( ordered_pair @ SV531 @ SV532 ) @ SV283 )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV465 @ SV531 ) @ ( apply @ SV465 @ SV532 ) ) @ SV319 )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3521]) ).
thf(3529,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( ( relation_rng @ SV434 )
= ( relation_field @ SV319 ) )
= $false )
| ( ( ( relation_dom @ SV434 )
= ( relation_field @ SV283 ) )
= $false )
| ( ( ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
= $false )
| ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
= $false )
| ( ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 )
= $false )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3522]) ).
thf(3530,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( ( relation_rng @ SV434 )
= ( relation_field @ SV319 ) )
= $false )
| ( ( ( relation_dom @ SV434 )
= ( relation_field @ SV283 ) )
= $false )
| ( ( ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 )
= $true )
| ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3523]) ).
thf(3531,plain,
! [SV283: $i,SV319: $i,SV434: $i] :
( ( ( ( relation_rng @ SV434 )
= ( relation_field @ SV319 ) )
= $false )
| ( ( ( relation_dom @ SV434 )
= ( relation_field @ SV283 ) )
= $false )
| ( ( ~ ( one_to_one @ SV434 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 )
= $true )
| ( ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3524]) ).
thf(3532,plain,
! [SV283: $i,SV319: $i,SV530: $i,SV529: $i,SV465: $i] :
( ( ( in @ ( ordered_pair @ ( apply @ SV465 @ SV529 ) @ ( apply @ SV465 @ SV530 ) ) @ SV319 )
= $false )
| ( ( in @ SV529 @ ( relation_field @ SV283 ) )
= $false )
| ( ( in @ SV530 @ ( relation_field @ SV283 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV529 @ SV530 ) @ SV283 )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3525]) ).
thf(3533,plain,
! [SV465: $i,SV319: $i,SV283: $i,SV533: $i] :
( ( ( ! [SY4072: $i] :
~ ( in @ ( ordered_pair @ SV533 @ SY4072 ) @ SV283 ) )
= $true )
| ( ( in @ SV533 @ ( relation_field @ SV283 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3526]) ).
thf(3534,plain,
! [SV465: $i,SV319: $i,SV283: $i,SV535: $i,SV534: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV534 @ SV535 ) @ SV283 )
| ( in @ SV535 @ ( relation_field @ SV283 ) ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3527]) ).
thf(3535,plain,
! [SV319: $i,SV283: $i,SV434: $i] :
( ( ( one_to_one @ SV434 )
= $false )
| ( ( ( relation_dom @ SV434 )
= ( relation_field @ SV283 ) )
= $false )
| ( ( ( relation_rng @ SV434 )
= ( relation_field @ SV319 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( apply @ SV434 @ ( sK10_D @ SV434 @ SV319 @ SV283 ) ) @ ( apply @ SV434 @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) ) @ SV319 )
= $false )
| ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
= $false )
| ( ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 )
= $false )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3529]) ).
thf(3536,plain,
! [SV319: $i,SV283: $i,SV434: $i] :
( ( ( one_to_one @ SV434 )
= $false )
| ( ( ( relation_dom @ SV434 )
= ( relation_field @ SV283 ) )
= $false )
| ( ( ( relation_rng @ SV434 )
= ( relation_field @ SV319 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 )
= $true )
| ( ( in @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3530]) ).
thf(3537,plain,
! [SV319: $i,SV283: $i,SV434: $i] :
( ( ( one_to_one @ SV434 )
= $false )
| ( ( ( relation_dom @ SV434 )
= ( relation_field @ SV283 ) )
= $false )
| ( ( ( relation_rng @ SV434 )
= ( relation_field @ SV319 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK10_D @ SV434 @ SV319 @ SV283 ) @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) ) @ SV283 )
= $true )
| ( ( in @ ( sK11_SY3094 @ SV434 @ SV319 @ SV283 ) @ ( relation_field @ SV283 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV434 )
= $true )
| ( ( function @ SV434 )
= $false )
| ( ( relation @ SV434 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3531]) ).
thf(3538,plain,
! [SV465: $i,SV319: $i,SV283: $i,SV536: $i,SV533: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV533 @ SV536 ) @ SV283 ) )
= $true )
| ( ( in @ SV533 @ ( relation_field @ SV283 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3533]) ).
thf(3539,plain,
! [SV465: $i,SV319: $i,SV283: $i,SV535: $i,SV534: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV534 @ SV535 ) @ SV283 ) )
= $true )
| ( ( in @ SV535 @ ( relation_field @ SV283 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3534]) ).
thf(3540,plain,
! [SV465: $i,SV319: $i,SV283: $i,SV536: $i,SV533: $i] :
( ( ( in @ ( ordered_pair @ SV533 @ SV536 ) @ SV283 )
= $false )
| ( ( in @ SV533 @ ( relation_field @ SV283 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3538]) ).
thf(3541,plain,
! [SV465: $i,SV319: $i,SV283: $i,SV535: $i,SV534: $i] :
( ( ( in @ ( ordered_pair @ SV534 @ SV535 ) @ SV283 )
= $false )
| ( ( in @ SV535 @ ( relation_field @ SV283 ) )
= $true )
| ( ( relation_isomorphism @ SV283 @ SV319 @ SV465 )
= $false )
| ( ( function @ SV465 )
= $false )
| ( ( relation @ SV465 )
= $false )
| ( ( relation @ SV319 )
= $false )
| ( ( relation @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3539]) ).
thf(3542,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[2067,3541,3540,3537,3536,3535,3532,3528,3517,3498,3497,3480,3479,3478,3467,3466,3465,3464,3463,3453,3452,3451,3450,3445,3431,3425,3424,3423,3414,3413,3407,3405,3404,3403,3402,3401,3397,3396,3394,3391,3390,3389,3388,3376,3375,3374,3370,3369,3368,3367,3360,3354,3353,3347,3346,3345,3344,3341,3325,3321,3320,3315,3308,3299,3298,3296,3294,3293,3284,3261,3259,3256,3255,3253,3250,3249,3248,3239,3237,3233,3232,3227,3224,3223,3219,3218,3217,3216,3203,3202,3193,3192,3176,3175,3173,3153,3149,3147,3143,3142,3140,3139,3136,3135,3134,3123,3101,3097,3096,3082,3074,3069,3064,3056,3054,3049,3047,3041,3037,3023,3019,3016,3012,3007,2984,2983,2975,2966,2963,2962,2950,2944,2923,2922,2918,2917,2908,2899,2882,2879,2854,2836,2826,2824,2823,2822,2821,2818,2793,2768,2740,2738,2734,2733,2730,2727,2718,2717,2687,2686,2643,2632,2631,2566,2486,2204,2152,2106]) ).
thf(3543,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[3542,1985]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU267+2 : TPTP v8.1.0. Released v3.3.0.
% 0.13/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jun 19 22:15:18 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.21/0.49 .........
% 0.48/0.68
% 0.48/0.68 No.of.Axioms: 341
% 0.48/0.68
% 0.48/0.68 Length.of.Defs: 0
% 0.48/0.68
% 0.48/0.68 Contains.Choice.Funs: false
% 0.56/0.77 ...................
% 0.61/0.83 (rf:2,axioms:106,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:343,loop_count:0,foatp_calls:0,translation:fof_full).........................................................................................................................................................................................................eprover: CPU time limit exceeded, terminating
% 75.61/75.84 .......ignored arguments false
% 75.72/75.98 ..........
% 76.01/76.22 (rf:0,axioms:341,ps:0,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,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:343,loop_count:0,foatp_calls:0,translation:fof_full).......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................eprover: CPU time limit exceeded, terminating
% 150.22/150.52 ................................................
% 150.47/150.80 (rf:2,axioms:106,ps:0,u:1,ude:true,rLeibEQ:false,rAndEQ:false,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:343,loop_count:0,foatp_calls:0,translation:fof_full).........................................................................................................................................................................................................eprover: CPU time limit exceeded, terminating
% 224.62/225.01 ............................
% 225.77/226.17 (rf:-1,axioms:40,ps:0,u:1,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:343,loop_count:0,foatp_calls:0,translation:fof_full).............................................................................................................................................................................................................................................................................................
% 227.55/228.04
% 227.55/228.04 ********************************
% 227.55/228.04 * All subproblems solved! *
% 227.55/228.04 ********************************
% 227.55/228.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:-1,axioms:40,ps:0,u:1,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:3542,loop_count:0,foatp_calls:1,translation:fof_full)
% 231.85/232.27
% 231.85/232.27 %**** Beginning of derivation protocol ****
% 231.85/232.27 % SZS output start CNFRefutation
% See solution above
% 231.93/232.29
% 231.93/232.29 %**** End of derivation protocol ****
% 231.93/232.29 %**** no. of clauses in derivation: 3242 ****
% 231.93/232.29 %**** clause counter: 3542 ****
% 231.93/232.29
% 231.93/232.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:-1,axioms:40,ps:0,u:1,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:3542,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------